text
stringlengths
481
13.8k
embedding
sequencelengths
1.02k
1.02k
Convolutional Neural Networks (CNNs) are widely used in fault diagnosis of mechanical systems due to their powerful feature extraction and classification capabilities. However, the CNN is a typical black-box model, and the mechanism of CNN's decision-making are not clear, which limits its application in high-reliability-required fault diagnosis scenarios. To tackle this issue, we propose a novel interpretable neural network termed as Time-Frequency Network (TFN), where the physically meaningful time-frequency transform (TFT) method is embedded into the traditional convolutional layer as an adaptive preprocessing layer. This preprocessing layer named as time-frequency convolutional (TFconv) layer, is constrained by a well-designed kernel function to extract fault-related time-frequency information. It not only improves the diagnostic performance but also reveals the logical foundation of the CNN prediction in the frequency domain. Different TFT methods correspond to different kernel functions of the TFconv layer. In this study, four typical TFT methods are considered to formulate the TFNs and their effectiveness and interpretability are proved through three mechanical fault diagnosis experiments. Experimental results also show that the proposed TFconv layer can be easily generalized to other CNNs with different depths. The code of TFN is available on https://github.com/ChenQian0618/TFN.
[ -0.0015636743046343327, -0.004007973708212376, -0.018967313691973686, -0.02480201981961727, 0.07164224982261658, 0.03768172860145569, 0.005035370122641325, -0.00312509061768651, -0.009090762585401535, 0.04277580603957176, -0.01620350405573845, -0.01119974721223116, 0.013349375687539577, 0.015038369223475456, -0.013096477836370468, 0.03188315033912659, 0.006507594604045153, 0.005893415305763483, 0.050976913422346115, 0.008855928666889668, 0.021857570856809616, 0.021875634789466858, 0.026897456496953964, -0.03618240728974342, -0.008598514832556248, 0.014523542486131191, 0.014035811647772789, -0.025018788874149323, -0.08439551293849945, 0.025018788874149323, 0.018840864300727844, 0.017106710001826286, -0.014948049560189247, -0.04555767774581909, -0.021929826587438583, -0.03717593476176262, 0.00030116253765299916, 0.08461228013038635, -0.029408367350697517, 0.04479898884892464, 0.006286309566348791, -0.06123732402920723, 0.015526100993156433, -0.04107778146862984, 0.008043044246733189, -0.0006700655212625861, -0.05177173390984535, -0.004308289848268032, 0.05372265726327896, -0.009881067089736462, 0.025849737226963043, -0.0072708032093942165, 0.0008394165197387338, 0.04613573104143143, 0.06929391622543335, 0.03710367903113365, 0.06709009408950806, 0.06965520232915878, 0.08764705061912537, 0.003285409649834037, 0.030925752595067024, 0.044473834335803986, -0.06662043184041977, -0.014957081526517868, 0.02489233948290348, -0.05574583634734154, 0.016248665750026703, -0.04118616506457329, 0.013385503552854061, -0.03265990689396858, -0.07529120147228241, 0.009881067089736462, -0.015255139209330082, 0.0034412124659866095, 0.03807913884520531, 0.02270658314228058, 0.030094804242253304, 0.06784878671169281, 0.031214777380228043, -0.008562386967241764, 0.003077672328799963, 0.08663546293973923, -0.05657678470015526, 0.01695316471159458, 0.02572328969836235, 0.013701626099646091, -0.01972600631415844, -0.04035521671175957, -0.004170550964772701, -0.0015749643789604306, -0.022146595641970634, 0.05805804207921028, -0.024747828021645546, -0.01950923539698124, 0.06564496457576752, -0.022796904668211937, 0.015670614317059517, 0.009528816677629948, -0.05935865640640259, 0.02848709747195244, 0.0636940449476242, 0.004457318689674139, -0.012211336754262447, 0.00034801632864400744, 0.030492214486002922, -0.065681092441082, -0.006421790458261967, 0.02158660814166069, 0.028035495430231094, 0.13150671124458313, 0.02839677780866623, 0.006421790458261967, -0.04982081055641174, -0.008792703971266747, -0.016293825581669807, -0.01724219135940075, -0.04740021750330925, -0.03533339500427246, -0.020213736221194267, -0.002626069588586688, -0.011633285321295261, 0.0790485367178917, 0.017431864514946938, 0.01808217167854309, -0.03376181796193123, 0.08071043342351913, 0.03477340564131737, -0.019436979666352272, 0.02673487924039364, 0.007049518171697855, -0.014613863080739975, 0.00887850858271122, 0.06560883671045303, -0.02158660814166069, 0.009682361967861652, -0.028649674728512764, 0.0016223826678469777, 0.055709708482027054, 0.01941891573369503, -0.033328279852867126, 0.009384304285049438, -0.016655107960104942, -0.0017623795429244637, -0.011380387470126152, 0.05195237323641777, -0.03818752244114876, 0.026590365916490555, 0.04562993720173836, 0.03757334500551224, 0.049025990068912506, -0.056323885917663574, 0.006837264634668827, -0.02445880137383938, 0.0005743821966461837, 0.009456560015678406, -0.014758376404643059, 0.02767421305179596, 0.012175208888947964, -0.007812726311385632, -0.06636752933263779, 0.012057791464030743, -0.04812278226017952, -0.013060349971055984, 0.011461676098406315, 0.04021070525050163, 0.025127174332737923, 0.0470750629901886, -0.0077088577672839165, -0.020719531923532486, 0.05267493799328804, 0.034339867532253265, 0.03553209826350212, 0.019888581708073616, 0.011642317287623882, -0.026463918387889862, 0.03256958723068237, 0.02034018561244011, -0.002510910853743553, -0.040969397872686386, -0.025560712441802025, -0.03786236792802811, 0.006421790458261967, 0.03159412369132042, 0.0120397275313735, 0.019798262044787407, 0.05213301628828049, 0.047653116285800934, 0.016077056527137756, 0.024133648723363876, 0.015300299040973186, 0.006796620320528746, -0.02108081430196762, 0.09740167111158371, -0.02438654564321041, 0.03706754744052887, -0.026771007105708122, -0.032461199909448624, -0.009682361967861652, -0.005514068994671106, 0.020918237045407295, -0.035369522869586945, -0.006963713560253382, 0.01983438991010189, -0.01849764585494995, 0.020809851586818695, -0.01022428460419178, 0.02220078743994236, -0.0015523842303082347, -0.004066682420670986, -0.026211019605398178, 0.0165286585688591, 0.0276922769844532, -0.034032780677080154, -0.03786236792802811, 0.012157144024968147, -0.012464234605431557, 0.026481982320547104, -0.020918237045407295, 0.017377670854330063, 0.02675294317305088, 0.05010983347892761, 0.03735657408833504, 0.022435622289776802, -0.002939933445304632, 0.019780198112130165, -0.03379794582724571, 0.008589482866227627, -0.014207420870661736, -0.03894621506333351, 0.025759417563676834, -0.022182723507285118, 0.013764849863946438, -0.0027344543486833572, -0.05216914415359497, -0.023483339697122574, -0.03524307534098625, 0.018876992166042328, -0.052096884697675705, -0.04418480768799782, -0.011804894544184208, -0.018949249759316444, -0.000622647232376039, -0.0013864202192053199, 0.0014620637521147728, 0.03354504704475403, -0.03695916384458542, -0.022254981100559235, 0.023519467562437057, 0.007397252134978771, -0.009050117805600166, -0.02136983908712864, -0.08706899732351303, 0.02252594195306301, 0.012301657348871231, -0.019364723935723305, -0.00410281028598547, 0.014939016662538052, 0.012075856328010559, 0.03441212698817253, -0.07912079244852066, 0.016393177211284637, 0.005852770991623402, -0.006873392965644598, 0.00899141002446413, -0.013746785931289196, 0.008368197828531265, 0.014180324971675873, 0.006724364124238491, 0.036308854818344116, -0.03576693311333656, 0.018732478842139244, -0.010305573232471943, -0.059141889214515686, -0.03159412369132042, 0.03768172860145569, -0.058419324457645416, -0.014595799148082733, -0.01932859607040882, 0.020394377410411835, 0.04151131957769394, 0.0165286585688591, 0.03601983189582825, -0.030925752595067024, 0.0029941259417682886, 0.008711416274309158, -0.027710340917110443, -0.0028315489180386066, -0.013502920046448708, -0.040969397872686386, -0.047364089637994766, -0.026192955672740936, -0.023934943601489067, -0.06206827238202095, -0.03190121427178383, 0.04082488268613815, 0.042089369148015976, -0.006033412180840969, -0.06694558262825012, 0.018967313691973686, 0.01674542762339115, -0.0636940449476242, -0.021243391558527946, -0.016167376190423965, 0.006417274475097656, 0.01223843265324831, 0.04461834579706192, 0.03323795646429062, 0.06972745805978775, 0.02106275036931038, -0.0008749802364036441, -0.04154744744300842, 0.017079614102840424, -0.04718345031142235, -0.01900344155728817, -0.023284634575247765, -0.013466792181134224, -0.019888581708073616, -0.05502327159047127, -0.010675887577235699, -0.04169195890426636, 0.020737595856189728, -0.0022399493027478456, -0.08526258915662766, 0.05112142488360405, -0.013412600383162498, 0.007704341784119606, 0.030835431069135666, 0.02984190545976162, -0.043028704822063446, 0.002398010343313217, -0.011425548233091831, 0.04140293598175049, -0.0479421429336071, 0.020629210397601128, -0.012382945977151394, 0.013620337471365929, -0.05925027281045914, 0.04935114085674286, -0.01558932475745678, -0.029787713661789894, 0.022887224331498146, 0.027818726375699043, -0.05838319659233093, -0.060261864215135574, -0.007884982973337173, -0.06958293914794922, -0.013828074559569359, 0.017711857333779335, -0.01620350405573845, -0.054264578968286514, 0.0008066752925515175, -0.03948814049363136, 0.012771324254572392, 0.031539931893348694, -0.005667613819241524, -0.038693320006132126, -0.036923035979270935, 0.005816642660647631, 0.03224443271756172, 0.02086404524743557, -0.022995609790086746, -0.0433538593351841, -0.009000441990792751, 0.011687478050589561, -0.07001648098230362, -0.01141651626676321, -0.027854854241013527, -0.034646958112716675, -0.005934059154242277, 0.057696759700775146, -0.009357207454741001, 0.1099020317196846, -0.009036569856107235, 0.030708983540534973, -0.00826884526759386, -0.023393020033836365, 0.004818600602447987, -0.04346224293112755, -0.025145238265395164, 0.045304782688617706, -0.07045002281665802, -0.035261139273643494, 0.06279084086418152, -0.007749502081423998, -0.00826432928442955, 0.04913437366485596, -0.023103993386030197, -0.029408367350697517, -0.0034660506062209606, 0.05307234823703766, -0.027547763660550117, -0.03829590976238251, 0.028324520215392113, -0.054770372807979584, 0.03172057494521141, -0.009411400184035301, -0.008070140145719051, -0.004120874684303999, 0.058491580188274384, -0.05971993878483772, -0.04201711341738701, 0.035477906465530396, 0.01981632597744465, -0.031160585582256317, -0.050254348665475845, 0.008246265351772308, -0.03323795646429062, 0.06380242854356766, 0.019762134179472923, 0.044257063418626785, 0.03728431835770607, -0.016501562669873238, 0.009303015656769276, -0.042378395795822144, 0.016266729682683945, -0.001383033231832087, -0.01931053027510643, -0.029047084972262383, 0.011497804895043373, -0.03665207326412201, -0.010585566982626915, 0.04960403963923454, 0.03338247165083885, -0.02355559729039669, 0.004561187233775854, -0.0013570660958066583, 0.004416674375534058, -0.0003689029545057565, -0.022670455276966095, -0.02789098210632801, -0.007663697469979525, -0.04068037122488022, 0.019906647503376007, -0.0030821883119642735, 0.0033531500957906246, -0.0019114083843305707, 0.04035521671175957, -0.014198388904333115, -0.07485765963792801, 0.004592799581587315, -0.017684761434793472, 0.013177766464650631, -0.020412441343069077, 0.0071669346652925014, -0.07543571293354034, -0.05657678470015526, 0.008630127646028996, -0.026265213266015053, 0.01543578039854765, -0.05032660439610481, -0.053144603967666626, 0.03191927820444107, -0.03623659908771515, 0.026174891740083694, -0.023374956101179123, 0.010721048340201378, -0.03235281631350517, -0.03220830485224724, 0.020719531923532486, -0.06434435397386551, 0.047653116285800934, 0.09834100306034088, -0.0077720824629068375, -0.006471466738730669, -0.026084572076797485, 0.037970755249261856, 0.01891312003135681, 0.01981632597744465, -0.0028518710751086473, 0.0000018963785350933904, 0.07218417525291443, 0.005491488613188267, 0.01661897823214531, 0.021947890520095825, 0.02478395588696003, -0.010982977226376534, 0.008806252852082253, -0.05195237323641777, 0.011470708064734936, -0.06828232854604721, 0.06571722030639648, -0.021749185398221016, 0.06438048183917999, -0.03058253414928913, -0.011145554482936859, 0.0271503534168005, -0.008133364841341972, -0.012102952226996422, 0.0006796620436944067, 0.04284806177020073, 0.034646958112716675, -0.020737595856189728, -0.04310096055269241, 0.03004061058163643, 0.016808651387691498, -0.0700526088476181, -0.02344721183180809, 0.010305573232471943, 0.07344866544008255, -0.01733251102268696, 0.0545174777507782, 0.01764863356947899, 0.0407164990901947, -0.04935114085674286, -0.06163473427295685, 0.011922311037778854, 0.001054492313414812, -0.03368956223130226, -0.04169195890426636, -0.017070582136511803, 0.008779156021773815, -0.029986418783664703, 0.05000144988298416, -0.004746344406157732, 0.013277119025588036, -0.005387620069086552, -0.0068688769824802876, -0.020376313477754593, 0.019039569422602654, 0.03654368966817856, 0.04389578104019165, 0.01878667250275612, -0.0022038212046027184, 0.06582561135292053, -0.02436848171055317, 0.025976186618208885, -0.008481098338961601, 0.029390303418040276, 0.020918237045407295, 0.006177925039082766, 0.020809851586818695, -0.0002661633479874581, -0.01343066431581974, -0.027728404849767685, 0.018967313691973686, -0.031016072258353233, 0.03256958723068237, 0.0398494228720665, -0.06604237854480743, -0.03862106055021286, -0.03220830485224724, -0.022580133751034737, -0.011326195672154427, 0.003877009032294154, -0.03618240728974342, -0.015372555702924728, -0.002849613083526492, -0.03760947287082672, 0.0036895941011607647, -0.02859548293054104, -0.004152486566454172, 0.008088204078376293, -0.01007074024528265, 0.03768172860145569, 0.0038860412314534187, -0.023483339697122574, 0.017531216144561768, -0.0029896097257733345, -0.014532574452459812, -0.015833189710974693, -0.00580761069431901, 0.011723605915904045, 0.03222636878490448, 0.014388062059879303, -0.013719690032303333, 0.0019836649298667908, -0.0069817774929106236, 0.028035495430231094, -0.015517068095505238, 0.008892057463526726, 0.026048442348837852, -0.039307497441768646, -0.05722709372639656, 0.020267928019165993, -0.015751902014017105, 0.010702983476221561, 0.056865811347961426, -0.04169195890426636, 0.01068491954356432, 0.025669097900390625, 0.021243391558527946, -0.0025651033502072096, 0.019455043599009514, 0.047761499881744385, -0.018235716968774796, -0.039090730249881744, -0.018949249759316444, -0.048158910125494, 0.0182808768004179, -0.00022650697792414576, -0.017386702820658684, 0.037320446223020554, -0.02108081430196762, 0.030907688662409782, -0.043751269578933716, -0.004581509158015251, 0.012428105808794498, -0.00981784239411354, 0.06557270884513855, -0.05296396464109421, 0.01787443459033966, 0.0716061219573021, 0.02066533826291561, 0.04494350031018257, 0.00024612346896901727, -0.0025628453586250544, -0.005830190610140562, -0.02077372372150421, -0.03974103555083275, 0.02312205731868744, 0.024494929239153862, 0.00015848432667553425, 0.052927836775779724, 0.011678445152938366, 0.04985693842172623, 0.028125815093517303, 0.05267493799328804, 0.019274402409791946, -0.0236459169536829, -0.008300457149744034, 0.04989306628704071, -0.017431864514946938, 0.06167086213827133, -0.033111508935689926, 0.004859244916588068, 0.04938726872205734, -0.005690193735063076, -0.02088210918009281, 0.011019106023013592, -0.05567358061671257, 0.013999683782458305, 0.0022941415663808584, -0.027511635795235634, -0.007406284101307392, 0.022760774940252304, -0.007297899574041367, -0.009682361967861652, -0.027854854241013527, 0.04483511671423912, 0.0613095797598362, 0.040644243359565735, -0.003795720636844635, -0.018407326191663742, 0.03166637942194939, 0.0015422231517732143, 0.015878351405262947, -0.04367901384830475, -0.009126890450716019, 0.05444522202014923, 0.011281034909188747, 0.0052566551603376865, 0.04404029622673988, 0.00671533215790987, 0.032388944178819656, 0.016185440123081207, -0.021731121465563774, 0.060550887137651443, -0.005636001471430063, 0.021442096680402756, 0.0011007816065102816, 0.007198547013103962, 0.046749912202358246, 0.048809219151735306, -0.017477024346590042, 0.0075598289258778095, -0.0259400587528944, -0.0014078713720664382, -0.034538574516773224, 0.01543578039854765, 0.03251539543271065, -0.025362007319927216, -0.03685078024864197, -0.03117864951491356, 0.024512995034456253, 0.010784272104501724, -0.016357049345970154, 0.050651758909225464, 0.024151712656021118, 0.025795545428991318, -0.0867077186703682, -0.031070265918970108, -0.05422845110297203, -0.01674542762339115, 0.027204547077417374, -0.010847496800124645, -0.0058708349242806435, 0.026156827807426453, 0.002718648174777627, -0.02077372372150421, 0.02323044277727604, 0.00960107333958149, 0.006001799833029509, 0.015860287472605705, -0.0003347504825796932, -0.0027683244552463293, -0.01590544730424881, -0.029932226985692978, -0.020737595856189728, 0.029896099120378494, 0.023573661223053932, -0.008034012280404568, 0.01867828704416752, -0.00908172968775034, -0.015562228858470917, -0.02933611162006855, 0.011714573949575424, -0.0006886941264383495, -0.0400661900639534, -0.042089369148015976, -0.029047084972262383, 0.010061708278954029, 0.01140748430043459, 0.01950923539698124, -0.030438020825386047, 0.006444370374083519, 0.05090465396642685, 0.018768608570098877, 0.03607402369379997, -0.04624411463737488, 0.022435622289776802, -0.002567361341789365, 0.029516752809286118, -0.05939478427171707, -0.023483339697122574, -0.030510278418660164, 0.04852019250392914, 0.019780198112130165, 0.030510278418660164, -0.031214777380228043, 0.0014315805165097117, 0.042306140065193176, -0.0006920811138115823, -0.0290109571069479, -0.0023167217150330544, 0.0030257380567491055, -0.009510752744972706, 0.022760774940252304, 0.0330573171377182, -0.012066824361681938, 0.019455043599009514, 0.007519184611737728, 0.053144603967666626, -0.01920214667916298, 0.029281917959451675, 0.0015467392513528466, 0.017793146893382072, -0.03419535607099533, 0.029914163053035736, -0.03410503640770912, -0.019455043599009514, 0.0324070081114769, -0.02666262350976467, 0.02613876387476921, -0.04266742244362831, -0.023374956101179123, 0.020213736221194267, 0.0255065206438303, -0.030329637229442596, -0.017224127426743507, 0.014586767181754112, -0.019256338477134705, 0.03916298598051071, 0.008752060122787952, 0.007907562889158726, 0.03638111427426338, -0.024350417777895927, -0.028739996254444122, -0.0306547898799181, 0.02456718683242798, -0.016338985413312912, 0.0026915520429611206, 0.05177173390984535, 0.028992893174290657, -0.017422832548618317, -0.014279677532613277, 0.008910121396183968, 0.05997283756732941, 0.03462889418005943, 0.052096884697675705, -0.018199589103460312, 0.0032131532207131386, -0.0035112109035253525, -0.019906647503376007, 0.00020025756384711713, -0.017079614102840424, -0.031557995826005936, -0.017594441771507263, -0.057696759700775146, -0.01456870324909687, 0.054083939641714096, -0.007352091837674379, -0.02686132863163948, 0.0024160745088011026, 0.0004118052020203322, 0.02727680280804634, 0.03452051058411598, -0.04754473268985748, 0.016709299758076668, -0.02366398088634014, 0.0004199905088171363, -0.009027537889778614, -0.03916298598051071, 0.025777481496334076, 0.002252368489280343, 0.04624411463737488, 0.0278006624430418, -0.0516633465886116, -0.0365617536008358, -0.0021891440264880657, -0.020936300978064537, 0.009054633788764477, -0.010124932043254375, 0.03265990689396858, 0.015562228858470917, 0.010856528766453266, -0.004606347531080246, -0.028776124119758606, 0.0071579026989638805, 0.01022428460419178, -0.03499017655849457, -0.045485422015190125, -0.053867168724536896, -0.0072708032093942165, -0.018660223111510277, -0.03441212698817253, -0.028649674728512764, 0.027620021253824234, 0.015426747500896454, 0.03553209826350212, -0.013810010626912117, -0.0008089333423413336, 0.03717593476176262, -0.010937817394733429, 0.0009449786157347262, -0.050651758909225464, 0.006317921448498964, 0.005414716433733702, -0.033816009759902954, 0.015372555702924728, 0.0023799461778253317, -0.010919753462076187, 0.005663097836077213, 0.013385503552854061, 0.0028744512237608433, -0.014695151709020138, 0.01799185201525688, -0.009718489833176136, -0.005505037028342485, 0.011669413186609745, 0.0059747034683823586, 0.016230599954724312, 0.007722406182438135, 0.019545365124940872, -0.012401009909808636, 0.02005115896463394, -0.0001858627365436405, 0.020285993814468384, 0.034646958112716675, 0.028432905673980713, -0.036001767963171005, 0.029191598296165466, 0.00010965477849822491, -0.007433380465954542, -0.034972112625837326, 0.01620350405573845, -0.03891008719801903, -0.00801143143326044, -0.024079455062747, 0.0028315489180386066, -0.03172057494521141, 0.00167770404368639, -0.06127345189452171, 0.07088355720043182, 0.03739270195364952, -0.013493888080120087, -0.010603630915284157, -0.02624714933335781, -0.0032763774506747723, 0.041980985552072525, 0.007726922165602446, 0.01746799238026142, 0.019762134179472923, 0.04129454866051674, -0.003262829501181841, -0.006065024062991142, -0.01775701716542244, 0.003251539310440421, -0.04873696342110634, -0.02984190545976162, -0.05151883512735367, 0.010856528766453266, 0.034448254853487015, -0.04255903884768486, -0.025795545428991318, 0.04573832079768181, 0.004617637488991022, 0.012220368720591068, -0.008187556639313698, -0.002777356654405594, 0.0005035370122641325, -0.00008389931463170797, -0.015652548521757126, -0.02377236634492874, -0.07243707031011581, -0.00908172968775034, -0.02230917289853096, 0.020069222897291183, -0.015517068095505238, 0.00033221024204976857, -0.01900344155728817, -0.008417874574661255, 0.0010623952839523554, -0.03553209826350212, 0.0027615504804998636, -0.023916877806186676, 0.009573977440595627, -0.031539931893348694, 0.01343066431581974, 0.00534697575494647, -0.003172508906573057, 0.025452326983213425, 0.008110783994197845, 0.010910721495747566, 0.021026620641350746, -0.017946690320968628, -0.019798262044787407, -0.022128531709313393, 0.007853371091187, 0.016366081312298775, -0.0038702350575476885, -0.030383829027414322, 0.013177766464650631, 0.04133067652583122, -0.006521143019199371, 0.009998483583331108, 0.05784127116203308, -0.032461199909448624, 0.00038358004530891776, 0.010612662881612778, -0.03542371466755867, 0.02108081430196762, 0.01767572946846485, -0.024151712656021118, 0.02324850670993328, 0.01136232353746891, -0.011452644132077694, 0.04082488268613815, -0.019996967166662216, -0.012111984193325043, 0.03757334500551224, -0.00805207621306181, 0.004732795991003513, 0.0013965812977403402, -0.0027728404384106398, 0.0030934785027056932, -0.02642778865993023, -0.015282235108315945, 0.008454002439975739, 0.03443019092082977, 0.031232841312885284, 0.0027141321916133165, -0.024296224117279053, -0.0017239932203665376, 0.005324395839124918, -0.03419535607099533, -0.0218936987221241, -0.009221727028489113, -0.042703550308942795, -0.03477340564131737, -0.0011764250230044127, -0.016763491556048393, -0.02005115896463394, 0.03489985689520836, 0.030311573296785355, 0.022670455276966095, 0.009045601822435856, 0.04617185890674591, -0.03128703311085701, -0.04013844579458237, 0.02077372372150421, -0.018027979880571365, 0.007717890199273825, 0.020484698936343193, 0.00756434490904212, 0.014180324971675873, -0.026608429849147797, 0.023067865520715714, 0.010197188705205917, -0.04689442366361618, -0.020701467990875244, -0.010459118522703648, 0.023682044818997383, 0.0035021789371967316, -0.014415157958865166, -0.024242032319307327, 0.0026328437961637974, -0.014017747715115547, -0.030004482716321945, -0.0034637926146388054, -0.01176876574754715, -0.042378395795822144, -0.007004357874393463, 0.01599576696753502, 0.05368652939796448, -0.04010231792926788, -0.04190872982144356, 0.013448728248476982, -0.025380071252584457, -0.019780198112130165, 0.003863461082801223, -0.025669097900390625, 0.028017431497573853, -0.0353514589369297, 0.008119815960526466, -0.0076998258009552956, 0.0063359858468174934, -0.02209240384399891, 0.016149312257766724, -0.015869319438934326, 0.023013673722743988, 0.038693320006132126, -0.008643675595521927, -0.018985377624630928, -0.019762134179472923 ]
In this work, we introduce a learning model designed to meet the needs of applications in which computational resources are limited, and robustness and interpretability are prioritized. Learning problems can be formulated as constrained stochastic optimization problems, with the constraints originating mainly from model assumptions that define a trade-off between complexity and performance. This trade-off is closely related to over-fitting, generalization capacity, and robustness to noise and adversarial attacks, and depends on both the structure and complexity of the model, as well as the properties of the optimization methods used. We develop an online prototype-based learning algorithm based on annealing optimization that is formulated as an online gradient-free stochastic approximation algorithm. The learning model can be viewed as an interpretable and progressively growing competitive-learning neural network model to be used for supervised, unsupervised, and reinforcement learning. The annealing nature of the algorithm contributes to minimal hyper-parameter tuning requirements, poor local minima prevention, and robustness with respect to the initial conditions. At the same time, it provides online control over the performance-complexity trade-off by progressively increasing the complexity of the learning model as needed, through an intuitive bifurcation phenomenon. Finally, the use of stochastic approximation enables the study of the convergence of the learning algorithm through mathematical tools from dynamical systems and control, and allows for its integration with reinforcement learning algorithms, constructing an adaptive state-action aggregation scheme.
[ -0.0488174743950367, -0.021503375843167305, -0.04008288308978081, -0.05137123167514801, 0.08023978769779205, 0.02170693688094616, -0.02709203213453293, 0.026777438819408417, -0.04633773863315582, 0.024926891550421715, 0.0055377669632434845, 0.004092025570571423, 0.0194492656737566, -0.02973831631243229, 0.021966012194752693, 0.01981937699019909, -0.010168764740228653, -0.008327469229698181, 0.027147548273205757, -0.019689837470650673, 0.018061354756355286, -0.026906978338956833, -0.014647092670202255, 0.048114266246557236, 0.03621523827314377, 0.011982303112745285, 0.0018019718118011951, -0.0004091447335667908, -0.08438502252101898, 0.056922879070043564, 0.056145645678043365, 0.00242190551944077, -0.0032315205316990614, 0.012306149117648602, -0.06528735905885696, -0.027924779802560806, 0.03343941643834114, 0.0024034001398831606, 0.0037774324882775545, 0.051630306988954544, 0.02666640654206276, -0.017644980922341347, 0.0159517303109169, -0.024815857410430908, 0.02705502137541771, -0.01559087261557579, -0.019319728016853333, 0.017719004303216934, 0.0003556523297447711, 0.014193708077073097, 0.007203260902315378, -0.06591654568910599, 0.08475513011217117, 0.0030510921496897936, -0.031070712953805923, 0.014989444054663181, 0.07402195036411285, 0.03379102051258087, 0.071764275431633, 0.02318737469613552, -0.0005409963196143508, -0.016534652560949326, -0.07787109166383743, 0.007503974717110395, 0.039490707218647, -0.04637474939227104, 0.042044464498758316, 0.02890557050704956, -0.018061354756355286, 0.002159358933568001, -0.06954362243413925, -0.04989079385995865, -0.028461439535021782, 0.013971642591059208, 0.02474183589220047, 0.049631714820861816, 0.03245862200856209, 0.004466761834919453, -0.00399718526750803, -0.045449476689100266, -0.0007251837523654103, 0.013573774136602879, 0.014989444054663181, -0.03266218304634094, 0.049631714820861816, -0.0404529944062233, 0.023427946493029594, -0.07280058413743973, 0.09733886271715164, -0.029479240998625755, -0.036659371107816696, 0.013009357266128063, -0.019615815952420235, 0.03684442490339279, 0.015766674652695656, 0.027332603931427002, -0.03349493071436882, 0.011732478626072407, -0.06025386601686478, -0.04160033538937569, -0.03040451556444168, 0.014776631258428097, -0.018422212451696396, 0.010983006097376347, -0.005375843960791826, -0.01636810228228569, -0.021466365084052086, 0.011538171209394932, 0.003201449289917946, 0.12280240654945374, -0.02657387964427471, 0.011353116482496262, 0.0066064586862921715, 0.05969870090484619, -0.058070216327905655, -0.005750580225139856, -0.008817864581942558, -0.058107227087020874, 0.04141527786850929, -0.026388823986053467, -0.031755413860082626, 0.03841739147901535, 0.01294458843767643, -0.029423724859952927, -0.03438319265842438, 0.00047507055569440126, 0.0350123792886734, 0.008211810141801834, 0.012537467293441296, 0.06132718175649643, 0.02435322105884552, -0.0262592863291502, 0.022558188065886497, -0.048188287764787674, 0.04222952201962471, -0.004499146249145269, 0.03118174523115158, -0.020245002582669258, -0.009030677378177643, 0.0009067688370123506, 0.026795944198966026, 0.005394349340349436, -0.014110433869063854, 0.007753798738121986, 0.04378398135304451, 0.02896108664572239, -0.02627779170870781, 0.053110748529434204, -0.027258582413196564, 0.02398311160504818, -0.03617822751402855, 0.08023978769779205, -0.04504235461354256, 0.012833555229008198, 0.0708019956946373, -0.02209555171430111, -0.05966169014573097, 0.0005271172267384827, 0.07302264869213104, -0.02664790116250515, 0.039046578109264374, 0.010733182542026043, 0.023131858557462692, 0.07750097662210464, 0.04633773863315582, 0.019856387749314308, -0.006203964352607727, 0.003201449289917946, -0.05181536450982094, 0.059180546551942825, -0.030978184193372726, -0.016682695597410202, -0.0103075560182333, 0.038935545831918716, 0.026906978338956833, 0.05832929536700249, 0.03662235662341118, 0.01941225491464138, -0.02126280404627323, 0.00990043580532074, 0.010279797948896885, -0.014212213456630707, 0.025334011763334274, 0.010945995338261127, 0.032588161528110504, 0.026000209152698517, 0.08682774752378464, -0.030534053221344948, 0.026832954958081245, 0.0024681692011654377, 0.04023092985153198, 0.0008246507495641708, 0.06077202036976814, 0.013268434442579746, 0.00676838168874383, -0.07169025391340256, -0.02172544226050377, 0.03612270951271057, -0.015868455171585083, 0.02973831631243229, -0.008475513197481632, -0.07317069172859192, -0.03699246793985367, 0.011852764524519444, 0.02668491192162037, 0.03260666877031326, 0.016654938459396362, -0.0053110746666789055, 0.04330283775925636, -0.06721192598342896, 0.00695806322619319, -0.03160737082362175, -0.014064169488847256, -0.04222952201962471, -0.037899237126111984, -0.04152631387114525, 0.034808821976184845, -0.03963875398039818, -0.018505487591028214, 0.00741144735366106, 0.0007714474922977388, 0.03399457782506943, 0.04271066188812256, -0.045486487448215485, 0.011528918519616127, 0.00309504265896976, -0.02022649720311165, 0.0044135586358606815, 0.04230354353785515, 0.015341048128902912, 0.01713608019053936, 0.022669222205877304, 0.03325435891747475, -0.009275875054299831, -0.006157700903713703, 0.02929418534040451, -0.00734667805954814, -0.01906065084040165, 0.04485730081796646, 0.0065833269618451595, -0.03545651212334633, -0.03775119408965111, -0.030182449147105217, -0.006079052574932575, 0.028331900015473366, -0.03042302094399929, 0.0387134775519371, 0.0379362478852272, 0.008332095108926296, -0.005810722708702087, -0.009067688137292862, 0.006759128998965025, 0.02131832018494606, 0.018385201692581177, -0.04448718950152397, 0.020800167694687843, 0.039046578109264374, -0.06173430383205414, 0.012639247812330723, -0.013601533137261868, 0.10451898723840714, 0.03086715191602707, 0.01159368734806776, 0.08505121618509293, 0.005486876703798771, -0.005986524745821953, 0.06887742131948471, 0.02355748414993286, 0.008711458183825016, 0.03808429092168808, 0.035937655717134476, 0.012722522020339966, 0.014711862429976463, 0.007980491034686565, 0.03986081853508949, -0.0320885144174099, 0.052000418305397034, -0.0002480891707818955, -0.044006045907735825, -0.019597310572862625, 0.030182449147105217, 0.001640048809349537, 0.02400161698460579, 0.020078452304005623, 0.05710793286561966, -0.0027179934550076723, -0.08416295051574707, -0.027314098551869392, -0.0488174743950367, -0.00429558614268899, -0.01906065084040165, -0.015044961124658585, -0.04119321331381798, -0.0250934399664402, 0.02555607631802559, 0.07287460565567017, -0.008540282025933266, -0.03615972027182579, 0.033735502511262894, -0.020800167694687843, -0.04848437383770943, -0.053480856120586395, 0.018338937312364578, 0.013046368025243282, 0.015738915652036667, 0.02174394764006138, -0.018588760867714882, 0.02511194534599781, -0.04374697059392929, 0.013277687132358551, -0.005042745266109705, 0.006009656935930252, 0.011519665829837322, -0.014508301392197609, -0.01523926854133606, 0.04800323396921158, 0.048928506672382355, 0.0065278103575110435, -0.03247712925076485, -0.014758125878870487, 0.003555366536602378, 0.004073520191013813, -0.0935637429356575, 0.024538274854421616, 0.02018948644399643, -0.012685511261224747, 0.02551906555891037, 0.01795032247900963, -0.068470299243927, 0.04445017874240875, -0.046226706355810165, 0.026407329365611076, -0.08638361096382141, 0.013286939822137356, -0.028720514848828316, 0.007018205709755421, -0.025611594319343567, 0.02096671611070633, -0.023150363937020302, -0.016238564625382423, -0.030941173434257507, -0.0694325864315033, -0.006217843387275934, 0.010742435231804848, 0.005676558241248131, -0.005371217615902424, -0.06162327155470848, -0.015313290059566498, 0.0011745201190933585, 0.004443630110472441, 0.0011606409680098295, 0.012407928705215454, 0.037529125809669495, 0.01182500645518303, 0.024982407689094543, -0.0058801183477044106, 0.009035304188728333, 0.02544504404067993, -0.00853565614670515, 0.046300727874040604, 0.07912946492433548, -0.024575285613536835, -0.03127427399158478, 0.026000209152698517, -0.03797325864434242, -0.007874084636569023, -0.023909088224172592, -0.008086897432804108, -0.007198634557425976, 0.0010577042121440172, -0.0034697786904871464, 0.024852868169546127, 0.005570151377469301, 0.028776032850146294, 0.03421664610505104, -0.028664998710155487, 0.029886361211538315, -0.02204003557562828, -0.05581254884600639, 0.05599760264158249, -0.01105702854692936, -0.0021570457611232996, -0.0047420309856534, 0.004207685124129057, 0.02775822952389717, 0.04263664036989212, -0.0037010973319411278, -0.03754763305187225, 0.0041868663392961025, 0.030534053221344948, 0.05014986917376518, -0.09348972141742706, -0.0008165545878000557, -0.06887742131948471, 0.0008448911248706281, 0.014610081911087036, 0.002118878299370408, -0.07342977076768875, -0.008461633697152138, -0.020855683833360672, -0.012778038159012794, -0.03719602897763252, -0.006587953306734562, 0.023890582844614983, 0.006995073985308409, 0.014628587290644646, -0.04078609123826027, -0.03171840310096741, -0.004094338975846767, 0.01085346844047308, 0.032144028693437576, -0.04948367178440094, 0.01122357789427042, 0.02670341730117798, -0.017635729163885117, 0.03758464381098747, -0.11540021747350693, -0.02363150753080845, 0.0026231526862829924, 0.0022715486120432615, -0.019227201119065285, -0.020707638934254646, 0.035641565918922424, -0.03429066762328148, 0.002715680282562971, 0.008813237771391869, -0.023446451872587204, -0.0601058192551136, -0.04411708191037178, -0.01795957423746586, 0.06195636838674545, 0.020837178453803062, -0.002219501882791519, -0.026851462200284004, -0.023501968011260033, 0.00420074537396431, -0.06636067479848862, 0.041341256350278854, -0.001959268469363451, -0.02859097719192505, -0.026166757568717003, -0.007129238918423653, -0.017654234543442726, -0.002937746001407504, -0.009669116698205471, -0.07542836666107178, -0.012629995122551918, -0.004272454418241978, -0.00020095802028663456, -0.01745992712676525, -0.05977272242307663, 0.026555374264717102, -0.039749786257743835, -0.05133422091603279, 0.028794538229703903, -0.011667709797620773, 0.011353116482496262, 0.0013601533137261868, 0.01428623590618372, -0.030959678813815117, 0.046966925263404846, 0.018089113757014275, 0.05862538143992424, -0.03164438158273697, 0.006213217042386532, 0.04918758198618889, -0.023853572085499763, -0.0326806902885437, 0.002766570309177041, -0.030941173434257507, -0.005792217329144478, -0.04145228862762451, -0.04519039765000343, 0.04615268483757973, -0.00495021790266037, 0.003268531523644924, -0.016904762014746666, -0.10496312379837036, 0.00004619143146555871, -0.03926864266395569, 0.03145932778716087, -0.06447311490774155, 0.016617927700281143, -0.012667005881667137, -0.030145438387989998, 0.014443532563745975, 0.027258582413196564, 0.02050407975912094, 0.020282013341784477, -0.018838586285710335, -0.07257851958274841, -0.01010399591177702, 0.010927489958703518, 0.01747843250632286, -0.010039226152002811, -0.01757095940411091, 0.024519769474864006, -0.04989079385995865, 0.03963875398039818, 0.034457217901945114, -0.007689029909670353, 0.0022472599521279335, -0.005551645997911692, 0.010131753981113434, 0.0027989549562335014, 0.008577292785048485, 0.010964500717818737, 0.021133266389369965, 0.043598927557468414, 0.010770193301141262, -0.0017140706768259406, 0.010464852675795555, 0.023131858557462692, -0.03875048831105232, 0.07154221087694168, 0.03127427399158478, 0.018894102424383163, -0.02551906555891037, 0.04848437383770943, 0.014202960766851902, 0.07213439047336578, 0.016164543107151985, -0.021207287907600403, 0.014175202697515488, -0.06451012939214706, 0.050408944487571716, 0.04363593831658363, -0.05185237526893616, 0.0025445043575018644, -0.026370318606495857, -0.009752391837537289, 0.04848437383770943, -0.05436912178993225, -0.045523498207330704, -0.011954544112086296, -0.004244695883244276, 0.025722626596689224, 0.01391612645238638, -0.016654938459396362, -0.010520368814468384, -0.02018948644399643, 0.018718300387263298, 0.007897216826677322, 0.046966925263404846, -0.04148930311203003, -0.017376651987433434, 0.012889071367681026, -0.009844918735325336, 0.008221062831580639, 0.003016394330188632, -0.012953841127455235, 0.010501863434910774, 0.014748873189091682, 0.0010328374337404966, -0.023094847798347473, 0.011232830584049225, 0.028294889256358147, -0.0556274950504303, -0.04641176015138626, 0.007735293358564377, -0.021577397361397743, -0.0028405922930687666, 0.011862017214298248, -0.010631402023136616, -0.0015174499712884426, -0.03845440223813057, 0.04796622321009636, 0.04652279242873192, 0.019208695739507675, 0.0350123792886734, -0.015146740712225437, -0.011667709797620773, -0.016951026394963264, 0.012315401807427406, 0.016201553866267204, 0.019615815952420235, -0.01408267579972744, 0.016229311004281044, -0.001622699899598956, -0.024519769474864006, 0.022706232964992523, -0.019282717257738113, 0.042488597333431244, 0.04833633080124855, 0.013527510687708855, 0.03919462114572525, -0.038676466792821884, -0.03741809353232384, -0.00714311795309186, -0.06306669861078262, -0.035178929567337036, 0.039823807775974274, -0.004325657617300749, 0.01937524415552616, -0.01747843250632286, -0.04211848974227905, 0.012815049849450588, -0.03155185654759407, 0.013268434442579746, -0.03771418333053589, 0.0063797663897275925, -0.012167357839643955, 0.01291682943701744, 0.010807204060256481, -0.01791331171989441, 0.0164328720420599, 0.01594247668981552, 0.029090624302625656, 0.02738812007009983, 0.007522480562329292, -0.009678369387984276, 0.034771811217069626, 0.03227356821298599, -0.05203742906451225, 0.04633773863315582, -0.0048669432289898396, 0.021022232249379158, 0.006944183725863695, -0.022558188065886497, -0.0007448458345606923, 0.034512732177972794, -0.000594488752540201, 0.0006147291278466582, 0.02546354942023754, -0.011843511834740639, 0.03403158858418465, 0.0011375091271474957, -0.014730367809534073, 0.0011779898777604103, -0.005098261404782534, 0.0007165092974901199, 0.016895510256290436, -0.02250267192721367, 0.03038601018488407, 0.005098261404782534, -0.013620038516819477, -0.021984517574310303, 0.03410561382770538, -0.005190789233893156, -0.026462845504283905, -0.048928506672382355, -0.019856387749314308, -0.009493314661085606, 0.03349493071436882, 0.0036594599951058626, 0.043932024389505386, 0.023316914215683937, -0.0258706696331501, 0.043598927557468414, 0.018005838617682457, -0.007776930928230286, 0.018098365515470505, 0.024260692298412323, 0.0402679406106472, -0.01900513470172882, -0.01388836745172739, 0.02777673490345478, 0.0258706696331501, -0.02779524028301239, -0.007194008212536573, 0.05832929536700249, -0.0017221668967977166, -0.010215029120445251, 0.03299528360366821, 0.027721218764781952, -0.010742435231804848, 0.02931269071996212, 0.043191805481910706, -0.02129981480538845, 0.08475513011217117, -0.047374047338962555, -0.011454896070063114, -0.017783772200345993, 0.045449476689100266, 0.01445278525352478, -0.03878749907016754, 0.004922459367662668, 0.04581958428025246, 0.002831339370459318, -0.01566489413380623, -0.022206583991646767, -0.0076520186848938465, 0.01747843250632286, -0.00838298536837101, -0.047818176448345184, -0.005634920671582222, -0.002419592346996069, -0.00044384252396412194, -0.02886855974793434, -0.0028914823196828365, -0.027203066274523735, -0.006740623619407415, 0.014443532563745975, -0.0083644799888134, -0.027221571654081345, -0.0023363176733255386, -0.010131753981113434, -0.015831444412469864, 0.03008992224931717, 0.006125316023826599, -0.032921262085437775, 0.021503375843167305, -0.011556676588952541, 0.024519769474864006, 0.029997393488883972, 0.011926786042749882, 0.016877003014087677, -0.02170693688094616, -0.03769567608833313, -0.003333300817757845, 0.004272454418241978, 0.0564047247171402, -0.010557380504906178, 0.003941668663173914, 0.06835927069187164, 0.010834962129592896, 0.00166202406398952, -0.020356034860014915, 0.017321135848760605, 0.03260666877031326, 0.020078452304005623, 0.0076520186848938465, 0.05929157882928848, -0.07035785913467407, -0.024501264095306396, 0.04878046363592148, 0.008887260220944881, -0.017450673505663872, 0.005699689965695143, -0.012676258571445942, -0.0016527712577953935, -0.028239373117685318, -0.024279199540615082, 0.0014121999265626073, 0.026536868885159492, -0.008063766174018383, 0.01008549053221941, 0.06077202036976814, -0.0049132066778838634, 0.025315506383776665, 0.03604868799448013, -0.011519665829837322, 0.0005892841145396233, -0.008669820614159107, -0.028627987951040268, -0.005792217329144478, -0.02094821073114872, 0.0047420309856534, -0.00724489800632, 0.020411550998687744, 0.003176004160195589, -0.03421664610505104, 0.006180832628160715, -0.02440873719751835, -0.05988375470042229, 0.0007095697801560163, 0.016895510256290436, 0.007323546335101128, -0.011473401449620724, 0.017385905608534813, -0.02470482513308525, 0.059180546551942825, 0.025408033281564713, 0.018514739349484444, 0.017644980922341347, -0.01753394864499569, -0.028461439535021782, 0.018746057525277138, 0.02287278138101101, -0.014563818462193012, 0.006282612681388855, 0.03767717257142067, 0.03697396442294121, -0.04193343222141266, -0.02853546105325222, 0.010131753981113434, -0.010881226509809494, 0.06054995208978653, -0.01795957423746586, 0.02204003557562828, -0.01199155580252409, 0.057329997420310974, 0.012518961913883686, 0.0381213016808033, -0.015822190791368484, -0.013758829794824123, -0.023113353177905083, -0.024279199540615082, 0.0262592863291502, -0.001945389318279922, 0.003067284356802702, 0.004399679601192474, -0.011843511834740639, -0.017987333238124847, 0.05051998049020767, 0.003849141299724579, -0.016146037727594376, 0.00722639262676239, -0.019301222637295723, -0.030311986804008484, 0.011602940037846565, -0.01868128962814808, 0.01105702854692936, 0.013462741859257221, -0.04345088452100754, -0.011713973246514797, -0.04063804820179939, -0.017635729163885117, -0.0025583836250007153, 0.002139696851372719, 0.017062058672308922, -0.007198634557425976, -0.00598189840093255, -0.009770897217094898, 0.013610785827040672, -0.04078609123826027, 0.004029569681733847, 0.05185237526893616, -0.008771601133048534, -0.022706232964992523, -0.01786704733967781, -0.06332577764987946, 0.01065916009247303, -0.03299528360366821, -0.030515547841787338, 0.018561003729701042, -0.02355748414993286, 0.007624260615557432, -0.0012491203378885984, -0.012481951154768467, -0.004839184693992138, 0.032514140009880066, -0.028442932292819023, 0.03305079787969589, -0.0713941678404808, 0.055405426770448685, -0.025352517142891884, 0.0163866076618433, -0.020374540239572525, 0.024223681539297104, -0.024149660021066666, -0.0035276084672659636, 0.008563414216041565, -0.011862017214298248, 0.018783068284392357, -0.02355748414993286, -0.002276174956932664, 0.04267365112900734, 0.0033032293431460857, -0.027961790561676025, 0.022928297519683838, -0.0008541438728570938, 0.0449313223361969, -0.009419293142855167, -0.029479240998625755, -0.01980087161064148, 0.026055725291371346, 0.023538978770375252, -0.026462845504283905, 0.008915018290281296, -0.0029215537942945957, 0.03549352288246155, 0.012102588079869747, -0.005274063907563686, 0.019208695739507675, -0.010585138574242592, -0.006361261010169983, 0.0026555373333394527, -0.03079313039779663, -0.047337036579847336, 0.02966429479420185, 0.00855416152626276, -0.032144028693437576, 0.04578257352113724, 0.0016412053955718875, 0.03012693300843239, 0.008817864581942558, 0.01678447611629963, 0.008887260220944881, -0.03223655745387077, 0.023835066705942154, 0.002276174956932664, 0.02211405709385872, -0.05599760264158249, 0.03604868799448013, 0.023094847798347473, -0.037566136568784714, -0.007268029730767012, -0.014591576531529427, -0.004954844247549772, 0.022188078612089157, 0.009622853249311447, -0.045486487448215485, 0.016914015635848045, 0.006166953593492508, 0.013620038516819477, -0.012759532779455185, 0.010446347296237946, 0.011639950796961784, -0.0038583939895033836, 0.002290053991600871, -0.02400161698460579, -0.01598874107003212, -0.022373134270310402, 0.013592280447483063, 0.016849245876073837, -0.002268078736960888, 0.0036710258573293686, 0.02009695954620838, -0.01719159632921219, -0.00521854730322957, 0.0030742238741368055, 0.019874893128871918, -0.07135715335607529, 0.03541950136423111, 0.00429558614268899, -0.04652279242873192, -0.0037404214963316917, -0.005662678740918636, 0.015507597476243973, 0.034475721418857574, 0.03841739147901535, -0.006250228267163038, 0.028350405395030975, -0.042784687131643295, 0.02631480246782303, -0.00910932570695877, -0.00950256735086441, 0.015803685411810875, 0.017793025821447372, -0.010770193301141262, 0.046300727874040604, 0.010196522809565067, 0.03573409467935562, 0.03834336996078491, 0.007670524064451456, -0.0034073228016495705, 0.03266218304634094, 0.018736805766820908, 0.003363372292369604, -0.017626475542783737, -0.02087418921291828, 0.02098522149026394, 0.005824601743370295, 0.06795214861631393, -0.043598927557468414, 0.014961685985326767, 0.014202960766851902, -0.036400292068719864, -0.005075129680335522, -0.008336721919476986, -0.03469778597354889, 0.014027158729732037, -0.025815153494477272, -0.007726040668785572, 0.01043709460645914, -0.016229311004281044, -0.017062058672308922, -0.003268531523644924, 0.05603461340069771, 0.01823715679347515, 0.009289754554629326, -0.0464857816696167, -0.02326139621436596, 0.014989444054663181, 0.02855396643280983, -0.025037923827767372, -0.0031158614438027143, -0.0062085906974971294, 0.01791331171989441, 0.031015194952487946, -0.02709203213453293, 0.009053809568285942, 0.01682148687541485, 0.04422811418771744, -0.015109729953110218, -0.003719602944329381, -0.006504678633064032, -0.018116870895028114, 0.00854953471571207, 0.07565043121576309, -0.01935673877596855, -0.007443832233548164, 0.008285831660032272, -0.03353194147348404, -0.033235855400562286, 0.008679073303937912, 0.010298303328454494, -0.02518596686422825, 0.019486278295516968, -0.011954544112086296, 0.014332499355077744, 0.041341256350278854, -0.012491203844547272, -0.0509641095995903, 0.00033714683377183974, -0.016636433079838753, -0.025685615837574005, 0.009257369674742222, 0.0042030587792396545, 0.0022842709440737963, -0.027203066274523735, -0.001860958058387041, 0.06676779687404633, 0.05377694591879845, -0.005921755917370319, 0.0647692009806633, -0.014397269114851952, -0.059143535792827606, 0.005329580046236515, -0.015581619925796986, 0.005893997382372618, -0.03680741414427757, 0.03301378712058067, -0.016516147181391716, 0.008729963563382626, -0.021966012194752693, -0.012981599196791649, -0.002321281936019659, -0.0540730319917202, 0.043598927557468414, -0.01682148687541485, -0.003733481978997588, 0.0030510921496897936 ]
The spread of COVID-19 leads to the global shutdown of many corporate offices, and encourages companies to open more opportunities that allow employees to work from a remote location. As the workplace type expands from onsite offices to remote areas, an emerging challenge for an online hiring marketplace is how these remote opportunities and user intentions to work remotely can be modeled and matched without prior information. Despite the unprecedented amount of remote jobs posted amid COVID-19, there is no existing approach that can be directly applied. Introducing a brand new workplace type naturally leads to the cold-start problem, which is particularly more common for less active job seekers. It is challenging, if not impossible, to onboard a new workplace type for any predictive model if existing information sources can provide little information related to a new category of jobs, including data from resumes and job descriptions. Hence, in this work, we aim to propose a principled approach that jointly models the remoteness of job seekers and job opportunities with limited information, which also suffices the needs of web-scale applications. Existing research on the emerging type of remote workplace mainly focuses on qualitative studies, and classic predictive modeling approaches are inapplicable considering the problem of cold-start and information scarcity. We precisely try to close this gap with a novel graph neural architecture. Extensive experiments on large-scale data from real-world applications have been conducted to validate the superiority of the proposed approach over competitive baselines. The improvement may translate to more rapid onboarding of the new workplace type that can benefit job seekers who are interested in working remotely.
[ -0.018076926469802856, -0.045881692320108414, -0.019838660955429077, 0.0054862708784639835, 0.03661343827843666, -0.01261937990784645, 0.02274935320019722, 0.028723930940032005, -0.054422274231910706, -0.009823583997786045, 0.003422935027629137, -0.000006732171186740743, -0.005093710497021675, -0.026847301051020622, -0.04300929978489876, 0.049251966178417206, -0.0035138940438628197, -0.004890249110758305, 0.03393253684043884, -0.041898638010025024, 0.039524126797914505, -0.0304090678691864, -0.01000550203025341, 0.02636856772005558, 0.056184008717536926, 0.021753590553998947, 0.03665173426270485, -0.004011775832623243, -0.06231177970767021, 0.047337036579847336, 0.0386241115629673, -0.009512408636510372, 0.03757090121507645, -0.027594123035669327, -0.05189456790685654, 0.019120562821626663, 0.04967325180768967, 0.043200790882110596, -0.012054475955665112, 0.004205662291496992, -0.02161954529583454, 0.04549870640039444, 0.012628954835236073, 0.006041599903255701, 0.029336707666516304, -0.013145985081791878, -0.009263467974960804, -0.03220910206437111, 0.010905519127845764, -0.012600230984389782, 0.014735376462340355, 0.02186848595738411, 0.042319923639297485, -0.006094260606914759, -0.046456169337034225, 0.027804763987660408, 0.07288218289613724, -0.02594728395342827, 0.05790744349360466, 0.027230285108089447, -0.014811973087489605, 0.05603081360459328, -0.04680085554718971, -0.027326032519340515, 0.002606696682050824, 0.04450294375419617, -0.016554558649659157, -0.0010065344395115972, -0.030370770022273064, -0.05174137279391289, -0.0921463668346405, -0.005050624255090952, 0.05005623772740364, -0.03081120178103447, -0.01546304952353239, 0.03734111040830612, 0.007276729214936495, 0.017837561666965485, 0.012245968915522099, -0.012131073512136936, 0.06541396677494049, 0.00541446078568697, 0.008238980546593666, -0.00734375137835741, 0.05181797221302986, -0.02202167920768261, 0.003521075239405036, -0.07966103404760361, 0.052507344633340836, 0.047337036579847336, -0.052928630262613297, -0.011815110221505165, -0.026234522461891174, -0.034564461559057236, -0.008698564022779465, -0.020508887246251106, -0.023898310959339142, -0.002846062881872058, -0.04672425985336304, 0.008444835431873798, -0.013347052969038486, 0.0011938383104279637, 0.013576844707131386, -0.014735376462340355, -0.005376162473112345, -0.04385186731815338, -0.017205635085701942, 0.018603531643748283, -0.0014014884363859892, 0.1319768875837326, 0.004581466782838106, 0.007923017255961895, 0.0018862048164010048, 0.03511979058384895, -0.023649370297789574, 0.06292455643415451, -0.01553964614868164, -0.017234358936548233, 0.04461783915758133, -0.03205590695142746, 0.006199581548571587, 0.015137511305510998, -0.004330132622271776, -0.028168601915240288, -0.04266460984945297, 0.04787321761250496, -0.045575302094221115, 0.0006106827058829367, -0.010800197720527649, 0.017588619142770767, 0.004804077558219433, 0.024223847314715385, -0.03330060839653015, -0.04147735610604286, 0.034200627356767654, -0.005266054067760706, 0.016688603907823563, 0.029911186546087265, -0.03841346874833107, -0.013423650525510311, -0.0140651511028409, -0.05909470096230507, -0.021638695150613785, -0.009454960003495216, 0.008703351020812988, 0.017655642703175545, -0.05357970669865608, 0.04017520323395729, -0.02025994472205639, -0.02177273854613304, -0.07552478462457657, 0.05365630239248276, 0.004722693003714085, 0.037819840013980865, 0.06510757654905319, -0.009986353106796741, 0.0187088530510664, -0.014591756276786327, -0.012839596718549728, -0.04534551128745079, 0.06437990069389343, -0.051166895776987076, 0.033779341727495193, 0.022557860240340233, -0.004097947385162115, 0.005735211540013552, 0.02135145477950573, -0.04212843254208565, -0.047183841466903687, 0.0343729704618454, 0.013548120856285095, 0.02336212992668152, -0.022481262683868408, 0.05216265842318535, -0.03623045235872269, 0.00453838100656867, -0.006644802633672953, -0.02135145477950573, -0.018938643857836723, 0.006730974186211824, -0.05507335066795349, 0.027881361544132233, 0.010244868695735931, 0.01193958055227995, 0.03308996930718422, 0.0480647087097168, 0.0240323543548584, 0.007688438519835472, 0.03653683885931969, -0.01630561798810959, -0.002644995227456093, -0.021274857223033905, 0.032802727073431015, -0.002628239570185542, 0.005807021167129278, -0.037609200924634933, -0.005625103134661913, -0.0031596324406564236, 0.038126230239868164, -0.005687338300049305, -0.0648011863231659, -0.0465327687561512, 0.05036262422800064, 0.008722499944269657, 0.06284795701503754, -0.008176745846867561, 0.04450294375419617, -0.022577010095119476, -0.0012554751010611653, -0.01015869714319706, 0.001147760427556932, -0.04699235036969185, -0.02868563123047352, -0.03902624547481537, -0.00428704684600234, -0.01147999707609415, 0.002561217173933983, 0.03266868367791176, -0.007875144481658936, 0.00997677817940712, -0.013998128473758698, 0.02186848595738411, 0.06407351046800613, -0.011930005624890327, -0.0018670554272830486, 0.007329389452934265, -0.019915258511900902, 0.05993726849555969, 0.009119847789406776, -0.002248844364657998, -0.03289847448468208, 0.005395311396569014, 0.033530402928590775, 0.012772574089467525, 0.04124756529927254, 0.001101084053516388, -0.009086336940526962, -0.03500489518046379, -0.027057942003011703, -0.02363022044301033, -0.010015076957643032, -0.03251548856496811, -0.02703879401087761, -0.02363022044301033, 0.050745610147714615, -0.024108951911330223, -0.03347295522689819, 0.11267440766096115, 0.029489902779459953, 0.04308589547872543, -0.027785615995526314, 0.01289704442024231, -0.007099598180502653, 0.0043827928602695465, 0.0005849509034305811, 0.017751388251781464, 0.008779947645962238, -0.028934571892023087, 0.02998778410255909, 0.004780140705406666, 0.0358857624232769, 0.015577944926917553, -0.06208198890089989, 0.015041764825582504, -0.017617344856262207, -0.014859846793115139, 0.08463984727859497, 0.0032912837341427803, 0.03929433599114418, 0.0021483106538653374, -0.0010340615408495069, -0.065069280564785, 0.0059458534233272076, -0.015127936378121376, -0.042894404381513596, -0.027115389704704285, 0.02910691685974598, -0.05334991216659546, 0.04170714691281319, -0.03630704805254936, -0.029968634247779846, -0.01943652704358101, 0.02384086139500141, 0.0042152367532253265, -0.03866241127252579, 0.010378913953900337, -0.024434490129351616, -0.02332383207976818, -0.06514587253332138, -0.0517030730843544, -0.014716226607561111, -0.03473680466413498, -0.03144313022494316, 0.03081120178103447, 0.036000657826662064, 0.01861310750246048, 0.018421614542603493, 0.035138942301273346, 0.02301744371652603, -0.037245362997055054, 0.017330104485154152, -0.039217740297317505, -0.006912892684340477, 0.05269883945584297, -0.049098771065473557, -0.007243217900395393, 0.03305166959762573, 0.0818057507276535, -0.005807021167129278, -0.06453309953212738, 0.05342651158571243, 0.026502612978219986, 0.0007719556451775134, -0.0371113196015358, 0.040826279670000076, 0.03624960035085678, 0.015673691406846046, -0.02476002834737301, -0.013404500670731068, -0.05461376532912254, -0.03550277650356293, -0.004832801409065723, -0.09528685361146927, 0.047068946063518524, -0.011269355192780495, 0.0006540678441524506, -0.016525834798812866, 0.04798811301589012, 0.026636658236384392, -0.06365223228931427, -0.014783249236643314, -0.005495845340192318, -0.018651405349373817, -0.05993726849555969, -0.02043228968977928, 0.008794309571385384, 0.02445363998413086, 0.04450294375419617, -0.02973884344100952, 0.015549221076071262, 0.04094117507338524, -0.042894404381513596, 0.0025205248966813087, 0.0027957959100604057, 0.03722621500492096, -0.05553293228149414, -0.020355692133307457, 0.002774253021925688, 0.011566169559955597, 0.02238551713526249, 0.0011178395943716168, -0.03582831472158432, -0.05978407338261604, 0.030581410974264145, 0.013404500670731068, -0.0031309083569794893, -0.033530402928590775, -0.0325346402823925, 0.009536344558000565, 0.025966433808207512, -0.006544268690049648, -0.08862289786338806, -0.07387794554233551, 0.048524294048547745, -0.07161833345890045, 0.006802784278988838, -0.03173036873340607, -0.026291970163583755, 0.011594893410801888, -0.027632420882582664, -0.03173036873340607, 0.04251141846179962, -0.016592856496572495, 0.002503769239410758, -0.05852022022008896, 0.01711946167051792, -0.024434490129351616, 0.0019364716717973351, -0.006975127849727869, 0.035024046897888184, -0.0308686513453722, 0.03716876730322838, 0.04473273456096649, 0.01907268911600113, -0.019972706213593483, 0.021600395441055298, 0.014333241619169712, 0.009617729112505913, -0.015108787454664707, 0.04932856187224388, -0.028034556657075882, -0.06526076793670654, -0.006769272964447737, -0.05086050555109978, 0.055494632571935654, -0.009608155116438866, -0.027938809245824814, 0.0093544265255332, 0.04239652305841446, 0.02025994472205639, -0.03609640523791313, 0.020796125754714012, -0.012312991544604301, 0.08992505073547363, -0.03226654976606369, -0.04063478857278824, -0.0029178725089877844, -0.04178374260663986, -0.0053330762311816216, -0.0003488760848995298, 0.011872557923197746, -0.0211408119648695, -0.06556715816259384, -0.02181103825569153, -0.000623548636212945, 0.02880052663385868, 0.018574807792901993, -0.011355526745319366, 0.039830517023801804, 0.029853738844394684, 0.010445935651659966, 0.004612584598362446, 0.0608181357383728, 0.03351125121116638, -0.04051988944411278, -0.00700385170057416, 0.047949813306331635, 0.010838496498763561, 0.010283167473971844, -0.014256644062697887, 0.043966762721538544, 0.00350192585028708, 0.04936686158180237, -0.01590348221361637, -0.00232663843780756, 0.014515159651637077, 0.02031739428639412, 0.014141748659312725, 0.0008300018962472677, 0.018201397731900215, -0.05151158198714256, -0.016430087387561798, -0.060052163898944855, -0.036268748342990875, -0.018421614542603493, 0.028762228786945343, 0.0046580638736486435, 0.006424585822969675, -0.0051272218115627766, -0.04002200812101364, -0.01706201396882534, -0.0019400621531531215, -0.09237615764141083, -0.035541076213121414, 0.009378363378345966, -0.06503097712993622, -0.011307653971016407, -0.04266460984945297, 0.06009046360850334, -0.007295878138393164, -0.015922632068395615, 0.062120288610458374, 0.010177846066653728, -0.04243481904268265, -0.03226654976606369, 0.018565233796834946, -0.03877730667591095, -0.01142254937440157, 0.029087767004966736, 0.0077219498343765736, -0.033224012702703476, -0.03804963454604149, 0.004339707084000111, 0.023342980071902275, 0.044234853237867355, 0.00439476128667593, -0.03728366270661354, -0.025928134098649025, -0.01287789549678564, -0.014046002179384232, 0.009632091037929058, 0.06633313000202179, 0.007382050156593323, -0.010800197720527649, 0.010206569917500019, -0.036785781383514404, -0.009531557559967041, -0.019235458225011826, -0.0014014884363859892, -0.009986353106796741, 0.015625817701220512, -0.011652341112494469, 0.007961316034197807, 0.0001044234522851184, -0.013586418703198433, -0.03433467075228691, 0.006860231980681419, 0.0014134567463770509, 0.06185219809412956, 0.03464106097817421, 0.0034612335730344057, -0.012676827609539032, -0.003676663152873516, -0.013404500670731068, -0.012983216904103756, -0.02269190549850464, 0.053273316472768784, 0.03743685781955719, 0.026713255792856216, -0.034353822469711304, 0.013145985081791878, 0.07717162370681763, -0.028092004358768463, -0.020604632794857025, 0.004076404497027397, -0.006319264881312847, -0.027881361544132233, -0.00909591093659401, 0.016468387097120285, 0.029068617150187492, -0.008143234066665173, -0.01256193220615387, -0.01980036310851574, 0.0203748419880867, -0.03925604000687599, 0.05859681963920593, 0.0021219803020358086, -0.00913899764418602, 0.01577901281416416, -0.01251405943185091, -0.0368049293756485, 0.015807736665010452, -0.004545561969280243, 0.020508887246251106, 0.01307896338403225, -0.007669289596378803, -0.003279315307736397, 0.004579073283821344, -0.0377049446105957, -0.0052086059004068375, -0.002346984576433897, 0.03914114087820053, 0.01629604399204254, -0.005194243974983692, 0.013002365827560425, -0.0015726351412013173, 0.03397083654999733, -0.05514994636178017, 0.00510807242244482, 0.0462263785302639, -0.0049357288517057896, 0.006070323754101992, 0.028302645310759544, 0.0034660210367292166, -0.04327739030122757, -0.04607318341732025, -0.013643867336213589, -0.01873757690191269, 0.007664502132683992, -0.027172837406396866, 0.02022164687514305, -0.0044282726012170315, -0.029145214706659317, -0.05365630239248276, 0.016994992271065712, -0.015654541552066803, 0.044541239738464355, 0.05300522595643997, -0.017646068707108498, 0.03479425609111786, -0.0030303746461868286, 0.002970533212646842, -0.02579408884048462, -0.010455510579049587, 0.03511979058384895, 0.04434974864125252, 0.011594893410801888, -0.02269190549850464, 0.01377791166305542, 0.008310790173709393, 0.02016419917345047, -0.0028125515673309565, -0.0063719251193106174, 0.06836295127868652, 0.0048950365744531155, 0.02889627404510975, -0.022059978917241096, -0.0374177061021328, -0.018718428909778595, -0.05936278775334358, -0.024587685242295265, 0.0684395506978035, -0.02885797619819641, 0.005505419801920652, 0.011269355192780495, 0.01794288121163845, 0.01833544299006462, 0.01745457574725151, 0.019331205636262894, -0.03504319489002228, 0.020853573456406593, 0.010541682131588459, 0.00688895583152771, 0.028168601915240288, -0.02430044487118721, -0.02196423150599003, 0.04565190151333809, -0.014122598804533482, -0.00997677817940712, 0.010177846066653728, 0.010694876313209534, -0.023649370297789574, 0.10264017432928085, -0.03385594114661217, 0.03933263570070267, -0.030370770022273064, -0.0027431354392319918, 0.028723930940032005, -0.04726044088602066, -0.02250041253864765, 0.02420469932258129, -0.02332383207976818, 0.01876630075275898, 0.03443041816353798, -0.0020178561098873615, 0.009454960003495216, 0.009694326668977737, -0.014601331204175949, 0.01742585189640522, 0.031519725918769836, -0.055341437458992004, 0.014113024808466434, -0.03240059316158295, -0.008746436797082424, -0.007913443259894848, -0.0060990480706095695, -0.03889220207929611, 0.06238837540149689, 0.011671490035951138, -0.02579408884048462, -0.04163055121898651, 0.03634534776210785, -0.019685467705130577, 0.09482727199792862, 0.0017737026792019606, 0.0018610713304951787, 0.005036262329667807, 0.0016121305525302887, 0.03199845924973488, 0.036785781383514404, 0.04419655352830887, 0.01307896338403225, 0.0014505585422739387, 0.023955758661031723, -0.024434490129351616, -0.031768668442964554, 0.006400648970156908, -0.009890606626868248, -0.01745457574725151, -0.0022883398924022913, 0.03644109144806862, 0.01711946167051792, 0.03211335465312004, -0.022423814982175827, 0.03423892334103584, 0.00017009951989166439, 0.011920430697500706, 0.04768172279000282, 0.013031089678406715, 0.050017938017845154, 0.010819347575306892, -0.019474824890494347, -0.06300115585327148, 0.0056298901326954365, 0.025162162259221077, -0.05775424838066101, 0.02518131211400032, 0.02368766814470291, 0.027115389704704285, 0.009000164456665516, -0.03050481341779232, -0.018756726756691933, -0.01106828823685646, -0.009100698865950108, -0.004567104857414961, -0.003992626443505287, 0.021945083513855934, 0.010388487949967384, 0.03278357908129692, -0.010915093123912811, -0.031002694740891457, 0.001160327112302184, -0.009770923294126987, -0.036575138568878174, 0.014926869422197342, 0.028168601915240288, 0.010053375735878944, -0.0349665991961956, 0.02196423150599003, 0.001995116239413619, -0.04419655352830887, -0.018134374171495438, -0.029968634247779846, 0.026406867429614067, 0.028972871601581573, 0.04833279922604561, 0.0030040442943573, 0.027785615995526314, -0.043660372495651245, 0.014697077684104443, 0.02952820062637329, -0.006525119300931692, -0.02730688266456127, 0.02284509874880314, 0.021274857223033905, -0.0017210422083735466, 0.0017306167865172029, 0.027172837406396866, -0.01491729449480772, 0.057103171944618225, -0.057409562170505524, 0.014122598804533482, 0.038604963570833206, -0.05790744349360466, -0.02548770047724247, -0.008602817542850971, 0.002783827483654022, 0.00396868959069252, -0.015396026894450188, 0.0026713255792856216, 0.05365630239248276, -0.0308686513453722, 0.0004769369261339307, 0.007477796636521816, 0.0034588398411870003, -0.037245362997055054, -0.007779398001730442, 0.017722664400935173, 0.02250041253864765, 0.01367259118705988, -0.031060144305229187, -0.016927970573306084, 0.013433224521577358, -0.01639178954064846, -0.02543025277554989, -0.0346793569624424, -0.037819840013980865, 0.018009904772043228, -0.023438727483153343, 0.0020956501830369234, 0.022194024175405502, 0.012485334649682045, 0.023400427773594856, -0.02083442360162735, -0.06545226275920868, 0.024989819154143333, 0.004617371596395969, -0.030734606087207794, -0.027957959100604057, -0.008095361292362213, 0.02786221168935299, 0.03810708224773407, 0.006247454788535833, -0.0033942111767828465, 0.061086226254701614, 0.005763935390859842, -0.05258394032716751, 0.0238791611045599, -0.02682815119624138, -0.045881692320108414, -0.000041926465200958773, -0.0322473980486393, 0.06162240356206894, -0.01082892157137394, -0.007688438519835472, 0.048524294048547745, 0.03519639000296593, -0.006391074508428574, 0.0063958619721233845, 0.002145916922017932, -0.01693754456937313, 0.003391817444935441, -0.0018574808491393924, 0.04285610467195511, -0.01739712804555893, 0.015032189898192883, -0.03263038396835327, -0.06269476562738419, 0.026962196454405785, -0.014208771288394928, -0.002218923531472683, 0.024070654064416885, 0.008598029613494873, 0.02977714128792286, 0.009751774370670319, -0.015099212527275085, 0.03940923139452934, -0.005610741209238768, -0.014505584724247456, -0.024645132943987846, 0.05802233889698982, -0.027728168293833733, 0.007674076594412327, 0.028360094875097275, -0.04875408485531807, -0.010627854615449905, -0.012676827609539032, -0.021849336102604866, -0.005874043796211481, 0.007707587908953428, 0.020202497020363808, 0.009340064600110054, -0.004686788190156221, 0.008966653607785702, 0.021638695150613785, -0.01313641108572483, -0.02430044487118721, 0.02414725162088871, -0.033587850630283356, -0.016889670863747597, 0.020700378343462944, -0.060626640915870667, 0.021485500037670135, -0.020911021158099174, -0.028723930940032005, -0.009071975015103817, 0.039485830813646317, 0.0036599074956029654, 0.08035040646791458, 0.005739998538047075, -0.0034971386194229126, 0.0468391552567482, -0.04411995783448219, 0.03810708224773407, 0.0010550060542300344, 0.0019029603572562337, -0.0027191988192498684, 0.010407637804746628, 0.02301744371652603, 0.003935178276151419, -0.031194187700748444, -0.011566169559955597, -0.01812480017542839, -0.03755175322294235, -0.0035545863211154938, 0.022328069433569908, -0.026406867429614067, 0.01639178954064846, -0.02621537446975708, 0.0371113196015358, -0.008808672428131104, 0.04595828801393509, 0.026809001341462135, 0.02590898610651493, -0.03215165436267853, -0.028838826343417168, -0.02502811886370182, 0.011384251527488232, -0.0001638161629671231, -0.00973262544721365, -0.009742199443280697, -0.007985252887010574, -0.011901281774044037, -0.0018526935018599033, 0.01739712804555893, -0.018507786095142365, -0.03247718885540962, -0.07395454496145248, -0.011365101672708988, -0.020451437681913376, -0.010168271139264107, 0.02460683323442936, -0.02922181226313114, 0.07253749668598175, 0.028206899762153625, 0.0043660374358296394, 0.010723601095378399, -0.009368788450956345, 0.02414725162088871, -0.01199702825397253, 0.015185385011136532, 0.03050481341779232, 0.018421614542603493, -0.025411102920770645, 0.06158410757780075, -0.04415825754404068, -0.045422106981277466, -0.04825620353221893, -0.011173608712852001, -0.05185626819729805, -0.03573257103562355, 0.03326231241226196, -0.01310768723487854, -0.047490231692790985, 0.010034226812422276, 0.012456610798835754, -0.01815352402627468, 0.023036591708660126, 0.02181103825569153, 0.02786221168935299, -0.0005122434231452644, -0.029643096029758453, -0.026847301051020622, -0.012312991544604301, 0.006912892684340477, 0.047490231692790985, 0.018526935949921608, -0.051626477390527725, -0.005433610174804926, -0.0006600519991479814, -0.006094260606914759, -0.0513966865837574, -0.038796454668045044, -0.004804077558219433, 0.034660208970308304, 0.04063478857278824, -0.016382215544581413, -0.029547350481152534, 0.03282187879085541, -0.0014553457731381059, 0.009459747932851315, 0.024549385532736778, -0.056490395218133926, 0.022251471877098083, -0.054460570216178894, 0.049098771065473557, 0.018440762534737587, 0.026196224614977837, -0.03998371213674545, -0.0004901020438410342, -0.027172837406396866, 0.03370274603366852, 0.014601331204175949, -0.027938809245824814, 0.056643590331077576, 0.009842733852565289, -0.006740549113601446, -0.004634127486497164, 0.018862048164010048, -0.022155724465847015, -0.009919330477714539, 0.025717493146657944, -0.03990711271762848, 0.05729466676712036, -0.002575579099357128, -0.018546083942055702, 0.02424299716949463, -0.02460683323442936, -0.0017521597910672426, 0.026119627058506012, -0.02424299716949463, -0.04224332794547081, 0.02110251411795616, -0.006055961828678846, 0.018957793712615967, -0.008487921208143234, -0.027421778067946434, 0.017052439972758293, -0.01688009686768055, 0.03630704805254936, 0.012494909577071667, 0.010895944200456142, -0.026694105938076973, -0.021849336102604866, -0.005826170556247234, 0.029030319303274155, -0.019685467705130577, -0.008219831623136997, -0.010579980909824371, 0.012734276242554188, 0.021638695150613785, -0.013720463961362839, -0.006084686145186424, 0.04611148312687874, -0.05246904492378235, 0.003688631346449256, 0.017473723739385605, -0.02782391384243965, -0.023974906653165817, 0.001111855497583747, 0.02895372174680233, 0.01374918781220913, -0.012973641976714134, -0.01663115620613098, 0.028360094875097275, -0.06284795701503754, -0.0038418257609009743, -0.037513453513383865, -0.062426675111055374, -0.0014816761249676347, 0.0027455289382487535, 0.004129065200686455, 0.022002531215548515, -0.0093544265255332, -0.04856259003281593, 0.024166399613022804, 0.02284509874880314, 0.010407637804746628, -0.025257909670472145, 0.01377791166305542, 0.006443735212087631, -0.007568755652755499, -0.04691575467586517, 0.023974906653165817, 0.02119826152920723, -0.01623859442770481, 0.07858867198228836, 0.024319594725966454, -0.004672425799071789, 0.04595828801393509, -0.029336707666516304, 0.000043908716179430485, -0.02320893667638302, -0.017253506928682327, -0.048524294048547745, -0.034564461559057236, -0.013461948372423649, 0.00431098323315382, 0.00027003485593013465, -0.07782270014286041, 0.013050238601863384, -0.04829450324177742, -0.005203818902373314, -0.03117503970861435 ]
Predict+Optimize is a recently proposed framework which combines machine learning and constrained optimization, tackling optimization problems that contain parameters that are unknown at solving time. The goal is to predict the unknown parameters and use the estimates to solve for an estimated optimal solution to the optimization problem. However, all prior works have focused on the case where unknown parameters appear only in the optimization objective and not the constraints, for the simple reason that if the constraints were not known exactly, the estimated optimal solution might not even be feasible under the true parameters. The contributions of this paper are two-fold. First, we propose a novel and practically relevant framework for the Predict+Optimize setting, but with unknown parameters in both the objective and the constraints. We introduce the notion of a correction function, and an additional penalty term in the loss function, modelling practical scenarios where an estimated optimal solution can be modified into a feasible solution after the true parameters are revealed, but at an additional cost. Second, we propose a corresponding algorithmic approach for our framework, which handles all packing and covering linear programs. Our approach is inspired by the prior work of Mandi and Guns, though with crucial modifications and re-derivations for our very different setting. Experimentation demonstrates the superior empirical performance of our method over classical approaches.
[ -0.009015760384500027, 0.05390329286456108, -0.023317521438002586, -0.019978994503617287, 0.013145447708666325, 0.01813584938645363, -0.04934759438037872, 0.01624923385679722, -0.061519306153059006, 0.0032581062987446785, 0.05779824033379555, -0.01650136336684227, 0.032689739018678665, -0.04475712031126022, -0.044374581426382065, -0.025351935997605324, 0.040201421827077866, 0.0181532371789217, 0.008311539888381958, -0.059015411883592606, 0.03381996974349022, -0.0701090544462204, 0.014058326371014118, 0.07817716151475906, 0.025543205440044403, 0.008441951125860214, -0.004473103675991297, -0.0038297418504953384, -0.029368599876761436, 0.035645727068185806, 0.04444413259625435, 0.02404782362282276, -0.011024092324078083, 0.04927804321050644, -0.03051621839404106, -0.015005980618298054, 0.008194169960916042, 0.01777939312160015, -0.009085312485694885, 0.05039088428020477, -0.006929181050509214, -0.004053614567965269, -0.029977185651659966, -0.0022778487764298916, 0.0037015043199062347, -0.024099987000226974, -0.00657707080245018, -0.005790256895124912, -0.031872496008872986, -0.026829928159713745, -0.028360087424516678, -0.0926441103219986, 0.032063763588666916, -0.03717588260769844, -0.0033233119174838066, 0.001644267700612545, 0.07031771540641785, 0.01923130266368389, 0.037488870322704315, 0.018066296353936195, -0.053138211369514465, -0.0036906367167830467, -0.07337802648544312, -0.0181532371789217, 0.03069010004401207, -0.03234197571873665, 0.02486506663262844, 0.04152292385697365, 0.04406159371137619, 0.0035037139896303415, -0.0479913167655468, -0.028725238516926765, 0.026256119832396507, 0.01607535220682621, -0.021144000813364983, -0.0015953636029735208, 0.01691867783665657, -0.029490316286683083, 0.019978994503617287, -0.02592574432492256, -0.0006841153954155743, 0.046461161226034164, 0.043957263231277466, 0.006177143193781376, 0.02566492184996605, -0.04997356981039047, 0.042948752641677856, -0.06520559638738632, 0.06012825295329094, -0.032446302473545074, -0.02989024482667446, 0.05491180345416069, -0.0252476055175066, 0.0534164234995842, 0.04402681812644005, 0.04183591157197952, -0.015171168372035027, 0.0004925739485770464, -0.01900525763630867, 0.035645727068185806, -0.03950589522719383, -0.00025552441366016865, 0.010832822881639004, 0.04100127890706062, 0.034567657858133316, -0.015988411381840706, -0.010632858611643314, 0.009580875746905804, 0.01963123120367527, 0.11705708503723145, 0.004297048784792423, 0.032272420823574066, 0.044131144881248474, 0.05790256708860397, -0.03343743085861206, -0.010424201376736164, -0.0868016853928566, -0.03258540853857994, 0.08360226452350616, 0.02507372386753559, 0.0008558234549127519, 0.008802755735814571, 0.05988482013344765, 0.028307922184467316, -0.04068829119205475, -0.011510960757732391, 0.004242710769176483, 0.028933895751833916, -0.0031689919997006655, 0.008063758723437786, -0.010815435089170933, -0.03908858075737953, 0.0032363710924983025, -0.0909748449921608, 0.05512046441435814, 0.027612395584583282, 0.07275205850601196, -0.04559175297617912, -0.051016855984926224, -0.00037683401023969054, 0.016579609364271164, -0.022917592898011208, -0.02230900712311268, -0.020587580278515816, 0.013119366019964218, 0.0035015405155718327, -0.00443398067727685, 0.028029711917042732, -0.022848039865493774, 0.029125165194272995, -0.06200617551803589, -0.0010090565774589777, 0.009572180919349194, 0.03616736829280853, 0.03298533707857132, 0.011832642368972301, -0.021456988528370857, 0.005138200707733631, 0.041244711726903915, -0.010424201376736164, 0.08701034635305405, 0.012562944553792477, 0.03449810668826103, 0.06138020008802414, 0.05616375058889389, 0.002471292158588767, -0.0033689558040350676, -0.02356095425784588, -0.05407717451453209, 0.03340265154838562, -0.012423839420080185, -0.05407717451453209, 0.00479478482156992, 0.044965777546167374, -0.030863981693983078, 0.01902264542877674, 0.015814529731869698, 0.040583960711956024, 0.031159579753875732, 0.02797754667699337, -0.01672740839421749, 0.004703497048467398, 0.01632748171687126, 0.00022061225899960846, 0.04406159371137619, 0.009128782898187637, 0.02649955451488495, -0.041244711726903915, 0.06242348998785019, -0.020118098706007004, -0.0017203409224748611, 0.018448837101459503, 0.03093353472650051, -0.009207029826939106, -0.012484697625041008, -0.07247384637594223, -0.05244268476963043, 0.01544937863945961, -0.019057421013712883, 0.029385987669229507, -0.005846768151968718, -0.06830068677663803, 0.04127948731184006, 0.0017257747240364552, -0.04493100196123123, 0.027421126142144203, 0.018518388271331787, -0.03759320080280304, 0.036828119307756424, -0.0446527898311615, 0.011867417953908443, -0.011224056594073772, -0.0325506329536438, 0.007815977558493614, -0.04242710769176483, -0.047747883945703506, -0.0007889876724220812, -0.017657674849033356, -0.029612034559249878, -0.059224069118499756, -0.019666006788611412, 0.08986200392246246, 0.04580041021108627, -0.017405547201633453, -0.009111395105719566, 0.005159935913980007, 0.008072452619671822, -0.0034580701030790806, 0.054807476699352264, 0.0056250691413879395, 0.06388409435749054, -0.007659483700990677, 0.03274190425872803, -0.01750987581908703, -0.00396884698420763, 0.0014269157545641065, -0.039992764592170715, 0.007785547990351915, -0.024934619665145874, -0.0041970666497945786, -0.004036226309835911, -0.05825033038854599, -0.005598986987024546, -0.03759320080280304, 0.012545556761324406, 0.06475350260734558, 0.007303026504814625, 0.032272420823574066, 0.04221845045685768, 0.016214458271861076, -0.03794096037745476, 0.012136934325098991, -0.003914509434252977, 0.025421487167477608, -0.025404099375009537, -0.0005776128964498639, 0.04795654118061066, -0.05651151388883591, -0.04580041021108627, 0.014353925362229347, 0.048582516610622406, 0.02689948119223118, 0.00032847319380380213, 0.03489803522825241, 0.03399385139346123, 0.03741931915283203, 0.01710994727909565, -0.014067020267248154, -0.029177330434322357, 0.06367543339729309, 0.03961022570729256, -0.0012291254242882133, 0.05894585698843002, -0.008989677764475346, 0.027699336409568787, -0.047539226710796356, 0.012762908823788166, -0.01757942885160446, 0.027664560824632645, -0.013180224224925041, -0.04868684336543083, 0.014910345897078514, 0.03637602925300598, -0.006868322845548391, 0.02403043583035469, -0.04343562200665474, -0.03442855551838875, 0.005081689450889826, 0.0033363529946655035, 0.017857639119029045, 0.008194169960916042, 0.022500276565551758, -0.023908717557787895, 0.059224069118499756, -0.0007705127936787903, 0.0034754581283777952, -0.05616375058889389, -0.022448113188147545, -0.016996925696730614, 0.0450701080262661, 0.011502266861498356, -0.015779754146933556, 0.016440503299236298, 0.053555529564619064, -0.0019735561218112707, -0.016179680824279785, -0.013084589503705502, 0.025108501315116882, -0.030672712251544, -0.016423115506768227, 0.03731498867273331, -0.0200311578810215, -0.03275929018855095, 0.022256843745708466, -0.04694802686572075, 0.06788337230682373, 0.039401568472385406, -0.0007629054598510265, -0.008807102218270302, -0.04152292385697365, 0.0009894948452711105, -0.017301218584179878, -0.0788726881146431, -0.03908858075737953, 0.026812540367245674, -0.03668901324272156, -0.01210215874016285, 0.045904740691185, 0.01589277759194374, -0.008820143528282642, -0.04712190851569176, 0.033107053488492966, -0.04430502653121948, -0.011563125066459179, -0.04239233210682869, 0.0055294344201684, -0.032463692128658295, 0.02526499517261982, -0.02529977075755596, 0.0021778668742626905, -0.0033711292780935764, -0.06186706945300102, 0.01794457994401455, 0.0471566878259182, 0.04475712031126022, -0.0047078439965844154, -0.009415687993168831, -0.04719146341085434, -0.020361533388495445, 0.021370047703385353, 0.0010389424860477448, -0.008754937909543514, -0.0475740022957325, 0.016605691984295845, 0.02006593532860279, -0.01923130266368389, -0.02462163195014, -0.01756204105913639, -0.00026870137662626803, 0.013145447708666325, 0.013267165049910545, -0.04722623899579048, -0.04221845045685768, 0.01646658591926098, -0.024969395250082016, 0.04844341054558754, -0.0009107047808356583, 0.007924653589725494, -0.04684370011091232, -0.04364427924156189, -0.017475100234150887, -0.00910270120948553, 0.08833184838294983, 0.028464416041970253, -0.036619462072849274, 0.0031233481131494045, 0.01651005633175373, 0.0019355193944647908, -0.06329289823770523, 0.028429638594388962, -0.019335633143782616, -0.03154211863875389, 0.05553777888417244, 0.017996743321418762, -0.01376272737979889, 0.05365985631942749, -0.04277487099170685, -0.032881006598472595, -0.0355587862432003, 0.001314979512244463, 0.045243989676237106, -0.02964681014418602, 0.03545445576310158, -0.009911250323057175, 0.002284369431436062, -0.008620179258286953, -0.013101977296173573, -0.03155950829386711, -0.0016073179431259632, 0.016866514459252357, 0.0200311578810215, -0.0696917399764061, -0.009207029826939106, -0.007702954113483429, 0.0326375737786293, 0.029733750969171524, -0.014406089670956135, -0.03675856813788414, -0.014232208020985126, 0.0711175724864006, 0.03242891654372215, 0.019526902586221695, -0.000120494507427793, 0.009746062569320202, -0.001374751329421997, 0.013893138617277145, -0.07476907968521118, -0.03522840887308121, 0.02509111352264881, 0.0021017936524003744, -0.022621994838118553, -0.021161388605833054, 0.048582516610622406, -0.0017909803427755833, 0.03300272673368454, 0.0194051843136549, -0.02232639491558075, 0.006694441195577383, -0.02676037698984146, -0.014353925362229347, 0.08617571741342545, 0.0563376322388649, -0.022413335740566254, -0.04100127890706062, 0.0026690822560340166, 0.04861729219555855, -0.016562221571803093, 0.014206125400960445, -0.025960521772503853, 0.007455172948539257, 0.023282743990421295, -0.07400400191545486, -0.03281145542860031, -0.010250319726765156, 0.039401568472385406, -0.011867417953908443, -0.0363064743578434, 0.023960882797837257, -0.0260822381824255, 0.0016344869509339333, -0.04903460666537285, -0.0033059236593544483, -0.07275205850601196, -0.00010453272261656821, 0.06996995210647583, -0.0027255939785391092, 0.028690461069345474, -0.02401304617524147, 0.047469671815633774, -0.0034624170511960983, -0.018744435161352158, 0.043992042541503906, 0.005925015080720186, -0.060267359018325806, 0.03091614693403244, 0.01855316571891308, -0.0294207651168108, -0.04566130414605141, 0.01694476045668125, -0.005581598728895187, -0.012562944553792477, -0.033802580088377, 0.016657855361700058, 0.017240358516573906, 0.03401123732328415, 0.023126250132918358, 0.010259013622999191, -0.06663142144680023, -0.00917225331068039, -0.03627169877290726, 0.042879197746515274, -0.061310648918151855, 0.03168122470378876, -0.060649897903203964, -0.010632858611643314, -0.02175258658826351, -0.009285276755690575, 0.03481109440326691, 0.04493100196123123, -0.003940591588616371, -0.0375584214925766, -0.0242043174803257, -0.016136210411787033, 0.013727950863540173, 0.009111395105719566, 0.008494115434587002, -0.05052999034523964, 0.0073551912792027, 0.05178193747997284, -0.022621994838118553, 0.06631843745708466, -0.021613480523228645, -0.04997356981039047, 0.015927553176879883, 0.03908858075737953, -0.06729217618703842, 0.018744435161352158, 0.013197612017393112, 0.0027668906841427088, -0.02589096873998642, 0.010485059581696987, 0.06673575192689896, 0.00573374517261982, 0.01055461261421442, 0.047539226710796356, 0.0413142666220665, 0.0788726881146431, -0.011754395440220833, -0.028707850724458694, 0.01857055351138115, 0.04451368749141693, -0.022621994838118553, -0.02696903422474861, 0.00297554861754179, -0.05018222704529762, 0.04159247502684593, 0.05094730481505394, -0.0055337813682854176, 0.07942911237478256, -0.01441478356719017, -0.011641371995210648, 0.05428583174943924, -0.030411889776587486, -0.042948752641677856, -0.0162753164768219, -0.013823586516082287, -0.005972832441329956, 0.039158131927251816, -0.029107777401804924, -0.03298533707857132, -0.04893027991056442, 0.042705316096544266, 0.02757761999964714, -0.010067744180560112, 0.021004894748330116, 0.01771853305399418, 0.0020778849720954895, -0.0016051443526521325, -0.0023560954723507166, 0.011189280077815056, -0.007685566321015358, 0.004014491103589535, 0.005916321184486151, 0.0032059417571872473, -0.024169540032744408, -0.01982250064611435, -0.0075812372379004955, -0.043992042541503906, -0.03070748783648014, -0.02397827059030533, 0.007029163185507059, -0.04197501391172409, -0.01388444472104311, -0.00684224022552371, -0.0008324580849148333, -0.011510960757732391, 0.03489803522825241, 0.024169540032744408, -0.02173519879579544, 0.042079344391822815, 0.014301760122179985, 0.00971128698438406, -0.03484586998820305, 0.022865429520606995, 0.009972108528017998, 0.02465640939772129, 0.014327842742204666, 0.007211738731712103, 0.013015036471188068, -0.012249957770109177, 0.023282743990421295, -0.021039672195911407, 0.009841698221862316, -0.005955444183200598, 0.019474737346172333, -0.01629270426928997, 0.0009786273585632443, -0.014162654988467693, -0.0005143091548234224, -0.04277487099170685, -0.040062315762043, 0.041418593376874924, 0.0035971752367913723, 0.021352658048272133, -0.011658760719001293, -0.01919652707874775, 0.016431810334324837, -0.0036276045721024275, -0.0014008334837853909, -0.03136823698878288, 0.018066296353936195, 0.009328747168183327, -0.03675856813788414, 0.022239454090595245, -0.00005511910421773791, -0.0034776318352669477, 0.036654237657785416, 0.0007379099843092263, 0.02877740189433098, 0.04197501391172409, -0.011067562736570835, 0.013649704866111279, 0.017179500311613083, -0.04868684336543083, 0.016153600066900253, -0.0041036056354641914, -0.0015051624504849315, -0.005086036399006844, 0.0101199084892869, -0.014571276493370533, 0.03696722537279129, -0.015310273505747318, -0.015501543879508972, 0.013606234453618526, -0.012441227212548256, 0.03364608809351921, -0.03908858075737953, -0.052338358014822006, -0.013423658907413483, -0.03216809406876564, -0.05494658276438713, 0.023108862340450287, -0.027421126142144203, 0.011171892285346985, 0.024134764447808266, 0.017370769754052162, -0.028342697769403458, 0.06280603259801865, -0.004703497048467398, -0.012554250657558441, -0.05327731743454933, -0.0028712197672575712, 0.012928095646202564, 0.05529434606432915, 0.007768159732222557, 0.02213512547314167, 0.04350517317652702, -0.037036776542663574, 0.06475350260734558, 0.04493100196123123, -0.035610947757959366, 0.008989677764475346, 0.048756398260593414, 0.03230720013380051, -0.03461982309818268, -0.00991994421929121, 0.0147103825584054, 0.04461801424622536, -0.007755118887871504, 0.003966673742979765, 0.021787362173199654, 0.008289804682135582, -0.027664560824632645, 0.02006593532860279, -0.003531969618052244, 0.005051259882748127, -0.01118058618158102, 0.02401304617524147, 0.0020909260492771864, 0.03091614693403244, -0.025821415707468987, 0.004055787809193134, -0.0358891598880291, 0.028255756944417953, 0.002899475395679474, -0.03025539591908455, 0.010302484035491943, 0.04336606711149216, 0.013988773338496685, -0.042948752641677856, 0.012067382223904133, 0.0008791887667030096, 0.02342185005545616, -0.01054591778665781, -0.056685395538806915, -0.005603333935141563, 0.0031820330768823624, -0.003866691840812564, -0.035993486642837524, 0.03072487562894821, -0.06287558376789093, -0.03168122470378876, -0.00026720709865912795, 0.003255932591855526, -0.02335229702293873, 0.006494477391242981, 0.014345230534672737, -0.010658941231667995, 0.022187290713191032, 0.02759500779211521, -0.03961022570729256, 0.029959797859191895, 0.03178555518388748, 0.03668901324272156, -0.012136934325098991, 0.008694079704582691, 0.02170042134821415, -0.007137839216738939, -0.042461883276700974, 0.0045948210172355175, -0.01691867783665657, 0.02922949381172657, -0.06687486171722412, -0.008176781237125397, 0.042670540511608124, -0.028760014101862907, 0.0162753164768219, 0.032898396253585815, 0.026464777067303658, 0.014806017279624939, 0.010832822881639004, 0.014040937647223473, 0.011954358778893948, -0.04816519841551781, -0.036619462072849274, 0.044583238661289215, 0.024586856365203857, -0.01689259521663189, 0.03284623101353645, 0.005399023182690144, -0.03988843411207199, 0.005316429305821657, -0.04767833277583122, -0.023769613355398178, 0.01777939312160015, 0.007820324040949345, 0.022465500980615616, 0.023143639788031578, -0.02298714593052864, -0.000380637648049742, 0.007437784690409899, -0.010563306510448456, 0.0013160662492737174, -0.011119727045297623, -0.031211744993925095, 0.030550993978977203, 0.027055975049734116, -0.01750118099153042, 0.0057815625332295895, 0.007059592287987471, 0.05505090951919556, 0.0035906548146158457, 0.02112661302089691, 0.0383930541574955, -0.026690823957324028, 0.03446333110332489, -0.03512408211827278, -0.01084151677787304, 0.027438513934612274, -0.026777764782309532, 0.0007042204379104078, 0.023247968405485153, -0.000302390952128917, -0.0006031517405062914, 0.036862894892692566, -0.016336174681782722, 0.005716357380151749, 0.01337149366736412, 0.02296975813806057, -0.023143639788031578, 0.03147256746888161, 0.004473103675991297, 0.04660026356577873, -0.06517081707715988, 0.012249957770109177, -0.02820359356701374, 0.028290534391999245, 0.04552219808101654, 0.004768702667206526, 0.049834463745355606, -0.015797141939401627, 0.0071334922686219215, -0.03877559304237366, 0.007359538227319717, 0.022187290713191032, 0.013849668204784393, -0.003431987715885043, -0.018048908561468124, 0.005859809461981058, -0.006981345824897289, 0.018361896276474, -0.002038761507719755, -0.006550988648086786, -0.017031701281666756, 0.0065031712874770164, 0.004071002826094627, 0.00022169902513269335, 0.02735157310962677, 0.007329108659178019, -0.045035332441329956, 0.038740817457437515, -0.004959972109645605, 0.010902375914156437, 0.027021199464797974, -0.017066476866602898, -0.0011726139346137643, -0.015379826538264751, -0.045626528561115265, 0.0363064743578434, 0.028864342719316483, 0.022030796855688095, -0.0098069217056036, -0.040618740022182465, -0.020587580278515816, 0.01565803773701191, -0.01628401130437851, -0.016440503299236298, 0.017457710579037666, -0.0032515856437385082, -0.01565803773701191, 0.02088317833840847, -0.0634320005774498, -0.016649162396788597, 0.007303026504814625, -0.04079262167215347, -0.021648257970809937, -0.022848039865493774, -0.05025177821516991, 0.02863829769194126, -0.027612395584583282, 0.00793769396841526, 0.03870604187250137, -0.013467129319906235, 0.002984242746606469, -0.01753595843911171, 0.03658468648791313, 0.011667454615235329, 0.018900929018855095, 0.014040937647223473, 0.025404099375009537, -0.047747883945703506, -0.004620903171598911, -0.02105705998837948, -0.04235755279660225, -0.027073362842202187, 0.0049295430071651936, 0.009667816571891308, 0.05988482013344765, -0.0037058512680232525, 0.017648981884121895, -0.009189642034471035, -0.00604673195630312, 0.02192646823823452, -0.027455901727080345, -0.01344974059611559, -0.011171892285346985, 0.009467852301895618, 0.02004854753613472, 0.0013334543909877539, -0.0022430724930018187, -0.009946026839315891, 0.05432060733437538, 0.006711829453706741, -0.01817062497138977, 0.0058076451532542706, -0.026012685149908066, 0.012815073132514954, -0.03550662100315094, -0.0030385807622224092, -0.07442131638526917, 0.001444303896278143, 0.022674158215522766, -0.0187792107462883, 0.012606414966285229, 0.00679442286491394, -0.027038587257266045, 0.016814349219202995, -0.03216809406876564, -0.00016464412328787148, -0.01881398819386959, 0.010685023851692677, -0.010780658572912216, 0.048756398260593414, -0.039123356342315674, 0.05011267215013504, 0.009746062569320202, -0.023265356197953224, -0.0208657905459404, -0.054181501269340515, -0.017162112519145012, 0.032881006598472595, 0.05261656641960144, -0.011128421872854233, 0.018953092396259308, 0.011867417953908443, 0.027212468907237053, -0.034532882273197174, -0.013745339587330818, -0.004373122006654739, -0.015736283734440804, -0.014806017279624939, -0.032898396253585815, 0.010163378901779652, -0.009259194135665894, 0.052303582429885864, -0.0006629235576838255, 0.00392102962359786, -0.00045480902190320194, 0.035645727068185806, 0.004529615398496389, 0.017153417691588402, -0.030411889776587486, 0.03381996974349022, -0.04027097672224045, -0.002438689349219203, 0.017605511471629143, -0.02359573170542717, -0.0004882268840447068, -0.008598444052040577, -0.003947112243622541, 0.04235755279660225, 0.01568411849439144, 0.04152292385697365, 0.02046586200594902, -0.033298324793577194, 0.03696722537279129, 0.01525810919702053, 0.008841878734529018, 0.005820685997605324, -0.0023365337401628494, -0.0446527898311615, 0.017162112519145012, 0.01002427376806736, 0.02484767884016037, 0.04691325128078461, 0.020622355863451958, -0.0375584214925766, -0.022448113188147545, 0.03399385139346123, -0.0446527898311615, -0.00020675607083830982, -0.01178917195647955, 0.032915785908699036, 0.01171092502772808, 0.04134904220700264, -0.016996925696730614, -0.00012280387454666197, 0.02173519879579544, -0.021387435495853424, 0.001666002906858921, -0.01876182295382023, -0.022500276565551758, 0.015440684743225574, -0.06437095999717712, -0.03345481678843498, 0.03302011266350746, -0.01002427376806736, 0.06937875598669052, -0.02230900712311268, 0.012328204698860645, -0.00014331645797938108, 0.03284623101353645, -0.034602437168359756, -0.02632567286491394, -0.026673436164855957, 0.020952731370925903, -0.021352658048272133, -0.05139939859509468, -0.0007449739496223629, 0.00261474447324872, 0.033280935138463974, 0.00211700820364058, -0.006320595741271973, 0.03249846771359444, 0.02547365240752697, 0.004977360367774963, 0.011024092324078083, 0.005051259882748127, 0.009763451293110847, 0.011145809665322304, 0.10655463486909866, -0.018935704603791237, 0.018518388271331787, 0.043922487646341324, -0.0396450012922287, 0.008954901248216629, 0.0059641385450959206, -0.0011128421174362302, -0.061727963387966156, -0.02192646823823452, -0.030794428661465645, 0.014180043712258339, 0.03637602925300598, -0.0075812372379004955, -0.0028364434838294983, 0.016527444124221802, -0.0034080790355801582, -0.01879660040140152, 0.05974571406841278, 0.023926107212901115, 0.012823767028748989, 0.026464777067303658, -0.015762366354465485, 0.02968158759176731, 0.045035332441329956, 0.01045028306543827, 0.0652751475572586, -0.0008172434754669666, -0.04364427924156189, 0.015614566393196583, -0.051295068114995956, -0.02716030366718769, 0.003914509434252977, -0.006763993762433529, -0.04580041021108627, 0.005390329286456108, -0.013510599732398987, 0.0011976094683632255, -0.004451368469744921, -0.018883539363741875, -0.01065024733543396, -0.030968310311436653, -0.04847818613052368, -0.003973194397985935 ]
Non-intrusive load monitoring (NILM) aims at energy consumption and appliance state information retrieval from aggregated consumption measurements, with the help of signal processing and machine learning algorithms. Representation learning with deep neural networks is successfully applied to several related disciplines. The main advantage of representation learning lies in replacing an expert-driven, hand-crafted feature extraction with hierarchical learning from many representations in raw data format. In this paper, we show how the NILM processing-chain can be improved, reduced in complexity and alternatively designed with recent deep learning algorithms. On the basis of an event-based appliance recognition approach, we evaluate seven different classification models: a classical machine learning approach that is based on a hand-crafted feature extraction, three different deep neural network architectures for automated feature extraction on raw waveform data, as well as three baseline approaches for raw data processing. We evaluate all approaches on two large-scale energy consumption datasets with more than 50,000 events of 44 appliances. We show that with the use of deep learning, we are able to reach and surpass the performance of the state-of-the-art classical machine learning approach for appliance recognition with an F-Score of 0.75 and 0.86 compared to 0.69 and 0.87 of the classical approach.
[ -0.01813017949461937, 0.017160097137093544, -0.03407531976699829, -0.010294174775481224, -0.03793681040406227, 0.015116331167519093, 0.004374788608402014, 0.01800774224102497, -0.008391682989895344, 0.04091298580169678, 0.032040972262620926, -0.08589466661214828, -0.019816050305962563, -0.03241770341992378, -0.025655381381511688, -0.012290849350392818, 0.010256501846015453, -0.016547909006476402, 0.028292497619986534, -0.07093844562768936, 0.014541816897690296, -0.06509912014007568, -0.005768693517893553, -0.03772960975766182, -0.007708858232945204, 0.030119644477963448, -0.012601652182638645, -0.02147366665303707, -0.06253734976053238, 0.012422705069184303, 0.018714113160967827, 0.04234456643462181, 0.01123600173741579, -0.019816050305962563, -0.0684896931052208, -0.03865260258316994, 0.015191677957773209, 0.02092740684747696, -0.0003699616063386202, 0.0011154769454151392, 0.03394346311688423, -0.014325196854770184, -0.08024370670318604, 0.010812180116772652, 0.030383355915546417, -0.024186130613088608, -0.02827366255223751, -0.045094702392816544, 0.026032112538814545, -0.018770622089505196, 0.006818830966949463, -0.06762321293354034, -0.00475151976570487, -0.02452518790960312, -0.04034788906574249, 0.022829899564385414, 0.044830989092588425, 0.04366312175989151, 0.018817713484168053, 0.04931408911943436, 0.015907466411590576, 0.02567421831190586, -0.024431005120277405, -0.006781158037483692, 0.010152900591492653, -0.03266257792711258, 0.03040219284594059, -0.028179479762911797, 0.07267141342163086, -0.004193487111479044, -0.0684143528342247, 0.04411520063877106, -0.04927641525864601, 0.03496063873171806, -0.01406148448586464, 0.029554547742009163, -0.028518537059426308, 0.0510847233235836, 0.030967287719249725, 0.025824910029768944, 0.04498168081045151, 0.06920548528432846, 0.01537062507122755, -0.016171177849173546, 0.03192795440554619, 0.02680441178381443, -0.004365370608866215, -0.07768193632364273, 0.02840551733970642, -0.013524643145501614, -0.01140553131699562, 0.056622669100761414, 0.015850957483053207, 0.03891631215810776, -0.012573396787047386, -0.0036401632241904736, 0.014852619729936123, -0.024299150332808495, -0.017169514670968056, 0.02680441178381443, -0.032643742859363556, -0.0009712596074678004, -0.005594455171376467, -0.019853724166750908, 0.01846923679113388, -0.03539387881755829, -0.0636298656463623, 0.02639000676572323, -0.02347034215927124, 0.07587362080812454, -0.012865363620221615, -0.04125204309821129, 0.019382810220122337, -0.003206922672688961, 0.021228792145848274, -0.003192795207723975, -0.02394125610589981, -0.07203096896409988, 0.05342045798897743, -0.007897223345935345, 0.008410519920289516, 0.07813400775194168, 0.03155122324824333, 0.05221491679549217, -0.022170620039105415, 0.11844422668218613, 0.036806620657444, -0.012950127944350243, 0.024091947823762894, 0.06509912014007568, -0.03966977447271347, -0.01453239843249321, -0.011810516938567162, -0.014014393091201782, 0.017838213592767715, -0.00830220989882946, 0.01163156982511282, -0.010444867424666882, -0.004014539532363415, -0.021567849442362785, 0.013486970216035843, -0.013006637804210186, -0.0024275605101138353, -0.008693068288266659, 0.03100496158003807, 0.018704693764448166, -0.028349008411169052, 0.062386654317379, -0.02612629532814026, -0.039632100611925125, -0.05134843662381172, 0.07414066046476364, -0.009606640785932541, 0.03254956007003784, -0.025617707520723343, 0.011867026798427105, -0.002865510294213891, -0.027896931394934654, -0.054362282156944275, -0.032624904066324234, 0.02060718648135662, 0.007294454146176577, 0.033566731959581375, 0.02220829203724861, 0.001116654253564775, 0.03546922281384468, 0.019759541377425194, 0.014777273871004581, -0.06491075456142426, 0.04426589235663414, 0.0021426575258374214, -0.011838771402835846, 0.00972907803952694, -0.032361194491386414, 0.00043088608072139323, 0.001886009587906301, 0.02793460339307785, -0.03497947379946709, 0.02446867898106575, -0.011857608333230019, -0.014805528335273266, 0.021285301074385643, 0.028349008411169052, 0.007836004719138145, 0.03302047401666641, 0.01446647010743618, 0.03827587142586708, -0.002976174931973219, 0.008744868449866772, -0.051838185638189316, -0.022980591282248497, 0.0298747681081295, 0.01679278537631035, -0.004395979922264814, -0.020701369270682335, -0.05692405626177788, 0.0022144720423966646, 0.0009700823575258255, -0.012884200550615788, -0.0044901627115905285, -0.04211852699518204, -0.045094702392816544, 0.028556210920214653, 0.025014938786625862, -0.000360837671905756, -0.02213294617831707, 0.07108914107084274, -0.01979721337556839, -0.0041793594136834145, -0.05865701660513878, -0.004240578506141901, 0.0370514951646328, -0.059749536216259, 0.004104013554751873, -0.01409915741533041, -0.005782820750027895, 0.009653732180595398, -0.015059822238981724, 0.0009918621508404613, -0.03234235569834709, 0.010510794818401337, 0.01594514027237892, 0.030684739351272583, -0.024883082136511803, -0.02032463811337948, -0.011942372657358646, 0.01262990664690733, -0.004426589235663414, -0.025824910029768944, 0.008556502871215343, -0.020588349550962448, 0.0077936225570738316, 0.04471797123551369, -0.013929628767073154, -0.03266257792711258, -0.028706902638077736, 0.02714346908032894, -0.0335855707526207, -0.04053625464439392, 0.000054155083489604294, 0.03047753870487213, -0.014362869784235954, -0.041779469698667526, 0.024770064279437065, 0.002573543693870306, -0.07986697554588318, 0.06340382993221283, 0.06133180856704712, 0.050707992166280746, 0.011188910342752934, -0.05613292008638382, -0.04614954814314842, 0.0059806047938764095, 0.0402725450694561, -0.029893605038523674, -0.02580607309937477, 0.029309671372175217, 0.0048975031822919846, -0.019627684727311134, -0.03066590428352356, -0.030232662335038185, -0.0021285300608724356, 0.02793460339307785, 0.05922211334109306, -0.05059497430920601, 0.030119644477963448, 0.05104704946279526, -0.0056227101013064384, 0.051423780620098114, 0.029573384672403336, 0.0044006891548633575, -0.025711890310049057, -0.06788692623376846, 0.02659720927476883, -0.043098025023937225, -0.05334511026740074, 0.005321325268596411, -0.0675101950764656, 0.011697497218847275, 0.014541816897690296, 0.01316674891859293, -0.009776169434189796, 0.010115227662026882, 0.011754007078707218, -0.037239860743284225, 0.001635247957892716, -0.002491133753210306, -0.023413831368088722, -0.03880329430103302, -0.0006422086153179407, -0.05771518871188164, 0.0015622563660144806, -0.057225439697504044, 0.0008417583303526044, 0.0073839277029037476, -0.005919385701417923, 0.01960884965956211, -0.04697835445404053, 0.06897944957017899, 0.05033126100897789, -0.03294512629508972, 0.012319103814661503, 0.049427106976509094, 0.05432461202144623, -0.05360882356762886, 0.0011119451373815536, 0.003192795207723975, 0.06038998067378998, -0.019816050305962563, -0.0005062322597950697, -0.02433682233095169, 0.008744868449866772, -0.00019719512783922255, -0.06246200203895569, -0.08212736248970032, 0.07022266089916229, 0.015088076703250408, 0.005858167074620724, 0.021699706092476845, -0.02446867898106575, 0.03305814415216446, 0.04660162329673767, -0.032700251787900925, 0.05018056929111481, -0.027557872235774994, -0.021567849442362785, 0.03381160646677017, 0.011838771402835846, 0.024186130613088608, -0.039632100611925125, -0.02827366255223751, 0.023413831368088722, -0.025109121575951576, -0.03313349187374115, 0.017621593549847603, -0.04144040867686272, -0.033114656805992126, 0.017226025462150574, -0.05534178391098976, 0.010294174775481224, -0.020437657833099365, -0.0034753435757011175, 0.0053071980364620686, -0.03138169273734093, 0.002552352612838149, -0.025485852733254433, -0.10601210594177246, -0.003472988959401846, -0.014909129589796066, 0.03701382130384445, 0.001068974263034761, -0.025052612647414207, 0.016425471752882004, -0.019175607711076736, 0.019345136359333992, -0.019090844318270683, -0.05368416756391525, 0.01083101611584425, -0.04279664158821106, 0.018893059343099594, 0.00993628054857254, -0.032963961362838745, 0.0264088436961174, -0.0006086560315452516, -0.07911351323127747, 0.005688637960702181, 0.016500817611813545, -0.024148456752300262, 0.02266036905348301, 0.07745589315891266, 0.021549012511968613, 0.033114656805992126, -0.019985578954219818, -0.008344591595232487, -0.047430433332920074, 0.03087310492992401, 0.04558445140719414, 0.01878945901989937, 0.007906641811132431, 0.04874899238348007, -0.0335855707526207, 0.0437384694814682, -0.03974512219429016, 0.024412168189883232, -0.0028278371319174767, 0.0389539860188961, 0.03982046619057655, 0.005062323063611984, -0.020230455324053764, 0.03739055246114731, 0.01666092872619629, -0.039104677736759186, 0.005321325268596411, -0.043098025023937225, 0.06408194452524185, -0.004501935560256243, 0.006145424675196409, 0.04208085313439369, 0.07357556372880936, -0.018845967948436737, -0.06506144255399704, 0.03194678947329521, -0.03799332305788994, -0.012903036549687386, -0.0025452887639403343, -0.00802907906472683, -0.009842097759246826, -0.009573676623404026, 0.047505781054496765, 0.021492503583431244, -0.030816596001386642, -0.02454402483999729, -0.033039309084415436, -0.03652407228946686, -0.03379277139902115, 0.0017588628688827157, -0.09501156210899353, -0.0038897476624697447, -0.012855945155024529, -0.05884538218379021, -0.033510223031044006, 0.03492296487092972, 0.03059055656194687, 0.02567421831190586, -0.032040972262620926, 0.04532073810696602, 0.008396392688155174, -0.039895813912153244, 0.019703030586242676, -0.002186217112466693, 0.02900828793644905, 0.05368416756391525, 0.05534178391098976, -0.007911351509392262, -0.03418833762407303, 0.0015987522201612592, 0.020513003692030907, 0.04392683506011963, -0.053495801985263824, 0.0012490986846387386, -0.01846923679113388, -0.058091919869184494, -0.048296913504600525, 0.05100937932729721, -0.04705370217561722, -0.03298280015587807, -0.028254825621843338, -0.03128750994801521, 0.015285860747098923, -0.003242241218686104, -0.06381823122501373, 0.03594013676047325, -0.06114344298839569, -0.018035996705293655, 0.05925978720188141, 0.041289716958999634, 0.03518667444586754, -0.03565758839249611, 0.018233779817819595, -0.06913013756275177, 0.015398879535496235, 0.10232014209032059, 0.004054567310959101, -0.020381147041916847, 0.02105926349759102, -0.013213840313255787, -0.04686533659696579, -0.017301371321082115, -0.009455948136746883, 0.0636298656463623, 0.01780053973197937, -0.06649301946163177, -0.06054067239165306, 0.05051962658762932, -0.039104677736759186, 0.015116331167519093, -0.003910938743501902, -0.07093844562768936, 0.014136831276118755, -0.03801215812563896, 0.0342448465526104, -0.013336277566850185, 0.008306918665766716, -0.02486424706876278, 0.0020484747365117073, 0.032963961362838745, 0.046375587582588196, 0.00813739001750946, -0.01409915741533041, -0.025561198592185974, -0.019571175798773766, 0.022829899564385414, -0.0268609207123518, 0.03047753870487213, -0.03300163522362709, -0.031570058315992355, 0.0015481290174648166, 0.01826203614473343, 0.05255397409200668, 0.008914397098124027, -0.021643195301294327, 0.003767309943214059, 0.023677542805671692, 0.01453239843249321, -0.05255397409200668, 0.016255943104624748, 0.022961754351854324, -0.00983267929404974, 0.03480994328856468, 0.04792018234729767, -0.005683929193764925, -0.015587245114147663, -0.0069742328487336636, -0.01619943231344223, 0.008857888169586658, 0.03066590428352356, -0.007308581378310919, -0.04219387099146843, 0.023978928104043007, 0.04712904989719391, 0.0068894680589437485, 0.013298604637384415, 0.030345682054758072, -0.008222154341638088, -0.07093844562768936, 0.055643171072006226, 0.048635970801115036, 0.003329360159114003, 0.041176699101924896, 0.009795006364583969, -0.018695276230573654, 0.02320663072168827, -0.046036530286073685, -0.04079996794462204, 0.027011612430214882, 0.012253175489604473, -0.005688637960702181, 0.054625995457172394, -0.02520330436527729, -0.04260827600955963, 0.0011684547644108534, 0.018120761960744858, -0.0030138480942696333, -0.0006445631734095514, -0.006771739572286606, -0.012074228376150131, 0.013618825934827328, -0.014673672616481781, 0.02060718648135662, -0.01516342256218195, -0.01893073320388794, 0.02846202813088894, 0.02814180590212345, 0.025014938786625862, -0.03140052780508995, 0.0011048814048990607, -0.013251513242721558, -0.011575059965252876, 0.005344870965927839, -0.004235869273543358, -0.011320766992866993, -0.016915222629904747, 0.0029714656993746758, -0.0022297766990959644, 0.024242639541625977, 0.005391962360590696, 0.0006098333396948874, 0.04712904989719391, 0.012234339490532875, -0.004546672105789185, -0.007360382005572319, -0.0061171697452664375, -0.06649301946163177, -0.014617162756621838, 0.0018330317689105868, 0.04434124007821083, 0.02733183465898037, -0.07048637419939041, -0.00491633964702487, 0.029761748388409615, -0.021247629076242447, -0.007944314740598202, 0.05952349677681923, 0.023281976580619812, 0.008824924007058144, -0.011857608333230019, 0.03187144175171852, -0.005848748609423637, 0.032022133469581604, 0.025222141295671463, 0.01945815607905388, 0.028763411566615105, -0.0169999860227108, 0.0021826853044331074, -0.030835432931780815, 0.033962298184633255, -0.01130193006247282, 0.0035907174460589886, 0.05059497430920601, -0.052101898938417435, -0.005552073009312153, 0.0255423616617918, 0.004118140786886215, 0.05119774490594864, 0.0394437350332737, 0.02680441178381443, -0.004796256776899099, 0.015822703018784523, 0.011358439922332764, -0.00015275264740921557, 0.0370514951646328, 0.045358411967754364, 0.024562861770391464, 0.0046738190576434135, -0.006456227507442236, 0.0378803014755249, 0.03326534852385521, 0.002479360904544592, -0.022434331476688385, 0.00354127143509686, 0.04347475618124008, -0.02294291742146015, 0.03914235159754753, -0.029987787827849388, -0.015022148378193378, 0.029968950897455215, 0.007661766838282347, -0.011518550105392933, -0.00766647607088089, -0.0169999860227108, 0.009813842363655567, -0.01653849147260189, -0.020362310111522675, 0.005024649668484926, 0.018431564792990685, -0.03000662475824356, -0.018167853355407715, -0.0033034600783139467, 0.024355659261345863, 0.004902212414890528, -0.008391682989895344, 0.01960884965956211, -0.034112993627786636, 0.03844539821147919, 0.0007781849708408117, 0.011603315360844135, -0.0641196146607399, -0.004902212414890528, 0.05632128566503525, -0.011612732894718647, 0.025975603610277176, 0.03245537728071213, 0.016425471752882004, 0.03675010800361633, -0.018149016425013542, -0.02827366255223751, 0.04185481369495392, 0.010774506255984306, 0.010473121888935566, 0.01794181391596794, -0.024562861770391464, 0.005457890219986439, 0.024562861770391464, -0.010859271511435509, 0.02279222570359707, -0.03712683916091919, -0.0181961078196764, 0.02460053376853466, -0.000029579270631074905, 0.04079996794462204, 0.010313010774552822, -0.025787238031625748, -0.0350736565887928, 0.0072897449135780334, 0.015577826648950577, -0.024506350979208946, 0.043286390602588654, 0.027972277253866196, 0.018384473398327827, -0.03179609775543213, -0.09568967670202255, -0.006847085896879435, 0.011424367316067219, 0.04550910368561745, -0.01792297698557377, -0.010322429239749908, -0.011980045586824417, -0.01692464016377926, -0.09056613594293594, 0.020569512620568275, -0.022980591282248497, -0.00696952361613512, 0.004742101300507784, 0.0026936265639960766, 0.04193016141653061, -0.028028786182403564, 0.005627419333904982, 0.00840110145509243, 0.035902462899684906, -0.006192516069859266, -0.002082616090774536, -0.019307464361190796, -0.0004370668320916593, -0.030308010056614876, 0.034301359206438065, 0.014494725503027439, 0.007252071984112263, -0.028367845341563225, -0.009121599607169628, -0.03253072127699852, 0.01673627458512783, 0.008688358590006828, 0.019985578954219818, 0.03605315834283829, 0.05127308890223503, 0.019627684727311134, 0.0028090004343539476, -0.031249836087226868, -0.005745147820562124, 0.015700263902544975, 0.03631686791777611, 0.015182259492576122, -0.00889556109905243, -0.05206422507762909, -0.027746237814426422, -0.008165644481778145, 0.010765088722109795, -0.01974070444703102, -0.0015304697444662452, -0.0025499979965388775, 0.03232352063059807, -0.016255943104624748, 0.016350125893950462, 0.00936176534742117, 0.037032656371593475, 0.014880874194204807, 0.007454564794898033, 0.06038998067378998, -0.019910233095288277, -0.02407311089336872, 0.002287463517859578, -0.009065089747309685, 0.016444308683276176, 0.026032112538814545, 0.009229909628629684, -0.009258164092898369, 0.020889734849333763, 0.008189190179109573, 0.014777273871004581, -0.02446867898106575, 0.021228792145848274, -0.037691935896873474, 0.04064927622675896, -0.03707033023238182, -0.03281326964497566, 0.040310218930244446, 0.0424199104309082, -0.011132401414215565, 0.00873074121773243, 0.02266036905348301, -0.017904140055179596, -0.022283639758825302, -0.03384928032755852, -0.03827587142586708, 0.07026033103466034, -0.009258164092898369, -0.026371169835329056, 0.0002257442829431966, 0.01873294822871685, 0.015238769352436066, 0.026239315047860146, 0.0541362464427948, 0.06592792272567749, -0.034508559852838516, -0.026634881272912025, -0.004471326246857643, 0.003894456662237644, -0.0012443895684555173, 0.01306314766407013, -0.008650685660541058, -0.06457169353961945, 0.018440982326865196, 0.0481085479259491, 0.02874457649886608, 0.012950127944350243, 0.0012773536145687103, -0.02541050687432289, -0.03373626247048378, 0.012196666561067104, 0.02785925753414631, -0.018827131018042564, 0.02480773627758026, -0.009540712460875511, -0.014240431599318981, 0.004447780549526215, -0.008824924007058144, -0.014004974626004696, 0.004944594576954842, -0.05172516778111458, -0.036222685128450394, 0.026446515694260597, -0.02606978453695774, -0.01846923679113388, 0.035092491656541824, -0.040310218930244446, -0.01152796857059002, 0.015097495168447495, -0.043964508920907974, -0.016284197568893433, -0.030289173126220703, 0.010444867424666882, -0.0049398853443562984, -0.022114109247922897, -0.024713553488254547, 0.013844864442944527, -0.03955675661563873, -0.03701382130384445, 0.012874782085418701, -0.04965314641594887, -0.0016976441256701946, -0.011471458710730076, -0.03951908275485039, -0.012450959533452988, -0.02467588149011135, -0.047957856208086014, 0.004607891198247671, 0.009149854071438313, 0.024506350979208946, 0.0311933271586895, -0.00850470270961523, -0.0005574441747739911, 0.03132518380880356, -0.00850470270961523, -0.02220829203724861, -0.01779112219810486, -0.007878387346863747, -0.005787529982626438, 0.025824910029768944, 0.02126646600663662, 0.026371169835329056, -0.0031763133592903614, 0.0030891941860318184, 0.03266257792711258, -0.02799111418426037, -0.002404014812782407, 0.041101351380348206, 0.005472017917782068, -0.01672685705125332, 0.004935176111757755, 0.023508014157414436, 0.006442100275307894, 0.041967835277318954, 0.03607199341058731, -0.007991406135261059, -0.03092961572110653, 0.008264536038041115, 0.01537062507122755, 0.02079555206000805, -0.015813283622264862, -0.011659824289381504, 0.051235415041446686, -0.027633219957351685, 0.008250408805906773, -0.023960091173648834, 0.007647639140486717, -0.052893031388521194, 0.014984475448727608, -0.002349859569221735, -0.0005506747984327376, -0.048975031822919846, 0.000673995295073837, -0.027765074744820595, -0.00013582919200416654, 0.011885862797498703, 0.023037100210785866, -0.026710228994488716, -0.009578385390341282, 0.017913559451699257, -0.022754551842808723, -0.019853724166750908, 0.000687534105964005, 0.019043752923607826, 0.06815063953399658, 0.015775611624121666, 0.05104704946279526, 0.013157330453395844, -0.029234325513243675, -0.036166176199913025, 0.04532073810696602, -0.04144040867686272, 0.011424367316067219, 0.05635895952582359, -0.004680882673710585, -0.0049869767390191555, 0.039707448333501816, -0.0003555398725438863, -0.054512977600097656, -0.0029243743047118187, 0.014023811556398869, 0.016029903665184975, 0.01463599968701601, -0.024713553488254547, 0.049427106976509094, 0.005712183658033609, 0.02279222570359707, 0.005128250923007727, -0.015888629481196404, -0.03151354938745499, 0.021718543022871017, -0.010652069002389908, -0.029893605038523674, -0.017631011083722115, 0.03285094350576401, -0.023508014157414436, 0.024770064279437065, -0.025372833013534546, -0.029309671372175217, -0.015285860747098923, 0.020569512620568275, -0.01486203819513321, 0.0138637013733387, 0.020305801182985306, -0.018450401723384857, -0.00889556109905243, -0.05779053643345833, 0.007435728330165148, 0.0024416877422481775, -0.012893619015812874, 0.013421041890978813, 0.024110784754157066, -0.020852060988545418, 0.04000883176922798, 0.051574476063251495, 0.004245287273079157, 0.03637337684631348, 0.02407311089336872, -0.004610245581716299, 0.018770622089505196, -0.06351684778928757, -0.0032657869160175323, -0.007454564794898033, -0.007779495324939489, -0.027181141078472137, -0.007355672772973776, 0.039293043315410614, -0.01974070444703102, 0.0450570285320282, -0.0026441807858645916, -0.02072020433843136, 0.00913572683930397, 0.005552073009312153, -0.011706915684044361, 0.003920357208698988, 0.0220764372497797, 0.006418554577976465, -0.05481436103582382, -0.015257605351507664, -0.01416508574038744, -0.023978928104043007, -0.002056715777143836, 0.007755949627608061, 0.0024487515911459923, 0.012272012419998646, 0.02439333312213421, 0.027821585536003113, 0.029780585318803787, -0.045170046389102936, -0.025184467434883118, -0.04441658407449722, 0.008735449984669685, 0.008476447314023972, -0.01927920989692211, 0.010793343186378479, 0.013637661933898926, -0.019382810220122337, 0.023677542805671692, 0.007459274027496576, -0.016547909006476402, -0.027181141078472137, 0.02380939945578575, -0.008674231357872486, 0.0326814129948616, 0.03752240911126137, 0.002804291434586048, 0.00755345681682229, 0.011207747273147106, 0.016246523708105087, -0.0014115639496594667, -0.044755641371011734, -0.01767810247838497, 0.00019189735758118331, -0.0004473680746741593, 0.06427031010389328, -0.009319383651018143, -0.041176699101924896, -0.05417391657829285, 0.0216620322316885, -0.05481436103582382, 0.022905245423316956, 0.07515783607959747, -0.05632128566503525, 0.02399776503443718, 0.012563979253172874, 0.02313128300011158, 0.01727311685681343, 0.013995557092130184, -0.016321871429681778, -0.04961547255516052, -0.020946243777871132, 0.046036530286073685, 0.018761204555630684, 0.010275337845087051, -0.008000824600458145, 0.022698042914271355, -0.023489177227020264, 0.04046091064810753, 0.03631686791777611, 0.004541963338851929, 0.006446809507906437, -0.025900255888700485, -0.0017047077417373657, -0.021549012511968613, 0.03189028054475784, -0.04539608582854271 ]
Although beam emittance is critical for the performance of high-brightness accelerators, optimization is often time limited as emittance calculations, commonly done via quadrupole scans, are typically slow. Such calculations are a type of $\textit{multi-point query}$, i.e. each query requires multiple secondary measurements. Traditional black-box optimizers such as Bayesian optimization are slow and inefficient when dealing with such objectives as they must acquire the full series of measurements, but return only the emittance, with each query. We propose applying Bayesian Algorithm Execution (BAX) to instead query and model individual beam-size measurements. BAX avoids the slow multi-point query on the accelerator by acquiring points through a $\textit{virtual objective}$, i.e. calculating the emittance objective from a fast learned model rather than directly from the accelerator. Here, we use BAX to minimize emittance at the Linac Coherent Light Source (LCLS) and the Facility for Advanced Accelerator Experimental Tests II (FACET-II). In simulation, BAX is 20$\times$ faster and more robust to noise compared to existing methods. In live LCLS and FACET-II tests, BAX performed the first automated emittance tuning, matching the hand-tuned emittance at FACET-II and achieving a 24% lower emittance at LCLS. Our method represents a conceptual shift for optimizing multi-point queries, and we anticipate that it can be readily adapted to similar problems in particle accelerators and other scientific instruments.
[ 0.026901237666606903, 0.0011556822573766112, -0.027706898748874664, -0.04570655897259712, -0.005448041018098593, 0.006744959857314825, -0.04511705040931702, 0.03985077515244484, -0.037944696843624115, 0.029927382245659828, -0.0014590335777029395, -0.03643162548542023, -0.0030973758548498154, 0.015248619951307774, -0.03059549070894718, 0.03733553737401962, 0.013440793380141258, -0.012615482322871685, -0.007167440839111805, -0.04503845050930977, 0.011416814289987087, -0.05883294716477394, -0.050304725766181946, 0.004160947632044554, -0.010670104064047337, 0.06692886352539062, -0.005197499878704548, 0.02141880802810192, -0.043623629957437515, 0.013882924802601337, 0.015199494548141956, 0.03580281510949135, -0.04495984688401222, 0.02929857186973095, -0.0403616800904274, 0.005025560036301613, 0.02192971669137478, -0.01529774535447359, -0.019719058647751808, -0.006690921261906624, -0.016958193853497505, -0.030064933001995087, -0.026999488472938538, 0.015563024207949638, 0.012006322853267193, -0.01789158210158348, -0.028866266831755638, -0.026626134291291237, 0.02660648338496685, -0.03641197457909584, 0.012055449187755585, -0.011662443168461323, -0.011799994856119156, -0.02861081250011921, -0.015228969976305962, 0.006361779291182756, 0.019591333344578743, 0.06834368407726288, 0.06618215143680573, -0.005899997428059578, 0.03908441215753555, -0.009628638625144958, -0.01720382273197174, -0.004725893028080463, 0.022931881248950958, -0.026075925678014755, 0.02391439490020275, 0.013519395142793655, -0.033326879143714905, -0.02454320341348648, -0.03835735470056534, -0.03299282491207123, -0.03727658838033676, -0.019787834957242012, -0.00629300344735384, 0.0010635715443640947, 0.043938033282756805, 0.02892521768808365, -0.06433502584695816, 0.054745689034461975, 0.051365841180086136, 0.006189839448779821, -0.013539045117795467, 0.02310873381793499, 0.08756165951490402, -0.03134220093488693, -0.01065045315772295, -0.052309054881334305, 0.004978890530765057, -0.006509156432002783, -0.04378082975745201, -0.004288674332201481, -0.020396994426846504, 0.012350203469395638, -0.019679758697748184, 0.05423478037118912, 0.020593496039509773, 0.0029475425835698843, -0.0180880855768919, 0.07188073545694351, -0.004686592612415552, -0.03786609694361687, 0.03735518828034401, -0.011691918596625328, 0.0010482198558747768, -0.0455886572599411, -0.042680416256189346, -0.015867603942751884, 0.02680298686027527, 0.12584041059017181, -0.006676183547824621, -0.009672852233052254, -0.025879422202706337, -0.014796663075685501, -0.07750071585178375, -0.011495416052639484, -0.013597995974123478, -0.03552771359682083, -0.027392495423555374, -0.016182009130716324, 0.027569347992539406, 0.051876746118068695, 0.026252778246998787, -0.006690921261906624, -0.04067608714103699, -0.014040127396583557, 0.05376317352056503, -0.034191492944955826, 0.01512089278548956, -0.04342712461948395, 0.022204820066690445, -0.02990773133933544, 0.015572849661111832, -0.09141311794519424, -0.0004264725430402905, 0.009957781061530113, 0.0411083921790123, -0.009830053895711899, 0.0010641856351867318, -0.020534545183181763, -0.04877200350165367, -0.05384177714586258, 0.003603370627388358, 0.007447457406669855, -0.021497409790754318, -0.009157031774520874, -0.03552771359682083, 0.040007974952459335, -0.059618961066007614, 0.029573677107691765, -0.03242296725511551, 0.03859315812587738, -0.007860112935304642, 0.060680076479911804, 0.06020846962928772, -0.038809310644865036, -0.02973087877035141, 0.018186336383223534, 0.03234436735510826, 0.0182354636490345, 0.04315202310681343, -0.03654952719807625, -0.023128382861614227, 0.06763627380132675, 0.04067608714103699, -0.007609572261571884, 0.044802647083997726, -0.028021303936839104, -0.09463576227426529, 0.042012304067611694, 0.03328758105635643, 0.004885551519691944, -0.050304725766181946, 0.016466937959194183, -0.03935951739549637, 0.04877200350165367, 0.04165859892964363, -0.029259271919727325, -0.014413482509553432, -0.04535285383462906, -0.07156632840633392, 0.03491855412721634, 0.030988497659564018, 0.06166258826851845, 0.03336618095636368, -0.008513485081493855, 0.04460614174604416, -0.0011305053485557437, 0.035449109971523285, -0.0013288503978401423, 0.03016318567097187, 0.0016739584971219301, 0.04629606753587723, -0.000019314462406327948, 0.044566843658685684, 0.0033258104231208563, -0.01582830399274826, -0.030654441565275192, 0.019306402653455734, -0.013263940811157227, -0.025447117164731026, -0.00733938068151474, -0.05329156666994095, -0.021654611453413963, -0.028492910787463188, 0.027765849605202675, 0.06193769350647926, -0.04330922290682793, 0.010375349782407284, -0.029947031289339066, 0.014826138503849506, -0.004300955682992935, -0.05466708913445473, -0.030005982145667076, -0.044566843658685684, -0.014246455393731594, -0.049243610352277756, -0.006720396690070629, -0.07164493203163147, -0.03177450969815254, -0.013234465382993221, 0.018824972212314606, 0.08598963916301727, -0.03855385631322861, 0.01258600689470768, -0.019856611266732216, 0.03558666259050369, -0.013018312864005566, 0.038946863263845444, -0.020848950371146202, -0.02898416854441166, 0.02198866754770279, -0.011397164314985275, -0.008931053802371025, -0.04197300598025322, -0.013882924802601337, 0.008891752921044827, 0.010630803182721138, 0.007702911272644997, 0.007044626399874687, -0.05211254954338074, 0.04236600920557976, -0.053802475333213806, 0.0021897784899920225, 0.03890756145119667, 0.007845375686883926, -0.012448454275727272, 0.025702569633722305, 0.03641197457909584, -0.0017267686780542135, -0.018422139808535576, -0.049322210252285004, 0.041069090366363525, 0.02067209780216217, -0.03409324213862419, -0.009235633537173271, -0.004512196406722069, -0.02754969708621502, 0.04205160588026047, -0.03173520788550377, 0.038946863263845444, 0.0000013960528804091155, 0.006469855550676584, 0.05238765478134155, -0.012232301756739616, -0.025132711976766586, 0.07062311470508575, 0.007707823533564806, -0.04157999902963638, 0.03311072662472725, 0.029691578820347786, -0.04279831796884537, 0.018127385526895523, -0.04759298637509346, 0.038435954600572586, -0.04472404345870018, -0.006853036116808653, 0.03379848599433899, -0.007786424830555916, -0.03197101131081581, 0.006067025009542704, 0.005113986320793629, 0.0472392812371254, -0.007319730706512928, 0.009348622523248196, -0.011200661770999432, -0.019886085763573647, -0.03753204271197319, -0.018127385526895523, 0.004647292196750641, -0.02391439490020275, -0.012163525447249413, 0.011348038911819458, 0.05832204222679138, 0.04688557609915733, 0.0093044089153409, -0.0517195463180542, -0.05458848550915718, 0.01002164464443922, -0.00812539178878069, -0.002410844201222062, 0.0015302657848224044, 0.015228969976305962, -0.0004633168282452971, -0.029082419350743294, 0.010846956633031368, -0.04323062300682068, 0.08363160490989685, -0.008670687675476074, 0.025466768071055412, 0.04067608714103699, 0.01361764594912529, -0.0031047447118908167, -0.06798998266458511, 0.020750699564814568, 0.04099049046635628, 0.03311072662472725, -0.01354887057095766, -0.012733384035527706, -0.07019080966711044, -0.012301077134907246, -0.00005541993959923275, -0.06897249072790146, 0.02330523543059826, 0.02603662572801113, 0.018589168787002563, 0.009274933487176895, -0.0088180648162961, 0.008248206228017807, 0.011878596618771553, -0.03334653005003929, -0.02817850559949875, -0.025565018877387047, -0.023442788049578667, -0.046335369348526, -0.042012304067611694, -0.03611722216010094, 0.05116933584213257, -0.018471267074346542, 0.03660847619175911, -0.038003649562597275, -0.01623113453388214, -0.042876917868852615, 0.032757021486759186, -0.015032466500997543, -0.05234835296869278, -0.0675576776266098, -0.003799873637035489, -0.010699579492211342, -0.03702113404870033, 0.0013177971122786403, -0.02230307087302208, 0.02823745645582676, 0.0007276745745912194, 0.03149940446019173, -0.017125220969319344, -0.009721977636218071, -0.0065337191335856915, -0.041383497416973114, 0.04028308019042015, 0.041501399129629135, -0.06527823954820633, -0.0013767479686066508, 0.0547063872218132, -0.03702113404870033, 0.05828274041414261, -0.026783335953950882, -0.02953437529504299, -0.027019139379262924, -0.014914564788341522, -0.02236202172935009, 0.033012475818395615, 0.027431795373558998, 0.009648289531469345, -0.023599989712238312, -0.015445122495293617, 0.005782095715403557, -0.00811556726694107, -0.07581079006195068, 0.06075867637991905, -0.05678931996226311, 0.014413482509553432, 0.024896908551454544, 0.04315202310681343, 0.037060435861349106, 0.02910207025706768, -0.0023003113456070423, -0.037630293518304825, -0.008975266478955746, 0.041069090366363525, 0.013627471402287483, -0.028394659981131554, -0.07852253317832947, -0.03385743871331215, -0.012094749137759209, -0.013195165432989597, 0.04684627428650856, -0.039123713970184326, -0.024405652657151222, -0.007467107847332954, 0.010483426041901112, -0.034329045563936234, -0.03992937505245209, 0.018441790714859962, 0.01248775515705347, 0.03729623928666115, -0.018019309267401695, -0.02155636064708233, 0.04429173842072487, -0.01505211740732193, -0.01568092592060566, -0.036883581429719925, 0.013195165432989597, -0.056199811398983, 0.032639119774103165, 0.04232671111822128, -0.03022213652729988, -0.01605428196489811, -0.021713562309741974, -0.04366292804479599, -0.031086748465895653, 0.026468930765986443, -0.0028468347154557705, 0.015150368213653564, 0.03267842158675194, 0.05458848550915718, 0.029691578820347786, 0.0034903816413134336, -0.014216979965567589, -0.039870426058769226, 0.022086918354034424, 0.02929857186973095, -0.02222447097301483, -0.03733553737401962, 0.031460102647542953, 0.039438117295503616, 0.021713562309741974, 0.04283761605620384, 0.008095916360616684, -0.05148374289274216, -0.006420730147510767, -0.006700746715068817, -0.002064507920295, -0.0002883065026253462, 0.01817651279270649, 0.00011283560888841748, -0.038573507219552994, -0.036254771053791046, -0.0015744789270684123, 0.018225638195872307, -0.05317366495728493, -0.018441790714859962, -0.07066241651773453, -0.013686422258615494, 0.021576011553406715, -0.027372844517230988, 0.009137381799519062, -0.03568491339683533, 0.02973087877035141, -0.07180213183164597, -0.029593326151371002, 0.029593326151371002, 0.056003306061029434, -0.0532129667699337, 0.05164094269275665, 0.005629806313663721, -0.00543330330401659, -0.034505896270275116, -0.0066614458337426186, 0.013037962839007378, 0.030025633051991463, -0.04126559570431709, 0.023030132055282593, 0.0675576776266098, 0.014256280846893787, -0.004767649807035923, -0.06653586030006409, -0.015307570807635784, 0.025447117164731026, -0.03342513367533684, -0.02167426235973835, -0.08064476400613785, -0.023089082911610603, -0.0692082941532135, 0.00920124538242817, -0.006229139864444733, 0.0064895059913396835, 0.01742980070412159, -0.0057427952997386456, -0.024464603513479233, -0.04810389503836632, -0.02448425255715847, -0.061426784843206406, 0.027588997036218643, 0.0055905054323375225, 0.0009008426568470895, -0.029495075345039368, -0.008877015672624111, 0.010473600588738918, 0.027431795373558998, 0.03480065241456032, -0.023875094950199127, -0.04346642643213272, 0.009692502208054066, 0.01080765575170517, 0.021910065785050392, -0.011544541455805302, 0.053998976945877075, 0.003551788628101349, -0.019964687526226044, 0.010689754039049149, -0.016211483627557755, 0.009107906371355057, -0.025506068021059036, 0.03505610674619675, -0.014374182559549809, -0.03446659818291664, -0.020279092714190483, 0.03998832777142525, -0.008351370692253113, 0.02460215426981449, -0.06468873471021652, 0.036687079817056656, 0.025899073109030724, 0.015779176726937294, 0.041186992079019547, 0.03711938485503197, -0.01512089278548956, 0.035075753927230835, 0.015592499636113644, -0.03004528395831585, 0.013450618833303452, -0.025623969733715057, -0.06386341899633408, -0.020829299464821815, -0.015307570807635784, 0.0017697536386549473, 0.055688902735710144, -0.02642963081598282, -0.030340038239955902, -0.040636785328388214, 0.040872588753700256, 0.06480663269758224, -0.013204989954829216, 0.01702697016298771, 0.0021836378145962954, 0.04865410178899765, 0.007300080265849829, 0.011564191430807114, 0.009854617528617382, -0.00024486094480380416, 0.0012305990094318986, -0.02222447097301483, 0.029770178720355034, -0.018186336383223534, -0.03959532082080841, 0.012448454275727272, -0.06213419511914253, -0.008169605396687984, -0.03578316420316696, -0.01668309047818184, -0.0021050365176051855, -0.00727551756426692, -0.039949025958776474, -0.027058439329266548, -0.020829299464821815, 0.03299282491207123, 0.0636669173836708, -0.0532129667699337, 0.018500741571187973, 0.0002701914054341614, 0.013597995974123478, 0.01729224994778633, -0.013912400230765343, -0.022951530292630196, 0.012635132297873497, 0.016388336196541786, -0.04444894194602966, -0.0142366299405694, 0.014305406250059605, 0.04908640682697296, -0.053370170295238495, 0.028119554743170738, 0.004016026854515076, 0.03623512387275696, 0.0050402977503836155, -0.049440111964941025, -0.03790539503097534, -0.011534716002643108, -0.012134050019085407, -0.018618643283843994, 0.03193170949816704, -0.010218147188425064, 0.0018360733520239592, -0.011004158295691013, -0.008582261390984058, -0.017596827819943428, -0.015199494548141956, 0.03151905536651611, -0.027883751317858696, 0.03303212672472, 0.0006478452705778182, 0.018441790714859962, -0.004819232039153576, -0.024503903463482857, 0.021595660597085953, -0.014777013100683689, 0.0176361296325922, 0.0007424122886732221, 0.04767158627510071, 0.0078109875321388245, -0.026881586760282516, 0.029868431389331818, -0.009933218359947205, 0.06032637134194374, 0.034270092844963074, -0.020888250321149826, -0.012635132297873497, 0.009299496188759804, 0.018009483814239502, 0.030398989096283913, -0.04688557609915733, -0.009373185224831104, -0.04405593499541283, 0.035075753927230835, -0.004976434167474508, -0.0017157153924927115, 0.005978598725050688, 0.002900873078033328, -0.018913397565484047, 0.01961098238825798, -0.007010238710790873, -0.026390330865979195, -0.012546706013381481, 0.08245258778333664, 0.018274763599038124, -0.01467876136302948, 0.058046936988830566, 0.013460444286465645, 0.007742211688309908, -0.022342372685670853, 0.0024280380457639694, -0.005236800294369459, 0.037944696843624115, -0.016496412456035614, 0.0357242152094841, 0.006784260272979736, -0.000981900142505765, 0.06464943289756775, 0.0777365192770958, -0.007712736260145903, 0.060797978192567825, 0.018441790714859962, 0.05529589578509331, -0.017842456698417664, -0.01645711250603199, 0.018530217930674553, 0.0027461270801723003, -0.0025299738626927137, 0.054549187421798706, 0.014777013100683689, 0.030890244990587234, 0.0220476184040308, -0.006808822974562645, 0.018382839858531952, -0.02049524523317814, 0.015847953036427498, 0.055688902735710144, 0.010257448069751263, 0.03933986648917198, -0.006587757263332605, -0.031578004360198975, -0.015002991072833538, 0.030890244990587234, 0.04940081387758255, -0.021634962409734726, -0.028217807412147522, 0.06138748675584793, -0.0115838423371315, -0.031145699322223663, 0.011967022903263569, -0.031126048415899277, -0.016162358224391937, -0.06020846962928772, -0.01623113453388214, -0.03279632329940796, -0.003971813712269068, 0.017184171825647354, 0.009098080918192863, -0.02224412001669407, -0.0494794137775898, -0.02611522562801838, 0.027215642854571342, -0.02411089837551117, -0.008651036769151688, 0.015130718238651752, -0.03540981188416481, -0.0006278879591263831, -0.0015806197188794613, -0.06571054458618164, -0.004937133751809597, 0.007599747274070978, 0.03521330654621124, 0.0087443757802248, 0.0023003113456070423, 0.005639631301164627, -0.012409154325723648, -0.058990150690078735, -0.013381842523813248, -0.016928719356656075, 0.0046620299108326435, -0.005831221584230661, -0.00015735578199382871, 0.033503733575344086, 0.015690751373767853, -0.0013620102545246482, 0.016466937959194183, 0.024032296612858772, 0.0030875508673489094, 0.0269798394292593, 0.0554530993103981, 0.02261747606098652, 0.008169605396687984, -0.10729054361581802, 0.005344877019524574, 0.04311272129416466, 0.04830039665102959, -0.00047099273069761693, 0.004703786689788103, -0.005909822881221771, 0.003301247488707304, -0.006450205575674772, -0.0038563681300729513, -0.0009843563893809915, 0.017105571925640106, 0.0070544518530368805, -0.015366521663963795, 0.040558185428380966, -0.005197499878704548, 0.0005870521999895573, 0.029829129576683044, -0.0115838423371315, 0.024837957695126534, -0.0026748948730528355, 0.01000690646469593, 0.029278922826051712, 0.009225808084011078, 0.01754770241677761, 0.05026542395353317, 0.015592499636113644, 0.04173720255494118, -0.024562854319810867, -0.002315049059689045, -0.026134876534342766, -0.06893319636583328, -0.01177051942795515, 0.018500741571187973, -0.016064107418060303, 0.00924545805901289, 0.02273537777364254, -0.013696247711777687, 0.05344877019524574, 0.043191321194171906, -0.0005136706749908626, 0.040951188653707504, 0.00042186700738966465, 0.021576011553406715, -0.019935213029384613, 0.03116535022854805, 0.015268269926309586, 0.0010562026873230934, -0.010689754039049149, 0.026586832478642464, -0.037689242511987686, 0.0036746030673384666, 0.030870595946907997, 0.010473600588738918, 0.042012304067611694, -0.020947201177477837, 0.01929657906293869, -0.020200490951538086, 0.007285342551767826, -0.059108052402734756, -0.02430739998817444, -0.03696218132972717, -0.01869724504649639, -0.029396824538707733, -0.003217733930796385, 0.028748365119099617, 0.013912400230765343, -0.02947542443871498, -0.029121719300746918, 0.01588725484907627, 0.017508402466773987, 0.028001653030514717, 0.0065238941460847855, 0.016869768500328064, -0.033444780856370926, -0.033326879143714905, 0.007147790398448706, 0.03193170949816704, 0.01625078357756138, -0.017842456698417664, 0.031027797609567642, -0.01393205113708973, -0.05360597372055054, 0.01461981050670147, -0.06213419511914253, -0.001868005027063191, 0.020338043570518494, 0.011122060008347034, 0.01512089278548956, 0.01495386566966772, 0.03222646564245224, 0.06850088387727737, -0.035508062690496445, -0.038435954600572586, 0.021693913266062737, 0.011662443168461323, 0.00847418513149023, -0.008267857134342194, 0.001790632028132677, 0.008906491100788116, -0.015042291954159737, -0.03147975355386734, -0.017302073538303375, -0.029593326151371002, -0.007201828993856907, 0.03159765526652336, 0.004745543468743563, 0.030870595946907997, 0.036628127098083496, 0.002620856510475278, 0.0532129667699337, -0.03792504593729973, 0.04551005735993385, 0.0009776016231626272, -0.005379265174269676, -0.0038735622074455023, 0.03686393052339554, 0.022951530292630196, -0.0209275521337986, -0.043741531670093536, -0.004745543468743563, -0.021458109840750694, 0.027431795373558998, 0.0038588244933634996, 0.009515649639070034, -0.003397042630240321, -0.007521145977079868, 0.010905907489359379, 0.016751866787672043, -0.00009379939729114994, -0.0296719279140234, -0.010620977729558945, 0.007467107847332954, -0.001159980776719749, 0.04684627428650856, -0.020279092714190483, -0.006042462307959795, -0.025702569633722305, 0.0048683579079806805, 0.0182354636490345, -0.0247397068887949, 0.02872871421277523, 0.03515435755252838, 0.02973087877035141, -0.07254884392023087, 0.00018145809008274227, -0.042444612830877304, -0.033582333475351334, 0.06146608665585518, -0.04358432814478874, 0.024837957695126534, 0.0021160899195820093, 0.01208492461591959, 0.011053284630179405, 0.020907901227474213, 0.03953637182712555, -0.015985505655407906, -0.029318222776055336, 0.019817311316728592, 0.0027485834434628487, -0.012792333960533142, 0.029259271919727325, 0.0494794137775898, -0.05352737009525299, -0.013401493430137634, -0.01499316655099392, -0.020003987476229668, 0.009697414934635162, 0.011043459177017212, 0.008105741813778877, 0.021084753796458244, 0.006027724593877792, -0.022381672635674477, -0.06417782604694366, -0.007722561247646809, 0.017469102516770363, -0.01625078357756138, -0.008331719785928726, -0.014924390241503716, -0.03877000883221626, -0.030516890808939934, -0.00834154523909092, -0.013499744236469269, -0.020534545183181763, 0.01058167777955532, -0.006749872118234634, -0.035449109971523285, 0.02434670180082321, 0.016014980152249336, 0.043623629957437515, -0.01499316655099392, 0.030988497659564018, 0.015671100467443466, 0.008159779943525791, -0.08331719785928726, 0.01677151769399643, -0.010110070928931236, 0.0023494369816035032, -0.00024731724988669157, 0.009874267503619194, 0.03256051987409592, 0.000708024250343442, 0.014580510556697845, 0.014924390241503716, -0.006361779291182756, 0.0027191080152988434, -0.007452370133250952, 0.030398989096283913, 0.019453780725598335, 0.06166258826851845, 0.003799873637035489, 0.03509540483355522, -0.01271373312920332, 0.013372018001973629, -0.037060435861349106, -0.0070741018280386925, 0.023835793137550354, 0.013539045117795467, -0.04963661730289459, -0.007963277399539948, -0.01714487187564373, 0.0027363018598407507, -0.0387110598385334, 0.018854446709156036, 0.02542746625840664, -0.021458109840750694, 0.0494794137775898, -0.01777368038892746, -0.007123227696865797, 0.02566326968371868, -0.03552771359682083, -0.028630463406443596, -0.00030135552515275776, -0.007447457406669855, 0.024641456082463264, -0.023148033767938614, 0.009628638625144958, -0.0011753325816243887, -0.0031366765033453703, -0.02230307087302208, -0.02192971669137478, 0.00424937391653657, -0.010837131179869175, -0.034446947276592255, -0.021654611453413963, -0.06264510005712509, -0.036510225385427475, -0.010974682867527008, -0.007992752827703953, 0.007324642967432737, 0.041501399129629135, 0.011475765146315098, -0.031322550028562546, 0.022067267447710037, 0.003006493439897895, 0.028571512550115585, 0.022813979536294937, 0.06461013108491898, 0.013863274827599525, 0.05132653936743736, -0.013765023089945316, 0.004256742540746927, 0.02798200398683548, 0.02179216407239437, -0.01399100199341774, -0.04248391091823578, 0.011790170334279537, -0.00435008155182004, -0.045313552021980286, 0.05875434726476669, -0.02729424275457859, -0.026272429153323174, 0.009019480086863041, 0.025014810264110565, -0.024562854319810867, 0.0016776429256424308, -0.010424475185573101, -0.0026110312901437283, -0.04083328694105148, -0.02729424275457859, 0.0639813244342804, -0.015209319069981575, 0.012625306844711304, 0.014138379134237766, 0.056121207773685455, -0.0322854146361351, 0.022637126967310905, 0.012114400044083595, -0.020573846995830536, 0.05466708913445473, 0.046335369348526, -0.00795836467295885, 0.015641625970602036, -0.005885259713977575, -0.00515328673645854, 0.028433959931135178, 0.007344293408095837, 0.03035968728363514, -0.01720382273197174, -0.003647583769634366, -0.03256051987409592 ]
Designing profitable and reliable trading strategies is challenging in the highly volatile cryptocurrency market. Existing works applied deep reinforcement learning methods and optimistically reported increased profits in backtesting, which may suffer from the false positive issue due to overfitting. In this paper, we propose a practical approach to address backtest overfitting for cryptocurrency trading using deep reinforcement learning. First, we formulate the detection of backtest overfitting as a hypothesis test. Then, we train the DRL agents, estimate the probability of overfitting, and reject the overfitted agents, increasing the chance of good trading performance. Finally, on 10 cryptocurrencies over a testing period from 05/01/2022 to 06/27/2022 (during which the crypto market crashed two times), we show that the less overfitted deep reinforcement learning agents have a higher return than that of more overfitted agents, an equal weight strategy, and the S&P DBM Index (market benchmark), offering confidence in possible deployment to a real market.
[ 0.001117504434660077, -0.05689193680882454, -0.024991562590003014, -0.03630650043487549, 0.028639838099479675, 0.015888500958681107, -0.055446725338697433, 0.0166022926568985, -0.07627890259027481, 0.010601146146655083, 0.007142334710806608, -0.012848271988332272, 0.022999992594122887, -0.06309576332569122, -0.009129499085247517, 0.04032489284873009, 0.02155478298664093, 0.014337543398141861, 0.015218769200146198, -0.05012412369251251, 0.0038135044742375612, -0.008763790130615234, -0.02980305626988411, 0.039937153458595276, 0.005476817954331636, 0.010812640190124512, 0.004104309249669313, -0.0017547408351674676, -0.02181915007531643, 0.08269422501325607, 0.08220074325799942, 0.05400151386857033, -0.0007644633878953755, -0.008953253738582134, 0.0024674320593476295, -0.01321838703006506, 0.03796320781111717, 0.010213406756520271, -0.02106129564344883, -0.021131794899702072, 0.02883370779454708, -0.012011107057332993, -0.04413178563117981, -0.0028243286069482565, 0.004961301106959581, -0.024180835112929344, -0.008459767326712608, -0.02930956892669201, -0.042686577886343, -0.04102987051010132, -0.007609384600073099, -0.03144213557243347, 0.07564441859722137, -0.05519998073577881, -0.03902067616581917, 0.008997315540909767, 0.052521057426929474, -0.02573179267346859, 0.05022986978292465, -0.018470492213964462, 0.036236003041267395, -0.006604786962270737, -0.02752949297428131, 0.026877386495471, 0.012601528316736221, -0.01063639484345913, 0.020885050296783447, 0.022559380158782005, 0.021078919991850853, -0.009570111520588398, -0.07219001650810242, 0.023845968768000603, -0.01191417220979929, -0.007653445936739445, 0.006353637669235468, -0.02351110428571701, 0.01126206573098898, -0.0033134089317172766, -0.02948581427335739, -0.003740803338587284, 0.017615703865885735, 0.03708197921514511, -0.02513255923986435, -0.03961991146206856, 0.0754329264163971, -0.02627815306186676, 0.0608045794069767, -0.06249653175473213, 0.007503637578338385, -0.024357080459594727, -0.035795390605926514, -0.008860724978148937, -0.01910497434437275, -0.04599998518824577, -0.054424501955509186, 0.018488116562366486, -0.06806588172912598, -0.019404591992497444, -0.07078005373477936, -0.02056781016290188, -0.02883370779454708, 0.010750954039394855, -0.0016897504683583975, -0.013553252443671227, -0.01311263907700777, -0.07705438137054443, -0.07113254815340042, 0.015765128657221794, 0.024832941591739655, 0.1388106793165207, -0.042580828070640564, 0.001890229294076562, -0.04032489284873009, 0.0033750946167856455, -0.043673548847436905, -0.021924898028373718, -0.03958466276526451, -0.02677163854241371, -0.0063712624832987785, -0.04702220857143402, -0.010997697710990906, 0.04141760990023613, 0.0160735584795475, -0.022894246503710747, 0.011491184122860432, 0.013799995183944702, 0.0022581410594284534, 0.038350947201251984, 0.02953868731856346, 0.056927185505628586, -0.05548197403550148, 0.004582373891025782, 0.010451337322592735, 0.014337543398141861, -0.005027392879128456, 0.015703443437814713, 0.02442757785320282, -0.007239269558340311, -0.006155361887067556, 0.02328198403120041, 0.0014496163930743933, -0.043673548847436905, 0.019668959081172943, 0.0407126322388649, 0.03687048703432083, 0.03817469999194145, 0.0035601521376520395, 0.03627125173807144, -0.014161298051476479, -0.007878158241510391, -0.029009953141212463, 0.03746971860527992, 0.0012326145078986883, -0.002566570183262229, 0.019721832126379013, -0.012857084162533283, 0.0019838595762848854, -0.011755552142858505, -0.008481797762215137, -0.09129498898983002, 0.05942986533045769, -0.02599615976214409, 0.026877386495471, 0.030596159398555756, 0.06457622349262238, 0.0884750708937645, 0.033627577126026154, -0.01780957356095314, -0.09326893836259842, 0.0447310209274292, -0.05639845132827759, -0.02735324762761593, 0.016628731042146683, 0.02040918916463852, 0.02403983846306801, 0.05816090106964111, 0.024797692894935608, -0.03810420259833336, -0.04335630685091019, -0.04642297327518463, -0.07162602990865707, 0.00008688335219630972, 0.0278996080160141, 0.017236776649951935, 0.03718772903084755, 0.01889348030090332, 0.05153408274054527, 0.007221645209938288, 0.016567043960094452, 0.013086202554404736, 0.021237540990114212, -0.028974702581763268, -0.0021204494405537844, -0.01012528408318758, -0.0027494244277477264, -0.005490036681294441, 0.005181607324630022, 0.01037202775478363, 0.03364520147442818, -0.01088313851505518, 0.02529118023812771, -0.05012412369251251, 0.0016192523762583733, -0.004996550269424915, 0.009719920344650745, 0.0031393668614327908, 0.06979308277368546, 0.0376812145113945, 0.014786968939006329, -0.05304979160428047, -0.007274518720805645, 0.006089270114898682, -0.049806881695985794, -0.004042623098939657, -0.07768886536359787, 0.004022795706987381, 0.040254391729831696, 0.04554174840450287, -0.009103062562644482, -0.0017029688460752368, -0.0532965362071991, 0.023317234590649605, 0.04067738354206085, -0.016584668308496475, -0.030419914051890373, 0.04409653693437576, 0.004020592663437128, 0.06119231879711151, -0.04152335971593857, 0.0070498064160346985, -0.004379692021757364, -0.05389576777815819, -0.007596166338771582, 0.015342140570282936, 0.03746971860527992, 0.006803062744438648, 0.008649230934679508, 0.024744819849729538, 0.05717392638325691, -0.023704973980784416, 0.015826815739274025, -0.021854398772120476, -0.019686583429574966, -0.01522758137434721, -0.012284287251532078, 0.02876320853829384, 0.01058352179825306, 0.027071256190538406, 0.06425898522138596, 0.055728718638420105, -0.02335248328745365, -0.05646894872188568, -0.018329495564103127, 0.013403443619608879, -0.007181989960372448, 0.03459692373871803, 0.03600688651204109, -0.03799845650792122, -0.02758236601948738, -0.04088887572288513, 0.07120304554700851, 0.006728158798068762, 0.008045591413974762, 0.005009768530726433, -0.033574700355529785, 0.04652871936559677, 0.02938006818294525, 0.04543600231409073, 0.012116854079067707, -0.024797692894935608, -0.0013670014450326562, -0.04388504475355148, -0.06119231879711151, 0.01199348270893097, 0.051710329949855804, -0.01624099165201187, 0.006225860211998224, 0.002172221429646015, 0.026613017544150352, 0.08290571719408035, 0.030913399532437325, 0.010231031104922295, 0.023370107635855675, -0.00006715904601151124, 0.009631797671318054, -0.04007814824581146, -0.053931016474962234, -0.012425282970070839, -0.04892565682530403, 0.004049232229590416, 0.028040604665875435, -0.0382099486887455, 0.004267335869371891, -0.009288120083510876, 0.043074317276477814, -0.014443290419876575, -0.00843773689121008, -0.01780076138675213, -0.03334558382630348, 0.007314173970371485, -0.046387724578380585, -0.008433330804109573, 0.007027775514870882, 0.06803063303232193, -0.023528728634119034, -0.012962831184267998, 0.015571258962154388, 0.00039792852476239204, -0.028357844799757004, -0.056116458028554916, 0.004921645857393742, -0.008653637021780014, -0.008821070194244385, 0.0025819914881139994, -0.026507271453738213, 0.019510338082909584, 0.03500228747725487, -0.03230573609471321, -0.0213432889431715, -0.020867425948381424, 0.06817162781953812, 0.009860916063189507, -0.08213024586439133, 0.06281377375125885, 0.01704290695488453, 0.013597313314676285, -0.012451720423996449, 0.02534405328333378, -0.10694555938243866, 0.01949271373450756, -0.06788963079452515, 0.031953245401382446, -0.09270495176315308, -0.010195782408118248, -0.04335630685091019, 0.03001455031335354, -0.008918005041778088, -0.010662832297384739, -0.01617930456995964, -0.01938696764409542, -0.025326428934931755, 0.002612834330648184, -0.05516473203897476, -0.04659922048449516, 0.024727195501327515, -0.07550342381000519, -0.016267428174614906, 0.02393409237265587, -0.055834464728832245, 0.027370871976017952, 0.0009643914527259767, -0.01535976491868496, -0.0060672396793961525, 0.028005355969071388, 0.05801990628242493, -0.012901145033538342, 0.03630650043487549, -0.022488880902528763, 0.03364520147442818, 0.004555937368422747, -0.03006742335855961, -0.03278159722685814, -0.04917239770293236, -0.030878150835633278, -0.005150764714926481, 0.04261607676744461, -0.04659922048449516, 0.02079692855477333, 0.014875090681016445, 0.013288884423673153, -0.038033705204725266, 0.015236393548548222, -0.0008300045155920088, -0.028851332142949104, -0.029732557013630867, -0.0008509336621500552, -0.00018657202599570155, 0.011438310146331787, -0.03799845650792122, 0.04402603954076767, -0.03435017913579941, 0.007428733166307211, -0.024797692894935608, 0.008292334154248238, 0.01327126007527113, -0.007948656566441059, -0.0035403245128691196, -0.04191109910607338, -0.001848371117375791, 0.06771338731050491, -0.008164556697010994, -0.07416395843029022, -0.04127661511301994, -0.0005749998381361365, 0.01910497434437275, 0.03997240215539932, 0.05075860396027565, 0.04892565682530403, 0.020603058859705925, -0.042263589799404144, -0.041347112506628036, -0.021026046946644783, 0.0021876429673284292, -0.043849796056747437, -0.0457179918885231, 0.01462834794074297, 0.025255931541323662, 0.003476435784250498, -0.030807653442025185, 0.020937925204634666, 0.0119406096637249, -0.0238812193274498, -0.02199539542198181, -0.007234863471239805, 0.019298844039440155, 0.04240458458662033, -0.022030644118785858, -0.015218769200146198, -0.042157839983701706, -0.007842909544706345, -0.010380839928984642, 0.050018373876810074, 0.07095629721879959, -0.04120611771941185, 0.013394631445407867, -0.035636771470308304, 0.03736397251486778, -0.01055708434432745, 0.0025731793139129877, 0.007521261926740408, 0.01834711991250515, 0.04815017804503441, 0.026242904365062714, -0.023704973980784416, -0.07000457495450974, -0.009340993128716946, 0.03473791852593422, 0.040571633726358414, -0.010654019191861153, -0.0041880253702402115, -0.00030567520298063755, -0.04726894944906235, -0.03473791852593422, 0.013403443619608879, -0.012645590119063854, -0.07557392120361328, -0.05971185863018036, -0.0008145830943249166, -0.04314481467008591, 0.015183520503342152, -0.02046206220984459, 0.01878773421049118, -0.07564441859722137, 0.020990798249840736, 0.02121991664171219, -0.020832177251577377, -0.012266662903130054, -0.05498848855495453, 0.09016702324151993, 0.004842335823923349, 0.010336778126657009, 0.012486969120800495, -0.00876819621771574, 0.004701339639723301, -0.039937153458595276, 0.06457622349262238, -0.051921822130680084, -0.0472337007522583, -0.0035050755832344294, -0.005868963431566954, -0.0029124512802809477, -0.04131186380982399, 0.0025577577762305737, -0.005309385247528553, 0.024727195501327515, 0.017677389085292816, 0.006384480744600296, -0.06700840592384338, -0.03891493007540703, -0.014275857247412205, 0.0687708631157875, 0.033028341829776764, 0.012301911599934101, -0.01980995573103428, 0.05343753099441528, 0.01506014820188284, 0.04702220857143402, -0.018382370471954346, 0.02204826846718788, 0.02063830755650997, -0.029397692531347275, -0.017395397648215294, -0.04755094274878502, -0.0231233648955822, -0.03849194198846817, -0.035901136696338654, -0.01479578111320734, -0.03399769216775894, 0.07067430764436722, 0.016849037259817123, 0.03586588799953461, -0.050406113266944885, 0.015077772550284863, 0.010830264538526535, -0.006547507364302874, 0.029521062970161438, -0.022136392071843147, 0.0301379207521677, -0.008587544783949852, -0.03209424391388893, 0.03600688651204109, -0.008503829129040241, 0.004970113281160593, -0.021572407335042953, -0.013623750768601894, 0.036729488521814346, 0.008318771608173847, -0.015553634613752365, 0.044272784143686295, 0.004370879847556353, 0.04102987051010132, -0.01758045330643654, -0.004487642087042332, 0.017554016783833504, -0.009473176673054695, 0.0512520894408226, 0.006481415592133999, -0.06267277896404266, 0.03274634853005409, 0.028904205188155174, -0.027229877188801765, 0.03274634853005409, -0.046281978487968445, -0.027018383145332336, -0.007922220043838024, -0.011720302514731884, 0.006243484560400248, -0.013773558661341667, -0.006662067025899887, -0.003703351365402341, -0.01949271373450756, 0.04261607676744461, 0.027758611366152763, 0.03405056521296501, 0.008309959433972836, 0.0014936777297407389, 0.04184059798717499, -0.016637543216347694, 0.03339845687150955, -0.011473559774458408, 0.004829117096960545, -0.005313791334629059, -0.00906781293451786, -0.003646071534603834, -0.04332105815410614, -0.010962449014186859, 0.0017536393133923411, -0.02051493525505066, -0.034931790083646774, -0.013385819271206856, -0.038033705204725266, -0.006499039940536022, -0.02476244419813156, 0.011059383861720562, 0.030085047706961632, -0.035425275564193726, 0.011059383861720562, 0.060346342623233795, -0.01246053259819746, 0.01910497434437275, -0.03061378374695778, -0.015809189528226852, -0.03507278487086296, -0.010777391493320465, -0.01824137382209301, -0.009235246106982231, -0.020885050296783447, -0.011922984384000301, -0.010266280733048916, 0.010997697710990906, -0.0016666182782500982, -0.012909957207739353, 0.02703600749373436, 0.003004979807883501, -0.006565132178366184, -0.030701905488967896, -0.018875855952501297, -0.02210114151239395, -0.0003255027695558965, -0.01959846168756485, -0.05294404551386833, 0.011922984384000301, -0.03128351643681526, -0.00792662613093853, -0.04561224579811096, -0.020920298993587494, 0.007860533893108368, -0.0005309385014697909, 0.04007814824581146, -0.034068189561367035, -0.024145586416125298, 0.0004855003207921982, -0.0004150022577960044, 0.03373332321643829, -0.011799613013863564, -0.0008680073660798371, 0.011799613013863564, -0.004727776162326336, 0.015500761568546295, -0.007459576241672039, -0.0010068004485219717, 0.014663596637547016, 0.007587353698909283, -0.018646737560629845, 0.020021449774503708, -0.0006003350717946887, -0.006111300550401211, -0.0009021548903547227, -0.02398696541786194, -0.01183486171066761, 0.027000756934285164, 0.013509191572666168, 0.038950178772211075, -0.013288884423673153, 0.0030864933505654335, 0.032499607652425766, -0.014910340309143066, 0.01446972694247961, 0.011394249275326729, -0.012398846447467804, -0.04335630685091019, -0.0069484650157392025, -0.015976622700691223, -0.018435243517160416, 0.008649230934679508, -0.00035992564517073333, -0.0021788307931274176, 0.019475089386105537, 0.04807967692613602, -0.05646894872188568, -0.01617930456995964, 0.029397692531347275, 0.04441377893090248, 0.07649039477109909, -0.029415316879749298, -0.0025577577762305737, -0.030032174661755562, 0.032164741307497025, 0.03789270669221878, 0.01715746521949768, -0.028692711144685745, 0.027124129235744476, 0.02682451345026493, 0.04726894944906235, -0.05357852578163147, -0.030331790447235107, 0.045471251010894775, -0.00914712343364954, 0.019193097949028015, 0.02241838350892067, 0.0015829018084332347, 0.0036482748109847307, 0.0018648940604180098, -0.02361685037612915, 0.04300381615757942, -0.013667811639606953, 0.05227431282401085, 0.026736389845609665, 0.028481217101216316, 0.02486819215118885, -0.02648964710533619, -0.029767807573080063, -0.04832642152905464, -0.004489845130592585, -0.0020763883367180824, -0.01514827087521553, 0.003282566089183092, 0.06380074471235275, 0.006728158798068762, -0.027652865275740623, -0.022982368245720863, -0.024145586416125298, -0.004846741911023855, 0.002949903253465891, -0.03620075434446335, -0.026049034669995308, -0.009499614126980305, 0.02458619885146618, 0.0030908994376659393, -0.011596931144595146, -0.010195782408118248, -0.03665899112820625, 0.054530251771211624, -0.03567202016711235, 0.03131876513361931, 0.019351717084646225, -0.024445202201604843, -0.08079078048467636, -0.012037544511258602, -0.0018792139599099755, 0.00042381451930850744, -0.02063830755650997, 0.0009533761185593903, 0.04102987051010132, 0.06563369929790497, -0.05075860396027565, 0.002511493396013975, -0.004377488978207111, -0.029503438621759415, -0.03142451122403145, 0.013095014728605747, 0.04148811101913452, 0.003835535142570734, 0.019245970994234085, 0.054107263684272766, 0.015315704047679901, 0.008371644653379917, 0.025502674281597137, -0.001010105013847351, 0.024286583065986633, 0.023422980681061745, -0.0045603434555232525, 0.02953868731856346, -0.027652865275740623, -0.01672566495835781, 0.0010012928396463394, 0.021255165338516235, 0.016355549916625023, -0.06041684001684189, -0.004776243586093187, 0.031953245401382446, -0.04233408719301224, 0.005256511736661196, -0.0008938934188336134, -0.039055924862623215, -0.017545204609632492, 0.03323983773589134, 0.040360141545534134, -0.005868963431566954, -0.012857084162533283, 0.008596357889473438, -0.017977004870772362, 0.03620075434446335, 0.007212833035737276, -0.0028970297425985336, -0.01926359534263611, 0.034773167222738266, 0.01650535874068737, -0.01387049350887537, -0.005260917823761702, 0.02121991664171219, -0.0013262447901070118, 0.04325056076049805, -0.02855171449482441, -0.08100227266550064, 0.018223749473690987, -0.006247890647500753, 0.021924898028373718, 0.003366282442584634, -0.014002677984535694, -0.005278542172163725, -0.007807660382241011, 0.004498657770454884, -0.028780832886695862, 0.07472794502973557, -0.001321838703006506, -0.017677389085292816, 0.016355549916625023, 0.04631722718477249, 0.012204976752400398, 0.04110037162899971, 0.0004519035865087062, 0.03604213520884514, -0.029820680618286133, 0.007441951893270016, 0.01135018840432167, 0.042263589799404144, -0.011306126601994038, 0.002610631287097931, 0.01547432504594326, -0.032446734607219696, -0.02150190807878971, -0.00025472932611592114, 0.043215312063694, -0.042580828070640564, 0.04691645875573158, 0.010927199386060238, -0.028639838099479675, 0.009940226562321186, 0.008098464459180832, -0.03806895390152931, 0.00990497786551714, -0.014126049354672432, -0.00521245039999485, 0.0033883131109178066, 0.03516090661287308, -0.0814252644777298, 0.041946347802877426, 0.012363597750663757, -0.0001973119651665911, 0.030913399532437325, -0.0226298775523901, -0.021783901378512383, 0.036940984427928925, 0.001152202719822526, 0.03241148218512535, 0.0009814652148634195, -0.0050846729427576065, 0.04300381615757942, 0.020761679857969284, -0.00009424985182704404, 0.02437470480799675, -0.01802106760442257, 0.028639838099479675, 0.041347112506628036, -0.027159377932548523, -0.0000240960180235561, 0.03898542746901512, -0.026049034669995308, -0.020391564816236496, -0.000835512182675302, -0.06358925253152847, -0.00982566736638546, -0.00995785091072321, -0.0316888801753521, -0.02583753876388073, 0.031459759920835495, -0.05135783925652504, -0.0067105344496667385, -0.030049799010157585, 0.021096544340252876, 0.05505898594856262, -0.004793868400156498, -0.02648964710533619, -0.013403443619608879, 0.059465114027261734, -0.007948656566441059, -0.023493479937314987, -0.0012623559450730681, 0.029556311666965485, 0.035636771470308304, -0.004974519368261099, -0.007367047481238842, 0.0055076610296964645, -0.04127661511301994, -0.030472787097096443, 0.013932179659605026, 0.026877386495471, -0.027547117322683334, -0.0032759567257016897, 0.0283930953592062, -0.002780267270281911, 0.01926359534263611, 0.02121991664171219, -0.017950568348169327, -0.03071952983736992, 0.01868198625743389, 0.033186960965394974, -0.02925669588148594, 0.032605353742837906, 0.0013383616460487247, -0.0026789263356477022, 0.0036725085228681564, -0.04702220857143402, 0.08213024586439133, 0.004701339639723301, 0.0030137922149151564, -0.020990798249840736, 0.007666664198040962, -0.056645192205905914, -0.0006196118774823844, 0.006106894463300705, -0.008177774958312511, 0.03947891294956207, 0.02231263741850853, -0.015624132938683033, 0.010944823734462261, -0.009499614126980305, 0.008975284174084663, -0.03708197921514511, 0.01468122098594904, -0.016144055873155594, 0.03533715382218361, -0.029080450534820557, -0.011693865992128849, -0.042052093893289566, -0.016760913655161858, -0.01688428595662117, -0.005666281562298536, -0.015615320764482021, -0.051287341862916946, 0.030367041006684303, 0.030155545100569725, -0.019175473600625992, 0.03516090661287308, 0.013914555311203003, -0.0031812251545488834, -0.008296740241348743, 0.03426205739378929, 0.018981603905558586, -0.016540607437491417, 0.0017426239792257547, 0.0031591944862157106, -0.0034455927088856697, 0.05445975437760353, -0.021255165338516235, -0.012187352403998375, 0.008627200499176979, 0.040465887635946274, -0.02307048998773098, -0.023387731984257698, -0.06506971269845963, 0.008719729259610176, -0.018435243517160416, 0.04740994796156883, 0.01899922825396061, -0.010962449014186859, 0.008001529611647129, -0.028322596102952957, -0.02215401642024517, 0.03620075434446335, 0.014222984202206135, -0.05386051908135414, 0.01889348030090332, -0.01742183417081833, -0.00026299082674086094, 0.004082278348505497, 0.041347112506628036, -0.028216850012540817, 0.0013361586024984717, -0.009790418669581413, 0.014813405461609364, 0.0010883138747885823, 0.022436007857322693, 0.017298461869359016, 0.029979301616549492, -0.004428159445524216, 0.02322911098599434, -0.004569155629724264, -0.013147888705134392, -0.0015179114416241646, 0.010759767144918442, -0.008354020304977894, -0.05900687724351883, -0.022506507113575935, -0.038950178772211075, 0.04550649970769882, 0.027053631842136383, -0.00705861859023571, -0.042475081980228424, -0.051604580134153366, -0.008539077825844288, 0.01563294604420662, -0.0049260519444942474, -0.03701148182153702, 0.010539459995925426, -0.020444437861442566, -0.025203056633472443, -0.02351110428571701, 0.0401838943362236, -0.015809189528226852, -0.007270112633705139, -0.023493479937314987, -0.004417144227772951, -0.04021914303302765, -0.015201144851744175, -0.023193862289190292, -0.0067105344496667385, -0.054917991161346436, -0.011632179841399193, 0.011773176491260529, -0.040465887635946274, -0.03316933661699295, 0.012918769381940365, -0.007794442120939493, 0.008481797762215137, 0.013720685616135597, -0.01596781052649021, -0.014178922399878502, 0.008252679370343685, 0.02204826846718788, -0.022647501900792122, -0.006604786962270737, 0.011323750950396061, -0.04184059798717499, -0.07254250347614288, 0.00027180308825336397, -0.025978535413742065, -0.012416470795869827, -0.0043400367721915245, 0.015439075417816639, -0.006344825495034456, 0.006723752710968256, -0.02943294122815132, 0.0006477009155787528, 0.004965707194060087, -0.04490726441144943, -0.02476244419813156, 0.0652812048792839, 0.03188274800777435, -0.0010459048207849264, 0.033574700355529785, 0.032270487397909164, -0.0049921441823244095, 0.02252413146197796, 0.010010724887251854, 0.039549414068460464, -0.024357080459594727, -0.009781606495380402, 0.011385437101125717, 0.006847124081104994, -0.013465129770338535, -0.015289267525076866, 0.01954558677971363, 0.02599615976214409, 0.004939270671457052, -0.027652865275740623, 0.02925669588148594, -0.006142143625766039, -0.03332795947790146, 0.02904520183801651, 0.006547507364302874, -0.007477200590074062, 0.009085437282919884 ]
With the growing rates of cyber-attacks and cyber espionage, the need for better and more powerful intrusion detection systems (IDS) is even more warranted nowadays. The basic task of an IDS is to act as the first line of defense, in detecting attacks on the internet. As intrusion tactics from intruders become more sophisticated and difficult to detect, researchers have started to apply novel Machine Learning (ML) techniques to effectively detect intruders and hence preserve internet users' information and overall trust in the entire internet network security. Over the last decade, there has been an explosion of research on intrusion detection techniques based on ML and Deep Learning (DL) architectures on various cyber security-based datasets such as the DARPA, KDDCUP'99, NSL-KDD, CAIDA, CTU-13, UNSW-NB15. In this research, we review contemporary literature and provide a comprehensive survey of different types of intrusion detection technique that applies Support Vector Machines (SVMs) algorithms as a classifier. We focus only on studies that have been evaluated on the two most widely used datasets in cybersecurity namely: the KDDCUP'99 and the NSL-KDD datasets. We provide a summary of each method, identifying the role of the SVMs classifier, and all other algorithms involved in the studies. Furthermore, we present a critical review of each method, in tabular form, highlighting the performance measures, strengths, and limitations of each of the methods surveyed.
[ -0.011148597113788128, 0.0215681791305542, -0.026831313967704773, -0.007161240093410015, 0.07887588441371918, -0.02183489315211773, -0.01634949818253517, -0.003516164608299732, 0.00559207983314991, 0.07446622848510742, 0.03536612540483475, -0.08534811437129974, 0.008961551822721958, -0.04039810597896576, -0.06280198693275452, 0.003162770066410303, 0.015869414433836937, -0.05031982436776161, -0.015904976055026054, -0.07332825660705566, 0.024377554655075073, 0.014962591230869293, -0.012028750032186508, 0.007147904485464096, -0.04267405718564987, 0.017531925812363625, 0.04054035618901253, -0.004725262988358736, -0.0832144096493721, 0.07411061227321625, 0.006685602478682995, -0.0008612602832727134, 0.012588847428560257, -0.013549013063311577, -0.03246784582734108, -0.023559635505080223, -0.025871148332953453, 0.08677058666944504, 0.011930955573916435, -0.0027560328599065542, 0.027631452307105064, -0.06443782895803452, 0.0023804123047739267, 0.000295328936772421, 0.018758803606033325, -0.018509872257709503, -0.05522734299302101, -0.04551899433135986, -0.006196628790348768, -0.0057254359126091, -0.00019017182057723403, -0.05401824414730072, -0.03278790041804314, 0.0009173810831271112, -0.01827872171998024, 0.03602401539683342, 0.03147211670875549, 0.002130368957296014, 0.03509941324591637, -0.04238956421613693, 0.008770408108830452, 0.027898164466023445, 0.03325020149350166, 0.00549428490921855, -0.006401108577847481, -0.03965131193399429, -0.00880152452737093, -0.07290151715278625, 0.04445214197039604, 0.01152199599891901, -0.055298466235399246, 0.03787322714924812, 0.049039606004953384, -0.0306719783693552, 0.011886503547430038, -0.009397183544933796, -0.01743413135409355, 0.06902528554201126, -0.004491888917982578, -0.02604895643889904, 0.02252834662795067, 0.02633344940841198, 0.00961944367736578, -0.00573432631790638, 0.05227572098374367, 0.014082439243793488, -0.02796928770840168, -0.06906084716320038, 0.05309363827109337, -0.05401824414730072, 0.014509179629385471, 0.030174115672707558, 0.044416580349206924, 0.015024824067950249, 0.012855559587478638, 0.00257377908565104, -0.012980026192963123, -0.04868398606777191, 0.0021036977414041758, -0.02496432326734066, 0.0019336682744324207, -0.022457223385572433, -0.0023826349060982466, 0.008179194293916225, -0.004429656080901623, -0.03669968992471695, -0.04295855015516281, 0.061841823160648346, 0.007992495782673359, 0.10824985802173615, -0.029498443007469177, -0.0022892854176461697, -0.00524535309523344, 0.005600970238447189, 0.016260594129562378, 0.05074656754732132, 0.0236129779368639, -0.10867659747600555, -0.06354878097772598, -0.005458723288029432, 0.022314975038170815, 0.07780902832746506, -0.0034494863357394934, 0.0030116327106952667, -0.08093846589326859, 0.06970096379518509, -0.025568872690200806, -0.0029760710895061493, -0.0066767120733857155, 0.019950121641159058, 0.0061655123718082905, 0.010312897153198719, 0.04381203278899193, 0.031063158065080643, 0.023933034390211105, 0.05896132439374924, 0.03755316883325577, 0.015851633623242378, 0.03204110637307167, 0.03837108984589577, -0.013095601461827755, 0.006312204524874687, -0.038406651467084885, 0.039757996797561646, 0.031721048057079315, 0.025817804038524628, -0.0057254359126091, 0.03204110637307167, -0.047403763979673386, 0.019950121641159058, 0.008312550373375416, 0.05881907418370247, 0.04544787108898163, -0.013966863043606281, 0.04953746870160103, -0.004609687253832817, 0.013753493316471577, -0.029142824932932854, 0.018456529825925827, 0.0028271563351154327, 0.013228957541286945, -0.0009962836047634482, 0.021372590214014053, 0.059139132499694824, 0.044807761907577515, 0.0215681791305542, -0.009308278560638428, 0.019274448975920677, -0.06347765773534775, 0.04772382229566574, -0.01719408854842186, -0.03298348933458328, 0.002704913029447198, 0.026671286672353745, 0.0027804814744740725, 0.003220557700842619, 0.023648539558053017, -0.04665696993470192, -0.0025026556104421616, -0.002878276165574789, -0.06479344516992569, 0.023684101179242134, -0.04573236405849457, 0.005400935187935829, 0.015522688627243042, -0.006303314119577408, 0.06568248569965363, 0.005009756423532963, 0.04829280823469162, -0.006241080816835165, -0.021585959941148758, -0.005636531859636307, 0.0058276760391891, 0.010117308236658573, -0.01866989955306053, -0.006485567893832922, -0.042069509625434875, 0.05568964406847954, -0.006458896212279797, -0.03291236609220505, -0.032538969069719315, -0.026262326166033745, 0.04790163040161133, -0.018314283341169357, 0.025444407016038895, -0.021781550720334053, 0.030351923778653145, -0.013353424146771431, -0.0033516916446387768, -0.035810645669698715, -0.08805080503225327, 0.019701190292835236, -0.009717238135635853, 0.017131855711340904, -0.025568872690200806, -0.0215681791305542, 0.011646461673080921, 0.01775418594479561, -0.014295808970928192, -0.0017791970167309046, 0.038406651467084885, 0.030387485399842262, 0.0002549052587710321, -0.019967902451753616, -0.04142939671874046, -0.04349197819828987, -0.006818958558142185, 0.0012668861309066415, -0.016002772375941277, -0.0019203325500711799, 0.010961898602545261, -0.015318208374083042, 0.02044798620045185, -0.03534834459424019, -0.002602672902867198, -0.07823577523231506, 0.023417389020323753, -0.045910172164440155, -0.04683477804064751, -0.007267925422638655, 0.022297194227576256, -0.04601685702800751, -0.014749221503734589, -0.020021244883537292, 0.010579610243439674, 0.013193395920097828, 0.010464034974575043, 0.06507793813943863, 0.018616557121276855, 0.011904284358024597, -0.010872994549572468, 0.025551091879606247, -0.014935920014977455, 0.009028229862451553, -0.039473503828048706, -0.01743413135409355, 0.03765985742211342, -0.04054035618901253, -0.025871148332953453, -0.028556056320667267, 0.06596697866916656, -0.027791479602456093, -0.008614825084805489, 0.06162844970822334, -0.03726867586374283, 0.03748204559087753, 0.0850636214017868, 0.03829996660351753, 0.02412862330675125, -0.01317561510950327, 0.007107897661626339, -0.021390371024608612, -0.0836411565542221, -0.028840551152825356, -0.006965650711208582, -0.0322011336684227, 0.08371227979660034, 0.0018947726348415017, -0.016687335446476936, 0.025551091879606247, -0.04093153402209282, -0.029907401651144028, 0.029338413849473, -0.0012802217388525605, 0.0070723360404372215, -0.034726012498140335, -0.04676365479826927, 0.014891467988491058, 0.014358042739331722, 0.003756206016987562, -0.01452696043998003, 0.00010411525727249682, -0.05988592654466629, -0.048648424446582794, 0.030174115672707558, -0.023292923346161842, 0.012846669182181358, -0.01706962287425995, -0.06127283349633217, -0.01868768036365509, -0.0799427330493927, -0.007423507981002331, 0.03150767832994461, 0.05768110230565071, -0.061735138297080994, -0.027062464505434036, 0.022883962839841843, 0.08470800518989563, -0.05078212916851044, -0.06223300099372864, -0.056827619671821594, -0.02617342211306095, -0.0006751168984919786, -0.008783743716776371, 0.05430273711681366, 0.0490751676261425, 0.02427086979150772, 0.005374263972043991, 0.046443600207567215, 0.003702863585203886, 0.023808568716049194, -0.0008657054859213531, -0.07773790508508682, 0.07716891914606094, -0.014589193277060986, -0.0548006035387516, -0.0027560328599065542, 0.017131855711340904, -0.08470800518989563, 0.00021684310922864825, 0.0021192559506744146, 0.03179217129945755, -0.0515289232134819, -0.025888929143548012, 0.03476157784461975, 0.03773098066449165, -0.003916233777999878, 0.04935966059565544, -0.04142939671874046, 0.005792114417999983, -0.010757418349385262, -0.004531896207481623, -0.08570373058319092, -0.03972243517637253, -0.025977833196520805, 0.021497055888175964, 0.005529846530407667, -0.007103452458977699, -0.030085209757089615, -0.019683409482240677, 0.0009468306670896709, -0.0335346981883049, -0.02386191114783287, -0.025017665699124336, -0.00812585186213255, -0.03028080053627491, -0.03559727594256401, -0.020643575116991997, 0.006578917149454355, -0.02700912207365036, 0.013442328199744225, -0.05138667672872543, -0.02398637682199478, 0.006912308279424906, -0.03765985742211342, -0.019132202491164207, -0.03202332556247711, 0.010872994549572468, -0.0026471251621842384, 0.03449486196041107, 0.008894873782992363, 0.005018646828830242, 0.01635838858783245, -0.012722203508019447, -0.05103106051683426, 0.0028604953549802303, 0.0069300890900194645, -0.003033858723938465, 0.00023142897407524288, 0.04011361300945282, 0.03285902366042137, 0.03451264277100563, -0.05227572098374367, -0.0008890428580343723, -0.028751647099852562, 0.0233107041567564, 0.0382288433611393, -0.0028916120063513517, -0.005192010197788477, 0.0658247321844101, 0.0016447292873635888, 0.0035361680202186108, -0.0316854864358902, -0.008214755915105343, 0.04619466885924339, -0.038797829300165176, -0.037304237484931946, 0.009717238135635853, -0.005432052072137594, -0.022279413416981697, -0.03132987022399902, 0.039864681661129, -0.020287958905100822, -0.023381827399134636, -0.029782935976982117, -0.0455901175737381, 0.03387253358960152, -0.047119271010160446, -0.01813647523522377, -0.025319941341876984, 0.011708694510161877, 0.014713659882545471, 0.02590670995414257, 0.02373744361102581, 0.011077473871409893, 0.03851333633065224, 0.012179886922240257, 0.02702690288424492, 0.014464727602899075, -0.03765985742211342, -0.014909248799085617, -0.015611592680215836, 0.06073940917849541, -0.0065744719468057156, -0.026493476703763008, 0.03463710844516754, 0.004676365293562412, -0.02686687558889389, 0.03837108984589577, 0.023079553619027138, -0.000985726248472929, 0.0327167771756649, 0.04174945130944252, -0.036913059651851654, -0.0068011777475476265, -0.07510633766651154, -0.009210484102368355, -0.004685255698859692, 0.01248216163367033, -0.012304353527724743, 0.014598083682358265, 0.0182965025305748, -0.018180927261710167, -0.0012179886689409614, -0.03876226767897606, -0.023541854694485664, 0.005423161666840315, -0.005845456849783659, 0.0313832126557827, -0.0015413780929520726, -0.041251588612794876, 0.00880152452737093, -0.044665515422821045, -0.004500779323279858, 0.06902528554201126, -0.009334949776530266, 0.030067428946495056, -0.03003186732530594, -0.0014780337223783135, 0.022563908249139786, -0.0032872359734028578, 0.11372636258602142, -0.024324212223291397, -0.011930955573916435, 0.028467152267694473, 0.07389724254608154, -0.03751760721206665, -0.06088165566325188, -0.01213543489575386, -0.023488512262701988, 0.038940075784921646, -0.04445214197039604, 0.0277025755494833, 0.004627468064427376, -0.014989262446761131, 0.0071701304987072945, 0.0029694032855331898, -0.027524767443537712, -0.008276988752186298, 0.004371868446469307, 0.0474393256008625, 0.023826349526643753, -0.043171919882297516, 0.005334257148206234, -0.020003464072942734, -0.002259280299767852, 0.023648539558053017, -0.01675845868885517, -0.03412146493792534, -0.04217619448900223, 0.02018127217888832, -0.016162799671292305, -0.03600623458623886, -0.03467267006635666, -0.045092254877090454, -0.007756899110972881, -0.024786515161395073, 0.025533311069011688, 0.07816465198993683, 0.06984321027994156, -0.03968687355518341, -0.022297194227576256, 0.005236462689936161, 0.0236129779368639, -0.00810807105153799, 0.04704814776778221, 0.016056114807724953, -0.014171343296766281, 0.028556056320667267, 0.0325034074485302, -0.0037628738209605217, -0.00446744030341506, -0.005787669215351343, -0.027471425011754036, -0.012988916598260403, 0.0253555029630661, -0.001115748775191605, -0.030725320801138878, 0.014295808970928192, 0.016322826966643333, 0.028733866289258003, -0.03790878877043724, -0.0199323408305645, 0.0007123455870896578, -0.0199323408305645, 0.01215321570634842, 0.05632975697517395, -0.00982392393052578, -0.045625679194927216, 0.0018458752892911434, -0.020661355927586555, 0.01744302175939083, -0.010748527944087982, -0.014073548838496208, 0.011308625340461731, 0.01610945723950863, 0.012971135787665844, -0.0014458060031756759, -0.023755226284265518, -0.02222607098519802, -0.04601685702800751, 0.007654658984392881, -0.012313243933022022, -0.030920911580324173, 0.004218508489429951, -0.0003928458027075976, 0.03488604351878166, -0.018865490332245827, 0.015940537676215172, -0.01438471395522356, -0.0064144441857934, 0.01610945723950863, -0.018580995500087738, -0.050284262746572495, -0.0338369719684124, -0.02293730527162552, -0.027222491800785065, 0.01964784786105156, 0.01743413135409355, 0.0009696123888716102, -0.035810645669698715, 0.044274333864450455, 0.01651841588318348, -0.017416350543498993, 0.0028849442023783922, -0.0019325569737702608, -0.0155404694378376, 0.033748067915439606, -0.0021848229225724936, 0.02480429597198963, -0.01609167642891407, -0.017985336482524872, -0.047119271010160446, -0.041678328067064285, -0.00927271693944931, 0.05270246043801308, 0.009432745166122913, -0.041927263140678406, 0.015504907816648483, 0.008912654593586922, -0.04246068745851517, 0.02864496037364006, -0.012028750032186508, -0.013575684279203415, 0.0038339972961694, 0.017967555671930313, -0.014944810420274734, 0.012366586364805698, -0.0023092888295650482, -0.010570719838142395, 0.0066900476813316345, -0.013228957541286945, -0.02905392087996006, -0.047261517494916916, -0.04573236405849457, 0.01771862432360649, 0.038833390921354294, -0.007885809987783432, 0.025462187826633453, -0.007716892287135124, 0.0425318107008934, 0.04950190708041191, 0.0701277032494545, 0.07453735172748566, 0.009414964355528355, 0.031187623739242554, -0.009121580049395561, 0.006161067169159651, 0.003402811475098133, -0.008628160692751408, -0.0281115360558033, -0.01302447821944952, 0.07553308457136154, -0.024715391919016838, 0.0079747149720788, -0.010917446576058865, 0.054907288402318954, 0.009379401803016663, 0.0023226244375109673, -0.005912134889513254, -0.0026337895542383194, -0.02071469835937023, 0.028467152267694473, 0.009014894254505634, -0.004329638555645943, 0.03794435039162636, 0.048897355794906616, 0.0018603221978992224, -0.01030400674790144, -0.053947120904922485, -0.05199122801423073, 0.0018280943622812629, 0.005854347255080938, -0.0322011336684227, -0.04800831526517868, -0.013664589263498783, 0.0033316882327198982, -0.005423161666840315, -0.009423854760825634, -0.0010840765899047256, 0.019878998398780823, 0.042780742049217224, -0.0009879488497972488, 0.04633691534399986, -0.006761170923709869, 0.02549774944782257, -0.0883352980017662, -0.014206904917955399, 0.03406812250614166, 0.055334027856588364, 0.04295855015516281, 0.004418543074280024, -0.01467809733003378, 0.024590926244854927, -0.019221106544137, -0.015167071484029293, 0.01662510074675083, -0.012562175281345844, 0.026937998831272125, 0.004336306359618902, -0.002051466377452016, -0.003189441282302141, -0.03163214400410652, 0.02837824821472168, 0.01452696043998003, 0.016331717371940613, 0.042922988533973694, 0.008339222520589828, -0.004609687253832817, 0.030085209757089615, -0.020785821601748466, -0.043563101440668106, -0.04896848276257515, 0.039509065449237823, -0.015193742699921131, -0.012739984318614006, 0.045910172164440155, 0.07517746835947037, 0.043989840894937515, -0.058321211487054825, -0.00743239838629961, 0.041002657264471054, 0.017007390037178993, 0.03042304702103138, -0.016847362741827965, -0.006125505547970533, 0.0031227630097419024, 0.017780857160687447, -0.048897355794906616, -0.004105155356228352, 0.009592772461473942, 0.0036184045020490885, 0.010730747133493423, -0.002115922048687935, 0.041287150233983994, -0.039864681661129, -0.006765616126358509, -0.021728208288550377, -0.012455490417778492, 0.02700912207365036, 0.012802217155694962, -0.013255628757178783, -0.08541923761367798, 0.016589539125561714, -0.02905392087996006, 0.032414503395557404, 0.019132202491164207, -0.008561482653021812, 0.0028582727536559105, -0.030476389452815056, -0.021763769909739494, 0.01743413135409355, 0.0018881048308685422, 0.01634949818253517, 0.06454451382160187, 0.021372590214014053, 0.05170673131942749, 0.02371966280043125, 0.0010073967278003693, 0.009032675065100193, 0.06618034839630127, 0.003411702113226056, -0.013620136305689812, -0.0513155534863472, -0.028538275510072708, 0.011646461673080921, -0.013575684279203415, -0.04189170151948929, -0.03424593061208725, -0.017389679327607155, 0.051777858287096024, -0.028591617941856384, -0.05007089301943779, 0.022688373923301697, -0.008014721795916557, -0.02948066219687462, 0.08499249815940857, 0.009441635571420193, -0.0004925852990709245, 0.0001864211808424443, -0.02892945520579815, -0.029409537091851234, -0.0032072220928967, -0.05999261140823364, 0.00538759957998991, -0.027204710990190506, 0.014562522061169147, -0.0001965618139365688, -0.04541230946779251, 0.020945850759744644, 0.016731787472963333, -0.01911442168056965, 0.03001408651471138, -0.06219743937253952, -0.02455536462366581, -0.018198708072304726, 0.038406651467084885, 0.014411385171115398, 0.02523103728890419, 0.004649694077670574, -0.030494170263409615, 0.02784482203423977, -0.0069167534820735455, -0.001839207485318184, 0.08492137491703033, -0.0212659053504467, 0.005547627341002226, 0.010464034974575043, 0.01438471395522356, 0.016714006662368774, 0.014882577583193779, 0.043563101440668106, 0.05416049063205719, -0.023541854694485664, -0.03380141034722328, -0.01745191216468811, 0.06326428800821304, -0.01607389561831951, -0.004898626357316971, 0.00606771744787693, -0.03618404641747475, 0.020554671064019203, -0.001496925950050354, 0.05003533139824867, -0.028413809835910797, 0.011744256131350994, 0.006303314119577408, -0.027240272611379623, -0.004034032113850117, 0.03317907825112343, -0.03602401539683342, 0.0216748658567667, -0.013415656983852386, -0.0007590203313156962, 0.005961032584309578, 0.00927271693944931, -0.04327860847115517, 0.0338369719684124, -0.031969983130693436, -0.01431358978152275, 0.0515289232134819, -0.032236695289611816, -0.009397183544933796, 0.0017047396395355463, 0.020536890253424644, -0.058890201151371, -0.027204710990190506, -0.017487473785877228, 0.014224685728549957, 0.0045741256326437, 0.015255975537002087, -0.009210484102368355, 0.005329811945557594, 0.0306719783693552, 0.015193742699921131, 0.009761691093444824, -0.0341392457485199, -0.011557557620108128, -0.009601662866771221, -0.0310809388756752, 0.022670593112707138, -0.004382981453090906, -0.02510656975209713, -0.02060801349580288, -0.039260134100914, -0.022457223385572433, 0.02194157801568508, 0.026404572650790215, 0.045625679194927216, 0.0037717644590884447, -0.00044757750583812594, 0.02948066219687462, -0.011726475320756435, 0.006983431521803141, 0.007121233269572258, 0.031881075352430344, -0.021230343729257584, 0.04690590128302574, 0.01827872171998024, -0.006298868916928768, -0.011833160184323788, 0.0014635868137702346, 0.006058827042579651, -0.01634949818253517, 0.014606974087655544, -0.028751647099852562, -0.01690959557890892, 0.0031316534150391817, 0.023417389020323753, 0.03561505675315857, -0.010410691611468792, 0.009014894254505634, 0.018776584416627884, 0.0253555029630661, -0.024502022191882133, 0.027773698791861534, 0.01936335302889347, 0.026777971535921097, 0.016669554635882378, -0.026084518060088158, 0.014100220054388046, 0.0351705364882946, 0.023826349526643753, 0.01180648896843195, 0.006898972671478987, 0.020928069949150085, 0.022617250680923462, -0.003485047956928611, 0.03573952242732048, -0.029089482501149178, -0.003036081325262785, -0.02222607098519802, 0.003822884289547801, 0.04587461054325104, -0.008290324360132217, -0.021070316433906555, -0.021319247782230377, 0.0439542792737484, -0.03339245170354843, -0.0011224165791645646, -0.03557949513196945, -0.0042496249079704285, 0.026671286672353745, -0.01991456001996994, 0.029534004628658295, -0.023648539558053017, -0.007370165549218655, -0.029391756281256676, 0.03534834459424019, -0.03639741614460945, -0.05142223834991455, -0.00490751676261425, -0.027471425011754036, -0.002340405248105526, 0.022475004196166992, 0.005605415441095829, -0.04285186529159546, 0.011602009646594524, -0.04800831526517868, -0.029658470302820206, -0.00014134393131826073, -0.02018127217888832, -0.004694146104156971, 0.002313734032213688, -0.0006217743502929807, -0.003796213073655963, 0.006205519195646048, -0.03477935865521431, -0.0056809838861227036, -0.0036206271033734083, -0.032236695289611816, -0.02416418492794037, -0.03958018869161606, -0.0064188893884420395, 0.024448677897453308, 0.0253555029630661, -0.018367625772953033, -0.0022303862497210503, 0.015896085649728775, 0.0061655123718082905, 0.05266689881682396, 0.029302852228283882, -0.03141877427697182, 0.0341392457485199, -0.01405576802790165, -0.006774506531655788, -0.054373860359191895, -0.0005423161201179028, -0.00559207983314991, 0.011877613142132759, -0.015433784574270248, 0.031045377254486084, 0.02661794424057007, -0.0019625620916485786, 0.011504214257001877, -0.05896132439374924, -0.000984614947810769, 0.05743217095732689, -0.030227458104491234, -0.012642189860343933, -0.01744302175939083, 0.019967902451753616, 0.02603117562830448, 0.0060366010293364525, -0.006001039408147335, -0.011495323851704597, 0.05679205805063248, 0.015424894168972969, -0.018580995500087738, 0.008472578600049019, -0.021657085046172142, 0.016020553186535835, 0.01909664086997509, -0.004387426655739546, -0.03180995211005211, -0.057894472032785416, -0.03070753999054432, -0.021105878055095673, -0.02073247916996479, -0.001987010706216097, 0.00640999898314476, 0.02194157801568508, -0.012517723254859447, 0.023292923346161842, -0.0341392457485199, 0.03958018869161606, -0.013629026710987091, 0.010179541073739529, -0.04228287935256958, 0.04103821888566017, 0.010801870375871658, -0.009326059371232986, -0.03261009231209755, -0.0281115360558033, -0.0053964899852871895, -0.008196975104510784, 0.0474393256008625, -0.02727583423256874, 0.04619466885924339, -0.015638263896107674, -0.00719680218026042, 0.016127238050103188, -0.05999261140823364, -0.005952142179012299, -0.02075025998055935, -0.01840318739414215, 0.05362706631422043, -0.0024759843945503235, -0.05369818955659866, 0.04011361300945282, -0.009548320434987545, 0.001879214309155941, 0.009637224487960339, 0.007876919582486153, -0.02620898373425007, 0.003965131007134914, 0.0012802217388525605, 0.002789371879771352, -0.02414640411734581, 0.036628566682338715, 0.003782877465710044, -0.00011856220226036385, 0.014553631655871868, 0.025444407016038895, 0.0006073273834772408, -0.0032916811760514975, 0.009850595146417618, -0.04146495833992958, 0.018047569319605827, -0.00024240309721790254, -0.02866274118423462, -0.01989677920937538, -0.013886849395930767, 0.01467809733003378, 0.03556171432137489, 0.004067371133714914, 0.02265281230211258, 0.019043298438191414, 0.009121580049395561, -0.023950815200805664, -0.0016247258754447103, 0.004047367721796036, -0.015255975537002087, 0.00860593467950821 ]
Cross-dataset emotion recognition as an extremely challenging task in the field of EEG-based affective computing is influenced by many factors, which makes the universal models yield unsatisfactory results. Facing the situation that lacks EEG information decoding research, we first analyzed the impact of different EEG information(individual, session, emotion and trial) for emotion recognition by sample space visualization, sample aggregation phenomena quantification, and energy pattern analysis on five public datasets. Based on these phenomena and patterns, we provided the processing methods and interpretable work of various EEG differences. Through the analysis of emotional feature distribution patterns, the Individual Emotional Feature Distribution Difference(IEFDD) was found, which was also considered as the main factor of the stability for emotion recognition. After analyzing the limitations of traditional modeling approach suffering from IEFDD, the Weight-based Channel-model Matrix Framework(WCMF) was proposed. To reasonably characterize emotional feature distribution patterns, four weight extraction methods were designed, and the optimal was the correction T-test(CT) weight extraction method. Finally, the performance of WCMF was validated on cross-dataset tasks in two kinds of experiments that simulated different practical scenarios, and the results showed that WCMF had more stable and better emotion recognition ability.
[ -0.006380424369126558, -0.01248934119939804, -0.034735433757305145, -0.020757179707288742, 0.006503040436655283, 0.002614353783428669, 0.01740274950861931, 0.01998644880950451, -0.020827246829867363, 0.02245629020035267, 0.009415176697075367, -0.05969659984111786, -0.017481574788689613, -0.02156294323503971, -0.001205361564643681, -0.013163730502128601, 0.010667613707482815, 0.021352743729948997, -0.009327593259513378, 0.01181495189666748, 0.015134348534047604, -0.02960306592285633, -0.005999437998980284, -0.029112601652741432, -0.0008117852848954499, 0.04368641972541809, 0.07377994805574417, -0.02674786001443863, -0.05349572002887726, 0.04375648498535156, 0.016115279868245125, -0.0020428744610399008, -0.026012161746621132, -0.034507717937231064, -0.07448061555624008, -0.0203718151897192, 0.023367155343294144, 0.08681230992078781, 0.02744852378964424, 0.05437155067920685, -0.0044119954109191895, 0.02786892279982567, -0.025416597723960876, 0.024961166083812714, 0.02793898992240429, -0.03461281582713127, -0.037205275148153305, -0.022263608872890472, 0.022000858560204506, 0.0018600447801873088, -0.0150817995890975, -0.05370591953396797, 0.03780084103345871, 0.011806193739175797, -0.03881680220365524, 0.04666424170136452, 0.061413224786520004, 0.02054698020219803, 0.06277952343225479, 0.02609974518418312, 0.004466734826564789, 0.031634993851184845, -0.07875467091798782, -0.016062729060649872, -0.03874673694372177, 0.01666705124080181, 0.014302310533821583, -0.000901010527741164, 0.03025118075311184, -0.01998644880950451, -0.04480748251080513, 0.00251801242120564, -0.012209075503051281, -0.036329444497823715, -0.02124764584004879, -0.01590508036315441, 0.06309481710195541, 0.05230459198355675, 0.018672702834010124, -0.01738523319363594, 0.022631457075476646, 0.025644313544034958, -0.016518160700798035, -0.0024610834661871195, 0.007869335822761059, -0.04386158660054207, -0.06355024874210358, -0.05815513804554939, -0.009064844809472561, -0.005246223881840706, -0.0034879944287240505, 0.043336085975170135, -0.04186469316482544, 0.0021359312813729048, -0.017367716878652573, -0.03175760805606842, 0.04936179891228676, 0.016316719353199005, -0.05493208020925522, -0.06071256101131439, 0.005592177156358957, 0.03223055973649025, -0.01630796119570732, -0.07342962175607681, 0.02315695583820343, -0.03384208679199219, -0.014424926601350307, 0.029305284842848778, 0.03822123631834984, 0.15849027037620544, -0.015370823442935944, 0.03548864647746086, -0.049501933157444, 0.021703077480196953, -0.002106372034177184, -0.0029778233729302883, 0.028219254687428474, -0.06302475184202194, 0.004372583236545324, -0.030986879020929337, 0.013803087174892426, 0.07742340862751007, -0.005526489578187466, 0.006025712937116623, -0.019566049799323082, 0.08828370273113251, 0.015572263859212399, -0.02609974518418312, -0.0005725740920752287, 0.05790990591049194, -0.014643884263932705, 0.005609693471342325, -0.004144867416471243, -0.0016804995248094201, 0.007295667193830013, -0.01026473194360733, 0.00043682040995918214, 0.07854446768760681, 0.01893545314669609, -0.04018309712409973, 0.00865758303552866, -0.03955249860882759, -0.025504181161522865, 0.050097499042749405, -0.02228112518787384, -0.0013465891825035214, 0.007558416109532118, 0.04992233216762543, 0.018480021506547928, -0.0006847899057902396, -0.043581318110227585, 0.04631391167640686, -0.029795749112963676, 0.029270252212882042, 0.007554037030786276, 0.010974154807627201, 0.053040288388729095, -0.01610651984810829, -0.03217800706624985, -0.01967114955186844, 0.062289055436849594, -0.043266020715236664, 0.03541858121752739, 0.02277158945798874, 0.06158839166164398, 0.003639075206592679, -0.007891232147812843, 0.02355983667075634, -0.04964206740260124, 0.04235515743494034, -0.009327593259513378, 0.04368641972541809, -0.010361073538661003, -0.014302310533821583, -0.016430577263236046, 0.07567174732685089, 0.04382655397057533, -0.022894205525517464, -0.06232408806681633, 0.030671579763293266, -0.034980665892362595, -0.013408963568508625, 0.05633341148495674, 0.03375450149178505, 0.049466900527477264, -0.003665350144729018, 0.06102786213159561, -0.02371748723089695, 0.06880523264408112, -0.004720725584775209, 0.07048682868480682, 0.02315695583820343, 0.09143669158220291, -0.007308804430067539, 0.01177991833537817, -0.02299930527806282, -0.020949862897396088, 0.014433684758841991, 0.016316719353199005, -0.0005602577584795654, -0.04939683526754379, -0.04718974232673645, 0.00652493629604578, -0.05545758083462715, -0.04974716529250145, -0.01967114955186844, 0.05475691705942154, -0.0015513146063312888, -0.031634993851184845, -0.028709718957543373, 0.009546550922095776, 0.005644726566970348, -0.019163168966770172, -0.03174009174108505, -0.009143669158220291, -0.02070463076233864, 0.0499923974275589, 0.013321380130946636, 0.01771804876625538, -0.02196582593023777, 0.03468288481235504, 0.001818442833609879, 0.045403048396110535, -0.02848200313746929, 0.01590508036315441, 0.0009223588858731091, 0.035295963287353516, 0.00804012268781662, -0.00742266234010458, -0.005022887140512466, 0.012165283784270287, -0.0034442029427736998, 0.02306937240064144, -0.029585549607872963, 0.010974154807627201, -0.020652079954743385, 0.016010180115699768, -0.02762369066476822, -0.01925075240433216, 0.026222361251711845, -0.03428000211715698, -0.022806623950600624, -0.021072478964924812, -0.017245100811123848, 0.007006642874330282, -0.012813398614525795, -0.022631457075476646, 0.04711967334151268, 0.0443870835006237, -0.007251875475049019, -0.048345837742090225, 0.020739663392305374, -0.0005282352212816477, 0.040778663009405136, 0.020441880449652672, 0.016404302790760994, 0.03941236808896065, -0.030513931065797806, -0.008202151395380497, -0.037590641528367996, 0.08253825455904007, 0.012892222963273525, -0.05283008888363838, -0.018024589866399765, -0.0001702395238680765, 0.01121938694268465, 0.044527217745780945, 0.0035799567122012377, 0.07511121034622192, -0.06400568783283234, -0.010369831696152687, -0.010194665752351284, -0.04242522269487381, -0.06659813970327377, 0.04154939204454422, 0.006774547975510359, 0.06071256101131439, -0.020652079954743385, 0.029392868280410767, 0.01853257045149803, 0.039762698113918304, 0.03484053164720535, 0.035313479602336884, 0.003941236529499292, -0.02348977141082287, -0.009844333864748478, 0.019233234226703644, -0.030338764190673828, 0.005110470112413168, -0.018357405439019203, -0.016921043395996094, -0.055842943489551544, -0.04323098808526993, 0.030338764190673828, 0.03615427762269974, -0.013741778209805489, -0.03023366443812847, -0.016141554340720177, 0.009879366494715214, -0.06151832640171051, -0.018269822001457214, -0.012944772839546204, 0.031967807561159134, 0.04768020659685135, -0.06137819215655327, 0.010895329527556896, 0.04512277990579605, 0.05868063494563103, -0.02261394076049328, -0.022859172895550728, 0.021072478964924812, 0.0030040983110666275, -0.03962256759405136, -0.029410384595394135, -0.00899477768689394, 0.030058499425649643, 0.008924711495637894, 0.03860660269856453, -0.000514824059791863, -0.00983557477593422, -0.03221303969621658, 0.03501569852232933, -0.11743133515119553, 0.050903260707855225, -0.048275768756866455, -0.04400171712040901, 0.03885183483362198, 0.03564629703760147, -0.002888050628826022, -0.01484532468020916, -0.016763392835855484, -0.004646280314773321, 0.011088012717664242, 0.004825825337320566, 0.0004004187067039311, -0.007864956744015217, -0.025661829859018326, -0.023892652243375778, -0.04116402938961983, 0.006008196622133255, 0.022561389952898026, 0.01783190667629242, -0.08835376799106598, -0.06295468658208847, -0.03315893933176994, 0.015616055577993393, -0.014521267265081406, -0.01046617329120636, -0.01576494611799717, -0.06088772788643837, 0.0008539346163161099, -0.030934328213334084, -0.023051856085658073, 0.04655914381146431, 0.014503750950098038, -0.038011036813259125, 0.03119707852602005, -0.019058069214224815, 0.004482062067836523, -0.005868063773959875, -0.07013649493455887, -0.01807713881134987, -0.038081105798482895, -0.03170505911111832, -0.0572793073952198, -0.046348944306373596, -0.0067044817842543125, -0.03294873982667923, 0.002782951109111309, 0.028919918462634087, -0.00983557477593422, 0.07385002076625824, -0.014801532961428165, 0.03452523425221443, -0.03406980261206627, 0.04480748251080513, 0.01491539180278778, -0.002176438458263874, -0.02028423175215721, 0.04456225037574768, -0.01608024537563324, -0.023279571905732155, 0.020406847819685936, 0.006954092998057604, 0.026765376329421997, 0.0255392137914896, 0.01926826871931553, 0.00557028129696846, 0.0007356975111179054, 0.04648907482624054, -0.03955249860882759, -0.0732194185256958, -0.038956936448812485, -0.028131671249866486, 0.009152427315711975, -0.014827808365225792, -0.017525365576148033, 0.04750503972172737, 0.06460124999284744, 0.028079122304916382, -0.018567604944109917, -0.01691228523850441, -0.017350200563669205, -0.040708597749471664, 0.015712397173047066, -0.036084212362766266, 0.029970915988087654, 0.04473741725087166, 0.06214892491698265, 0.03286115452647209, -0.014608850702643394, 0.004142677877098322, -0.008456142619252205, -0.022386224940419197, -0.000263296504272148, -0.013207522220909595, -0.046524111181497574, 0.03804607316851616, -0.002384448191151023, 0.017604190856218338, -0.03885183483362198, 0.006218395661562681, 0.0829586535692215, 0.01599266193807125, 0.010282248258590698, 0.06225402280688286, -0.03415738418698311, -0.019198201596736908, -0.03272102400660515, -0.010124599561095238, -0.006573107093572617, -0.005425769370049238, 0.04323098808526993, -0.04820570349693298, 0.004685692489147186, 0.01313745602965355, -0.001954196486622095, 0.0014735845616087317, -0.021860726177692413, -0.03382457047700882, -0.014889116398990154, 0.015221931971609592, -0.01877780258655548, -0.05650857463479042, -0.06425091624259949, -0.022140992805361748, 0.004957200028002262, 0.03145982697606087, -0.03128466010093689, -0.0437915176153183, -0.04263542219996452, 0.027991538867354393, -0.041339192539453506, -0.024470699951052666, 0.009248768910765648, -0.031004395335912704, -0.008793337270617485, -0.027028124779462814, 0.01942591741681099, -0.050412796437740326, 0.016745876520872116, 0.018427470698952675, 0.03604917973279953, -0.008180256001651287, 0.010667613707482815, 0.010212182067334652, -0.010107082314789295, -0.07230855524539948, -0.021948309615254402, 0.04876623675227165, -0.030111048370599747, -0.05030769854784012, -0.03329906985163689, 0.025486664846539497, -0.014477476477622986, -0.0010690604103729129, -0.005469560623168945, -0.057034075260162354, 0.05307532101869583, 0.0029165151063352823, 0.0021589219104498625, -0.016772150993347168, -0.002248694421723485, -0.016973592340946198, 0.01989886537194252, -0.016386786475777626, -0.02499619871377945, 0.018339887261390686, -0.01869022101163864, -0.011333244852721691, 0.03937733545899391, -0.04291568696498871, 0.052024323493242264, 0.00860065408051014, -0.00023236875131260604, -0.004799550399184227, -0.01909310184419155, -0.030268697068095207, 0.08316884934902191, -0.02937535010278225, 0.03389463573694229, 0.05195425823330879, 0.0072825294919312, 0.001925732009112835, 0.00686213094741106, 0.026800408959388733, -0.013768053613603115, -0.008605033159255981, 0.0050141289830207825, 0.021843209862709045, 0.05955646559596062, 0.02189575880765915, 0.03724030777812004, -0.056858908385038376, -0.025136331096291542, 0.03540106490254402, -0.013566612266004086, -0.01592259667813778, 0.004359445534646511, 0.02023168094456196, -0.011902534402906895, 0.03997289761900902, 0.03165251016616821, 0.02729087509214878, -0.006288462318480015, -0.004350687377154827, 0.020967379212379456, 0.003868980798870325, -0.005719172302633524, -0.010518723167479038, -0.026327461004257202, -0.006757031194865704, 0.026607727631926537, -0.049501933157444, 0.013706745579838753, -0.036819908767938614, 0.016605744138360023, 0.0009365911246277392, 0.005885580088943243, -0.013093664310872555, -0.0022267987951636314, 0.04529794678092003, -0.03145982697606087, -0.01981128379702568, 0.007330700289458036, -0.010869055055081844, 0.008885298855602741, -0.030426347628235817, 0.0024194815196096897, 0.035208381712436676, 0.021668042987585068, -0.04130415990948677, -0.04021812975406647, -0.020634563639760017, 0.01551971398293972, -0.025346530601382256, -0.019320817664265633, -0.0016246653394773602, -0.029638100415468216, -0.03906203433871269, -0.006446111481636763, 0.00781678594648838, -0.008167117834091187, 0.04305582121014595, 0.030776679515838623, 0.032020360231399536, 0.01612403802573681, 0.08183758705854416, 0.0021567323710769415, 0.009152427315711975, -0.02189575880765915, -0.033789537847042084, -0.03280860558152199, 0.03501569852232933, 0.00233627762645483, 0.05552764609456062, 0.05706910789012909, -0.03170505911111832, 0.026958059519529343, 0.04021812975406647, 0.04382655397057533, -0.014617608860135078, 0.03312390670180321, 0.04631391167640686, 0.016737118363380432, 0.013505304232239723, -0.016053970903158188, -0.06078262999653816, -0.017218824476003647, -0.029795749112963676, 0.016448095440864563, 0.07567174732685089, 0.010028257966041565, -0.029900848865509033, -0.01273457333445549, -0.028271805495023727, 0.03170505911111832, -0.006555590312927961, 0.062043823301792145, -0.07609214633703232, 0.0020483483094722033, 0.04274052381515503, -0.021685559302568436, 0.01771804876625538, 0.006980367936193943, -0.006126433610916138, 0.01740274950861931, -0.004346308298408985, 0.006669448222965002, 0.019846316426992416, 0.012778365053236485, -0.017288891598582268, 0.03622434288263321, 0.0010230793850496411, 0.041654493659734726, 0.02618732862174511, 0.0531453862786293, -0.033001288771629333, 0.022018374875187874, -0.019198201596736908, 0.02890240214765072, 0.01682470180094242, 0.022946756333112717, -0.03527844697237015, 0.023209504783153534, 0.021545426920056343, -0.01284843124449253, -0.03072413057088852, -0.009064844809472561, -0.006476765498518944, -0.04260038956999779, 0.046944510191679, -0.04291568696498871, -0.0005331617430783808, 0.008026985451579094, 0.009739234112203121, 0.0026734722778201103, -0.02681792713701725, 0.000978193012997508, 0.04526291415095329, -0.002712884685024619, 0.03336913883686066, -0.014967940747737885, 0.021545426920056343, 0.005443285685032606, 0.004175521433353424, -0.04491258040070534, 0.01870773732662201, 0.07609214633703232, 0.015545989386737347, 0.023927686735987663, 0.029340317472815514, 0.010343557223677635, 0.02762369066476822, -0.014626367017626762, -0.0484159030020237, 0.02420795150101185, 0.014398651197552681, 0.013461512513458729, -0.029410384595394135, -0.01293601468205452, -0.007374492008239031, 0.010991671122610569, -0.011280694976449013, 0.051779091358184814, -0.02587202936410904, -0.015694880858063698, 0.0032734160777181387, -0.018585121259093285, 0.05819017067551613, -0.010912846773862839, -0.03773077204823494, -0.06971609592437744, 0.010247215628623962, 0.010369831696152687, -0.045473113656044006, 0.025329014286398888, 0.03268599137663841, 0.03790593892335892, -0.0727289542555809, -0.037835873663425446, -0.02333212085068226, -0.0028070362750440836, -0.004055094439536333, -0.0011221576714888215, 0.006065125577151775, -0.03534851595759392, -0.0015567884547635913, 0.007383250165730715, -0.04032323136925697, 0.01567736454308033, -0.001558978110551834, 0.00010215740621788427, -0.023840103298425674, -0.040077999234199524, 0.009958191774785519, -0.03766070678830147, 0.015817496925592422, 0.012515615671873093, 0.039272233843803406, -0.013934461399912834, -0.0028136051259934902, -0.014118385501205921, 0.02364742010831833, 0.04473741725087166, 0.008710132911801338, 0.018182238563895226, -0.011998875997960567, -0.04764517396688461, -0.017621707171201706, 0.004628763534128666, 0.00543014844879508, -0.04400171712040901, 0.024785999208688736, 0.03492811694741249, 0.025171365588903427, 0.03468288481235504, 0.0028486382216215134, -0.024610834196209908, 0.05318041890859604, 0.013461512513458729, 0.01572115533053875, 0.019233234226703644, -0.03874673694372177, -0.015397097915410995, 0.034017253667116165, -0.0008621455053798854, 0.0075058662332594395, -0.02045939676463604, -0.00435725599527359, 0.03741547465324402, -0.007851819507777691, -0.03040883131325245, 0.00883712898939848, 0.001139674335718155, -0.03223055973649025, 0.029340317472815514, 0.04344118759036064, -0.012708298861980438, -0.01942591741681099, -0.037520572543144226, -0.022736556828022003, -0.006735135801136494, 0.007970056496560574, 0.0038142413832247257, -0.00024235868477262557, -0.028079122304916382, 0.03853653743863106, -0.06411078572273254, 0.009520276449620724, 0.007663515862077475, -0.0052900156006217, 0.03128466010093689, -0.0582602359354496, -0.04403674975037575, 0.005552764516323805, -0.008753924630582333, 0.014932908117771149, -0.0018304855329915881, 0.018339887261390686, 0.012139009311795235, 0.02858710289001465, 0.01877780258655548, 0.01731516607105732, 0.08863403648138046, 0.03843143582344055, -0.02364742010831833, 0.019706184044480324, 0.013426479883491993, -0.013978253118693829, 0.02681792713701725, 0.00023784268705639988, 0.017972039058804512, -0.00380986207164824, 0.017061175778508186, 0.011683577671647072, 0.008311630226671696, -0.031722575426101685, -0.013277588412165642, 0.03773077204823494, -0.04354628548026085, -0.014547542668879032, 0.017507849261164665, 0.011131804436445236, -0.04361635446548462, 0.008920332416892052, -0.029007501900196075, -0.05433651804924011, -0.009099877439439297, 0.025731896981596947, -0.013636679388582706, 0.016027696430683136, 0.008101430721580982, -0.01523944828659296, 0.03881680220365524, -0.015064282342791557, -0.020669596269726753, 0.0557028129696846, -0.05990679934620857, -0.0073175630532205105, 0.016220377758145332, -0.03629441186785698, 0.008013848215341568, -0.004768896382302046, -0.02212347462773323, -0.018760286271572113, -0.0013181247049942613, -0.005522110499441624, -0.0016246653394773602, -0.008224047720432281, 0.014022044837474823, -0.027413491159677505, 0.002314381767064333, 0.0074927289970219135, -0.00865758303552866, -0.0031091978307813406, -0.05419638380408287, -0.00613081268966198, -0.0008676194702275097, -0.033631887286901474, 0.0032077287323772907, -0.05871566757559776, -0.013715503737330437, 0.011841226369142532, -0.036819908767938614, -0.034350067377090454, 0.035225898027420044, -0.027273358777165413, 0.06383051723241806, -0.03843143582344055, 0.017393991351127625, -0.005749826319515705, -0.027343424037098885, 0.00455431779846549, -0.019933899864554405, 0.022088441997766495, -0.037520572543144226, 0.0013684849254786968, 0.03972766548395157, -0.0014308878453448415, 0.025329014286398888, -0.023577352985739708, -0.056543610990047455, -0.02953300066292286, -0.010702647268772125, -0.020249199122190475, 0.011604752391576767, 0.002169869840145111, -0.01798955537378788, -0.03636447712779045, 0.03962256759405136, 0.011797435581684113, 0.0252414308488369, -0.013873153366148472, -0.03342168778181076, 0.00660814018920064, -0.0074883499182760715, 0.023910168558359146, 0.004979095887392759, 0.0033434825018048286, 0.018882902339100838, -0.029568033292889595, -0.013163730502128601, -0.0008473658817820251, 0.04908153414726257, -0.025661829859018326, -0.025101298466324806, -0.04217999055981636, 0.006853372789919376, -0.019636116921901703, 0.006292841397225857, -0.028849853202700615, -0.00860065408051014, 0.012927256524562836, -0.02643256075680256, 0.013452754355967045, -0.016544435173273087, -0.015940112993121147, 0.03692501038312912, 0.017954522743821144, 0.008710132911801338, 0.008062019012868404, 0.04655914381146431, -0.023262055590748787, 0.029795749112963676, 0.004825825337320566, -0.04855603724718094, -0.024295534938573837, -0.025136331096291542, -0.01071140542626381, -0.007243117317557335, -0.016649534925818443, 0.0028333112131804228, -0.0022070924751460552, -0.01093912124633789, -0.003798914374783635, 0.002885861089453101, -0.015940112993121147, 0.010308523662388325, 0.03145982697606087, 0.0038580328691750765, -0.06582741439342499, -0.0008834939217194915, -0.0006158182513900101, -0.003168316325172782, -0.05230459198355675, 0.02969064936041832, -0.057034075260162354, 0.039272233843803406, -0.02983078360557556, -0.005819892976433039, -0.025206398218870163, -0.007129259407520294, -0.0012743332190439105, 0.049536965787410736, -0.002585889305919409, 0.033544301986694336, 0.0014002338284626603, 0.021913276985287666, -0.011490894481539726, -0.013785569928586483, 0.037520572543144226, -0.009073602966964245, 0.02380506880581379, -0.030338764190673828, 0.0018545708153396845, -0.041584424674510956, -0.029480449855327606, 0.00268660974688828, 0.023437220603227615, -0.011946326121687889, 0.03853653743863106, 0.012331691570580006, -0.013601645827293396, 0.03822123631834984, -0.019443433731794357, -0.032826121896505356, 0.026397528126835823, 0.0032164871226996183, 0.004821446258574724, 0.016903527081012726, 0.0391671359539032, 0.004044146742671728, 0.016973592340946198, -0.017280133441090584, -0.01702614314854145, 0.041654493659734726, -0.03305383771657944, 0.027588656172156334, -0.008237184956669807, -0.02984829992055893, -0.047154705971479416, 0.0017549451440572739, -0.04274052381515503, -0.019706184044480324, -0.012322933413088322, -0.011517169885337353, 0.0030807333532720804, 0.000016652751583023928, 0.00390839297324419, -0.014302310533821583, -0.032580889761447906, -0.04704960808157921, -0.006958472542464733, -0.050903260707855225, 0.008351042866706848, -0.033071354031562805, 0.0009984466014429927, -0.015423373319208622, 0.030461380258202553, 0.018287338316440582, -0.024418151006102562, -0.005745447240769863, -0.011158078908920288, 0.007076709531247616, -0.01201639324426651, 0.03056648001074791, 0.01217404194176197, 0.01065885554999113, -0.009660408832132816, -0.0005988490302115679, 0.030373796820640564, 0.03221303969621658, 0.005565902218222618, 0.02052946388721466, -0.029165152460336685, 0.019933899864554405, 0.008206530474126339, -0.03119707852602005, 0.04119906201958656, 0.0034595299512147903, -0.03464784845709801, 0.01630796119570732, 0.0013870963593944907, -0.09690187126398087, -0.024558283388614655, -0.0008709038374945521, -0.018585121259093285, 0.02906005270779133, 0.045332979410886765, -0.012305417098104954, -0.021300194784998894, 0.014705192297697067, 0.03717024251818657, -0.0008626929484307766, 0.0018720874795690179, 0.04400171712040901, 0.04179462417960167, -0.011920051649212837, 0.01512559037655592, 0.029550516977906227, 0.0018808457534760237, 0.02068711444735527, -0.022088441997766495, -0.005088574718683958, -0.018042106181383133, -0.0474349744617939, 0.0013860015897080302, 0.02403278648853302, -0.0366097092628479, 0.027325907722115517, 0.013268830254673958, -0.03955249860882759, -0.04319595545530319 ]
Deep learning techniques have been applied widely in industrial recommendation systems. However, far less attention has been paid to the overfitting problem of models in recommendation systems, which, on the contrary, is recognized as a critical issue for deep neural networks. In the context of Click-Through Rate (CTR) prediction, we observe an interesting one-epoch overfitting problem: the model performance exhibits a dramatic degradation at the beginning of the second epoch. Such a phenomenon has been witnessed widely in real-world applications of CTR models. Thereby, the best performance is usually achieved by training with only one epoch. To understand the underlying factors behind the one-epoch phenomenon, we conduct extensive experiments on the production data set collected from the display advertising system of Alibaba. The results show that the model structure, the optimization algorithm with a fast convergence rate, and the feature sparsity are closely related to the one-epoch phenomenon. We also provide a likely hypothesis for explaining such a phenomenon and conduct a set of proof-of-concept experiments. We hope this work can shed light on future research on training more epochs for better performance.
[ -0.02295105531811714, -0.050171226263046265, -0.015215564519166946, -0.041596509516239166, -0.003705829381942749, -0.029847318306565285, -0.015096978284418583, 0.03780173882842064, -0.015826741233468056, -0.0018529146909713745, -0.012141437269747257, -0.03758281096816063, -0.011256598867475986, -0.10362639278173447, 0.031142648309469223, -0.000535349827259779, 0.019575901329517365, -0.026216747239232063, 0.029044579714536667, -0.04940497502684593, 0.00302167609333992, -0.05312676727771759, -0.05998654291033745, 0.01995902694761753, -0.01169445738196373, 0.05695802718400955, 0.0031334212981164455, 0.0018095849081873894, -0.06341642886400223, -0.008611206896603107, 0.05367409065365791, 0.03907882422208786, -0.0006214390741661191, -0.0013067324180155993, -0.037838228046894073, 0.0008728653192520142, 0.07720895856618881, 0.0215462613850832, -0.039188288152217865, 0.005240612663328648, 0.0839957594871521, -0.02844252437353134, -0.029920294880867004, 0.005012561567127705, 0.00034635249176062644, -0.006818725727498531, 0.006285086274147034, -0.024994393810629845, -0.05892838537693024, -0.037692274898290634, 0.026563383638858795, -0.029391217976808548, 0.05597284436225891, 0.015671666711568832, -0.033696819096803665, 0.04473448917269707, 0.04955092817544937, -0.03125211223959923, 0.05068206042051315, 0.05469575896859169, 0.0026681970339268446, 0.023261206224560738, -0.03356911242008209, -0.01750519685447216, 0.0018574756104499102, -0.014412824995815754, -0.0009714973857626319, 0.01995902694761753, 0.004109479486942291, -0.016419675201177597, -0.10238578915596008, 0.004038783721625805, 0.032620418816804886, 0.010426493361592293, -0.040319424122571945, -0.02701948583126068, 0.06775852292776108, 0.03537527471780777, -0.019557656720280647, -0.027712762355804443, 0.013737794011831284, 0.046887293457984924, -0.0016339856665581465, 0.03977210074663162, 0.10858877748250961, -0.0009099236340261996, -0.028479013592004776, -0.04130460321903229, -0.02816886268556118, -0.027201926335692406, -0.08041991293430328, 0.03407994657754898, -0.029628390446305275, -0.027986422181129456, -0.058855410665273666, 0.0029737853910773993, -0.054659269750118256, 0.026271479204297066, -0.057651299983263016, 0.0910014808177948, -0.011338697746396065, -0.010627178475260735, 0.01747783087193966, -0.008465254679322243, 0.029008090496063232, -0.048602234572172165, -0.0549146868288517, 0.03342315927147865, -0.009135724045336246, 0.12128666043281555, 0.011603236198425293, -0.0033569112420082092, -0.05484171211719513, 0.002554171485826373, -0.05060908570885658, 0.004948707297444344, -0.046376459300518036, -0.05363760143518448, 0.03701724484562874, -0.0423627607524395, -0.01664772443473339, 0.0036419748794287443, 0.0013683062279596925, 0.03429887443780899, 0.008556474931538105, 0.05863648280501366, 0.03272988274693489, 0.0352475680410862, 0.008451571688055992, 0.010718398727476597, 0.02081649750471115, 0.006599796935915947, -0.00806388445198536, -0.03167172893881798, 0.04900360479950905, -0.0282418392598629, 0.0604608878493309, 0.004597508814185858, 0.0017537124222144485, -0.0392247773706913, -0.0017628344940021634, 0.054951176047325134, -0.006805042736232281, 0.007457268889993429, -0.013299936428666115, 0.0094139464199543, -0.02424638532102108, -0.005582689307630062, -0.004221224691718817, 0.016246356070041656, -0.05356462672352791, 0.037400368601083755, -0.06458405405282974, 0.0502077154815197, -0.004608911462128162, -0.03245622292160988, 0.017341000959277153, -0.02295105531811714, -0.0013785684714093804, -0.02495790459215641, 0.009122041054069996, -0.018490377813577652, -0.01408443134278059, 0.0353570319712162, 0.01637406460940838, 0.04185192659497261, 0.05892838537693024, -0.011858653277158737, -0.119243323802948, 0.060789283365011215, -0.03356911242008209, 0.0018973846454173326, 0.008428766392171383, 0.016173379495739937, 0.052944328635931015, 0.04407770186662674, 0.015954449772834778, -0.025778887793421745, -0.06721120327711105, 0.02233075723052025, -0.01294417679309845, 0.035265810787677765, 0.03320423141121864, -0.042472224682569504, 0.019922537729144096, -0.009003454819321632, 0.015024001710116863, 0.02152801677584648, -0.028424279764294624, 0.018234960734844208, 0.022130072116851807, 0.015434494242072105, 0.06950995326042175, 0.006522259674966335, -0.03278461471199989, -0.014275995083153248, -0.01433072704821825, -0.005965814925730228, -0.02147328481078148, -0.007429902441799641, 0.007001166697591543, -0.010827862657606602, 0.028935115784406662, -0.05111991986632347, -0.011347819119691849, -0.016857532784342766, 0.02253144234418869, 0.018545109778642654, 0.00741621945053339, -0.028114130720496178, 0.015927083790302277, 0.006225793156772852, -0.040392398834228516, -0.006950995419174433, -0.024063944816589355, 0.0008819873910397291, -0.014011455699801445, 0.03196363151073456, -0.01301715336740017, -0.013911113142967224, 0.0015906560001894832, 0.007607782259583473, 0.03486444056034088, -0.02753031998872757, -0.021929387003183365, -0.04243573546409607, -0.0074025364592671394, -0.024374093860387802, 0.027822226285934448, -0.02238548919558525, 0.0108004966750741, -0.0030718473717570305, -0.05589986965060234, -0.04885765165090561, 0.03364208713173866, 0.0149054154753685, -0.022859835997223854, 0.004305603448301554, 0.006681895349174738, -0.005769690964370966, 0.016173379495739937, -0.02125435695052147, -0.00043301191180944443, 0.004212102387100458, -0.012688759714365005, -0.013801648281514645, -0.014878049492835999, 0.00609808461740613, 0.001301031094044447, 0.03395223617553711, 0.010362639091908932, -0.030978452414274216, -0.02530454285442829, 0.048894140869379044, 0.008456132374703884, 0.019156286492943764, 0.06761257350444794, -0.010928205214440823, -0.009012577123939991, -0.02309700846672058, 0.07140734046697617, 0.06604357808828354, 0.009669363498687744, 0.007867760956287384, -0.004866608884185553, -0.0015427651815116405, 0.04922253638505936, 0.008515425957739353, 0.01760553941130638, 0.06436512619256973, 0.053163256496191025, -0.03707197681069374, 0.019375216215848923, -0.008045640774071217, 0.008579280227422714, -0.028898626565933228, 0.04283710569143295, -0.0270924624055624, -0.014075309969484806, 0.03189065679907799, 0.037765249609947205, 0.016045670956373215, 0.03201836347579956, 0.007420780602842569, -0.043749310076236725, -0.027110707014799118, -0.062431249767541885, -0.010143710300326347, -0.034463070333004, -0.029646635055541992, -0.04349389299750328, -0.03864096850156784, -0.03601381927728653, 0.026070794090628624, 0.06659089773893356, 0.02680055797100067, -0.010590690188109875, 0.01990429498255253, 0.0020729838870465755, -0.06837882101535797, -0.06283262372016907, -0.0008774263551458716, 0.016027426347136497, 0.026417432352900505, -0.028679698705673218, 0.03116089291870594, 0.013345546089112759, -0.020725278183817863, -0.031051428988575935, 0.0019338726997375488, 0.007571294438093901, -0.003206397406756878, 0.009943025186657906, -0.04177894815802574, 0.003826696425676346, 0.02203885093331337, 0.02395448088645935, 0.030631814152002335, -0.03086898848414421, -0.05181319639086723, -0.005035366863012314, 0.0008529108599759638, -0.07308579236268997, 0.03564893826842308, 0.01423038449138403, 0.01005248911678791, 0.021126648411154747, 0.012095826677978039, -0.034335363656282425, 0.04626699164509773, -0.01875491626560688, -0.05236051604151726, -0.025614691898226738, 0.036123283207416534, -0.027420856058597565, 0.016063915565609932, -0.00406386936083436, 0.020925963297486305, -0.0028871260583400726, -0.039188288152217865, -0.021071914583444595, 0.048456285148859024, 0.016237232834100723, 0.03331369534134865, 0.02174694649875164, -0.005815301556140184, -0.011010304093360901, 0.00682784803211689, -0.03493741899728775, -0.008980649523437023, 0.0009640857460908592, 0.0018061641603708267, 0.019922537729144096, 0.019283995032310486, 0.06750310212373734, -0.008209837600588799, 0.009199578315019608, 0.04072079062461853, 0.004059308208525181, 0.005724080838263035, -0.013883747160434723, -0.031708214432001114, -0.011539381928741932, 0.024410583078861237, -0.014047943986952305, 0.007744613103568554, -0.006960117723792791, 0.018444767221808434, 0.04626699164509773, 0.0019920258782804012, -0.09640173614025116, -0.003156226361170411, -0.027840470895171165, 0.00881189201027155, -0.023626087233424187, 0.028862139210104942, -0.02616201527416706, 0.005427614785730839, -0.0494779534637928, 0.04469800367951393, 0.0018688782583922148, -0.04301954805850983, 0.02809588797390461, 0.028041154146194458, 0.03750983253121376, 0.04291008040308952, -0.020232686772942543, 0.025414006784558296, -0.046668361872434616, 0.00536376005038619, 0.024374093860387802, -0.05728641897439957, -0.011539381928741932, -0.024939659982919693, 0.064219169318676, 0.004374018870294094, 0.012460708618164062, -0.01981307379901409, 0.002179027535021305, -0.040465373545885086, -0.012396854348480701, -0.006627162918448448, 0.024301117286086082, -0.01290768850594759, -0.026654604822397232, 0.05049962177872658, 0.035539474338293076, -0.015361517667770386, 0.049879319965839386, 0.027293147519230843, -0.013153983280062675, -0.026344455778598785, 0.010782252997159958, 0.028296571224927902, 0.03123386949300766, -0.00019712161156348884, -0.03460902348160744, -0.0439317524433136, -0.01212319266051054, 0.0008312460267916322, -0.029354728758335114, 0.021783433854579926, 0.07016674429178238, -0.01785183511674404, -0.0024492680095136166, 0.02068878896534443, 0.005313589237630367, -0.046887293457984924, -0.0215462613850832, 0.011283964850008488, 0.04685080423951149, -0.0015974974958226085, 0.03588610887527466, -0.010718398727476597, -0.01757817342877388, -0.016456162557005882, 0.02738436870276928, 0.05425790324807167, -0.05524308234453201, -0.008068445138633251, -0.0025655741337686777, -0.005377443507313728, 0.0014515448128804564, 0.03984507545828819, -0.04294656962156296, -0.019156286492943764, -0.04137757793068886, -0.004225785844027996, -0.03991805389523506, -0.03595908731222153, -0.05619177594780922, -0.0042166635394096375, -0.04280061647295952, -0.059147316962480545, 0.04747110232710838, -0.03657938539981842, 0.02324296161532402, -0.027493832632899284, 0.028223596513271332, -0.0180981308221817, -0.0006106066284701228, 0.03304003179073334, 0.002148240804672241, -0.007785662077367306, 0.010900839231908321, 0.003993173595517874, -0.05411195009946823, -0.03192714601755142, 0.007831272669136524, -0.017268024384975433, -0.019776586443185806, -0.017952177673578262, -0.04407770186662674, 0.053309209644794464, 0.05075503885746002, 0.02944594994187355, -0.05319974571466446, -0.09348268061876297, 0.03123386949300766, -0.020944206044077873, 0.01642879657447338, 0.026362698525190353, 0.012497196905314922, 0.022057095542550087, 0.005190441384911537, 0.02858847752213478, 0.029573658481240273, -0.01369218435138464, 0.006075279321521521, -0.021272599697113037, -0.03710846230387688, 0.04528181254863739, -0.026910021901130676, 0.0510469414293766, -0.045172348618507385, -0.05542552471160889, -0.0005108343320898712, -0.00828737486153841, 0.02689177729189396, -0.02446531504392624, 0.016191624104976654, -0.037838228046894073, -0.01072752010077238, -0.02909931167960167, -0.000750287901610136, 0.0021071915980428457, -0.0038517818320542574, 0.00035290897358208895, -0.01415740791708231, -0.01365569606423378, -0.017642028629779816, 0.029117556288838387, 0.0003566147934179753, -0.009149407036602497, 0.0199772696942091, 0.01897384598851204, 0.015799375250935555, 0.0045883869752287865, 0.019429948180913925, -0.011019425466656685, -0.007055899128317833, 0.015753764659166336, -0.01497839204967022, 0.02059756964445114, -0.059147316962480545, 0.03885989636182785, 0.010490347631275654, -0.023443646728992462, 0.07691705226898193, 0.010061611421406269, -0.022221293300390244, 0.022166559472680092, -0.01855423115193844, -0.02946419268846512, 0.007958981208503246, 0.008351229131221771, 0.019375216215848923, 0.018937358632683754, -0.016346698626875877, -0.0456102080643177, -0.014467557892203331, 0.04933200031518936, -0.008305618539452553, 0.03672533854842186, 0.011940752156078815, -0.012205291539430618, 0.021436797454953194, -0.04137757793068886, 0.01904682256281376, 0.03274812921881676, 0.0059430100955069065, -0.0017799383495002985, 0.004109479486942291, -0.04265466332435608, -0.022987544536590576, -0.03400696814060211, -0.009651119820773602, -0.04564669355750084, 0.015024001710116863, 0.03750983253121376, -0.043968237936496735, -0.019922537729144096, -0.030686546117067337, -0.023370670154690742, -0.005126587115228176, -0.02375379577279091, 0.007001166697591543, 0.05170372873544693, -0.026654604822397232, 0.012661393731832504, -0.01701260730624199, -0.010280540212988853, 0.013591841794550419, -0.019740097224712372, 0.020123222842812538, 0.03816661983728409, 0.023498378694057465, -0.04447907209396362, 0.04093972221016884, 0.02302403189241886, 0.03623274713754654, -0.021874655038118362, 0.026982998475432396, 0.03636045753955841, -0.016465283930301666, -0.00033038892433978617, -0.026508651673793793, -0.04798193648457527, 0.019648876041173935, -0.03371506556868553, -0.023279448971152306, 0.07377906888723373, -0.01072752010077238, -0.0015553080011159182, -0.07494669407606125, -0.012177925556898117, -0.021126648411154747, 0.030504105612635612, 0.04422365501523018, -0.05367409065365791, 0.013974967412650585, 0.01579025387763977, 0.028333060443401337, 0.03929775208234787, 0.023589598014950752, 0.014358093030750751, 0.0038130132015794516, 0.0006647687405347824, -0.0047389003448188305, 0.04385877400636673, -0.029573658481240273, 0.009851804934442043, 0.039188288152217865, -0.02844252437353134, 0.032346758991479874, 0.0028278327081352472, 0.06896263360977173, -0.0076944418251514435, -0.0361415259540081, -0.005204124376177788, 0.04940497502684593, 0.026417432352900505, 0.04137757793068886, -0.0063398187048733234, -0.04086674377322197, 0.05206861346960068, 0.03813013434410095, -0.02397272363305092, -0.007078703958541155, -0.033769797533750534, 0.004613472614437342, 0.022878078743815422, -0.019575901329517365, -0.07439936697483063, -0.012323877774178982, -0.0003836958494503051, 0.009778828360140324, 0.013135739602148533, 0.018736673519015312, -0.034554291516542435, -0.04356686770915985, 0.017915688455104828, -0.0020342152565717697, 0.02132733166217804, 0.006499454379081726, -0.0017787980614230037, -0.004141406621783972, 0.0006664791144430637, 0.06965591013431549, -0.002547329990193248, -0.008305618539452553, 0.05236051604151726, -0.01558044645935297, 0.037619296461343765, 0.004130003973841667, -0.02118138037621975, 0.05272539705038071, 0.04250871390104294, 0.05148480087518692, 0.002763978438451886, -0.0034754977095872164, 0.004907658323645592, -0.007375170476734638, -0.008132299408316612, 0.04331145063042641, -0.03479146584868431, 0.006399111822247505, -0.03407994657754898, 0.04885765165090561, 0.058782435953617096, -0.04192490130662918, -0.02838779240846634, -0.06713822484016418, 0.027366124093532562, 0.01932048425078392, -0.036542896181344986, 0.032547444105148315, 0.040611326694488525, 0.03010273538529873, 0.022421978414058685, 0.04287359490990639, 0.00599318090826273, 0.03871394321322441, -0.04028293490409851, -0.04641294479370117, -0.02503088116645813, -0.020360395312309265, 0.04280061647295952, -0.029610145837068558, 0.012506318278610706, -0.042545199394226074, -0.043676335364580154, 0.016656847670674324, -0.0006282805697992444, -0.015927083790302277, -0.015425371937453747, -0.014622632414102554, 0.006800481583923101, 0.010919083841145039, 0.006645407062023878, -0.016638603061437607, 0.012460708618164062, -0.035758402198553085, 0.03123386949300766, 0.03185416758060455, 0.03636045753955841, 0.013664817437529564, -0.022020608186721802, -0.039115313440561295, -0.023516623303294182, -0.003222360974177718, 0.05819862335920334, -0.003525668988004327, 0.014887171797454357, 0.009632875211536884, 0.010563324205577374, 0.034827955067157745, 0.021692214533686638, 0.004207541700452566, 0.013135739602148533, 0.004472080618143082, 0.027475588023662567, 0.0745818093419075, -0.07947122305631638, -0.03349613398313522, -0.0017616942059248686, -0.0001677600375842303, 0.027931690216064453, -0.041815437376499176, 0.005824423395097256, -0.00186773797031492, 0.0070057278499007225, -0.00035148364258930087, -0.027585051953792572, 0.00017816487525124103, -0.018271448090672493, -0.015553080476820469, 0.03528405725955963, -0.017569052055478096, -0.01640143059194088, -0.005984059069305658, -0.02368081919848919, -0.03656114265322685, -0.0203968845307827, -0.02667284943163395, -0.031416311860084534, 0.01679367758333683, 0.020980695262551308, 0.027110707014799118, -0.016684213653206825, -0.017787979915738106, -0.009062748402357101, 0.05133884772658348, -0.014449313282966614, -0.06648143380880356, 0.01865457370877266, -0.002159643219783902, 0.011895141564309597, -0.01152113825082779, 0.011612358503043652, 0.012889443896710873, 0.01300803106278181, -0.005742324981838465, -0.01026229653507471, 0.06947346776723862, 0.02638094313442707, -0.02052459307014942, 0.027293147519230843, 0.012068460695445538, -0.03787471726536751, 0.020159712061285973, -0.011712701059877872, 0.03557595983147621, -0.028898626565933228, -0.0070741428062319756, 0.03316774219274521, 0.048237353563308716, 0.0017240657471120358, -0.01369218435138464, 0.030996697023510933, -0.03736387938261032, 0.005847228690981865, -0.012187046930193901, 0.048164378851652145, 0.01027141883969307, 0.0007172204786911607, 0.004004576243460178, -0.002688721753656864, 0.048894140869379044, 0.04261817783117294, -0.0004358625446911901, -0.012989786453545094, -0.007001166697591543, 0.001272524707019329, -0.015726398676633835, -0.027001243084669113, -0.00536832120269537, -0.001546186045743525, 0.03621450439095497, -0.06257720291614532, 0.034335363656282425, -0.0368712916970253, 0.0063398187048733234, 0.024063944816589355, -0.03309476748108864, -0.026618115603923798, -0.004084393847733736, -0.019429948180913925, -0.02616201527416706, 0.0054230536334216595, 0.013263448141515255, 0.029993271455168724, 0.004789071623235941, -0.009897414594888687, 0.023334180936217308, -0.011247476562857628, -0.02767627313733101, 0.0017970420885831118, -0.04893063008785248, -0.007904249243438244, -0.01738661155104637, -0.041122160851955414, -0.025414006784558296, -0.036615874618291855, -0.01027141883969307, -0.014613510109484196, 0.009067309089004993, -0.010462981648743153, 0.037473347038030624, -0.0019281714921817183, -0.018736673519015312, 0.018079886212944984, -0.0017274866113439202, 0.054367367178201675, -0.008611206896603107, 0.024082189425826073, -0.05433087795972824, 0.003678463166579604, 0.017596418038010597, 0.006358062848448753, 0.04327496513724327, -0.015325029380619526, -0.024793708696961403, -0.03820310905575752, -0.0005957833491265774, 0.04115865007042885, -0.029062824323773384, 0.03802066668868065, -0.029008090496063232, 0.043238475918769836, 0.04130460321903229, 0.04929551109671593, 0.05703100189566612, -0.00477538863196969, -0.05976761505007744, -0.007566733285784721, 0.023845015093684196, 0.022987544536590576, 0.0008660238236188889, 0.02468424290418625, 0.0215462613850832, 0.016994362697005272, -0.003927038982510567, -0.0028688819147646427, 0.05170372873544693, 0.03672533854842186, -0.02360784262418747, -0.013318180106580257, 0.009751462377607822, -0.027694517746567726, -0.007160802371799946, -0.006932751275599003, -0.02988380752503872, 0.056374214589595795, 0.016711579635739326, 0.004531374201178551, 0.04458853602409363, -0.007498317863792181, 0.0007240620325319469, -0.037254415452480316, 0.023990968242287636, 0.01155762653797865, -0.010627178475260735, -0.003313581459224224, -0.01659299246966839, -0.05298081412911415, -0.03780173882842064, -0.02623498998582363, -0.007899687625467777, -0.0738520473241806, 0.0017354683950543404, 0.06859774887561798, 0.014522289857268333, 0.024118676781654358, -0.011165378615260124, -0.023571355268359184, 0.009318165481090546, -0.009541654959321022, 0.009094675071537495, 0.00833754613995552, -0.007019410841166973, -0.016757190227508545, -0.012451586313545704, 0.0005513133946806192, 0.031416311860084534, 0.016556505113840103, -0.0027160877361893654, -0.0203968845307827, 0.03659762814640999, -0.026490407064557076, -0.013263448141515255, -0.025359274819493294, 0.044114191085100174, -0.02032390795648098, 0.05852701514959335, 0.00927711557596922, -0.02461126819252968, 0.004517690744251013, 0.026052549481391907, -0.017341000959277153, -0.003817574353888631, 0.043822284787893295, -0.002451548585668206, 0.04955092817544937, -0.04955092817544937, 0.0047981939278542995, 0.011283964850008488, 0.03258393332362175, -0.05148480087518692, 0.0028666015714406967, -0.04400472715497017, 0.03522932529449463, 0.018618086352944374, -0.007872321642935276, 0.041596509516239166, 0.025140345096588135, -0.022002363577485085, 0.012314755469560623, -0.005003439728170633, -0.0024401459377259016, 0.01226002350449562, -0.00887574627995491, -0.007265706080943346, 0.028989847749471664, 0.023845015093684196, -0.03650641068816185, 0.026143770664930344, 0.009651119820773602, -0.019940782338380814, -0.04305603355169296, -0.04301954805850983, -0.010919083841145039, -0.004957829602062702, -0.0282418392598629, -0.03179943561553955, -0.0005045629222877324, -0.005172197241336107, 0.019065067172050476, -0.0447709783911705, -0.004120882134884596, -0.008104933425784111, 0.011037670075893402, -0.03885989636182785, -0.02282334677875042, -0.0075302449986338615, 0.02282334677875042, -0.0038221352733671665, -0.0070923869498074055, -0.06133660674095154, 0.02532278746366501, 0.02225778065621853, -0.013026274740695953, -0.040392398834228516, -0.011293087154626846, 0.03435360640287399, 0.025924840942025185, 0.012707003392279148, 0.007986347191035748, 0.007785662077367306, -0.00437629921361804, -0.004597508814185858, -0.010225808247923851, -0.011803921312093735, -0.00883925799280405, -0.012542806565761566, -0.03831257298588753, 0.04126811400055885, -0.025760645046830177, -0.04677782952785492, 0.005482346750795841, -0.0021117525175213814, 0.04418716952204704, 0.046595387160778046, -0.037400368601083755, -0.05155777558684349, 0.03645167872309685, -0.014248628169298172, -0.01290768850594759, 0.045099373906850815, 0.05276188626885414, -0.05870945751667023, 0.031762946397066116, -0.001805023872293532, 0.05849052965641022, 0.012396854348480701, 0.005071855150163174, 0.05049962177872658, -0.03344140201807022, -0.027767494320869446, -0.00818703230470419, 0.009122041054069996, 0.026198502629995346, -0.019721852615475655, -0.007813028059899807, 0.05823511257767677, -0.011347819119691849, -0.03267515078186989, -0.0047343396581709385, -0.035904355347156525, -0.018253205344080925, 0.04590211063623428, -0.010882595553994179, 0.027293147519230843, -0.035411763936281204 ]
Research articles are being shared in increasing numbers on multiple online platforms. Although the scholarly impact of these articles has been widely studied, the online interest determined by how long the research articles are shared online remains unclear. Being cognizant of how long a research article is mentioned online could be valuable information to the researchers. In this paper, we analyzed multiple social media platforms on which users share and/or discuss scholarly articles. We built three clusters for papers, based on the number of yearly online mentions having publication dates ranging from the year 1920 to 2016. Using the online social media metrics for each of these three clusters, we built machine learning models to predict the long-term online interest in research articles. We addressed the prediction task with two different approaches: regression and classification. For the regression approach, the Multi-Layer Perceptron model performed best, and for the classification approach, the tree-based models performed better than other models. We found that old articles are most evident in the contexts of economics and industry (i.e., patents). In contrast, recently published articles are most evident in research platforms (i.e., Mendeley) followed by social media platforms (i.e., Twitter).
[ -0.015220616944134235, -0.015513160265982151, -0.038481999188661575, -0.04276149347424507, 0.016909010708332062, -0.0044424813240766525, -0.0174355898052454, 0.02415573038160801, 0.009102280251681805, 0.042560890316963196, 0.02694742940366268, -0.05135391280055046, 0.013966859318315983, -0.02771640196442604, -0.02228345163166523, -0.009595424868166447, 0.0032158882822841406, -0.030892586335539818, 0.04456690326333046, -0.00714641809463501, -0.022835105657577515, -0.05763941630721092, -0.023938411846756935, -0.009779308922588825, 0.025392770767211914, 0.014134027063846588, -0.007242539897561073, -0.021029694005846977, -0.05666984245181084, 0.02841850556433201, 0.029388077557086945, 0.026295475661754608, 0.027231615036725998, -0.08238023519515991, -0.052356917411088943, -0.03834826499223709, 0.07856880873441696, -0.025810690596699715, 0.05342679098248482, -0.0044006891548633575, 0.011108292266726494, 0.036175087094306946, 0.022417185828089714, -0.04266119375824928, -0.011175159364938736, -0.06332311779260635, -0.005374440923333168, -0.036007918417453766, 0.012211599387228489, -0.03597448393702507, 0.0005048986058682203, -0.021731797605752945, 0.02007683925330639, -0.03774646297097206, -0.06191890686750412, 0.0060974410735070705, 0.011016350239515305, 0.012729818932712078, 0.05229004845023155, 0.041457585990428925, 0.04667321592569351, 0.044700637459754944, 0.014811056666076183, -0.022383753210306168, 0.011325609870254993, 0.0070879096165299416, -0.04617171362042427, -0.00639834301546216, -0.010322604328393936, -0.02407214604318142, -0.042828358709812164, 0.021664930507540703, 0.04386479780077934, 0.003378876717761159, -0.032363664358854294, -0.011200234293937683, 0.00824554543942213, 0.020478039979934692, -0.07174836844205856, 0.011751888319849968, 0.018990248441696167, 0.02738206647336483, -0.03470401093363762, 0.021046411246061325, 0.029070459306240082, -0.013548940420150757, 0.04473407194018364, -0.06666646897792816, 0.023119289427995682, -0.0077607594430446625, -0.04356389865279198, 0.021029694005846977, 0.0374455600976944, 0.005286677740514278, 0.028268054127693176, 0.010807390324771404, 0.057873450219631195, 0.022667936980724335, -0.02484111674129963, -0.009436615742743015, 0.01947503536939621, -0.028435222804546356, 0.032196495682001114, -0.03707779198884964, 0.02577725611627102, -0.0739549845457077, -0.06188547611236572, 0.0314776748418808, 0.015964513644576073, 0.11962518841028214, -0.006766112055629492, -0.013039079494774342, -0.015020015649497509, -0.0416916199028492, -0.029154043644666672, 0.04062174633145332, -0.024640515446662903, -0.048010557889938354, 0.038749467581510544, 0.055499669164419174, 0.025392770767211914, 0.0011764426017180085, 0.03463714197278023, 0.02983943000435829, 0.004939804784953594, 0.020461324602365494, -0.03821453079581261, 0.008592418394982815, 0.052256617695093155, 0.0015306291170418262, -0.034018624573946, -0.003044541459530592, -0.04891326278448105, -0.026930714026093483, 0.009110638871788979, 0.026562944054603577, 0.08879946917295456, 0.042126256972551346, 0.026763545349240303, -0.024623800069093704, 0.01972578652203083, -0.04981596767902374, -0.03480431064963341, -0.0221162848174572, 0.016466015949845314, -0.013782975263893604, -0.04797712340950966, 0.03614165261387825, -0.03207947686314583, -0.0005354589666239917, -0.014384779147803783, 0.048177726566791534, -0.00575892673805356, 0.01700095273554325, 0.020946109667420387, 0.0007856881129555404, -0.006899845786392689, -0.023487059399485588, 0.002513783983886242, -0.010088569484651089, -0.010464697144925594, 0.02457364834845066, 0.018304860219359398, 0.018756214529275894, 0.03139409050345421, -0.014760905876755714, -0.020093554630875587, 0.0036526138428598642, -0.014877923764288425, 0.05088584125041962, -0.011450986377894878, -0.04466720297932625, -0.04416570067405701, 0.03410220518708229, 0.006377446930855513, 0.02209956757724285, 0.007932106032967567, -0.025626804679632187, -0.026395777240395546, 0.010707089677453041, -0.052156317979097366, 0.07602786272764206, 0.003247232176363468, -0.026462644338607788, 0.03614165261387825, 0.04152445122599602, 0.1513870507478714, 0.05994632840156555, 0.0009674829198047519, 0.005541608668863773, -0.04343016445636749, -0.02450678125023842, 0.05921079218387604, 0.038481999188661575, -0.015170467086136341, 0.0009758413070812821, -0.012136373668909073, 0.009561991319060326, -0.03697749227285385, 0.004977417644113302, -0.02923762798309326, -0.08806393295526505, 0.013874917291104794, 0.012479066848754883, 0.022768238559365273, 0.003604553174227476, 0.03383473679423332, -0.022935405373573303, -0.011693378910422325, 0.02280167117714882, 0.0075852335430681705, -0.02654622681438923, -0.07917061448097229, 0.013808050192892551, 0.0022003445774316788, 0.02499156817793846, 0.04643918201327324, 0.025559937581419945, -0.0016842143377289176, -0.015788987278938293, 0.0007156866486184299, -0.012529217638075352, 0.008462863974273205, 0.008387638255953789, -0.02592770755290985, 0.008701077662408352, -0.010272453539073467, 0.012930420227348804, 0.0051069725304841995, -0.020026687532663345, 0.08853200078010559, -0.020895959809422493, -0.019792653620243073, 0.06255414336919785, -0.012537576258182526, -0.004055905621498823, 0.006703423801809549, -0.026379060000181198, -0.017067819833755493, -0.034018624573946, 0.010966199450194836, -0.022751521319150925, -0.006761932745575905, 0.004701591096818447, -0.029404794797301292, -0.0323302298784256, 0.04042114317417145, -0.00790285225957632, 0.03624195232987404, 0.05436293035745621, 0.0174355898052454, -0.06940802186727524, -0.0015922721941024065, 0.055399369448423386, -0.00039754563476890326, 0.00790703110396862, 0.05426263064146042, -0.0033663392532616854, -0.04185878857970238, -0.03724496066570282, 0.046472616493701935, -0.022567637264728546, -0.03751242905855179, 0.06947489082813263, -0.015671970322728157, 0.04657291620969772, 0.06827127933502197, 0.0075517999939620495, 0.05810748413205147, 0.02611159160733223, -0.013498790562152863, -0.03724496066570282, 0.023420192301273346, -0.03844856470823288, -0.07255077362060547, 0.0078694187104702, 0.015705402940511703, -0.04072204604744911, -0.03433624282479286, 0.048512060195207596, -0.03460371121764183, 0.02373781055212021, 0.021364029496908188, 0.06412552297115326, -0.04032084345817566, -0.009277806617319584, -0.05085240676999092, -0.0357404500246048, -0.02373781055212021, -0.020695358514785767, -0.01632392406463623, -0.0705447643995285, -0.007865238934755325, 0.01634064130485058, 0.005261602811515331, -0.03309920057654381, -0.0024782607797533274, 0.08465371280908585, 0.025810690596699715, -0.0015473458915948868, -0.05509846657514572, 0.007392990868538618, 0.03415235877037048, -0.0053577241487801075, -0.010999632999300957, -0.03784676268696785, 0.059311091899871826, 0.05927766114473343, -0.053961727768182755, -0.04750905558466911, -0.03971904143691063, 0.012169807218015194, -0.005006671883165836, 0.030223917216062546, 0.04821115732192993, 0.046639781445264816, 0.041123248636722565, -0.003999486565589905, 0.023854827508330345, -0.06927428394556046, 0.06753574311733246, -0.011133367195725441, -0.050551507622003555, 0.06435955315828323, -0.07863567769527435, -0.014092235825955868, -0.013891634531319141, 0.05894332379102707, -0.010982916690409184, 0.01776992529630661, 0.00542459124699235, -0.04363076388835907, -0.006565510760992765, 0.024289464578032494, 0.0620860755443573, -0.003890827763825655, -0.016374073922634125, 0.03888320177793503, -0.010932765901088715, -0.02542620338499546, -0.014209252782166004, -0.08752899616956711, 0.007622846402227879, -0.008742869831621647, 0.014209252782166004, -0.04516870528459549, -0.01812097616493702, 0.03197917714715004, 0.02286853827536106, 0.00011695207649609074, 0.0008165096514858305, -0.0024636336602270603, -0.010782315395772457, 0.027783269062638283, -0.0042544174939394, 0.025108585134148598, -0.018940098583698273, -0.03348368778824806, 0.007008505053818226, -0.001579734613187611, -0.03251411393284798, -0.06265444308519363, -0.0007391945691779256, 0.0025388591457158327, -0.06669990718364716, -0.020795660093426704, 0.0077649387530982494, 0.040956079959869385, 0.036007918417453766, 0.0038406774401664734, -0.014986582100391388, -0.0011388298589736223, -0.020778942853212357, 0.007769118063151836, 0.019157415255904198, 0.038816336542367935, 0.04353046417236328, 0.01887323148548603, -0.0026161742862313986, 0.02261778712272644, -0.008575702086091042, 0.03079228661954403, 0.02074550837278366, 0.00947840791195631, -0.045703642070293427, -0.005136226769536734, -0.013590732589364052, 0.0061016203835606575, 0.016198547556996346, 0.030725419521331787, 0.012988928705453873, 0.00181272451300174, 0.017301855608820915, -0.035941049456596375, 0.02711459808051586, 0.014468362554907799, 0.04924760013818741, 0.003615000983700156, -0.016181832179427147, 0.0006927010836079717, -0.035238947719335556, 0.0022839284501969814, 0.01054828055202961, 0.042828358709812164, 0.024272747337818146, -0.019157415255904198, -0.023018989711999893, -0.05717134475708008, -0.01501165796071291, 0.025894273072481155, -0.031059755012392998, 0.019943105056881905, 0.014944790862500668, -0.006536256056278944, -0.028535522520542145, 0.010748881846666336, -0.01735200546681881, 0.032012611627578735, 0.008262262679636478, 0.034135639667510986, -0.03249739855527878, 0.009938118979334831, 0.015095241367816925, -0.01674184389412403, -0.042995527386665344, 0.011375760659575462, 0.0391172356903553, -0.07810074090957642, 0.011994280852377415, -0.00682462053373456, 0.012403842061758041, 0.03804736211895943, 0.06435955315828323, -0.028100887313485146, 0.04135728254914284, -0.022500770166516304, -0.0016392880352213979, -0.017836790531873703, -0.02186553180217743, -0.022751521319150925, -0.01972578652203083, -0.020461324602365494, 0.0041541168466210365, 0.017134686931967735, -0.0407889150083065, -0.01607317291200161, -0.032614413648843765, -0.025710389018058777, -0.025793973356485367, -0.04824459180235863, -0.02627875842154026, 0.053527090698480606, -0.017059462144970894, -0.02771640196442604, 0.03182872757315636, 0.008960187435150146, 0.00026799069019034505, -0.04058831185102463, 0.0884651392698288, 0.0075517999939620495, 0.010748881846666336, 0.039919640868902206, 0.031845442950725555, -0.0008535999804735184, -0.03334995359182358, 0.018505461513996124, 0.011559644713997841, -0.05342679098248482, 0.0028920008335262537, 0.0030299141071736813, -0.0029567782767117023, 0.004137400072067976, -0.05155451223254204, -0.019006965681910515, 0.06048126518726349, 0.0001935488253366202, 0.017285138368606567, 0.005207273177802563, 0.039685606956481934, 0.00435889745131135, -0.023938411846756935, 0.05085240676999092, 0.01054828055202961, 0.030073465779423714, -0.051253609359264374, 0.020628491416573524, -0.06452672183513641, -0.0004787786747328937, 0.024857833981513977, 0.020126989111304283, -0.07602786272764206, 0.05168824642896652, 0.006862233392894268, -0.04159132018685341, -0.004517706576734781, 0.018321577459573746, -0.033132635056972504, 0.005771464202553034, 0.05503160133957863, -0.014769264496862888, 0.02686384692788124, -0.031862158328294754, -0.006937458645552397, 0.06880621612071991, -0.016399148851633072, 0.023336607962846756, 0.021113278344273567, -0.013791333884000778, -0.03027406707406044, 0.04015367850661278, -0.019943105056881905, 0.02474081702530384, -0.02067864127457142, 0.008993620984256268, 0.004852042067795992, 0.07696399837732315, 0.019675636664032936, 0.06646586954593658, 0.025559937581419945, 0.0033287263941019773, 0.02694742940366268, 0.001663318369537592, -0.012219957076013088, 0.03216306120157242, -0.021832099184393883, 0.0331827849149704, -0.020177138969302177, -0.011116650886833668, 0.05426263064146042, -0.025325903668999672, -0.05901019275188446, 0.02900359220802784, -0.032112911343574524, -0.007326123770326376, -0.023169441148638725, -0.01143426913768053, -0.003966053016483784, 0.04182535409927368, 0.00991304311901331, -0.03838169947266579, -0.00767299672588706, 0.03045795112848282, -0.008701077662408352, -0.00287946336902678, 0.011116650886833668, 0.03527238219976425, 0.014869565144181252, -0.025493070483207703, 0.005692059639841318, -0.02662981115281582, -0.018739497289061546, 0.0099966274574399, 0.08532238751649857, -0.046305447816848755, -0.054463230073451996, -0.00149301637429744, 0.04296209290623665, -0.0013916708994656801, -0.006364909466356039, 0.04493467137217522, -0.012512500397861004, -0.0023403475061059, -0.033717721700668335, -0.010857541114091873, -0.010623506270349026, -0.058207787573337555, -0.02082909271121025, 0.02992301434278488, -0.0051153311505913734, 0.029454944655299187, 0.01003006100654602, -0.03614165261387825, -0.04363076388835907, 0.005328469909727573, -0.02892000786960125, 0.03311591595411301, 0.04841176047921181, -0.03079228661954403, 0.01922428235411644, -0.0010134540498256683, 0.03463714197278023, 0.023838110268115997, 0.03520551323890686, -0.0016486912500113249, -0.016549600288271904, -0.006649094633758068, 0.018672630190849304, -0.0331493504345417, -0.016114965081214905, -0.0005934452638030052, 0.004429943393915892, 0.03324965015053749, -0.029906297102570534, -0.03493804484605789, -0.04015367850661278, 0.03411892428994179, -0.020260723307728767, 0.00863421056419611, 0.03467057645320892, -0.05051807314157486, 0.0014188357163220644, 0.038147665560245514, 0.025626804679632187, 0.008395996876060963, -0.025994574651122093, -0.01649109087884426, 0.04429943487048149, -0.008500476367771626, 0.02320287376642227, 0.03289860114455223, 0.019709069281816483, -0.013264755718410015, 0.04032084345817566, 0.005019209813326597, 0.026395777240395546, 0.0006958354497328401, 0.07087909430265427, 0.04483437165617943, -0.06429269164800644, 0.0011952489148825407, 0.0036129115615040064, -0.01386655867099762, 0.03226336091756821, 0.03971904143691063, -0.03961874172091484, 0.03851543366909027, -0.014276119880378246, 0.029471661895513535, 0.015964513644576073, -0.0391172356903553, -0.03136065602302551, 0.02492470107972622, 0.02161478064954281, -0.014902998693287373, -0.013925068080425262, -0.00672014057636261, 0.045469608157873154, 0.01912398263812065, -0.017067819833755493, -0.01863919571042061, -0.04132385179400444, 0.003213798627257347, 0.002591099124401808, 0.07529232650995255, 0.01037275418639183, 0.012571009807288647, -0.01504509150981903, -0.015521518886089325, 0.05028403922915459, 0.013089229352772236, -0.005412053782492876, 0.004206356592476368, 0.018756214529275894, 0.032530829310417175, -0.024005278944969177, -0.010531564243137836, 0.035238947719335556, 0.01045633852481842, 0.015412860549986362, 0.013665957376360893, 0.024021996185183525, -0.01895681582391262, -0.007927927188575268, -0.008074198849499226, 0.011659945361316204, -0.020895959809422493, -0.01634064130485058, 0.022266734391450882, -0.009595424868166447, 0.027933718636631966, 0.01982608623802662, -0.027917003259062767, -0.02983943000435829, 0.005662804935127497, 0.030324216932058334, -0.014008651487529278, -0.0112754600122571, -0.0010865898802876472, 0.00426904484629631, -0.018171126022934914, -0.00990468543022871, -0.03480431064963341, -0.004114414565265179, 0.016566317528486252, -0.04262775927782059, -0.006937458645552397, 0.01810425892472267, 0.0127632524818182, -0.037713028490543365, -0.012487425468862057, -0.003205440239980817, 0.0013133110478520393, 0.013298189267516136, -0.008404355496168137, 0.03630882129073143, -0.00025349410134367645, -0.050317469984292984, 0.0022254197392612696, 0.03281501680612564, 0.006904025096446276, 0.00875122845172882, 0.007881956174969673, 0.007154776714742184, 0.051320478320121765, -0.02041117288172245, 0.012704744003713131, -0.0032702176831662655, -0.025158734992146492, -0.044867806136608124, -0.01625705696642399, -0.027331914752721786, 0.04038771241903305, -0.05927766114473343, 0.018555613234639168, 0.008266441524028778, -0.02457364834845066, 0.008943471126258373, 0.024958133697509766, -0.002720654010772705, 0.04964880272746086, 0.019742503762245178, -0.01870606280863285, 0.02313600666821003, -0.06365745514631271, -0.027148030698299408, 0.013156096450984478, -0.010180511511862278, -0.006511181127279997, -0.021648215129971504, 0.0036526138428598642, 0.042059388011693954, -0.026395777240395546, -0.004089339170604944, -0.008053302764892578, 0.012880269438028336, 0.048010557889938354, -0.010782315395772457, 0.034235939383506775, -0.028251338750123978, -0.0024239313788712025, 0.005098614376038313, 0.001566152204759419, 0.00694999611005187, -0.02006012201309204, -0.0357404500246048, 0.017803357914090157, 0.00035941050737164915, -0.02413901314139366, 0.0019736234098672867, 0.005591758992522955, 0.0020509385503828526, 0.008976904675364494, 0.05045120418071747, -0.04523557424545288, -0.05743881314992905, -0.02892000786960125, 0.02550978772342205, 0.0276495348662138, 0.029739130288362503, 0.03734526038169861, -0.033801306039094925, 0.02405542880296707, 0.018772929906845093, -0.013273113407194614, 0.022835105657577515, 0.06359058618545532, -0.06867248564958572, 0.020862527191638947, -0.027515800669789314, -0.022049417719244957, -0.011158443056046963, -0.028000585734844208, 0.041892219334840775, 0.020695358514785767, 0.00021170219406485558, 0.0043714349158108234, 0.024189162999391556, -0.011125009506940842, -0.01997653767466545, 0.0073052276857197285, -0.05924422666430473, -0.00491055054590106, -0.006590585689991713, 0.057271648198366165, -0.01343192346394062, 0.02823462150990963, 0.01989295333623886, -0.0004335911653470248, 0.006540435366332531, 0.012805044651031494, -0.060514699667692184, -0.05315932258963585, 0.0015504802577197552, 0.007919568568468094, 0.0340019054710865, 0.03500491380691528, 0.03898350149393082, -0.0085046561434865, -0.01054828055202961, -0.004208446480333805, 0.021380746737122536, -0.04493467137217522, 0.01904039829969406, 0.01922428235411644, -0.017535889521241188, -0.05666984245181084, -0.022768238559365273, -0.04523557424545288, 0.024790966883301735, 0.03691062331199646, 0.031594689935445786, -0.005696238484233618, -0.028685973957180977, 0.014259402640163898, 0.01810425892472267, -0.02696414664387703, -0.03426937386393547, -0.03650942072272301, 0.007359557319432497, -0.011618154123425484, -0.013707749545574188, -0.05095271021127701, 0.023336607962846756, -0.02721489779651165, 0.0063858055509626865, -0.0112754600122571, 0.017151404172182083, 0.035071779042482376, 0.05666984245181084, 0.02321959100663662, 0.02270137146115303, 0.06817097961902618, -0.002047804184257984, 0.006114157848060131, 0.005065180826932192, 0.028000585734844208, -0.0285020899027586, 0.024774249643087387, -0.0073428405448794365, 0.02688056230545044, 0.0060681868344545364, 0.0013091318542137742, 0.01033932063728571, -0.03395175561308861, -0.001159725827164948, 0.012729818932712078, -0.005269960965961218, -0.000933004601392895, 0.03767959401011467, 0.03460371121764183, 0.009954835288226604, 0.05596774071455002, 0.02186553180217743, -0.005503995809704065, -0.0015671970322728157, -0.017920374870300293, 0.00960378348827362, 0.0074765742756426334, 0.01471075601875782, -0.011618154123425484, 0.0748911201953888, -0.011559644713997841, -0.02271808683872223, 0.010531564243137836, -0.0077983723022043705, -0.041022948920726776, -0.0110581424087286, -0.0026997579261660576, 0.0323135107755661, -0.06920742243528366, 0.006001319736242294, 0.03707779198884964, -0.003706943243741989, 0.023754527792334557, 0.0451018400490284, 0.018154410645365715, 0.0008055392536334693, 0.027866851538419724, 0.033717721700668335, -0.02992301434278488, 0.026512794196605682, 0.009378107264637947, 0.039518438279628754, -0.027532516047358513, 0.0225509200245142, -0.010063494555652142, -0.03801393136382103, 0.00544130802154541, -0.035172078758478165, 0.014936432242393494, -0.011484419927001, -0.0165830347687006, 0.01195248868316412, -0.037044357508420944, 0.0036526138428598642, -0.003485446097329259, -0.02280167117714882, 0.03537268191576004, -0.023269740864634514, -0.007041938602924347, -0.004726666025817394, 0.028853140771389008, 0.025108585134148598, -0.06626527011394501, 0.004296209197491407, -0.022082850337028503, 0.0020645209588110447, -0.019926387816667557, 0.04319612681865692, -0.015178825706243515, -0.0002988122287206352, 0.0017291406402364373, 0.005341007374227047, -0.011509494855999947, 0.08137722313404083, 0.06445986032485962, -0.022667936980724335, -0.044767506420612335, -0.0110581424087286, 0.0015160018811002374, 0.0501503050327301, 0.0038344087079167366, -0.02985614724457264, 0.05118674412369728, -0.053025588393211365, 0.07769953459501266, 0.00448427302762866, 0.02413901314139366, -0.023587359115481377, -0.021915683522820473, 0.005002493038773537, 0.0014867475256323814, 0.0178702250123024, 0.001614212873391807, -0.000032029587600845844, -0.022133000195026398, 0.004881296306848526, 0.025543222203850746, -0.015697045251727104, -0.058040618896484375, -0.03684375807642937, 0.025827405974268913, 0.00013105684774927795, 0.03684375807642937, -0.03945157304406166, -0.019240999594330788, 0.05901019275188446, 0.04266119375824928, 0.003915902692824602, 0.024640515446662903, 0.010381112806499004, 0.004091429058462381, -0.03187887743115425, 0.022216584533452988, -0.02201598323881626, 0.008521372452378273, -0.017385438084602356, 0.011726812459528446, -0.0012318168301135302, 0.029538528993725777, 0.037813328206539154, 0.017669623717665672, -0.0004187028098385781, -0.008784662000834942, -0.03256426379084587, 0.0027917001862078905, 0.01292206160724163, -0.019240999594330788, -0.015036732889711857, 0.00040485922363586724, 0.006389984395354986, 0.0006660587387159467, -0.03164484351873398, 0.02490798383951187, 0.01641586609184742, 0.03156125918030739, -0.0031573795713484287, -0.02373781055212021, 0.019291149452328682, 0.03884976729750633, 0.01624869927763939, 0.000325193366734311, -0.017059462144970894, -0.0029442408122122288, 0.0016737664118409157, -0.04436630383133888, 0.0216983649879694, -0.02499156817793846, -0.023620793595910072, 0.053025588393211365, -0.009871251881122589, 0.01462717168033123, 0.04329643025994301, -0.028635824099183083, -0.05713791400194168, -0.0005495637306012213, 0.0019349658396095037, -0.03443654254078865, 0.0029442408122122288, 0.01905711553990841, -0.052758120000362396, 0.0007830761023797095, 0.002434379421174526, 0.012144732289016247, 0.01699259504675865, 0.00673685735091567, 0.00767717557027936, 0.01206950657069683, -0.00909392163157463, 0.026930714026093483, 0.023687660694122314, 0.01461881399154663, -0.04058831185102463, 0.03238037973642349, 0.0010458427714183927, 0.0017698878655210137, -0.03503834456205368, -0.03450340777635574, 0.006147591397166252, -0.08144409209489822, 0.023420192301273346, -0.02236703597009182, -0.002716474700719118, -0.008793019689619541 ]
In recent years, reinforcement learning and its multi-agent analogue have achieved great success in solving various complex control problems. However, multi-agent reinforcement learning remains challenging both in its theoretical analysis and empirical design of algorithms, especially for large swarms of embodied robotic agents where a definitive toolchain remains part of active research. We use emerging state-of-the-art mean-field control techniques in order to convert many-agent swarm control into more classical single-agent control of distributions. This allows profiting from advances in single-agent reinforcement learning at the cost of assuming weak interaction between agents. However, the mean-field model is violated by the nature of real systems with embodied, physically colliding agents. Thus, we combine collision avoidance and learning of mean-field control into a unified framework for tractably designing intelligent robotic swarm behavior. On the theoretical side, we provide novel approximation guarantees for general mean-field control both in continuous spaces and with collision avoidance. On the practical side, we show that our approach outperforms multi-agent reinforcement learning and allows for decentralized open-loop application while avoiding collisions, both in simulation and real UAV swarms. Overall, we propose a framework for the design of swarm behavior that is both mathematically well-founded and practically useful, enabling the solution of otherwise intractable swarm problems.
[ -0.011759134009480476, -0.024790938943624496, -0.03131119906902313, -0.040899816900491714, 0.019839724525809288, 0.018462449312210083, -0.04529314860701561, 0.023082420229911804, -0.06377303600311279, 0.01254365686327219, 0.0011495446087792516, 0.024145886301994324, 0.03511177748441696, -0.042957011610269547, 0.01448753196746111, 0.07140906155109406, -0.012386752292513847, 0.006463600788265467, -0.02934117428958416, -0.036820296198129654, -0.009196356870234013, 0.019543349742889404, -0.02632511779665947, 0.05132526159286499, 0.033281225711107254, -0.005657284986227751, 0.015324356034398079, 0.007095578126609325, -0.08138122409582138, 0.05397520959377289, 0.0319213829934597, 0.01942131109535694, -0.009144055657088757, 0.02330906130373478, -0.026307683438062668, -0.03200855478644371, -0.00607133936136961, 0.004236426204442978, -0.04857071489095688, 0.06848017126321793, 0.0090830372646451, -0.0001740661246003583, -0.08612323552370071, -0.04804769903421402, 0.02198408730328083, 0.01578635349869728, -0.06373816728591919, 0.0012388931354507804, -0.03668082505464554, 0.005866491235792637, 0.020606813952326775, -0.0513949990272522, 0.01623091660439968, 0.0039051829371601343, -0.06216911971569061, -0.002639049431309104, 0.03908669948577881, 0.007867026142776012, 0.05547451972961426, 0.005591908469796181, 0.023274192586541176, -0.04511881247162819, -0.0789404883980751, -0.00219557574018836, -0.021025225520133972, -0.04128336161375046, 0.02402384951710701, -0.04581616446375847, 0.0086384741589427, -0.06000732257962227, -0.038249872624874115, -0.013118973933160305, -0.08284566551446915, -0.0585080087184906, 0.04372410103678703, 0.0036284206435084343, 0.03251413628458977, 0.044805001467466354, -0.03251413628458977, 0.025836968794465065, 0.009370695799589157, 0.016291934996843338, 0.007452972233295441, 0.009422997012734413, 0.08947053551673889, 0.014513682574033737, 0.06415657699108124, -0.061123088002204895, 0.007862667553126812, -0.028853025287389755, -0.06248292699456215, 0.05718303844332695, 0.002154170535504818, 0.017067741602659225, 0.02215842716395855, -0.02365773729979992, 0.011576077900826931, 0.006768693216145039, -0.025313954800367355, -0.027074772864580154, -0.027946466580033302, 0.02808593586087227, 0.019438745453953743, 0.000708795094396919, 0.022977817803621292, -0.011070496402680874, -0.047454945743083954, 0.03828474134206772, -0.002133467700332403, 0.18424095213413239, 0.005190929397940636, -0.04797796159982681, -0.06331975013017654, 0.028783291578292847, -0.09867560863494873, -0.037273578345775604, -0.0682360976934433, -0.03654135391116142, 0.018183508887887, -0.010625933296978474, 0.03432725742459297, 0.047385212033987045, 0.05069764330983162, -0.031415801495313644, -0.01346765086054802, -0.00465483870357275, 0.051464732736349106, 0.04501420632004738, 0.025836968794465065, 0.02676096372306347, -0.0163878221064806, -0.04159717261791229, 0.009954730048775673, 0.020798586308956146, 0.025139614939689636, -0.04194584861397743, 0.0015385374426841736, -0.04114389047026634, 0.002410230226814747, -0.015359223820269108, 0.008621039800345898, -0.048012830317020416, -0.00662922253832221, 0.025505727156996727, 0.023431098088622093, 0.001007349812425673, -0.02545342408120632, 0.01835784688591957, -0.02111239545047283, 0.00018468988128006458, -0.029027365148067474, 0.04919833317399025, -0.005997245199978352, 0.029149401932954788, 0.01392093114554882, -0.0425734668970108, 0.016431406140327454, -0.0013511235592886806, 0.03171217814087868, -0.06325002014636993, 0.061192821711301804, -0.024686334654688835, 0.017250796779990196, 0.051464732736349106, 0.06216911971569061, 0.02782442793250084, 0.02287321537733078, 0.013859912753105164, -0.06687626242637634, 0.0505233034491539, -0.04724574089050293, -0.017869699746370316, -0.013528669252991676, -0.00816340185701847, 0.045258279889822006, 0.027806995436549187, 0.025052446871995926, -0.00689073046669364, -0.003464978188276291, 0.04403791204094887, -0.09337571263313293, -0.005870849825441837, 0.02845204807817936, 0.03331609070301056, 0.048884522169828415, 0.048361506313085556, 0.03556505963206291, -0.026534324511885643, 0.05627647787332535, 0.00040751631604507565, 0.01701544038951397, 0.010224954225122929, 0.0037046936340630054, 0.008485928177833557, 0.04013272747397423, -0.06405197829008102, -0.042782675474882126, 0.024442261084914207, -0.0005578832933679223, 0.014592134393751621, -0.022018956020474434, -0.08786661922931671, -0.0070868609473109245, -0.0052475896663963795, 0.06551641970872879, 0.014688020572066307, 0.020066363736987114, -0.03964458033442497, 0.031520403921604156, -0.033368393778800964, -0.008786661550402641, -0.032130591571331024, -0.04009786248207092, -0.04864044860005379, -0.04403791204094887, -0.038598548620939255, -0.0010759956203401089, -0.03136350214481354, -0.004615612328052521, -0.03352529928088188, 0.010303406976163387, 0.012299583293497562, 0.0011152217630296946, 0.011114081367850304, -0.02304755337536335, 0.06813149899244308, 0.003979276865720749, -0.02020583488047123, -0.034780535846948624, -0.04539775103330612, -0.044003043323755264, 0.009867561049759388, -0.00811545830219984, 0.033821675926446915, 0.02526165172457695, -0.0029615757521241903, 0.03436212241649628, 0.04243399575352669, 0.05638108029961586, -0.035320986062288284, -0.0033865259028971195, -0.008206985890865326, -0.016701631247997284, -0.007422462571412325, 0.045606959611177444, 0.018322980031371117, 0.002175962785258889, 0.058821819722652435, -0.013319463469088078, -0.029742153361439705, -0.08626270294189453, -0.011471475474536419, 0.005853415932506323, 0.005334759131073952, 0.005020949523895979, 0.06705059856176376, 0.016004277393221855, -0.027719825506210327, 0.038772888481616974, -0.019090069457888603, 0.0478733591735363, 0.07119985669851303, 0.014565983787178993, 0.019804855808615685, -0.01399938389658928, -0.04361949861049652, 0.025226784870028496, 0.033664770424366, 0.007871384732425213, -0.0044892169535160065, -0.05620674043893814, -0.012909768149256706, -0.05725277215242386, 0.01825324445962906, -0.016065295785665512, -0.0288007240742445, -0.01001574844121933, 0.032793078571558, -0.009239941835403442, 0.023954113945364952, 0.009109187871217728, -0.08145096153020859, 0.07649974524974823, 0.030823051929473877, -0.013197426684200764, -0.023605436086654663, -0.04414251446723938, -0.034867703914642334, -0.06021652743220329, 0.007631668820977211, -0.010207520797848701, 0.00394440907984972, -0.030596410855650902, -0.017503587529063225, 0.028591519221663475, 0.008899982087314129, -0.006537694949656725, 0.006581279449164867, -0.0086384741589427, 0.014731605537235737, -0.0029724719934165478, -0.020502211526036263, 0.044630661606788635, 0.0013238831888884306, 0.001554881688207388, -0.0010100738145411015, 0.017224647104740143, 0.012822598218917847, -0.0177215114235878, -0.0022533254232257605, -0.03314175456762314, 0.024233054369688034, -0.025418557226657867, -0.04895425960421562, 0.00020879763178527355, 0.05069764330983162, 0.06530721485614777, -0.020990358665585518, -0.06373816728591919, -0.01719849556684494, 0.030247734859585762, 0.035408154129981995, -0.031520403921604156, 0.02011866681277752, 0.020676549524068832, -0.02906223200261593, 0.020415041595697403, -0.010974610224366188, -0.02278604544699192, -0.030108263716101646, -0.05481203272938728, 0.010931025259196758, -0.02187948487699032, -0.032217759639024734, 0.019961761310696602, 0.017529739066958427, -0.02517448365688324, 0.0011244835332036018, -0.019194671884179115, -0.006106206681579351, 0.01002446562051773, -0.05662515386939049, 0.0203801728785038, -0.005522172898054123, -0.004789950791746378, -0.009144055657088757, -0.028242841362953186, 0.039574846625328064, 0.021670278161764145, 0.006075697485357523, 0.0008210255182348192, -0.03197368606925011, -0.040028125047683716, -0.010625933296978474, 0.03584400191903114, -0.06781768798828125, 0.020449908450245857, -0.014966962859034538, -0.034274954348802567, 0.013458934612572193, 0.020850887522101402, -0.038424212485551834, -0.06216911971569061, -0.015289489179849625, -0.04846610873937607, 0.06021652743220329, -0.02048477716743946, -0.000999722513370216, 0.012343167327344418, 0.04225965961813927, 0.0018327337456867099, 0.00856002140790224, 0.025488292798399925, 0.015899673104286194, -0.022315330803394318, 0.0047594415955245495, 0.015411525964736938, -0.027859296649694443, -0.07545371353626251, 0.022385066375136375, 0.019996628165245056, 0.017956867814064026, 0.0015374479116871953, 0.014234740287065506, 0.014496248215436935, 0.05770605057477951, 0.0168411023914814, -0.02977702021598816, 0.01675393246114254, 0.04742008075118065, 0.022228162735700607, -0.02438995987176895, -0.028051069006323814, 0.0019460538169369102, 0.030439507216215134, -0.028347443789243698, 0.013615839183330536, -0.018950598314404488, 0.007740630768239498, 0.02004893124103546, 0.008093666285276413, 0.013641989789903164, 0.0025671347975730896, 0.020258136093616486, 0.01400810107588768, -0.011244835332036018, -0.012779014185070992, -0.017163628712296486, -0.018863428384065628, -0.025017578154802322, 0.004077342338860035, -0.02428535744547844, 0.023099854588508606, -0.002432022476568818, -0.0004745276819448918, 0.028434613719582558, -0.0033233282156288624, 0.008838963694870472, -0.015943259000778198, -0.10857803374528885, -0.005905717611312866, 0.0010754507966339588, 0.019839724525809288, 0.040376801043748856, -0.023099854588508606, 0.027876731008291245, 0.02170514687895775, -0.033560167998075485, -0.04299188032746315, -0.00979782547801733, 0.03554762527346611, 0.06896831840276718, 0.01236060168594122, -0.10132554918527603, -0.003591373562812805, -0.016710348427295685, 0.021844618022441864, 0.009867561049759388, 0.010547480545938015, -0.05094171687960625, -0.018026603385806084, -0.002647766377776861, -0.01827067695558071, -0.002314344048500061, 0.025662630796432495, -0.038877490907907486, 0.00101388746406883, -0.01276157982647419, 0.02472120337188244, 0.027859296649694443, -0.026708662509918213, 0.006328488700091839, -0.07984704524278641, -0.023814642801880836, 0.028783291578292847, -0.015673033893108368, 0.05265023559331894, -0.043480027467012405, 0.0022032030392438173, -0.03040463849902153, 0.037970930337905884, -0.0046591972932219505, 0.014130137860774994, -0.02519191801548004, 0.00979782547801733, 0.051918014883995056, 0.0029899056535214186, 0.003966201562434435, 0.005116835702210665, 0.02480837143957615, 0.0203801728785038, -0.06429605185985565, 0.023866944015026093, -0.020676549524068832, -0.026081044226884842, 0.009370695799589157, -0.015899673104286194, -0.077964186668396, -0.012918484397232533, -0.04550235718488693, 0.04483987018465996, 0.039923522621393204, 0.02233276516199112, -0.04009786248207092, -0.0026586626190692186, -0.009466581977903843, -0.012160112150013447, 0.01370300818234682, -0.005169137381017208, -0.02287321537733078, -0.014531116001307964, -0.049058862030506134, -0.023361362516880035, -0.0009566826629452407, 0.011820152401924133, -0.002693530172109604, -0.0073178596794605255, -0.010704385116696358, 0.07573265582323074, 0.011314569972455502, 0.005984169896692038, -0.021060094237327576, 0.029846755787730217, 0.018619354814291, -0.024930410087108612, 0.023605436086654663, 0.03263617306947708, -0.012273432686924934, 0.020101232454180717, 0.013389199040830135, 0.050035156309604645, 0.04086495190858841, 0.03685516491532326, -0.03828474134206772, 0.03432725742459297, -0.008581814356148243, 0.03845907747745514, -0.022367633879184723, 0.010381858795881271, 0.03312432020902634, 0.004550235345959663, 0.022367633879184723, 0.02482580579817295, -0.010965893045067787, 0.00882588792592287, 0.010102917440235615, -0.0007752616074867547, -0.04173664376139641, 0.08828502893447876, -0.01665804535150528, -0.0301431305706501, 0.005522172898054123, -0.10062819719314575, -0.05247589573264122, -0.023622870445251465, -0.05505610629916191, 0.03884262219071388, 0.019892025738954544, 0.029899057000875473, -0.00558319129049778, -0.012717995792627335, 0.0717577412724495, -0.0003500390739645809, 0.04309648275375366, -0.01027725636959076, -0.006088773254305124, 0.03003852814435959, -0.009170206263661385, -0.032932545989751816, 0.0037046936340630054, 0.008873830549418926, 0.023605436086654663, -0.018828561529517174, -0.012779014185070992, -0.03953997790813446, -0.03591373562812805, 0.037273578345775604, 0.022018956020474434, -0.03490257263183594, -0.06527234613895416, 0.02649945579469204, 0.019735122099518776, 0.018410148099064827, -0.008411834016442299, -0.016361670568585396, -0.021844618022441864, -0.00487276166677475, 0.03392627835273743, 0.008089307695627213, 0.013877347111701965, 0.0024712486192584038, -0.019630517810583115, -0.010660801082849503, -0.014173721894621849, 0.020014062523841858, -0.015184885822236538, -0.001605004072189331, 0.03587887063622475, 0.025122182443737984, -0.011079213581979275, -0.0097542405128479, -0.021391337737441063, 0.019804855808615685, 0.032827943563461304, 0.023988980799913406, 0.018567053601145744, -0.005535248201340437, 0.0015581506304442883, -0.00766653660684824, -0.030265167355537415, -0.005557040683925152, 0.02074628509581089, -0.03164244443178177, 0.009736807085573673, 0.010076766833662987, -0.050035156309604645, -0.006498468574136496, -0.020153533667325974, 0.03361246734857559, -0.03500717505812645, -0.022908082231879234, 0.030195433646440506, 0.02808593586087227, 0.0024908618070185184, -0.01613503135740757, 0.007099936716258526, 0.029742153361439705, 0.01746872067451477, 0.004572027828544378, 0.003375629661604762, 0.004633046220988035, 0.0015363582642748952, 0.003861598437651992, -0.026359984651207924, 0.0068166363053023815, 0.014993113465607166, 0.0372038409113884, -0.021827183663845062, 0.022001521661877632, -0.013580971397459507, 0.01702415756881237, -0.003369092009961605, -0.00520836329087615, -0.014583418145775795, 0.006023396272212267, 0.004911988042294979, 0.009911145083606243, 0.01630065217614174, 0.03308945149183273, 0.022106125950813293, -0.008921774104237556, 0.03551275655627251, -0.005081967916339636, -0.014592134393751621, 0.020850887522101402, -0.01656216010451317, 0.02597643993794918, 0.03485027328133583, -0.0012890155194327235, -0.044909603893756866, -0.014016817323863506, 0.010163935832679272, 0.002110585803166032, -0.001006804988719523, -0.011462758295238018, 0.03127633035182953, -0.012003207579255104, -0.014993113465607166, 0.046757593750953674, 0.00777549808844924, 0.023117288947105408, 0.013659423217177391, 0.007644744589924812, 0.06157636642456055, -0.012752863578498363, 0.01746000349521637, 0.0319213829934597, 0.02421562187373638, -0.03947024419903755, 0.02897506393492222, 0.041527435183525085, -0.05805473029613495, -0.006995333358645439, 0.029097100719809532, 0.00662486394867301, -0.0033516581170260906, 0.04438658803701401, 0.033106885850429535, 0.01922953873872757, 0.0664229765534401, -0.006149791646748781, 0.03570453077554703, 0.0075619337148964405, -0.03387397527694702, 0.0081982696428895, -0.03758738562464714, 0.020781151950359344, 0.027283979579806328, 0.006350280717015266, 0.005068892613053322, -0.02313472330570221, 0.018567053601145744, -0.021670278161764145, -0.024163320660591125, -0.02979445457458496, -0.014914660714566708, -0.0003099956957157701, 0.030422072857618332, -0.024041282013058662, -0.015847371891140938, -0.052162088453769684, -0.015829937532544136, 0.00607133936136961, 0.017250796779990196, -0.004460887052118778, 0.03615780919790268, -0.03525124862790108, -0.04142283275723457, 0.0638427659869194, -0.013833762146532536, -0.030334902927279472, -0.027876731008291245, -0.024790938943624496, 0.03539071977138519, 0.03626241534948349, -0.006912522483617067, 0.012421620078384876, 0.027981333434581757, 0.022106125950813293, 0.014740322716534138, 0.0046722725965082645, -0.0007469316478818655, -0.02623794786632061, 0.044456325471401215, 0.044735267758369446, -0.013162558898329735, 0.023866944015026093, -0.034867703914642334, -0.02526165172457695, 0.027057338505983353, 0.011907321400940418, -0.01834041252732277, 0.014722888357937336, -0.03591373562812805, -0.023256760090589523, -0.003194753546267748, -0.004955572541803122, -0.01825324445962906, 0.016108879819512367, -0.012491355650126934, 0.0261507797986269, -0.022280463948845863, -0.01555099617689848, 0.024616599082946777, -0.010094200260937214, 0.03155527263879776, 0.03206085413694382, 0.007867026142776012, -0.00766653660684824, 0.0003249779110774398, 0.05097658559679985, -0.0029288872610777617, 0.04386357218027115, -0.022053822875022888, -0.0026695586275309324, -0.003423572750762105, -0.061925046145915985, 0.028591519221663475, -0.02411101758480072, -0.004619970917701721, 0.023971548303961754, -0.015315639786422253, 0.038598548620939255, 0.008721284568309784, -0.028469480574131012, 0.038075532764196396, 0.02480837143957615, 0.01090487465262413, 0.010312124155461788, 0.015036697499454021, 0.036750562489032745, 0.05212721973657608, 0.0016834563575685024, 0.027632655575871468, 0.023866944015026093, -0.02004893124103546, -0.033560167998075485, 0.03570453077554703, 0.039749182760715485, -0.011924754828214645, 0.032793078571558, -0.025558028370141983, -0.003007339546456933, -0.0381452701985836, -0.0016714705852791667, -0.030875353142619133, -0.01889829710125923, -0.013537386432290077, -0.03050924278795719, 0.027423450723290443, -0.02306498773396015, 0.029393475502729416, -0.025836968794465065, 0.03469336777925491, 0.004471783060580492, 0.012927201576530933, -0.034606195986270905, -0.0212867334485054, -0.00307053723372519, 0.036924898624420166, -0.002235891530290246, -0.02758035436272621, -0.022210728377103806, 0.01975255459547043, 0.05366139858961105, -0.01809633895754814, -0.048187170177698135, 0.012255998328328133, -0.0019318887498229742, -0.016858534887433052, -0.011671964079141617, -0.0054916637018322945, -0.027266545221209526, 0.04288727790117264, -0.03661109134554863, 0.010469028726220131, 0.019700253382325172, -0.01399938389658928, 0.019055200740695, 0.02118213102221489, 0.018218375742435455, 0.025418557226657867, 0.0049642897211015224, 0.04602536931633949, 0.018671656027436256, -0.026534324511885643, -0.00003422074587433599, 0.04327082261443138, 0.01046031154692173, -0.02996879257261753, -0.017224647104740143, -0.0629362091422081, 0.00580983143299818, 0.007993421517312527, -0.06802689284086227, -0.005975453183054924, -0.0025714931543916464, -0.03342069685459137, 0.04138796776533127, 0.01712004281580448, -0.013641989789903164, 0.042155057191848755, -0.03615780919790268, -0.02606360986828804, -0.01879369281232357, 0.013441500253975391, 0.01746872067451477, 0.028225407004356384, -0.020885756239295006, -0.005025308113545179, 0.00978910829871893, -0.002132378052920103, -0.00432141637429595, -0.0014611748047173023, -0.02022326923906803, 0.025035012513399124, 0.016074012964963913, 0.01461828500032425, -0.0407603457570076, -0.03464106470346451, -0.0023535701911896467, 0.019630517810583115, 0.077964186668396, -0.007365802768617868, -0.0001923171803355217, -0.0010939742205664515, 0.04728060960769653, 0.05223182216286659, -0.03392627835273743, 0.019456179812550545, -0.0037046936340630054, 0.03307201713323593, 0.03919130191206932, 0.03518151491880417, 0.03640188276767731, 0.007801649160683155, -0.04682732746005058, -0.03664596006274223, -0.03866828605532646, -0.07119985669851303, 0.02773725986480713, 0.012003207579255104, -0.014653152786195278, 0.02578466758131981, -0.009553750976920128, 0.01259595900774002, -0.0051865712739527225, 0.008019572123885155, -0.01889829710125923, -0.008241853676736355, 0.006899447180330753, -0.011079213581979275, 0.03776172548532486, -0.023187024518847466, 0.030003661289811134, -0.03765712305903435, 0.00031571617000736296, -0.0319388173520565, -0.012639543041586876, 0.000791605853009969, -0.0088607557117939, 0.031781911849975586, -0.0655512884259224, -0.029724719002842903, 0.00520836329087615, 0.027702391147613525, -0.04619970917701721, 0.007692687679082155, 0.0014557266840711236, 0.006202092859894037, -0.009553750976920128, -0.017712794244289398, -0.001784790656529367, 0.006698958110064268, 0.011541210114955902, 0.022053822875022888, 0.021077528595924377, -0.010634650476276875, 0.05547451972961426, 0.006489751860499382, -0.017669210210442543, -0.0425386019051075, 0.009832693263888359, -0.0208334531635046, -0.0029005571268498898, -0.004271293990314007, -0.03228749334812164, 0.00722197350114584, 0.01755588874220848, 0.04947727546095848, 0.031956251710653305, -0.025052446871995926, -0.014522398822009563, -0.006145433057099581, -0.0297072846442461, -0.008738718926906586, 0.017747661098837852, 0.009518883191049099, 0.0026652002707123756, -0.0036981559824198484, -0.027092207223176956, 0.025139614939689636, -0.0023731831461191177, -0.020101232454180717, 0.04494447261095047, -0.03251413628458977, -0.035774264484643936, 0.020449908450245857, -0.009065603837370872, 0.011950906366109848, -0.04501420632004738, -0.020816020667552948, 0.012177546508610249, -0.029585247859358788, 0.034867703914642334, -0.03845907747745514, 0.0029354249127209187, 0.01467058714479208, -0.013267162255942822, 0.014051685109734535, 0.005177854094654322, -0.031677309423685074, 0.014173721894621849, -0.015612015500664711, -0.03971431776881218, 0.0016998006030917168, -0.03424008563160896, -0.04086495190858841, 0.008490285836160183, 0.0567646250128746, -0.007108653429895639, 0.01851475238800049, -0.09198100864887238, -0.016902120783925056, -0.036367017775774, 0.03021286614239216, -0.02465146780014038, -0.03587887063622475, -0.05930996686220169, 0.05087198317050934, -0.006162866950035095, -0.03176448121666908, -0.004088238347321749, -0.05271996930241585, 0.012935918755829334, 0.029149401932954788, -0.03640188276767731, -0.02775469422340393, -0.020589379593729973, -0.05073251202702522, 0.004273473285138607, 0.0011495446087792516, 0.023204457014799118, -0.028940195217728615, 0.0005769515410065651, 0.017573323100805283, -0.02695273607969284, -0.012465205043554306, 0.045083943754434586, 0.003896465990692377, -0.03654135391116142, 0.008259288035333157, 0.016239633783698082, -0.06046060100197792, -0.023082420229911804, -0.03272334113717079, 0.01623091660439968, -0.026290249079465866, 0.022454801946878433, 0.02153080888092518, 0.011985774151980877, -0.04128336161375046, -0.02438995987176895, 0.04225965961813927, 0.015367940999567509, 0.009588618762791157, 0.013136408291757107, 0.048814788460731506, -0.02623794786632061, -0.006489751860499382, 0.00009534138371236622, 0.004606895614415407, -0.0049424972385168076, -0.02367517165839672, 0.02135646902024746, 0.019473614171147346, -0.010992043651640415, -0.01940387859940529, 0.01002446562051773, -0.055544253438711166, 0.05240616202354431, -0.057392243295907974, 0.019281841814517975, -0.02207125723361969 ]
The robustness of signal temporal logic not only assesses whether a signal adheres to a specification but also provides a measure of how much a formula is fulfilled or violated. The calculation of robustness is based on evaluating the robustness of underlying predicates. However, the robustness of predicates is usually defined in a model-free way, i.e., without including the system dynamics. Moreover, it is often nontrivial to define the robustness of complicated predicates precisely. To address these issues, we propose a notion of model predictive robustness, which provides a more systematic way of evaluating robustness compared to previous approaches by considering model-based predictions. In particular, we use Gaussian process regression to learn the robustness based on precomputed predictions so that robustness values can be efficiently computed online. We evaluate our approach for the use case of autonomous driving with predicates used in formalized traffic rules on a recorded dataset, which highlights the advantage of our approach compared to traditional approaches in terms of precision. By incorporating our robustness definitions into a trajectory planner, autonomous vehicles obey traffic rules more robustly than human drivers in the dataset.
[ -0.0033362056128680706, -0.024448387324810028, -0.03735429793596268, -0.03636441007256508, 0.06447351723909378, 0.0005789916031062603, -0.06391320377588272, 0.032572947442531586, -0.07672572880983353, -0.03729826584458351, 0.06947899609804153, 0.06159723550081253, 0.05106332525610924, 0.006672411225736141, -0.04079089313745499, 0.019517621025443077, 0.014698916114866734, -0.0024887300096452236, -0.0005460147513076663, -0.019797777757048607, -0.007629615254700184, -0.019041353836655617, -0.006700427271425724, 0.031041420996189117, -0.004076287616044283, -0.005808593239635229, 0.011682556010782719, -0.008866976015269756, -0.042210355401039124, 0.026241393759846687, 0.02060089446604252, 0.041351206600666046, -0.028239848092198372, 0.017659243196249008, -0.009343243204057217, -0.03593483567237854, 0.07392415404319763, 0.026689644902944565, -0.02784762904047966, 0.048373814672231674, -0.007115993648767471, -0.0032241428270936012, -0.010132352821528912, -0.06563150137662888, 0.008091874420642853, -0.012224193662405014, -0.02360791526734829, 0.016006316989660263, -0.02358923852443695, 0.021702846512198448, -0.046730224043130875, -0.04433955252170563, 0.03993174433708191, -0.006541671231389046, -0.01818220503628254, -0.04590843245387077, 0.03840021789073944, 0.026409488171339035, 0.031788505613803864, -0.007382142823189497, -0.00469730282202363, 0.02566240169107914, -0.04385394603013992, 0.011729249730706215, 0.036700598895549774, -0.0430695042014122, 0.04934502765536308, -0.02250596322119236, -0.008801606483757496, -0.008451409637928009, -0.030014177784323692, -0.019536297768354416, -0.02441103383898735, -0.007013269234448671, 0.016744064167141914, 0.054126378148794174, 0.004720649216324091, 0.03742900490760803, 0.009179818443953991, 0.007452182471752167, 0.02784762904047966, 0.045759014785289764, -0.07186967134475708, 0.01987248659133911, 0.02002190425992012, -0.06021512672305107, 0.07948994636535645, -0.0504656545817852, 0.059318624436855316, -0.018630456179380417, -0.01330746803432703, -0.0014521483099088073, 0.004921428859233856, 0.027362022548913956, 0.015399308875203133, 0.04023057967424393, 0.012588398531079292, 0.01859310083091259, -0.05524700507521629, -0.01571682095527649, 0.049718569964170456, -0.022991569712758064, 0.038474924862384796, 0.02358923852443695, 0.07213114947080612, -0.06480970233678818, -0.11041930317878723, -0.0023264724295586348, 0.034123148769140244, 0.14650355279445648, -0.004449830856174231, 0.011747926473617554, 0.01829426735639572, 0.011775942519307137, -0.07829460501670837, 0.030406398698687553, -0.045049283653497696, -0.09525346010923386, 0.06645329296588898, 0.019125400111079216, 0.019274817779660225, 0.08748376369476318, 0.03692472353577614, -0.030910680070519447, -0.02687641605734825, -0.013811751268804073, 0.003754106815904379, -0.008437401615083218, 0.008824952878057957, 0.0021373662166297436, -0.02990211546421051, 0.005080184433609247, -0.025905204936861992, -0.04415277764201164, 0.014456112869083881, 0.025625048205256462, -0.0016027328092604876, 0.022972892969846725, -0.035206425935029984, -0.010944808833301067, -0.034515369683504105, -0.024784576147794724, -0.0010966988047584891, 0.05005475878715515, 0.03046242892742157, 0.011028856039047241, -0.03662588819861412, 0.05976687744259834, -0.07011401653289795, 0.05610615387558937, -0.016529276967048645, -0.007405489217489958, 0.010533912107348442, -0.015063120052218437, 0.030686555430293083, 0.05065242573618889, -0.1040690690279007, 0.012588398531079292, 0.014652223326265812, -0.05087655410170555, 0.04385394603013992, -0.040006451308727264, 0.02676435373723507, 0.09622467309236526, 0.04183681309223175, 0.054126378148794174, 0.026428164914250374, -0.04120178893208504, 0.006163459271192551, 0.02373865619301796, -0.052594851702451706, -0.0054397196508944035, -0.006261514034122229, 0.019835131242871284, 0.06376378238201141, 0.044526323676109314, 0.0286881010979414, 0.025438277050852776, 0.021721523255109787, 0.023906750604510307, -0.02866942249238491, -0.03332003206014633, -0.018359636887907982, 0.008110552094876766, 0.028071753680706024, 0.029827406629920006, 0.03914730250835419, 0.007045954465866089, 0.01757519692182541, 0.00603738846257329, -0.01671604812145233, 0.040940310806035995, 0.04333098605275154, 0.006238167639821768, -0.01482031773775816, -0.01762188971042633, -0.026558905839920044, -0.017874030396342278, -0.05009211227297783, 0.0227674450725317, -0.011318352073431015, -0.01077671442180872, -0.022748766466975212, 0.00895102322101593, 0.059617459774017334, 0.03718620166182518, 0.05748826265335083, 0.031639087945222855, 0.01256038248538971, -0.06847042590379715, -0.015249892137944698, -0.05012946575880051, -0.04557224363088608, 0.0045829052105546, -0.05771239101886749, -0.02962195686995983, 0.0031984616070985794, -0.034347277134656906, -0.010739360004663467, -0.0466928705573082, 0.016034331172704697, 0.022561995312571526, -0.03277839720249176, -0.02151607535779476, -0.027063189074397087, 0.055620547384023666, 0.007629615254700184, -0.024056168273091316, -0.00538835721090436, 0.024765899404883385, -0.03247956186532974, -0.015744837000966072, 0.0508018434047699, -0.0016891146078705788, 0.040940310806035995, 0.048784710466861725, -0.009712117724120617, -0.00006245171243790537, 0.003459941828623414, -0.018144849687814713, -0.004316756036132574, -0.04284537956118584, 0.010552588850259781, -0.06436145305633545, 0.033525481820106506, 0.01578219048678875, -0.03473949804902077, 0.06574356555938721, 0.010739360004663467, -0.0009852196089923382, -0.057301491498947144, -0.020470155403017998, -0.021329304203391075, 0.011290336027741432, -0.003999244421720505, 0.011374383233487606, 0.04019322246313095, -0.00911444891244173, -0.00939460564404726, -0.043704528361558914, 0.06869455426931381, 0.01712694577872753, 0.011514462530612946, 0.029304446652531624, -0.042733315378427505, 0.01117827370762825, 0.05065242573618889, 0.05184776335954666, 0.02015264332294464, 0.03709281608462334, 0.010832746513187885, -0.014923041686415672, -0.006602372042834759, 0.01729504019021988, 0.02086237445473671, -0.019312171265482903, -0.01275649294257164, -0.035057008266448975, -0.0012525363126769662, -0.051250096410512924, -0.015352616086602211, 0.0237573329359293, -0.0028459306340664625, 0.004564228001981974, 0.057973869144916534, -0.031470995396375656, -0.017519164830446243, -0.0008095376542769372, -0.05154893174767494, -0.027137896046042442, 0.001124130911193788, 0.020414123311638832, -0.03350680321455002, 0.04351775720715523, 0.010459203273057938, 0.0033198632299900055, -0.03388034924864769, -0.05629292502999306, 0.0211238544434309, -0.019078707322478294, -0.01002029050141573, 0.013270114548504353, 0.01714562252163887, 0.004235043656080961, -0.007396150846034288, -0.016781417652964592, -0.02045147866010666, -0.019554974511265755, -0.0027151904068887234, -0.02400013618171215, -0.04482515528798103, 0.031209515407681465, -0.03277839720249176, 0.012364272028207779, 0.02538224495947361, 0.03160173445940018, -0.052632205188274384, -0.022039035335183144, -0.030387720093131065, 0.012635091319680214, -0.01826625131070614, -0.03488891199231148, -0.07220585644245148, -0.017369749024510384, 0.01619308814406395, 0.007559576071798801, -0.0010879439068958163, 0.02043280005455017, -0.05801122263073921, -0.026278747245669365, -0.009254527278244495, 0.03528113290667534, -0.0636143684387207, -0.014530821703374386, 0.011122241616249084, -0.020806344226002693, -0.038213446736335754, 0.059057142585515976, 0.00008463083213428035, -0.05677853152155876, 0.01623978093266487, -0.03733561933040619, -0.012635091319680214, -0.04949444532394409, 0.027212604880332947, -0.06787275522947311, 0.004725318402051926, 0.005187578033655882, -0.007765024434775114, 0.024504419416189194, 0.0009671261068433523, -0.02622271701693535, 0.02045147866010666, 0.016809433698654175, 0.06686419248580933, -0.0002775307511910796, 0.013643656857311726, -0.036439117044210434, -0.007120662834495306, -0.031060097739100456, 0.04598313942551613, -0.033955056220293045, -0.03940878435969353, 0.03350680321455002, -0.059057142585515976, 0.028333233669400215, -0.05341664329171181, 0.002584450412541628, -0.02073163539171219, 0.025438277050852776, -0.02454177290201187, 0.06380113959312439, 0.04814969003200531, -0.01826625131070614, -0.04049205780029297, -0.02743673138320446, -0.0035229772329330444, -0.00399457523599267, -0.012887232936918736, 0.058496829122304916, -0.03854963555932045, 0.002297289203852415, -0.03832550719380379, -0.012261548079550266, -0.048896774649620056, 0.05285632982850075, -0.00795646570622921, -0.020937083289027214, 0.009768148884177208, 0.025008702650666237, 0.021086500957608223, -0.01606234721839428, -0.014063892886042595, -0.0422477088868618, 0.03361886739730835, -0.04542282596230507, -0.0037377644330263138, -0.024579128250479698, 0.023253049701452255, -0.02045147866010666, 0.014960396103560925, -0.031340256333351135, -0.008675535209476948, 0.032871782779693604, 0.029173705726861954, 0.05547112971544266, 0.013372838497161865, -0.05995364859700203, 0.013559609651565552, 0.0044918544590473175, 0.030667878687381744, -0.02358923852443695, 0.019853809848427773, -0.0013155716005712748, 0.06025248020887375, -0.018322283402085304, -0.01009499840438366, -0.016566630452871323, -0.022860830649733543, 0.025027379393577576, -0.04538547247648239, -0.010636636056005955, 0.02577446587383747, -0.020544864237308502, 0.046991705894470215, 0.037242233753204346, -0.07717397809028625, 0.010730021633207798, -0.0025587694253772497, -0.04448896646499634, 0.030294334515929222, 0.011374383233487606, 0.00654634041711688, -0.08464483916759491, 0.03152702748775482, 0.049718569964170456, 0.0031751152127981186, 0.021628137677907944, -0.0025400922168046236, -0.0033198632299900055, -0.019293494522571564, 0.003798465011641383, -0.030499784275889397, 0.011047533713281155, 0.00888565368950367, -0.059318624436855316, 0.004300413653254509, -0.036009542644023895, 0.00355099281296134, 0.007984480820596218, -0.01974174566566944, 0.059505395591259, -0.036401763558387756, 0.008516780100762844, 0.03692472353577614, -0.04841116815805435, 0.03234882280230522, -0.024074845016002655, 0.030929358676075935, -0.025737110525369644, 0.008400047197937965, 0.051773056387901306, -0.0025891198311001062, -0.00651365565136075, 0.003298851428553462, 0.04377923533320427, -0.029453864321112633, 0.028613392263650894, -0.0011538976104930043, 0.03275971859693527, 0.01166387926787138, -0.059318624436855316, -0.03373093158006668, -0.004622594453394413, 0.0021758878137916327, 0.043555110692977905, -0.01708025299012661, 0.01803278736770153, -0.02222580648958683, 0.0017789984121918678, 0.05117538571357727, 0.01680009439587593, 0.022281838580965996, -0.04400336369872093, 0.02207638882100582, -0.025139441713690758, 0.03623366728425026, -0.021497398614883423, 0.019386880099773407, -0.06081279739737511, -0.05595673620700836, -0.07717397809028625, -0.004246716853231192, -0.06518325209617615, 0.0010015621082857251, 0.040006451308727264, 0.004748665262013674, -0.00796580407768488, 0.04463838413357735, 0.016660016030073166, -0.002663828432559967, -0.00607007322832942, -0.010197723284363747, 0.0325542688369751, -0.041089728474617004, 0.039446137845516205, 0.028463974595069885, -0.003485622815787792, 0.004760338459163904, -0.000779770954977721, -0.010104337707161903, -0.019405556842684746, -0.019237462431192398, -0.029173705726861954, 0.03843757137656212, 0.016921496018767357, 0.028594713658094406, -0.02129194885492325, 0.03630837798118591, 0.02209506742656231, 0.0015770517056807876, 0.012102792039513588, -0.027137896046042442, 0.015380632132291794, -0.026017267256975174, 0.05035359412431717, -0.006457624025642872, -0.026241393759846687, -0.03388034924864769, -0.04209829121828079, -0.03275971859693527, 0.03899788483977318, -0.06932957470417023, -0.03647647053003311, 0.013671672903001308, -0.01948026567697525, -0.009945581667125225, 0.04336833953857422, -0.026951124891638756, 0.029734021052718163, -0.0015677132178097963, -0.014997750520706177, 0.0058786324225366116, 0.035748060792684555, -0.022188453003764153, 0.022748766466975212, 0.019685715436935425, 0.01213080808520317, -0.007284088060259819, 0.016249120235443115, 0.007041284814476967, 0.013531594537198544, -0.013905136846005917, 0.019162753596901894, -0.0215347521007061, 0.025979913771152496, -0.0032007964327931404, 0.013765058480203152, -0.007844402454793453, 0.016958851367235184, 0.0042257048189640045, -0.020955760031938553, -0.020395446568727493, -0.006681750062853098, 0.06764863431453705, 0.014474790543317795, -0.009749471209943295, 0.009035070426762104, -0.010235077701508999, 0.008105882443487644, -0.0223565474152565, 0.012485673651099205, -0.013223420828580856, -0.03401108831167221, 0.03171379864215851, 0.00016517603944521397, 0.02525150403380394, -0.039296720176935196, -0.02825852669775486, -0.023495852947235107, -0.04702905938029289, -0.010179045610129833, -0.018060803413391113, 0.049307674169540405, 0.027679534628987312, -0.033544160425662994, -0.03619631379842758, -0.025699757039546967, -0.012784508056938648, -0.014708254486322403, -0.028856195509433746, 0.06163458898663521, 0.000002193288310081698, 0.031340256333351135, -0.05203453451395035, -0.03212469443678856, 0.022823475301265717, -0.026951124891638756, 0.03746635839343071, -0.033263999968767166, 0.016155732795596123, 0.04362981766462326, -0.023626593872904778, 0.03869905322790146, 0.009184488095343113, -0.013830428943037987, 0.03488891199231148, 0.01022573933005333, 0.00012176625750726089, 0.020937083289027214, -0.010926132090389729, -0.006102758459746838, 0.043405693024396896, -0.008624173700809479, 0.02004058100283146, 0.025905204936861992, 0.014726932160556316, 0.026428164914250374, -0.016370519995689392, -0.011813296936452389, 0.04049205780029297, 0.003772784024477005, 0.008633512072265148, 0.00798915047198534, -0.031751152127981186, 0.018611779436469078, -0.03634573146700859, -0.028613392263650894, 0.00399457523599267, -0.031639087945222855, -0.00559380603954196, -0.0051175388507544994, -0.015053781680762768, -0.0237573329359293, -0.011262320913374424, 0.030630523338913918, -0.03195660188794136, 0.04609520360827446, -0.004468507599085569, 0.03651382401585579, -0.009221842512488365, 0.01441875845193863, -0.05322987213730812, 0.027193928137421608, -0.010066983290016651, 0.009861534461379051, 0.018929289653897285, -0.013064665719866753, 0.009081763215363026, 0.007793040480464697, 0.004162669647485018, 0.048336461186409, 0.028370589017868042, 0.03709281608462334, 0.018835904076695442, 0.018135512247681618, 0.012709799222648144, -0.015399308875203133, -0.03453404828906059, -0.02304760180413723, -0.019256141036748886, 0.024653837084770203, -0.002299624029546976, 0.04934502765536308, 0.03393637761473656, 0.025606371462345123, 0.05352870747447014, 0.0025307536125183105, -0.05689059570431709, 0.0812082439661026, -0.0003878426505252719, -0.00607007322832942, 0.0003539903264027089, 0.017649905756115913, 0.0315643809735775, 0.010954148136079311, -0.0024957340210676193, 0.02499002404510975, -0.03169512003660202, -0.004884074442088604, -0.016155732795596123, -0.007811717223376036, -0.008642850443720818, 0.0655941441655159, -0.04030528664588928, -0.01604367047548294, 0.019928516820073128, 0.003389902412891388, -0.007937788031995296, -0.003973563201725483, -0.03457140177488327, 0.004620259627699852, -0.0414259172976017, -0.00014708255184814334, 0.04097766429185867, -0.020787665620446205, 0.01837831363081932, -0.014568176120519638, 0.009329236112535, -0.02058221772313118, -0.013755720108747482, -0.024784576147794724, -0.036177635192871094, 0.009086432866752148, -0.015343277715146542, 0.003347878810018301, 0.003417918225750327, -0.029864760115742683, 0.0015373628120869398, 0.00480002723634243, -0.0012455323012545705, 0.040118515491485596, -0.013017972931265831, -0.0011013681069016457, 0.08524250984191895, 0.030387720093131065, 0.03720488026738167, -0.011234304867684841, -0.02209506742656231, 0.05954274907708168, 0.022319192066788673, -0.027231283485889435, 0.02209506742656231, -0.0051782396622002125, -0.029864760115742683, 0.011019517667591572, 0.014904364943504333, -0.01593160815536976, -0.018070140853524208, -0.010421848855912685, 0.06596768647432327, -0.0282772034406662, -0.00959071610122919, 0.01653861440718174, 0.03343209624290466, 0.0013832763070240617, 0.01070200651884079, 0.02413087524473667, -0.011337028816342354, -0.021478720009326935, 0.06611710786819458, -0.014073231257498264, 0.017192315310239792, 0.010907454416155815, -0.02635345607995987, -0.0008585651521570981, 0.0045899092219769955, -0.0031751152127981186, -0.0025821158196777105, 0.0025470962282270193, 0.034926269203424454, -0.007508213631808758, 0.03937143087387085, -0.029248414561152458, -0.03662588819861412, 0.019554974511265755, 0.04348040372133255, -0.012859216891229153, -0.006999261677265167, -0.01530592329800129, -0.022972892969846725, 0.03630837798118591, 0.013316807337105274, -0.008283315226435661, 0.04105237126350403, -0.014166616834700108, -0.03401108831167221, -0.0348515585064888, 0.03798932209610939, -0.012018744833767414, 0.007765024434775114, 0.034085795283317566, -0.004319090396165848, -0.03707414120435715, 0.004113642033189535, -0.006793812848627567, 0.05188512057065964, -0.009319896809756756, 0.03526245802640915, 0.026801709085702896, -0.02620404027402401, 0.0033105246257036924, -0.07343854755163193, 0.02400013618171215, 0.016678694635629654, 0.007223387248814106, -0.00803117360919714, 0.0014521483099088073, -0.007466190028935671, -0.029958145692944527, 0.013410192914307117, -0.01009499840438366, -0.009693440049886703, 0.007741678040474653, 0.024765899404883385, 0.006219490431249142, -0.05281897634267807, 0.015838222578167915, 0.009992274455726147, -0.021777555346488953, 0.03305855393409729, 0.010113676078617573, -0.009417952038347721, 0.04097766429185867, 0.014288018457591534, 0.0015653785085305572, 0.006765797268599272, -0.029715344309806824, -0.0014416424091905355, -0.036831337958574295, 0.009002385661005974, -0.008488764055073261, 0.004804696422070265, -0.018555747345089912, 0.017976755276322365, -0.03634573146700859, 0.03511304035782814, 0.012000068090856075, 0.029939468950033188, 0.006714434828609228, 0.011944036930799484, -0.06099956855177879, -0.017136283218860626, 0.004575901199132204, 0.04228506609797478, -0.061410464346408844, 0.0007867749081924558, 0.014549498446285725, 0.01826625131070614, 0.007853740826249123, 0.005477074068039656, 0.10033364593982697, -0.04019322246313095, 0.0038941854145377874, -0.05154893174767494, 0.021721523255109787, -0.0311534833163023, 0.001849037711508572, -0.007582922466099262, -0.007316772826015949, -0.014782963320612907, -0.002645151223987341, -0.0010645975125953555, -0.0041276500560343266, -0.0017451461171731353, -0.04736524820327759, -0.005467735230922699, -0.004365783650428057, -0.0031214184127748013, -0.030817294493317604, -0.00664906483143568, 0.021702846512198448, 0.04194887727499008, -0.025064732879400253, -0.05435050278902054, -0.004148661624640226, 0.00007974266918608919, 0.022057712078094482, -0.0006612878059968352, -0.0286881010979414, 0.003128422424197197, -0.01623978093266487, 0.023981459438800812, 0.007335450034588575, 0.05158628523349762, 0.015735497698187828, -0.013681011274456978, -0.02728731371462345, -0.03851228207349777, -0.060289837419986725, 0.023533206433057785, 0.02138533443212509, -0.05789916217327118, 0.041089728474617004, 0.0060233804397284985, 0.08412187546491623, 0.00047597545199096203, 0.019442912191152573, -0.016398536041378975, -0.05143686756491661, 0.02222580648958683, -0.007064631674438715, 0.05091390758752823, -0.0015863903099671006, 0.028706777840852737, -0.019685715436935425, -0.011645202524960041, -0.0017066244035959244, -0.031620413064956665, -0.034515369683504105, 0.01325143687427044, 0.03866169601678848, -0.018779873847961426, -0.004837381653487682, 0.020003225654363632, 0.01446545124053955, -0.0009577875025570393, -0.010468541644513607, -0.010515234433114529, -0.02553166262805462, -0.0009000051068142056, -0.04594578593969345, -0.0063035376369953156, 0.0037681148387491703, 0.015474017709493637, 0.007288757245987654, 0.020638249814510345, 0.030537137761712074, 0.024877961724996567, -0.00434477161616087, -0.02261802740395069, -0.01694951206445694, 0.020937083289027214, -0.004921428859233856, 0.02676435373723507, 0.060289837419986725, -0.04407807067036629, -0.05565790459513664, 0.030649200081825256, 0.019368203356862068, 0.022804798558354378, -0.00890900008380413, -0.017939401790499687, 0.018733179196715355, -0.043443046510219574, -0.002542426809668541, 0.03266633301973343, -0.03240485116839409, 0.026428164914250374, 0.0029976824298501015, 0.020638249814510345, 0.008115220814943314, 0.018004771322011948, 0.02099311538040638, 0.0024397026281803846, 0.0301635954529047, 0.011691895313560963, -0.014493467286229134, -0.02937915548682213, -0.015670128166675568, -0.027137896046042442, -0.0019634352065622807, -0.021497398614883423, -0.018079480156302452, 0.01235493365675211, -0.016491921618580818, 0.01653861440718174, 0.009212503209710121, -0.012018744833767414, -0.019097384065389633, 0.022468609735369682, -0.019667036831378937, 0.009487991221249104, -0.01961100660264492, -0.013699688948690891, 0.04460103064775467, 0.004578236024826765, -0.02456044964492321, 0.012896571308374405, 0.08598959445953369, -0.03236749768257141, 0.03305855393409729, -0.04777614772319794, -0.024373678490519524, -0.04531076177954674, 0.008101212792098522, -0.0537528321146965, -0.03541187196969986, -0.06331553310155869, -0.012663106434047222, 0.014689577743411064, -0.013316807337105274, -0.011402399279177189, 0.04250919073820114, 0.0017836677143350244, 0.06331553310155869, 0.016613323241472244, -0.0537528321146965, 0.0008428063592873514, 0.022263161838054657, 0.02181490883231163, -0.007881756871938705, 0.011514462530612946, 0.008652188815176487, 0.006331553217023611, -0.05722678452730179, 0.00503816083073616, 0.02635345607995987, -0.015427324920892715, 0.002458379603922367, -0.007671638857573271, 0.019144076853990555, -0.024485742673277855, -0.006364238448441029, -0.005939333233982325, -0.0021945650223642588, 0.027100542560219765, 0.006840505637228489, 0.024653837084770203, -0.019853809848427773, -0.017267024144530296, -0.030088886618614197, -0.03996909782290459, 0.0075128828175365925, 0.012438980862498283, -0.01880788803100586, 0.05035359412431717, -0.015810206532478333, -0.045759014785289764, -0.019237462431192398, -0.022823475301265717, -0.03802667558193207, -0.011514462530612946, 0.02196432650089264, -0.03460875526070595, 0.005705868825316429, -0.052893683314323425, 0.05606880038976669, 0.013568948023021221, -0.041650041937828064, 0.036158960312604904, -0.030070209875702858, 0.005836608819663525, 0.011411737650632858 ]
Hybrid modeling combining data-driven techniques and numerical methods is an emerging and promising research direction for efficient climate simulation. However, previous works lack practical platforms, making developing hybrid modeling a challenging programming problem. Furthermore, the lack of standard data sets and evaluation metrics may hamper researchers from comprehensively comparing various algorithms under a uniform condition. To address these problems, we propose a framework called NeuroClim for hybrid modeling under the real-world scenario, a basic setting to simulate the real climate that we live in. NeuroClim consists of three parts: (1) Platform. We develop a user-friendly platform NeuroGCM for efficiently developing hybrid modeling in climate simulation. (2) Dataset. We provide an open-source dataset for data-driven methods in hybrid modeling. We investigate the characteristics of the data, i.e., heterogeneity and stiffness, which reveals the difficulty of regressing climate simulation data; (3) Metrics. We propose a methodology for quantitatively evaluating hybrid modeling, including the approximation ability of machine learning models and the stability during simulation. We believe that NeuroClim allows researchers to work without high level of climate-related expertise and focus only on machine learning algorithm design, which will accelerate hybrid modeling research in the AI-Climate intersection. The codes and data are released at https://github.com/x-w19/NeuroClim.
[ -0.0178195983171463, -0.009247258305549622, -0.03297458216547966, -0.032115593552589417, 0.016119154170155525, -0.023034876212477684, -0.009641691111028194, 0.025278760120272636, -0.04592951014637947, 0.06258333474397659, 0.008554808795452118, -0.03395628184080124, 0.015680894255638123, -0.05080294609069824, -0.042563680559396744, -0.005973465740680695, 0.0023249622900038958, 0.004336569458246231, 0.035481423139572144, -0.019598927348852158, 0.010658450424671173, 0.0182140301913023, 0.027645356953144073, 0.0695253536105156, 0.004531594458967447, 0.01903795637190342, 0.04098594933748245, -0.01117559615522623, -0.10209673643112183, 0.03057292476296425, 0.07566097378730774, -0.0011471420293673873, 0.01488326396793127, 0.0031839492730796337, -0.012288773432374, -0.05094318836927414, 0.057008687406778336, 0.04007437080144882, -0.011640150099992752, 0.04116125404834747, -0.000573023222386837, 0.014506361447274685, 0.020247550681233406, -0.03849663957953453, -0.0004656498203985393, -0.033184945583343506, -0.04442190006375313, -0.017416398972272873, 0.02143961377441883, -0.01895030401647091, 0.0043694390915334225, -0.04862918332219124, 0.046280115842819214, 0.028907541185617447, -0.04038991779088974, 0.045789264142513275, 0.05343249812722206, 0.04238837957382202, 0.037620123475790024, -0.003385548247024417, 0.0482785739004612, 0.029643816873431206, -0.016049033030867577, -0.013673670589923859, 0.036147575825452805, -0.024998273700475693, 0.012919865548610687, -0.001128516043536365, 0.03783048689365387, 0.011596323922276497, -0.02860952541232109, -0.011561263352632523, -0.024928152561187744, -0.008975537493824959, 0.03199288249015808, -0.02636564150452614, 0.02661106549203396, 0.02333289198577404, 0.011464846320450306, -0.01830168254673481, 0.005964700598269701, -0.018178969621658325, -0.016522351652383804, -0.012262477539479733, 0.048348695039749146, 0.013480836525559425, -0.009001833386719227, -0.08288347721099854, 0.019493745639920235, -0.006740418262779713, -0.04038991779088974, 0.012762092053890228, -0.006950782611966133, -0.01632075197994709, -0.017197269946336746, 0.013419480063021183, 0.02101888507604599, 0.026067625731229782, -0.030222317203879356, -0.05795532464981079, -0.020002124831080437, 0.008160375989973545, 0.03625275567173958, -0.006175064481794834, -0.032431140542030334, -0.04550877958536148, 0.004851523321121931, 0.06927993148565292, -0.03274668753147125, 0.09753885120153427, -0.0281186755746603, 0.02340301312506199, -0.016110388562083244, -0.038952428847551346, -0.03320247679948807, -0.008256793022155762, -0.018582167103886604, -0.04890966787934303, 0.059147391468286514, -0.07481952011585236, 0.027838191017508507, 0.06177694350481033, -0.017574172466993332, -0.0005631623789668083, -0.02505086548626423, 0.020177429541945457, -0.0013016281882300973, -0.05760471895337105, 0.040915828198194504, 0.045473720878362656, 0.02070333994925022, 0.007612552959471941, -0.022473905235528946, -0.020247550681233406, 0.027925841510295868, 0.018810061737895012, 0.04007437080144882, 0.028662117198109627, -0.00296701118350029, -0.04003931209445, -0.016925549134612083, -0.03996919095516205, -0.006065499968826771, -0.0205981582403183, 0.006665914319455624, -0.028223857283592224, -0.02257908694446087, 0.07622195035219193, -0.02257908694446087, -0.020212490111589432, -0.09704799950122833, 0.07692316174507141, -0.049260273575782776, 0.014602778479456902, 0.04519323259592056, 0.020650748163461685, -0.008936094120144844, -0.01772318035364151, 0.005153921898454428, -0.04098594933748245, 0.05900714546442032, -0.0020696765277534723, 0.07713352888822556, 0.025944912806153297, -0.010491912253201008, -0.039618585258722305, 0.01863475888967514, 0.03588461875915527, -0.03164227679371834, 0.042002711445093155, 0.001146046444773674, 0.03586708754301071, 0.01805625669658184, 0.06970065832138062, -0.03751494362950325, 0.084426149725914, 0.041827406734228134, -0.017267391085624695, -0.03511328622698784, 0.08681027591228485, -0.028258919715881348, -0.06773725897073746, 0.07113814353942871, 0.05571144074201584, 0.033184945583343506, 0.05248585715889931, 0.06163669750094414, 0.026172807440161705, 0.05104836821556091, -0.07019151002168655, 0.04403623193502426, -0.023560786619782448, -0.014401179738342762, 0.015602008439600468, -0.00786674302071333, -0.030958592891693115, 0.011552498675882816, -0.002342492574825883, -0.004454899579286575, 0.054624561220407486, -0.04533347487449646, -0.039864007383584976, -0.02743499167263508, 0.005127626471221447, -0.05423889309167862, 0.033272597938776016, -0.016031501814723015, -0.006293394602835178, 0.002701864577829838, -0.06675556302070618, -0.031116364523768425, 0.036568302661180496, -0.05813062936067581, -0.035148344933986664, -0.00521527836099267, -0.031957823783159256, 0.022561555728316307, -0.006543201860040426, -0.025909852236509323, -0.006626470945775509, -0.01124571729451418, 0.017284922301769257, 0.021299371495842934, -0.0009499256848357618, -0.02983665093779564, -0.010824989527463913, 0.016715185716748238, -0.001953538041561842, 0.00007217572419904172, -0.02119418978691101, -0.013542192988097668, 0.02391139231622219, 0.031940292567014694, 0.028486812487244606, 0.039022549986839294, 0.02629552036523819, 0.03884724900126457, -0.0062232729978859425, -0.02960875630378723, 0.010386730544269085, -0.011333368718624115, -0.05588674545288086, -0.02704932540655136, -0.03206300362944603, 0.013498366810381413, -0.04312465339899063, -0.04277404770255089, 0.08099020272493362, 0.05315200984477997, 0.048664242029190063, -0.01614544913172722, 0.000598770915530622, -0.007573109585791826, 0.06514276564121246, -0.053292252123355865, 0.027312280610203743, 0.029135435819625854, 0.021860342472791672, 0.022105766460299492, 0.018827592954039574, 0.04775266349315643, 0.014445005916059017, 0.019073016941547394, 0.05437913537025452, -0.04428165405988693, 0.033518023788928986, 0.09277059137821198, 0.010483147576451302, 0.03951340168714523, 0.01970410905778408, -0.03428935632109642, -0.01639963872730732, 0.010781163349747658, -0.02317511849105358, 0.014778082258999348, -0.05434407293796539, 0.024174347519874573, -0.007695822045207024, 0.04095089063048363, -0.0031927144154906273, -0.012130999937653542, 0.011973226442933083, 0.0728561207652092, 0.04940051585435867, -0.0076914397068321705, -0.03786554932594299, -0.02424446865916252, -0.0446673221886158, -0.00890541635453701, -0.0031883318442851305, 0.0018461645813658834, -0.029398391023278236, -0.0623028539121151, 0.01847698539495468, 0.023701028898358345, -0.020405324175953865, 0.004706898238509893, 0.0009236301411874592, 0.02235119231045246, -0.02068580873310566, -0.025208638980984688, -0.005245956126600504, 0.045789264142513275, 0.002124458784237504, -0.04855905845761299, 0.05595686659216881, 0.04161704331636429, 0.006280246656388044, -0.031116364523768425, 0.0042664483189582825, 0.027014264836907387, -0.013629844412207603, -0.024612607434391975, -0.02275438979268074, 0.0318000502884388, 0.07467927783727646, 0.008427713997662067, 0.039267975836992264, -0.004382586572319269, -0.024700257927179337, 0.019581397995352745, 0.031624745577573776, -0.06423118710517883, 0.05259104073047638, 0.01607532799243927, -0.029906772077083588, -0.010658450424671173, 0.034990571439266205, 0.0494355782866478, -0.005206512752920389, -0.08870355784893036, -0.008042046800255775, -0.0241392869502306, 0.013498366810381413, 0.005552737507969141, -0.02084358222782612, -0.00882214680314064, -0.014594013802707195, -0.026067625731229782, -0.013445775955915451, -0.005013679154217243, -0.05315200984477997, -0.038040854036808014, -0.026067625731229782, -0.053046829998493195, -0.05055752024054527, 0.045543842017650604, -0.01845945417881012, -0.0004500368668232113, 0.02275438979268074, 0.0009181519271805882, -0.013813912868499756, -0.006700974889099598, 0.00026761170011013746, 0.02415681816637516, -0.032343488186597824, 0.055185530334711075, -0.03632287681102753, -0.009405030868947506, 0.034815266728401184, 0.015216341242194176, -0.07341708987951279, 0.015488061122596264, 0.0013487410033121705, -0.05129379406571388, -0.011973226442933083, -0.008375123143196106, -0.04400116950273514, 0.03947833925485611, 0.017951074987649918, 0.022614147514104843, 0.04680602625012398, -0.0017311216797679663, -0.0016292266082018614, -0.0006842313450761139, 0.01228000782430172, -0.03372838720679283, 0.00849345326423645, -0.033009644597768784, 0.03579696640372276, -0.022806981578469276, 0.03593721240758896, 0.017907248809933662, 0.010824989527463913, 0.006644001230597496, 0.04820845276117325, 0.02150973491370678, -0.02513851784169674, 0.004509681835770607, -0.008239262737333775, 0.0305028036236763, -0.04140667989850044, -0.011806688271462917, -0.011210656724870205, 0.03302717208862305, -0.019178198650479317, -0.005394964013248682, -0.025909852236509323, 0.03982894867658615, 0.020720869302749634, -0.02769794687628746, -0.011701506562530994, -0.015303992666304111, 0.013042577542364597, -0.0051802173256874084, -0.004200709518045187, -0.039618585258722305, -0.04869930446147919, -0.009676751680672169, 0.02612021565437317, -0.005903344135731459, 0.021316900849342346, 0.006591410376131535, 0.02193046361207962, 0.02727722004055977, -0.023701028898358345, -0.027242159470915794, 0.03625275567173958, -0.04368562251329422, -0.02662859670817852, 0.0064292545430362225, 0.011552498675882816, 0.03215065598487854, 0.012989986687898636, -0.02308746613562107, 0.048839546740055084, 0.013226646929979324, 0.005675449967384338, -0.00224607577547431, -0.011631385423243046, 0.03600733354687691, 0.016171744093298912, 0.006126855965703726, -0.03579696640372276, -0.017863422632217407, -0.025085926055908203, -0.035235997289419174, 0.012095939368009567, 0.014374883845448494, 0.006052352022379637, -0.03716433420777321, -0.03453478217124939, 0.030888471752405167, 0.012043348513543606, -0.05490504577755928, -0.018284151330590248, -0.02555924467742443, 0.010079949162900448, -0.01731121726334095, -0.06584398448467255, -0.021790221333503723, 0.026505883783102036, -0.04067040607333183, -0.007240033242851496, 0.0027369253803044558, 0.022123297676444054, -0.03204547241330147, 0.001133994315750897, 0.04477250576019287, -0.0014648796059191227, -0.025681957602500916, 0.05630747228860855, 0.032361019402742386, -0.024454833939671516, -0.01447130087763071, 0.01583866775035858, -0.003775598481297493, -0.022281071171164513, -0.006604558322578669, 0.0482785739004612, -0.027715478092432022, -0.0020674853585660458, -0.023438073694705963, 0.025015804916620255, -0.007713352330029011, -0.03197535127401352, -0.012788387946784496, -0.06829822808504105, 0.04613987356424332, -0.05599192902445793, 0.04280910640954971, 0.02126431092619896, 0.023227708414196968, -0.003538938704878092, -0.004259874112904072, 0.014374883845448494, -0.009089484810829163, -0.001827538595534861, 0.011771627701818943, -0.005868283566087484, -0.005451937671750784, -0.004393543116748333, 0.03146697208285332, -0.07022657245397568, -0.030976122245192528, 0.029696406796574593, -0.02406916581094265, -0.0016193657647818327, 0.060374513268470764, 0.01343701034784317, -0.030713167041540146, -0.012805918231606483, -0.023473134264349937, 0.008309383876621723, -0.011762863025069237, 0.05374804139137268, 0.05273128300905228, -0.010579564608633518, -0.01599644124507904, 0.020492974668741226, -0.008397036232054234, 0.036883849650621414, 0.02159738726913929, -0.023683497682213783, 0.02867964655160904, 0.017942309379577637, 0.004393543116748333, 0.0007932481821626425, 0.0075468141585588455, 0.045543842017650604, 0.031852640211582184, -0.004628011491149664, 0.006337220314890146, 0.015698425471782684, -0.031870171427726746, 0.004229196347296238, 0.012665675021708012, -0.02496321313083172, 0.06647507101297379, -0.019984595477581024, -0.03769024461507797, 0.032343488186597824, -0.018021196126937866, -0.03428935632109642, 0.006696592550724745, -0.047121573239564896, 0.003889545565471053, 0.021807750687003136, -0.00296701118350029, -0.019002895802259445, -0.032781749963760376, 0.07930728793144226, 0.02389386296272278, -0.011210656724870205, 0.015268932096660137, -0.020230019465088844, -0.002739116782322526, 0.007498605642467737, 0.013945390470325947, -0.0017037305515259504, -0.03237855061888695, 0.004485577344894409, 0.03544636070728302, -0.005088183097541332, -0.026821430772542953, -0.05083800479769707, -0.007231268100440502, -0.04989136755466461, -0.0048427581787109375, -0.038531702011823654, 0.02718956768512726, 0.008418949320912361, -0.0031576536130160093, -0.02834657020866871, -0.014523892663419247, 0.006232038140296936, -0.004535977263003588, 0.049575820565223694, -0.001167959300801158, 0.018529577180743217, 0.012095939368009567, -0.06423118710517883, -0.030380090698599815, 0.045543842017650604, -0.02769794687628746, 0.021579856052994728, 0.009177136234939098, -0.008892267942428589, -0.0011350899003446102, -0.003961858339607716, 0.027136975899338722, -0.004715663380920887, 0.032185714691877365, 0.048594120889902115, 0.021001355722546577, 0.04978618398308754, -0.015076098032295704, -0.06286382675170898, -0.01476055197417736, -0.032115593552589417, 0.01567213051021099, -0.0008348827832378447, 0.018196498975157738, -0.02787325158715248, 0.003013028297573328, -0.034815266728401184, 0.01042179111391306, 0.017837127670645714, 0.04445695877075195, -0.0529065877199173, 0.029328269883990288, 0.021141598001122475, 0.007971924729645252, 0.002045572269707918, -0.014821908436715603, 0.03811097517609596, 0.023104997351765633, 0.01240271981805563, 0.06524795293807983, -0.014769316650927067, -0.014497596770524979, 0.01248160656541586, 0.04154692217707634, -0.0423533171415329, 0.04305453225970268, 0.01607532799243927, 0.012551728636026382, 0.05143403634428978, -0.04168716445565224, 0.014173285104334354, 0.012954926118254662, -0.0040319799445569515, 0.015339053235948086, 0.02266673743724823, 0.015943849459290504, 0.04922521486878395, -0.021579856052994728, -0.0516093410551548, -0.010290313512086868, 0.017039496451616287, -0.013138994574546814, 0.0027456905227154493, -0.06882414221763611, -0.003683564020320773, 0.04287922754883766, -0.020826051011681557, -0.03241360932588577, 0.0149621507152915, 0.021579856052994728, 0.00562285864725709, -0.01912560872733593, 0.004143735859543085, -0.017635527998209, 0.05210018903017044, -0.0003240375081077218, 0.026681188493967056, 0.00033499396522529423, 0.032694097608327866, 0.053467556834220886, 0.03125660866498947, 0.02787325158715248, -0.005500146187841892, 0.006911339238286018, 0.05501022934913635, 0.008454009890556335, 0.00012709501606877893, 0.06023427098989487, 0.002335918601602316, -0.011701506562530994, -0.007787856739014387, 0.019160669296979904, -0.007923716679215431, 0.0482785739004612, -0.03979388624429703, 0.036392997950315475, -0.01352466270327568, 0.005057504866272211, 0.008861590176820755, -0.0005127626354806125, 0.03839145973324776, 0.0038391458801925182, -0.024507423862814903, -0.043475259095430374, 0.013735027052462101, 0.03783048689365387, -0.049751125276088715, 0.009571569040417671, 0.03344790264964104, 0.027750538662075996, -0.04007437080144882, -0.054028529673814774, 0.015268932096660137, -0.037550002336502075, -0.0193009115755558, -0.10174613445997238, -0.0011361856013536453, -0.015444235876202583, -0.03158968314528465, -0.016855427995324135, -0.010106245055794716, -0.002074059098958969, 0.020317671820521355, 0.012227416969835758, -0.00931737944483757, -0.021457144990563393, 0.005938404705375433, -0.012972456403076649, -0.03199288249015808, 0.061461396515369415, 0.021001355722546577, 0.014848203398287296, -0.019143138080835342, -0.0071742944419384, 0.037059154361486435, 0.0038983109407126904, 0.0069420174695551395, 0.011280777864158154, -0.02317511849105358, -0.07944753021001816, -0.010868814773857594, -0.0050618876703083515, 0.026593536138534546, 0.011087944731116295, 0.021737629547715187, 0.01657494343817234, -0.028329040855169296, -0.023280300199985504, -0.0008557000546716154, 0.011517438106238842, 0.03584956005215645, 0.009054424241185188, 0.007814152166247368, 0.01186804473400116, -0.06672050058841705, -0.03379850834608078, 0.04070546478033066, 0.009878350421786308, -0.05662301927804947, -0.05711387097835541, -0.005438790190964937, -0.02836410142481327, -0.019020427018404007, -0.008015750907361507, 0.008712582290172577, 0.04284416884183884, -0.07355733215808868, 0.043650563806295395, 0.06324949115514755, -0.03793567046523094, 0.023227708414196968, -0.02143961377441883, -0.04287922754883766, 0.028591996058821678, -0.011894340626895428, 0.022140827029943466, -0.0012391763739287853, -0.06689580529928207, -0.029696406796574593, -0.05830593407154083, -0.006047969684004784, 0.03323753550648689, -0.014988446608185768, 0.029047785326838493, -0.02496321313083172, -0.052555978298187256, 0.025524184107780457, 0.0002971941721625626, -0.0446673221886158, 0.012621849775314331, 0.06444155424833298, -0.01896783523261547, 0.049014847725629807, 0.008221732452511787, 0.030870940536260605, 0.035814497619867325, -0.006692209746688604, 0.006644001230597496, 0.02613774687051773, 0.00840580090880394, -0.03201041370630264, 0.0037339639384299517, 0.002934141783043742, 0.0479980893433094, -0.019563866779208183, -0.027329809963703156, 0.0018132951809093356, -0.0018417820101603866, 0.012052113190293312, -0.01954633742570877, -0.012578023597598076, -0.005026827100664377, 0.0011213943362236023, 0.03108130395412445, 0.010334139689803123, -0.030888471752405167, 0.015794841572642326, -0.0035959123633801937, -0.027978433296084404, -0.0030261760111898184, 0.02762782573699951, -0.024016574025154114, -0.017574172466993332, 0.015470530837774277, 0.04024967551231384, 0.039618585258722305, 0.02943345159292221, 0.00644678482785821, 0.010640920139849186, -0.02852187491953373, -0.018178969621658325, 0.012429015710949898, -0.004632394295185804, 0.028802359476685524, 0.0004026501555927098, -0.008046428672969341, 0.007516135927289724, -0.03283433988690376, -0.04217801243066788, 0.010719806887209415, 0.018669819459319115, 0.01055326871573925, -0.01199952233582735, 0.014611544087529182, -0.015119924210011959, 0.0516093410551548, -0.06240803375840187, -0.029713938012719154, 0.049751125276088715, -0.01573348604142666, -0.005583415273576975, -0.05136391520500183, -0.04533347487449646, 0.010579564608633518, 0.014409945346415043, -0.030765758827328682, 0.015076098032295704, -0.024297060444951057, -0.008142845705151558, 0.04764748364686966, -0.014313528314232826, -0.011692740954458714, 0.034657496958971024, -0.06864883750677109, 0.031186487525701523, -0.00902812834829092, 0.05479986220598221, -0.018091317266225815, -0.017293687909841537, -0.05111848935484886, -0.008458392694592476, 0.010088714770972729, -0.025769609957933426, -0.013621079735457897, -0.0517495833337307, 0.01253419741988182, 0.05795532464981079, -0.019581397995352745, 0.03479773923754692, -0.014935855753719807, 0.034990571439266205, 0.021562326699495316, 0.015505591407418251, 0.05069776251912117, 0.03404393419623375, -0.02918802760541439, 0.005579032935202122, 0.07376769930124283, 0.02201811596751213, 0.028574464842677116, -0.023210179060697556, 0.003254070645198226, -0.020966295152902603, 0.00898430310189724, 0.04508805274963379, 0.059848602861166, -0.02513851784169674, -0.007332067470997572, -0.04301946982741356, -0.021983055397868156, -0.04771760478615761, -0.003902693511918187, -0.03288692981004715, 0.001369558391161263, 0.025997504591941833, 0.03130919858813286, 0.015698425471782684, 0.026751309633255005, -0.019160669296979904, -0.005841988138854504, -0.017013201490044594, 0.02333289198577404, 0.014637839049100876, 0.04631517454981804, -0.008090254850685596, 0.04589444771409035, -0.004869053605943918, -0.029310740530490875, -0.018529577180743217, -0.008506600745022297, -0.031011182814836502, -0.02999442256987095, 0.00017530347395222634, 0.0020127028692513704, -0.012297538109123707, 0.011938165873289108, -0.0004270282806828618, -0.009299849160015583, 0.034429602324962616, 0.0006677966448478401, 0.016960609704256058, -0.0016588090220466256, -0.04922521486878395, -0.013866504654288292, -0.027908312156796455, 0.05399346724152565, -0.005377433728426695, 0.026032565161585808, -0.020317671820521355, 0.023630907759070396, -0.0033241920173168182, -0.029117906466126442, -0.004939175210893154, -0.001010734005831182, -0.006135621108114719, 0.018564637750387192, 0.0021003547590225935, -0.006959547754377127, -0.008116550743579865, 0.033991340547800064, -0.02515604719519615, -0.0013892799615859985, 0.031957823783159256, -0.010018592700362206, 0.03849663957953453, -0.027838191017508507, 0.017837127670645714, -0.0013443584321066737, 0.0031357407569885254, -0.006284629460424185, 0.0039158412255346775, -0.009913410991430283, 0.019896943122148514, 0.07825546711683273, 0.0019217642256990075, 0.04424659535288811, -0.022631676867604256, 0.010115009732544422, -0.002570386976003647, 0.03385109826922417, -0.009273553267121315, -0.03716433420777321, -0.024051636457443237, -0.03067810647189617, 0.05578156188130379, 0.011009057983756065, 0.0030678105540573597, 0.015312758274376392, 0.026909081265330315, 0.004229196347296238, -0.024104226380586624, -0.017179740592837334, -0.014672900550067425, -0.0015886876499280334, 0.0102640176191926, -0.024121757596731186, 0.01405933778733015, -0.02605009451508522, 0.0010074471356347203, -0.013226646929979324, 0.018319211900234222, 0.011052883230149746, 0.008589870296418667, -0.05038221552968025, -0.016513586044311523, -0.019230790436267853, 0.002931950381025672, -0.027750538662075996, -0.005951552651822567, -0.005557119846343994, -0.012315068393945694, 0.04796302691102028, 0.01903795637190342, 0.014129459857940674, -0.03381603956222534, -0.015014741569757462, 0.0015602008206769824, -0.018196498975157738, 0.002263606060296297, -0.031607214361429214, 0.01401551254093647, 0.00841018371284008, 0.016259396448731422, 0.009247258305549622, -0.007906186394393444, -0.020790990442037582, -0.03947833925485611, 0.0012928630458191037, -0.002217588946223259, -0.03684878721833229, 0.03790060803294182, -0.00033335050102323294, 0.00910701509565115, 0.04873436316847801, -0.00758187472820282, -0.007235650438815355, 0.054624561220407486, -0.007967542856931686, -0.02612021565437317, 0.026418233290314674, -0.014322292990982533, 0.006486228201538324, -0.042072832584381104, 0.021825281903147697, 0.05234561488032341, 0.009203432127833366, 0.008664374239742756, 0.04961087927222252, 0.047507237643003464, -0.03201041370630264, 0.03171239793300629, -0.018897714093327522, -0.03996919095516205, -0.0129023352637887, -0.05367792025208473, -0.04329995810985565, -0.0033724005334079266, -0.08281335979700089, -0.003696711966767907, 0.02175516076385975, -0.05325719341635704, 0.01779330149292946, -0.02143961377441883, -0.003718624822795391, -0.009045658633112907 ]
Kratom (KT) typically exerts antidepressant (AD) effects. However, evaluating which form of KT extracts possesses AD properties similar to the standard AD fluoxetine (flu) remained challenging. Here, we adopted an autoencoder (AE)-based anomaly detector called ANet to measure the similarity of mice's local field potential (LFP) features that responded to KT leave extracts and AD flu. The features that responded to KT syrup had the highest similarity to those that responded to the AD flu at 85.62 $\pm$ 0.29%. This finding presents the higher feasibility of using KT syrup as an alternative substance for depressant therapy than KT alkaloids and KT aqueous, which are the other candidates in this study. Apart from the similarity measurement, we utilized ANet as a multi-task AE and evaluated the performance in discriminating multi-class LFP responses corresponding to the effect of different KT extracts and AD flu simultaneously. Furthermore, we visualized learned latent features among LFP responses qualitatively and quantitatively as t-SNE projection and maximum mean discrepancy distance, respectively. The classification results reported the accuracy and F1-score of 79.78 $\pm$ 0.39% and 79.53 $\pm$ 0.00%. In summary, the outcomes of this research might help therapeutic design devices for an alternative substance profile evaluation, such as Kratom-based form in real-world applications.
[ 0.005707520991563797, -0.04278000444173813, -0.024270163848996162, -0.07926205545663834, -0.04193515703082085, 0.010272577404975891, -0.015428067184984684, -0.01208707969635725, -0.011482245288789272, 0.044815316796302795, 0.0032713839318603277, -0.04504572972655296, -0.014832833781838417, -0.06401639431715012, 0.003237782046198845, 0.006518766283988953, -0.027092723175883293, -0.003204180160537362, -0.05180451273918152, -0.02599826082587242, -0.043087221682071686, -0.03196979686617851, 0.010243775323033333, -0.06551408022642136, 0.03292984887957573, 0.05307178199291229, -0.003098574234172702, 0.0173769760876894, -0.06685815751552582, -0.006797181908041239, 0.002115718787536025, 0.011299834586679935, 0.019085872918367386, 0.04247278720140457, -0.023290909826755524, 0.018193023279309273, 0.054838281124830246, 0.0019261082634329796, 0.031393762677907944, 0.019489094614982605, -0.006278752814978361, -0.011578250676393509, -0.02350212074816227, 0.015869691967964172, -0.022465262562036514, -0.07227285951375961, -0.014333605766296387, -0.058640096336603165, 0.026171071454882622, -0.01501524355262518, 0.01452561654150486, -0.015658479183912277, -0.008818095549941063, -0.009365326724946499, 0.004217036999762058, 0.010070965625345707, 0.07680431753396988, 0.07027594745159149, 0.06578289717435837, 0.017895406112074852, 0.017309773713350296, 0.050767652690410614, -0.009206917136907578, 0.01221188623458147, 0.017261769622564316, -0.039266206324100494, 0.026036662980914116, -0.04926997050642967, -0.03262263163924217, 0.02225404977798462, -0.0415511354804039, 0.021889230236411095, -0.036117229610681534, 0.01658013090491295, 0.008184459991753101, -0.02980007417500019, -0.01510164886713028, 0.05345580354332924, -0.013719171285629272, 0.04769548028707504, 0.05241894721984863, 0.08663526922464371, 0.023694131523370743, 0.0059763360768556595, 0.07112079858779907, 0.012019875459372997, 0.0313553623855114, -0.05802566185593605, -0.015370463952422142, 0.01915307715535164, 0.002733753528445959, 0.030856134369969368, 0.003938621375709772, 0.03924700617790222, -0.0006720377714373171, 0.01514965109527111, 0.008669286966323853, 0.019681105390191078, -0.04923156648874283, 0.039362210780382156, 0.008458075113594532, -0.09554456919431686, -0.004481052048504353, -0.006283553317189217, 0.03433153033256531, -0.035464394837617874, -0.03095213882625103, 0.016608932986855507, -0.00546270702034235, 0.17511384189128876, -0.05587514117360115, -0.01328714657574892, -0.02415495738387108, -0.0350995734333992, 0.03540679067373276, -0.025479832664132118, -0.010032563470304012, -0.02937765046954155, 0.010752604342997074, -0.03821014612913132, -0.0087748933583498, 0.041090309619903564, -0.06167386472225189, -0.00517469085752964, 0.01684894599020481, 0.053417403250932693, 0.026555093005299568, 0.02160121314227581, 0.02309889905154705, 0.04047587513923645, -0.0074308174662292, 0.01026297640055418, 0.001659693312831223, 0.0006954390555620193, -0.016071302816271782, 0.012183085083961487, -0.0335058830678463, 0.0021625214722007513, 0.016013700515031815, -0.00585632910951972, 0.00535710109397769, -0.036386046558618546, -0.06639733165502548, -0.0320466011762619, 0.010791006498038769, -0.042818404734134674, -0.030740927904844284, 0.03955422341823578, 0.010579794645309448, -0.0054579065181314945, -0.01055099256336689, -0.0014388809213414788, -0.007440418004989624, -0.005529910791665316, -0.0002980667632073164, 0.013632765971124172, 0.019181877374649048, -0.02599826082587242, -0.03540679067373276, -0.08348628878593445, -0.00535710109397769, -0.010368582792580128, 0.03279544413089752, 0.04024546220898628, 0.07181203365325928, 0.01862504705786705, -0.03694287687540054, -0.012384695932269096, -0.05568312853574753, 0.07223445922136307, -0.005693119950592518, 0.014804031699895859, 0.02889762446284294, 0.039112597703933716, -0.03175858408212662, 0.022945290431380272, 0.05733442306518555, 0.013959184288978577, -0.024769391864538193, 0.017290571704506874, -0.03640524670481682, 0.027207929641008377, 0.018145019188523293, -0.011530248448252678, 0.05833287909626961, -0.0326034314930439, 0.06075221300125122, -0.00918771605938673, 0.033217865973711014, 0.03156657516956329, 0.025614239275455475, -0.022906888276338577, 0.0566047802567482, 0.027361538261175156, 0.008578082546591759, 0.045736972242593765, -0.01551447156816721, -0.014045589603483677, 0.009907756932079792, -0.00012720715312752873, -0.012691913172602654, -0.08748011291027069, -0.02764955349266529, 0.010704601183533669, -0.002731353510171175, -0.03769171983003616, 0.04950038343667984, 0.03947741910815239, 0.001353676081635058, -0.007282009348273277, -0.05652797594666481, -0.05280296877026558, -0.06747259199619293, -0.03922780603170395, 0.012394296936690807, 0.006590770557522774, 0.028359994292259216, -0.04930837079882622, 0.04446969926357269, 0.03625163808465004, -0.013767173513770103, 0.03367869183421135, 0.05898571386933327, 0.004375446122139692, 0.018682649359107018, 0.018231425434350967, 0.007152401842176914, -0.007243607193231583, 0.024289365857839584, -0.013584763742983341, 0.02300289273262024, -0.005405103787779808, -0.013882379978895187, -0.01575448550283909, -0.03312186151742935, -0.0275727491825819, 0.02069876343011856, -0.019085872918367386, 0.03335227444767952, -0.0008676487486809492, -0.07100559026002884, -0.0009972560219466686, -0.05744962766766548, -0.008846897631883621, -0.021140387281775475, -0.04197355732321739, 0.009446931071579456, 0.051842913031578064, 0.032142605632543564, 0.0766507089138031, -0.020737165585160255, 0.03365949168801308, 0.011021419428288937, 0.03291064873337746, -0.016570530831813812, -0.026094267144799232, 0.034158721566200256, -0.0072868093848228455, 0.0011850666487589478, 0.023271707817912102, 0.02995368279516697, 0.04055267944931984, 0.037038881331682205, 0.020333942025899887, -0.045314546674489975, -0.012960728257894516, 0.02724633179605007, -0.03876698017120361, -0.0086884880438447, 0.030740927904844284, -0.008242063224315643, -0.006105943117290735, -0.022369256243109703, 0.016637735068798065, 0.03888218477368355, -0.023233305662870407, -0.03304505720734596, -0.027591951191425323, 0.050114817917346954, 0.02524941973388195, -0.02359812706708908, 0.012250288389623165, 0.010128568857908249, 0.0018937063869088888, 0.01084860973060131, 0.009898155927658081, -0.0016788943903520703, -0.006139545235782862, -0.06259551644325256, -0.016743341460824013, -0.03527238219976425, -0.050614044070243835, -0.01695455238223076, -0.046543415635824203, 0.011117424815893173, -0.0019537098705768585, -0.04289520904421806, 0.026267075911164284, 0.03312186151742935, -0.013536760583519936, -0.05191971734166145, -0.03319866582751274, 0.01564887911081314, 0.032142605632543564, 0.000730241066776216, 0.06397799402475357, 0.023482920601963997, 0.060637008398771286, -0.0708903819322586, -0.031585775315761566, 0.02524941973388195, 0.005664318334311247, -0.006888387259095907, -0.04289520904421806, -0.047887492924928665, -0.046236198395490646, 0.052918173372745514, -0.013181541115045547, 0.01493843924254179, -0.008702889084815979, -0.013623165898025036, 0.043240830302238464, -0.032392218708992004, 0.0640932023525238, 0.006845184601843357, -0.014880836009979248, 0.014544817619025707, 0.03657805547118187, 0.03402431309223175, -0.007176403421908617, -0.029358450323343277, 0.04231917858123779, -0.038190945982933044, -0.017357775941491127, -0.009307723492383957, 0.007248407229781151, -0.025556636974215508, 0.014717627316713333, 0.06935429573059082, 0.01850024051964283, 0.00693158945068717, 0.0019225080031901598, -0.048617132008075714, -0.021620415151119232, 0.021946832537651062, -0.04377846047282219, -0.039669428020715714, 0.0010236575035378337, 0.0036506052128970623, 0.00711399968713522, 0.0011598651763051748, -0.02839839644730091, -0.061712268739938736, 0.02010352909564972, -0.011453444138169289, -0.009797350503504276, 0.0018685050308704376, 0.013402353040874004, -0.0074740201234817505, 0.031240155920386314, -0.04193515703082085, 0.00248173950240016, 0.032065801322460175, 0.019258681684732437, -0.03004968911409378, 0.041167113929986954, -0.04827151447534561, -0.006264352239668369, 0.02169721946120262, -0.0018697050400078297, 0.008035651408135891, 0.012778318487107754, 0.015620077960193157, 0.00721960561349988, -0.008592482656240463, -0.0023761335760354996, -0.023463718593120575, 0.03252662718296051, -0.029089635238051414, 0.052111729979515076, -0.017194567248225212, -0.019930720329284668, 0.03435073047876358, 0.0075316233560442924, 0.015159252099692822, 0.02467338740825653, 0.03394750878214836, -0.028532803058624268, 0.01832742989063263, 0.040091853588819504, 0.011098223738372326, -0.04354804754257202, 0.004944277927279472, -0.009259720332920551, 0.050767652690410614, 0.012202286161482334, 0.016560930758714676, 0.042165569961071014, 0.05287977308034897, -0.05975375697016716, -0.05810246616601944, -0.005352300591766834, -0.025383826345205307, -0.045468155294656754, -0.007493221201002598, 0.00876529235392809, -0.01655133068561554, -0.009058109484612942, 0.04807950183749199, 0.01018617209047079, -0.005549111869186163, 0.03292984887957573, 0.024711789563298225, -0.03383230045437813, -0.005995537154376507, 0.06854785233736038, -0.028110379353165627, 0.02880161814391613, -0.04178154841065407, -0.027687955647706985, -0.02730393409729004, 0.001689694938249886, 0.03410111740231514, -0.02523021772503853, -0.004005825147032738, 0.06386278569698334, 0.04669702425599098, -0.03120175376534462, 0.0010950615396723151, -0.025115011259913445, 0.02524941973388195, 0.029281646013259888, 0.014544817619025707, 0.01592729426920414, -0.005549111869186163, -0.011971873231232166, 0.007853241637349129, 0.0037682116962969303, -0.01732897385954857, -0.004987480118870735, -0.026958314701914787, 0.011386239901185036, 0.022292451933026314, -0.030587319284677505, -0.0683942437171936, -0.013018331490457058, -0.040514275431632996, 0.009058109484612942, -0.009888555854558945, -0.0662437230348587, -0.06762620061635971, 0.01852904073894024, -0.03569480776786804, -0.04527614265680313, 0.0240013487637043, 0.004375446122139692, 0.033640291541814804, -0.024020550772547722, 0.09439250826835632, -0.03947741910815239, 0.0486939363181591, 0.030683323740959167, -0.006883586756885052, -0.03692367672920227, -0.06351716816425323, 0.03617483377456665, -0.017040958628058434, 0.0018901062430813909, 0.015543273650109768, -0.0023761335760354996, 0.0387093760073185, -0.02425096370279789, -0.004958678502589464, 0.01965230517089367, 0.02970406971871853, 0.019613903015851974, -0.00871249008923769, -0.031336162239313126, 0.008544480428099632, 0.048386719077825546, 0.06609011441469193, 0.016992954537272453, -0.002420536009594798, 0.001778499921783805, 0.05430065095424652, -0.008482076227664948, 0.03458114340901375, 0.028782417997717857, 0.02597906067967415, -0.026382282376289368, -0.012240688316524029, -0.007560424972325563, -0.03922780603170395, -0.03408191725611687, -0.018807457759976387, -0.0012852721847593784, -0.023636529222130775, -0.0009984561474993825, 0.0455065593123436, 0.02425096370279789, 0.041512731462717056, -0.05468467250466347, -0.007560424972325563, 0.0007128400611691177, -0.013469557277858257, 0.032987453043460846, -0.010877410881221294, 0.012960728257894516, 0.02939685247838497, -0.09116672724485397, 0.015504871495068073, -0.030664123594760895, 0.00502588227391243, -0.015360862948000431, -0.014698426239192486, 0.05783364921808243, 0.01121343020349741, -0.02647828869521618, 0.04466170817613602, -0.004459450487047434, 0.012903125025331974, 0.011952672153711319, -0.011847065761685371, 0.03335227444767952, -0.07784117758274078, -0.005712321028113365, 0.09047548472881317, -0.011895068921148777, 0.014093591831624508, -0.05733442306518555, -0.0541086420416832, 0.012279090471565723, -0.008582882583141327, -0.019719507545232773, -0.012931927107274532, -0.04293361306190491, -0.015092047862708569, 0.01394958421587944, -0.019633103162050247, -0.025863854214549065, -0.011146225966513157, 0.012269489467144012, 0.04792589321732521, 0.018596244975924492, -0.06574449688196182, 0.034965164959430695, 0.04039907082915306, -0.06105943024158478, -0.004224237520247698, 0.02649748884141445, 0.03275704011321068, 0.06655094027519226, 0.010003762319684029, 0.02407815307378769, -0.01207747869193554, -0.01187586784362793, 0.00850127823650837, 0.01777059957385063, -0.01062779687345028, -0.025710245594382286, -0.012903125025331974, -0.01960430108010769, 0.017693795263767242, 0.0009978560265153646, 0.008266064338386059, -0.019037870690226555, 0.018644247204065323, 0.016340117901563644, 0.00788684282451868, 0.008328467607498169, 0.034062713384628296, 0.014496814459562302, 0.0037514108698815107, -0.02367493137717247, 0.0005562312435358763, 0.03498436510562897, 0.03997664526104927, -0.038267750293016434, -0.0009204517118632793, -0.01874985359609127, 0.04032226651906967, -0.02125559374690056, -0.004034626763314009, 0.03425472602248192, 0.03490756079554558, -0.0010884611401706934, -0.0059187328442931175, -0.05272616446018219, -0.04923156648874283, -0.0020881174132227898, 0.021063582971692085, 0.02457738108932972, -0.02715032547712326, 0.006024338770657778, -0.05572153255343437, -0.0033289871644228697, 0.004718665033578873, 0.015284058637917042, 0.03379390016198158, -0.049615588039159775, -0.021332398056983948, 0.0056451172567903996, 0.05157409980893135, 0.09431570023298264, 0.02947365678846836, -0.004764267709106207, 0.015764085575938225, 0.02450057677924633, 0.004137832671403885, 0.010042164474725723, 0.01121343020349741, -0.018855459988117218, 0.03369789198040962, 0.010675800032913685, 0.00043202427332289517, 0.0043874466791749, 0.028667211532592773, 0.019057070836424828, -0.020218735560774803, 0.0192490816116333, 0.020833170041441917, -0.026593495160341263, 0.02724633179605007, -0.004881874192506075, 0.025537434965372086, 0.007411616388708353, -0.010282177478075027, 0.0022393257822841406, -0.03352508321404457, -0.0032425823155790567, -0.039362210780382156, -0.01431440468877554, -0.018068214878439903, -0.02152440883219242, 0.030740927904844284, -0.006921988911926746, -0.029166439548134804, -0.006557168439030647, 0.033736295998096466, -0.013047133572399616, 0.01005176454782486, 0.002050915267318487, -0.013517559505999088, -0.025134213268756866, 0.009994161315262318, 0.02060275711119175, -0.0329490527510643, 0.051842913031578064, 0.0852527916431427, 0.020065126940608025, -0.010013362392783165, 0.002282528206706047, 0.009005306288599968, 0.03187379240989685, -0.03258423134684563, -0.0397462323307991, 0.0086884880438447, -0.010301378555595875, 0.03550279513001442, 0.0050642844289541245, -0.016944952309131622, 0.026132669299840927, 0.00048332716687582433, -0.00841487292200327, 0.009403728879988194, -0.007728434167802334, -0.034638747572898865, 0.02599826082587242, 0.04493052512407303, 0.030164895579218864, -0.0031705782748758793, -0.05456946790218353, -0.04615939408540726, 0.06428521126508713, 0.04032226651906967, 0.010915813036262989, 0.04769548028707504, 0.03632844239473343, -0.012509503401815891, -0.07104399055242538, -0.034965164959430695, -0.040514275431632996, -0.052265338599681854, 0.02630547806620598, 0.028763215988874435, -0.0004755267291329801, -0.012442299164831638, 0.040091853588819504, -0.06098262593150139, -0.036539655178785324, 0.0306257214397192, -0.01472722738981247, 0.04600578546524048, -0.05253415182232857, 0.022714877501130104, -0.00005599064752459526, -0.058140866458415985, -0.0569504015147686, -0.0007710433565080166, -0.021582012996077538, -0.02052595280110836, 0.039938244968652725, -0.03519557788968086, -0.013507959432899952, 0.004531454760581255, -0.02044914849102497, 0.023962946608662605, 0.006360357627272606, 0.0017292972188442945, 0.02225404977798462, -0.0010098566999658942, 0.01473682839423418, -0.04128231853246689, 0.07330971956253052, 0.011933471076190472, 0.01481363270431757, 0.051266882568597794, -0.056412771344184875, -0.023482920601963997, 0.02085237205028534, -0.001299672992900014, 0.025307022035121918, 0.009706145152449608, -0.05595194548368454, -0.02572944574058056, 0.03955422341823578, 0.04327923059463501, 0.025211017578840256, -0.016436124220490456, -0.0015708883292973042, 0.018644247204065323, -0.0018985066562891006, -0.028206385672092438, 0.014141594991087914, -0.024020550772547722, 0.016589732840657234, 0.024884598329663277, 0.04926997050642967, -0.010963816195726395, -0.01617690920829773, 0.004829071462154388, -0.03540679067373276, -0.0076804314740002155, -0.05890890955924988, 0.02457738108932972, -0.01055099256336689, 0.006067540962249041, 0.008131656795740128, -0.01013816986232996, -0.020007524639368057, 0.025614239275455475, -0.06489964574575424, 0.034158721566200256, -0.03830615431070328, -0.06420841068029404, 0.0014160795835778117, 0.005414704326540232, -0.028744015842676163, 0.017866604030132294, -0.01920107938349247, -0.044239286333322525, 0.022196447476744652, -0.009043708443641663, 0.027515146881341934, 0.0433560349047184, -0.01337355189025402, -0.035963620990514755, 0.018509840592741966, 0.026017462834715843, -0.03229621425271034, 0.015111248940229416, 0.004481052048504353, 0.03680846840143204, -0.020045926794409752, 0.002026913920417428, -0.004925076849758625, 0.0023173303343355656, -0.02382853999733925, -0.02755354903638363, 0.058563292026519775, -0.0218508280813694, -0.022714877501130104, -0.017444180324673653, 0.028763215988874435, -0.0014772830763831735, -0.03302585706114769, 0.012567106634378433, -0.03004968911409378, -0.03070252574980259, 0.02067956142127514, 0.0017664992483332753, -0.04519933834671974, 0.02524941973388195, -0.024558180943131447, 0.03799893707036972, 0.036117229610681534, -0.011741460300981998, 0.005275496281683445, -0.018970666453242302, -0.022964490577578545, 0.0086356857791543, 0.025595039129257202, 0.01113662589341402, 0.009768549352884293, 0.008938102051615715, -0.027745559811592102, -0.028091179206967354, -0.005769924260675907, -0.01423760037869215, -0.00020281139586586505, 0.00817485898733139, -0.01200067438185215, 0.019345087930560112, 0.016781743615865707, 0.0297232698649168, -0.0350995734333992, -0.06501485407352448, -0.024769391864538193, -0.04231917858123779, -0.01552407257258892, -0.0397462323307991, -0.0194218922406435, 0.015466469340026379, -0.01977711170911789, -0.03498436510562897, -0.01608090288937092, 0.05464627221226692, 0.017914606258273125, -0.014199198223650455, -0.050767652690410614, -0.009955759160220623, 0.015370463952422142, 0.003957822453230619, -0.009528535418212414, -0.028686411678791046, 0.0017424979014322162, -0.02092917636036873, -0.0051362887024879456, -0.029243243858218193, 0.0013332748785614967, -0.014093591831624508, -0.008299666456878185, -0.008386070840060711, -0.02259966917335987, 0.0032521828543394804, -0.030836932361125946, -0.016042500734329224, 0.027265531942248344, 0.021966034546494484, 0.019239481538534164, -0.03102894313633442, -0.031220953911542892, -0.0007014393922872841, 0.009965360164642334, 0.00003782087514991872, 0.04185835272073746, 0.02690071240067482, -0.002170922001823783, 0.00862608477473259, 0.0027793562039732933, 0.021217191591858864, 0.052265338599681854, 0.00693158945068717, -0.012250288389623165, 0.036136429756879807, -0.041090309619903564, -0.015005643479526043, -0.02169721946120262, -0.0010482588550075889, -0.01935468800365925, -0.021466806530952454, -0.022311653941869736, 0.0031201753299683332, 0.040667884051799774, -0.0014808832202106714, -0.0015924895415082574, 0.027783961966633797, 0.00942292995750904, 0.022081241011619568, -0.04082149267196655, 0.025134213268756866, 0.021562810987234116, 0.033313870429992676, -0.003660205751657486, 0.02657429315149784, -0.02359812706708908, -0.0013416754081845284, -0.03673166409134865, -0.011107823811471462, -0.031067345291376114, -0.03054891712963581, -0.011290234513580799, 0.038363754749298096, -0.011655054986476898, 0.06105943024158478, -0.029032031074166298, 0.013383151963353157, -0.02872481383383274, -0.02384774014353752, -0.0040778289549052715, 0.00686918618157506, -0.063401959836483, -0.011539848521351814, -0.011971873231232166, -0.02062195912003517, -0.020487550646066666, 0.007930045947432518, -0.0332946702837944, -0.00321618071757257, 0.0218508280813694, -0.021005980670452118, -0.042818404734134674, 0.015072846785187721, -0.0008802494849078357, 0.0292048417031765, -0.012605508789420128, -0.025307022035121918, -0.009278921410441399, 0.02515341341495514, -0.020218735560774803, 0.007013194262981415, 0.039112597703933716, -0.004577057436108589, 0.02392454445362091, -0.026190271601080894, -0.0018169020768254995, -0.004805069882422686, -0.004997080657631159, 0.018961066380143166, -0.040091853588819504, -0.013459956273436546, 0.03275704011321068, 0.01266311202198267, 0.021812425926327705, -0.025691043585538864, -0.0026401483919471502, -0.012432699091732502, 0.028763215988874435, -0.01994992047548294, -0.018193023279309273, 0.034158721566200256, 0.03179698809981346, -0.026171071454882622, 0.024961402639746666, -0.019258681684732437, -0.09324043989181519, 0.010867810808122158, -0.01617690920829773, 0.009086910635232925, -0.03483075648546219, -0.014131993986666203, -0.001963310409337282, -0.02332931198179722, 0.013632765971124172, -0.04719625413417816, -0.04132072255015373, -0.026132669299840927, -0.04500732943415642, 0.030760128051042557, 0.001798901124857366, -0.01460242085158825, 0.016186509281396866, 0.0013932782458141446, 0.023118099197745323, -0.0015228856354951859, -0.019287483766674995, -0.0069363899528980255, -0.037864528596401215, -0.055990345776081085, -0.026843108236789703, -0.00011768161493819207, -0.0010842609917744994, 0.0018925063777714968, 0.005078685469925404, 0.0056451172567903996, 0.027131125330924988, -0.016810543835163116, -0.018317829817533493, -0.051266882568597794, -0.019757909700274467, 0.009984561242163181, -0.049961209297180176, 0.031259357929229736, 0.011155826970934868, -0.010800606571137905, -0.04458490386605263, 0.022465262562036514, -0.02630547806620598, -0.04197355732321739, 0.032469023019075394, 0.0019957120530307293, -0.02515341341495514, 0.028782417997717857, 0.01481363270431757, -0.09178116172552109, 0.004958678502589464, -0.013383151963353157, 0.04900115355849266, 0.02325250767171383, 0.02067956142127514, -0.0036506052128970623, -0.00871249008923769, 0.027860766276717186, 0.017060158774256706, 0.017463382333517075, 0.004008225165307522, 0.041512731462717056, -0.025287821888923645, -0.04569856822490692, 0.008083654567599297, 0.031316958367824554, -0.00015780887042637914, -0.04278000444173813, 0.03183538839221001, 0.0249038003385067, 0.036117229610681534, 0.02044914849102497, -0.0025825451593846083, -0.0021505209151655436, -0.005016281735152006, 0.04750347137451172, -0.043663252145051956, 0.0024937400594353676, -0.026113467290997505 ]
In this paper, we provide a characterization of the expected value of submodular set functions with pairwise independent random input. The set of pairwise independent (uncorrelated) probability distributions contains the mutually independent distribution and is contained within the set of arbitrarily dependent (correlated) distributions. We study the ratio of the maximum expected value of a function with arbitrary dependence among the random input with given marginal probabilities to the maximum expected value of the function with pairwise independent random input with the same marginal probabilities. The definition of the ratio is inspired from the correlation gap ratio of Agrawal et al. (2012) and Calinescu et al. (2007). Our results show that for any monotone submodular set function defined on n variables, the ratio is bounded from above by 4/3 in the following cases: (a) for small n (specifically n = 2, 3) with general marginal probabilities, and (b) for general n with small marginal probabilities. The bound is tight in cases (a) and (b). This contrasts with the e/(e-1) bound on the correlation gap ratio for monotone submodular set functions with mutually independent random input which is known to be tight in case (b). Our results illustrate a fundamental difference in the behavior of submodular functions with weaker notions of independence. We discuss an application in distributionally robust optimization and end the paper with a conjecture.
[ -0.031214332208037376, -0.002290899632498622, -0.030069982632994652, 0.0004929505521431565, 0.009726970456540585, -0.013679376803338528, -0.06144276261329651, 0.039788149297237396, -0.033467818051576614, 0.014973372220993042, -0.03341500461101532, 0.005655726883560419, 0.014471619389951229, -0.03248191997408867, -0.03742903098464012, 0.020457446575164795, 0.01615293323993683, 0.01839761808514595, 0.06535115838050842, -0.01913704350590706, 0.031513623893260956, -0.009515705518424511, -0.02989392913877964, 0.01211249828338623, -0.010792095214128494, 0.005506081506609917, -0.003481463063508272, -0.02943618781864643, -0.01760537549853325, 0.018045511096715927, 0.006685641594231129, 0.0008879711385816336, -0.03505230322480202, 0.04045715555548668, -0.04232332482933998, -0.005356435663998127, 0.0018122533801943064, 0.012658265419304371, -0.01784304901957512, 0.03079180233180523, -0.03450653702020645, 0.007869603112339973, 0.009709364734590054, -0.028168601915240288, 0.0456683449447155, -0.023397544398903847, -0.04309796169400215, 0.0030941448640078306, 0.006654832046478987, -0.003974413499236107, -0.00605184817686677, -0.029383372515439987, 0.00803685374557972, 0.02529892511665821, 0.0018012500368058681, 0.02741157077252865, -0.0019376917043700814, 0.037464238703250885, 0.04415428265929222, 0.01738530956208706, -0.004731444641947746, 0.012605449184775352, -0.04602045193314552, -0.04425991326570511, -0.012596646323800087, 0.0059550185687839985, 0.01640821062028408, 0.019524361938238144, 0.03371429443359375, -0.023714441806077957, -0.09915347397327423, 0.0392247773706913, 0.009929431602358818, 0.023837678134441376, 0.0030325260013341904, 0.013344874605536461, 0.054471034556627274, 0.005704141687601805, -0.01634659245610237, 0.00920761190354824, -0.006245506927371025, 0.03661918267607689, 0.0031139508355408907, 0.05316823348402977, 0.012156511656939983, -0.009973445907235146, 0.015034991316497326, -0.05390766263008118, 0.0225524865090847, 0.03873182833194733, -0.052358388900756836, 0.0024383445270359516, -0.03295726329088211, 0.007561509031802416, 0.07513974606990814, 0.050351373851299286, -0.012447000481188297, 0.0013523129746317863, -0.010712871327996254, 0.043907806277275085, 0.006998137105256319, 0.04517539590597153, 0.018802542239427567, 0.022499671205878258, -0.006980531383305788, -0.047710567712783813, 0.019225070253014565, 0.02558061107993126, 0.06577368080615997, 0.14133596420288086, 0.01132905948907137, 0.031478412449359894, -0.01607370749115944, 0.04644298180937767, -0.03161925449967384, -0.04168953001499176, -0.03540441021323204, -0.0767594426870346, 0.03693607822060585, -0.04718240723013878, 0.008028051815927029, 0.007605522405356169, 0.03788676857948303, -0.02007012814283371, 0.006324731279164553, 0.060316018760204315, -0.04232332482933998, 0.0031227534636855125, -0.014955766499042511, -0.02742917649447918, -0.0365135483443737, 0.03603820502758026, -0.04411907121539116, -0.021108845248818398, -0.033485423773527145, -0.027640439569950104, 0.031337570399045944, 0.020263787358999252, -0.029911532998085022, -0.008375757373869419, 0.008309737779200077, -0.031003067269921303, -0.03693607822060585, -0.008217309601604939, 0.009295638650655746, -0.011373072862625122, -0.04440075904130936, 0.02285177819430828, -0.0628511905670166, 0.027393965050578117, -0.012447000481188297, 0.07352004945278168, -0.0013974267058074474, 0.0588371679186821, 0.039471253752708435, -0.025651032105088234, 0.043450068682432175, 0.0193307027220726, 0.004132862202823162, -0.04873168095946312, 0.04309796169400215, 0.05383723974227905, -0.00956852175295353, 0.03774592652916908, 0.0141019057482481, -0.006368744652718306, -0.019665203988552094, -0.044964130967855453, -0.013010372407734394, 0.057217471301555634, -0.0027728467248380184, -0.06654831767082214, -0.008903918787837029, 0.03813324496150017, 0.015598363243043423, 0.029964350163936615, -0.02116166241466999, 0.012843121774494648, 0.00019297141989227384, -0.027182700112462044, -0.012763897888362408, 0.0024933614768087864, 0.01602969504892826, 0.010431185364723206, 0.020351814106106758, 0.011285046115517616, 0.06978771090507507, -0.011989261023700237, -0.03139038383960724, 0.038238875567913055, 0.028714368119835854, 0.03830929845571518, 0.00926923006772995, -0.011038570664823055, 0.01002626121044159, 0.037147343158721924, -0.06947081536054611, 0.0007493288139812648, 0.028943238779902458, 0.017191650345921516, -0.024876395240426064, -0.05901322141289711, 0.04890773445367813, -0.007341441698372364, 0.07158345729112625, -0.002845468930900097, 0.006210296414792538, 0.03489385545253754, -0.019506756216287613, -0.007425067480653524, 0.017878258600831032, -0.0343656949698925, -0.03383753076195717, 0.0004450858978088945, -0.02406654879450798, -0.007328237872570753, -0.006892504636198282, 0.031478412449359894, -0.020932791754603386, -0.06087939068675041, -0.02098560892045498, 0.015369493514299393, 0.05598509684205055, -0.013089597225189209, 0.006236704532057047, 0.008613429963588715, 0.014577250927686691, 0.016997991129755974, -0.008278927765786648, -0.007345843128859997, 0.004634615033864975, 0.008780681528151035, -0.04337964579463005, 0.017825443297624588, -0.0014920555986464024, -0.014515632763504982, -0.016971582546830177, -0.012508619576692581, -0.003195375669747591, -0.011003360152244568, -0.06133712828159332, 0.0001767414651112631, 0.012174117378890514, -0.004238494206219912, 0.04292190819978714, 0.02147855795919895, -0.015703994780778885, 0.03336218744516373, 0.07950587570667267, 0.011971655301749706, -0.08774519711732864, -0.011161807924509048, 0.010404776781797409, 0.008626634255051613, -0.05330907925963402, 0.06566805392503738, 0.00609146011993289, -0.025827085599303246, 0.008380158804357052, -0.05742873623967171, 0.04211205989122391, 0.06693563610315323, -0.030774196609854698, -0.014216341078281403, 0.037464238703250885, 0.03005237691104412, 0.02684819884598255, 0.015818430110812187, -0.02515808306634426, 0.037921980023384094, 0.018133537843823433, -0.01901380531489849, -0.004766655620187521, -0.08915362507104874, -0.018978595733642578, -0.024753158912062645, 0.02621440403163433, -0.0410909466445446, 0.02066871151328087, -0.008521001785993576, -0.015123018063604832, 0.021654611453413963, 0.004639016464352608, -0.0730270966887474, 0.02561582252383232, -0.027939731255173683, 0.04246416687965393, 0.033168528228998184, -0.08429454267024994, -0.04985842481255531, 0.004381537903100252, 0.002085136715322733, 0.043450068682432175, 0.02971787378191948, 0.02543976902961731, -0.018168747425079346, -0.06299203634262085, 0.00786520168185234, -0.024911606684327126, 0.03711213171482086, -0.030105192214250565, 0.010730477049946785, 0.011584337800741196, -0.017420519143342972, -0.03774592652916908, -0.02987632341682911, -0.008776280097663403, 0.03637270629405975, 0.033467818051576614, -0.010035064071416855, 0.010827305726706982, 0.032552339136600494, -0.02822141721844673, -0.01571279764175415, -0.006060650572180748, -0.0282038114964962, 0.013388887979090214, -0.02066871151328087, 0.014013879001140594, -0.012341368943452835, -0.003987617790699005, 0.025175686925649643, -0.06971728801727295, 0.051090799272060394, -0.0679919645190239, -0.038098033517599106, -0.03276360407471657, 0.08351990580558777, -0.013212834484875202, 0.008560613729059696, -0.06147797405719757, -0.004049236420542002, -0.019348308444023132, 0.006254309788346291, 0.0016901161288842559, -0.041936006397008896, 0.0346473790705204, 0.0022325818426907063, 0.037147343158721924, -0.02130250446498394, -0.02174264006316662, 0.03908393532037735, -0.01716524176299572, 0.03985857218503952, 0.03711213171482086, -0.04112615808844566, -0.04950631782412529, -0.025334136560559273, 0.004533384460955858, -0.015070201829075813, 0.0008973240037448704, -0.0269890408962965, -0.04640777036547661, -0.00021098942670505494, 0.013969865627586842, -0.049717582762241364, 0.010985754430294037, 0.047886621206998825, 0.010695265606045723, 0.0016417013248428702, 0.02392570674419403, -0.014471619389951229, -0.052323177456855774, 0.04077405110001564, -0.06506946682929993, -0.02357359789311886, -0.025334136560559273, -0.0007630829932168126, 0.0059418142773211, -0.0024449466727674007, -0.03665439411997795, 0.025474978610873222, 0.009322046302258968, 0.024189786985516548, -0.014726896770298481, 0.04239374399185181, -0.007763970643281937, 0.02621440403163433, -0.05179501697421074, -0.009876616299152374, -0.011822009459137917, 0.0017363302176818252, 0.011777996085584164, -0.0416543185710907, 0.013978668488562107, -0.02408415451645851, -0.00068000762257725, 0.018344800919294357, 0.032217837870121, 0.035650886595249176, -0.02005252242088318, -0.005730549804866314, 0.03153122961521149, -0.009885418228805065, 0.04246416687965393, -0.028133390471339226, -0.04337964579463005, -0.06165402755141258, 0.006879300810396671, 0.0011729581747204065, 0.00010006180673372, -0.03184812515974045, -0.005787767469882965, -0.02466513216495514, 0.030263641849160194, -0.021760243922472, 0.040668416768312454, -0.008485791273415089, 0.0502457432448864, 0.0026892211753875017, 0.04425991326570511, -0.03616144135594368, -0.07066798210144043, 0.018027905374765396, -0.017350098118185997, 0.020122945308685303, -0.03542201593518257, -0.02653130143880844, -0.020193366333842278, -0.01502618845552206, -0.021566584706306458, -0.0147797130048275, 0.08697056025266647, -0.020791949704289436, -0.06436525285243988, -0.0015778818633407354, -0.023379938676953316, 0.012693475931882858, 0.04626692831516266, -0.007090565282851458, 0.0005776764010079205, 0.03739381954073906, 0.023820074275135994, -0.024013733491301537, 0.0015965874772518873, 0.031672071665525436, -0.09119584411382675, 0.03890788182616234, 0.03999941423535347, -0.012402987107634544, 0.03019321896135807, -0.00782558973878622, -0.04246416687965393, -0.012966359034180641, 0.013776206411421299, 0.019436335191130638, -0.027798889204859734, -0.015519138425588608, -0.02070392295718193, 0.019049016758799553, -0.029981955885887146, -0.020598290488123894, -0.11584337055683136, -0.032587550580501556, 0.0008841199451126158, 0.008160091936588287, 0.09028036892414093, -0.04320359230041504, 0.014533237554132938, -0.012350170873105526, 0.017235662788152695, 0.009163598529994488, 0.0251228716224432, -0.030721381306648254, -0.03528117388486862, 0.025175686925649643, 0.02191869355738163, -0.02514047734439373, -0.00047396973241120577, -0.020651105791330338, -0.017270874232053757, -0.04524581506848335, -0.04563313350081444, -0.024629920721054077, 0.04721761867403984, 0.03337979316711426, 0.0038489752914756536, -0.06894265115261078, 0.0017913470510393381, 0.026901014149188995, 0.04806267470121384, 0.06605537235736847, 0.0070201437920331955, -0.023063043132424355, 0.033503029495477676, -0.003001716686412692, 0.007521897088736296, 0.03223544359207153, -0.022482065483927727, 0.026584116742014885, -0.02450668253004551, 0.037957191467285156, 0.03820366412401199, -0.001159754116088152, 0.007253414951264858, 0.037147343158721924, -0.016962779685854912, -0.05098516866564751, 0.0910550057888031, -0.016953976824879646, 0.027235517278313637, -0.03999941423535347, 0.01050160638988018, -0.03540441021323204, -0.004471765365451574, -0.10668858140707016, 0.02098560892045498, -0.0014194333925843239, -0.04799225553870201, -0.0010090081486850977, 0.013133610598742962, 0.039471253752708435, 0.037147343158721924, 0.0004915751051157713, 0.04095010459423065, 0.0003785155713558197, 0.0028080574702471495, -0.037182554602622986, 0.023872889578342438, 0.004339725244790316, -0.028415076434612274, -0.0011575535172596574, 0.003875383408740163, 0.0432388037443161, -0.006175085436552763, 0.005977025255560875, 0.0004981771344318986, -0.03383753076195717, 0.06175965815782547, -0.015976877883076668, 0.0016626076539978385, 0.053097814321517944, -0.030774196609854698, -0.05535130202770233, -0.017807837575674057, -0.04168953001499176, -0.00586259039118886, 0.013934655115008354, -0.03535159304738045, 0.027077067643404007, -0.04718240723013878, 0.035474833101034164, -0.009638943709433079, 0.014621264301240444, 0.009022755548357964, 0.030298851430416107, 0.015422309748828411, -0.013767403550446033, -0.0636962503194809, 0.07084403187036514, 0.016751514747738838, -0.021355321630835533, -0.0695764422416687, -0.06390751153230667, -0.033045291900634766, 0.016557855531573296, 0.0024383445270359516, -0.045914821326732635, -0.0031799711287021637, -0.0679919645190239, 0.00036421121330931783, 0.02822141721844673, -0.001310500199906528, -0.013520929031074047, 0.002770646009594202, -0.012235736474394798, -0.026478486135601997, 0.06531594693660736, -0.0056953392922878265, 0.047288037836551666, 0.0008659644518047571, 0.018626486882567406, -0.014392394572496414, -0.01555434986948967, -0.02558061107993126, 0.05073869228363037, -0.037147343158721924, 0.016276169568300247, -0.001956397434696555, -0.017596572637557983, 0.010439988225698471, -0.03711213171482086, 0.011980458162724972, -0.02760522998869419, 0.03542201593518257, -0.04799225553870201, -0.007090565282851458, -0.017050806432962418, 0.01440119743347168, -0.008996346965432167, 0.017517348751425743, 0.05665409937500954, -0.004828274250030518, -0.0019971097353845835, -0.025774270296096802, -0.04348528012633324, 0.009480495005846024, -0.012350170873105526, 0.018203958868980408, -0.05271049588918686, 0.007059755735099316, -0.03859098255634308, -0.007926820777356625, -0.01838001236319542, -0.01768459938466549, 0.019700415432453156, 0.03596778213977814, 0.0351579375565052, 0.03612622991204262, 0.004920702427625656, -0.021091239526867867, 0.007169789168983698, 0.011866023764014244, -0.042534589767456055, -0.0036333093885332346, -0.014163524843752384, -0.018045511096715927, 0.018186353147029877, -0.0012862927978858352, -0.033960770815610886, 0.033467818051576614, -0.028432682156562805, 0.015413506887853146, 0.024559499695897102, 0.03672481328248978, 0.002907087793573737, -0.03954167291522026, -0.011478705331683159, -0.016478631645441055, -0.029770690947771072, -0.01978844217956066, 0.03908393532037735, -0.03160164877772331, -0.004533384460955858, 0.014181130565702915, -0.0059418142773211, -0.03341500461101532, 0.047288037836551666, -0.013749798759818077, -0.0010167104192078114, -0.03450653702020645, 0.005638121627271175, 0.0004932255833409727, 0.008129281923174858, -0.007433869875967503, 0.009181203320622444, 0.0034286470618098974, -0.039928991347551346, 0.028573524206876755, 0.014145919121801853, -0.03433048352599144, 0.04806267470121384, 0.006271915044635534, 0.0226933304220438, -0.025210898369550705, -0.013670573942363262, -0.022306011989712715, 0.024154575541615486, 0.03589736297726631, -0.010756884701550007, 0.03841492906212807, -0.020932791754603386, -0.018309591338038445, 0.0000940099562285468, 0.005096756387501955, -0.002570384880527854, 0.01836240664124489, 0.027693256735801697, -0.022728540003299713, 0.019365914165973663, -0.005721746943891048, 0.023344729095697403, -0.010748081840574741, 0.028767183423042297, 0.01762298122048378, -0.016813134774565697, -0.016733909025788307, 0.0526752844452858, 0.034418508410453796, -0.03468259051442146, -0.02191869355738163, 0.02760522998869419, 0.012975161895155907, -0.037464238703250885, 0.044541601091623306, -0.0033362186513841152, 0.02174264006316662, 0.0679919645190239, -0.00705095287412405, 0.004766655620187521, -0.024876395240426064, -0.03661918267607689, -0.004595003090798855, 0.013547336682677269, 0.017587769776582718, 0.022129956632852554, -0.02514047734439373, 0.029911532998085022, -0.01790466718375683, -0.016020892187952995, -0.018890568986535072, -0.030246036127209663, -0.02480597421526909, 0.029612243175506592, 0.02346796542406082, -0.002629803027957678, 0.00017949231551028788, -0.000008024716407817323, 0.014990977942943573, 0.013732193037867546, 0.003237188560888171, 0.00397881492972374, -0.04570355638861656, 0.0036927275359630585, 0.049717582762241364, -0.0005336629692465067, 0.01913704350590706, -0.036865655332803726, 0.004366133362054825, -0.002885080873966217, 0.06066812574863434, 0.013785009272396564, -0.00008101223647827283, -0.013987471349537373, 0.055844251066446304, -0.038696616888046265, -0.0017187248449772596, 0.013547336682677269, -0.013512126170098782, 0.0058097741566598415, 0.0029026863630861044, 0.02316867560148239, 0.036548759788274765, -0.02329191192984581, 0.01991168037056923, 0.02896084263920784, 0.0005229346570558846, 0.005396047607064247, -0.030122797936201096, -0.004823872819542885, 0.05440061166882515, 0.013177623972296715, -0.00027879764093086123, -0.003771951887756586, 0.015219847671687603, 0.024242602288722992, 0.06306245923042297, -0.013829022645950317, 0.02973547950387001, 0.0004291310324333608, -0.0060694534331560135, -0.010219920426607132, 0.029629847034811974, 0.01822156459093094, -0.01770220510661602, 0.009982247836887836, 0.04049236327409744, -0.0432388037443161, 0.011936444789171219, -0.019242675974965096, -0.02587990276515484, -0.008529804646968842, -0.0076935491524636745, 0.027552412822842598, 0.021073635667562485, -0.00244934787042439, -0.04816830903291702, -0.00203122035600245, 0.022446854040026665, -0.000919880869332701, 0.04552750289440155, 0.0012620853958651423, -0.025052450597286224, -0.0073502445593476295, 0.012728686444461346, 0.0001268137275474146, -0.010466395877301693, -0.018115932121872902, -0.005303619429469109, 0.08394243568181992, 0.009498100727796555, 0.06024559587240219, 0.018045511096715927, -0.0072798230685293674, -0.003611302701756358, -0.005616114940494299, -0.006879300810396671, -0.03429527208209038, 0.011707575060427189, 0.02744678035378456, 0.01754375733435154, -0.03130235895514488, 0.006712049711495638, -0.029172107577323914, 0.042217690497636795, -0.013652969151735306, -0.016179339960217476, 0.005431258585304022, -0.005057144444435835, -0.045457080006599426, -0.016258563846349716, -0.02832704968750477, 0.020281393080949783, 0.015589560382068157, -0.02223558910191059, -0.011707575060427189, -0.012667068280279636, 0.002085136715322733, -0.004555391147732735, 0.01734129525721073, -0.013899444602429867, -0.0206863172352314, -0.01809832639992237, 0.03299247473478317, -0.0067604645155370235, 0.004108654800802469, -0.03397837653756142, 0.012614252045750618, -0.02253488078713417, -0.009999853558838367, 0.029788296669721603, -0.02160179615020752, 0.02607356198132038, 0.019207464531064034, 0.02315106987953186, -0.016196945682168007, 0.0013038981705904007, 0.002924693049862981, 0.05605551600456238, -0.017975088208913803, -0.00033725297544151545, 0.03644312918186188, -0.03528117388486862, -0.012253341265022755, -0.02728833258152008, 0.03110869973897934, -0.03760508447885513, 0.02804536372423172, 0.013925852254033089, 0.04985842481255531, 0.030932646244764328, -0.026689749211072922, -0.02251727506518364, -0.005123164504766464, 0.01694517396390438, -0.02100321277976036, 0.03355584666132927, 0.07577353715896606, 0.05672452226281166, 0.016135327517986298, 0.00025087661924771965, 0.02910168655216694, 0.021760243922472, -0.08049178123474121, -0.010827305726706982, -0.015703994780778885, -0.04992884770035744, -0.029629847034811974, 0.02850310318171978, 0.018802542239427567, 0.012094893492758274, 0.06781590729951859, 0.004903097171336412, -0.035510044544935226, 0.015703994780778885, -0.013820219784975052, -0.012270946986973286, -0.06408356875181198, 0.029453793540596962, -0.029612243175506592, 0.0135649424046278, 0.03841492906212807, 0.05084432661533356, 0.01303678099066019, 0.016901161521673203, 0.027393965050578117, 0.045140184462070465, 0.022728540003299713, 0.012499816715717316, -0.0383797213435173, -0.0018826748710125685, -0.023256702348589897, 0.012147709727287292, -0.07232288271188736, 0.0014997579855844378, -0.018908172845840454, 0.019207464531064034, -0.06996376067399979, -0.015079004690051079, 0.04785141348838806, 0.05848505720496178, 0.0011520517291501164, -0.029823506250977516, -0.013864233158528805, 0.01301917526870966, -0.031073488295078278, -0.02420739270746708, 0.020615894347429276, 0.014911753125488758, -0.027992548421025276, 0.03140798956155777, -0.003576091956347227, 0.028626341372728348, -0.010202315635979176, 0.019823653623461723, 0.009991050697863102, -0.004245096351951361, 0.03711213171482086, 0.05133727565407753, -0.011417086236178875, -0.01587124727666378, 0.0026011941954493523, -0.03036927431821823, -0.06626663357019424, 0.009278032928705215, 0.00001678872104093898, -0.03693607822060585, 0.0018232567235827446, -0.0006618521292693913, -0.0027486393228173256, -0.003234987845644355, 0.011584337800741196, 0.03982336074113846, -0.01178679894655943, -0.0034176434855908155, -0.019348308444023132, -0.007006939500570297, 0.032710786908864975, 0.005933011882007122, -0.0010167104192078114, -0.05651325732469559, 0.0251228716224432, -0.005374040920287371, 0.015686389058828354, 0.004564193543046713, 0.043520487844944, 0.01211249828338623, -0.019489150494337082, -0.07309751957654953, -0.01917225494980812, -0.05098516866564751, 0.00613107206299901, 0.013705785386264324, 0.012402987107634544, 0.012068484909832478, 0.015343084931373596, 0.054647088050842285, 0.057992108166217804, -0.03154883533716202, 0.04218247905373573, -0.009172400459647179, 0.006421560887247324, 0.03202417865395546, -0.028767183423042297, -0.012623054906725883, -0.016593066975474358, -0.02422499656677246, -0.03911914676427841, -0.03742903098464012, 0.04204163700342178, 0.034700196236371994, 0.005840583238750696, -0.05866111069917679, -0.028168601915240288, -0.029207319021224976, 0.054787930101156235, 0.02251727506518364, -0.04112615808844566, -0.0410909466445446, 0.02558061107993126, 0.005466469097882509, -0.032411497086286545, 0.038837458938360214, 0.023820074275135994, 0.01441880315542221, 0.03036927431821823, 0.0438021756708622, -0.04200642555952072, 0.0013016974553465843, -0.022165168076753616, 0.037781137973070145, 0.02316867560148239, -0.015545547008514404, 0.013300861231982708, -0.06337935477495193, 0.0496823713183403, 0.02987632341682911, -0.023239096626639366, -0.05102038010954857, -0.009304441511631012, -0.021249689161777496, 0.012728686444461346, 0.004837077111005783, -0.04031630977988243, -0.013635363429784775, 0.007605522405356169, 0.02959463745355606, -0.00013637289521284401, -0.034876249730587006, -0.012376579456031322, -0.016742711886763573, -0.026284826919436455, -0.031355176120996475, 0.03323895111680031, 0.028626341372728348, -0.003591496730223298, 0.01571279764175415, 0.006179486867040396, -0.054787930101156235, 0.05408371612429619, 0.0006156379822641611, -0.004412347450852394, 0.0386614054441452, 0.009101979434490204, -0.047886621206998825, 0.006830886006355286, 0.0219010878354311, 0.013001570478081703, 0.05006968975067139, -0.02389049530029297, -0.03019321896135807, -0.031777702271938324, -0.059224486351013184, 0.02957703173160553 ]
Both in academic and industry-based research, online evaluation methods are seen as the golden standard for interactive applications like recommendation systems. Naturally, the reason for this is that we can directly measure utility metrics that rely on interventions, being the recommendations that are being shown to users. Nevertheless, online evaluation methods are costly for a number of reasons, and a clear need remains for reliable offline evaluation procedures. In industry, offline metrics are often used as a first-line evaluation to generate promising candidate models to evaluate online. In academic work, limited access to online systems makes offline metrics the de facto approach to validating novel methods. Two classes of offline metrics exist: proxy-based methods, and counterfactual methods. The first class is often poorly correlated with the online metrics we care about, and the latter class only provides theoretical guarantees under assumptions that cannot be fulfilled in real-world environments. Here, we make the case that simulation-based comparisons provide ways forward beyond offline metrics, and argue that they are a preferable means of evaluation.
[ -0.020874377340078354, -0.013524243608117104, -0.0471792034804821, 0.01995777152478695, 0.01399119384586811, -0.034467797726392746, -0.06755204498767853, 0.017527904361486435, -0.019006578251719475, -0.008435358293354511, 0.02774026431143284, -0.02063225395977497, 0.01876445673406124, -0.047386735677719116, 0.020545782521367073, 0.014293845742940903, 0.025647638365626335, 0.02281135320663452, 0.00727663142606616, 0.0047862334176898, -0.003130291821435094, -0.06533835828304291, -0.03355119377374649, 0.02614917792379856, -0.029279468581080437, 0.039292942732572556, 0.012434694916009903, 0.005201299674808979, -0.002304482739418745, 0.004470610059797764, 0.00960705615580082, 0.01437167078256607, -0.015945464372634888, -0.03495204076170921, -0.08010780066251755, -0.017882440239191055, 0.043028540909290314, 0.009658939205110073, 0.027463553473353386, 0.05835140496492386, 0.009434111416339874, 0.02142779901623726, -0.02326100878417492, 0.02033824846148491, -0.01886822283267975, -0.08301325887441635, -0.034502387046813965, -0.04178334400057793, 0.03662960231304169, 0.009434111416339874, 0.004284694790840149, -0.018954694271087646, 0.054823342710733414, 0.03061114065349102, -0.01478673703968525, 0.016135703772306442, 0.010169124230742455, -0.035972412675619125, 0.051848698407411575, -0.02250005304813385, -0.013221591711044312, 0.023900901898741722, -0.029365941882133484, -0.023503130301833153, -0.030887851491570473, -0.019802121445536613, -0.03346472233533859, -0.012503872625529766, 0.01511533185839653, -0.018729867413640022, -0.05904318392276764, -0.006550265476107597, 0.06170652434229851, 0.006891830358654261, -0.034485094249248505, 0.014544615522027016, 0.04247511923313141, 0.03884328901767731, -0.009252520278096199, 0.02353771962225437, 0.041472043842077255, 0.020787904039025307, 0.008534801192581654, -0.0024341910611838102, 0.04621071740984917, -0.035626526921987534, 0.029711829498410225, -0.0589740052819252, 0.0038069363217800856, -0.009537877514958382, -0.05053432285785675, -0.020891672000288963, 0.01459649857133627, 0.0034869892988353968, -0.05568806454539299, 0.03908541053533554, -0.014440848492085934, 0.01955999992787838, 0.0010609051678329706, 0.05305930972099304, 0.007060450967401266, -0.05835140496492386, 0.03652583435177803, 0.034087322652339935, -0.039292942732572556, -0.030887851491570473, -0.026495065540075302, 0.03690631315112114, 0.02364148572087288, 0.16464297473430634, 0.0044662863947451115, 0.014501378871500492, -0.020580371841788292, -0.0269447211176157, -0.05724456161260605, 0.00998753309249878, -0.03389708325266838, -0.052575066685676575, 0.07152976095676422, -0.012071511708199978, 0.001104141236282885, 0.08571119606494904, 0.06481952220201492, -0.032288700342178345, -0.04579564929008484, 0.06194864585995674, -0.04610694944858551, 0.004717055708169937, 0.021981220692396164, 0.01367989368736744, 0.01770084910094738, 0.016152996569871902, -0.01848774589598179, -0.047386735677719116, -0.008227825164794922, 0.008219177834689617, 0.0347445085644722, 0.08771734684705734, -0.0206841379404068, -0.00830565020442009, -0.03697549179196358, -0.03284212201833725, -0.06353973597288132, -0.009927002713084221, 0.028120743110775948, 0.00042857759399339557, -0.004196060821413994, 0.05506546422839165, -0.01384419109672308, -0.013048646971583366, -0.015348806045949459, 0.027809442952275276, -0.00830565020442009, 0.013939310796558857, 0.043789494782686234, 0.006887506693601608, -0.025543872267007828, -0.061429813504219055, 0.004474933724850416, 0.005482334177941084, 0.04140286520123482, -0.022949708625674248, -0.020096126943826675, 0.04344360902905464, 0.05063809081912041, 0.008193235844373703, 0.007328514475375414, -0.03284212201833725, -0.04787098243832588, 0.03662960231304169, -0.03680254518985748, -0.014605145901441574, -0.0684167668223381, 0.040053900331258774, 0.044273741543293, 0.07678727060556412, 0.08508859574794769, -0.01665453612804413, -0.033447425812482834, 0.014449495822191238, -0.07436604797840118, -0.009978885762393475, -0.007635490503162146, 0.009416816756129265, 0.022448169067502022, -0.006679973565042019, 0.06461198627948761, 0.021324031054973602, 0.03908541053533554, 0.035591937601566315, 0.0008463461417704821, 0.03763267770409584, 0.007596578449010849, 0.039223767817020416, 0.002704416401684284, -0.013169708661735058, -0.06540752947330475, -0.0007215020013973117, -0.0059233419597148895, -0.024886684492230415, -0.04918535798788071, -0.0522637665271759, 0.063332200050354, -0.015564986504614353, 0.026010822504758835, 0.008958514779806137, 0.04067649692296982, 0.02135862037539482, -0.021842865273356438, -0.07976190745830536, -0.008603978902101517, -0.018314801156520844, -0.04949665814638138, -0.022361697629094124, -0.007553342264145613, -0.014250610023736954, 0.0009117407025769353, 0.01992318220436573, -0.06402397900819778, -0.0028449336532503366, -0.013965251855552197, 0.00745389936491847, 0.04942747950553894, -0.03346472233533859, -0.004660848993808031, 0.015366100706160069, -0.004118236247450113, 0.017562493681907654, 0.07073421776294708, -0.01733766496181488, -0.003294588765129447, 0.0038090981543064117, 0.0027109018992632627, -0.0280342698097229, 0.010471777059137821, 0.006870212033390999, 0.05426992103457451, -0.041852518916130066, 0.003216763958334923, 0.0017251193057745695, -0.016741007566452026, -0.028103448450565338, 0.039984721690416336, -0.009883766993880272, 0.059977080672979355, -0.021773686632514, -0.009330344386398792, 0.023727957159280777, 0.03704466670751572, 0.03209846094250679, -0.043374430388212204, -0.06900477409362793, -0.07159893959760666, 0.03429485484957695, -0.0024147348012775183, 0.031839046627283096, 0.08903172612190247, -0.03348201513290405, -0.02806885913014412, -0.03825527802109718, 0.048113103955984116, 0.01347236055880785, -0.023364774882793427, 0.028968170285224915, -0.01382689643651247, 0.001312214881181717, 0.044412095099687576, -0.0038955702912062407, -0.0056639257818460464, 0.06170652434229851, -0.009952944703400135, -0.031545039266347885, -0.027083076536655426, -0.027792148292064667, 0.008067851886153221, -0.02507692389190197, 0.02030366100370884, -0.05160657688975334, 0.052229177206754684, 0.049669601023197174, -0.04908159002661705, -0.02208498679101467, -0.019802121445536613, 0.017476020380854607, -0.005936312954872847, -0.0640585646033287, 0.029625358060002327, 0.0205976665019989, -0.05420074239373207, -0.03398355469107628, -0.0014646219788119197, -0.08225230872631073, -0.036664191633462906, 0.004877028986811638, 0.019058462232351303, 0.035557348281145096, -0.0037896418944001198, 0.021272148936986923, 0.05267883464694023, -0.05976954847574234, -0.02289782464504242, 0.022621113806962967, 0.024143023416399956, 0.02357230708003044, -0.02841474860906601, -0.02464456297457218, 0.04392785206437111, 0.05160657688975334, 0.00644217524677515, -0.047006260603666306, 0.023001590743660927, -0.009390875697135925, 0.001545689650811255, -0.05343978852033615, 0.022206047549843788, 0.008993103168904781, 0.028674164786934853, -0.002496883273124695, -0.04496551677584648, -0.03358578309416771, -0.003443753346800804, 0.0005201839958317578, -0.10425081849098206, -0.03178716078400612, -0.03649124503135681, 0.021877452731132507, -0.015400690026581287, 0.02253464236855507, -0.004678143188357353, -0.00008025696297409013, -0.03407002612948418, -0.009650291875004768, -0.014423554763197899, -0.009321697987616062, 0.0095724668353796, -0.05506546422839165, -0.018677983433008194, -0.007419310510158539, -0.031596921384334564, -0.007445252034813166, 0.023503130301833153, -0.013792308047413826, 0.015737930312752724, 0.061775702983140945, 0.027117665857076645, -0.04278641939163208, -0.03835904598236084, 0.020148010924458504, 0.05191787704825401, 0.01954270526766777, 0.0010479344055056572, -0.00926116667687893, -0.05561888590455055, 0.002985450904816389, 0.0943584069609642, -0.007657108828425407, 0.01238281186670065, -0.00043398208799771965, -0.0162827055901289, -0.011941803619265556, 0.036110769957304, -0.025976233184337616, -0.06374726444482803, 0.068036288022995, -0.07045750319957733, 0.058109283447265625, -0.020753314718604088, 0.013377241790294647, 0.052955545485019684, -0.019369760528206825, -0.010290185920894146, -0.03066302463412285, 0.0031670425087213516, -0.019283289089798927, -0.025284456089138985, 0.03280753269791603, -0.01621352694928646, -0.01586763933300972, -0.055515117943286896, 0.027861326932907104, -0.03714843466877937, 0.000029437685952871107, 0.042959362268447876, 0.027031194418668747, -0.03170068934559822, 0.007384721655398607, 0.04873570427298546, 0.021116498857736588, -0.007250689435750246, 0.05354355275630951, 0.019854005426168442, -0.019854005426168442, -0.007030185777693987, -0.028587691485881805, -0.007410663180053234, -0.030784085392951965, -0.013956604525446892, -0.01125867385417223, -0.006913448218256235, -0.019681060686707497, -0.033741433173418045, 0.0049116178415715694, -0.05572265386581421, 0.048528168350458145, -0.032271407544612885, 0.02320912480354309, 0.042198408395051956, -0.03462344780564308, 0.007877612486481667, 0.010549602098762989, 0.016836127266287804, -0.0464528389275074, 0.0019283288856968284, 0.07083798199892044, -0.023900901898741722, 0.024523502215743065, -0.055169232189655304, -0.023797135800123215, 0.04766344651579857, -0.028501220047473907, -0.037874799221754074, -0.0045743766240775585, 0.05043055862188339, 0.00015267738490365446, 0.00011754807928809896, 0.01199368666857481, -0.031181856989860535, -0.01992318220436573, -0.02104732021689415, -0.02734249271452427, 0.018885517492890358, 0.03197740018367767, 0.02033824846148491, -0.049565836787223816, 0.014440848492085934, 0.015530398115515709, 0.007843024097383022, -0.011310556903481483, -0.035384401679039, 0.0011349469423294067, -0.012235809117555618, -0.041126154363155365, 0.034450504928827286, 0.024886684492230415, 0.0172857828438282, -0.01803809031844139, -0.025007745251059532, -0.03387978672981262, -0.013878779485821724, -0.02843204326927662, -0.08744063973426819, 0.03984636440873146, -0.07761739939451218, -0.012694111093878746, 0.008984455838799477, -0.008383475244045258, 0.057763393968343735, -0.05465039610862732, 0.010264243930578232, -0.03953506797552109, 0.008772599510848522, 0.041126154363155365, -0.0005428829463198781, 0.005049973260611296, 0.028950875625014305, 0.059562016278505325, -0.06170652434229851, -0.022794058546423912, 0.005577453412115574, -0.00373343494720757, 0.01878175139427185, 0.023105358704924583, -0.005616365931928158, 0.0063643502071499825, 0.035557348281145096, -0.03939671069383621, -0.0012279044603928924, -0.02985018491744995, 0.051502812653779984, -0.035626526921987534, 0.0003394031955394894, 0.06167193502187729, 0.023745251819491386, -0.031095383688807487, 0.02208498679101467, 0.02282864786684513, 0.023122653365135193, 0.02403925731778145, 0.013576127588748932, -0.05561888590455055, -0.06879723817110062, -0.03253082185983658, 0.015227745287120342, -0.009174695238471031, -0.016879362985491753, 0.007116657681763172, -0.022949708625674248, 0.009114164859056473, 0.01693989336490631, 0.016490237787365913, -0.007436604704707861, 0.008366180583834648, -0.037771034985780716, 0.007432281039655209, 0.001971564954146743, -0.01090413797646761, 0.010912785306572914, -0.021618036553263664, -0.040019311010837555, 0.02035554312169552, -0.020372837781906128, 0.0310262069106102, 0.020372837781906128, -0.008897984400391579, 0.027550026774406433, 0.030801380053162575, -0.02955617941915989, -0.04399703070521355, 0.04617612808942795, 0.03479639068245888, -0.010099946521222591, -0.002477427013218403, 0.0018105106428265572, 0.01730307750403881, -0.008335915394127369, 0.07201400399208069, -0.025007745251059532, -0.007142599672079086, 0.054823342710733414, 0.011198143474757671, -0.018366685137152672, 0.05236753448843956, -0.05489252135157585, -0.027567321434617043, 0.006403262726962566, -0.023053474724292755, -0.0012365516740828753, 0.011016551405191422, -0.017986206337809563, 0.0024882361758500338, -0.020493898540735245, 0.02697931043803692, 0.03296318277716637, 0.0009819993283599615, 0.00526615371927619, 0.039258357137441635, 0.032617293298244476, -0.029711829498410225, 0.016775596886873245, 0.029210291802883148, 0.0019780504517257214, 0.006334085017442703, -0.0024147348012775183, 0.018055384978652, -0.009546524845063686, 0.0038955702912062407, -0.02097814343869686, 0.0010814423440024257, 0.02291511930525303, -0.006009814329445362, -0.007990026846528053, 0.0039820424281060696, 0.007233395241200924, -0.004933236166834831, 0.015054801478981972, -0.01142297126352787, 0.04973877966403961, 0.02692742645740509, -0.010999257676303387, -0.03315342217683792, -0.03953506797552109, 0.049669601023197174, -0.032669179141521454, -0.06779416650533676, -0.024938568472862244, 0.031164562329649925, -0.02616647258400917, -0.030559256672859192, 0.0035864324308931828, -0.0191449336707592, 0.03728679195046425, -0.026650715619325638, -0.03178716078400612, 0.0515374019742012, -0.03884328901767731, -0.026616128161549568, -0.01766625978052616, -0.008236472494900227, -0.0017197148408740759, 0.023451246321201324, 0.03512498736381531, 0.05195246636867523, -0.05530758574604988, -0.005460716318339109, -0.027844032272696495, -0.014821326360106468, -0.03469262644648552, 0.01159591507166624, 0.019854005426168442, -0.013420477509498596, 0.020891672000288963, -0.020805198699235916, 0.016455650329589844, 0.014778089709579945, -0.00007741959416307509, 0.0331188328564167, 0.018660688772797585, 0.017778674140572548, 0.0055298940278589725, 0.014925092458724976, -0.03180445730686188, -0.04672954976558685, 0.0399155430495739, -0.022984297946095467, 0.0006134118302725255, -0.04430832713842392, 0.035557348281145096, 0.009183342568576336, -0.005979549139738083, 0.0064724404364824295, 0.03536710888147354, -0.004535464104264975, 0.04095320776104927, 0.003374575637280941, -0.02134132571518421, 0.013973899185657501, 0.013714483007788658, -0.023900901898741722, -0.005404509138315916, -0.017216604202985764, -0.040745675563812256, 0.015668753534555435, -0.012019628658890724, -0.02210228145122528, 0.00926116667687893, -0.007881936617195606, -0.0015921684680506587, 0.051779523491859436, 0.025924349203705788, -0.0018256432376801968, 0.013126472011208534, 0.011941803619265556, -0.02106461487710476, 0.0727749615907669, 0.001691611367277801, 0.06156817078590393, -0.026616128161549568, 0.0025228250306099653, 0.012495225295424461, 0.04607236012816429, -0.005486657842993736, 0.025889761745929718, 0.019784826785326004, 0.02729061059653759, 0.013221591711044312, -0.011872625909745693, 0.009477347135543823, 0.00012930289085488766, 0.010229655541479588, 0.034554269164800644, 0.021618036553263664, 0.014492732472717762, 0.011111671105027199, 0.050741855055093765, -0.008059204556047916, 0.007427957374602556, 0.02473103441298008, -0.017156073823571205, -0.006165464408695698, 0.022067692130804062, 0.0019964256789535284, -0.026771776378154755, -0.02578599378466606, 0.027394376695156097, 0.02253464236855507, -0.02952159196138382, 0.007609548978507519, 0.020839788019657135, -0.0016181101091206074, 0.009485994465649128, 0.0010430703405290842, 0.007505782414227724, -0.006507029291242361, 0.004885676316916943, 0.00041776857688091695, -0.018539628013968468, -0.03221952170133591, 0.03873952105641365, -0.012443342246115208, 0.012469284236431122, -0.02912382036447525, -0.009624349884688854, -0.003772347467020154, 0.025388222187757492, 0.002170450985431671, 0.012711405754089355, -0.012616286054253578, -0.03579946979880333, 0.028138037770986557, -0.01955999992787838, -0.025630345568060875, 0.027722971513867378, -0.03095702826976776, 0.02870875410735607, -0.006986949592828751, -0.030161485075950623, 0.015686048194766045, 0.02876063622534275, -0.0346580371260643, 0.007886259816586971, -0.012123394757509232, -0.014025782234966755, -0.04818228259682655, 0.009485994465649128, -0.003627506550401449, 0.008297002874314785, 0.04133368656039238, 0.0039258357137441635, -0.011492148973047733, 0.052540477365255356, 0.024973155930638313, -0.022413581609725952, 0.025336340069770813, -0.04928912594914436, -0.024627268314361572, 0.030801380053162575, 0.008361856453120708, -0.03649124503135681, -0.0007901392527855933, -0.0023606896866112947, 0.05599936470389366, 0.008785570040345192, 0.005011061206459999, 0.009451406076550484, -0.00795111432671547, 0.01086090225726366, -0.026719894260168076, 0.003141100751236081, 0.0007263660663738847, -0.014648381620645523, 0.014423554763197899, -0.02360689640045166, -0.033343661576509476, -0.0007096120971255004, -0.03138938918709755, 0.0181418564170599, 0.02028636634349823, 0.03732137754559517, -0.004513846244663, -0.015452573075890541, 0.03832445666193962, 0.016023289412260056, 0.01307458896189928, -0.04800933599472046, -0.06962737441062927, -0.026840955018997192, -0.00905363354831934, 0.05523840710520744, 0.02429867349565029, -0.027826737612485886, -0.0101172411814332, 0.06174111366271973, 0.034882865846157074, 0.018971988931298256, -0.0012430371716618538, 0.011016551405191422, -0.07242906838655472, 0.007985702715814114, 0.002345557091757655, -0.03534981608390808, 0.015340158715844154, 0.04641824960708618, 0.06430068612098694, -0.0420946404337883, 0.011371087282896042, 0.05980413779616356, 0.0254055168479681, -0.013602068647742271, -0.022984297946095467, 0.003724787849932909, -0.001186830224469304, -0.012901644222438335, -0.018539628013968468, 0.0745735839009285, -0.0377364456653595, 0.017795968800783157, -0.01459649857133627, -0.005988196469843388, 0.0031475862488150597, 0.02217145822942257, -0.016758302226662636, -0.02578599378466606, 0.003022201592102647, 0.03517686948180199, 0.0269447211176157, -0.02614917792379856, -0.01957729458808899, -0.03424296900629997, -0.026460478082299232, -0.012460636906325817, 0.022309813648462296, -0.004643554333597422, 0.017138779163360596, -0.008439681492745876, -0.008616949431598186, -0.018971988931298256, 0.006939389742910862, -0.04676413908600807, -0.023883607238531113, 0.05537676438689232, 0.034502387046813965, 0.012426047585904598, -0.0023585278540849686, -0.017086897045373917, 0.022033102810382843, -0.046349070966243744, -0.009105517528951168, 0.03649124503135681, -0.010670662857592106, 0.016161644831299782, 0.0008425629930570722, -0.0627787783741951, -0.02365878038108349, -0.03842822462320328, -0.005845517385751009, -0.0016570225125178695, -0.01735495962202549, 0.039673421531915665, 0.05053432285785675, -0.006814005319029093, 0.01879904419183731, 0.06302089989185333, -0.037010081112384796, -0.02474832907319069, -0.02504233457148075, 0.03552275896072388, -0.013705835677683353, 0.012279044836759567, 0.0021326192654669285, 0.006066021043807268, 0.033395543694496155, -0.03142397850751877, 0.031579628586769104, -0.0391891784965992, 0.006338408682495356, -0.0033594430424273014, -0.016300000250339508, 0.012019628658890724, -0.022603819146752357, 0.04513845965266228, 0.022033102810382843, 0.022378992289304733, 0.0152882756665349, -0.028241803869605064, -0.027965093031525612, -0.01810726709663868, 0.011198143474757671, 0.032340582460165024, -0.02692742645740509, -0.004496551584452391, 0.002870875410735607, 0.00764413783326745, -0.027446260675787926, -0.015167214907705784, 0.005949283950030804, -0.007384721655398607, -0.02799968235194683, -0.05022302269935608, -0.01879904419183731, -0.09574196487665176, -0.03512498736381531, 0.02253464236855507, -0.03694090247154236, 0.03714843466877937, -0.004360358230769634, 0.0428210087120533, 0.013792308047413826, 0.03289400413632393, 0.02623564936220646, -0.01701771840453148, -0.013316710479557514, 0.02135862037539482, 0.05541135370731354, -0.01883363351225853, 0.011500795371830463, -0.006654032040387392, -0.04897782579064369, -0.00976270530372858, -0.023001590743660927, -0.02288052998483181, 0.020078832283616066, -0.010316126979887486, -0.019006578251719475, -0.00866018608212471, -0.014241962693631649, -0.0042241644114255905, 0.0011003580875694752, 0.041472043842077255, 0.00010727950575528666, 0.045899417251348495, 0.01251251995563507, 0.015366100706160069, -0.02654694952070713, -0.044861748814582825, -0.01403442956507206, -0.0024255437310785055, -0.005149416625499725, -0.03946588933467865, 0.0411953330039978, -0.00618275860324502, -0.015582281164824963, -0.03469262644648552, 0.04513845965266228, -0.011716975830495358, 0.009978885762393475, 0.005460716318339109, -0.05682949721813202, 0.005754721350967884, 0.013048646971583366, -0.011587267741560936, 0.03642207011580467, 0.010575544089078903, 0.007747904397547245, 0.014812679030001163, -0.011915861628949642, 0.03439861908555031, -0.002141266595572233, 0.03176986798644066, -0.005006737541407347, 0.04181792959570885, -0.02135862037539482, 0.021687215194106102, 0.002587679075077176, -0.019663766026496887, 0.00680968165397644, 0.021687215194106102, -0.004016631282866001, -0.016109760850667953, -0.007367426995187998, -0.023727957159280777, -0.021618036553263664, 0.007531723938882351, 0.00901039782911539, 0.00042236241279169917, 0.007648461498320103, -0.0042955041863024235, 0.060011669993400574, 0.01124137919396162, -0.012408752925693989, -0.04794015735387802, -0.04164498671889305, -0.03977718949317932, 0.023088064044713974, -0.0195945892482996, 0.004902970977127552, -0.0044792573899030685, -0.03062843531370163, 0.014769443310797215, -0.012633580714464188, 0.020528487861156464, -0.04451586306095123, -0.015296922996640205, 0.020822493359446526, -0.01845315657556057, -0.042648062109947205, -0.02910652570426464, -0.013048646971583366, -0.011293262243270874, -0.04164498671889305, 0.030092308297753334, -0.014328435063362122, 0.015720637515187263, 0.028103448450565338, 0.04095320776104927, 0.01629135198891163, -0.037425145506858826, 0.011085729114711285, -0.029020052403211594, -0.024108434095978737, 0.0727749615907669, 0.05873188376426697, 0.029348647221922874, -0.026616128161549568, 0.03825527802109718, -0.0013878779718652368, -0.01876445673406124, 0.0181418564170599, -0.0025314721278846264, 0.0010219926480203867, 0.009918355382978916, 0.016005994752049446, -0.029296763241291046, 0.04351278394460678, -0.026010822504758835, -0.0457264706492424, -0.02687554433941841, 0.0012095292331650853, 0.029608063399791718, -0.011889920569956303, 0.015521750785410404, -0.011128965765237808, 0.001400848850607872, -0.009684880264103413, -0.012996763922274113, 0.021514270454645157, -0.008915278129279613, 0.06672190874814987, -0.014164137654006481, -0.023122653365135193, 0.05340519919991493, -0.0048683821223676205, -0.00000755364635551814, -0.029262175783514977, -0.007423634175211191, -0.0019412997644394636, -0.010099946521222591, -0.046003181487321854, -0.015279628336429596, 0.019854005426168442, -0.07810164242982864, 0.019698355346918106, -0.039258357137441635, 0.034882865846157074, -0.013204297050833702 ]
High-quality medical systematic reviews require comprehensive literature searches to ensure the recommendations and outcomes are sufficiently reliable. Indeed, searching for relevant medical literature is a key phase in constructing systematic reviews and often involves domain (medical researchers) and search (information specialists) experts in developing the search queries. Queries in this context are highly complex, based on Boolean logic, include free-text terms and index terms from standardised terminologies (e.g., the Medical Subject Headings (MeSH) thesaurus), and are difficult and time-consuming to build. The use of MeSH terms, in particular, has been shown to improve the quality of the search results. However, identifying the correct MeSH terms to include in a query is difficult: information experts are often unfamiliar with the MeSH database and unsure about the appropriateness of MeSH terms for a query. Naturally, the full value of the MeSH terminology is often not fully exploited. This article investigates methods to suggest MeSH terms based on an initial Boolean query that includes only free-text terms. In this context, we devise lexical and pre-trained language models based methods. These methods promise to automatically identify highly effective MeSH terms for inclusion in a systematic review query. Our study contributes an empirical evaluation of several MeSH term suggestion methods. We further contribute an extensive analysis of MeSH term suggestions for each method and how these suggestions impact the effectiveness of Boolean queries.
[ 0.037893131375312805, 0.06476148217916489, -0.02632075920701027, -0.015505884774029255, 0.06111089140176773, 0.005475886166095734, -0.035867054015398026, 0.00010352847311878577, -0.0028839667793363333, -0.0009845186723396182, 0.04114215821027756, -0.025882689282298088, -0.02593744732439518, 0.012548905797302723, -0.0050013093277812, 0.052532002329826355, -0.01323339156806469, -0.05479536950588226, 0.02124643884599209, -0.029971349984407425, -0.04694659635424614, 0.03360368683934212, -0.008195576258003712, 0.006972628645598888, 0.003230772912502289, 0.015834437683224678, -0.016208622604608536, 0.0071734110824763775, -0.02250589244067669, 0.06939773261547089, 0.013023482635617256, 0.0041183228604495525, -0.012311617843806744, -0.02458672970533371, -0.030847491696476936, -0.013315530493855476, 0.0018047608900815248, 0.01985921338200569, -0.0052020917646586895, 0.0027790123131126165, 0.04048505052924156, 0.013744474388659, -0.009582800790667534, -0.04508479684591293, -0.003808022476732731, -0.020607585087418556, -0.0019519253401085734, -0.0070867096073925495, 0.03606783598661423, -0.053590673953294754, 0.03057369776070118, -0.019786201417446136, 0.04855285957455635, -0.03395049646496773, -0.036688439548015594, 0.0036437460221350193, 0.017039133235812187, 0.026594555005431175, 0.030902251601219177, -0.026302507147192955, 0.013954383321106434, -0.006940685678273439, 0.04815129190683365, 0.007762068882584572, -0.0025713848881423473, -0.05399223789572716, -0.0143742011860013, -0.008013047277927399, -0.03318386897444725, 0.00978358369320631, -0.013780980370938778, 0.014994801953434944, 0.021848786622285843, 0.04957502335309982, -0.006529994308948517, -0.011928305961191654, -0.013589324429631233, 0.030409421771764755, -0.04008348658680916, 0.003283250145614147, 0.06735339760780334, 0.028967438265681267, 0.04110565409064293, -0.007031950633972883, 0.055379461497068405, -0.025134317576885223, -0.009409397840499878, -0.04406263306736946, 0.004367019049823284, 0.02027903124690056, -0.030883997678756714, -0.005685795098543167, 0.06509003788232803, 0.029003944247961044, -0.0061877514235675335, 0.02502479963004589, 0.005996095482259989, -0.005681232083588839, -0.07385145127773285, -0.026831842958927155, -0.017687112092971802, -0.07224519550800323, -0.010349424555897713, -0.027215154841542244, 0.03756457939743996, -0.056146085262298584, -0.006835731212049723, -0.03760108724236488, 0.014337695203721523, 0.14631567895412445, -0.011964811012148857, -0.009327259846031666, -0.0038490917067974806, -0.009149293415248394, -0.03975493460893631, 0.016445912420749664, -0.0657106339931488, -0.07607831060886383, -0.024422451853752136, -0.04723864421248436, 0.03486314415931702, 0.04110565409064293, -0.030172133818268776, 0.01903783157467842, -0.08082408457994461, 0.020151261240243912, -0.040266018360853195, 0.0031737324316054583, 0.030391167849302292, 0.003796614473685622, 0.0292777381837368, -0.011599752120673656, -0.03714476153254509, -0.019056083634495735, 0.029241232201457024, 0.07914480566978455, 0.025426365435123444, 0.04249287769198418, -0.0008185309125110507, -0.04136119410395622, -0.02632075920701027, -0.06607569754123688, -0.046873584389686584, -0.019585419446229935, 0.048224303871393204, -0.0012149622198194265, -0.015980461612343788, 0.035812295973300934, -0.03964541479945183, 0.008610831573605537, 0.003999678418040276, 0.0006559655303135514, 0.018170814961194992, -0.022834446281194687, 0.044026125222444534, -0.023984381929039955, 0.03309260681271553, -0.027817502617836, 0.07615132629871368, 0.028237320482730865, 0.03239899501204491, -0.05439380183815956, -0.0050286888144910336, 0.04289444163441658, 0.09571848809719086, 0.02681358903646469, -0.03670668974518776, -0.005238597746938467, -0.01504956092685461, 0.04336901754140854, 0.00495111383497715, 0.004100069869309664, -0.03873276710510254, 0.010541081428527832, 0.009956986643373966, 0.054612837731838226, 0.045522868633270264, -0.025298593565821648, -0.022451134398579597, -0.011846167035400867, -0.08104311674833298, 0.0016975246835500002, 0.04362456128001213, -0.013032609596848488, 0.059395112097263336, -0.026339013129472733, 0.05479536950588226, 0.03154110535979271, 0.003529665060341358, 0.04767671599984169, -0.05505090951919556, 0.007625171449035406, -0.014675375074148178, 0.031851403415203094, 0.011910052970051765, 0.02434944175183773, -0.011818788014352322, 0.019238613545894623, -0.0226519163697958, -0.04125167801976204, -0.021027402952313423, -0.021136920899152756, -0.01835334487259388, 0.0226519163697958, 0.05096224695444107, -0.019640179350972176, 0.024312935769557953, -0.01219297293573618, -0.021611496806144714, -0.03249025717377663, -0.017504582181572914, 0.010522828437387943, -0.021812280640006065, 0.005735991057008505, -0.007228170055896044, -0.0006063402979634702, -0.001719200168736279, -0.007944597862660885, -0.035775791853666306, 0.025590641424059868, 0.016153864562511444, -0.01965843141078949, 0.06629472970962524, -0.02308998629450798, 0.003525101812556386, 0.03323863074183464, 0.026485037058591843, -0.016345519572496414, 0.04187227785587311, -0.007050203625112772, 0.03468061238527298, 0.030829239636659622, 0.011152555234730244, 0.005891141016036272, 0.02792702056467533, -0.05756981670856476, 0.003075622720643878, -0.05081622302532196, 0.024751005694270134, -0.043843597173690796, -0.007073019631206989, -0.03374971076846123, 0.003255870658904314, -0.020753609016537666, 0.07607831060886383, -0.02153848670423031, 0.005380058195441961, 0.02467799372971058, -0.0000720136085874401, -0.010732737369835377, 0.03738205134868622, -0.01441983412951231, -0.024093899875879288, 0.030117373913526535, -0.02449546381831169, -0.0003519397578202188, 0.054028745740652084, -0.06355678290128708, -0.034425072371959686, -0.030975263565778732, 0.05618259310722351, -0.030172133818268776, 0.04523082077503204, 0.022633662447333336, 0.009929606691002846, 0.02226860448718071, 0.10141341388225555, 0.03292832896113396, -0.01263104472309351, -0.009719697758555412, -0.000055257965868804604, -0.06432341039180756, 0.017458951100707054, 0.008752291090786457, -0.01377185434103012, -0.0985659509897232, 0.03362194076180458, -0.03495440632104874, 0.028328584507107735, -0.023162998259067535, -0.0360313318669796, 0.0005721160559915006, -0.0013096494367346168, 0.04855285957455635, 0.007031950633972883, -0.012895711697638035, 0.01749545708298683, 0.012028696946799755, 0.004492508247494698, 0.03573928400874138, 0.013014356605708599, -0.010632345452904701, -0.003705349750816822, -0.035575006157159805, 0.07724650204181671, -0.00029575490043498576, 0.023984381929039955, 0.061037879437208176, 0.006333774887025356, -0.015670161694288254, -0.05056068301200867, 0.012621917761862278, -0.0096375597640872, 0.008843556046485901, -0.05906656011939049, 0.013443300500512123, 0.04504828900098801, 0.11557770520448685, -0.051035258919000626, -0.05767933651804924, 0.037363797426223755, 0.000983948353677988, -0.03329338878393173, -0.03667018562555313, 0.0421278178691864, 0.06114739552140236, 0.016792718321084976, -0.026503289118409157, -0.019913973286747932, -0.043405525386333466, 0.005544334650039673, -0.0006930418312549591, -0.06494401395320892, -0.005809002555906773, -0.046691056340932846, -0.036597173660993576, -0.05362717807292938, 0.015597149729728699, 0.02845635637640953, 0.05516042560338974, -0.024568475782871246, 0.029788821935653687, -0.028912680223584175, -0.014730134047567844, -0.014921789988875389, -0.012594538740813732, 0.01475751306861639, 0.030975263565778732, -0.02057107910513878, -0.007027387153357267, -0.027507202699780464, 0.012265984900295734, -0.074180006980896, -0.0030664962250739336, 0.059541136026382446, 0.020352043211460114, 0.009728824719786644, 0.04307697340846062, 0.026156483218073845, -0.01989571936428547, 0.0010170318419113755, -0.018946565687656403, -0.016491543501615524, -0.04055806249380112, -0.049392495304346085, -0.02535335347056389, -0.06567412614822388, -0.05486838147044182, 0.024897029623389244, 0.051619354635477066, 0.01757759414613247, -0.12105359137058258, 0.041178666055202484, 0.022305110469460487, -0.0492829754948616, 0.0104315634816885, -0.02414865791797638, 0.019092589616775513, -0.02414865791797638, -0.012311617843806744, 0.034461576491594315, 0.02652154304087162, 0.05271453037858009, -0.011508487164974213, -0.0285476204007864, 0.008487624116241932, 0.03170538321137428, -0.021082162857055664, -0.03135857358574867, 0.03121255151927471, 0.0063611543737351894, 0.0627901628613472, 0.019877467304468155, 0.008236645720899105, -0.03723602741956711, -0.03650590777397156, 0.02097264491021633, -0.0467640683054924, -0.022907458245754242, 0.03546549007296562, -0.01850849576294422, 0.023747093975543976, 0.016993500292301178, -0.06472497433423996, 0.03289182484149933, -0.02004174329340458, 0.019475901499390602, 0.04519431293010712, -0.0014009142760187387, 0.005389184691011906, 0.004795963875949383, -0.057168252766132355, -0.04621648043394089, 0.0039289481937885284, 0.006224257405847311, -0.006406786851584911, -0.007625171449035406, -0.03628687188029289, -0.016646694391965866, -0.018243826925754547, -0.06925170868635178, 0.0019713190849870443, -0.020023491233587265, 0.016016967594623566, 0.022049568593502045, 0.02279794029891491, 0.0009172109421342611, 0.040886618196964264, 0.005060631316155195, -0.013936130329966545, -0.0650535300374031, -0.004216432571411133, 0.0012822700664401054, 0.01816168986260891, -0.0303364098072052, -0.006826604716479778, 0.02599220722913742, -0.029040450230240822, -0.02613823115825653, -0.045960936695337296, 0.04139769822359085, -0.008688406087458134, 0.0016633004415780306, -0.029259486123919487, 0.07476410269737244, -0.006452419329434633, 0.0008784233941696584, -0.035428982228040695, -0.058811020106077194, 0.040119994431734085, 0.009144729934632778, -0.03170538321137428, -0.05592705309391022, 0.027452442795038223, -0.013096494600176811, -0.003639182774350047, 0.007305745035409927, -0.009436776861548424, 0.0017557060346007347, 0.015980461612343788, 0.0022804783657193184, -0.02274318039417267, -0.06775496900081635, 0.052678026258945465, 0.04902743548154831, -0.025572389364242554, 0.02767147868871689, -0.037217773497104645, 0.040886618196964264, -0.026028713211417198, -0.022670168429613113, 0.056693676859140396, -0.009920480661094189, -0.05621909722685814, 0.0008287982200272381, 0.031194299459457397, -0.0488814115524292, -0.031230805441737175, 0.016938742250204086, 0.013297277502715588, -0.022086074575781822, 0.04033903032541275, -0.02241462841629982, -0.0226519163697958, -0.006662328261882067, 0.007511090487241745, 0.04523082077503204, 0.004424059763550758, 0.013242518529295921, -0.008058679290115833, 0.01892831362783909, 0.01802479289472103, -0.031851403415203094, 0.056839700788259506, 0.013142126612365246, 0.05110827088356018, 0.016108231619000435, 0.005722301080822945, 0.05468584969639778, -0.008729475550353527, -0.02347329817712307, -0.007739252410829067, -0.029934844002127647, 0.010422436520457268, 0.04439118504524231, 0.004887228365987539, -0.07980191707611084, -0.02004174329340458, -0.004428622778505087, -0.007337687537074089, 0.0009662657394073904, -0.01651892438530922, 0.0032535891514271498, 0.04563238471746445, -0.031230805441737175, 0.029825327917933464, -0.04829731583595276, -0.01985921338200569, 0.0006901898304931819, -0.009646686725318432, 0.01865451969206333, -0.011344211176037788, -0.0210639089345932, -0.02241462841629982, -0.005197528749704361, 0.042529381811618805, -0.0016062599606812, 0.016692327335476875, 0.04314998537302017, 0.048662375658750534, 0.01031291950494051, -0.008277714252471924, -0.002831489546224475, 0.06289967894554138, -0.02690485492348671, -0.020260779187083244, 0.01055933441966772, 0.0031760139390826225, 0.031668875366449356, -0.017458951100707054, -0.05888402834534645, 0.019786201417446136, 0.0272881668061018, -0.03656066581606865, 0.02024252526462078, -0.01686573028564453, -0.018462862819433212, 0.020990896970033646, -0.0020443308167159557, -0.05888402834534645, 0.022524144500494003, 0.019640179350972176, -0.021264690905809402, -0.03493615239858627, -0.007561286445707083, 0.03468061238527298, 0.06012523174285889, -0.036341629922389984, 0.010604966431856155, 0.018590634688735008, -0.01038593053817749, 0.03239899501204491, -0.012941344641149044, -0.021264690905809402, -0.010741863399744034, -0.0016176680801436305, -0.0014317161403596401, -0.029624544084072113, -0.006712523754686117, -0.0077073099091649055, -0.02893093228340149, 0.018298586830496788, -0.013105620630085468, -0.0024093899410218, 0.0035981135442852974, -0.03637813776731491, -0.006603006273508072, -0.0031805771868675947, 0.043405525386333466, -0.01709389127790928, 0.015615402720868587, -0.0004155399219598621, -0.04187227785587311, 0.03278230503201485, -0.017030006274580956, 0.040302522480487823, 0.043296005576848984, -0.012430261820554733, -0.0052020917646586895, -0.0019964168313890696, -0.020662344992160797, -0.02646678313612938, 0.021848786622285843, 0.01144460216164589, -0.0021675382740795612, 0.022286856546998024, -0.00551695516332984, -0.04245636984705925, -0.027890514582395554, 0.023874863982200623, 0.027324672788381577, 0.00008092618372756988, -0.024513717740774155, -0.05318911001086235, -0.011380717158317566, 0.033786218613386154, -0.01744069717824459, 0.017988286912441254, 0.011453729122877121, -0.018627138808369637, 0.008277714252471924, 0.03594006597995758, 0.005211218260228634, 0.023108240216970444, 0.01749545708298683, -0.009267937391996384, 0.01762322708964348, -0.021082162857055664, 0.0006650920258834958, -0.0009993492858484387, -0.027215154841542244, -0.005037815310060978, 0.006634948775172234, -0.037090003490448, 0.01415516622364521, -0.03336640074849129, 0.005653852596879005, -0.009099097922444344, -0.012986976653337479, 0.03249025717377663, 0.00015814472862984985, -0.024239923804998398, 0.01719428226351738, 0.014921789988875389, -0.010851381346583366, 0.05662066489458084, -0.014337695203721523, 0.01618124358355999, 0.0025919193867594004, 0.007652550935745239, -0.042967453598976135, -0.03468061238527298, 0.024751005694270134, -0.02091788500547409, 0.06308221071958542, -0.014401581138372421, -0.028219066560268402, 0.0653090700507164, 0.05322561413049698, 0.016728833317756653, -0.014702755026519299, 0.021648002788424492, -0.004791400395333767, 0.05892053619027138, -0.0022622256074100733, 0.014292063191533089, 0.01055933441966772, 0.03522820025682449, 0.05472235754132271, 0.0349726602435112, -0.009701444767415524, -0.003661999013274908, 0.027306418865919113, 0.060782335698604584, 0.014082154259085655, -0.024860523641109467, -0.03681620955467224, 0.024568475782871246, 0.04815129190683365, 0.028967438265681267, 0.06154896318912506, 0.024751005694270134, -0.003299221396446228, 0.01743157207965851, 0.07491012662649155, 0.020899632945656776, 0.027707984670996666, 0.02024252526462078, 0.0032672788947820663, 0.011590626090765, 0.013452427461743355, -0.03957240283489227, -0.030829239636659622, -0.0009611321147531271, 0.014219051226973534, -0.024860523641109467, 0.006279016379266977, 0.018663644790649414, -0.011827914044260979, -0.03095700964331627, 0.016071725636720657, -0.009719697758555412, -0.03778361529111862, -0.05727776885032654, 0.0038490917067974806, -0.005635599605739117, -0.0026375518646091223, 0.03745506331324577, -0.0016427658265456557, -0.016555428504943848, 0.00891200453042984, 0.02256065048277378, 0.014447213150560856, 0.002432206179946661, 0.07078495621681213, -0.007292055059224367, 0.003125818446278572, -0.029770568013191223, 0.012275111861526966, -0.0036711255088448524, -0.014100407250225544, 0.00045347181730903685, -0.029332498088479042, 0.01734030619263649, -0.002564540132880211, 0.002749351318925619, 0.0154328728094697, -0.019877467304468155, -0.007360503543168306, -0.00040926545625552535, -0.035191696137189865, 0.00015315369819290936, -0.026740577071905136, 0.014164292253553867, 0.0075841024518013, -0.03163237124681473, 0.0149035369977355, 0.0035570445470511913, -0.00004042743967147544, 0.04336901754140854, 0.010011745616793633, 0.039207346737384796, 0.0077209994196891785, -0.007620608434081078, 0.007857896387577057, 0.026977866888046265, -0.007383320014923811, 0.007862459868192673, 0.009354638867080212, -0.0035570445470511913, -0.005685795098543167, 0.0016404842026531696, -0.05829993635416031, 0.027160394936800003, -0.025170823559165, 0.011198187246918678, 0.033840976655483246, 0.010294666513800621, -0.032873570919036865, -0.018143435940146446, -0.040412042289972305, 0.02206782065331936, 0.0008362134685739875, -0.052532002329826355, 0.0018150281393900514, 0.004786837380379438, 0.026302507147192955, 0.028876174241304398, -0.029295992106199265, -0.008081495761871338, 0.007675367407500744, -0.01661931537091732, 0.03479013219475746, -0.0287484023720026, 0.02893093228340149, 0.03356718271970749, 0.010112136602401733, -0.007511090487241745, 0.010011745616793633, -0.012311617843806744, 0.03511868417263031, 0.03274580091238022, 0.05877451226115227, 0.04168974608182907, 0.022870952263474464, 0.012859206646680832, -0.07724650204181671, 0.02893093228340149, 0.009810962714254856, 0.014173419214785099, -0.0011094373185187578, -0.0118552939966321, 0.049830563366413116, -0.03964541479945183, 0.019384637475013733, -0.033457666635513306, 0.05307959020137787, 0.007511090487241745, -0.014365075156092644, 0.03594006597995758, -0.04008348658680916, -0.029113462194800377, -0.016628440469503403, 0.002274774480611086, -0.014958295971155167, -0.009267937391996384, 0.017814883962273598, -0.03028165176510811, 0.0011533584911376238, -0.01849936880171299, 0.0029113462660461664, -0.017267294228076935, -0.006320085376501083, -0.009984365664422512, 0.038951802998781204, -0.009222305379807949, 0.06633123755455017, -0.04753069207072258, 0.010595839470624924, 0.010906140320003033, 0.0022394093684852123, 0.0007643424323759973, 0.023400288075208664, 0.03771060332655907, -0.036834459751844406, -0.0226519163697958, -0.012913964688777924, -0.0036916600074619055, 0.015368987806141376, 0.037363797426223755, 0.028675390407443047, 0.026777083054184914, 0.0203337911516428, -0.0024025451857596636, 0.028365090489387512, -0.010769243352115154, -0.026868348941206932, 0.03157760947942734, -0.009838342666625977, 0.017312927171587944, -0.011992190964519978, -0.028657138347625732, 0.0036300562787801027, -0.04661804437637329, -0.0013450145488604903, -0.04052155837416649, 0.01865451969206333, 0.025043053552508354, 0.0049146078526973724, 0.013981763273477554, 0.026266001164913177, -0.04304046556353569, -0.03619560971856117, 0.006251636892557144, 0.014146039262413979, 0.0190743375569582, 0.003413302358239889, 0.015204710885882378, 0.02197655662894249, 0.038185179233551025, -0.05556199327111244, -0.008136254735291004, -0.030500685796141624, 0.021648002788424492, 0.008291404694318771, 0.032581523060798645, -0.006247073411941528, 0.004691009409725666, -0.02203131653368473, 0.0692882165312767, 0.0358305498957634, -0.045522868633270264, -0.01865451969206333, 0.02840159647166729, 0.01826208084821701, -0.019913973286747932, 0.004357893019914627, 0.030975263565778732, -0.004992182832211256, 0.009304443374276161, 0.013872245326638222, -0.019840961322188377, 0.013744474388659, -0.02493353560566902, -0.006119302939623594, 0.00263983360491693, -0.0027676040772348642, -0.043442029505968094, -0.00022174487821757793, -0.047129128128290176, -0.0031075654551386833, 0.04095963016152382, -0.023400288075208664, -0.001603978336788714, 0.020863126963377, 0.02526208944618702, -0.0285476204007864, 0.03873276710510254, 0.024477211758494377, 0.004542703740298748, 0.04913695156574249, -0.001983867958188057, -0.007958288304507732, -0.0018001976422965527, 0.024805765599012375, -0.027817502617836, -0.04179926589131355, -0.04753069207072258, 0.025499377399683, -0.019913973286747932, -0.02400263398885727, 0.02989833801984787, 0.005809002555906773, -0.03844072297215462, 0.018179941922426224, 0.02376534603536129, -0.009445903822779655, 0.00551695516332984, -0.008323347195982933, 0.006415913347154856, -0.012183846905827522, -0.05362717807292938, -0.07115001231431961, -0.07863372564315796, -0.01376272737979889, -0.00941852480173111, 0.013279024511575699, -0.07056592404842377, 0.05873800814151764, -0.0203337911516428, -0.02203131653368473, 0.007889839820563793, -0.026101725175976753, -0.013069115579128265, -0.010577586479485035, 0.017687112092971802, 0.017331179231405258, -0.032453753054142, 0.018490241840481758, -0.024696247652173042, 0.030080867931246758, 0.01777837797999382, 0.008775107562541962, 0.018033917993307114, -0.04347853735089302, -0.03121255151927471, -0.007314871530979872, 0.030829239636659622, 0.05519693344831467, -0.029642798006534576, -0.046545032411813736, -0.0032490259036421776, 0.0029592602513730526, -0.013927004300057888, 0.034607600420713425, -0.0535176619887352, 0.024604981765151024, -0.006443292833864689, -0.013224265538156033, -0.0362321138381958, 0.006146682426333427, 0.02778099663555622, -0.0029113462660461664, -0.02540811151266098, -0.009071717970073223, -0.07695445418357849, 0.04844333976507187, 0.025809677317738533, 0.011791408061981201, 0.021921798586845398, -0.01806129887700081, 0.012932217679917812, 0.02071710303425789, -0.0116910170763731, 0.022305110469460487, -0.029204726219177246, -0.01719428226351738, 0.006603006273508072, 0.016491543501615524, 0.021100414916872978, -0.04975755140185356, -0.0016678636893630028, 0.023582816123962402, 0.014173419214785099, -0.028711896389722824, 0.002984357997775078, -0.03811216726899147, -0.0012001317227259278, -0.060782335698604584, -0.005512392148375511, 0.024550223723053932, -0.007205353584140539, -0.029186474159359932, 0.019603673368692398, 0.017376812174916267, -0.01744069717824459, 0.003983707167208195, 0.01995047926902771, -0.024075645953416824, 0.01584356464445591, 0.04136119410395622, -0.01855412870645523, -0.023601070046424866, -0.011143428273499012, 0.004351047798991203, -0.02878490835428238, 0.013945257291197777, -0.023199504241347313, -0.014867031015455723, 0.036779701709747314, 0.055525485426187515, -0.03484489023685455, 0.014748387038707733, -0.007889839820563793, -0.015715792775154114, 0.02221384458243847, -0.002836052794009447, -0.002715126844123006, 0.03884228691458702, 0.009427650831639767, -0.0013552817981690168, -0.015761425718665123, -0.015807058662176132, 0.01502218097448349, -0.0058135660365223885, 0.043734077364206314, 0.06268064677715302, 0.06370280683040619, -0.0030938757117837667, 0.02506130561232567, 0.052824050188064575, 0.02506130561232567, -0.025225583463907242, 0.07549421489238739, -0.0024139531888067722, 0.020224273204803467, -0.043880101293325424, -0.03294658288359642, 0.05957764387130737, -0.04548636078834534, 0.006575626786798239, -0.05789836868643761, -0.014000016264617443, -0.045522868633270264 ]
Most knowledge graphs (KGs) are incomplete, which motivates one important research topic on automatically complementing knowledge graphs. However, evaluation of knowledge graph completion (KGC) models often ignores the incompleteness -- facts in the test set are ranked against all unknown triplets which may contain a large number of missing facts not included in the KG yet. Treating all unknown triplets as false is called the closed-world assumption. This closed-world assumption might negatively affect the fairness and consistency of the evaluation metrics. In this paper, we study KGC evaluation under a more realistic setting, namely the open-world assumption, where unknown triplets are considered to include many missing facts not included in the training or test sets. For the currently most used metrics such as mean reciprocal rank (MRR) and Hits@K, we point out that their behavior may be unexpected under the open-world assumption. Specifically, with not many missing facts, their numbers show a logarithmic trend with respect to the true strength of the model, and thus, the metric increase could be insignificant in terms of reflecting the true model improvement. Further, considering the variance, we show that the degradation in the reported numbers may result in incorrect comparisons between different models, where stronger models may have lower metric numbers. We validate the phenomenon both theoretically and experimentally. Finally, we suggest possible causes and solutions for this problem. Our code and data are available at https://github.com/GraphPKU/Open-World-KG .
[ 0.01161448284983635, -0.01172219030559063, -0.030229967087507248, 0.027375712990760803, 0.002223715651780367, -0.013248049654066563, -0.04311899095773697, 0.019261730834841728, -0.02310330606997013, 0.016847282648086548, 0.018005140125751495, -0.008024225011467934, 0.01605742610991001, -0.049832772463560104, -0.07683150470256805, 0.022744281217455864, 0.04667334631085396, 0.0037563068326562643, -0.027268005535006523, -0.051771510392427444, -0.08415563404560089, -0.0801345482468605, -0.006152803543955088, 0.06652747094631195, 0.007768419571220875, 0.017879482358694077, 0.016847282648086548, 0.02890157140791416, -0.03751818835735321, 0.0599932000041008, 0.023929065093398094, 0.021110713481903076, 0.031540412455797195, 0.013786588795483112, -0.05062263086438179, 0.028847718611359596, 0.07148202508687973, -0.0002813303144648671, -0.007081782910972834, -0.01831928826868534, -0.013696831651031971, -0.015025227330625057, -0.022098034620285034, 0.0059867543168365955, -0.015671472996473312, -0.030122259631752968, -0.026406342163681984, -0.017744846642017365, -0.03992366045713425, -0.046170711517333984, -0.04211371764540672, -0.011111846193671227, 0.045847587287425995, -0.01177604403346777, -0.018435971811413765, 0.008176811039447784, 0.04362162575125694, -0.02204417996108532, 0.059490565210580826, 0.018184654414653778, -0.004927628207951784, 0.0361538901925087, -0.05342302843928337, 0.0029350353870540857, 0.0011157846311107278, -0.06412199884653091, -0.028201472014188766, 0.007606857921928167, -0.023462332785129547, -0.04728369042277336, -0.01489956770092249, 0.0009890036890283227, 0.04731959104537964, 0.012027362361550331, -0.03667448088526726, -0.010770772583782673, 0.05191512033343315, -0.001008076942525804, 0.0032491828314960003, 0.025024093687534332, 0.057013288140296936, 0.01836416684091091, -0.002335911151021719, 0.0053808982484042645, 0.04021088406443596, -0.03548969328403473, -0.01102208998054266, -0.035956427454948425, -0.0578390471637249, -0.012117118574678898, -0.007597882300615311, -0.04954555258154869, -0.040246784687042236, -0.02495228871703148, 0.016084352508187294, -0.009334669448435307, -0.019513048231601715, 0.017484553158283234, -0.053494833409786224, 0.03527427837252617, 0.017655091360211372, -0.045524463057518005, 0.0389183908700943, 0.0237675029784441, 0.015725327655673027, -0.026729466393589973, -0.010357892140746117, 0.029817087575793266, 0.05055082216858864, 0.1645773947238922, 0.05087394639849663, 0.07754956185817719, 0.0078043220564723015, -0.04674515128135681, -0.04039039462804794, 0.03798492252826691, -0.008665983565151691, 0.010250184684991837, 0.05191512033343315, 0.023049453273415565, -0.003792209317907691, 0.03748228773474693, 0.02721415087580681, -0.03719506785273552, -0.07036904245615005, 0.07395930588245392, -0.02331872098147869, -0.02278018370270729, -0.046709246933460236, -0.03730277344584465, 0.05564898997545242, -0.002593961078673601, -0.0022730818018317223, -0.0842992439866066, 0.051125265657901764, -0.012889023870229721, 0.053494833409786224, 0.03482549637556076, -0.0049725063145160675, 0.025849852710962296, -0.04545265808701515, -0.035435840487480164, -0.01509703230112791, 0.020661931484937668, -0.023282818496227264, -0.003621672047302127, -0.04879159852862358, 0.0192258283495903, -0.024898434057831764, 0.04243684187531471, 0.006839440204203129, 0.015761230140924454, -0.008773691952228546, -0.001749128568917513, 0.004833383951336145, 0.02620887942612171, 0.02944011054933071, -0.015402204357087612, 0.01627284102141857, 0.02610117197036743, 0.07453374564647675, -0.004561870824545622, 0.017493529245257378, 0.018777046352624893, 0.004294845275580883, 0.04372933506965637, 0.024898434057831764, -0.024341944605112076, -0.041000738739967346, 0.0339997373521328, 0.0006641976069658995, 0.016757525503635406, -0.031037775799632072, 0.0578390471637249, -0.025311315432190895, 0.05152019485831261, 0.0983012467622757, 0.026711514219641685, -0.044662803411483765, 0.012942877598106861, -0.014585420489311218, -0.02247501164674759, -0.026370439678430557, -0.0006900025764480233, 0.06580942124128342, -0.04362162575125694, 0.035435840487480164, 0.03021201677620411, -0.0199977345764637, 0.03482549637556076, 0.02344438061118126, 0.0208414439111948, 0.005071238614618778, 0.03443056717514992, 0.009370571933686733, -0.026747416704893112, -0.05270497873425484, -0.00235161860473454, -0.0028632301837205887, -0.01870524138212204, 0.00012054008402628824, -0.04717598110437393, 0.022205742076039314, -0.034987058490514755, 0.06904064863920212, 0.007292710244655609, 0.022062132135033607, 0.03148655593395233, -0.038092631846666336, -0.015447081997990608, -0.0507662408053875, -0.01322112325578928, -0.05406927689909935, -0.03312012553215027, 0.031127531081438065, 0.0027936690021306276, -0.008836520835757256, 0.03942102566361427, -0.03701555356383324, -0.04846847429871559, -0.04074942320585251, -0.044878218322992325, 0.050048187375068665, 0.00106249179225415, -0.036836039274930954, 0.020590126514434814, -0.007333100773394108, -0.03873887658119202, 0.0470682755112648, 0.018561631441116333, 0.02848869189620018, 0.00551104499027133, -0.018328264355659485, -0.013005707412958145, 0.007027928717434406, 0.02033880725502968, -0.007871638983488083, -0.043478015810251236, -0.001063613803125918, -0.010851552709937096, 0.011156724765896797, -0.03873887658119202, 0.004059234634041786, -0.044985923916101456, 0.03495115414261818, 0.01872319169342518, -0.05439240112900734, 0.03913380578160286, 0.08724325150251389, 0.03870297595858574, -0.027698835358023643, -0.02331872098147869, -0.014800836332142353, -0.01096823625266552, -0.0372309684753418, 0.044339679181575775, 0.03820033743977547, 0.009684719145298004, -0.02751932293176651, 0.00014922006812412292, 0.08867935836315155, 0.01890270598232746, -0.057049188762903214, 0.004209576640278101, -0.02224164456129074, 0.016694696620106697, 0.06074715405702591, -0.02613707445561886, -0.008890374563634396, 0.054248787462711334, 0.01317624468356371, -0.01182989776134491, -0.047247786074876785, -0.02922469563782215, -0.0014091760385781527, -0.04656563699245453, -0.009226961061358452, -0.08006273955106735, 0.04135976359248161, 0.007754955906420946, -0.010492526926100254, -0.027806542813777924, -0.05241775885224342, 0.0014046882279217243, 0.004712212830781937, -0.04031858965754509, 0.012718486599624157, 0.03161221742630005, -0.04247274622321129, -0.0002688485838007182, -0.01767304167151451, -0.0303017720580101, -0.05995729938149452, 0.04548856243491173, -0.003637379501014948, 0.06487595289945602, -0.000258470478001982, 0.00002733013388933614, 0.03247387707233429, -0.03525632619857788, -0.01650620810687542, -0.006538756191730499, -0.0041086007840931416, -0.0019387389766052365, -0.047894034534692764, -0.011049017310142517, 0.010941309854388237, 0.03051718696951866, -0.004968018736690283, -0.04635022208094597, 0.04010317474603653, -0.03633340448141098, -0.002096934709697962, -0.018525728955864906, 0.02967347763478756, 0.022977646440267563, 0.042400941252708435, -0.004088405519723892, -0.02525746077299118, -0.022313449531793594, 0.024593263864517212, -0.009756524115800858, -0.0941365510225296, -0.030481284484267235, -0.03469983860850334, 0.01848982647061348, -0.02267247624695301, 0.06006500497460365, 0.001764835906215012, -0.03690784424543381, -0.037338677793741226, -0.00032284267945215106, -0.035956427454948425, -0.025885755196213722, -0.043370310217142105, -0.028398936614394188, 0.011291359551250935, -0.017915384843945503, 0.00972062163054943, 0.012018386274576187, 0.011327262036502361, 0.02344438061118126, -0.009980915114283562, 0.025508778169751167, 0.009774475358426571, -0.02870410867035389, 0.013598100282251835, -0.00719846598803997, 0.07047675549983978, 0.06343984603881836, 0.0010181745747104287, 0.0552181601524353, -0.03301241621375084, 0.007297198288142681, 0.07105119526386261, 0.012072240002453327, 0.004328504204750061, 0.0011017601937055588, 0.015770206227898598, -0.0033142564352601767, -0.021667202934622765, -0.03970824554562569, -0.04150337725877762, 0.038308046758174896, -0.06871752440929413, 0.013059561140835285, 0.023785455152392387, 0.029709380120038986, 0.025329265743494034, -0.024575311690568924, -0.02581395022571087, 0.009819353930652142, 0.050586726516485214, -0.019405340775847435, 0.00017306162044405937, 0.02008748985826969, -0.052525464445352554, 0.033820223063230515, -0.04290357604622841, 0.031342945992946625, -0.012395363301038742, -0.002813864266499877, 0.05446420609951019, 0.015662498772144318, -0.023193063214421272, 0.060352224856615067, 0.03697965294122696, 0.004146747291088104, -0.009177595376968384, -0.0186154842376709, -0.05762363225221634, -0.009087839163839817, -0.01052842941135168, 0.014764933846890926, 0.018373142927885056, 0.005075726192444563, -0.039815954864025116, 0.039062000811100006, -0.0006933684344403446, 0.01231458317488432, 0.018453922122716904, 0.0067945620976388454, -0.002549082739278674, 0.02913493849337101, -0.02602936513721943, 0.006004705559462309, 0.0072568077594041824, -0.008383250795304775, 0.025095898658037186, -0.0110759437084198, 0.006767635233700275, -0.006063047330826521, -0.017960263416171074, -0.009096814319491386, 0.011363164521753788, 0.04602709785103798, -0.048109449446201324, -0.0019398609874770045, 0.027878347784280777, 0.013023658655583858, -0.017816651612520218, -0.034987058490514755, 0.06975869834423065, -0.013113414868712425, -0.03701555356383324, 0.009289790876209736, -0.0064220731146633625, 0.017358895391225815, 0.019531000405550003, -0.05902383103966713, 0.044447384774684906, -0.005591826047748327, 0.08128342777490616, -0.019100168719887733, -0.00629192590713501, 0.0018635679734870791, -0.021792862564325333, 0.013571172952651978, -0.00910579040646553, -0.012897999957203865, 0.021146615967154503, -0.021218420937657356, -0.035956427454948425, -0.006040608044713736, -0.020661931484937668, -0.006897781975567341, -0.03769770264625549, -0.033048320561647415, -0.025778047740459442, -0.044770509004592896, -0.0636911690235138, 0.05392566695809364, -0.04545265808701515, -0.012871072627604008, 0.015716351568698883, 0.014854690060019493, 0.07769317179918289, -0.05008409172296524, 0.019261730834841728, -0.04836076870560646, -0.025293363258242607, 0.05600801482796669, -0.014208443462848663, -0.05493093654513359, -0.014791860245168209, 0.041539277881383896, -0.01870524138212204, -0.010088623501360416, 0.001079321140423417, 0.01715245470404625, -0.0013048341497778893, 0.031145483255386353, -0.03525632619857788, -0.03902609646320343, 0.012996731325984001, 0.01156062912195921, 0.012978780083358288, -0.028327131643891335, 0.03008635714650154, -0.045201338827610016, 0.0518433153629303, 0.08034995943307877, -0.01525859348475933, -0.0037742580752819777, 0.02547287568449974, 0.006969586946070194, 0.051017556339502335, -0.034879349172115326, 0.004508017096668482, -0.024162432178854942, -0.05855709686875343, -0.017331967130303383, 0.026424294337630272, -0.0006187584367580712, 0.002672497881576419, 0.015913816168904305, -0.03502295911312103, -0.03105572611093521, 0.015267569571733475, -0.05299219861626625, 0.021541545167565346, -0.04976096749305725, -0.044985923916101456, 0.04372933506965637, -0.020374711602926254, 0.014791860245168209, 0.0013126878766342998, 0.016928063705563545, -0.04200601205229759, -0.04096483811736107, 0.004593285731971264, -0.008612129837274551, -0.008468519896268845, -0.036800138652324677, 0.01398405246436596, 0.02409062720835209, 0.00661056162789464, -0.005246263463050127, 0.07525179535150528, 0.016954990103840828, -0.023731600493192673, -0.009541109204292297, 0.0025378630962222815, 0.0595264658331871, -0.02182876504957676, 0.04236503690481186, -0.017439674586057663, 0.021254323422908783, 0.07740595191717148, -0.05234595388174057, 0.027501370757818222, 0.008100518025457859, -0.05159199982881546, -0.00013793040125165135, -0.004797481466084719, -0.004074942320585251, 0.04200601205229759, 0.02987094223499298, -0.03364071249961853, -0.00462245661765337, -0.01494444627314806, 0.003217768156901002, 0.017448650673031807, 0.010178379714488983, 0.014019954949617386, -0.002813864266499877, 0.007979347370564938, -0.02558058314025402, 0.02793220244348049, 0.04516543820500374, 0.03328168764710426, -0.025077948346734047, 0.02570624276995659, 0.009033985435962677, 0.0030988408252596855, -0.009110278449952602, -0.009123741649091244, -0.005699533503502607, 0.026155024766921997, -0.03881068155169487, -0.007916517555713654, 0.03031972423195839, -0.05044311657547951, -0.03394588455557823, 0.024216286838054657, -0.038308046758174896, 0.03654881939291954, 0.03974414989352226, -0.027860397472977638, 0.026298634707927704, -0.010295063257217407, -0.015608644112944603, -0.02538312040269375, -0.03748228773474693, -0.024772776290774345, -0.00905193667858839, -0.0021204957738518715, -0.04354982078075409, -0.009487255476415157, 0.011587555520236492, 0.029924795031547546, -0.0015011763898655772, -0.010070672258734703, 0.05984959006309509, -0.018794996663928032, -0.00789856631308794, -0.006996514275670052, -0.05482323095202446, -0.02602936513721943, -0.02803990989923477, -0.009074375964701176, 0.09499821066856384, 0.00034640374360606074, 0.001288004801608622, -0.020805541425943375, -0.019854122772812843, 0.0009912475943565369, -0.030176112428307533, 0.05335122346878052, -0.019082218408584595, 0.004232015926390886, -0.0481453500688076, 0.04351392015814781, -0.01548298541456461, -0.028416886925697327, -0.013212147168815136, 0.015698401257395744, 0.02965552546083927, 0.040569908916950226, 0.009146180935204029, -0.03866707161068916, -0.018067970871925354, 0.029260598123073578, -0.07033314555883408, 0.01745762676000595, 0.004072698298841715, 0.00232469174079597, 0.009936037473380566, 0.012305607087910175, -0.048109449446201324, 0.06440921872854233, -0.04688876122236252, 0.022941743955016136, 0.010016818530857563, -0.05126887559890747, 0.053782057017087936, -0.020823493599891663, 0.003329963656142354, 0.004481090232729912, 0.020159294828772545, -0.06178832799196243, -0.0009143936913460493, -0.012556925415992737, -0.025401070713996887, -0.014854690060019493, 0.021469738334417343, -0.008912813849747181, 0.03075055405497551, 0.0023875210899859667, -0.00543026439845562, -0.008522373624145985, -0.02559853531420231, -0.05342302843928337, 0.01883089914917946, 0.003639623522758484, 0.019907977432012558, 0.007081782910972834, 0.045201338827610016, 0.0147290313616395, 0.025724194943904877, 0.01262873038649559, 0.024252189323306084, 0.02301354892551899, 0.029745282605290413, 0.037554092705249786, -0.03766179829835892, 0.01328395213931799, 0.013499367982149124, -0.0055379718542099, 0.012538974173367023, 0.0031302557326853275, 0.017574310302734375, -0.006817001383751631, -0.011596531607210636, 0.0023448867723345757, -0.022941743955016136, -0.031235238537192345, 0.009173107333481312, 0.0021227397955954075, 0.014477713033556938, 0.021110713481903076, -0.04171879217028618, -0.04021088406443596, -0.012817218899726868, -0.038308046758174896, -0.03157631307840347, -0.0372309684753418, -0.020590126514434814, -0.009684719145298004, -0.006125876680016518, -0.010725894011557102, -0.02527541108429432, 0.02064397931098938, -0.011443945579230785, 0.025526730343699455, -0.007476711180061102, 0.008473007008433342, 0.04818125441670418, -0.039815954864025116, 0.007611345499753952, 0.02267247624695301, 0.006763147190213203, -0.03040947951376438, 0.07320535182952881, 0.008374275639653206, 0.020015684887766838, 0.014199468307197094, -0.0031818656716495752, 0.018400069326162338, -0.01257487665861845, -0.05482323095202446, 0.06042403355240822, -0.04125205799937248, 0.050586726516485214, 0.0006170754786580801, 0.026190927252173424, 0.019818220287561417, 0.018759094178676605, -0.03794902190566063, 0.012700535356998444, 0.01548298541456461, 0.048109449446201324, -0.02904518134891987, 0.043370310217142105, 0.00851339753717184, -0.029386255890130997, 0.016524160280823708, 0.02107481099665165, 0.0023852773010730743, -0.005214849021285772, -0.006902270019054413, -0.031881485134363174, 0.06085486337542534, -0.05008409172296524, 0.005259727127850056, -0.031001873314380646, 0.00274205906316638, 0.003693477250635624, 0.029260598123073578, 0.01945919543504715, 0.014675176702439785, -0.004792993422597647, -0.012287655845284462, 0.027914250269532204, -0.007620321121066809, 0.030876213684678078, -0.029296500608325005, 0.012942877598106861, 0.007849200628697872, -0.05022770166397095, -0.0208414439111948, -0.014217419549822807, 0.010905406437814236, -0.02010544203221798, 0.012287655845284462, 0.041754692792892456, 0.0492224283516407, 0.0034556228201836348, 0.01095926109701395, 0.03529223054647446, 0.03374841809272766, -0.051125265657901764, 0.005259727127850056, -0.02633453719317913, -0.039600539952516556, -0.0022899110335856676, 0.0027106443885713816, -0.005977778695523739, 0.009693695232272148, -0.042400941252708435, -0.023695698007941246, 0.031648118048906326, 0.030140209943056107, -0.0028744498267769814, 0.041216153651475906, 0.0014506883453577757, -0.05392566695809364, 0.0044586509466171265, -0.015572741627693176, -0.046709246933460236, 0.026819223538041115, -0.02698078379034996, 0.043693430721759796, -0.024647116661071777, 0.002282057423144579, 0.006440024357289076, -0.0035902573727071285, -0.000880734995007515, -0.039600539952516556, -0.02719620056450367, -0.02891952358186245, -0.029188793152570724, -0.012808242812752724, 0.05923924595117569, 0.006619537249207497, 0.00041540400707162917, -0.00881408154964447, 0.0034825496841222048, 0.026711514219641685, 0.00020167148613836616, -0.0199977345764637, -0.04082122817635536, 0.04868388921022415, 0.017717920243740082, 0.020284954458475113, 0.010618186555802822, 0.012996731325984001, 0.01924378052353859, -0.01656903699040413, -0.0068798307329416275, -0.008158859796822071, 0.01805899478495121, 0.012799267657101154, 0.03604618459939957, -0.055289965122938156, -0.014226394705474377, 0.003608208615332842, 0.03096597082912922, -0.012996731325984001, 0.05514635518193245, 0.014594396576285362, 0.04688876122236252, 0.002365082036703825, -0.0068259770050644875, -0.008594178594648838, -0.009092327207326889, 0.007566467393189669, -0.02172105759382248, -0.025131801143288612, -0.01965666003525257, -0.00307864579372108, -0.017870506271719933, -0.028398936614394188, -0.030696701258420944, -0.004770554602146149, -0.02008748985826969, -0.01031301449984312, -0.006552219856530428, 0.020015684887766838, -0.047355495393276215, 0.006426560692489147, 0.03827214241027832, -0.018292361870408058, -0.024916386231780052, -0.010779747739434242, 0.012081216089427471, 0.016129231080412865, -0.025006143376231194, 0.014370005577802658, 0.03633340448141098, -0.007059343624860048, -0.030122259631752968, 0.003516208380460739, -0.017664065584540367, 0.005968803074210882, -0.005313580855727196, -0.00671826908364892, -0.007831249386072159, 0.002295520855113864, 0.0606035441160202, 0.042616356164216995, 0.018435971811413765, -0.004685285966843367, 0.002100300509482622, -0.014962397515773773, -0.005502069368958473, -0.01753840781748295, 0.03791311755776405, -0.016156157478690147, 0.012494095601141453, 0.0025804974138736725, -0.027591127902269363, -0.04688876122236252, -0.005690557882189751, 0.018032068386673927, 0.004350943025201559, 0.018794996663928032, -0.04785813018679619, -0.002600692678242922, -0.03310217335820198, -0.01575225405395031, 0.00711768539622426, -0.028345081955194473, 0.07403110712766647, 0.0063637313432991505, 0.004801969043910503, 0.009927061386406422, -0.006516317371279001, 0.040246784687042236, -0.005475142505019903, 0.04405245929956436, 0.046063002198934555, 0.04419606924057007, 0.012224826030433178, 0.01601254753768444, 0.001523615443147719, -0.01332883071154356, -0.04871979355812073, -0.01958485320210457, -0.020033637061715126, 0.0006771000917069614, -0.032958563417196274, -0.021110713481903076, -0.03697965294122696, 0.010546380653977394, 0.00053208734607324, -0.01594971865415573, 0.025544680655002594, -0.006063047330826521, 0.01883089914917946, -0.0007444174261763692, -0.023911114782094955, -0.005138556007295847, -0.017717920243740082, 0.023498235270380974, -0.007153587881475687, 0.005425776354968548, -0.007086270488798618, 0.05712099373340607, 0.02773473784327507, 0.0002451472682878375, -0.04642202705144882, 0.01584201119840145, -0.004418260417878628, 0.032617487013339996, 0.0028632301837205887, -0.016497232019901276, 0.00464938348159194, -0.012458193115890026, 0.04990457743406296, 0.013095463626086712, 0.0724513977766037, 0.042293231934309006, 0.05988549441099167, -0.022977646440267563, -0.0332278311252594, -0.014558494091033936, 0.0039649903774261475, -0.009702670387923717, 0.004151235334575176, -0.02708849124610424, 0.01570737548172474, 0.02890157140791416, 0.02784244529902935, -0.019154023379087448, 0.01947714574635029, -0.022762231528759003, 0.015617619268596172, 0.014468736946582794, -0.029745282605290413, -0.021308178082108498, -0.008131933398544788, -0.003080889582633972, 0.05902383103966713, 0.0232289656996727, -0.0084999343380332, 0.06724552065134048, 0.0009155156440101564, 0.018112849444150925, -0.0014147857436910272, 0.022708378732204437, -0.06257818639278412, 0.006399633828550577, -0.042185522615909576, -0.008827545680105686, 0.009801402688026428, -0.024970240890979767, 0.011740141548216343, -0.035848721861839294, 0.015016251243650913, -0.023893162608146667, -0.0027936690021306276, -0.009271839633584023, -0.015877913683652878, -0.0299966000020504, -0.01409175992012024, -0.04566807299852371, -0.04161108285188675, -0.055002741515636444, 0.00906091183423996, -0.008540324866771698, 0.009478279389441013, 0.012108143419027328, 0.0395287349820137, 0.03171992301940918, -0.002032983349636197, -0.016649818047881126, -0.002670253859832883, 0.016084352508187294, 0.022277547046542168, 0.02635248936712742, 0.03394588455557823, -0.02385726012289524, 0.034448519349098206, -0.027339810505509377, -0.019836172461509705, 0.04462689906358719, 0.017224259674549103, 0.007822273299098015, 0.00004431723937159404, -0.0022068864200264215, -0.013723758980631828, 0.002349374582991004, -0.007001001853495836, -0.0410725437104702, 0.01956690289080143, -0.020446516573429108, 0.005344995763152838, -0.025221558287739754, -0.005488606169819832, -0.04258045181632042, -0.03085826151072979, 0.00038987951120361686, 0.02525746077299118, 0.04247274622321129, -0.0556848905980587, 0.04512953385710716, -0.012386388145387173, -0.014845713973045349, 0.02127227559685707, 0.02321101352572441, -0.028865668922662735, -0.024000870063900948, 0.02452145703136921, -0.01439693197607994, -0.042077817022800446, -0.0746055468916893, 0.03895429149270058, 0.017637139186263084, -0.030014552175998688, 0.012458193115890026, -0.036800138652324677, 0.019423292949795723, -0.03469983860850334 ]
Federated Learning (FL) is a machine learning paradigm that allows decentralized clients to learn collaboratively without sharing their private data. However, excessive computation and communication demands pose challenges to current FL frameworks, especially when training large-scale models. To prevent these issues from hindering the deployment of FL systems, we propose a lightweight framework where clients jointly learn to fuse the representations generated by multiple fixed pre-trained models rather than training a large-scale model from scratch. This leads us to a more practical FL problem by considering how to capture more client-specific and class-relevant information from the pre-trained models and jointly improve each client's ability to exploit those off-the-shelf models. In this work, we design a Federated Prototype-wise Contrastive Learning (FedPCL) approach which shares knowledge across clients through their class prototypes and builds client-specific representations in a prototype-wise contrastive manner. Sharing prototypes rather than learnable model parameters allows each client to fuse the representations in a personalized way while keeping the shared knowledge in a compact form for efficient communication. We perform a thorough evaluation of the proposed FedPCL in the lightweight framework, measuring and visualizing its ability to fuse various pre-trained models on popular FL datasets.
[ -0.0292582456022501, -0.011661894619464874, -0.03253599628806114, -0.0400230698287487, 0.04054060950875282, -0.0152760474011302, 0.02247847430408001, 0.03902249410748482, -0.03646929934620857, 0.008052055723965168, -0.042783282697200775, -0.033743590116500854, -0.012998872436583042, -0.05682586133480072, -0.02499716728925705, 0.039298515766859055, 0.010238660499453545, -0.01949399523437023, 0.006590005476027727, -0.024169104173779488, 0.01763085275888443, -0.057446908205747604, -0.0277746319770813, 0.007918357849121094, 0.03539971634745598, 0.06141471117734909, 0.04895925521850586, 0.019839022308588028, -0.07376666367053986, 0.050856903195381165, 0.07079943269491196, 0.023944837972521782, -0.022633736953139305, -0.022047191858291626, -0.04630255326628685, -0.028309421613812447, 0.030828114598989487, 0.02504892274737358, 0.027464106678962708, 0.03250149264931679, -0.05168496444821358, -0.010126527398824692, -0.01627662405371666, -0.007461197674274445, 0.007957173511385918, -0.022754495963454247, -0.041299667209386826, 0.005658434238284826, -0.026049498468637466, -0.0559287928044796, -0.009177704341709614, -0.037607885897159576, 0.03395060449838638, 0.0011234924895688891, -0.007142047863453627, 0.015810837969183922, 0.06876377761363983, -0.016173116862773895, 0.04416338726878166, -0.001484692096710205, -0.043507836759090424, 0.0013100224314257503, -0.028706202283501625, -0.02810240536928177, -0.018941953778266907, 0.0422312393784523, 0.021012112498283386, -0.003855670802295208, 0.001974198268726468, -0.030069056898355484, -0.008444522507488728, 0.014611870981752872, -0.003271282184869051, -0.0036659063771367073, -0.009134575724601746, 0.03527895733714104, 0.03267400711774826, 0.011247863061726093, 0.052927061915397644, -0.005033073481172323, -0.0016248590545728803, 0.019528498873114586, 0.07100644707679749, 0.029223741963505745, 0.026204761117696762, -0.0023871518205851316, -0.02770562656223774, -0.06614157557487488, 0.025083424523472786, 0.04236925020813942, -0.010721697472035885, 0.06790120899677277, -0.04602653160691261, 0.01413745991885662, 0.01462912280112505, -0.00006523156480398029, -0.029016725718975067, -0.03527895733714104, -0.0792180746793747, -0.027998898178339005, -0.07245556265115738, 0.06303633749485016, -0.019873524084687233, 0.022443972527980804, 0.01248995866626501, -0.028982223942875862, 0.011127104051411152, 0.008427271619439125, 0.021684912964701653, 0.10647516697645187, -0.0019547906704247, -0.019200723618268967, -0.028826961293816566, 0.051443446427583694, 0.005835260264575481, 0.014905143529176712, -0.02014954574406147, -0.04657857492566109, 0.0400230698287487, -0.041299667209386826, 0.05979308858513832, -0.00047441141214221716, -0.002003310015425086, 0.002745116828009486, -0.02912023477256298, 0.03657280653715134, 0.03453715145587921, 0.01413745991885662, -0.025393947958946228, 0.03550322353839874, -0.0008059602696448565, -0.009005190804600716, 0.011601515114307404, -0.0477861650288105, 0.050925906747579575, 0.02299601398408413, 0.03208746388554573, 0.0385049544274807, 0.024427874013781548, 0.015103533864021301, 0.0741116851568222, 0.010117901489138603, 0.035882752388715744, 0.01230019424110651, 0.0496148057281971, -0.03224272280931473, -0.017389334738254547, 0.03757338225841522, 0.04502595588564873, 0.014646373689174652, -0.04371485486626625, 0.03940202295780182, 0.04074762761592865, 0.020563578233122826, 0.039816055446863174, -0.0312766507267952, 0.038711968809366226, -0.017415210604667664, 0.028326673433184624, 0.0024518442805856466, 0.05872350558638573, 0.023996591567993164, 0.05406564846634865, 0.04944229498505592, 0.05993109941482544, 0.01769985817372799, -0.0030081996228545904, 0.010368045419454575, -0.09695243835449219, 0.04958030581474304, -0.012067301198840141, 0.047303128987550735, 0.05717088654637337, -0.011705023236572742, -0.011023595929145813, 0.04074762761592865, 0.026480782777071, -0.06044863909482956, 0.0035429906565696, 0.02001153491437435, 0.009358842857182026, 0.04016108065843582, 0.060724660754203796, 0.01452561467885971, 0.043749358505010605, 0.015086282975971699, 0.049304284155368805, 0.024376120418310165, 0.005248715169727802, 0.001891176332719624, 0.0426107682287693, 0.040851134806871414, 0.04954580217599869, 0.01278323121368885, 0.008479025214910507, -0.049304284155368805, -0.007918357849121094, 0.022098945453763008, 0.016035106033086777, 0.03125939890742302, -0.02829217165708542, -0.04312830790877342, -0.01866593211889267, -0.013533663004636765, 0.001835109549574554, 0.028067903593182564, 0.053720623254776, -0.010764826089143753, 0.02177117019891739, -0.07790698111057281, -0.009194955229759216, -0.0448189377784729, -0.03260500356554985, 0.0012906146002933383, 0.0036939396522939205, -0.018700435757637024, 0.020563578233122826, -0.018683183938264847, -0.0005903187557123601, 0.01452561467885971, 0.03353657200932503, 0.000778465997427702, -0.011584264226257801, -0.056860361248254776, -0.06565853953361511, -0.015897095203399658, 0.038194429129362106, -0.026894813403487206, 0.011679146438837051, 0.030534842982888222, -0.008767984807491302, -0.013921817764639854, -0.0060120862908661366, 0.003335974644869566, -0.005956019274890423, -0.025152429938316345, 0.03643479570746422, -0.040333595126867294, -0.04688909649848938, 0.04399087652564049, -0.004261076916009188, 0.028447432443499565, -0.03909149765968323, -0.016233496367931366, 0.03495118021965027, 0.0037845091428607702, -0.030517591163516045, 0.07459472119808197, -0.014491111971437931, 0.011118478141725063, -0.0370558425784111, 0.012058675289154053, 0.011765402741730213, 0.00669782655313611, -0.01475850772112608, -0.002751586027443409, 0.017682606354355812, -0.04985632374882698, 0.0059258295223116875, -0.044853441417217255, 0.05251302942633629, 0.010911461897194386, -0.00021591110271401703, 0.033674582839012146, 0.010859708301723003, -0.009781500324606895, 0.04995983466506004, -0.005033073481172323, 0.0070299142971634865, 0.01239507645368576, -0.013016123324632645, -0.001187106710858643, -0.040851134806871414, 0.011868910863995552, 0.024841906502842903, -0.040782127529382706, -0.025945991277694702, -0.02453138306736946, -0.00810380931943655, 0.057446908205747604, 0.021788422018289566, 0.016613025218248367, 0.005274592433124781, -0.006715077906847, -0.028136909008026123, -0.05127093568444252, -0.055963292717933655, -0.04947679489850998, -0.005291843321174383, 0.0070946067571640015, -0.06220827251672745, -0.007983050309121609, -0.02956876903772354, -0.0024216545280069113, 0.02221970446407795, 0.018113890662789345, -0.005800757557153702, 0.06538251787424088, 0.04437040537595749, 0.026653295382857323, -0.03086261823773384, -0.04623354598879814, 0.025721723213791847, -0.01833815686404705, 0.02706732600927353, 0.03674532100558281, -0.030948875471949577, 0.011316868476569653, -0.0396435409784317, -0.014870640821754932, 0.016509516164660454, -0.06793571263551712, -0.02215069904923439, -0.041679199784994125, -0.021477898582816124, 0.03420937433838844, 0.02299601398408413, 0.006715077906847, -0.00749138742685318, -0.10771726816892624, 0.007422382012009621, 0.03653830289840698, -0.09688343107700348, 0.01989077590405941, 0.0459575280547142, -0.061759740114212036, 0.036400292068719864, 0.02996554970741272, -0.048855748027563095, 0.015000025741755962, -0.04837271198630333, -0.06438194215297699, -0.0515124537050724, -0.01504315435886383, 0.021460646763443947, 0.030465837568044662, -0.07935608923435211, 0.00849196407943964, -0.0392640121281147, -0.004571600817143917, -0.029758533462882042, -0.01530192419886589, -0.021874679252505302, 0.010014393366873264, 0.04385286569595337, 0.006037963088601828, -0.020822348073124886, -0.02285800315439701, 0.05154695361852646, -0.04009207710623741, 0.0009811690542846918, 0.022512977942824364, -0.023410046473145485, -0.024772901087999344, 0.021477898582816124, -0.04161019250750542, 0.015224292874336243, -0.011774028651416302, -0.018717685714364052, -0.011817156337201595, -0.010980467312037945, -0.030500341206789017, -0.008082245476543903, 0.05430716648697853, -0.03543421998620033, -0.003963491413742304, 0.0008803565870039165, -0.007366314996033907, -0.03398510813713074, 0.0740426778793335, -0.051822975277900696, 0.03106963448226452, -0.021598657593131065, 0.04257626831531525, -0.005865450017154217, 0.0012765979627147317, -0.012610717676579952, -0.017717109993100166, -0.03802191838622093, 0.04437040537595749, 0.015517565421760082, 0.04023008793592453, 0.049235276877880096, 0.016966676339507103, 0.04140317812561989, 0.0012280786177143455, -0.0253766980022192, -0.06393340229988098, -0.039298515766859055, 0.01400807499885559, 0.04057511314749718, -0.07376666367053986, 0.009686618112027645, 0.003534364979714155, 0.028205914422869682, -0.021684912964701653, 0.01236057374626398, -0.011558386497199535, -0.01217080932110548, -0.015707330778241158, -0.03778040036559105, 0.07093743979930878, -0.03081086464226246, 0.014102957211434841, 0.017337581142783165, -0.03388160094618797, 0.005766254849731922, 0.041955217719078064, 0.03746987506747246, 0.05617031082510948, 0.01381831057369709, -0.04971831664443016, -0.015198416076600552, 0.02603224664926529, 0.042265743017196655, 0.013119631446897984, -0.06358838081359863, 0.014706753194332123, -0.045232970267534256, 0.012222562916576862, 0.026653295382857323, -0.005619618576020002, 0.0777689665555954, 0.03650379925966263, -0.022875254973769188, 0.044266898185014725, 0.011653268709778786, 0.01892470195889473, -0.0496148057281971, 0.029465259984135628, 0.04060961678624153, -0.010066146962344646, 0.012472706846892834, -0.024134602397680283, -0.059310052543878555, 0.020235802978277206, 0.036779820919036865, -0.018803942948579788, -0.03034507855772972, 0.023220282047986984, -0.006909155286848545, 0.011989669874310493, 0.023168528452515602, -0.004189915023744106, -0.054031144827604294, -0.020891353487968445, 0.0039052683860063553, -0.0340886153280735, -0.0025381010491400957, -0.016354255378246307, -0.05824046954512596, 0.003948396537452936, -0.10564710944890976, -0.025859734043478966, -0.024324366822838783, -0.01911446638405323, 0.02266823872923851, -0.00016739174316171557, 0.03198395296931267, -0.07859703153371811, 0.012800482101738453, 0.0073102484457194805, 0.050339363515377045, -0.021753918379545212, -0.02351355366408825, -0.0053177205845713615, 0.008884431794285774, -0.09860856831073761, -0.019200723618268967, -0.010600938461720943, -0.016164490953087807, -0.03947103023529053, 0.02918924018740654, 0.02848193608224392, -0.003523582825437188, 0.0021003487054258585, -0.002680424368008971, -0.09584835171699524, 0.01333527360111475, -0.02937900461256504, -0.009324340149760246, -0.020701589062809944, 0.04016108065843582, -0.02435886859893799, 0.03395060449838638, 0.017277199774980545, -0.025928739458322525, 0.0060552144423127174, 0.010531933046877384, -0.03229447826743126, 0.03860846161842346, -0.01970101147890091, -0.012188060209155083, 0.012222562916576862, -0.021460646763443947, -0.03650379925966263, -0.013844187371432781, 0.026049498468637466, 0.07832100987434387, 0.013516412116587162, 0.02156415395438671, 0.014827513135969639, 0.010600938461720943, 0.04447391256690025, -0.03657280653715134, -0.018200146034359932, -0.012162183411419392, -0.03805641829967499, -0.01749284192919731, -0.001362854614853859, -0.0033079413697123528, 0.04668208211660385, 0.013421529904007912, -0.04305930435657501, -0.025273188948631287, 0.013870064169168472, 0.012343321926891804, -0.026256514713168144, -0.0029413506854325533, 0.015767710283398628, -0.010324916802346706, 0.03905699774622917, -0.002570447279140353, -0.019804518669843674, 0.010333542712032795, 0.020166797563433647, 0.05341009795665741, 0.0266705472022295, 0.04954580217599869, -0.048476219177246094, -0.02803340181708336, 0.031863193958997726, -0.03029332496225834, -0.00004760961019201204, 0.012645220384001732, -0.013542288914322853, 0.04354234039783478, -0.01569007895886898, -0.02763662114739418, -0.020253054797649384, 0.0025726037565618753, 0.021167373284697533, -0.008306512609124184, 0.038194429129362106, 0.001122414250858128, 0.014102957211434841, 0.026325520128011703, -0.0355377271771431, 0.004476718604564667, 0.0024259674828499556, 0.03954003378748894, 0.01814839243888855, -0.01963200606405735, 0.031138639897108078, -0.010549184866249561, -0.048338208347558975, 0.08018415421247482, -0.050925906747579575, -0.0327947661280632, -0.02479015290737152, 0.012205311097204685, 0.004653544630855322, 0.01963200606405735, -0.021684912964701653, -0.0033316619228571653, -0.026429027318954468, 0.016449136659502983, 0.043887365609407425, -0.02435886859893799, 0.019545748829841614, 0.03709034621715546, 0.0041683511808514595, -0.02860269509255886, 0.003456733888015151, -0.023944837972521782, 0.018510669469833374, 0.03643479570746422, 0.033346809446811676, 0.02299601398408413, -0.007323186844587326, 0.011756776832044125, -0.00724986894056201, -0.013576791621744633, 0.03184594213962555, 0.027619369328022003, 0.0800461396574974, 0.0006523156771436334, -0.015474437735974789, 0.011653268709778786, -0.055894289165735245, 0.018320905044674873, 0.026636043563485146, 0.04333532601594925, 0.013930443674325943, -0.009833254851400852, -0.022961512207984924, 0.009401971474289894, -0.028757955878973007, 0.03539971634745598, -0.026636043563485146, 0.0025337880942970514, 0.03022431954741478, 0.007517264224588871, 0.006460620556026697, -0.008250445127487183, -0.0285336896777153, 0.022133449092507362, -0.011575638316571712, 0.03557223081588745, -0.005658434238284826, 0.025790728628635406, 0.023461800068616867, 0.033743590116500854, -0.031242147088050842, 0.030120810493826866, 0.028568191453814507, 0.01788962259888649, -0.041437678039073944, -0.021391641348600388, -0.01539680641144514, 0.05696387216448784, -0.03524445369839668, 0.056411828845739365, 0.031138639897108078, 0.009427848272025585, 0.06500298529863358, 0.021650411188602448, -0.05830947309732437, -0.011515258811414242, 0.0008738873875699937, 0.0069652218371629715, -0.0016906297532841563, -0.05030485987663269, -0.0006976004224270582, -0.029534265398979187, -0.052340514957904816, -0.019666509702801704, 0.030103560537099838, 0.01414608582854271, -0.004899376071989536, 0.012740102596580982, -0.009100073017179966, -0.002160728210583329, 0.04236925020813942, -0.00034044409403577447, 0.02356530725955963, 0.0018933328101411462, -0.028257668018341064, 0.0563083216547966, 0.02014954574406147, 0.009410597383975983, -0.0022362028248608112, 0.011075349524617195, 0.029810287058353424, -0.015784962102770805, -0.036779820919036865, 0.014706753194332123, -0.00033047067699953914, -0.023858580738306046, 0.01814839243888855, 0.04495694860816002, 0.029758533462882042, -0.0015235075261443853, 0.028395678848028183, -0.007055791560560465, -0.03198395296931267, 0.0022211079485714436, 0.03319154679775238, 0.018683183938264847, 0.07066141813993454, -0.0006684887921437621, 0.023461800068616867, -0.008539405651390553, 0.01520704198628664, 0.02278899773955345, -0.04267977550625801, 0.016431886702775955, -0.00036928613553754985, -0.011273739859461784, -0.022581983357667923, -0.048648733645677567, 0.017337581142783165, -0.010954590514302254, -0.025618216022849083, -0.01970101147890091, 0.004856247454881668, -0.02292700856924057, 0.026894813403487206, -0.07031639665365219, 0.009669367223978043, -0.030327826738357544, -0.05051187425851822, -0.004838996101170778, -0.02434161864221096, 0.012326071038842201, -0.005770567804574966, -0.006521000526845455, -0.018579674884676933, 0.0023569620680063963, 0.03493393212556839, 0.006158722564578056, -0.010419799946248531, -0.02627376653254032, -0.012041423469781876, -0.004920939914882183, -0.0015310549642890692, -0.004075625445693731, 0.020046038553118706, -0.031794190406799316, 0.04378385841846466, 0.008668790571391582, -0.025480205193161964, -0.006693513598293066, 0.021529652178287506, 0.032190971076488495, -0.017156440764665604, -0.020874101668596268, 0.003023294499143958, 0.01717369258403778, 0.04161019250750542, -0.04254176467657089, 0.01826915144920349, 0.006598631385713816, -0.03022431954741478, -0.05230601504445076, 0.011152980849146843, -0.014585994184017181, -0.028982223942875862, -0.01330077089369297, 0.017872370779514313, 0.04902826249599457, -0.026756802573800087, -0.024203607812523842, 0.007051478605717421, 0.03960903733968735, 0.013533663004636765, 0.0017531657358631492, 0.044646427035331726, 0.023358292877674103, -0.016828665509819984, 0.06824623793363571, -0.0013854969292879105, -0.00580938346683979, -0.013188636861741543, -0.009591735899448395, -0.000899225240573287, 0.028619946911931038, 0.0156383253633976, -0.030966125428676605, 0.01304200105369091, 0.04364584758877754, -0.006766831502318382, 0.04578501358628273, -0.011187483556568623, -0.08342739939689636, 0.018700435757637024, 0.021650411188602448, 0.018510669469833374, 0.016897670924663544, 0.015258795581758022, 0.012550338171422482, -0.0037974475417286158, -0.009514104574918747, 0.02473839744925499, 0.008677415549755096, 0.025876985862851143, 0.011368622072041035, -0.01685454323887825, -0.003197964048013091, -0.037366367876529694, 0.031138639897108078, 0.0009676914196461439, 0.03577924519777298, -0.03571024164557457, -0.02841293066740036, 0.04192071780562401, 0.006111281458288431, -0.005360848736017942, -0.008703292347490788, 0.034709662199020386, 0.014120208099484444, 0.0309316236525774, -0.00008423497638432309, -0.007129109464585781, -0.009307089261710644, 0.010419799946248531, 0.027222588658332825, -0.011420376598834991, -0.010023019276559353, 0.04971831664443016, 0.029396256431937218, 0.018251899629831314, 0.01840716227889061, 0.013533663004636765, 0.08798175305128098, -0.026584289968013763, -0.0034416390117257833, 0.032311730086803436, -0.03508919104933739, -0.067418172955513, 0.06524450331926346, -0.03488217666745186, -0.0005574334063567221, -0.001854517264291644, -0.023789575323462486, 0.01504315435886383, 0.017423836514353752, -0.05406564846634865, -0.017596350982785225, 0.00219630915671587, -0.0003622777876444161, 0.03495118021965027, 0.009289837442338467, 0.036193277686834335, -0.012412327341735363, -0.03950553014874458, -0.026498032733798027, 0.018424414098262787, -0.03493393212556839, -0.03222547098994255, 0.008893057703971863, -0.018579674884676933, 0.013274893164634705, 0.039747048169374466, -0.041679199784994125, -0.021426143124699593, -0.0290684811770916, -0.007405130658298731, -0.003512800671160221, -0.0344681441783905, 0.01892470195889473, -0.015491688624024391, -0.028878716751933098, 0.010506056249141693, -0.04944229498505592, 0.043162811547517776, -0.006818585563451052, 0.0559287928044796, 0.013128257356584072, 0.03351932018995285, -0.00028922921046614647, -0.01588846929371357, -0.024203607812523842, -0.02810240536928177, -0.02480740286409855, 0.021684912964701653, 0.012636594474315643, 0.014508362859487534, 0.020097792148590088, 0.00724986894056201, 0.02687756158411503, 0.0020345780067145824, 0.06555502861738205, 0.00041295355185866356, -0.03131115064024925, 0.0034998622722923756, 0.007918357849121094, 0.04133417084813118, 0.00712048402056098, -0.027740128338336945, 0.0054471055045723915, -0.0038858605548739433, -0.017190944403409958, 0.009643489494919777, 0.003493393072858453, -0.03643479570746422, -0.016966676339507103, 0.011083975434303284, -0.054721198976039886, -0.03284652158617973, 0.015871217474341393, -0.024703895673155785, 0.005610993131995201, 0.011032221838831902, 0.009565859101712704, 0.01553481724113226, -0.04198972135782242, 0.025204183533787727, -0.005257341079413891, -0.014939646236598492, 0.005067576188594103, 0.030396832153201103, 0.04029909148812294, -0.0008857476641424, 0.06120769679546356, 0.013309395872056484, -0.005067576188594103, -0.02732609584927559, -0.013326647691428661, -0.01821739785373211, -0.028067903593182564, 0.02829217165708542, 0.011265113949775696, 0.003650811268016696, -0.0026545473374426365, -0.008698980323970318, -0.021978186443448067, 0.0014350945129990578, 0.044335901737213135, 0.004023871384561062, -0.01840716227889061, -0.037366367876529694, -0.012567589059472084, -0.012567589059472084, 0.06420942395925522, 0.022875254973769188, -0.0015989820240065455, -0.029137486591935158, 0.008901682682335377, 0.01854517310857773, 0.019028209149837494, -0.02266823872923851, 0.03067285381257534, -0.050856903195381165, 0.01717369258403778, 0.06776320189237595, -0.01621624454855919, -0.00322815403342247, 0.03488217666745186, 0.01801038160920143, 0.023461800068616867, 0.06044863909482956, -0.013326647691428661, 0.0057964446023106575, -0.04954580217599869, -0.0029305685311555862, 0.018182896077632904, -0.005585115868598223, -0.013706176541745663, 0.00036281690699979663, -0.02240946888923645, 0.05672235041856766, 0.019977033138275146, -0.0011202578898519278, 0.01911446638405323, 0.013844187371432781, -0.021012112498283386, -0.0022232644259929657, -0.028723454102873802, 0.016742410138249397, -0.053893133997917175, -0.026480782777071, 0.01918347179889679, 0.01866593211889267, 0.03895349055528641, -0.044266898185014725, 0.03265675529837608, 0.0046923598274588585, -0.005563552025705576, 0.009660741314291954, -0.03081086464226246, -0.041817206889390945, 0.015051780268549919, -0.02654978632926941, 0.009902259334921837, -0.026636043563485146, -0.03343306481838226, 0.029465259984135628, -0.037745896726846695, 0.03350207209587097, 0.009031067602336407, 0.029016725718975067, 0.017389334738254547, -0.011135729029774666, -0.008759359829127789, 0.02523868717253208, -0.03571024164557457, -0.05213350057601929, 0.026687797158956528, 0.0014642061432823539, 0.0006091873510740697, 0.014353101141750813, 0.02937900461256504, 0.009686618112027645, 0.02713633142411709, -0.005257341079413891, -0.030586596578359604, -0.01756184734404087, -0.0309316236525774, 0.03584825247526169, 0.01975276507437229, 0.009746997617185116, 0.021357139572501183, 0.03733186423778534, -0.06272581219673157, -0.04319731518626213, 0.014680876396596432, 0.020356561988592148, -0.03950553014874458, 0.008289260789752007, 0.0021919962018728256, 0.009445100091397762, 0.049890827387571335, -0.02893047034740448, -0.03060384839773178, -0.0067711444571614265, 0.009065570309758186, -0.01252446137368679, 0.05140894278883934, -0.01468950230628252, -0.034381888806819916, 0.025911487638950348, -0.01704430766403675, 0.014896517619490623, -0.005080515053123236, -0.006404554005712271, 0.03895349055528641, 0.027015572413802147, -0.06434743851423264, 0.03840144723653793, -0.015922971069812775, 0.006814273074269295, 0.004718237090855837, 0.008349640294909477, -0.01963200606405735, -0.010497430339455605, -0.06051764264702797, 0.00593876838684082, 0.010945964604616165, -0.004955442622303963, -0.019269729033112526, -0.026049498468637466, 0.004925252869725227, -0.008789549581706524 ]
Link prediction (LP) has been recognized as an important task in graph learning with its broad practical applications. A typical application of LP is to retrieve the top scoring neighbors for a given source node, such as the friend recommendation. These services desire the high inference scalability to find the top scoring neighbors from many candidate nodes at low latencies. There are two popular decoders that the recent LP models mainly use to compute the edge scores from node embeddings: the HadamardMLP and Dot Product decoders. After theoretical and empirical analysis, we find that the HadamardMLP decoders are generally more effective for LP. However, HadamardMLP lacks the scalability for retrieving top scoring neighbors on large graphs, since to the best of our knowledge, there does not exist an algorithm to retrieve the top scoring neighbors for HadamardMLP decoders in sublinear complexity. To make HadamardMLP scalable, we propose the Flashlight algorithm to accelerate the top scoring neighbor retrievals for HadamardMLP: a sublinear algorithm that progressively applies approximate maximum inner product search (MIPS) techniques with adaptively adjusted query embeddings. Empirical results show that Flashlight improves the inference speed of LP by more than 100 times on the large OGBL-CITATION2 dataset without sacrificing effectiveness. Our work paves the way for large-scale LP applications with the effective HadamardMLP decoders by greatly accelerating their inference.
[ -0.026867231354117393, 0.012825548648834229, -0.0333782322704792, 0.004109133500605822, -0.011403605341911316, -0.030384669080376625, 0.019813647493720055, 0.046811848878860474, -0.03695179894566536, 0.037045348435640335, 0.024378832429647446, 0.06724292039871216, 0.0246781874448061, -0.026231098920106888, 0.00030988059006631374, 0.02808336727321148, 0.01898106373846531, -0.010692634619772434, 0.007937620393931866, 0.011534574441611767, -0.03670857101678848, -0.08524172008037567, -0.025089804083108902, -0.01134747639298439, 0.03403307497501373, 0.0028345303144305944, 0.013508454896509647, 0.006211644038558006, -0.052499618381261826, 0.036427926272153854, 0.023536892607808113, 0.021759463474154472, 0.01429426483809948, -0.020431069657206535, -0.015632014721632004, -0.05418349802494049, 0.10380180925130844, 0.0022732370998710394, -0.0138265211135149, -0.041386015713214874, -0.013349421322345734, 0.016483308747410774, -0.035380177199840546, -0.0033303392119705677, 0.0027363039553165436, -0.024771736934781075, 0.00500486372038722, -0.017334602773189545, 0.00857842992991209, -0.03610985726118088, 0.03981439396739006, -0.031469836831092834, -0.058860938996076584, -0.003171306336298585, -0.0030777573119848967, -0.013171679340302944, 0.036091148853302, 0.03436984866857529, 0.03191886842250824, 0.016979116946458817, -0.05399639904499054, -0.00500486372038722, -0.07154616713523865, -0.03427629917860031, 0.009060206823050976, 0.002469689818099141, 0.004684458952397108, 0.04853314533829689, 0.0018721465021371841, -0.03710147738456726, -0.06716807931661606, 0.0028462240006774664, 0.015819111838936806, -0.008017136715352535, -0.0001784736814443022, -0.02117946185171604, 0.004864540416747332, 0.018382349982857704, 0.03612856939435005, 0.007493263576179743, 0.03936535865068436, -0.010571020655333996, 0.0077505228109657764, 0.09025593847036362, 0.06076933816075325, -0.039140842854976654, -0.01233909372240305, -0.06443645060062408, 0.004864540416747332, 0.014266200363636017, -0.015482335351407528, -0.0020732765551656485, -0.041498273611068726, 0.0036998572759330273, 0.014743300154805183, -0.010196825489401817, -0.04292021691799164, -0.023106567561626434, -0.02537045069038868, 0.065858393907547, -0.030852412804961205, 0.0028041270561516285, -0.012666515074670315, 0.011805865913629532, 0.06185450404882431, -0.04329441115260124, -0.016249436885118484, 0.043668605387210846, 0.015791047364473343, 0.10582246631383896, 0.0037559866905212402, -0.03253629058599472, -0.0018265413818880916, -0.005042283330112696, -0.023967217653989792, 0.033490490168333054, -0.036820828914642334, -0.02776530012488365, 0.05070348083972931, -0.026586584746837616, 0.018812675029039383, -0.01610911265015602, 0.012853613123297691, -0.03876664489507675, -0.044791191816329956, 0.02421044372022152, -0.0015108140651136637, -0.012245545163750648, -0.01576298289000988, 0.019589129835367203, -0.0021118654403835535, 0.008124718442559242, 0.036427926272153854, -0.05220026150345802, 0.055642858147621155, 0.05410865694284439, 0.03532404825091362, 0.02033752202987671, -0.01554782036691904, 0.0018148478120565414, 0.021665915846824646, -0.03390210494399071, 0.014574911445379257, -0.05762609466910362, 0.02308785729110241, 0.033209845423698425, -0.002853240119293332, -0.01662363111972809, -0.013358776457607746, 0.005285510327666998, -0.03753180056810379, 0.02439754083752632, 0.023649150505661964, 0.05148928984999657, 0.023611731827259064, -0.015931369736790657, -0.025314319878816605, 0.005669060628861189, 0.009354885667562485, -0.015239108353853226, 0.031937580555677414, -0.013761037029325962, 0.018157832324504852, 0.009757145307958126, -0.019570421427488327, 0.07382875680923462, 0.04538990557193756, -0.008597140200436115, -0.07356682419776917, 0.034875012934207916, 0.06529710441827774, 0.05089057609438896, 0.0030660638585686684, -0.010121986269950867, -0.03985181450843811, 0.02001945488154888, 0.05051638185977936, -0.04939379543066025, -0.05878610163927078, 0.01398555375635624, -0.024996254593133926, -0.015360722318291664, 0.03725115582346916, 0.008625204674899578, -0.01638040505349636, -0.05294865369796753, 0.06656936556100845, 0.05437059700489044, 0.04557700455188751, 0.03614727780222893, -0.022320756688714027, 0.0330040380358696, 0.04770991578698158, -0.03274209797382355, 0.02153494581580162, -0.03745696321129799, 0.001320208190008998, -0.00035987075534649193, 0.017418796196579933, -0.008629881776869297, -0.053509946912527084, -0.02645561657845974, -0.0047101848758757114, 0.017175570130348206, 0.017166215926408768, -0.041423432528972626, 0.03661502152681351, -0.022414306178689003, -0.013929424807429314, -0.06825324892997742, 0.01053360104560852, -0.024023346602916718, -0.05410865694284439, -0.043706025928258896, -0.004488006234169006, -0.004567523021250963, -0.014930397272109985, 0.0058889007195830345, -0.012713289819657803, -0.024060765281319618, 0.022414306178689003, 0.04991766810417175, 0.07424037158489227, -0.004745265934616327, 0.01125392783433199, -0.002357431221753359, -0.029486600309610367, -0.0037349381018429995, 0.02703562006354332, -0.001941138762049377, -0.015164269134402275, -0.0388040654361248, -0.004109133500605822, 0.010028437711298466, -0.01219877041876316, -0.011020055040717125, -0.0330788753926754, -0.05223768204450607, -0.015042656101286411, 0.014256845228374004, 0.0033092908561229706, -0.015426206402480602, 0.019027836620807648, 0.039253100752830505, 0.006347289774566889, 0.02204011008143425, -0.029842084273695946, 0.0027807396836578846, 0.019851068034768105, 0.0026825135573744774, -0.03818664327263832, -0.06391257792711258, 0.0441550612449646, 0.010627150535583496, -0.027746589854359627, 0.043593768030405045, 0.04834605008363724, -0.0030216281302273273, 0.012638450600206852, -0.0038238095585256815, 0.01194618921726942, -0.01831686682999134, -0.032049838453531265, 0.045838940888643265, -0.025145933032035828, 0.027784010395407677, 0.028794337064027786, -0.039178259670734406, 0.03610985726118088, 0.006960034836083651, 0.012853613123297691, -0.060170624405145645, -0.010917151346802711, -0.024996254593133926, 0.012657159939408302, -0.026249809190630913, 0.003498727222904563, -0.017568474635481834, 0.06814098358154297, -0.05448285490274429, 0.014322330243885517, -0.007133100181818008, -0.026044001802802086, 0.01928977482020855, -0.015435561537742615, -0.06743001192808151, 0.01125392783433199, -0.04718604311347008, -0.019196225330233574, -0.006394064519554377, -0.04164795204997063, 0.013283937238156796, -0.029804665595293045, 0.017053956165909767, -0.009822630323469639, -0.026511745527386665, -0.026212388649582863, -0.0005031174514442682, 0.02924337238073349, -0.04976799339056015, -0.04104923829436302, 0.034332431852817535, -0.03756922110915184, -0.04520280659198761, -0.0440802201628685, -0.007563425227999687, -0.03459436818957329, 0.10657085478305817, -0.03575437143445015, -0.04198472574353218, 0.0030520313885062933, 0.024640768766403198, 0.025707226246595383, -0.02490270510315895, 0.007334230467677116, 0.018176542595028877, 0.019626550376415253, -0.05631641298532486, 0.008746817708015442, -0.065858393907547, 0.004869217984378338, 0.004986153915524483, -0.09272562712430954, 0.02381753921508789, 0.016979116946458817, 0.03734470158815384, 0.0011822236701846123, 0.028289174661040306, -0.039253100752830505, 0.005762609653174877, 0.00686648627743125, -0.04060020297765732, -0.05036670342087746, -0.0247904472053051, -0.011553283780813217, -0.010019082576036453, -0.028756918385624886, 0.025501418858766556, -0.015070720575749874, 0.012432643212378025, 0.018036220222711563, 0.012329739518463612, -0.004345344379544258, 0.015940725803375244, 0.012694579549133778, -0.04666217043995857, -0.03814922273159027, 0.0065110004507005215, 0.04845830798149109, 0.01623072661459446, 0.0011307718232274055, 0.0031853385735303164, 0.04546474292874336, 0.019158806651830673, 0.06290224939584732, -0.055867377668619156, -0.051414452493190765, 0.02664271369576454, -0.016118468716740608, 0.05212542414665222, 0.02204011008143425, -0.03768147900700569, -0.06297709047794342, 0.04737314209342003, -0.05770093575119972, 0.0327795185148716, -0.008283751085400581, -0.014107167720794678, -0.002602997003123164, 0.04288279637694359, -0.03732599318027496, 0.01208651252090931, -0.07001196593046188, -0.005140509456396103, 0.0012079495936632156, 0.029561437666416168, 0.06975002586841583, -0.01218006107956171, -0.027372395619750023, 0.04830862954258919, -0.01103876531124115, 0.02106720209121704, 0.04853314533829689, -0.01990719698369503, -0.02323753573000431, 0.027409814298152924, -0.010468116961419582, 0.016006208956241608, -0.011974253691732883, 0.04872024431824684, 0.016595566645264626, -0.0710597112774849, 0.022171078249812126, -0.02026268281042576, 0.02138526923954487, -0.008629881776869297, 0.0016967423725873232, -0.024547219276428223, -0.0005522305727936327, 0.020468490198254585, -0.04277053847908974, -0.015313947573304176, -0.03560469299554825, 0.024846576154232025, -0.03206854686141014, 0.02417302504181862, 0.04497829079627991, -0.0660829097032547, 0.06656936556100845, -0.020711716264486313, 0.026118841022253036, -0.017989445477724075, -0.0024439638946205378, -0.029598858207464218, 0.03399565443396568, 0.039103422313928604, -0.049318958073854446, -0.004085746128112078, 0.04093698039650917, 0.030609184876084328, -0.011628123000264168, 0.014864913187921047, 0.036315664649009705, -0.017456216737627983, -0.028102075681090355, 0.028139496222138405, 0.04209698364138603, 0.000748975551687181, 0.023443343117833138, -0.056615766137838364, 0.047934435307979584, -0.00939230527728796, 0.024004636332392693, -0.062228698283433914, -0.06907647848129272, -0.02381753921508789, 0.04879508167505264, 0.007975040003657341, -0.06514742225408554, -0.006047933362424374, -0.0054819630458951, -0.011132313869893551, 0.0031736448872834444, 0.008901173248887062, -0.012713289819657803, 0.025651097297668457, 0.010402632877230644, -0.024827865883708, 0.021591076627373695, -0.06054481863975525, -0.09235142916440964, -0.031619515269994736, -0.10387665033340454, -0.04883250221610069, -0.004663410596549511, -0.009144400246441364, -0.03786857798695564, -0.022264627739787102, 0.035305339843034744, -0.06215386092662811, -0.0018242027144879103, 0.0655590370297432, 0.04321957007050514, -0.09055529534816742, -0.048084113746881485, 0.03551114723086357, -0.028139496222138405, -0.010935861617326736, 0.028682079166173935, -0.0005118876579217613, -0.030197570100426674, -0.04516538605093956, 0.02862595021724701, 0.04224666208028793, 0.033172424882650375, 0.023761410266160965, 0.0006039747968316078, -0.06769195199012756, 0.031151769682765007, 0.020113004371523857, 0.00002634715747262817, 0.0166891161352396, 0.035193078219890594, -0.00675890501588583, 0.041498273611068726, -0.020187843590974808, -0.008821656927466393, 0.041386015713214874, 0.04164795204997063, -0.057738352566957474, -0.006988099776208401, 0.02378011867403984, -0.08179911971092224, -0.004450586624443531, -0.039253100752830505, -0.022171078249812126, -0.05444543436169624, -0.03152596578001976, 0.03637179359793663, 0.006819711532443762, 0.002523480448871851, 0.0389537438750267, 0.0050703478045761585, 0.01839170604944229, 0.03854212909936905, -0.006754227448254824, -0.03552985563874245, -0.014762009494006634, 0.01696040853857994, -0.015744272619485855, -0.0003575320297386497, 0.012947161681950092, 0.003213403280824423, -0.03944019600749016, 0.013714262284338474, 0.00201013102196157, -0.013358776457607746, -0.002939772792160511, -0.00993488822132349, 0.019888486713171005, -0.021665915846824646, -0.004637684673070908, -0.01867235079407692, 0.07401585578918457, -0.03992665186524391, 0.056915123015642166, 0.01411652285605669, -0.04119891673326492, 0.04632539302110672, -0.014808784238994122, 0.014182006940245628, 0.03644663468003273, -0.013527164235711098, -0.03521179035305977, -0.015360722318291664, 0.03706405684351921, 0.03075886331498623, 0.031114349141716957, -0.006515678018331528, -0.013555229641497135, -0.0006489951629191637, -0.019925907254219055, 0.01306877564638853, 0.03657760098576546, -0.020356230437755585, 0.008400687016546726, 0.040263429284095764, -0.07382875680923462, -0.03985181450843811, 0.03854212909936905, -0.008573752827942371, -0.009172465652227402, 0.01862557791173458, -0.01751234568655491, -0.004452925641089678, -0.013583294115960598, -0.006707453168928623, -0.05201316252350807, 0.0028251754119992256, 0.012385868467390537, -0.014556202106177807, -0.004637684673070908, -0.008943270891904831, -0.06844034045934677, -0.0009354885551147163, -0.026118841022253036, 0.02696078084409237, 0.010664569213986397, 0.006613904144614935, 0.02645561657845974, -0.027484653517603874, -0.010281018912792206, -0.01858815737068653, 0.003589937463402748, -0.0553060844540596, 0.028869176283478737, -0.006225676275789738, 0.006146159954369068, 0.00466808769851923, 0.010832957923412323, 0.03335952386260033, -0.020281391218304634, 0.0013131920713931322, 0.02630593813955784, 0.036502763628959656, -0.005117122549563646, -0.01568814367055893, -0.050067346543073654, 0.03854212909936905, -0.007923588156700134, 0.010449407622218132, 0.05212542414665222, -0.0031853385735303164, -0.014472007751464844, -0.003905664663761854, -0.009738435968756676, 0.016913633793592453, -0.005912287626415491, 0.034332431852817535, -0.029916923493146896, -0.005322929937392473, 0.007441811729222536, 0.02258269302546978, 0.01630556583404541, 0.005103090312331915, -0.02684852108359337, 0.05627899244427681, 0.03450081869959831, -0.023836249485611916, 0.013424260541796684, -0.02812078595161438, -0.0051826066337525845, 0.027091749012470245, -0.04116149619221687, 0.008381977677345276, -0.008428751491010189, 0.01750299148261547, 0.012404578737914562, -0.0026942070107907057, -0.02439754083752632, 0.028869176283478737, -0.021291719749569893, 0.05601705610752106, -0.02305043861269951, 0.005949707236140966, 0.023443343117833138, -0.00594502966850996, 0.0069272927939891815, -0.005640996154397726, -0.04520280659198761, -0.0031829997897148132, -0.004111472051590681, -0.04310731217265129, -0.007451166398823261, -0.03932793810963631, -0.031039509922266006, -0.023387214168906212, -0.00782536156475544, 0.007231326773762703, 0.0276904609054327, -0.012404578737914562, -0.023331085219979286, -0.002928079105913639, 0.049206700176000595, -0.00015684049867559224, 0.018765900284051895, 0.015444915741682053, -0.009186497889459133, 0.07326746731996536, 0.03075886331498623, 0.019738808274269104, 0.04490344971418381, 0.040338266640901566, 0.024303993210196495, 0.016333630308508873, 0.00002090232192131225, 0.04524022713303566, 0.040300846099853516, -0.002864933805540204, 0.023349793627858162, 0.024023346602916718, 0.04748539999127388, -0.008162138052284718, -0.030740154907107353, 0.01793331652879715, -0.03075886331498623, -0.01983235776424408, 0.03788728639483452, 0.008541010320186615, 0.05422091856598854, -0.029149822890758514, 0.004962767008692026, -0.020075583830475807, 0.01778363808989525, 0.0555306002497673, -0.03403307497501373, -0.013499099761247635, 0.03289177641272545, 0.02924337238073349, 0.022489145398139954, -0.014621686190366745, -0.01583782210946083, -0.02703562006354332, -0.010000372305512428, -0.020749136805534363, -0.0247904472053051, -0.007942297495901585, -0.019851068034768105, -0.036820828914642334, 0.010028437711298466, -0.023611731827259064, -0.05268671736121178, -0.0020113002974539995, 0.03148854523897171, 0.026773681864142418, -0.0019072273280471563, 0.026436906307935715, 0.011281992308795452, 0.0009015771211124957, -0.009775855578482151, 0.004254134371876717, 0.023462053388357162, -0.007652296219021082, -0.00018198175530415028, -0.022882049903273582, 0.013630067929625511, -0.005318252369761467, 0.011787155643105507, -0.05871126055717468, -0.02084268443286419, 0.004749943036586046, 0.014219426549971104, 0.02157236635684967, 0.0357917919754982, 0.029879504814743996, -0.021759463474154472, 0.03227435424923897, -0.023181406781077385, 0.014733945019543171, 0.02638077735900879, 0.006548420060425997, 0.0356421135365963, 0.020187843590974808, -0.04628797248005867, -0.03489372506737709, -0.0046049426309764385, 0.011160378344357014, 0.04011375084519386, 0.008798269554972649, -0.00328824226744473, 0.0055053504183888435, -0.005715834908187389, 0.004235424567013979, -0.014359749853610992, 0.011375540867447853, 0.006431483663618565, -0.024154314771294594, 0.03470662608742714, 0.016024919226765633, -0.0604325607419014, 0.02037494070827961, 0.01404168363660574, -0.019551711156964302, 0.010599085129797459, 0.00027246103854849935, -0.004078730009496212, 0.02873820811510086, 0.055755119770765305, -0.021703334525227547, -0.05321059003472328, 0.029112404212355614, -0.005355671979486942, 0.007736490573734045, -0.06619516760110855, -0.054520271718502045, 0.026231098920106888, 0.008087298832833767, -0.029187243431806564, -0.003575904993340373, -0.033752426505088806, -0.029654987156391144, 0.06331386417150497, 0.010421342216432095, -0.01739073172211647, 0.023611731827259064, -0.020674297586083412, -0.034875012934207916, -0.028027236461639404, -0.026249809190630913, -0.051377031952142715, -0.008985367603600025, 0.01320909895002842, 0.02378011867403984, -0.054669950157403946, -0.028289174661040306, 0.027054328471422195, 0.0042588114738464355, 0.05148928984999657, -0.028869176283478737, 0.026792392134666443, -0.014172651804983616, 0.01746557094156742, 0.013134259730577469, 0.023106567561626434, -0.028382722288370132, -0.016632987186312675, 0.021759463474154472, -0.0028275141958147287, 0.004417844582349062, 0.00274098152294755, 0.036895669996738434, 0.0020592440851032734, -0.005369704216718674, -0.004366392735391855, 0.07405327260494232, -0.01782105676829815, 0.027353685349225998, -0.029580147936940193, 0.004331312142312527, -0.02804594673216343, 0.08396945148706436, -0.0354924350976944, 0.01766202412545681, 0.026942070573568344, -0.03354661911725998, 0.00933149829506874, -0.0038144546560943127, -0.015313947573304176, 0.009097626432776451, 0.008456816896796227, 0.02823304571211338, 0.01051489170640707, -0.007105035707354546, 0.02935563027858734, 0.03899116441607475, 0.005430511198937893, -0.02044977992773056, -0.014331684447824955, -0.011319411918520927, -0.032087258994579315, 0.004586232826113701, 0.007942297495901585, -0.005495995283126831, -0.031226608902215958, 0.023256246000528336, -0.06091901659965515, 0.01510814018547535, 0.010599085129797459, 0.04052536562085152, -0.005552124697715044, 0.05425833538174629, 0.04187246784567833, -0.025501418858766556, 0.024004636332392693, -0.06402483582496643, 0.013667487539350986, 0.01898106373846531, 0.03768147900700569, 0.0275407824665308, 0.0709848701953888, 0.018073638901114464, 0.020636877045035362, -0.029430469498038292, -0.009275369346141815, -0.00045283493818715215, 0.029486600309610367, 0.013480390422046185, 0.029729826375842094, 0.034725334495306015, 0.03176918998360634, 0.011759091168642044, 0.007287455722689629, -0.019458161666989326, -0.009850694797933102, -0.017680734395980835, -0.019140096381306648, -0.02668013423681259, 0.01862557791173458, -0.0358666330575943, -0.013078129850327969, 0.03257371112704277, -0.030571766197681427, -0.047971852123737335, 0.013583294115960598, 0.01610911265015602, -0.0014359749620780349, -0.0063051930628716946, -0.023499472066760063, -0.0165394376963377, 0.019383322447538376, 0.02215236984193325, 0.004350021947175264, -0.03614727780222893, 0.053397685289382935, 0.034613076597452164, 0.003711550962179899, 0.002469689818099141, -0.008176170289516449, 0.026829812675714493, -0.01827944628894329, -0.016277501359581947, -0.027784010395407677, 0.013386840932071209, 0.014004264026880264, 0.014359749853610992, 0.002288438845425844, -0.017053956165909767, -0.018344931304454803, -0.0437808632850647, -0.04288279637694359, -0.031133059412240982, 0.029056275263428688, 0.008877786807715893, -0.018578803166747093, 0.007362294942140579, -0.005495995283126831, -0.008419397287070751, 0.01646459847688675, -0.009850694797933102, 0.025594966486096382, 0.00993488822132349, -0.023948507383465767, -0.013143613934516907, -0.0026731586549431086, 0.0029912246391177177, -0.025856904685497284, 0.003082434879615903, -0.013237163424491882, 0.03515566140413284, -0.03891632333397865, 0.04602603614330292, 0.010121986269950867, -0.0002800618822220713, -0.05601705610752106, 0.06357580423355103, 0.03354661911725998, 0.0033607427030801773, -0.028214335441589355, 0.014247491024434566, -0.03283564746379852, 0.019420742988586426, 0.04303247481584549, 0.00302630546502769, 0.034145332872867584, -0.03517436981201172, 0.016548791900277138, 0.011590703390538692, 0.005257445853203535, -0.00022831767273601145, 0.0194020327180624, -0.03175048157572746, 0.024547219276428223, 0.02421044372022152, -0.026399487629532814, 0.03944019600749016, -0.0043032472021877766, -0.04666217043995857, 0.007292133290320635, -0.05115251615643501, -0.022844631224870682, -0.020505908876657486, -0.029916923493146896, -0.008185524493455887, 0.014668460935354233, -0.017605895176529884, -0.047934435307979584, 0.02417302504181862, 0.023405924439430237, 0.00038179627154022455, 0.02660529501736164, 0.005552124697715044, -0.022414306178689003, 0.04292021691799164, -0.029879504814743996, -0.009097626432776451, -0.010262309573590755, -0.02254527434706688, -0.014518782496452332, -0.011628123000264168, 0.023143986240029335, 0.04726088047027588, 0.04333183169364929, -0.005575511604547501, -0.017961381003260612, -0.03678341209888458, 0.0249775443226099, -0.0362408272922039, -0.046699587255716324, -0.04086213931441307, 0.004183972720056772, -0.00016356432752218097, 0.022975599393248558, 0.06024546176195145, 0.06911389529705048, 0.06350096315145493, 0.022433016449213028, 0.03362146019935608, 0.0027947721537202597, 0.004537119530141354, 0.0004034294397570193, 0.06844034045934677, 0.04531506448984146, 0.017306538298726082, 0.045988619327545166, 0.028214335441589355, -0.054782211780548096, 0.03496856242418289, -0.013218453153967857, -0.00203351816162467, 0.013115549460053444, -0.027746589854359627, 0.003695179708302021, 0.0552312433719635, -0.0608815960586071, -0.017250409349799156, 0.020674297586083412, -0.03079628385603428, -0.025220772251486778, -0.018139123916625977, -0.004340666811913252, -0.016314920037984848, -0.003531469264999032, -0.01489297766238451, 0.05384672060608864, -0.00009347576997242868, 0.013807810842990875, 0.021871723234653473, -0.007427779026329517, -0.03648405522108078, 0.011628123000264168, 0.0302162803709507, 0.0386543869972229, -0.03216209635138512, -0.005748577415943146, 0.0035922760143876076, -0.04954347386956215, -0.00811536330729723, 0.050067346543073654, 0.026829812675714493, 0.017998799681663513, 0.012376513332128525, -0.03738212212920189, 0.011356831528246403, -0.022395595908164978 ]
As one of the most successful AI-powered applications, recommender systems aim to help people make appropriate decisions in an effective and efficient way, by providing personalized suggestions in many aspects of our lives, especially for various human-oriented online services such as e-commerce platforms and social media sites. In the past few decades, the rapid developments of recommender systems have significantly benefited human by creating economic value, saving time and effort, and promoting social good. However, recent studies have found that data-driven recommender systems can pose serious threats to users and society, such as spreading fake news to manipulate public opinion in social media sites, amplifying unfairness toward under-represented groups or individuals in job matching services, or inferring privacy information from recommendation results. Therefore, systems' trustworthiness has been attracting increasing attention from various aspects for mitigating negative impacts caused by recommender systems, so as to enhance the public's trust towards recommender systems techniques. In this survey, we provide a comprehensive overview of Trustworthy Recommender systems (TRec) with a specific focus on six of the most important aspects; namely, Safety & Robustness, Nondiscrimination & Fairness, Explainability, Privacy, Environmental Well-being, and Accountability & Auditability. For each aspect, we summarize the recent related technologies and discuss potential research directions to help achieve trustworthy recommender systems in the future.
[ -0.0000017617098819755483, -0.029927076771855354, -0.018737103790044785, -0.10137209296226501, 0.05992387235164642, -0.00372563349083066, -0.03158291429281235, -0.010301049798727036, -0.026458533480763435, 0.01562587358057499, 0.03635869547724724, -0.020236073061823845, -0.016506081447005272, -0.006858651526272297, -0.0019194638589397073, 0.035626642405986786, 0.012627936899662018, -0.02189190872013569, -0.006666922941803932, -0.01322055235505104, -0.013734732754528522, 0.003538262564688921, -0.0035622285213321447, 0.03597524017095566, 0.03196636959910393, 0.017089981585741043, -0.000665058265440166, -0.023356018587946892, -0.056856218725442886, 0.036149539053440094, 0.04350494220852852, 0.010327194817364216, -0.02609250694513321, -0.04929165542125702, -0.06069078668951988, -0.015704307705163956, 0.027295168489217758, 0.04113448038697243, -0.01383931189775467, 0.05567098781466484, -0.025046715512871742, 0.000526708725374192, -0.03442398086190224, 0.010963384993374348, 0.02499442547559738, -0.05040716752409935, -0.002893357537686825, -0.014893818646669388, 0.03771822527050972, 0.01842336729168892, 0.03128660470247269, -0.06438592076301575, 0.025743909180164337, 0.00381714035756886, -0.04106476157903671, 0.03526061400771141, 0.01673267036676407, -0.06808105111122131, 0.0025295091327279806, 0.03020595572888851, -0.005115665029734373, 0.0771794393658638, -0.010091891512274742, -0.0012789162574335933, -0.014092044904828072, -0.07128814607858658, 0.025447601452469826, 0.02305971086025238, -0.005699565634131432, -0.052115295082330704, -0.071392722427845, 0.020462660118937492, 0.025796199217438698, -0.05253361165523529, -0.006196316797286272, 0.019765466451644897, 0.03984466940164566, 0.013612723909318447, -0.06048163026571274, 0.020811257883906364, 0.03559178486466408, 0.05086034536361694, -0.01861509494483471, 0.0032680996228009462, 0.03416253253817558, 0.004884719382971525, -0.006470837164670229, -0.08045625686645508, 0.003331282874569297, -0.039286915212869644, -0.048315584659576416, 0.009054814465343952, -0.01683724857866764, -0.01649736613035202, 0.020567240193486214, 0.002592692384496331, -0.010388199239969254, -0.0022484525106847286, -0.026249375194311142, 0.03250669687986374, 0.008231253363192081, -0.00974329374730587, 0.011521140113472939, 0.032541558146476746, -0.005647276062518358, -0.06327040493488312, -0.01770002767443657, 0.050964921712875366, 0.0012070181546732783, 0.11928999423980713, 0.009699719958007336, 0.003329104045405984, -0.05845976620912552, 0.02229279652237892, -0.07941046357154846, 0.027434606105089188, -0.042284850031137466, -0.08903174847364426, -0.013473285362124443, -0.017778461799025536, -0.012174759991466999, 0.05141809955239296, 0.029944507405161858, 0.011294552125036716, -0.024610968306660652, 0.03820626437664032, -0.04901278018951416, -0.049187079071998596, 0.04221513122320175, 0.03363963961601257, 0.007046022452414036, 0.04591026157140732, -0.018632525578141212, -0.015381854958832264, 0.01396132167428732, 0.06163199990987778, 0.05570584535598755, 0.022902842611074448, 0.012549502775073051, -0.018388506025075912, -0.057135093957185745, -0.012523357756435871, -0.059017520397901535, 0.0011623541358858347, -0.03208838030695915, 0.010292334482073784, -0.027870353311300278, 0.019835185259580612, -0.03946121409535408, 0.053753700107336044, -0.019260000437498093, 0.06313096731901169, -0.0135081447660923, -0.016758814454078674, 0.06135312095284462, -0.013682443648576736, -0.001412908430211246, 0.007381547708064318, 0.014458072371780872, 0.008906660601496696, 0.013464570045471191, -0.024175221100449562, -0.02677227184176445, 0.06975431740283966, 0.06940571963787079, 0.019748035818338394, 0.03918233513832092, -0.006170171778649092, -0.05190613493323326, 0.049465954303741455, -0.03743935003876686, -0.01793533004820347, -0.06250349432229996, 0.04747895151376724, 0.022589104250073433, 0.04838530346751213, 0.06978917866945267, -0.008335832506418228, -0.012244479730725288, 0.0017048586159944534, -0.03541748598217964, 0.01795276068150997, 0.030833430588245392, 0.008375049568712711, 0.029909648001194, 0.04977969080209732, 0.05469491332769394, -0.021090134978294373, 0.0347202904522419, 0.012532072141766548, -0.020480090752243996, 0.03404052555561066, 0.007904443889856339, 0.008919732645154, -0.01581760123372078, -0.03078114055097103, -0.009368551895022392, -0.0036798801738768816, -0.012314199469983578, -0.021403873339295387, -0.033447910100221634, -0.002823638031259179, 0.04273802787065506, -0.004727850668132305, 0.048733901232481, -0.013255411759018898, 0.03125174716114998, -0.03729990869760513, -0.03628897666931152, -0.01790047064423561, -0.026284234598279, -0.03921719640493393, 0.008117958903312683, 0.0229202713817358, -0.027051148936152458, -0.01521627139300108, 0.024053212255239487, -0.0001377367734676227, -0.02928217127919197, 0.05030258744955063, -0.012017891742289066, -0.02088097669184208, 0.04096018150448799, -0.014161764644086361, 0.03900803625583649, -0.032733283936977386, -0.008052597753703594, 0.033831365406513214, -0.024105502292513847, -0.007751932367682457, -0.04573596268892288, 0.020950697362422943, -0.009891447611153126, 0.0016699988627806306, -0.0021057454869151115, 0.00032762697082944214, -0.027417177334427834, 0.0033160317689180374, -0.023756904527544975, 0.0018366719596087933, -0.03160034492611885, -0.0013410102110356092, 0.014170479960739613, -0.015024542808532715, 0.08373306691646576, 0.0015795814106240869, -0.0482458658516407, 0.03458084911108017, 0.03236725926399231, -0.021979058161377907, -0.04880362004041672, -0.006209389306604862, -0.02150845341384411, -0.000029804386940668337, -0.018493086099624634, 0.03946121409535408, 0.07125328481197357, -0.04528278857469559, 0.04221513122320175, -0.05783228948712349, 0.04597998037934303, 0.014911249279975891, 0.001689607510343194, 0.03397080674767494, -0.014806670136749744, 0.027138298377394676, 0.0882648304104805, 0.004133056383579969, 0.05908723920583725, 0.0371256098151207, 0.0462937206029892, 0.003250669687986374, -0.016610661521553993, -0.05856434255838394, -0.010954669676721096, -0.01116382796317339, 0.029160162433981895, -0.06745357811450958, -0.029317032545804977, 0.004069873131811619, 0.018458226695656776, -0.04988427087664604, 0.008806439116597176, -0.006392402574419975, -0.04336550086736679, -0.04660745710134506, -0.00000720003208698472, -0.020340651273727417, -0.029595909640192986, -0.016140054911375046, -0.030362823978066444, 0.0068499366752803326, -0.03208838030695915, 0.01288066990673542, 0.08791623264551163, 0.03918233513832092, 0.02996193617582321, 0.02835838869214058, -0.02464582771062851, -0.03782280534505844, 0.008680072613060474, 0.038031965494155884, -0.00008333654113812372, 0.06142284348607063, -0.030903149396181107, 0.026859421283006668, 0.00781729444861412, 0.05417201668024063, -0.022693684324622154, -0.00942955631762743, 0.008388122543692589, 0.007878298871219158, -0.022275365889072418, -0.00945570133626461, 0.03201866149902344, 0.060795366764068604, 0.017238136380910873, 0.0004360189486760646, 0.0015534366248175502, -0.019992053508758545, 0.007978520356118679, -0.0070808823220431805, -0.10945954918861389, -0.01692439801990986, -0.06403732299804688, -0.005760570056736469, -0.013996181078255177, -0.003701667534187436, -0.03299473226070404, 0.02311200089752674, -0.03018852509558201, 0.04134363681077957, 0.007006805390119553, -0.008296615444123745, 0.05521780997514725, 0.012427492998540401, 0.002461968455463648, -0.002195073524489999, -0.036777012050151825, -0.023983493447303772, 0.007303113117814064, -0.014083330519497395, -0.07153216004371643, -0.012723800726234913, 0.021491022780537605, -0.031199457123875618, 0.026371384039521217, 0.055740706622600555, 0.02088097669184208, 0.031007729470729828, 0.0009368552127853036, -0.018684813752770424, -0.015102977864444256, 0.03597524017095566, 0.06110910326242447, -0.025011856108903885, -0.00023366912500932813, -0.03139118477702141, 0.027033720165491104, 0.0014695554273203015, 0.07073038816452026, -0.03020595572888851, -0.031234316527843475, 0.05654247850179672, -0.006122239865362644, -0.028201520442962646, -0.0583551861345768, 0.06009817123413086, 0.012026606127619743, 0.0002456521615386009, -0.06020275130867958, 0.01795276068150997, -0.006144027225673199, 0.03531290590763092, 0.01683724857866764, 0.02541274204850197, -0.009969882667064667, -0.024436669424176216, -0.01708126626908779, 0.043923258781433105, 0.025011856108903885, -0.06856908649206161, 0.053997721523046494, 0.019312290474772453, -0.05343996360898018, 0.01847565546631813, 0.04559652507305145, 0.004723493475466967, 0.002708165207877755, 0.047200072556734085, 0.002168928738683462, -0.014196624979376793, 0.03705589100718498, -0.08798595517873764, 0.004063337109982967, -0.050337448716163635, -0.03264613449573517, 0.02349545806646347, 0.0010501493234187365, -0.0482458658516407, 0.013900317251682281, 0.0013562613166868687, 0.015782741829752922, 0.038415420800447464, -0.021299295127391815, 0.007102669682353735, 0.016070334240794182, -0.018928833305835724, 0.07390262186527252, 0.017883040010929108, 0.0229202713817358, 0.006209389306604862, -0.019382009282708168, 0.028340959921479225, 0.007473054341971874, 0.029735349118709564, -0.022257937118411064, -0.027434606105089188, 0.02431466057896614, -0.06790675222873688, -0.04514334723353386, 0.0588432215154171, 0.06347956508398056, -0.02860240824520588, -0.009821728803217411, 0.05633332207798958, -0.002409678651019931, -0.03660271689295769, -0.011224832385778427, -0.03984466940164566, 0.045701105147600174, 0.03020595572888851, 0.01430120412260294, -0.028009792789816856, 0.012915529310703278, -0.027295168489217758, 0.00642726244404912, 0.02054980956017971, 0.008592923171818256, -0.013743448071181774, -0.018754534423351288, 0.021351583302021027, -0.02286798134446144, 0.06431619822978973, -0.0026689479127526283, -0.031530626118183136, 0.03594037890434265, -0.022850552573800087, -0.04123906046152115, -0.0311123076826334, -0.04911735653877258, 0.023512886837124825, -0.0472697913646698, -0.012776090763509274, 0.02237994596362114, -0.023321159183979034, 0.02914273366332054, -0.0073684751987457275, 0.00981301348656416, -0.003984902519732714, 0.010414344258606434, 0.0723687931895256, 0.013124687597155571, -0.008584207855165005, -0.025691621005535126, 0.022031348198652267, -0.05845976620912552, -0.02546503208577633, -0.0011013495968654752, -0.02499442547559738, -0.002026221714913845, 0.035382624715566635, 0.0034010023809969425, -0.008745434693992138, -0.014144334942102432, 0.026615403592586517, 0.04549194499850273, -0.02079382911324501, 0.028428109362721443, -0.011128968559205532, -0.0032354185823351145, 0.06926628202199936, 0.031199457123875618, 0.006915298756211996, -0.02232765592634678, 0.00790880061686039, 0.005002371035516262, -0.009446986950933933, -0.02802722156047821, -0.027574045583605766, -0.04981455206871033, -0.031007729470729828, -0.01573045179247856, -0.01798762008547783, -0.04235456883907318, -0.023268869146704674, -0.025395313277840614, -0.01770874299108982, 0.046816617250442505, -0.023042280226945877, -0.01425762940198183, 0.029508760198950768, 0.0005751855205744505, 0.01087623555213213, -0.015957040712237358, 0.0033944661263376474, -0.012009176425635815, -0.029055584222078323, -0.053230807185173035, 0.023530317470431328, -0.004176631104201078, 0.03604495897889137, 0.024157792329788208, 0.01355171948671341, -0.0371256098151207, 0.006645135581493378, 0.016279492527246475, -0.023948634043335915, 0.025308163836598396, 0.008205108344554901, 0.009150679223239422, 0.015991900116205215, 0.003331282874569297, 0.014824099838733673, -0.06591974943876266, 0.010719366371631622, 0.0016580158844590187, 0.031199457123875618, 0.01992233470082283, -0.012026606127619743, 0.00642726244404912, 0.016750099137425423, -0.023042280226945877, -0.028149230405688286, 0.025743909180164337, -0.030519692227244377, 0.02827123925089836, 0.00432914262637496, -0.016715239733457565, -0.05894780158996582, -0.03628897666931152, 0.04109961912035942, 0.016140054911375046, 0.03149576485157013, 0.03297730162739754, 0.03782280534505844, 0.048350442200899124, -0.04409755766391754, -0.023181719705462456, 0.0019314468372613192, -0.0038018892519176006, -0.008932805620133877, -0.019382009282708168, -0.05277762934565544, 0.012192189693450928, 0.025534750893712044, -0.04374895989894867, 0.003372678766027093, -0.002063260180875659, -0.013176977634429932, -0.0038999321404844522, -0.01360400952398777, -0.010449203662574291, 0.008353262208402157, 0.02614479698240757, 0.0025229728780686855, 0.02860240824520588, 0.0520804338157177, 0.02131672389805317, -0.010274904780089855, -0.028881285339593887, 0.016802389174699783, -0.028968434780836105, -0.025099005550146103, -0.026319095864892006, 0.0180921982973814, -0.005529624409973621, -0.03212324157357216, -0.027957502752542496, 0.0008050418691709638, 0.010710651986300945, -0.01024876069277525, 0.016270779073238373, 0.013987465761601925, 0.029543619602918625, -0.028393249958753586, -0.04109961912035942, -0.016392787918448448, 0.01764773763716221, -0.04420213773846626, 0.005146167241036892, 0.029404181987047195, -0.023321159183979034, 0.0007772630196996033, -0.03540005534887314, -0.018946262076497078, 0.027765773236751556, -0.002579619875177741, 0.032436978071928024, -0.04326092451810837, 0.010728081688284874, 0.0236348956823349, 0.05678649991750717, 0.07222935557365417, -0.0015784921124577522, -0.012392633594572544, 0.012235764414072037, -0.0021406051237136126, -0.010867520235478878, 0.018649954348802567, -0.0530565083026886, -0.00976943876594305, 0.017665168270468712, -0.05441603809595108, 0.06912684440612793, -0.028811566531658173, 0.061283402144908905, 0.005294321104884148, 0.0032680996228009462, -0.010693221352994442, -0.010501493699848652, -0.022170787677168846, 0.06832506507635117, 0.023896344006061554, -0.013595294207334518, 0.057623133063316345, 0.00047850425471551716, 0.004320427775382996, -0.0009145232033915818, 0.006331398151814938, -0.05253361165523529, 0.031670063734054565, -0.02330372855067253, -0.012436208315193653, 0.016819819808006287, -0.014318633824586868, -0.01220090501010418, 0.06410703808069229, 0.03925205394625664, 0.03879887983202934, 0.04127391800284386, 0.01017904095351696, 0.0180921982973814, 0.11134197562932968, -0.011991746723651886, 0.03189665079116821, -0.009290117770433426, -0.04350494220852852, 0.024872416630387306, 0.03341304883360863, -0.03838055953383446, 0.012793520465493202, 0.0006138580502010882, 0.02522101439535618, 0.007185461465269327, -0.016532225534319878, 0.007146244402974844, 0.018580235540866852, 0.04451587423682213, 0.016671665012836456, -0.006078665144741535, 0.027051148936152458, 0.021281864494085312, 0.011747729033231735, 0.013752163387835026, 0.016366641968488693, 0.009760724380612373, 0.0038803236093372107, 0.023983493447303772, 0.05539210885763168, -0.0005016532959416509, -0.022606534883379936, -0.029020724818110466, 0.06720955669879913, -0.01215733028948307, -0.0002110647619701922, 0.04409755766391754, 0.04353979974985123, -0.025674190372228622, -0.003849821398034692, -0.0039042895659804344, -0.0029064298141747713, -0.0145887965336442, 0.007895728573203087, -0.04622400179505348, -0.006279108580201864, -0.0031308394391089678, 0.028637267649173737, 0.004832429811358452, 0.024297231808304787, -0.009098389185965061, 0.023600036278367043, 0.038520000874996185, -0.019033411517739296, -0.04458559304475784, 0.01024876069277525, -0.002895536134019494, -0.034755147993564606, -0.0022789547219872475, 0.011346842162311077, -0.01389160193502903, -0.02565675973892212, -0.029264742508530617, 0.013900317251682281, -0.026284234598279, 0.055113229900598526, 0.014309918507933617, 0.0014717341400682926, -0.02464582771062851, -0.004331321455538273, 0.0004251252976246178, -0.0008753060246817768, -0.039914388209581375, -0.0018061697483062744, 0.001740807667374611, 0.008841298520565033, 0.04123906046152115, 0.02271111309528351, -0.03078114055097103, 0.017002832144498825, 0.011346842162311077, -0.012044035829603672, 0.028131801635026932, -0.029125303030014038, -0.0462937206029892, 0.004645058885216713, -0.026510823518037796, 0.031077448278665543, -0.052115295082330704, -0.012741230428218842, 0.05821574851870537, 0.009830443188548088, -0.029195023700594902, 0.015346995554864407, -0.010867520235478878, 0.016811104491353035, -0.015434144996106625, -0.009324977174401283, -0.018127059563994408, -0.03072885051369667, 0.00979558378458023, 0.005581913981586695, -0.011808733455836773, -0.05082548409700394, 0.03302959352731705, 0.01454522181302309, -0.011181257665157318, 0.05584528669714928, -0.014736950397491455, 0.00986530352383852, 0.0008393569150939584, -0.008845656178891659, 0.07010291516780853, -0.05957527458667755, -0.03670729324221611, 0.047444090247154236, -0.017255565151572227, 0.021839620545506477, 0.026998860761523247, -0.03911261633038521, -0.014423212967813015, 0.07073038816452026, -0.029160162433981895, 0.03416253253817558, 0.03370935842394829, -0.006658208090811968, -0.048071566969156265, 0.0076429955661296844, 0.006514411885291338, -0.008662642911076546, -0.02136901393532753, 0.022118497639894485, 0.05330052599310875, -0.010972099378705025, -0.013760877773165703, -0.008135389536619186, 0.04615427926182747, -0.014431927353143692, -0.05985415354371071, 0.004239814355969429, 0.017037691548466682, 0.017743602395057678, -0.022083638235926628, 0.0022114140447229147, -0.04263344779610634, 0.021456163376569748, 0.03203609213232994, -0.039426352828741074, 0.01112025324255228, 0.05647275969386101, 0.013752163387835026, -0.0161574836820364, -0.013996181078255177, 0.01962602697312832, 0.031914081424474716, 0.016514796763658524, -0.01218347530812025, -0.00022590738080907613, -0.014126905240118504, -0.014710805378854275, 0.03771822527050972, -0.002666769316419959, 0.03479000926017761, -0.001327937818132341, -0.056856218725442886, -0.017089981585741043, -0.010937239974737167, -0.021247005090117455, 0.0129068149253726, 0.035626642405986786, 0.041936252266168594, 0.04866418242454529, -0.04357466101646423, -0.013394850306212902, -0.006327040959149599, -0.005106950178742409, 0.00030720134964212775, 0.006684353109449148, -0.003337819129228592, -0.0390777550637722, -0.010797801427543163, -0.03559178486466408, -0.0699286162853241, -0.028253810480237007, -0.02393120341002941, 0.01591346599161625, 0.010527637787163258, 0.021159855648875237, -0.004250708036124706, -0.06086508557200432, 0.0020785112865269184, 0.01121611800044775, -0.0070983124896883965, 0.006396760232746601, 0.010815231129527092, 0.012453638017177582, 0.006056877784430981, -0.014214054681360722, 0.023460596799850464, -0.02272854372859001, -0.0006906584021635354, 0.017839465290308, 0.007786791771650314, -0.013464570045471191, -0.041901394724845886, -0.014510362409055233, -0.028933575376868248, -0.0019586810376495123, 0.03421482443809509, -0.0015686878468841314, -0.005337895825505257, 0.03855485841631889, -0.00008823868847684935, -0.003536083735525608, 0.012044035829603672, 0.0061048101633787155, 0.006614633370190859, 0.045945122838020325, 0.0161574836820364, -0.018632525578141212, 0.021979058161377907, 0.011198688298463821, -0.02175247110426426, -0.005019800737500191, 0.02063695900142193, -0.029578479006886482, 0.010614787228405476, -0.023791765794157982, -0.04611942172050476, -0.04716521129012108, -0.003570943372324109, 0.033691927790641785, -0.024000924080610275, 0.005590628832578659, 0.020898407325148582, 0.023373447358608246, 0.03010137565433979, -0.013525574468076229, 0.014118189923465252, -0.004370538517832756, 0.03276814520359039, -0.009202968329191208, 0.02426237054169178, -0.012296769767999649, 0.03276814520359039, -0.08331475406885147, -0.03883373737335205, -0.0055862716399133205, 0.019364578649401665, -0.038903456181287766, 0.013447140343487263, 0.031844362616539, -0.011712868697941303, -0.029543619602918625, 0.04022812843322754, 0.0029434682801365852, -0.0018551911925897002, 0.022501954808831215, -0.02210106886923313, 0.04977969080209732, 0.011617004871368408, -0.010039601475000381, -0.06410703808069229, -0.023983493447303772, 0.010597357526421547, 0.012410063296556473, -0.008958950638771057, -0.02339087799191475, 0.013769593089818954, 0.00010512387234484777, -0.00013868998212274164, -0.06543171405792236, -0.009752009063959122, -0.03510374575853348, -0.014553937129676342, -0.00658413115888834, -0.02063695900142193, 0.03247183561325073, 0.0026754841674119234, -0.029125303030014038, 0.013638868927955627, 0.02093326672911644, -0.025691621005535126, 0.02710343897342682, -0.011861022561788559, -0.012113755568861961, -0.04043728485703468, 0.03275071457028389, -0.01943429931998253, -0.04071616381406784, -0.06281723082065582, 0.008226895704865456, 0.0014423212269321084, -0.0015109513187780976, 0.029212452471256256, 0.035766080021858215, -0.03782280534505844, 0.050476886332035065, -0.027852922677993774, -0.02807951159775257, 0.00942955631762743, 0.028916144743561745, 0.022902842611074448, 0.012723800726234913, -0.01770874299108982, 0.005882579367607832, 0.020584668964147568, 0.02464582771062851, 0.033552490174770355, 0.0008578761480748653, -0.07069552689790726, 0.047095492482185364, -0.019695747643709183, -0.001920553157106042, -0.0018519230652600527, 0.008357619866728783, -0.03015366569161415, -0.005041588097810745, -0.015686877071857452, 0.036881592124700546, -0.022885411977767944, 0.040402427315711975, -0.025116434320807457, -0.0313563272356987, -0.04221513122320175, 0.05866892263293266, -0.04660745710134506, 0.02663283236324787, -0.03308188170194626, 0.025883348658680916, -0.01852794550359249, -0.009019955061376095, 0.014850244857370853, 0.0033813936170190573, 0.01008317619562149, -0.04374895989894867, 0.051243800669908524, -0.004130878020077944, 0.02778320387005806, 0.013386135920882225, -0.003339997725561261, 0.006357543170452118, 0.005934868939220905, -0.0030436899978667498, 0.004026298876851797, -0.03553949296474457, 0.05696079507470131, 0.024175221100449562, -0.021107565611600876, 0.012871954590082169, -0.02300742082297802, -0.028689555823802948, 0.007516629062592983, 0.029944507405161858, -0.06504825502634048, -0.015800172463059425, 0.02464582771062851, 0.016619374975562096, -0.004082945641130209, 0.034946877509355545, -0.037509068846702576, 0.011233547702431679, 0.018196778371930122, 0.05099978297948837, -0.0035578710958361626, 0.008213823661208153, 0.042424291372299194, -0.013830597512423992, -0.0076691401191055775, 0.025743909180164337, 0.019364578649401665, 0.0065797739662230015, -0.003054583678022027, -0.024471528828144073, -0.006374972872436047, -0.005625488702207804, 0.008087457157671452, 0.01698540337383747, -0.010091891512274742, -0.06302639096975327, 0.03372678905725479, 0.02065438963472843, 0.04510848969221115, -0.021630462259054184 ]
Online social networks are actively involved in the removal of malicious social bots due to their role in the spread of low quality information. However, most of the existing bot detectors are supervised classifiers incapable of capturing the evolving behavior of sophisticated bots. Here we propose MulBot, an unsupervised bot detector based on multivariate time series (MTS). For the first time, we exploit multidimensional temporal features extracted from user timelines. We manage the multidimensionality with an LSTM autoencoder, which projects the MTS in a suitable latent space. Then, we perform a clustering step on this encoded representation to identify dense groups of very similar users -- a known sign of automation. Finally, we perform a binary classification task achieving f1-score $= 0.99$, outperforming state-of-the-art methods (f1-score $\le 0.97$). Not only does MulBot achieve excellent results in the binary classification task, but we also demonstrate its strengths in a novel and practically-relevant task: detecting and separating different botnets. In this multi-class classification task we achieve f1-score $= 0.96$. We conclude by estimating the importance of the different features used in our model and by evaluating MulBot's capability to generalize to new unseen bots, thus proposing a solution to the generalization deficiencies of supervised bot detectors.
[ 0.016131125390529633, -0.06327587366104126, -0.027304476127028465, -0.055931027978658676, 0.04605220630764961, 0.015047759748995304, -0.09298579394817352, 0.02141023613512516, 0.0138909462839365, 0.04994497448205948, 0.01814177818596363, 0.0138909462839365, -0.005660124588757753, -0.026551630347967148, -0.056812409311532974, 0.011806844733655453, 0.03512674197554588, -0.014083748683333397, -0.005453550722450018, -0.021759115159511566, -0.02210799604654312, -0.004211811814457178, -0.06603019684553146, 0.016250478103756905, -0.008841361850500107, 0.030260778963565826, 0.006082453299313784, -0.013349262997508049, -0.03771580010652542, 0.06779295951128006, 0.015708796679973602, 0.029728276655077934, 0.05244222283363342, -0.027286114171147346, -0.05530671402812004, -0.016810523346066475, 0.08696301281452179, 0.02651490643620491, 0.010438866913318634, 0.010723480023443699, 0.011017274111509323, -0.0027612042613327503, -0.04608893021941185, -0.01601177081465721, 0.008028837852180004, -0.019757645204663277, -0.05589430406689644, -0.038083042949438095, -0.008102286607027054, 0.008680693805217743, 0.025284644216299057, 0.01382667850703001, -0.0012807580642402172, -0.03191336989402771, 0.011246800422668457, 0.040359947830438614, 0.05549033731222153, 0.021795840933918953, 0.08145438134670258, 0.004953182768076658, 0.018325399607419968, 0.07690057158470154, 0.03408009931445122, -0.009249919094145298, -0.016856428235769272, -0.017847983166575432, 0.045023925602436066, -0.07366883754730225, -0.009121384471654892, -0.02991189807653427, -0.004232469480484724, 0.037642352283000946, -0.009337139315903187, -0.03275802731513977, 0.04271029680967331, 0.03558579459786415, 0.012862667441368103, 0.03925821930170059, 0.008322631940245628, -0.025358092039823532, 0.0013886356027796865, 0.03079327940940857, 0.003986875992268324, 0.01289939135313034, 0.06992296129465103, 0.00018103905313182622, -0.013551246374845505, -0.047888416796922684, 0.02735956385731697, -0.024899039417505264, -0.023925846442580223, 0.06052155792713165, 0.023154636844992638, -0.004200335592031479, -0.029765000566840172, -0.00929123442620039, 0.024476710706949234, 0.010677574202418327, -0.059346381574869156, -0.010549039579927921, -0.025284644216299057, -0.036797694861888885, 0.01518547534942627, 0.001942942151799798, -0.0024651149287819862, -0.03049948625266552, -0.04509737342596054, 0.008028837852180004, 0.00002634175689308904, 0.11832552403211594, 0.010916282422840595, 0.01562616601586342, -0.019078245386481285, 0.02309955097734928, -0.01055822055786848, 0.0414249487221241, -0.08652232587337494, -0.054682403802871704, -0.06033793464303017, -0.009456492960453033, 0.017269575968384743, 0.04329788684844971, -0.011944561265408993, -0.04821893572807312, -0.05222187936306, 0.02254868671298027, -0.020969543606042862, 0.03161957487463951, 0.033253803849220276, 0.027194304391741753, -0.016516730189323425, 0.007923255674540997, -0.006463467143476009, -0.00829049851745367, -0.06834381818771362, 0.04777824506163597, 0.027561547234654427, 0.057950861752033234, 0.034392256289720535, 0.019500574097037315, -0.04355495423078537, 0.007289762608706951, -0.0742197036743164, -0.015809787437319756, -0.01602095179259777, 0.013771592639386654, -0.005274519789963961, 0.09239820390939713, -0.02679033763706684, 0.03688950464129448, 0.033382341265678406, 0.013762411661446095, 0.040653739124536514, 0.03105035051703453, -0.015396639704704285, -0.01887626200914383, -0.014377542771399021, -0.026771975681185722, -0.05372757092118263, -0.020620664581656456, 0.02906724065542221, -0.024146191775798798, 0.10018374025821686, 0.001582585508003831, 0.03589795157313347, -0.01014507282525301, 0.014414266683161259, 0.003275343682616949, -0.010117529891431332, 0.05119359865784645, 0.0010747580090537667, 0.025872230529785156, -0.000734484929125756, 0.029820088297128677, 0.008464938960969448, 0.04017632454633713, 0.0528094656765461, -0.012109819799661636, -0.0034291264601051807, 0.020418681204319, -0.03841356188058853, 0.06059500575065613, -0.0024720008950680494, 0.004624959547072649, 0.06481829285621643, 0.04226960614323616, 0.07065744698047638, 0.03775252401828766, 0.022016186267137527, 0.01645246148109436, -0.009465674869716167, -0.018628373742103577, 0.07253038883209229, -0.0323907844722271, 0.016259659081697464, 0.02937939763069153, -0.042893920093774796, 0.02269558422267437, -0.026331285014748573, -0.01915169507265091, -0.020675750449299812, -0.04039667174220085, 0.007578966207802296, -0.019684195518493652, 0.04384874925017357, -0.005761116277426481, 0.005320425145328045, 0.03351087495684624, -0.03734855726361275, -0.015139570459723473, 0.02142859809100628, -0.04370185360312462, -0.05490274727344513, 0.002550039906054735, 0.03859718143939972, 0.002266574651002884, 0.02181420288980007, -0.0027589090168476105, 0.033382341265678406, 0.0018132596742361784, -0.0018763794796541333, 0.03804631903767586, -0.023026103153824806, -0.01438672374933958, -0.06779295951128006, -0.015378277748823166, 0.02455015853047371, 0.05148739367723465, -0.042893920093774796, 0.0066746314987540245, 0.024990849196910858, 0.021795840933918953, -0.021098079159855843, -0.008116058073937893, 0.0023124797735363245, 0.015708796679973602, 0.010392962023615837, 0.02298937737941742, 0.022199805825948715, -0.01614948734641075, -0.011540594510734081, 0.009181061759591103, -0.06816019862890244, -0.03797287121415138, 0.013119736686348915, -0.02835111878812313, 0.01671871356666088, -0.017655180767178535, -0.00878627598285675, 0.014772327616810799, 0.013799135573208332, 0.0006340670515783131, -0.022769032046198845, -0.01760927587747574, 0.020253421738743782, -0.03903787210583687, 0.04719065502285957, -0.038340114057064056, 0.0067939856089651585, -0.021667305380105972, 0.011522232554852962, 0.026845423504710197, -0.06573639810085297, 0.06379001587629318, -0.014974310994148254, -0.012082276865839958, 0.05167101323604584, 0.030756555497646332, 0.022640498355031013, 0.008845952339470387, 0.0007304681930691004, -0.05868534371256828, -0.03955201432108879, 0.01240361388772726, 0.030976900830864906, -0.010448047891259193, 0.004292146302759647, -0.03365777060389519, -0.011531413532793522, 0.034135185182094574, 0.04013960063457489, 0.009401407092809677, 0.023595327511429787, -0.022603772580623627, 0.041057705879211426, -0.0315094031393528, -0.003915722947567701, -0.02284248173236847, -0.040653739124536514, 0.02242015302181244, -0.029563017189502716, 0.004193449858576059, 0.004253126680850983, 0.007317306008189917, 0.006289027165621519, 0.00745043158531189, 0.0414249487221241, 0.02482558973133564, 0.02269558422267437, -0.008240003138780594, -0.026625078171491623, 0.03305182233452797, 0.03499820828437805, -0.013551246374845505, 0.030426038429141045, -0.002054262440651655, 0.06408380717039108, 0.028461290523409843, -0.03351087495684624, -0.08769749850034714, -0.05203825607895851, 0.004301327280700207, -0.07444004714488983, 0.008639378473162651, -0.009539122693240643, 0.03670588508248329, 0.055233266204595566, 0.008575111627578735, 0.015268105082213879, -0.022346703335642815, 0.03178483620285988, 0.04777824506163597, -0.05405808985233307, 0.03292328491806984, -0.02142859809100628, -0.006091634277254343, 0.004071800969541073, 0.0501653216779232, -0.007771768607199192, 0.014239826239645481, -0.0036678339820355177, 0.014221464283764362, -0.018683459609746933, 0.024201277643442154, 0.016278022900223732, -0.0567389614880085, 0.016241297125816345, 0.09401407092809677, 0.005297472700476646, 0.02735956385731697, -0.046309273689985275, -0.04634599760174751, -0.018251949921250343, -0.018408028408885002, 0.017912251874804497, -0.0201248861849308, -0.04168201982975006, 0.009396816603839397, -0.017489921301603317, 0.013422711752355099, 0.0010655769146978855, -0.06320242583751678, 0.02254868671298027, 0.02623947337269783, -0.007762587629258633, 0.0229710154235363, -0.03387811779975891, 0.0012887915363535285, -0.011476326733827591, 0.016489187255501747, -0.048549454659223557, -0.05945655331015587, 0.0058070216327905655, 0.010007357224822044, -0.03575105220079422, 0.007565194740891457, -0.0371098518371582, -0.016948239877820015, 0.00534796854481101, 0.03362104669213295, -0.018655916675925255, 0.009924727492034435, -0.004491834435611963, 0.02313627488911152, -0.05247894674539566, 0.02923250012099743, 0.045758411288261414, 0.001346173114143312, -0.02343006804585457, 0.02835111878812313, -0.01163240522146225, 0.01786634512245655, -0.021924374625086784, -0.031270693987607956, 0.01603931374847889, 0.0002576435508672148, 0.04847600311040878, 0.002673984272405505, -0.03106871247291565, 0.011540594510734081, 0.056959304958581924, -0.00620180694386363, 0.003252391004934907, -0.04410582035779953, 0.03470441326498985, 0.02298937737941742, -0.02056557685136795, -0.0029930260498076677, -0.03753218054771423, -0.03020569309592247, -0.0426001250743866, 0.03532872349023819, 0.017838802188634872, -0.003787187859416008, -0.017260394990444183, -0.02638637088239193, 0.023650415241718292, 0.002205749973654747, 0.0066746314987540245, -0.0714653804898262, -0.018224406987428665, -0.009305005893111229, -0.011044817045331001, 0.021079717203974724, 0.040653739124536514, 0.03520018979907036, -0.01816932111978531, 0.004579054657369852, -0.002678574761375785, -0.04322443902492523, 0.0028989200945943594, 0.029434483498334885, 0.06757261604070663, 0.034667689353227615, -0.006839890964329243, 0.07851643860340118, 0.02111644111573696, -0.03345578908920288, -0.013946032151579857, -0.03231733664870262, 0.0657731220126152, 0.04326116293668747, 0.0456482395529747, -0.01657181605696678, 0.027983875945210457, 0.00535255903378129, 0.02978336438536644, -0.028993792831897736, -0.018251949921250343, -0.049577731639146805, 0.00468234159052372, 0.0030940177384763956, 0.009392226114869118, -0.007005149964243174, -0.06055828183889389, -0.03591631352901459, -0.02921413816511631, -0.020620664581656456, -0.06680140644311905, -0.030866729095578194, -0.054682403802871704, 0.03279475122690201, -0.0516342893242836, 0.00381243578158319, 0.01997799053788185, -0.019482212141156197, 0.055416885763406754, -0.017655180767178535, 0.034392256289720535, -0.026331285014748573, -0.016424918547272682, 0.07704746723175049, 0.02341170608997345, 0.005889650899916887, -0.04212271049618721, 0.008809228427708149, -0.039809081703424454, -0.041645295917987823, 0.0067434897646307945, -0.004257717169821262, 0.05262584611773491, -0.0056738960556685925, 0.0013679781695827842, 0.03277638927102089, 0.03940511494874954, 0.0288101714104414, -0.04436288774013519, -0.026735251769423485, 0.017085954546928406, 0.02653326839208603, -0.007891122251749039, 0.021446960046887398, 0.014873319305479527, -0.019114969298243523, -0.01955566182732582, 0.01433163695037365, 0.00014632317470386624, 0.011696672067046165, -0.01728793792426586, -0.014854957349598408, -0.04311426356434822, -0.019078245386481285, -0.011696672067046165, 0.01756337098777294, 0.01760927587747574, 0.007822263985872269, 0.010907101444900036, 0.015075302682816982, 0.06158655881881714, -0.05622481927275658, 0.003986875992268324, -0.05380101874470711, -0.008262955583631992, 0.021795840933918953, 0.019629109650850296, 0.004085572436451912, -0.0013507637195289135, 0.03415354713797569, -0.03448406606912613, 0.013505341485142708, -0.020345231518149376, 0.02511938475072384, 0.03195009380578995, 0.009167290292680264, -0.008956125937402248, 0.05038566514849663, 0.02155713178217411, -0.014928406104445457, 0.018352942541241646, -0.004549216013401747, 0.03521855175495148, -0.014928406104445457, -0.02892034314572811, 0.058795519173145294, -0.07212641835212708, 0.013257453218102455, -0.028185859322547913, 0.01340434979647398, 0.02781861647963524, -0.05159756541252136, -0.06922520697116852, 0.019500574097037315, -0.04410582035779953, -0.01586487516760826, 0.010493953712284565, -0.0462358258664608, 0.012871848419308662, 0.0807933434844017, -0.060044143348932266, -0.017655180767178535, -0.014643792994320393, 0.011650767177343369, 0.006867433898150921, 0.0012991202529519796, -0.007046464830636978, 0.014551982283592224, 0.04098425805568695, -0.041608572006225586, 0.0054260073229670525, -0.04131477698683739, -0.014662154950201511, 0.0186008308082819, 0.014689698815345764, -0.03826666250824928, -0.0627250149846077, -0.008244593627750874, -0.00528370076790452, 0.0038055500481277704, 0.0450606495141983, 0.0037940735928714275, -0.01346861757338047, 0.05023876950144768, 0.019482212141156197, -0.018206045031547546, 0.004629550036042929, 0.008391490206122398, -0.025303006172180176, 0.05578412860631943, 0.012780037708580494, -0.010549039579927921, -0.0092269666492939, -0.027543185278773308, -0.023889122530817986, -0.035659242421388626, -0.03734855726361275, -0.005201071500778198, 0.064597949385643, -0.027690080925822258, 0.0005416826461441815, -0.04491375386714935, 0.01887626200914383, 0.0003081393660977483, 0.02069411240518093, 0.01490086317062378, -0.0018855604575946927, -0.007335667964071035, -0.058942414820194244, -0.0325927697122097, 0.00015163097123149782, 0.022218169644474983, 0.028167497366666794, 0.03918477147817612, -0.02341170608997345, -0.009630933403968811, -0.01532319188117981, -0.027267752215266228, 0.02111644111573696, -0.01859164983034134, -0.00553617998957634, -0.024348175153136253, -0.013092193752527237, 0.021502045914530754, 0.02466033212840557, 0.045317720621824265, 0.0011866522254422307, -0.013294177129864693, 0.0033051820937544107, 0.021208252757787704, 0.001942942151799798, 0.01480905245989561, -0.02750645950436592, -0.01490086317062378, 0.04366512969136238, -0.013652238063514233, 0.035677604377269745, 0.01199046615511179, 0.06867434084415436, -0.035145103931427, -0.0026326694060117006, -0.03619174286723137, 0.03345578908920288, -0.015956684947013855, 0.057399995625019073, 0.044766854494810104, -0.01163240522146225, 0.010796928778290749, 0.020822647958993912, -0.015359915792942047, 0.0005586101906374097, 0.002242474351078272, -0.015056940726935863, 0.06345950067043304, 0.02780025452375412, -0.031839922070503235, -0.029434483498334885, -0.01643409952521324, 0.034814585000276566, 0.007716682273894548, -0.012027190998196602, 0.039221495389938354, -0.009103022515773773, -0.002352647017687559, -0.01571797765791416, 0.033529236912727356, -0.004471176769584417, 0.020969543606042862, -0.11208239942789078, 0.021189890801906586, 0.033272165805101395, 0.05236877501010895, -0.03257440775632858, 0.01604849472641945, -0.02212635800242424, 0.02965482883155346, -0.0125413304194808, -0.0022883794736117125, -0.014588707126677036, -0.03125233203172684, 0.005173528101295233, 0.038670629262924194, -0.0077947210520505905, -0.03163793683052063, -0.0088597247377038, -0.03747709468007088, 0.020198335871100426, -0.015818968415260315, 0.020914457738399506, 0.014974310994148254, -0.03316199406981468, 0.03343742713332176, 0.031160522252321243, 0.0024995440617203712, -0.04002942889928818, 0.03145431727170944, 0.002667098306119442, 0.015213019214570522, 0.016636082902550697, 0.01524974312633276, -0.01475396566092968, -0.03387811779975891, -0.016856428235769272, -0.0044298623688519, -0.022493600845336914, 0.015286467038094997, -0.029177414253354073, -0.005228614434599876, 0.045611511915922165, 0.03900114819407463, -0.03178483620285988, -0.033529236912727356, -0.013863402418792248, -0.032978374511003494, 0.023319896310567856, -0.007409116718918085, -0.005563723389059305, -0.008492481894791126, -0.056665509939193726, 0.024862313643097878, 0.03578777611255646, 0.021924374625086784, 0.038927700370550156, 0.015424183569848537, -0.07164900749921799, 0.009933908469974995, -0.03246423229575157, -0.022456876933574677, 0.024366537109017372, 0.002630374161526561, 0.018610011786222458, -0.017196128144860268, -0.024293089285492897, 0.02001471444964409, 0.037642352283000946, 0.02541317790746689, 0.007955390028655529, -0.033712856471538544, 0.03564088046550751, 0.009066298604011536, -0.015139570459723473, 0.058097757399082184, 0.03617338091135025, 0.018646735697984695, 0.03571432828903198, -0.0924716517329216, -0.05023876950144768, -0.013725686818361282, 0.003190418938174844, 0.009185652248561382, -0.0516342893242836, -0.0037045583594590425, 0.05148739367723465, -0.0573265478014946, -0.026349646970629692, 0.01773781143128872, -0.029599742963910103, 0.004411499947309494, -0.00652314443141222, 0.013266634196043015, -0.01913333125412464, 0.023062827065587044, 0.030095519497990608, -0.013505341485142708, 0.017820440232753754, -0.017085954546928406, 0.009034164249897003, 0.016984963789582253, -0.03973563387989998, 0.027194304391741753, -0.038780804723501205, -0.001346173114143312, 0.03308854624629021, -0.011962923221290112, 0.031986817717552185, -0.014028661884367466, -0.039772357791662216, 0.02469705604016781, 0.012302622199058533, 0.016002589836716652, -0.011467145755887032, 0.0033304300159215927, 0.0005247550434432924, 0.0074182976968586445, 0.029122326523065567, -0.022218169644474983, 0.037825971841812134, 0.0035943856928497553, -0.017333844676613808, 0.02155713178217411, 0.02879180945456028, -0.027763530611991882, -0.00762487156316638, -0.021189890801906586, 0.049981698393821716, -0.027322839945554733, -0.008699055761098862, 0.020528852939605713, 0.007308125030249357, -0.06386346369981766, -0.014414266683161259, 0.030444400385022163, -0.05971362441778183, -0.0031950094271451235, -0.017526647076010704, 0.0558575764298439, -0.017104318365454674, 0.0411311537027359, -0.015157932415604591, -0.011219257488846779, -0.052001532167196274, 0.03885425254702568, -0.036816056817770004, -0.04627254977822304, 0.014983491972088814, 0.0050633554346859455, -0.012780037708580494, -0.012623959220945835, -0.042049262672662735, 0.028277669101953506, -0.019059883430600166, -0.009741106070578098, 0.030554572120308876, 0.0015711091691628098, -0.03659570962190628, 0.0501653216779232, -0.0405435673892498, -0.036375366151332855, -0.06580984592437744, -0.004643321968615055, 0.04528099671006203, 0.0035530708264559507, -0.0011614043032750487, 0.00022206692665349692, -0.03692622855305672, -0.0026854604948312044, 0.02952629327774048, -0.014799871481955051, -0.037385281175374985, 0.008065562695264816, -0.028461290523409843, -0.020198335871100426, -0.002080657985061407, -0.03172975033521652, -0.00602277647703886, -0.023595327511429787, -0.06801330298185349, 0.03191336989402771, 0.02750645950436592, 0.03195009380578995, 0.03316199406981468, 0.009667657315731049, 0.04168201982975006, 0.034245360642671585, -0.025927318260073662, 0.013018744997680187, -0.049871526658535004, -0.0011005797423422337, -0.011430421844124794, -0.01715022325515747, 0.02014324814081192, 0.04212271049618721, 0.021648943424224854, 0.012688226997852325, 0.014983491972088814, -0.0525156706571579, 0.012008828110992908, -0.011338611133396626, -0.03775252401828766, 0.022805755957961082, -0.005848336033523083, -0.0005950475460849702, 0.015378277748823166, 0.021630581468343735, 0.020179973915219307, 0.005485684145241976, 0.008510843850672245, 0.005660124588757753, 0.021667305380105972, 0.015800606459379196, 0.05916276201605797, 0.030003709718585014, -0.00010479320917511359, -0.062357768416404724, -0.044877029955387115, 0.006504782009869814, 0.0045193773694336414, -0.013881765305995941, 0.004728246480226517, -0.020822647958993912, -0.03362104669213295, -0.05119359865784645, -0.0017363682854920626, -0.03415354713797569, -0.032556045800447464, 0.07245694100856781, 0.016140306368470192, 0.012614778243005276, -0.0276349950581789, -0.0067297182977199554, -0.015038578771054745, -0.009529941715300083, 0.035530708730220795, 0.008391490206122398, 0.07120831310749054, -0.030738193541765213, 0.027488097548484802, -0.017214490100741386, 0.020345231518149376, -0.0306280218064785, 0.0004908998962491751, -0.029122326523065567, -0.023374982178211212, -0.009401407092809677, -0.019959628582000732, -0.019500574097037315, 0.03121560998260975, -0.027690080925822258, -0.01931695267558098, -0.03143595531582832, -0.03503493219614029, -0.022787394002079964, -0.009484036825597286, -0.05754689499735832, -0.006738899275660515, -0.01571797765791416, 0.016213754191994667, 0.010080805979669094, 0.010117529891431332, -0.018196864053606987, -0.018793633207678795, -0.01970255747437477, -0.05648189038038254, -0.007220904808491468, -0.01516711339354515, -0.028901981189846992, 0.04708048328757286, -0.014799871481955051, 0.004170497413724661, -0.023632051423192024, 0.01942712627351284, -0.03815649077296257, 0.033382341265678406, -0.006633317098021507, -0.03797287121415138, 0.04370185360312462, -0.03630191832780838, 0.028681635856628418, 0.01205473393201828, 0.01771026849746704, 0.01647082343697548, 0.039074596017599106, 0.002990730805322528, 0.007395345252007246, -0.005228614434599876, 0.054388608783483505, 0.04796186462044716, 0.024348175153136253, 0.024990849196910858, 0.01283512357622385, -0.01490086317062378, 0.03077491745352745, -0.018536563962697983, 0.04131477698683739, -0.0450606495141983, 0.01929859071969986, 0.021483683958649635, -0.008336403407156467, 0.02482558973133564, 0.02623947337269783, -0.012853486463427544, 0.032005179673433304, -0.03558579459786415, 0.013422711752355099, -0.0008343289373442531, 0.010852014645934105, -0.01885790005326271, 0.048733074218034744, -0.014882500283420086, 0.03037095069885254, -0.014772327616810799, 0.0022344407625496387, -0.002105905907228589, 0.010365418158471584, -0.011614043265581131, -0.001744401641190052, -0.06926193088293076, 0.03292328491806984, 0.017774535343050957, -0.012642322108149529, -0.031417593359947205, 0.03687114268541336, -0.01970255747437477, -0.031031988561153412, 0.001580290263518691, -0.03716493770480156, -0.00171915371902287, 0.05178118869662285, -0.022456876933574677, -0.015405821613967419, -0.01745319738984108, 0.005678486544638872, 0.02185092680156231, -0.05604119971394539, 0.03804631903767586, -0.0017409587744623423, 0.008207868784666061, 0.04010287672281265, 0.019812731072306633, -0.01190783642232418, -0.01714104227721691, 0.004175087902694941, -0.03187664598226547, 0.013688962906599045, 0.0008251479011960328, 0.010319513268768787, -0.0699964165687561, -0.010264426469802856, -0.01814177818596363, -0.0019578614737838507, -0.008946944028139114, 0.002740546828135848, -0.040066152811050415, 0.009860459715127945, 0.0001625334843993187, 0.030848367139697075, -0.0025362682063132524, 0.0029081013053655624, -0.015433364547789097, -0.05159756541252136, -0.037495456635951996, -0.016544273123145103, 0.021226614713668823, -0.018894623965024948, -0.0016158667858690023, 0.010861195623874664, 0.00196704245172441, 0.04796186462044716, -0.02554171346127987, 0.00010386075882706791, 0.026129301637411118, -0.019041521474719048, 0.03745873272418976, -0.020822647958993912, -0.020528852939605713, -0.015800606459379196 ]
Software vulnerabilities (SVs) have become a common, serious and crucial concern due to the ubiquity of computer software. Many machine learning-based approaches have been proposed to solve the software vulnerability detection (SVD) problem. However, there are still two open and significant issues for SVD in terms of i) learning automatic representations to improve the predictive performance of SVD, and ii) tackling the scarcity of labeled vulnerabilities datasets that conventionally need laborious labeling effort by experts. In this paper, we propose a novel end-to-end approach to tackle these two crucial issues. We first exploit the automatic representation learning with deep domain adaptation for software vulnerability detection. We then propose a novel cross-domain kernel classifier leveraging the max-margin principle to significantly improve the transfer learning process of software vulnerabilities from labeled projects into unlabeled ones. The experimental results on real-world software datasets show the superiority of our proposed method over state-of-the-art baselines. In short, our method obtains a higher performance on F1-measure, the most important measure in SVD, from 1.83% to 6.25% compared to the second highest method in the used datasets. Our released source code samples are publicly available at https://github.com/vannguyennd/dam2p
[ -0.026979709044098854, 0.010609160177409649, -0.019614826887845993, 0.01637987233698368, 0.07163513451814651, 0.06384140998125076, -0.02559995837509632, 0.036320991814136505, -0.021218320354819298, 0.022616716101765633, 0.01739603839814663, -0.0818900391459465, 0.023493044078350067, -0.024816857650876045, -0.010599837638437748, 0.02319471910595894, 0.002729201689362526, 0.0008413679315708578, -0.01791810616850853, -0.03481072187423706, -0.021777678281068802, -0.04467407241463661, -0.05142366141080856, 0.05161011219024658, -0.008688696660101414, 0.01978263445198536, 0.02796790935099125, -0.0011309522669762373, -0.015764577314257622, 0.05988861620426178, 0.049894750118255615, 0.00046554915024898946, -0.02860184758901596, 0.01978263445198536, -0.014282278716564178, 0.011103259399533272, -0.015522189438343048, 0.07271656394004822, -0.022337036207318306, 0.018980886787176132, 0.02785603702068329, -0.08121880888938904, -0.04609111323952675, 0.011643972247838974, 0.015689997002482414, 0.0035938762594014406, -0.015121315605938435, -0.026755966246128082, -0.05026765540242195, 0.00004406402149470523, -0.019819924607872963, -0.02166580595076084, -0.04400284215807915, -0.027166161686182022, -0.030391793698072433, 0.07372340559959412, 0.05780034512281418, 0.017545200884342194, 0.06682465970516205, -0.002475159941241145, -0.022765876725316048, 0.04683692380785942, 0.017284167930483818, 0.03287161514163017, 0.023269299417734146, -0.012688107788562775, 0.026457641273736954, -0.0006636551697738469, 0.0015755255008116364, 0.043368902057409286, -0.048962485045194626, -0.01409582607448101, -0.01435685995966196, 0.0331512950360775, 0.022915039211511612, -0.0056774853728711605, 0.023157428950071335, 0.031025733798742294, -0.025301635265350342, 0.0003828107437584549, 0.00357290031388402, 0.04023649916052818, -0.014459408819675446, -0.02082676999270916, 0.01742400787770748, -0.01548489835113287, 0.0026686047203838825, -0.06652633100748062, 0.04008733481168747, -0.05220676213502884, -0.03742106258869171, 0.006101665552705526, 0.022038711234927177, 0.022001421079039574, 0.004430582746863365, 0.007500060833990574, -0.017172295600175858, -0.04079585522413254, -0.0818154588341713, 0.0005261462647467852, -0.010133705101907253, -0.015158606693148613, 0.0404229499399662, 0.0007685348391532898, 0.010637127794325352, -0.039938174188137054, -0.06018693745136261, 0.006637717131525278, -0.023343881592154503, 0.13708004355430603, 0.01596967503428459, 0.008660729043185711, -0.004833786748349667, 0.005821986123919487, -0.009714187122881413, -0.02218787372112274, 0.01057186909019947, -0.10448810458183289, -0.009439169429242611, -0.04609111323952675, 0.036246407777071, 0.0497455857694149, 0.016911262646317482, -0.06443805992603302, -0.03044772893190384, 0.05959029123187065, -0.00246117589995265, -0.005085498094558716, -0.013480531983077526, 0.050827011466026306, -0.03509040176868439, 0.00916881300508976, 0.05448148772120476, -0.02837810479104519, 0.049260810017585754, 0.03919236361980438, 0.07801181823015213, 0.01948430947959423, -0.032069869339466095, 0.04154166579246521, 0.03637692704796791, 0.013955986127257347, -0.05358651280403137, 0.009928607381880283, 0.041392505168914795, 0.013676307164132595, 0.007560657802969217, 0.05929196625947952, -0.010077769868075848, 0.02060302533209324, -0.028210297226905823, 0.03287161514163017, 0.013005077838897705, 0.027333969250321388, 0.10612889379262924, 0.01522386446595192, 0.03132405877113342, 0.03395304083824158, 0.03203257918357849, -0.040460240095853806, 0.044189296662807465, -0.027632294222712517, 0.042212896049022675, 0.05873260647058487, -0.009984543547034264, 0.009285345673561096, 0.016529034823179245, -0.03410220146179199, -0.08099506050348282, 0.04612840339541435, 0.010189641267061234, -0.0056868079118430614, 0.039117783308029175, -0.0009701368398964405, -0.035910796374082565, 0.013098304159939289, 0.018067268654704094, 0.016724810004234314, -0.002204803517088294, -0.06041068211197853, -0.05709182471036911, 0.046240273863077164, -0.01750791072845459, 0.01285591535270214, 0.039304234087467194, -0.008488260209560394, 0.0403856597840786, -0.026644093915820122, 0.02259807102382183, -0.06022423133254051, 0.011755844578146935, -0.024089692160487175, 0.039826299995183945, -0.0027688229456543922, 0.03406491130590439, -0.02321336418390274, -0.051945727318525314, 0.04720982909202576, 0.0549289733171463, -0.04206373542547226, -0.03193935006856918, -0.05254237726330757, 0.014422117732465267, 0.01533573679625988, -0.011252421885728836, 0.042734965682029724, 0.018803756684064865, -0.002535757143050432, 0.005705453455448151, -0.05056598037481308, -0.05086430162191391, 0.03553788736462593, -0.05750202015042305, 0.01792742870748043, 0.026438996195793152, -0.028340814635157585, -0.013135594315826893, 0.03874487429857254, -0.034158140420913696, -0.035164982080459595, 0.020043667405843735, -0.012744043953716755, 0.055488329380750656, -0.014151761308312416, -0.033319100737571716, -0.05709182471036911, 0.01687397062778473, -0.01855204626917839, -0.003878216724842787, 0.010441352613270283, -0.035780277103185654, -0.062014177441596985, 0.020286057144403458, -0.017116360366344452, 0.011634649708867073, -0.05925467610359192, 0.03274109959602356, -0.009052279405295849, -0.019913149997591972, 0.009667573496699333, 0.008721326477825642, -0.06234979256987572, -0.01624935492873192, -0.05843428522348404, 0.01403056737035513, 0.045941952615976334, 0.0019682415295392275, 0.042734965682029724, 0.01212874986231327, 0.03193935006856918, 0.006563135888427496, 0.004693947266787291, 0.00688942801207304, 0.04463678225874901, -0.02714751660823822, 0.036432862281799316, -0.015130638144910336, -0.01186771597713232, -0.0012387452879920602, -0.09076518565416336, -0.003598537528887391, -0.02651357650756836, 0.000779605470597744, 0.07118765264749527, -0.0047964961268007755, 0.07111307233572006, 0.03738377243280411, -0.0016967197880148888, 0.06104462221264839, -0.03221902996301651, 0.011886361055076122, 0.008875149302184582, -0.08196461945772171, -0.0023667842615395784, 0.043667227029800415, -0.04210102558135986, 0.09292803704738617, 0.0724555253982544, 0.056196849793195724, -0.002521773101761937, -0.0017771275015547872, 0.00019140537187922746, 0.020770832896232605, 0.004761536605656147, 0.009140844456851482, -0.07890678942203522, -0.012632171623408794, 0.007593287155032158, -0.011783812195062637, 0.013023722916841507, -0.01751723326742649, -0.01595102995634079, -0.0196707621216774, -0.00818527489900589, 0.02912391535937786, 0.024182917550206184, -0.012911851517856121, 0.0038292729295790195, -0.02684919163584709, -0.033617425709962845, -0.0724555253982544, -0.03607860207557678, 0.05157282203435898, 0.01998773217201233, -0.0006613244768232107, 0.0062321824952960014, 0.003945805598050356, 0.06779421120882034, 0.0020987584721297026, -0.03324452042579651, -0.0004136919742450118, -0.00714580062776804, -0.007458108942955732, 0.027632294222712517, 0.0113922618329525, 0.04549446329474449, 0.010851548984646797, 0.01351782213896513, -0.0030857925303280354, 0.002743185730651021, 0.010217608883976936, 0.0008943903958424926, -0.07622187584638596, 0.045941952615976334, 0.0341954305768013, -0.024089692160487175, -0.02353033423423767, 0.01181177981197834, -0.0839783102273941, -0.002799121430143714, -0.010329481214284897, -0.006968670524656773, -0.05172198638319969, -0.030801989138126373, 0.02216922864317894, -0.010711709037423134, -0.014906895346939564, 0.0921822264790535, 0.009555702097713947, -0.0295341107994318, -0.01698584295809269, 0.025860993191599846, -0.00958366971462965, -0.018794434145092964, -0.019185984507203102, -0.029907016083598137, -0.023455752059817314, -0.014170407317578793, -0.042436640709638596, -0.021721743047237396, 0.001213108072988689, -0.008362405002117157, 0.007467431481927633, -0.006959347985684872, -0.007360221352428198, -0.017470620572566986, 0.0022362673189491034, -0.00957434717565775, -0.025115182623267174, -0.012464364990592003, -0.003234954783692956, -0.02766958437860012, -0.008278501220047474, -0.004078653175383806, -0.029347658157348633, -0.009257378056645393, 0.006036406848579645, -0.008679374121129513, 0.018505433574318886, 0.0403856597840786, -0.009243394248187542, 0.06779421120882034, 0.06156668812036514, 0.009206103160977364, -0.06145481765270233, -0.025301635265350342, 0.013079658150672913, 0.021796323359012604, -0.025003310292959213, 0.036843057721853256, -0.030690118670463562, -0.0013040037592872977, -0.1056814044713974, -0.02806113474071026, -0.005337209440767765, 0.016221387311816216, 0.023493044078350067, 0.019838569685816765, -0.0017002157401293516, 0.029664628207683563, 0.0007918414194136858, 0.024742277339100838, -0.029776500537991524, -0.02621525339782238, 0.022225163877010345, -0.008413678966462612, -0.003752361051738262, 0.011690585874021053, 0.05615955963730812, 0.001530077657662332, -0.03432594612240791, 0.0393415242433548, -0.030074823647737503, -0.016491742804646492, -0.008968375623226166, 0.00763990031555295, 0.038819458335638046, -0.021721743047237396, 0.008632761426270008, -0.016100192442536354, 0.026457641273736954, -0.008171290159225464, 0.01429160125553608, 0.01507470291107893, 0.0186452716588974, 0.039416104555130005, 0.04374180734157562, 0.0008739971672184765, -0.0028876864816993475, 0.02382865734398365, 0.017852848395705223, -0.03540737181901932, 0.08293417096138, 0.019633471965789795, -0.007947547361254692, 0.08450037240982056, -0.002752508269622922, -0.00468928599730134, -0.008497582748532295, -0.03826009854674339, 0.059329256415367126, 0.012669462710618973, 0.05395941808819771, -0.0331512950360775, -0.015410318039357662, -0.011951619759202003, 0.015056057833135128, -0.026140671223402023, 0.001759647624567151, -0.03716002777218819, -0.024593114852905273, -0.020453864708542824, 0.016426485031843185, -0.0024471920914947987, -0.08069673925638199, -0.042212896049022675, 0.024835502728819847, -0.007080542389303446, 0.006208875682204962, -0.05407128855586052, -0.07428276538848877, 0.041504375636577606, -0.08092048019170761, -0.03971442952752113, 0.05541374906897545, -0.00839503388851881, -0.06667549163103104, -0.02205735631287098, 0.02921714261174202, -0.01791810616850853, 0.04571820795536041, 0.037253253161907196, -0.0004413685528561473, -0.022970976307988167, -0.015102670527994633, 0.07696768641471863, -0.02039792761206627, -0.06287185847759247, -0.0040343706496059895, -0.0008530212217010558, 0.031864769756793976, -0.046277567744255066, 0.05157282203435898, 0.0025707168970257044, -0.009243394248187542, 0.035593826323747635, 0.01114055048674345, -0.06540761888027191, 0.03660066798329353, 0.00432803388684988, 0.04538259282708168, 0.017470620572566986, -0.017172295600175858, -0.03406491130590439, 0.05004391074180603, -0.04370451718568802, 0.005738082807511091, 0.0019391083624213934, -0.004290743265300989, -0.021274255588650703, 0.0052579669281840324, -0.0006933710537850857, -0.03471749648451805, 0.010292190127074718, -0.007360221352428198, -0.03462427109479904, -0.034661561250686646, 0.013266111724078655, 0.0880056843161583, 0.04847770929336548, 0.004381638951599598, 0.011569391936063766, -0.01238046120852232, 0.025413505733013153, 0.03203257918357849, 0.022299746051430702, -0.02921714261174202, -0.008749294094741344, 0.04903706535696983, 0.039304234087467194, 0.029962953180074692, -0.02351168915629387, -0.009993866086006165, -0.045830078423023224, -0.05261695757508278, 0.031864769756793976, 0.018514756113290787, -0.0028620492666959763, 0.0002887103764805943, 0.007141139358282089, 0.013275434263050556, -0.02103186771273613, -0.007010622415691614, -0.00403903191909194, 0.004654326010495424, 0.00011158030247315764, 0.07219449430704117, -0.021311545744538307, 0.006777556613087654, -0.010972742922604084, -0.010721031576395035, 0.03026127628982067, -0.04720982909202576, -0.040460240095853806, -0.006567797157913446, -0.009816735982894897, 0.021367482841014862, -0.0019682415295392275, -0.027930617332458496, -0.0020020361989736557, -0.038297388702631, 0.04195186123251915, -0.003787321038544178, -0.018365593627095222, -0.036115892231464386, 0.02030470222234726, 0.02237432636320591, -0.017843525856733322, 0.033822525292634964, 0.006828831043094397, 0.024425307288765907, 0.001841220655478537, -0.039117783308029175, 0.0014065527357161045, -0.009686218574643135, -0.017657073214650154, -0.04836583510041237, 0.04027378931641579, -0.006446602754294872, -0.038707584142684937, -0.020584380254149437, 0.012725397944450378, -0.009201441891491413, -0.021814968436956406, 0.009723509661853313, 0.0070246062241494656, -0.013545790687203407, 0.06917396187782288, -0.02246755361557007, -0.010404061526060104, -0.0052486443892121315, -0.0466504730284214, -0.013247465714812279, -0.0233252365142107, -0.03180883452296257, 0.03203257918357849, -0.00028011607355438173, -0.022299746051430702, 0.01690194010734558, -0.0038152888882905245, -0.01455263514071703, -0.04299599677324295, 0.007733126636594534, -0.034344591200351715, 0.035370081663131714, 0.028247587382793427, -0.011765167117118835, -0.015233187936246395, -0.009159490466117859, -0.01801133342087269, 0.02880694530904293, -0.015512866899371147, -0.012725397944450378, -0.0036754494067281485, 0.005024901125580072, 0.0023434776812791824, 0.02205735631287098, 0.002649959409609437, 0.05291528254747391, -0.024723630398511887, 0.0033538183197379112, 0.00019242503913119435, 0.04735899344086647, 0.01823507621884346, -0.009341281838715076, 0.011634649708867073, 0.023269299417734146, 0.008837859146296978, -0.002845734590664506, 0.017974043264985085, 0.03533279150724411, 0.00963960587978363, 0.08017466962337494, -0.0098353810608387, -0.014459408819675446, 0.02425749972462654, 0.03826009854674339, 0.02216922864317894, -0.006031745579093695, 0.02860184758901596, 0.023660849779844284, 0.012967786751687527, 0.027818746864795685, -0.04847770929336548, 0.013965308666229248, 0.025469442829489708, 0.023287944495677948, -0.022150583565235138, -0.010180318728089333, -0.0476200245320797, -0.019008854404091835, -0.010487965308129787, -0.02571183070540428, -0.027837391942739487, -0.006404650863260031, 0.015708642080426216, 0.04445032775402069, -0.015568802133202553, -0.0191673394292593, -0.019353792071342468, -0.01408650353550911, 0.02569318562746048, -0.05254237726330757, 0.05261695757508278, -0.01455263514071703, 0.0005561535363085568, -0.002638306003063917, 0.034661561250686646, 0.029254432767629623, 0.039639849215745926, -0.012501655146479607, 0.0014741418417543173, 0.006535167805850506, 0.015578124672174454, -0.011541423387825489, 0.005197369493544102, 0.0341954305768013, 0.001911140396259725, 0.002512450562790036, -0.005229998845607042, -0.008833197876811028, -0.015373026952147484, -0.01596035249531269, 0.010814257897436619, 0.026438996195793152, -0.04239935055375099, -0.006218198221176863, 0.0014764724764972925, 0.0064559257589280605, 0.03479207679629326, 0.008036112412810326, -0.07402173429727554, -0.07763891667127609, 0.03447511047124863, -0.006055052392184734, -0.03335639089345932, 0.03126812353730202, 0.04806751385331154, 0.00258936220780015, -0.035780277103185654, 0.0233252365142107, 0.009909962303936481, 0.013555113226175308, 0.0016337919514626265, 0.01232452504336834, -0.013955986127257347, -0.007714481558650732, 0.02351168915629387, -0.0684281513094902, 0.023064201697707176, -0.037458352744579315, 0.01844949647784233, 0.04329432174563408, 0.013666984625160694, 0.056196849793195724, -0.03587350249290466, -0.018570691347122192, -0.022560779005289078, 0.02052844502031803, -0.000998104689642787, 0.019558891654014587, -0.0028387426864355803, -0.05731556564569473, 0.04172812029719353, 0.05213218182325363, -0.001652437262237072, 0.013974631205201149, 0.03514633700251579, 0.03855842351913452, 0.005029562395066023, -0.01760113798081875, 0.06783150136470795, -0.005164740607142448, 0.010049802251160145, -0.00020189334463793784, 0.018477464094758034, 0.0424739308655262, 0.03188341483473778, -0.029925663024187088, 0.03397168591618538, 0.01987585984170437, -0.0025171118322759867, -0.0352582111954689, -0.0652211606502533, -0.046240273863077164, -0.02919849567115307, 0.0032536000944674015, -0.032069869339466095, 0.0020591372158378363, -0.01854272373020649, 0.05015578120946884, -0.025115182623267174, -0.028247587382793427, -0.009919284842908382, -0.011466842144727707, -0.04422658681869507, 0.049260810017585754, 0.019857214763760567, -0.01238046120852232, 0.0222624558955431, -0.010282867588102818, -0.06671278178691864, 0.018057946115732193, -0.015512866899371147, 0.006637717131525278, -0.024611759930849075, 0.013070335611701012, 0.036097247153520584, -0.008427662774920464, 0.02910527028143406, 0.03119354136288166, -0.017172295600175858, 0.020491154864430428, -0.028154361993074417, -0.01061848271638155, -0.0039784349501132965, 0.02205735631287098, 0.003880547359585762, 0.006031745579093695, -0.004076322540640831, -0.015121315605938435, 0.045941952615976334, 0.020640317350625992, 0.01855204626917839, 0.04049753025174141, -0.03328181058168411, -0.009704864583909512, 0.00871200393885374, 0.01583915948867798, 0.02505924552679062, 0.03171560913324356, -0.046986088156700134, 0.040982309728860855, -0.0038385954685509205, 0.03749564290046692, 0.042026445269584656, 0.018924951553344727, -0.04064669460058212, 0.0042278156615793705, 0.040982309728860855, -0.05679349973797798, -0.01937243714928627, -0.0305782463401556, 0.014962831512093544, -0.027016999199986458, 0.03462427109479904, 0.010748999193310738, -0.006241505034267902, -0.016100192442536354, 0.026383060961961746, -0.05276612192392349, -0.02798655442893505, 0.012753366492688656, -0.030000243335962296, 0.013611048460006714, -0.018216431140899658, -0.019819924607872963, 0.03201393410563469, -0.025301635265350342, -0.029254432767629623, 0.05295257270336151, -0.01575525477528572, -0.041578955948352814, -0.03363607078790665, -0.026028800755739212, -0.038819458335638046, 0.030895216390490532, 0.021069157868623734, -0.05272883176803589, 0.012100781314074993, -0.009042956866323948, -0.03408355638384819, -0.00198339088819921, 0.026476286351680756, 0.03453104570508003, -0.025954218581318855, -0.021218320354819298, -0.002016020007431507, -0.0000587763061048463, -0.03926694393157959, 0.005738082807511091, 0.0008868157747201622, -0.03156644478440285, -0.005835970398038626, -0.005854615475982428, -0.03975171968340874, 0.006950025446712971, 0.01989450491964817, 0.05336276814341545, -0.013200853019952774, 0.012781334109604359, 0.031063023954629898, -0.01605357974767685, 0.03576163202524185, -0.011420229449868202, 0.030596891418099403, 0.02796790935099125, -0.016818035393953323, -0.015531511977314949, 0.030951151624321938, 0.015923062339425087, -0.0002490891783963889, -0.018990209326148033, -0.0518338568508625, -0.013760210946202278, 0.01336866058409214, -0.030503666028380394, 0.018924951553344727, 0.03199528902769089, 0.033822525292634964, 0.002140710363164544, 0.009131521917879581, 0.0238473042845726, -0.026662738993763924, -0.03261058032512665, 0.061790432780981064, -0.00466131791472435, -0.01083290297538042, 0.0020358306355774403, -0.03492259606719017, 0.039304234087467194, 0.01434753742069006, 0.032069869339466095, 0.0033841170370578766, 0.036824412643909454, 0.03244277462363243, -0.0009713021572679281, -0.04288412630558014, 0.012632171623408794, -0.06846544146537781, 0.003999411128461361, -0.0037546916864812374, 0.01781555823981762, 0.04810480400919914, -0.004691616632044315, -0.036936283111572266, -0.00833909772336483, -0.007075880654156208, 0.0016664211871102452, -0.016398517414927483, -0.018887661397457123, -0.01926056668162346, 0.024294789880514145, -0.02466769516468048, 0.03281567990779877, -0.03926694393157959, -0.012520300224423409, -0.01594170741736889, 0.011653294786810875, -0.040348369628190994, -0.01449669897556305, -0.017116360366344452, -0.03026127628982067, 0.0017118690302595496, 0.02787468209862709, 0.0005238156300038099, -0.006260150112211704, -0.002010193420574069, -0.057464729994535446, -0.010329481214284897, -0.0032559307292103767, -0.0014671498211100698, -0.033393681049346924, -0.010515933856368065, 0.014645861461758614, 0.014916217885911465, 0.03647015243768692, -0.012977109290659428, -0.0066983141005039215, 0.002836412051692605, 0.012883882969617844, -0.035481952130794525, -0.006497877649962902, -0.028862882405519485, 0.0012166040251031518, 0.035892147570848465, 0.016846003010869026, -0.0014671498211100698, 0.019633471965789795, -0.004446897655725479, 0.04172812029719353, 0.048962485045194626, -0.031771544367074966, 0.044711362570524216, -0.0023434776812791824, 0.020360637456178665, -0.04579278826713562, 0.022150583565235138, -0.004230146296322346, -0.0033841170370578766, -0.03896861895918846, 0.01061848271638155, 0.004558769054710865, 0.015503544360399246, 0.033300455659627914, -0.011065969243645668, -0.011569391936063766, 0.02216922864317894, -0.004162556957453489, -0.023045556619763374, -0.007201736327260733, 0.04743357375264168, -0.01565270684659481, 0.011382938362658024, 0.025096537545323372, -0.012958464212715626, 0.021740388125181198, -0.005989793688058853, -0.03867029398679733, -0.03758886829018593, -0.0033491570502519608, -0.00834375899285078, -0.007015283685177565, -0.014226342551410198, -0.0057707116939127445, 0.004575083497911692, -0.017647750675678253, 0.0003562995116226375, -0.011671940796077251, 0.038819458335638046, 0.012809301726520061, 0.05067785084247589, -0.032069869339466095, -0.0009077917202375829, -0.026476286351680756, -0.013443241827189922, -0.0037453691475093365, -0.00541645148769021, -0.020472509786486626, 0.038595713675022125, 0.004682294093072414, -0.025432150810956955, 0.04228747636079788, 0.0049223517999053, 0.01927921175956726, 0.002542749047279358, -0.020453864708542824, -0.03544466197490692, -0.010170996189117432, -0.03322587534785271, 0.004136919975280762, 0.006264811381697655, -0.018365593627095222, -0.002402909565716982, -0.008432324044406414, 0.00006019655484124087, 0.03717867285013199, 0.020677607506513596, -0.056644339114427567, 0.0289933979511261, -0.007653884124010801, 0.019046146422624588, 0.004540123976767063, -0.02425749972462654, -0.009565024636685848, -0.005085498094558716, -0.022038711234927177, -0.040460240095853806, -0.002897009253501892, 0.000762125535402447, -0.04400284215807915, 0.018216431140899658, 0.03346826508641243, 0.041280634701251984, 0.02093864046037197, -0.0039877574890851974, 0.04198915511369705, -0.027483131736516953, -0.00963028334081173, -0.013135594315826893, -0.018524078652262688, -0.037141382694244385, 0.00026511246687732637, 0.036209117621183395, -0.012166040018200874, -0.009457814507186413, -0.03874487429857254, -0.00494565861299634, -0.01238046120852232, 0.008297146297991276, 0.031137604266405106, -0.020752187818288803, -0.016547679901123047, -0.010870194062590599 ]
Software vulnerabilities existing in a program or function of computer systems are a serious and crucial concern. Typically, in a program or function consisting of hundreds or thousands of source code statements, there are only few statements causing the corresponding vulnerabilities. Vulnerability labeling is currently done on a function or program level by experts with the assistance of machine learning tools. Extending this approach to the code statement level is much more costly and time-consuming and remains an open problem. In this paper we propose a novel end-to-end deep learning-based approach to identify the vulnerability-relevant code statements of a specific function. Inspired by the specific structures observed in real world vulnerable code, we first leverage mutual information for learning a set of latent variables representing the relevance of the source code statements to the corresponding function's vulnerability. We then propose novel clustered spatial contrastive learning in order to further improve the representation learning and the robust selection process of vulnerability-relevant code statements. Experimental results on real-world datasets of 200k+ C/C++ functions show the superiority of our method over other state-of-the-art baselines. In general, our method obtains a higher performance in VCP, VCA, and Top-10 ACC measures of between 3\% to 14\% over the baselines when running on real-world datasets in an unsupervised setting. Our released source code samples are publicly available at \href{https://github.com/vannguyennd/livuitcl}{https://github.com/vannguyennd/livuitcl.}
[ -0.007171095814555883, 0.051843807101249695, -0.007648853585124016, -0.01600724831223488, 0.05634702742099762, 0.02198631502687931, -0.02327294833958149, 0.0282681193202734, -0.022421499714255333, 0.03235507383942604, 0.04408615455031395, -0.03825845941901207, 0.006622383836656809, -0.03473913297057152, -0.029195252805948257, 0.03301731497049332, 0.046129632741212845, -0.011645935475826263, 0.007365036755800247, -0.06754831224679947, 0.03275241702795029, -0.007866445928812027, -0.03916667029261589, 0.062477461993694305, 0.006220310460776091, -0.005515499971807003, 0.03627174347639084, -0.00017354193551000208, -0.016764091327786446, 0.043404996395111084, 0.06849437206983566, 0.025675928220152855, -0.019677940756082535, -0.005047202575951815, -0.013244767673313618, -0.030027780681848526, -0.011475645005702972, 0.06486152112483978, -0.034852661192417145, 0.04389694333076477, 0.01799396239221096, -0.07825765758752823, -0.004664050415158272, 0.0321091003715992, 0.02743558958172798, -0.006877818610519171, -0.032317232340574265, -0.04734058305621147, -0.020113125443458557, -0.013821861706674099, 0.004943136591464281, -0.017606081441044807, -0.003535880008712411, -0.024767715483903885, -0.038580115884542465, 0.0372745618224144, 0.0609259307384491, -0.02289452776312828, 0.06947826594114304, -0.0053026373498141766, -0.06315862387418747, 0.05801208317279816, 0.007672504987567663, -0.00027952963137067854, 0.020434783771634102, 0.024956926703453064, 0.04987601190805435, 0.02016988955438137, 0.011655395850539207, 0.047681163996458054, -0.08635588735342026, -0.006754831410944462, 0.019469808787107468, 0.017747988924384117, 0.01857105642557144, 0.03371739387512207, 0.005610105115920305, 0.03992351517081261, -0.003746377071365714, 0.023973029106855392, 0.03606361150741577, 0.04741626977920532, -0.03708535060286522, 0.016073470935225487, 0.05971498042345047, -0.008164453320205212, -0.024938005954027176, -0.07916586846113205, 0.028665462508797646, -0.00041419462650083005, -0.030141307041049004, 0.020302336663007736, 0.00032609328627586365, 0.019337361678481102, -0.0004458283365238458, 0.0052884467877447605, -0.000001912434981932165, -0.06323430687189102, -0.08635588735342026, 0.02463526837527752, -0.011229670606553555, 0.05051932856440544, -0.018930558115243912, 0.01104046031832695, 0.05101127550005913, -0.062023356556892395, -0.005633756518363953, 0.026659825816750526, 0.0012629831908270717, 0.14788728952407837, -0.03909098729491234, -0.021607892587780952, 0.0057520135305821896, -0.0013055556919425726, 0.02934662066400051, -0.011494566686451435, -0.008500303141772747, -0.07530596852302551, -0.00474919518455863, -0.04953543096780777, 0.037312403321266174, 0.02107810229063034, 0.034587763249874115, -0.013519124127924442, -0.0429130494594574, 0.09233495593070984, -0.01591264270246029, 0.001169560244306922, -0.04382126033306122, 0.0485515333712101, -0.03928019851446152, -0.012705517001450062, -0.006433173082768917, 0.0073697674088180065, 0.014966587536036968, 0.014389494433999062, 0.056044287979602814, -0.010889091528952122, -0.008765198290348053, -0.0033513992093503475, -0.002700986573472619, -0.004011272452771664, -0.06395331025123596, 0.0191859919577837, 0.03135225921869278, -0.010274155996739864, 0.02289452776312828, 0.04499436914920807, -0.03996135666966438, -0.01825885847210884, -0.025884060189127922, 0.032960548996925354, 0.04264815151691437, 0.048929955810308456, 0.10996941477060318, -0.012733898125588894, 0.01852375455200672, 0.060471825301647186, -0.02045370638370514, -0.06508857011795044, 0.048929955810308456, -0.045864738523960114, 0.0020316527225077152, 0.010397142730653286, -0.006229771301150322, -0.0038977458607405424, 0.05581723526120186, 0.0026347627863287926, -0.09695170074701309, 0.04559984430670738, 0.04700000584125519, -0.015212561935186386, 0.03364171087741852, 0.03854227438569069, 0.00672171963378787, -0.005785125307738781, 0.03070894069969654, -0.017861515283584595, -0.0020103666465729475, 0.017880436033010483, -0.04245894029736519, 0.006551429629325867, 0.0009697062196210027, -0.02437037229537964, 0.033584948629140854, 0.01699114590883255, 0.046205319464206696, -0.03772866725921631, 0.00022941830684430897, -0.038031402975320816, -0.02136191911995411, -0.007360306568443775, 0.08423672616481781, -0.01844806969165802, -0.004441727418452501, -0.06773752719163895, -0.03714211285114288, 0.03536352887749672, 0.028287040069699287, 0.03197665512561798, -0.01209058053791523, -0.02034018002450466, 0.008637480437755585, 0.027057169005274773, 0.0031290764454752207, 0.008084038272500038, 0.010662037879228592, -0.006759562063962221, 0.012043277733027935, -0.04896779730916023, -0.07133253663778305, 0.029876412823796272, -0.0543413907289505, 0.022591790184378624, -0.011759461835026741, -0.020018519833683968, -0.000601631763856858, 0.007904288358986378, -0.059298716485500336, -0.0474541112780571, 0.01827777922153473, 0.023064816370606422, 0.0576336607336998, -0.045297104865312576, -0.04427536576986313, -0.05986635014414787, 0.04472947120666504, -0.01827777922153473, -0.020661838352680206, 0.023064816370606422, -0.022648552432656288, -0.03746377304196358, 0.008897645398974419, -0.024048713967204094, 0.008571256883442402, -0.06792673468589783, 0.03627174347639084, -0.0322604700922966, -0.018334543332457542, -0.016111314296722412, 0.03992351517081261, -0.014786837622523308, -0.012743358500301838, 0.008708435110747814, 0.021740339696407318, 0.05226007103919983, -0.04351852461695671, 0.04514573886990547, 0.014862521551549435, 0.010832328349351883, -0.01813587173819542, -0.029100647196173668, 0.03269565477967262, 0.019886072725057602, -0.05691466107964516, -0.00606421148404479, 0.007549517787992954, -0.06278020143508911, -0.004243055824190378, -0.05740660801529884, -0.0033277478069067, -0.02389734610915184, -0.005766204092651606, 0.05282770097255707, -0.009507850743830204, 0.029781807214021683, 0.04245894029736519, 0.009034823626279831, 0.043480679392814636, -0.02807890810072422, 0.030860308557748795, -0.017265500500798225, -0.08696135878562927, -0.04045330360531807, 0.037482693791389465, 0.00912942923605442, 0.013821861706674099, 0.04908132553100586, -0.023235106840729713, -0.008613829500973225, 0.008405697531998158, -0.016593802720308304, -0.004295088816434145, 0.014048914425075054, 0.02643277309834957, -0.027776170521974564, 0.0054161641746759415, -0.008013084530830383, -0.029743963852524757, -0.02463526837527752, -0.021324075758457184, 0.029971016570925713, -0.06069887802004814, -0.03328220918774605, 0.021967394277453423, 0.03619605675339699, -0.0317874439060688, -0.02361352927982807, -0.04726490005850792, -0.010397142730653286, -0.0498003251850605, -0.029592595994472504, 0.0010891456622630358, 0.012923109345138073, -0.019034624099731445, -0.015345009975135326, 0.009465279057621956, 0.04033977910876274, 0.015193641185760498, -0.039128828793764114, 0.004928945563733578, -0.01722765900194645, -0.026849037036299706, -0.0023840581998229027, 0.01696276292204857, 0.025392111390829086, 0.0034625607077032328, 0.017246579751372337, -0.0075022149831056595, 0.0266219824552536, 0.0022338719572871923, 0.02718961611390114, -0.03954509273171425, 0.04578905552625656, 0.038655802607536316, -0.015855878591537476, -0.009176732040941715, -0.014938206411898136, -0.0396207757294178, -0.026697667315602303, 0.0061446260660886765, 0.003375050611793995, -0.05082206800580025, -0.043215785175561905, 0.024408215656876564, 0.012279791757464409, -0.034322869032621384, 0.09142673760652542, 0.0129987932741642, -0.07205154001712799, -0.01732226461172104, -0.02317834459245205, -0.03920451179146767, -0.021570051088929176, 0.023216186091303825, -0.03700966387987137, -0.008703704923391342, -0.02734098583459854, 0.010993157513439655, -0.024237925186753273, 0.0010288346093147993, 0.0006835246458649635, 0.014190822839736938, -0.009697061963379383, 0.0374259278178215, -0.004638033919036388, -0.01890217512845993, -0.014919284731149673, -0.012771740555763245, 0.030198071151971817, -0.0009212209261022508, -0.0346066877245903, -0.02845733053982258, 0.019318439066410065, -0.005610105115920305, -0.04261031001806259, 0.024067634716629982, -0.023197265341877937, 0.040226250886917114, 0.050481487065553665, -0.031938809901475906, 0.06751047074794769, 0.02281884290277958, 0.0018045996548607945, -0.04423752427101135, 0.0032922709360718727, -0.036574479192495346, 0.011768922209739685, -0.032941628247499466, 0.0418156236410141, -0.03261997178196907, 0.0372745618224144, 0.0012558877933770418, -0.030954914167523384, -0.01212842296808958, 0.02626248262822628, -0.012024356983602047, -0.02071860060095787, 0.009176732040941715, 0.005576993338763714, -0.02563808672130108, -0.0018968399381265044, -0.015666667371988297, -0.034852661192417145, 0.047113530337810516, -0.0007521135848946869, -0.03668800741434097, -0.029952095821499825, 0.041588570922613144, -0.0541900210082531, -0.006087862886488438, 0.04389694333076477, -0.0038930156733840704, 0.007213667966425419, -0.018675122410058975, 0.007965781725943089, 0.022516105324029922, -0.021021338179707527, 0.0037582027725875378, -0.05328181013464928, 0.03388768434524536, -0.04351852461695671, -0.013566426001489162, 0.0034318140242248774, 0.024767715483903885, 0.01952657289803028, -0.0016555959591642022, -0.030784623697400093, -0.015146338380873203, 0.0056905196979641914, 0.03719887509942055, 0.0040680356323719025, 0.06777536869049072, 0.06243962049484253, 0.006404791492968798, 0.050935592502355576, -0.004557619336992502, 0.015099035575985909, 0.028589777648448944, -0.016924921423196793, 0.06489936262369156, 0.0038220614660531282, 0.03154146671295166, 0.0005629026563838124, 0.011428342200815678, -0.05664976313710213, -0.004938406404107809, -0.030103465542197227, -0.01553422026336193, -0.02361352927982807, 0.002627667272463441, -0.004205213859677315, -0.02618679776787758, 0.024786636233329773, -0.06300725042819977, -0.03545813634991646, 0.004053845070302486, 0.01381240040063858, 0.030917072668671608, -0.03700966387987137, -0.06153140589594841, 0.05517391860485077, -0.0972544401884079, -0.04397263005375862, 0.04488084092736244, -0.005326288752257824, -0.0452592633664608, -0.057936400175094604, 0.021588971838355064, -0.031314413994550705, -0.0005809367867186666, 0.04480515792965889, -0.040301937609910965, -0.037123192101716995, -0.014427335932850838, 0.045751214027404785, -0.0002934248186647892, -0.02917633205652237, 0.00306521775200963, -0.024881241843104362, 0.0021250757854431868, -0.026659825816750526, 0.017653383314609528, -0.0036777881905436516, 0.006584541872143745, -0.009441627189517021, 0.014484100043773651, -0.067018523812294, -0.013377215713262558, -0.010662037879228592, 0.06834299862384796, -0.01350020244717598, -0.017104672268033028, -0.030122386291623116, 0.03700966387987137, -0.019923914223909378, 0.0025117755867540836, -0.031049519777297974, 0.036952901631593704, -0.045675527304410934, 0.017558777704834938, 0.004777576774358749, -0.03089815191924572, 0.004775211680680513, -0.014238125644624233, -0.0016768822679296136, -0.04064251482486725, -0.030860308557748795, 0.09210789948701859, 0.029157409444451332, 0.01682085543870926, 0.0144462576135993, -0.016745170578360558, 0.049762483686208725, -0.02191063016653061, -0.018296699970960617, -0.02980072796344757, -0.017625002190470695, 0.024029793217778206, 0.028741145506501198, 0.0070386482402682304, -0.006821055430918932, -0.0020162793807685375, -0.05801208317279816, -0.013386676087975502, 0.007289352361112833, 0.06266666948795319, -0.009039553813636303, 0.0014427336864173412, 0.02671658806502819, 0.02953583188354969, 0.0011843424290418625, -0.014105677604675293, 0.011579710990190506, -0.006390600465238094, 0.01127697341144085, 0.056384868919849396, -0.02781401202082634, -0.02353784441947937, 0.0016922556096687913, -0.007142714224755764, 0.027965381741523743, -0.04647021368145943, -0.02635708823800087, 0.02179710380733013, 0.024408215656876564, 0.03424718603491783, 0.031844206154346466, -0.039582934230566025, 0.0081833740696311, -0.05297907069325447, 0.012639292515814304, -0.006802134215831757, 0.004472474101930857, -0.010709340684115887, 0.0198103878647089, -0.02635708823800087, 0.006243961863219738, -0.01885487325489521, -0.010737722739577293, 0.0055013089440763, 0.007994163781404495, -0.037596218287944794, 0.0020162793807685375, -0.06043398380279541, -0.009266607463359833, -0.031200889497995377, 0.026943642646074295, -0.01999959908425808, -0.035590581595897675, -0.04060467332601547, -0.01235547661781311, 0.016120774671435356, -0.011825685389339924, 0.02253502607345581, -0.005534420721232891, -0.03780435025691986, 0.0496489591896534, -0.03436071053147316, 0.007871176116168499, -0.030879229307174683, -0.03044404461979866, 0.018533214926719666, -0.01899678073823452, 0.019063005223870277, 0.017520936205983162, 0.013755637221038342, -0.0014628373319283128, -0.01017009001225233, 0.005208031740039587, -0.05169243738055229, -0.03390660509467125, 0.023481080308556557, 0.004351852461695671, 0.028116749599575996, 0.005226952955126762, -0.020378021523356438, -0.018817031756043434, -0.006948772817850113, -0.016546498984098434, 0.014181362465023994, 0.010255234315991402, 0.0110026178881526, 0.005638486705720425, -0.009101047180593014, 0.008372585289180279, 0.013575887307524681, -0.01813587173819542, 0.010964775457978249, -0.026943642646074295, -0.02052938938140869, 0.018656201660633087, 0.032317232340574265, 0.02281884290277958, 0.037652984261512756, 0.020226651802659035, 0.029743963852524757, -0.034587763249874115, 0.0006314915954135358, 0.042383257299661636, 0.008963869884610176, -0.003952144179493189, 0.04628100246191025, -0.010576893575489521, -0.0013067382387816906, -0.04998953640460968, 0.006669686641544104, 0.017606081441044807, -0.009309180080890656, 0.032222628593444824, 0.030954914167523384, -0.018334543332457542, 0.0160545501857996, -0.006385870277881622, -0.008505033329129219, 0.010179550386965275, -0.01646135374903679, -0.0288168303668499, -0.0028074176516383886, -0.04465378820896149, -0.020491547882556915, -0.03027375414967537, -0.006641305051743984, -0.022951290011405945, -0.03753945603966713, 0.005756743717938662, 0.02908172644674778, 0.024578504264354706, -0.009663950651884079, -0.02081320621073246, -0.0328848659992218, 0.0350797139108181, -0.007459642365574837, 0.06425604224205017, -0.023954108357429504, -0.00918619241565466, -0.0005543290171772242, 0.035306766629219055, 0.018958939239382744, 0.03191988915205002, 0.029479069635272026, 0.02454066276550293, 0.012620371766388416, 0.035212162882089615, -0.008850343525409698, -0.007322464603930712, 0.029024962335824966, 0.025032611563801765, 0.02007528394460678, -0.008921297267079353, 0.018221016973257065, -0.021853866055607796, -0.027132852002978325, 0.009943036362528801, -0.01262983214110136, -0.028041064739227295, 0.012875806540250778, 0.015278785489499569, -0.0027624801732599735, 0.0396207757294178, -0.03260105103254318, -0.09475685656070709, -0.029592595994472504, 0.05256280675530434, 0.009588265791535378, -0.022743158042430878, 0.030481887981295586, 0.03390660509467125, -0.014143520034849644, 0.01844806969165802, 0.002615841571241617, -0.004886373411864042, 0.018391305580735207, -0.0038788248784840107, -0.01567612960934639, -0.024975847452878952, -0.006617653649300337, 0.034493159502744675, -0.036574479192495346, 0.0024266305845230818, -0.04756763577461243, -0.04200483486056328, 0.05619565770030022, -0.0040585752576589584, 0.06629952043294907, -0.015467996709048748, -0.02018881030380726, -0.012336554937064648, 0.017511475831270218, -0.005146538373082876, -0.01658434234559536, 0.0018956573912873864, -0.03479589894413948, 0.024313610047101974, 0.037028588354587555, 0.027605880051851273, -0.00044730654917657375, 0.00790901854634285, -0.00547292735427618, 0.011021538637578487, -0.017312804237008095, 0.06849437206983566, 0.020794285461306572, -0.006452093832194805, -0.0032993662171065807, 0.0039426833391189575, 0.0378989577293396, 0.03462560847401619, -0.005236413329839706, 0.035495977848768234, 0.019488729536533356, -0.006220310460776091, -0.027605880051851273, -0.05487117916345596, -0.04771900549530983, -0.0692133754491806, -0.008154992945492268, 0.03275241702795029, 0.0077718403190374374, 0.002745924284681678, 0.04363204911351204, -0.007218398619443178, -0.02970612235367298, -0.006882548797875643, -0.011248592287302017, 0.007204207591712475, 0.049838170409202576, 0.0030699479393661022, -0.020926732569932938, 0.011844607070088387, 0.04136151820421219, -0.010378221981227398, 0.032146941870450974, -0.0028452598489820957, -0.004919485189020634, -0.02217552624642849, 0.0058939214795827866, 0.03169283643364906, 0.012894727289676666, 0.054114338010549545, 0.058314818888902664, -0.01359480805695057, 0.038939617574214935, -0.05237359553575516, -0.006319646257907152, 0.0116270137950778, 0.06743478775024414, 0.008481381461024284, 0.014342191629111767, -0.0378989577293396, -0.009119968861341476, 0.03509863466024399, 0.006844706833362579, 0.003334843320772052, 0.03587440028786659, -0.05316828191280365, 0.026054350659251213, 0.005359400529414415, 0.027643723413348198, -0.007010266184806824, 0.026243561878800392, -0.0005274255527183414, 0.07803060114383698, -0.020756443962454796, 0.012364936992526054, 0.012601450085639954, 0.0541900210082531, 0.0049762483686208725, 0.015505839139223099, 0.02817351371049881, -0.05017874762415886, -0.022762078791856766, -0.024029793217778206, 0.024143319576978683, -0.004768116399645805, 0.04514573886990547, 0.03769082576036453, -0.014398954808712006, -0.03426610678434372, 0.022648552432656288, -0.033490341156721115, -0.019848231226205826, 0.026035429909825325, -0.017047908157110214, 0.026111112907528877, -0.028324881568551064, -0.03551489859819412, 0.019734704867005348, -0.015600444748997688, -0.021778183057904243, 0.08733978122472763, -0.017047908157110214, -0.03316868469119072, -0.03886393457651138, 0.02535426989197731, -0.03687721863389015, -0.007294083014130592, -0.0018211555434390903, -0.02399195171892643, -0.007535326760262251, -0.022610710933804512, -0.05101127550005913, -0.0026418580673635006, 0.059942033141851425, -0.02743558958172798, -0.01281904336065054, 0.0033655900042504072, 0.0282681193202734, 0.009801127947866917, -0.03025483340024948, 0.009621378034353256, -0.011078301817178726, -0.034682370722293854, -0.017918279394507408, -0.021040258929133415, -0.02281884290277958, -0.0046593202278018, 0.023329712450504303, 0.027643723413348198, 0.03593116253614426, 0.028059987351298332, 0.03859903663396835, -0.016480274498462677, 0.029289858415722847, -0.027738327160477638, 0.030576491728425026, 0.002296548103913665, -0.03082246705889702, 0.000016491287169628777, 0.016120774671435356, -0.008050926961004734, 0.00022128813725430518, -0.006584541872143745, -0.035571660846471786, -0.015486917458474636, 0.007270431611686945, -0.03581763803958893, 0.03472021222114563, 0.030917072668671608, -0.023102659732103348, 0.008055657148361206, -0.00955988373607397, 0.031219810247421265, -0.02633816748857498, 0.0019394124392420053, 0.027151774615049362, -0.01877918839454651, -0.020226651802659035, -0.0029398654587566853, -0.04234541580080986, 0.014512481167912483, -0.032203707844018936, 0.025865139439702034, 0.015392311848700047, 0.05369807407259941, 0.03307407721877098, -0.028211355209350586, -0.01952657289803028, 0.005851349327713251, -0.04771900549530983, -0.028116749599575996, -0.03171175718307495, 0.0024006140884011984, 0.0646723061800003, -0.0035571663174778223, -0.02518397942185402, -0.00013229985779616982, -0.002533061895519495, 0.006206119898706675, -0.01780475303530693, -0.014077296480536461, -0.02946014702320099, 0.041853465139865875, -0.00018965442723128945, 0.011428342200815678, -0.037842195481061935, 0.009715983644127846, -0.05570371076464653, -0.003734551602974534, -0.03818277269601822, 0.001912213396281004, 0.027303142473101616, -0.04590258002281189, 0.04435105249285698, 0.04079388454556465, -0.0016283969162032008, -0.03299839422106743, 0.012828503735363483, -0.024313610047101974, -0.01553422026336193, -0.013802940025925636, -0.02743558958172798, -0.01646135374903679, -0.011333736591041088, 0.00531682837754488, 0.02291344851255417, 0.023405397310853004, -0.0012582528870552778, 0.0025046803057193756, 0.009990339167416096, 0.008751007728278637, -0.027416668832302094, -0.06198551505804062, -0.05895813927054405, 0.006641305051743984, 0.055665865540504456, 0.002455012407153845, 0.003323017619550228, -0.015638286247849464, 0.019677940756082535, 0.005576993338763714, 0.05782287195324898, -0.05426570400595665, 0.02734098583459854, 0.011901370249688625, -0.0012771739857271314, -0.024464977905154228, -0.004183927550911903, 0.0025992856826633215, 0.021664656698703766, -0.06300725042819977, 0.004919485189020634, 0.04454026371240616, 0.027322063222527504, 0.05733092501759529, -0.0048438007943332195, -0.02136191911995411, -0.006664956454187632, -0.008244868367910385, -0.02191063016653061, -0.03417149931192398, 0.01631944626569748, -0.002133353613317013, -0.0031811094377189875, 0.036404188722372055, -0.00350040290504694, 0.02891143597662449, -0.031749602407217026, -0.009072666056454182, -0.0029989939648658037, -0.052108701318502426, -0.005179650150239468, -0.037312403321266174, -0.003611564403399825, -0.014200283214449883, 0.002954056253656745, -0.024956926703453064, -0.025032611563801765, -0.024673109874129295, 0.03869364410638809, 0.029024962335824966, 0.0007550700102001429, -0.009801127947866917, -0.020321257412433624, -0.011532408185303211, 0.024294689297676086, -0.03806924819946289, -0.019961757585406303, 0.02891143597662449, 0.04469162970781326, 0.01332045253366232, -0.03886393457651138, 0.016745170578360558, 0.030595414340496063, 0.011343197897076607, -0.0030084543395787477, -0.013292070478200912, -0.04026409238576889, 0.02597866579890251, 0.00030924167367629707, 0.02698148414492607, 0.01772906817495823, 0.007776570972055197, 0.013982690870761871, -0.017747988924384117, -0.02870330400764942, 0.040566831827163696, 0.0346066877245903, -0.0612286701798439, 0.007521136198192835, 0.018694043159484863, 0.03954509273171425, 0.013282610103487968, -0.021248390898108482, 0.007346116006374359, 0.012204107828438282, -0.012204107828438282, -0.05373591557145119, 0.007100141607224941, -0.024673109874129295, -0.055930763483047485, 0.036669086664915085, 0.017672304064035416, 0.050746381282806396, 0.00725151039659977, 0.022024156525731087, 0.0166789460927248, 0.026962563395500183, -0.00474919518455863, 0.0158180370926857, -0.04404831305146217, -0.05729307979345322, 0.020302336663007736, 0.05078422278165817, 0.0035453406162559986, -0.034209344536066055, -0.05180596187710762, 0.01353804487735033, 0.018968399614095688, -0.01713305339217186, 0.01787097565829754, -0.02664090506732464, -0.03034943901002407, -0.04208051785826683 ]
Despite decades of research, existing navigation systems still face real-world challenges when deployed in the wild, e.g., in cluttered home environments or in human-occupied public spaces. To address this, we present a new class of implicit control policies combining the benefits of imitation learning with the robust handling of system constraints from Model Predictive Control (MPC). Our approach, called Performer-MPC, uses a learned cost function parameterized by vision context embeddings provided by Performers -- a low-rank implicit-attention Transformer. We jointly train the cost function and construct the controller relying on it, effectively solving end-to-end the corresponding bi-level optimization problem. We show that the resulting policy improves standard MPC performance by leveraging a few expert demonstrations of the desired navigation behavior in different challenging real-world scenarios. Compared with a standard MPC policy, Performer-MPC achieves >40% better goal reached in cluttered environments and >65% better on social metrics when navigating around humans.
[ 0.021318623796105385, 0.029275039210915565, -0.028285246342420578, -0.06825766712427139, 0.006933311466127634, 0.011001933366060257, -0.07663284242153168, 0.04507366195321083, -0.056532423943281174, -0.0007161725661717355, 0.00041518971556797624, -0.03310097008943558, 0.02851366065442562, -0.03007448837161064, 0.01586524397134781, -0.007704208139330149, 0.03056938387453556, 0.0035523108672350645, -0.08040166646242142, -0.0070951045490801334, -0.012515174224972725, -0.05131697282195091, -0.04922318086028099, 0.012486622668802738, 0.029579591006040573, -0.018682347610592842, -0.0009445863543078303, 0.024440279230475426, -0.042713385075330734, 0.0489947684109211, 0.03230152279138565, 0.03041710890829563, 0.005315380170941353, 0.028209108859300613, -0.02708607353270054, 0.02659117616713047, 0.0583978034555912, -0.016959726810455322, -0.02122345194220543, 0.03279642015695572, 0.0111256567761302, 0.006828621961176395, -0.015751037746667862, -0.047281663864851, -0.007323518395423889, 0.030455177649855614, -0.05470511317253113, 0.020861797034740448, -0.01729283109307289, -0.004339862614870071, 0.027542902156710625, -0.02537297084927559, 0.03745986893773079, -0.029941245913505554, -0.014018898829817772, -0.0009903881000354886, 0.0618240125477314, -0.008808208629488945, 0.032548971474170685, 0.0309120062738657, -0.005377242341637611, -0.017311865463852882, -0.08847229182720184, -0.040505386888980865, -0.015522623434662819, -0.04693904146552086, 0.02571559138596058, -0.036831729114055634, 0.041190627962350845, -0.045340146869421005, -0.04747200757265091, -0.011972691863775253, -0.09075643122196198, -0.029903177171945572, -0.0037474145647138357, -0.029827039688825607, 0.015046761371195316, 0.051545388996601105, 0.04195200651884079, -0.02329821139574051, 0.023241108283400536, 0.012144002132117748, -0.01622689887881279, -0.004225655924528837, 0.11557739973068237, -0.05234483629465103, 0.04046731814742088, -0.08436084538698196, 0.024421244859695435, -0.009003312326967716, -0.04347476735711098, 0.05820745974779129, -0.025772694498300552, 0.027600005269050598, 0.0055437940172851086, -0.020309796556830406, -0.007447242736816406, -0.002356707351282239, -0.036355867981910706, -0.029598625376820564, 0.01234386395663023, -0.015046761371195316, -0.001426396775059402, 0.002457828028127551, 0.05717959627509117, -0.01624593324959278, -0.02280331403017044, 0.004118586890399456, -0.000058776411606231704, 0.085579052567482, -0.00457779411226511, -0.0521925613284111, 0.017920969054102898, 0.07092249393463135, -0.026534073054790497, -0.009812277741730213, -0.06791504472494125, -0.0646030455827713, 0.04952773451805115, -0.0278093833476305, 0.0007518621860072017, 0.020671451464295387, 0.037041109055280685, 0.028399452567100525, -0.010792553424835205, 0.016303038224577904, 0.015180002897977829, -0.01381903700530529, 0.02449738420546055, 0.00847510527819395, -0.004492138512432575, 0.011373105458915234, -0.03603228181600571, 0.0022270348854362965, 0.03730759397149086, -0.0064051044173538685, -0.0018094658153131604, -0.03351972997188568, -0.031140418723225594, 0.008256208151578903, -0.017759175971150398, -0.0032882075756788254, -0.005895932205021381, 0.026343729346990585, -0.02419283241033554, 0.016264967620372772, -0.0157224852591753, 0.041000284254550934, -0.05303007736802101, 0.013295588083565235, -0.07050373405218124, 0.037726350128650665, 0.05771256238222122, 0.03730759397149086, 0.07781297713518143, 0.021014072000980377, -0.034281108528375626, 0.05352497473359108, -0.036146488040685654, -0.03780248761177063, 0.08207670599222183, -0.04926124960184097, -0.026629246771335602, 0.08527449518442154, 0.09654291719198227, -0.006348001305013895, 0.01827310584485531, -0.0009196036262437701, -0.04423614591360092, 0.045987319201231, -0.047091320157051086, -0.03469986841082573, 0.012144002132117748, -0.018748968839645386, 0.004061483312398195, -0.030950075015425682, 0.08177214860916138, 0.0014192588860169053, -0.028209108859300613, 0.005848345812410116, -0.04141904041171074, 0.011420691385865211, 0.006210001185536385, 0.03405269607901573, 0.030017385259270668, 0.08710180968046188, 0.029275039210915565, -0.01450427807867527, 0.028361383825540543, -0.025944003835320473, 0.012810208834707737, 0.03500441834330559, 0.01867283135652542, -0.01149682980030775, -0.010430898517370224, -0.07054180651903152, -0.02571559138596058, 0.03138786926865578, -0.010231036692857742, 0.041685525327920914, -0.039134904742240906, -0.039667870849370956, 0.036184556782245636, -0.0033810005988925695, 0.027352556586265564, 0.06094842404127121, 0.023164968937635422, -0.007623311597853899, -0.03214924782514572, -0.0295224878937006, -0.01726427860558033, -0.021128280088305473, -0.010764001868665218, -0.015046761371195316, -0.030474212020635605, -0.03435724601149559, -0.012810208834707737, -0.0010028794640675187, 0.02466869354248047, -0.021147314459085464, -0.006048208102583885, 0.029750902205705643, 0.0055675869807600975, -0.019833935424685478, -0.07164580374956131, 0.06250925362110138, 0.015751037746667862, 0.013343174941837788, 0.030474212020635605, 0.002288897056132555, -0.05040331929922104, -0.03576580062508583, 0.039667870849370956, 0.020633382722735405, 0.007851725444197655, 0.03801186755299568, 0.010449932888150215, 0.00557710463181138, -0.019405659288167953, 0.019586486741900444, 0.019063038751482964, -0.031483039259910583, 0.005734139122068882, 0.04849987104535103, 0.07118897885084152, 0.05599945783615112, -0.012400968000292778, 0.058283597230911255, 0.008265725336968899, -0.013923726975917816, -0.02674345299601555, -0.002137810690328479, -0.008579794317483902, 0.017340416088700294, -0.023260142654180527, 0.08390401303768158, 0.005524759646505117, -0.040353111922740936, 0.020271727815270424, -0.013447863981127739, 0.022403590381145477, 0.051012422889471054, 0.03346262499690056, 0.08024939149618149, -0.005224966444075108, -0.02712414227426052, -0.022403590381145477, 0.014780278317630291, 0.011734760366380215, 0.01571296900510788, -0.03371007367968559, -0.04157131910324097, -0.019986210390925407, -0.008256208151578903, -0.0022163279354572296, -0.05683697387576103, 0.001966500421985984, 0.009945519268512726, 0.039972420781850815, -0.012705519795417786, 0.029141798615455627, -0.03041710890829563, -0.0136382095515728, -0.027257384732365608, -0.0017416555201634765, -0.00899379514157772, 0.0055675869807600975, 0.010250071063637733, -0.035461246967315674, 0.008132483810186386, -0.026457935571670532, 0.022232279181480408, -0.019110623747110367, 0.00686193211004138, 0.05976828560233116, 0.00916034635156393, -0.03405269607901573, 0.004494518041610718, 0.026724418625235558, -0.008151519112288952, -0.013581105507910252, 0.04286566376686096, 0.019377106800675392, -0.013238484971225262, -0.008651173673570156, 0.020462073385715485, -0.055352285504341125, 0.040848005563020706, -0.014980140142142773, -0.047091320157051086, 0.06007283926010132, 0.008327587507665157, -0.006400345824658871, -0.04252304136753082, -0.019139176234602928, 0.06601160019636154, 0.07575725764036179, 0.0036379662342369556, -0.06342291086912155, -0.01045945007354021, -0.012905381619930267, 0.04488331824541092, -0.054476700723171234, -0.03673655912280083, -0.0015584485372528434, -0.004642035346478224, 0.039287179708480835, -0.0022960349451750517, -0.024554487317800522, -0.0003702802350744605, -0.01863476261496544, -0.03778345510363579, -0.03129269555211067, -0.02348855510354042, 0.009379243478178978, 0.01811131276190281, -0.040809936821460724, 0.010754484683275223, -0.010449932888150215, -0.019072555005550385, -0.010982898063957691, -0.016664693132042885, 0.019024968147277832, 0.0008785604732111096, 0.009479174390435219, -0.049832284450531006, 0.03744083270430565, 0.006305173505097628, 0.007413932122290134, -0.006105311214923859, 0.001139095053076744, -0.029903177171945572, -0.011411174200475216, -0.03312000632286072, 0.07198842614889145, -0.011896553449332714, -0.02385021187365055, 0.02590593509376049, -0.017473658546805382, -0.0291989017277956, 0.002315069315955043, -0.036374904215335846, -0.03216828033328056, 0.059806354343891144, -0.05059366300702095, 0.05417214706540108, -0.011982209049165249, -0.04606345668435097, 0.05512387305498123, 0.03717435151338577, -0.005853104405105114, -0.023431451991200447, -0.0012538967421278358, -0.015246623195707798, 0.004632518161088228, 0.0022710522171109915, 0.02811393514275551, -0.013105243444442749, -0.03458566218614578, 0.04903283715248108, -0.009764691814780235, 0.0070475186221301556, 0.02813297137618065, -0.005239242222160101, -0.007214070297777653, 0.11009547114372253, 0.03675559163093567, -0.02902759052813053, -0.032396696507930756, 0.013790485449135303, 0.04541628435254097, -0.02297462522983551, -0.03607035055756569, 0.011725243180990219, 0.010402346961200237, -0.03458566218614578, 0.05786483734846115, -0.00047675438690930605, -0.00751862209290266, 0.0038283111061900854, 0.019415175542235374, -0.012210622429847717, -0.022746210917830467, -0.006024414673447609, 0.015408416278660297, 0.006343242712318897, -0.010259588249027729, -0.001516810618340969, 0.016112692654132843, 0.006248069927096367, 0.01182041596621275, -0.05131697282195091, -0.004347000736743212, 0.0073663461953401566, -0.014304416254162788, -0.00846082903444767, 0.017673520371317863, 0.01849200390279293, -0.0023578968830406666, -0.06627807766199112, 0.02228938415646553, 0.013600139878690243, 0.03814511001110077, 0.010659311898052692, 0.008303795009851456, 0.06007283926010132, 0.033767178654670715, -0.06962814927101135, -0.017920969054102898, 0.025867866352200508, 0.011487312614917755, 0.00078279321314767, 0.026001108810305595, -0.04800497367978096, 0.015180002897977829, -0.0003241810773033649, -0.02834234945476055, 0.03279642015695572, -0.04008662700653076, -0.03801186755299568, -0.020785659551620483, -0.04442648962140083, 0.008770139887928963, -0.005244000814855099, 0.02276524528861046, 0.008142000995576382, 0.005815035663545132, -0.019605521112680435, 0.024954210966825485, -0.05717959627509117, -0.0656689777970314, 0.03532800450921059, -0.025506211444735527, -0.052915871143341064, 0.06151945888996124, 0.04199007526040077, 0.02350758947432041, -0.016855036839842796, -0.02209903858602047, -0.05165959522128105, 0.015598760917782784, 0.01710248552262783, 0.0018903623567894101, -0.00836089812219143, 0.042713385075330734, -0.03056938387453556, -0.01104000210762024, -0.00933641567826271, 0.013352692127227783, 0.018396830186247826, 0.07050373405218124, -0.03018869459629059, -0.007128415163606405, 0.027600005269050598, 0.016874071210622787, 0.017007313668727875, -0.012952967546880245, -0.041875869035720825, 0.011848967522382736, -0.03475697338581085, 0.035651590675115585, -0.03336745500564575, 0.04530207812786102, -0.04141904041171074, 0.020176555961370468, -0.020633382722735405, 0.051050491631031036, 0.0009796811500564218, -0.027866488322615623, -0.04659642279148102, 0.009555311873555183, -0.07130318135023117, -0.009169863536953926, 0.018063727766275406, -0.00029206040198914707, -0.029275039210915565, -0.009293587878346443, -0.013162347488105297, 0.046900972723960876, 0.01261986419558525, -0.007923104800283909, -0.04789076745510101, -0.006119587458670139, 0.016293520107865334, -0.0018689485732465982, 0.0020830866415053606, 0.03833545371890068, 0.00267910398542881, -0.018425382673740387, -0.03622262552380562, 0.037916697561740875, 0.04328441992402077, 0.05181187018752098, -0.0039972420781850815, 0.01811131276190281, -0.02678152173757553, 0.031502075493335724, 0.01165862288326025, 0.04926124960184097, 0.004739587195217609, 0.008765380829572678, 0.029788970947265625, 0.008080139756202698, 0.0013300346909090877, -0.050327181816101074, 0.06235697492957115, 0.0236408319324255, -0.05923531949520111, 0.012134484946727753, -0.0009499398292973638, 0.01918676123023033, 0.0229936596006155, -0.031844694167375565, -0.06521215289831161, -0.017378486692905426, -0.045492421835660934, 0.06083421781659126, 0.03607035055756569, -0.00033934920793399215, -0.009388760663568974, 0.0010754484683275223, 0.017321381717920303, -0.010192967019975185, 0.033424556255340576, -0.018587175756692886, 0.006576415151357651, -0.009964553639292717, -0.03742180019617081, -0.004692000802606344, 0.010649794712662697, -0.010992416180670261, 0.007984966970980167, -0.009203174151480198, -0.0008071811753325164, -0.01916772685945034, -0.06022511422634125, 0.014846899546682835, 0.008408484049141407, 0.008660690858960152, -0.023088831454515457, -0.018177933990955353, -0.022232279181480408, 0.01052607037127018, 0.01692165806889534, -0.0015370347537100315, -0.04023890197277069, -0.011192278005182743, 0.013552553951740265, -0.02729545347392559, 0.004071000497788191, -0.01880607195198536, -0.009193656966090202, 0.0035618282854557037, 0.016988279297947884, 0.04484524950385094, 0.013152830302715302, 0.03260607644915581, -0.0001549526205053553, -0.007052277214825153, -0.009117518551647663, -0.030607454478740692, -0.0010355949634686112, 0.027409659698605537, 0.02365986630320549, 0.003331035142764449, -0.019910072907805443, 0.015922347083687782, -0.029427316039800644, 0.020176555961370468, -0.02451641857624054, 0.007190277334302664, 0.04869021475315094, 0.001333603635430336, 0.005053656175732613, -0.018863175064325333, -0.023602763190865517, 0.01388565730303526, -0.006714414805173874, 0.023602763190865517, -0.07804138958454132, -0.04933738708496094, 0.03336745500564575, -0.01294345036149025, -0.010678346268832684, 0.00192010379396379, -0.04796690493822098, -0.0003643319651018828, 0.028075866401195526, -0.003331035142764449, 0.003397655673325062, -0.033595867455005646, 0.06445077061653137, -0.019567452371120453, -0.03924911096692085, 0.041685525327920914, 0.019605521112680435, 0.031007178127765656, 0.0028004487976431847, 0.010906760580837727, -0.032872557640075684, 0.028723038733005524, -0.013228967785835266, 0.02487807348370552, -0.011753794737160206, -0.033424556255340576, 0.009916967712342739, -0.01320041622966528, -0.008927173912525177, 0.004042448941618204, -0.01138262264430523, 0.003559448989108205, 0.024478349834680557, 0.0022603452671319246, -0.01729283109307289, 0.030873935669660568, 0.014875451102852821, -0.0005621121963486075, 0.05371531844139099, -0.015770072117447853, 0.0175973828881979, -0.012886347249150276, 0.005510483868420124, -0.017730623483657837, 0.03886841982603073, 0.006466966588050127, 0.01252469141036272, 0.00276000052690506, -0.02398345246911049, 0.03312000632286072, 0.003875897265970707, -0.016816968098282814, -0.0038663800805807114, 0.037555042654275894, 0.053106214851140976, -0.009617174044251442, 0.002826621290296316, -0.016131727024912834, -0.007252139039337635, -0.025487177073955536, 0.004294655751436949, 0.034262076020240784, -0.032701246440410614, 0.021489934995770454, 0.02312690019607544, -0.0015953278634697199, 0.03346262499690056, 0.013733381405472755, 0.027847453951835632, -0.053791455924510956, 0.06231890618801117, -0.033748142421245575, 0.004677725024521351, -0.06083421781659126, 0.013343174941837788, 0.020290762186050415, -0.04819531738758087, 0.02055724523961544, 0.027542902156710625, 0.0008476294460706413, 0.02466869354248047, -0.012886347249150276, -0.008608346804976463, -0.03018869459629059, -0.018035175278782845, 0.02156607247889042, -0.030264832079410553, 0.010107312351465225, -0.0012080949964001775, -0.013628692366182804, 0.03744083270430565, -0.045492421835660934, -0.026971867308020592, -0.014685106463730335, 0.04054345563054085, -0.011715725995600224, 0.004318449180573225, 0.0024840005207806826, 0.0014490002067759633, 0.044464558362960815, -0.00045355610200203955, -0.021547038108110428, 0.006990415044128895, -0.027371590957045555, -0.005881656426936388, 0.03852580115199089, -0.02761903963983059, -0.004099552519619465, 0.011868001893162727, -0.016360141336917877, -0.001046896679326892, 0.02449738420546055, -0.0030954834073781967, 0.005786483641713858, 0.03509959205985069, 0.016274485737085342, 0.039667870849370956, 0.008632139302790165, 0.0008910518954508007, -0.014095037244260311, 0.012334346771240234, 0.024973245337605476, -0.001284827827475965, 0.00557710463181138, -0.08679725974798203, -0.06936166435480118, 0.014390071853995323, 0.022346487268805504, -0.011258898302912712, 0.023184003308415413, -0.01660759001970291, 0.02367890067398548, -0.05771256238222122, -0.025677522644400597, -0.0014490002067759633, -0.005029862746596336, -0.0005053061177022755, 0.015950899571180344, 0.01970069296658039, 0.033234212547540665, -0.009812277741730213, 0.012372415512800217, -0.004170931875705719, 0.0494135245680809, -0.036527179181575775, -0.015180002897977829, 0.05055559426546097, -0.0008904570713639259, 0.03728855773806572, 0.05961601063609123, -0.028418486937880516, 0.07408221811056137, 0.004656311124563217, 0.01761641725897789, -0.04233269765973091, -0.019424693658947945, 0.04115255922079086, -0.03641297295689583, -0.017911450937390327, 0.0072426218539476395, -0.041190627962350845, 0.02969379909336567, 0.009869380854070187, 0.016141245141625404, 0.026553107425570488, 0.009046139195561409, -0.030950075015425682, -0.026457935571670532, -0.011268415488302708, 0.0216041412204504, -0.0022567762061953545, 0.004430276807397604, -0.016702761873602867, 0.04157131910324097, -0.043436698615550995, -0.020614348351955414, -0.0004473104199860245, -0.007794621866196394, 0.03452855721116066, -0.061900150030851364, -0.02592496946454048, -0.03146400675177574, -0.010202484205365181, -0.024897107854485512, 0.033595867455005646, -0.010916277766227722, 0.029103729873895645, -0.0015108623774722219, -0.0013050519628450274, -0.019272416830062866, -0.015141934156417847, 0.024725796654820442, 0.003899690229445696, -0.020157521590590477, 0.015075312927365303, 0.033614903688430786, 0.03213021159172058, -0.03924911096692085, 0.005006069783121347, -0.017159588634967804, -0.024211866781115532, -0.046634491533041, 0.0018594313878566027, -0.03224441781640053, 0.05074594169855118, -0.015475037507712841, -0.041342902928590775, 0.00759951863437891, -0.014999175444245338, 0.0019843452610075474, -0.0018320692470297217, -0.008751104585826397, 0.019472278654575348, -0.044807180762290955, -0.008375173434615135, 0.02209903858602047, -0.03055034950375557, -0.0027290694415569305, 0.030493246391415596, -0.014428140595555305, -0.08276194334030151, 0.022517796605825424, -0.051697663962841034, 0.034623730927705765, 0.018358761444687843, 0.013961795717477798, -0.034471455961465836, 0.023412417620420456, -0.010478484444320202, 0.029236970469355583, -0.014475726522505283, 0.016540968790650368, 0.0596921481192112, -0.03595614433288574, -0.011782347224652767, -0.009031863883137703, -0.006190966814756393, 0.04183780029416084, 0.003257276490330696, -0.02986510843038559, 0.02072855457663536, 0.003016966162249446, -0.0012348622549325228, -0.029979316517710686, -0.027847453951835632, -0.0278093833476305, -0.010897243395447731, -0.0023983451537787914, 0.02640083245933056, -0.026838624849915504, -0.016179313883185387, 0.028913384303450584, 0.06308028846979141, 0.0797925665974617, -0.013371726498007774, -0.024421244859695435, 0.012058346532285213, 0.027333522215485573, 0.03580386936664581, 0.01545600313693285, 0.0007007070234976709, 0.013990347273647785, 0.003652242012321949, -0.027600005269050598, -0.011335036717355251, -0.002643414307385683, 0.01312427781522274, 0.018235037103295326, -0.03679366037249565, -0.019053520634770393, -0.06403201073408127, -0.010744967497885227, 0.002493517706170678, -0.041723594069480896, 0.017559314146637917, -0.027238350361585617, 0.004080518148839474, 0.0005406983545981348, 0.017378486692905426, 0.019929107278585434, -0.002745724515989423, -0.00626234570518136, -0.004435035400092602, 0.038411591202020645, -0.007185518275946379, 0.0397820770740509, 0.009783726185560226, 0.006609725300222635, -0.015627313405275345, 0.012543726712465286, -0.014932554215192795, 0.014561382122337818, 0.057598356157541275, -0.059654079377651215, 0.008812966756522655, 0.03277738392353058, 0.006447932217270136, -0.040353111922740936, -0.0030883452855050564, -0.01354303676635027, 0.011592001654207706, -0.005515242461115122, -0.018863175064325333, -0.022555865347385406, -0.00005249354217085056, -0.01002165675163269, -0.008741587400436401, 0.0000674014154355973, -0.018016140908002853, 0.04126676544547081, -0.04884248971939087, -0.003930621314793825, -0.014656553976237774, 0.036527179181575775, 0.020119450986385345, -0.00018067890778183937, -0.04244690388441086, -0.057788699865341187, -0.021128280088305473, 0.06231890618801117, -0.008613104932010174, 0.03612745553255081, -0.03142593801021576, 0.008351380936801434, 0.03161628171801567, -0.010316691361367702, 0.0055628283880651, -0.013048140332102776, 0.022384556010365486, 0.022708142176270485, -0.008465588092803955, -0.04640607535839081, 0.018177933990955353, -0.008346621878445148, 0.015494071878492832, 0.059844423085451126, 0.04115255922079086, -0.01884414069354534, -0.03974400833249092, 0.00025309919146820903, 0.013171864673495293, -0.03395752236247063, -0.03761214390397072, -0.01044041570276022, 0.0109638636931777, 0.01729283109307289, -0.037231456488370895, 0.013800002634525299, 0.027409659698605537, -0.028456557542085648, -0.01605558954179287, -0.006857173517346382, -0.019091589376330376, 0.012676967307925224, -0.008408484049141407, -0.002315069315955043, -0.03886841982603073, -0.012933933176100254, -0.046900972723960876, 0.009031863883137703, 0.058093249797821045, 0.018425382673740387, 0.023583728820085526, -0.028589798137545586, -0.026534073054790497, -0.030093522742390633, 0.012610347010195255, -0.08093463629484177, 0.014123588800430298, -0.011972691863775253, 0.03694593906402588, 0.002893241820856929, -0.027714211493730545, -0.005458138883113861, 0.018758486956357956, 0.02143283188343048, 0.0018094658153131604, -0.03538510948419571, 0.007290208246558905, 0.0022294141817837954, -0.005434345919638872, 0.06711559742689133, -0.042789526283741, 0.06787697970867157, 0.03403365984559059, 0.01250565703958273, -0.02451641857624054, -0.001394276157952845, -0.035461246967315674, 0.0031168970745056868, 0.0026933797635138035, -0.0432082824409008, -0.020119450986385345, 0.010288139805197716, -0.06338483840227127, 0.010392829775810242, -0.003692690283060074, 0.019129658117890358, -0.05710345879197121, 0.08946208655834198, -0.014532830566167831, -0.030360005795955658, -0.017759175971150398, -0.03055034950375557, 0.061214908957481384, 0.018863175064325333, 0.060681942850351334, 0.052573252469301224, 0.02021462470293045, -0.03365297242999077, 0.02276524528861046, -0.06159559637308121, 0.012515174224972725, -0.0028623107355087996, -0.013000554405152798, -0.002819483168423176, 0.005762690678238869, -0.014685106463730335, 0.008275242522358894, -0.04130483418703079, -0.01814938336610794, 0.038906488567590714, -0.04469297453761101, 0.05184993892908096, 0.009802760556340218 ]
Convolution-augmented transformers (Conformers) are recently proposed in various speech-domain applications, such as automatic speech recognition (ASR) and speech separation, as they can capture both local and global dependencies. In this paper, we propose a conformer-based metric generative adversarial network (CMGAN) for speech enhancement (SE) in the time-frequency (TF) domain. The generator encodes the magnitude and complex spectrogram information using two-stage conformer blocks to model both time and frequency dependencies. The decoder then decouples the estimation into a magnitude mask decoder branch to filter out unwanted distortions and a complex refinement branch to further improve the magnitude estimation and implicitly enhance the phase information. Additionally, we include a metric discriminator to alleviate metric mismatch by optimizing the generator with respect to a corresponding evaluation score. Objective and subjective evaluations illustrate that CMGAN is able to show superior performance compared to state-of-the-art methods in three speech enhancement tasks (denoising, dereverberation and super-resolution). For instance, quantitative denoising analysis on Voice Bank+DEMAND dataset indicates that CMGAN outperforms various previous models with a margin, i.e., PESQ of 3.41 and SSNR of 11.10 dB.
[ 0.008857340551912785, -0.015618669800460339, -0.03613930195569992, -0.04026371240615845, -0.009981411509215832, -0.03715350106358528, -0.03426303341984749, 0.00996450800448656, -0.04300205036997795, 0.018475331366062164, -0.04080462083220482, -0.022701160982251167, 0.003006678307428956, -0.03512510284781456, -0.006583843845874071, 0.026859378442168236, 0.014807309955358505, -0.05006764084100723, 0.0038180379197001457, -0.023377293720841408, 0.008540403097867966, -0.020047340542078018, -0.008519274182617664, -0.01575389690697193, 0.005121706519275904, 0.0648411437869072, 0.042799212038517, 0.009296827018260956, -0.038708608597517014, 0.056457094848155975, 0.003515891032293439, 0.04847872629761696, -0.03559839725494385, -0.025118336081504822, -0.06930361688137054, 0.04100745916366577, 0.032860059291124344, 0.06220422312617302, 0.0014484033454209566, 0.016497641801834106, -0.01972617767751217, -0.026183245703577995, 0.0028059515170753, -0.01742732524871826, 0.013522657565772533, -0.02327587455511093, -0.04415147751569748, 0.02089250646531582, 0.021619349718093872, 0.016658224165439606, 0.017934424802660942, -0.03803247585892677, -0.005582321900874376, -0.011181547306478024, -0.017833003774285316, 0.057471293956041336, 0.03165992349386215, 0.004610381089150906, 0.07863425463438034, -0.021534832194447517, 0.024171750992536545, 0.020655859261751175, -0.04699123650789261, -0.024678850546479225, -0.022160254418849945, -0.07958084344863892, -0.02609873004257679, -0.021331992000341415, 0.003053162479773164, 0.020267082378268242, -0.045605164021253586, -0.010158896446228027, 0.0035919558722525835, 0.01454530842602253, -0.01348039973527193, 0.03668021038174629, 0.03985803201794624, 0.025693049654364586, 0.03762679547071457, -0.012077423743903637, -0.012001358903944492, 0.06037866696715355, -0.011916842311620712, 0.02227857895195484, 0.0792427733540535, -0.027805965393781662, -0.02525356225669384, -0.03847195953130722, 0.015998994931578636, -0.04178501293063164, 0.017123065888881683, 0.038573380559682846, 0.013666335493326187, -0.030307656154036522, -0.007775527890771627, 0.013505754061043262, -0.02177147939801216, -0.0017537196399644017, -0.0813387855887413, 0.010125089436769485, -0.02592969499528408, -0.03698446974158287, 0.03847195953130722, 0.015162279829382896, 0.017131516709923744, 0.06778232008218765, -0.010412446223199368, -0.01046315673738718, 0.02256593480706215, 0.1317782998085022, -0.02527046576142311, 0.006643005646765232, 0.03901286795735359, 0.06592295318841934, -0.05114945396780968, 0.012356328777968884, -0.06203519180417061, -0.03311360627412796, -0.02057134360074997, 0.033367156982421875, -0.06254228949546814, 0.05388779193162918, 0.019269786775112152, 0.015415829606354237, -0.03181205317378044, 0.09080464392900467, -0.02790738455951214, -0.033181220293045044, 0.005502031184732914, 0.004128636326640844, -0.0170554518699646, -0.013717046007514, 0.0006058784201741219, 0.0036278755869716406, 0.03745776042342186, -0.017478035762906075, 0.0015593314310535789, -0.0016998403007164598, 0.0011557646794244647, -0.033519286662340164, -0.004107507411390543, -0.01806965097784996, -0.017630165442824364, 0.017359711229801178, -0.007061362732201815, 0.0317782461643219, -0.029327264055609703, 0.12312379479408264, 0.01840771734714508, -0.0019005672074854374, -0.012846524827182293, -0.01588067039847374, 0.02423936314880848, 0.014934085309505463, 0.012745104730129242, 0.011316774412989616, 0.006250003352761269, -0.01975998282432556, 0.01464672852307558, -0.051419906318187714, 0.08870863169431686, -0.027569318190217018, -0.004001861438155174, -0.016793450340628624, 0.041075073182582855, 0.03630833700299263, 0.013869175687432289, 0.0009228157578036189, -0.01430866215378046, 0.05483437702059746, 0.008595339022576809, 0.030054107308387756, -0.009465860202908516, -0.04401624947786331, -0.01412272546440363, 0.036206915974617004, 0.02209264226257801, -0.041379332542419434, -0.05206223204731941, 0.06815419346094131, -0.06260990351438522, 0.019709274172782898, 0.03478703647851944, 0.0009159487672150135, 0.055949997156858444, 0.016260996460914612, 0.042900629341602325, -0.03711969405412674, -0.01162948552519083, -0.015770798549056053, 0.019354304298758507, 0.015179183334112167, 0.04164978489279747, -0.024036522954702377, 0.029344167560338974, -0.0003235401527490467, -0.042393531650304794, 0.00359829468652606, -0.002742564072832465, -0.020503729581832886, -0.04567277431488037, 0.03965519368648529, 0.05121706426143646, -0.017968231812119484, 0.03194727748632431, 0.06044628098607063, 0.05283978581428528, 0.03833673521876335, -0.05341449752449989, -0.030476689338684082, -0.007707914803177118, -0.02611563168466091, -0.04645032808184624, -0.013024009764194489, 0.0461798757314682, -0.025676146149635315, -0.004631510004401207, 0.009584183804690838, 0.020841795951128006, 0.025659242644906044, -0.01169709861278534, 0.02974984608590603, 0.08154162764549255, -0.019793789833784103, -0.04685600847005844, -0.0005604507750831544, 0.015432733111083508, 0.000020254274204489775, 0.01604125276207924, 0.002668611938133836, -0.05304262414574623, 0.042900629341602325, 0.05557812377810478, -0.06514540314674377, 0.024509817361831665, -0.04127791151404381, 0.028008803725242615, 0.004635735880583525, 0.0040398938581347466, 0.03407709673047066, -0.046754587441682816, -0.005430192220956087, -0.054124437272548676, -0.0358012355864048, 0.04117649048566818, -0.005840097554028034, -0.003898328635841608, 0.025625435635447502, -0.00019293557852506638, -0.012322521768510342, -0.04736310988664627, 0.0036321012303233147, -0.03931712731719017, 0.023546326905488968, -0.04269779101014137, 0.041751205921173096, -0.019354304298758507, -0.03881002590060234, 0.03485465049743652, -0.046078454703092575, 0.0337897390127182, -0.020858699455857277, 0.008941857144236565, 0.03225153684616089, -0.06108860671520233, -0.011976003646850586, -0.002913710195571184, 0.03485465049743652, 0.0011483693961054087, -0.002410836284980178, -0.013387431390583515, -0.011333676986396313, -0.05300881713628769, 0.027366477996110916, -0.009093986824154854, -0.00715433107689023, 0.028346870094537735, -0.015432733111083508, 0.04753214120864868, 0.0003232760354876518, 0.07315757870674133, 0.0049695768393576145, 0.00147270190063864, 0.020267082378268242, -0.01989521086215973, -0.015170731581747532, -0.002577756531536579, -0.007226170040667057, -0.04655174911022186, 0.01237323135137558, 0.026335375383496284, 0.0014906617579981685, -0.030375270172953606, 0.04668697714805603, 0.018441524356603622, 0.017325904220342636, 0.00008253574924310669, -0.019168367609381676, 0.07275189459323883, 0.0027129831723868847, -0.04634890705347061, 0.001480097183957696, 0.008840437047183514, -0.0016575820045545697, -0.022008124738931656, 0.0245774295181036, -0.005726000294089317, 0.0813387855887413, -0.01639622263610363, -0.00846011284738779, 0.005709096789360046, -0.027822868898510933, -0.008396725170314312, 0.01925288327038288, -0.021365799009799957, 0.029901975765824318, 0.001503339153714478, -0.03144017979502678, -0.012888782657682896, -0.014959439635276794, -0.02038540691137314, 0.04232591763138771, -0.023191357031464577, 0.0005657330621033907, -0.01774848811328411, 0.025000013411045074, 0.042055465281009674, 0.007462816778570414, 0.027349574491381645, 0.03512510284781456, -0.005704871378839016, 0.011029417626559734, 0.026217052713036537, -0.02812712825834751, -0.004694897681474686, 0.033705223351716995, -0.016937129199504852, 0.0009972959524020553, -0.05037190020084381, -0.03485465049743652, 0.009584183804690838, -0.0061232284642755985, -0.036206915974617004, 0.001820276491343975, 0.017292099073529243, -0.014655180275440216, -0.00022542165243066847, -0.029732942581176758, 0.003152469638735056, -0.013176139444112778, 0.0007057136972434819, -0.03691685572266579, -0.008367144502699375, 0.02023327723145485, 0.013362076133489609, -0.02476336620748043, -0.005387933924794197, -0.0017463244730606675, 0.01270284689962864, 0.005096351727843285, 0.020182566717267036, -0.05892498046159744, -0.04716026782989502, 0.0149847948923707, -0.06051389127969742, -0.048613954335451126, -0.07478029280900955, 0.01839081384241581, -0.004787866026163101, -0.02356323041021824, 0.018678171560168266, 0.004006087314337492, 0.0032834704034030437, -0.013007106259465218, 0.00795723870396614, 0.004394863732159138, -0.006414810661226511, 0.0017980908742174506, -0.029530104249715805, 0.0643678531050682, -0.035057488828897476, 0.06639625132083893, 0.018120361492037773, -0.00024377759837079793, 0.006030260119587183, 0.016108864918351173, 0.003084856318309903, 0.03223463520407677, -0.012178843840956688, 0.019945919513702393, 0.024374591186642647, -0.0667005106806755, -0.03881002590060234, -0.01908385008573532, 0.011333676986396313, 0.009981411509215832, 0.0016058156033977866, 0.007703688926994801, 0.07660585641860962, -0.018779590725898743, -0.029732942581176758, -0.012483103200793266, -0.0072515252977609634, -0.006516230758279562, -0.020300889387726784, 0.03059501200914383, -0.018999334424734116, -0.02557472698390484, 0.040398940443992615, -0.017799198627471924, 0.04503044858574867, -0.010843480937182903, -0.03803247585892677, -0.02205883525311947, 0.023867489770054817, 0.005159738939255476, -0.0559161901473999, -0.02860042080283165, 0.02188980206847191, -0.008967212401330471, 0.010302574373781681, 0.035902656614780426, 0.04881679266691208, 0.015043956227600574, 0.04337392374873161, 0.07430700212717056, 0.08343479782342911, 0.004863930866122246, -0.010818125680088997, -0.026521312072873116, -0.007686785887926817, 0.013319817371666431, 0.02907371334731579, -0.06399597972631454, -0.02456052601337433, -0.010099735110998154, -0.003915232140570879, -0.016599062830209732, 0.02592969499528408, 0.001693501602858305, 0.012381683103740215, -0.02092631347477436, 0.022346191108226776, 0.012322521768510342, -0.04962815344333649, -0.06636244058609009, 0.006262680981308222, 0.0019216964719817042, -0.026166342198848724, -0.0224476121366024, -0.05104803293943405, 0.044590964913368225, -0.05703180655837059, -0.0023601262364536524, 0.042900629341602325, -0.0112238060683012, 0.0041413139551877975, -0.009246117435395718, 0.019455723464488983, 0.015145376324653625, 0.02407032996416092, 0.0039025545120239258, -0.007712140679359436, -0.01312542986124754, 0.026707248762249947, -0.019844500347971916, -0.048749182373285294, -0.03025694563984871, -0.015145376324653625, 0.036544982343912125, 0.05250171944499016, 0.007665656507015228, 0.016987837851047516, -0.05385398492217064, -0.0014272741973400116, 0.04002706706523895, -0.0065500373020768166, -0.0732928067445755, 0.05882355943322182, 0.02408723346889019, 0.01673428900539875, -0.0320994071662426, 0.009237665683031082, 0.017123065888881683, -0.0118661317974329, -0.02927655354142189, 0.026402989402413368, -0.015779251232743263, -0.022143350914120674, 0.016024349257349968, 0.0011145627358928323, 0.03600407764315605, 0.02025017887353897, -0.014266403391957283, 0.0364435613155365, -0.022718064486980438, -0.002064318163320422, -0.024678850546479225, 0.08411093056201935, -0.0010955465259030461, 0.030003396794199944, -0.009110890328884125, 0.03816770017147064, -0.005489354021847248, 0.015677830204367638, 0.02325897105038166, -0.0057809362187981606, 0.02025017887353897, -0.07268428802490234, 0.055138636380434036, 0.013573367148637772, 0.0485125333070755, 0.04303585737943649, 0.013902982696890831, -0.01889791339635849, 0.02489859238266945, -0.020655859261751175, 0.03299528360366821, -0.04036513343453407, 0.0014980569249019027, 0.019624756649136543, -0.02592969499528408, -0.022498320788145065, 0.09465860575437546, 0.012001358903944492, 0.02439149282872677, 0.03610549494624138, 0.012770459987223148, 0.03691685572266579, -0.042055465281009674, -0.0044751544483006, -0.015356668271124363, 0.0017642842140048742, -0.037221115082502365, 0.0351589098572731, -0.00893340539187193, -0.04296824336051941, 0.00618661567568779, -0.04969576746225357, -0.0019174705957993865, 0.029310360550880432, 0.02611563168466091, -0.04966196045279503, -0.019962823018431664, -0.00523157836869359, -0.0019533901941031218, 0.005434418097138405, -0.05706561356782913, 0.002791160950437188, 0.03394186869263649, -0.02440839633345604, -0.016810353845357895, -0.05081138759851456, 0.03157540410757065, -0.03864099457859993, 0.0103786401450634, -0.07518597692251205, 0.026791764423251152, -0.005683741997927427, -0.043069664388895035, 0.019117657095193863, 0.007568462286144495, 0.04797162860631943, 0.03157540410757065, 0.03138946741819382, 0.011992907151579857, 0.0291244238615036, 0.04381341114640236, 0.012905686162412167, -0.004842801950871944, -0.02609873004257679, -0.03360380232334137, -0.04996621981263161, 0.007914980873465538, -0.0076360758394002914, 0.016615966334939003, 0.04499664157629013, 0.014410082250833511, 0.00580629101023078, 0.06352268159389496, 0.0239351037889719, -0.015145376324653625, 0.005159738939255476, 0.06335365027189255, -0.00038904050597921014, 0.012567619793117046, 0.006452843081206083, -0.03367141634225845, -0.013269107788801193, 0.005683741997927427, 0.023782974109053612, 0.03759298846125603, 0.042765405029058456, -0.04401624947786331, -0.0381338931620121, -0.0940500870347023, -0.001334305969066918, 0.009617989882826805, 0.014266403391957283, -0.06774851679801941, -0.018982430920004845, 0.004219491966068745, -0.010860384441912174, -0.009313730522990227, -0.06906697154045105, -0.05882355943322182, 0.024661947041749954, 0.015669379383325577, 0.02691008895635605, -0.011976003646850586, 0.018441524356603622, 0.0029982267878949642, 0.028870873153209686, -0.02846519462764263, 0.018644364550709724, -0.008316433988511562, -0.014773502945899963, -0.04263017699122429, 0.005379482172429562, -0.02712983265519142, 0.030865466222167015, -0.00647819833829999, 0.04631510376930237, 0.001055401167832315, 0.021027732640504837, 0.018272491171956062, 0.006000679451972246, -0.05047332122921944, -0.01603280007839203, -0.004219491966068745, -0.02327587455511093, 0.010285671800374985, -0.0368492417037487, -0.028482098132371902, 0.015982091426849365, 0.015297506004571915, 0.010767416097223759, -0.0381338931620121, 0.014367823489010334, 0.03299528360366821, -0.027805965393781662, 0.005649935454130173, -0.026639634743332863, -0.030037203803658485, 0.009643345139920712, 0.025507112964987755, -0.0019438819726929069, 0.014317113906145096, 0.01640467345714569, 0.0491548590362072, 0.02106153964996338, 0.03407709673047066, -0.018154168501496315, 0.02860042080283165, -0.01839081384241581, -0.009567280299961567, 0.054428696632385254, -0.008269949816167355, 0.018187973648309708, 0.020165663212537766, 0.026318471878767014, -0.015787702053785324, 0.015542604960501194, -0.037897247821092606, 0.04350915178656578, -0.025726856663823128, -0.010201155208051205, -0.05108183994889259, -0.021517928689718246, 0.01590602658689022, -0.002560853259637952, -0.020300889387726784, 0.004259637091308832, -0.02226167544722557, 0.004219491966068745, -0.05064235255122185, -0.002054810058325529, 0.011080127209424973, 0.005962647031992674, -0.02143341302871704, -0.009279923513531685, -0.0216024462133646, -0.018018940463662148, 0.030206236988306046, 0.047092653810977936, -0.006042937748134136, 0.008417854085564613, 0.005523160565644503, -0.002658047480508685, 0.017934424802660942, -0.00016401504399254918, -0.004961125086992979, -0.02980055660009384, -0.003131340490654111, 0.011671744287014008, 0.03924951329827309, -0.030341463163495064, -0.007767076604068279, 0.028363773599267006, 0.0103786401450634, 0.017849907279014587, -0.012922589667141438, -0.01742732524871826, -0.007923432625830173, 0.013987499289214611, 0.025726856663823128, -0.0029327264055609703, -0.017148420214653015, -0.03059501200914383, 0.04455715790390968, 0.011198450811207294, 0.035868849605321884, -0.02124747633934021, 0.009617989882826805, -0.028668034821748734, -0.0317782461643219, 0.022515224292874336, 0.006190841551870108, -0.014181886799633503, 0.03348547965288162, 0.026352278888225555, 0.04398244246840477, 0.012838073074817657, -0.05571334809064865, 0.03607168793678284, 0.07653824239969254, 0.053110238164663315, -0.02726505883038044, -0.007682560011744499, -0.009787023067474365, -0.0089503088966012, -0.0257437601685524, -0.08012174814939499, 0.018018940463662148, 0.005392159800976515, -0.003437713021412492, -0.00871366262435913, 0.04398244246840477, 0.024864787235856056, 0.010978708043694496, -0.019861403852701187, -0.0002981851575896144, 0.04198785126209259, -0.009499667212367058, 0.011933744885027409, 0.019185271114110947, 0.03769440948963165, 0.018627461045980453, 0.004175120498985052, 0.00527383666485548, 0.011519613675773144, -0.022870194166898727, 0.041548363864421844, -0.00819388497620821, -0.07295473664999008, 0.013438140973448753, -0.019472626969218254, -0.03316431865096092, -0.012077423743903637, -0.06784993410110474, 0.02843138761818409, 0.019827596843242645, 0.015779251232743263, -0.018137264996767044, 0.0056119030341506, 0.024340784177184105, -0.026707248762249947, -0.026453698053956032, 0.011688646860420704, -0.012347877025604248, 0.04655174911022186, 0.029547005891799927, 0.040906038135290146, -0.03164301812648773, 0.02824545092880726, 0.018610557541251183, 0.03526033088564873, 0.0038243765011429787, 0.02259974181652069, 0.00143044360447675, -0.03833673521876335, 0.00910243857651949, -0.03860718756914139, 0.0239351037889719, -0.06551727652549744, 0.03394186869263649, -0.0005181924789212644, -0.021298184990882874, -0.021467218175530434, 0.03446587175130844, 0.02860042080283165, -0.020114952698349953, 0.04536851495504379, -0.016962483525276184, 0.010099735110998154, -0.011773163452744484, 0.0024615463335067034, 0.024797173216938972, -0.026369182392954826, -0.04317108541727066, -0.023952007293701172, 0.028718743473291397, -0.031152822077274323, 0.03793105483055115, 0.0006349310278892517, -0.05649090185761452, -0.047396913170814514, 0.013598722405731678, 0.02177147939801216, 0.002298851730301976, 0.01837391033768654, 0.03701827675104141, 0.04597703740000725, 0.005911936983466148, 0.008755920454859734, -0.04066939279437065, -0.009896894916892052, 0.01169709861278534, -0.035564590245485306, -0.09303588420152664, 0.014849568717181683, -0.011494259350001812, -0.0684584528207779, 0.005282287951558828, -0.041413139551877975, 0.005941517651081085, 0.03914809226989746, -0.01053076982498169, 0.03340096399188042, 0.03864099457859993, 0.005421740468591452, -0.0009994088904932141, -0.03613930195569992, 0.002879903418943286, -0.07126440852880478, 0.02374916709959507, 0.049594346433877945, -0.029225843027234077, 0.0074205584824085236, 0.007817786186933517, -0.03194727748632431, 0.0415145605802536, -0.004610381089150906, -0.03307979926466942, -0.02177147939801216, -0.04066939279437065, -0.014570663683116436, -0.06984452903270721, -0.05456392467021942, -0.046078454703092575, 0.015677830204367638, 0.04192023724317551, 0.031372565776109695, -0.00635142344981432, -0.012322521768510342, 0.021331992000341415, -0.003258115379139781, 0.004365283064544201, -0.029158230870962143, -0.032538894563913345, 0.021044636145234108, 0.024188654497265816, -0.029158230870962143, 0.002172076841816306, 0.006693715695291758, 0.015382022596895695, 0.024306977167725563, -0.07701153308153152, -0.005962647031992674, -0.0695064589381218, -0.02008114568889141, 0.018306298181414604, -0.06318461894989014, -0.0067063928581774235, -0.01992901600897312, -0.007657204754650593, -0.01786681078374386, -0.03718730807304382, -0.007188137620687485, -0.03182895481586456, 0.039553772658109665, 0.00087844452355057, 0.04966196045279503, -0.04296824336051941, 0.05855310708284378, -0.05240029841661453, 0.002662273123860359, -0.024171750992536545, -0.016134221106767654, -0.0508451908826828, -0.022650452330708504, 0.024121040478348732, -0.027349574491381645, -0.03358690068125725, 0.04077081382274628, 0.05456392467021942, -0.0016470174305140972, -0.002056922996416688, -0.00477096252143383, 0.003703940426930785, -0.013674787245690823, -0.05016905814409256, 0.012407038360834122, -0.03559839725494385, -0.0043821861036121845, -0.02691008895635605, 0.01222110167145729, -0.0434415377676487, -0.001949164317920804, -0.06855987757444382, -0.03078094869852066, -0.021653154864907265, 0.015525701455771923, 0.004847027361392975, -0.04148075357079506, 0.005379482172429562, -0.0014579115668311715, 0.002658047480508685, 0.025794468820095062, 0.003342631971463561, 0.03826912119984627, 0.03395877406001091, 0.0330628976225853, -0.0020273420959711075, -0.03951996564865112, 0.0014980569249019027, -0.024628140032291412, 0.03613930195569992, 0.0023960459511727095, 0.012728201225399971, 0.013421237468719482, 0.026048019528388977, 0.05459773167967796, 0.015255248174071312, 0.0358012355864048, 0.0525355264544487, -0.014934085309505463, 0.019506433978676796, -0.009127793833613396, 0.0337897390127182, -0.009677152149379253, -0.004001861438155174, 0.0003644778917077929, 0.0618661567568779, 0.021788382902741432, -0.023884393274784088, 0.015973638743162155, -0.04428670182824135, -0.003879312425851822, 0.01975998282432556, -0.005954195279628038, -0.03206560015678406, 0.003991296980530024, -0.016108864918351173, -0.01823868416249752, 0.02089250646531582, -0.015593314543366432, -0.010496962815523148, 0.026893185451626778, -0.0022375772241503, -0.0006407415494322777, 0.0021699639037251472, -0.048242080956697464, -0.00015582749620079994, 0.009947605431079865, -0.004276540596038103, -0.023039227351546288, 0.005988001823425293, -0.015466539189219475, -0.0056541613303124905, 0.03776201978325844, -0.01195064838975668, -0.03297838196158409, -0.010260316543281078, 0.026876281946897507, 0.00878127571195364, 0.005840097554028034, 0.004415992647409439, -0.006626102142035961, 0.01574544422328472, -0.01044625323265791, -0.005134384147822857, 0.026825571432709694, 0.0306119155138731, 0.04797162860631943, -0.03718730807304382, 0.0364435613155365, 0.0028017256408929825, -0.05219746008515358, -0.012026713229715824, -0.03260650858283043, -0.02210954576730728, 0.011173095554113388, -0.01855984702706337, -0.017630165442824364, 0.004589251708239317, -0.019709274172782898, 0.008565758354961872, 0.02777215838432312, 0.0325050875544548, -0.027822868898510933, -0.032048698514699936, 0.036883048713207245, 0.04655174911022186, -0.03478703647851944, 0.013810014352202415, 0.014824213460087776, 0.03025694563984871, -0.051115646958351135, 0.03999326005578041, 0.0012656361795961857, -0.004323024768382311, -0.012635232880711555, -0.035564590245485306, 0.004551219288259745, 0.039722807705402374, -0.046281296759843826, 0.03495607152581215, -0.001836123294197023, 0.040060874074697495, -0.00236435211263597, -0.05807981267571449, -0.010125089436769485, -0.016362415626645088 ]
Epilepsy is one of the most common neurological diseases, characterized by transient and unprovoked events called epileptic seizures. Electroencephalogram (EEG) is an auxiliary method used to perform both the diagnosis and the monitoring of epilepsy. Given the unexpected nature of an epileptic seizure, its prediction would improve patient care, optimizing the quality of life and the treatment of epilepsy. Predicting an epileptic seizure implies the identification of two distinct states of EEG in a patient with epilepsy: the preictal and the interictal. In this paper, we developed two deep learning models called Temporal Multi-Channel Transformer (TMC-T) and Vision Transformer (TMC-ViT), adaptations of Transformer-based architectures for multi-channel temporal signals. Moreover, we accessed the impact of choosing different preictal duration, since its length is not a consensus among experts, and also evaluated how the sample size benefits each model. Our models are compared with fully connected, convolutional, and recurrent networks. The algorithms were patient-specific trained and evaluated on raw EEG signals from the CHB-MIT database. Experimental results and statistical validation demonstrated that our TMC-ViT model surpassed the CNN architecture, state-of-the-art in seizure prediction.
[ 0.009322980418801308, 0.022123869508504868, -0.013492829166352749, -0.048836395144462585, 0.006764623802155256, 0.008817682042717934, 0.04708833619952202, 0.010169696994125843, -0.053425051271915436, 0.05746743455529213, 0.028915807604789734, -0.04592296481132507, -0.012300143018364906, -0.05841430276632309, 0.02887938916683197, 0.03623580560088158, -0.0116264121606946, -0.011972382664680481, 0.016233276575803757, -0.037328340113162994, -0.020612528547644615, -0.018919095396995544, -0.016642976552248, -0.07669608294963837, 0.039404161274433136, 0.03980475664138794, 0.06813787668943405, 0.0031410432420670986, -0.04879997670650482, 0.05906982347369194, 0.02682177908718586, 0.006241116672754288, -0.008203130215406418, -0.0403510257601738, -0.03385043144226074, -0.03647252172231674, -0.014148351736366749, 0.047234006226062775, -0.010679547674953938, 0.02139551192522049, 0.02663968876004219, 0.015723425894975662, -0.022269541397690773, -0.041552815586328506, 0.006805593613535166, -0.030427150428295135, -0.039003562182188034, -0.06966742873191833, 0.03497938811779022, -0.010706860572099686, -0.019010139629244804, -0.03918565437197685, 0.0066917878575623035, -0.01841834932565689, -0.04348296299576759, -0.007329101208597422, 0.03492476046085358, 0.01005133893340826, 0.09716293960809708, 0.031173717230558395, 0.008453503251075745, 0.04632356017827988, -0.03636326640844345, -0.005599251016974449, -0.0034733565989881754, -0.0687934011220932, 0.011972382664680481, -0.025401480495929718, 0.010105965659022331, -0.0019642901606857777, -0.04053311422467232, -0.010961785912513733, -0.03838445991277695, 0.0021019952837377787, 0.010388203896582127, -0.0009963707998394966, 0.002277256455272436, 0.07301787286996841, 0.016205962747335434, 0.028059987351298332, 0.031064463779330254, 0.09126324206590652, 0.009404920972883701, 0.05710325762629509, 0.09046204388141632, -0.02505551092326641, 0.01924685575067997, -0.06398624181747437, -0.009077159687876701, -0.016023872420191765, -0.04213550314307213, 0.05258743837475777, -0.039950430393218994, 0.032011326402425766, -0.041807740926742554, -0.02989909052848816, 0.022779392078518867, 0.0036782072857022285, -0.061254896223545074, -0.008403428830206394, 0.005535519681870937, -0.019210439175367355, -0.011025517247617245, -0.02073998935520649, -0.0018311372259631753, -0.04315520450472832, -0.02066715434193611, 0.07727877050638199, 0.021104170009493828, 0.11551755666732788, -0.04432057589292526, -0.021796109154820442, 0.028151031583547592, -0.0020177788101136684, -0.0429731123149395, -0.04053311422467232, -0.05327937752008438, -0.027440883219242096, 0.03587162494659424, -0.040715206414461136, -0.01430312730371952, 0.009896562434732914, -0.06049012020230293, 0.0534614659845829, -0.048180874437093735, 0.07640474289655685, 0.04727042466402054, 0.002956677693873644, 0.012582382187247276, 0.0543719157576561, -0.008021040819585323, 0.02729521133005619, -0.00046944941277615726, -0.01973849907517433, 0.03497938811779022, -0.002129308646544814, -0.03428744524717331, 0.017416857182979584, -0.011380591429769993, -0.014812977984547615, -0.020394019782543182, 0.011881337501108646, 0.0007716041291132569, 0.0027677598409354687, 0.040897294878959656, 0.007502085994929075, 0.018181633204221725, 0.0411522202193737, 0.0012359322281554341, -0.014922231435775757, -0.053206540644168854, 0.015259097330272198, 0.013210590928792953, 0.023871928453445435, 0.010943576693534851, 0.013656710274517536, -0.012728054076433182, -0.016032977029681206, -0.016187753528356552, -0.03539819270372391, -0.003960445988923311, -0.03166535869240761, 0.02702207677066326, 0.004429326392710209, -0.0025378719437867403, 0.040132518857717514, 0.05364355817437172, -0.02381730265915394, -0.030991626903414726, 0.04909132048487663, -0.025619987398386, 0.0008063149289228022, 0.0016285626916214824, 0.013629396446049213, 0.011498949490487576, 0.021996406838297844, 0.05189549922943115, 0.0026380212511867285, -0.05276952683925629, 0.03206595405936241, -0.04617789015173912, 0.02944386750459671, -0.004336005542427301, -0.015614171512424946, 0.08172175288200378, 0.029935508966445923, 0.06343997269868851, 0.009641637094318867, -0.00507119158282876, -0.010169696994125843, 0.014985962770879269, -0.010233428329229355, 0.07822563499212265, -0.047889530658721924, 0.0030841403640806675, -0.0442841574549675, 0.030172225087881088, -0.02833312191069126, 0.02270655706524849, 0.021268049255013466, -0.005790445022284985, -0.03503401204943657, 0.01756252907216549, 0.017161931842565536, -0.019756706431508064, -0.01494954526424408, 0.03113729879260063, -0.05222325772047043, -0.003550744615495205, -0.019283274188637733, -0.04351938143372536, 0.005007460247725248, -0.044174905866384506, 0.0037351101636886597, -0.014785665087401867, -0.005849624052643776, 0.012127158232033253, -0.026020584627985954, 0.04249968007206917, -0.00764320557937026, 0.04202624782919884, 0.028642673045396805, 0.023325661197304726, -0.009414025582373142, 0.004852684214711189, 0.005276042502373457, -0.0465056486427784, 0.030427150428295135, -0.03497938811779022, 0.01051566656678915, -0.009887457825243473, 0.010898054577410221, 0.05768594145774841, -0.020412229001522064, -0.02019372209906578, -0.000014403561181097757, 0.08827697485685349, -0.007110593840479851, -0.030973417684435844, -0.015195365995168686, 0.0067327581346035, -0.00790268275886774, 0.02663968876004219, 0.0007050276617519557, -0.005585594568401575, 0.04570445790886879, -0.0035257074050605297, 0.10007636994123459, 0.011225815862417221, 0.017152827233076096, -0.02514655515551567, -0.015741635113954544, 0.010151487775146961, 0.03545282036066055, -0.06420474499464035, 0.014876709319651127, 0.014148351736366749, 0.005116714164614677, 0.012482233345508575, -0.01870058849453926, 0.03372297063469887, -0.060708627104759216, -0.025674615055322647, 0.07094205915927887, 0.02683998830616474, 0.03417819365859032, 0.08980652689933777, 0.037328340113162994, 0.017872082069516182, -0.06653548777103424, 0.0006407272885553539, -0.08317846804857254, -0.026949241757392883, -0.023580586537718773, 0.028296703472733498, -0.046032216399908066, 0.014548948034644127, 0.0381295345723629, 0.02785968780517578, -0.01116208452731371, -0.03337699919939041, -0.0007090108701959252, -0.03525251895189285, 0.034068938344717026, 0.004684251733124256, 0.0313740149140358, 0.008121190592646599, 0.003009028499945998, -0.025619987398386, -0.050438784062862396, 0.007420145906507969, 0.0009411749197170138, -0.022925063967704773, -0.03334058076143265, 0.028278494253754616, -0.002528767567127943, -0.04086087644100189, -0.021104170009493828, 0.007920891977846622, -0.009869249537587166, -0.05520952492952347, -0.005153132136911154, -0.005007460247725248, 0.048253707587718964, -0.09803696721792221, -0.001146594644524157, 0.05775877833366394, 0.06569787859916687, -0.026038793846964836, -0.032011326402425766, -0.028005359694361687, -0.01738043874502182, 0.006974026560783386, -0.0042813788168132305, -0.002106547588482499, 0.011671935208141804, 0.014121037907898426, -0.03159252181649208, 0.00232505495660007, 0.0025242152623832226, -0.0025560809299349785, 0.02066715434193611, -0.05233251303434372, 0.03264864161610603, -0.023962974548339844, -0.014521635137498379, 0.03638147562742233, -0.017999542877078056, -0.0031091775745153427, -0.025219392031431198, -0.01570521667599678, -0.05156773701310158, -0.06835638731718063, -0.02999013476073742, 0.04635997861623764, 0.03776535391807556, -0.07880832254886627, 0.04100654646754265, 0.000059107947890879586, -0.029188942164182663, 0.0017844768008217216, -0.031100880354642868, -0.037164460867643356, -0.021941781044006348, 0.0014146075118333101, -0.014767455868422985, -0.032102372497320175, 0.015359246172010899, -0.025638196617364883, -0.007807085756212473, 0.0009622290381230414, 0.00023059923842083663, -0.03492476046085358, 0.01467641070485115, -0.012354770675301552, 0.0033367895521223545, -0.003095520893111825, -0.005808653775602579, 0.036417894065380096, -0.03707341477274895, -0.02206924371421337, -0.019975215196609497, -0.035908043384552, 0.014239395968616009, -0.012882829643785954, -0.029698792845010757, -0.024928048253059387, -0.036782070994377136, -0.003111453726887703, 0.00008983554289443418, 0.0043929084204137325, 0.05757668986916542, 0.016469992697238922, -0.01868237927556038, 0.0178538728505373, -0.01430312730371952, 0.023598795756697655, 0.010542980395257473, 0.022105662152171135, 0.057904452085494995, -0.07250802218914032, -0.006910295225679874, -0.015168052166700363, 0.028096403926610947, 0.004399736877530813, 0.07185250520706177, 0.03301281854510307, -0.03885789215564728, -0.052114006131887436, 0.047707438468933105, -0.004447535146027803, -0.05160415545105934, 0.007210742682218552, -0.035270728170871735, 0.07866264879703522, -0.014985962770879269, 0.021158795803785324, 0.05000176653265953, 0.06307578831911087, -0.008580965921282768, -0.0381295345723629, 0.01126223336905241, -0.011699248105287552, 0.0014066410949453712, -0.07764294743537903, 0.005080296192318201, -0.029735209420323372, 0.016661185771226883, 0.05240534991025925, -0.017881184816360474, 0.01078880112618208, 0.01125312875956297, -0.015067903324961662, -0.03326774388551712, 0.006974026560783386, -0.01462178397923708, 0.005899698939174414, -0.004169848747551441, -0.006072683725506067, -0.03352266922593117, -0.06730026751756668, 0.03727371245622635, 0.04963758960366249, -0.03401431068778038, 0.005908803083002567, -0.0038785056676715612, 0.0033754834439605474, -0.001918767811730504, 0.011854024603962898, 0.032211627811193466, 0.0424632653594017, -0.005685743410140276, 0.01683417148888111, -0.04461191967129707, -0.038821473717689514, -0.06187400221824646, 0.036782070994377136, 0.005840519443154335, -0.022269541397690773, -0.035288937389850616, -0.0411522202193737, 0.029971925541758537, -0.02598416619002819, -0.04592296481132507, -0.028187450021505356, -0.030627448111772537, 0.020794617012143135, 0.028369538486003876, 0.03208416327834129, -0.0038329833187162876, 0.0023193645756691694, 0.004707012791186571, -0.03618117794394493, -0.02917073294520378, -0.028005359694361687, -0.002877013524994254, -0.010324472561478615, -0.0596160925924778, 0.016287902370095253, -0.016215067356824875, 0.007492981385439634, 0.027823271229863167, 0.017052678391337395, -0.026421181857585907, 0.014521635137498379, 0.053024452179670334, 0.007247160654515028, -0.050693705677986145, 0.009514174424111843, 0.019647452980279922, 0.03213879093527794, 0.005831415299326181, 0.033122073858976364, 0.032284460961818695, 0.017926707863807678, -0.023434914648532867, -0.01944715529680252, -0.02543789893388748, -0.03412356600165367, 0.04027818888425827, 0.06056295707821846, 0.01005133893340826, 0.0652608647942543, 0.045267440378665924, -0.023853719234466553, 0.00178675283677876, -0.02907968871295452, 0.008699323982000351, 0.008016488514840603, 0.014275814406573772, -0.018618648871779442, -0.012682531028985977, -0.0029680582229048014, -0.0011983762960880995, 0.03654535487294197, -0.05102146789431572, -0.04104296490550041, 0.026676107197999954, 0.08084772527217865, 0.0123820835724473, 0.014858500100672245, 0.00027839772519655526, 0.01718924567103386, 0.004820818547159433, -0.0061409673653542995, 0.04778027534484863, 0.0049300724640488625, -0.004524923395365477, -0.024891629815101624, 0.00490731094032526, 0.02438177913427353, -0.0317746102809906, -0.0074292500503361225, -0.02942565828561783, -0.01879163272678852, 0.02503730170428753, 0.03725550323724747, 0.03263043239712715, -0.023398496210575104, 0.03561669960618019, 0.013483724556863308, 0.019483573734760284, 0.013629396446049213, 0.08011936396360397, -0.04759818688035011, 0.003022685181349516, 0.02811461314558983, -0.017926707863807678, 0.04701549932360649, -0.002494625747203827, -0.03794744610786438, -0.03122834302484989, -0.03233908861875534, 0.02727700211107731, 0.020230140537023544, -0.018345514312386513, -0.008863205090165138, 0.014394172467291355, 0.0035962669644504786, -0.042863860726356506, 0.007788877002894878, 0.0028792896773666143, 0.003721453482285142, 0.0038807818200439215, -0.026566853746771812, -0.020448647439479828, 0.03871222212910652, -0.024236107245087624, -0.011808501556515694, -0.023380286991596222, 0.014822082594037056, -0.013146859593689442, 0.0004648971662390977, 0.0394405797123909, -0.012209098786115646, -0.010970890522003174, 0.0030591031536459923, 0.025547152385115623, -0.019665662199258804, -0.012318352237343788, 0.0018072379752993584, -0.02290685474872589, -0.0037442147731781006, -0.018063275143504143, -0.006996787618845701, -0.008844995871186256, -0.004839027766138315, 0.041989829391241074, 0.023398496210575104, 0.017972230911254883, -0.006664474494755268, -0.0061864894814789295, -0.03925848752260208, 0.034451328217983246, 0.025965958833694458, 0.011435218155384064, 0.06620772927999496, -0.007247160654515028, 0.04016893729567528, -0.008312384597957134, 0.0390399806201458, 0.03339520841836929, 0.02878834493458271, 0.034815505146980286, 0.002665334613993764, -0.05251460149884224, -0.0026289166416972876, -0.027877897024154663, -0.012828202918171883, -0.02345312386751175, 0.04253609851002693, 0.019574617967009544, 0.010606711730360985, 0.0020780961494892836, -0.02653043530881405, -0.0232528243213892, 0.03150147944688797, 0.023398496210575104, 0.041079383343458176, -0.06067220866680145, -0.033977895975112915, 0.04384714365005493, 0.030499985441565514, 0.04577729105949402, 0.017507901415228844, 0.013064919039607048, -0.002886118134483695, 0.017926707863807678, -0.008198577910661697, 0.024727748706936836, 0.02944386750459671, -0.0050848484970629215, -0.012828202918171883, 0.00818492192775011, 0.051349230110645294, 0.0390399806201458, 0.042390428483486176, 0.002096304902806878, -0.03202953562140465, -0.01467641070485115, 0.014849396422505379, 0.014457903802394867, 0.09213726967573166, -0.008576413616538048, 0.05382564663887024, 0.016642976552248, 0.008303279988467693, 0.0007568093715235591, -0.029407449066638947, -0.02430894412100315, 0.021249840036034584, 0.0023193645756691694, 0.02141372114419937, -0.045376695692539215, 0.02148655615746975, -0.005125818308442831, -0.025965958833694458, -0.0008928074385039508, 0.02691282331943512, 0.006819250527769327, -0.006218355149030685, 0.003582610283046961, -0.011426114477217197, 0.0004606294387485832, 0.004201714415103197, -0.021158795803785324, -0.002858804538846016, 0.02736804634332657, 0.07917249947786331, 0.014266709797084332, 0.033595506101846695, 0.04493968188762665, 0.038930729031562805, 0.034615207463502884, -0.054918184876441956, -0.05965251103043556, 0.015723425894975662, 0.023780884221196175, -0.015832679346203804, -0.009705368429422379, -0.05131281167268753, 0.03816595301032066, 0.02886117994785309, -0.013938948512077332, 0.029862672090530396, -0.0631486251950264, 0.00013713612861465663, -0.03166535869240761, -0.0017025364795699716, -0.03131938725709915, 0.040788039565086365, -0.08084772527217865, -0.025219392031431198, 0.004153916146606207, 0.04617789015173912, 0.00453402753919363, 0.013729546219110489, 0.049856096506118774, 0.00789813045412302, -0.026512226089835167, 0.027313420549035072, -0.0005070053739473224, -0.005212311167269945, 0.02578386850655079, 0.02578386850655079, -0.025292227044701576, -0.0023922002874314785, -0.0015488985227420926, -0.009605219587683678, 0.009236488491296768, 0.03243013471364975, -0.01691611111164093, 0.0171983502805233, -0.03787460923194885, 0.015359246172010899, 0.00039405300049111247, -0.010178801603615284, 0.015304619446396828, 0.020139094442129135, 0.000263887457549572, -0.0014988238690420985, -0.00794365257024765, -0.005162236280739307, -0.002342125866562128, -0.017781035974621773, 0.04147997871041298, 0.027404464781284332, -0.04002326354384422, -0.040788039565086365, -0.02933461219072342, -0.002136137103661895, 0.012190889567136765, 0.003054550848901272, 0.008571861311793327, 0.03652714565396309, 0.010725069791078568, -0.004297311417758465, 0.026002375409007072, -0.05058445408940315, 0.02802356891334057, 0.009750890545547009, 0.0640590712428093, -0.01616954430937767, -0.023289242759346962, -0.028151031583547592, 0.05382564663887024, -0.0007619305979460478, 0.018482081592082977, 0.00039519104757346213, 0.005749474745243788, 0.04712475463747978, 0.0016877417219802737, -0.024454616010189056, 0.016615664586424828, 0.039950430393218994, -0.016515513882040977, 0.0029111553449183702, 0.03867580369114876, -0.025492524728178978, -0.02942565828561783, 0.01823626086115837, 0.01424850057810545, -0.03834804147481918, -0.0034483193885535, 0.007452011574059725, 0.012218203395605087, -0.014057306572794914, 0.04005968198180199, -0.015823574736714363, -0.04086087644100189, 0.04501251503825188, 0.007502085994929075, 0.037164460867643356, -0.047816693782806396, -0.019410736858844757, 0.03758326545357704, -0.01242760568857193, -0.013392680324614048, 0.021177005022764206, -0.03787460923194885, 0.011881337501108646, 0.010943576693534851, -0.0390399806201458, 0.03426923602819443, 0.03372297063469887, 0.04879997670650482, -0.028369538486003876, 0.027404464781284332, -0.026038793846964836, -0.009923876263201237, 0.020685363560914993, 0.04122505709528923, 0.08550921082496643, -0.05768594145774841, -0.020958498120307922, -0.009787308983504772, 0.041261471807956696, -0.027586555108428, 0.024563869461417198, 0.006787384860217571, -0.045267440378665924, -0.0020177788101136684, -0.0044384305365383625, 0.016652081161737442, -0.045668039470911026, -0.02010267786681652, 0.008048354648053646, -0.04290027916431427, -0.02702207677066326, 0.015814470127224922, 0.0022078347392380238, -0.024072227999567986, 0.03539819270372391, -0.02272476628422737, 0.022178497165441513, 0.02270655706524849, -0.023799093440175056, -0.014394172467291355, -0.03820237144827843, -0.051531318575143814, 0.007866265252232552, -0.005312460009008646, 0.010807009413838387, -0.0021577600855380297, -0.02589312195777893, -0.04563162103295326, -0.025947749614715576, -0.03199312090873718, 0.011826710775494576, -0.005849624052643776, -0.015031485818326473, -0.03122834302484989, 0.01942894607782364, -0.018081484362483025, 0.024236107245087624, -0.021104170009493828, -0.05896056815981865, 0.015077007934451103, -0.021650437265634537, -0.05925191193819046, 0.003243468701839447, -0.008776712231338024, 0.0123820835724473, -0.024163272231817245, -0.009987607598304749, -0.06751877069473267, 0.023380286991596222, 0.027404464781284332, 0.024691332131624222, 0.007319996599107981, -0.0027085808105766773, -0.016042081639170647, 0.022742973640561104, 0.008134846575558186, -0.004183505661785603, 0.041734904050827026, -0.039112817496061325, -0.040423862636089325, -0.002144103404134512, 0.021340886130928993, -0.014758351258933544, 0.055755794048309326, -0.05655698850750923, -0.002330745104700327, -0.008840443566441536, -0.027222374454140663, 0.010069547221064568, -0.025000883266329765, 0.010278950445353985, 0.0007386003853753209, 0.047343261539936066, -0.01125312875956297, 0.053862065076828, 0.016670290380716324, 0.006136415060609579, -0.0037829086650162935, 0.02569282427430153, 0.03385043144226074, -0.00826686155050993, 0.00892693642526865, 0.016934320330619812, 0.0016524619422852993, 0.02252446673810482, -0.01392073929309845, 0.049674008041620255, -0.022597303614020348, -0.007192533928900957, 0.02645760029554367, -0.030518194660544395, -0.012809993699193, -0.02942565828561783, -0.0019813610706478357, 0.036763861775398254, 0.0223423782736063, 0.015477604232728481, 0.031100880354642868, -0.018809841945767403, 0.009805518202483654, -0.006068131420761347, -0.026111628860235214, 0.08441668003797531, -0.017316708341240883, 0.03521610423922539, 0.0072198472917079926, 0.04122505709528923, 0.01906476728618145, -0.008571861311793327, -0.025383271276950836, -0.016388051211833954, 0.002123618498444557, 0.012409397400915623, 0.008093876764178276, 0.033977895975112915, 0.004310968331992626, 0.0687934011220932, -0.01494954526424408, -0.0024240659549832344, 0.02421789988875389, 0.0006913709221407771, -0.024181481450796127, 0.02718595787882805, -0.05167699232697487, -0.03654535487294197, -0.03874863684177399, 0.011945068836212158, -0.039768338203430176, -0.008731190115213394, -0.01757163368165493, 0.0035939908120781183, -0.04712475463747978, -0.057613108307123184, -0.005790445022284985, -0.012964770197868347, -0.012891934253275394, 0.006737310439348221, -0.003216155106201768, 0.007543056271970272, 0.0038648489862680435, 0.03576236963272095, -0.03507043048739433, 0.04413848742842674, 0.03969550505280495, -0.005585594568401575, 0.07560354471206665, -0.01490402314811945, -0.036982372403144836, -0.03346804529428482, 0.007788877002894878, 0.03279431164264679, -0.0005758579354733229, -0.019793124869465828, 0.04544953256845474, 0.024272525683045387, 0.01050656195729971, 0.03918565437197685, -0.04785311222076416, -0.016315216198563576, -0.015095217153429985, -0.010898054577410221, 0.02365342155098915, 0.02867909148335457, 0.03889431059360504, -0.014321336522698402, 0.011389696039259434, -0.009659846313297749, -0.04792594909667969, 0.014357754029333591, -0.021067751571536064, 0.02886117994785309, -0.015222679823637009, -0.005917907692492008, 0.007884473539888859, 0.01084342785179615, 0.022360585629940033, -0.01908297650516033, -0.018991932272911072, -0.010333577170968056, -0.0469062477350235, 0.0028997748158872128, 0.01727118529379368, -0.0009531245450489223, 0.01420297846198082, -0.024509241804480553, -0.01130775548517704, -0.008817682042717934, -0.0015466223703697324, -0.015031485818326473, -0.0306638665497303, -0.015605066902935505, -0.009832831099629402, 0.005303355865180492, -0.01737133599817753, -0.02654864452779293, -0.02177789993584156, -0.022360585629940033, 0.035944461822509766, 0.016706708818674088, -0.04399281367659569, -0.019884169101715088, -0.00023500921088270843, 0.026894614100456238, -0.06252951920032501, 0.01606939546763897, -0.05812295898795128, 0.012855516746640205, -0.029571330174803734, 0.00010711982031352818, -0.03969550505280495, -0.051531318575143814, -0.007624996360391378, 0.029662374407052994, 0.010570293292403221, 0.02048506587743759, -0.02175969071686268, -0.020867452025413513, -0.004565893206745386, -0.020503273233771324, -0.011790293268859386, 0.041989829391241074, 0.027622971683740616, -0.011972382664680481, 0.042099084705114365, -0.03973191976547241, 0.04971042275428772, -0.010351786389946938, -0.0016809133812785149, 0.036873117089271545, 0.011426114477217197, 0.0033254087902605534, -0.0008905312861315906, 0.012400292791426182, -0.021996406838297844, -0.05925191193819046, -0.0007374623673968017, -0.031046254560351372, 0.007465668022632599, -0.008735742419958115, 0.025201182812452316, 0.0016536000184714794, -0.012937456369400024, 0.030245060101151466, 0.0013349434593692422, -0.08572772145271301, -0.05848713591694832 ]
The accuracy of recent deep learning based clinical decision support systems is promising. However, lack of model interpretability remains an obstacle to widespread adoption of artificial intelligence in healthcare. Using sleep as a case study, we propose a generalizable method to combine clinical interpretability with high accuracy derived from black-box deep learning. Clinician-determined sleep stages from polysomnogram (PSG) remain the gold standard for evaluating sleep quality. However, PSG manual annotation by experts is expensive and time-prohibitive. We propose SERF, interpretable Sleep staging using Embeddings, Rules, and Features to read PSG. SERF provides interpretation of classified sleep stages through meaningful features derived from the AASM Manual for the Scoring of Sleep and Associated Events. In SERF, the embeddings obtained from a hybrid of convolutional and recurrent neural networks are transposed to the interpretable feature space. These representative interpretable features are used to train simple models like a shallow decision tree for classification. Model results are validated on two publicly available datasets. SERF surpasses the current state-of-the-art for interpretable sleep staging by 2%. Using Gradient Boosted Trees as the classifier, SERF obtains 0.766 $\kappa$ and 0.870 AUC-ROC, within 2% of the current state-of-the-art black-box models.
[ 0.00037003649049438536, 0.05014187842607498, -0.0357612781226635, -0.04219070076942444, 0.06600619107484818, -0.012136008590459824, 0.028019342571496964, 0.0029912027530372143, -0.02895141765475273, 0.010300389491021633, 0.006163113750517368, -0.026231277734041214, 0.023149721324443817, -0.03692161664366722, -0.005720853339880705, 0.02440517023205757, 0.03846239671111107, 0.013068083673715591, -0.025679640471935272, -0.022921457886695862, 0.0006066220812499523, -0.005368947051465511, 0.002305223373696208, -0.06577792763710022, 0.057332176715135574, 0.0352286621928215, 0.033383533358573914, 0.02073393203318119, -0.11200127750635147, 0.02701117843389511, 0.014409132301807404, 0.01391456089913845, 0.0038828568067401648, -0.009824840351939201, -0.038995008915662766, -0.03810098022222519, 0.04173417389392853, 0.03707379475235939, 0.025394311174750328, 0.03967979922890663, 0.013657764531672001, -0.03454387187957764, 0.03937545046210289, -0.007670603692531586, 0.032204173505306244, -0.013847984373569489, -0.05835936218500137, -0.011536816135048866, 0.02625029906630516, -0.06216375529766083, 0.010252834297716618, -0.004650868475437164, 0.03591345250606537, -0.014818103983998299, 0.009192360565066338, 0.018879292532801628, 0.06684315204620361, 0.019992075860500336, 0.10066419094800949, 0.03385908156633377, 0.01585480011999607, 0.05029405280947685, -0.03589443117380142, -0.00836490560323, -0.012735200114548206, -0.07703892141580582, 0.015693113207817078, 0.012212095782160759, -0.01846080832183361, -0.05128319561481476, -0.05265277624130249, -0.02446223609149456, 0.014599351212382317, 0.03018784523010254, 0.029350878670811653, 0.001091384794563055, 0.0034334631636738777, 0.029179681092500687, -0.01144170667976141, -0.020600778982043266, 0.053908225148916245, 0.00951573345810175, 0.003958944696933031, 0.03382103890180588, 0.08537054061889648, 0.002019894076511264, -0.023225808516144753, -0.0587398000061512, -0.028361737728118896, 0.013676786795258522, -0.01300150714814663, 0.024195928126573563, -0.003975588828325272, -0.02615519054234028, 0.020201317965984344, -0.06189744547009468, -0.010756916366517544, 0.008811920881271362, 0.005378458183258772, -0.03530475124716759, -0.022407865151762962, -0.002028216142207384, 0.014551796950399876, -0.013172704726457596, -0.009206626564264297, -0.025926927104592323, -0.030777525156736374, 0.02579377219080925, 0.0030649127438664436, 0.13338196277618408, -0.03676944226026535, -0.03256558999419212, -0.015797734260559082, -0.004883887246251106, -0.06037569046020508, -0.023530159145593643, -0.04447333514690399, -0.05215820297598839, 0.0418863482773304, 0.04321788623929024, -0.0025275424122810364, 0.08065309375524521, -0.001063446281477809, 0.062239840626716614, -0.05653325468301773, 0.06341920047998428, 0.0612887442111969, -0.019954031333327293, -0.012116986326873302, 0.05352778360247612, 0.010148214176297188, -0.019630659371614456, -0.034600939601659775, 0.02058175764977932, 0.03534279391169548, 0.0064484430477023125, 0.035057466477155685, 0.04865816608071327, -0.005540144629776478, 0.001808274770155549, -0.013049062341451645, 0.0014147580368444324, -0.00882143247872591, 0.0012352382764220238, 0.05535389482975006, -0.002938892226666212, 0.009658398106694221, 0.056571297347545624, -0.04827772453427315, -0.007722914218902588, -0.04667988047003746, 0.03513355180621147, 0.01302052941173315, 0.024386148899793625, 0.027772055938839912, 0.0070476350374519825, -0.013847984373569489, -0.03254656866192818, -0.0418863482773304, 0.026117146015167236, 0.03079654648900032, -0.010443054139614105, -0.0009160260669887066, 0.0009195926832035184, 0.03865261375904083, 0.07981612533330917, -0.006419910117983818, 0.010300389491021633, -0.06083221733570099, 0.03568518906831741, -0.036389000713825226, -0.0018962512258440256, 0.005625743418931961, -0.02149481140077114, -0.007870334200561047, 0.06809860467910767, 0.04550052061676979, -0.013068083673715591, -0.0781421959400177, 0.008792899549007416, -0.03207101672887802, 0.019744791090488434, -0.017405090853571892, -0.02973131835460663, 0.03749227523803711, -0.005283348262310028, 0.0832400843501091, 0.020258383825421333, 0.07783784717321396, 0.010975669138133526, -0.0055829440243542194, 0.0393374040722847, 0.05269081890583038, -0.05664738640189171, -0.02691606804728508, -0.026212256401777267, 0.008241262286901474, 0.017205359414219856, 0.012953951954841614, 0.01195529941469431, -0.040022194385528564, -0.02507093921303749, 0.000043170923163415864, 0.008012998849153519, 0.016235239803791046, -0.03150035813450813, 0.04477768391370773, -0.03732107952237129, -0.02906554937362671, -0.03247047960758209, -0.024176906794309616, 0.0030554018449038267, -0.07072363048791885, -0.04219070076942444, -0.0206768661737442, -0.01594039984047413, -0.0006705239647999406, -0.008574146777391434, -0.0029222480952739716, 0.019801856949925423, -0.010813982225954533, 0.026839980855584145, 0.018080368638038635, -0.021171437576413155, 0.04687010124325752, 0.005464056972414255, -0.017814062535762787, -0.0172434039413929, 0.00961084384471178, 0.04260918125510216, 0.003830546513199806, -0.015512405894696712, 0.03888087719678879, 0.021209482103586197, 0.01585480011999607, -0.020924152806401253, 0.01746215671300888, -0.03640802577137947, -0.04173417389392853, -0.05440279468894005, -0.0194023959338665, -0.010756916366517544, -0.0319378636777401, 0.0023028457071632147, 0.044207025319337845, -0.010433543473482132, 0.016929540783166885, 0.09693589061498642, 0.002350400434806943, 0.016777366399765015, -0.046299442648887634, -0.007204566150903702, -0.010871048085391521, 0.01591186597943306, -0.0283427145332098, -0.014409132301807404, 0.03330744430422783, 0.009544266387820244, 0.045842915773391724, 0.02082904241979122, 0.05950067937374115, -0.004998018965125084, 0.0377776063978672, 0.05672347545623779, -0.041848305612802505, 0.00004644032378564589, 0.05531584843993187, -0.012839820235967636, 0.058245230466127396, -0.030454151332378387, 0.03895696625113487, -0.01882222667336464, -0.03254656866192818, -0.002453832421451807, -0.031595468521118164, -0.033935170620679855, 0.027410639449954033, -0.019801856949925423, 0.05071253702044487, -0.0019342951709404588, -0.05223429203033447, 0.023149721324443817, 0.03697868436574936, -0.008146152831614017, -0.029902515932917595, -0.040060240775346756, 0.04409289360046387, -0.04831577092409134, -0.053299520164728165, -0.007837045937776566, -0.025869861245155334, -0.0020900375675410032, -0.01080447155982256, -0.006733772344887257, 0.06806056201457977, -0.021570898592472076, 0.009724975563585758, -0.018498852849006653, 0.04633748531341553, 0.008769121952354908, -0.019935010001063347, 0.03454387187957764, 0.062239840626716614, 0.024538323283195496, 0.006367600057274103, 0.06726163625717163, -0.01585480011999607, 0.07216930389404297, -0.06482682377099991, 0.025926927104592323, 0.011489261873066425, 0.032660700380802155, 0.006044226698577404, -0.032185148447752, -0.021418722346425056, 0.0577126145362854, -0.021646985784173012, -0.024576367810368538, 0.009862883947789669, -0.020182296633720398, 0.0429135337471962, -0.020410560071468353, -0.05915828421711922, 0.05581042170524597, 0.006277245469391346, -0.005359436385333538, 0.005159705877304077, 0.04401680827140808, 0.00924467109143734, 0.01685345359146595, -0.01205040980130434, 0.00031118732294999063, -0.018879292532801628, -0.013695809058845043, 0.01869858242571354, -0.005697075743228197, -0.06372355669736862, 0.014703972265124321, 0.0037473253905773163, -0.05189189687371254, 0.05714195594191551, -0.04112546890974045, -0.06931600719690323, -0.020258383825421333, 0.010785449296236038, -0.0031124677043408155, -0.02267417125403881, 0.03471507132053375, -0.04618531093001366, -0.03300309553742409, 0.001023618970066309, -0.020030120387673378, -0.01039549894630909, -0.04930491000413895, -0.027791079133749008, -0.027695968747138977, -0.009872395545244217, -0.01169850304722786, -0.0037164147943258286, -0.026383453980088234, 0.014485219493508339, -0.0658920556306839, -0.04728858172893524, 0.004686534404754639, -0.01067131757736206, -0.020867086946964264, 0.03566616773605347, 0.014352066442370415, 0.01691051945090294, 0.012202585116028786, -0.0028651822358369827, 0.04683205485343933, -0.011165888048708439, 0.005934850312769413, 0.01643497124314308, -0.003951811231672764, 0.0008018943481147289, -0.0017595309764146805, 0.007642070762813091, 0.05577237531542778, -0.03810098022222519, -0.011384640820324421, -0.04576682671904564, 0.022293733432888985, 0.017604820430278778, -0.0002391119342064485, 0.027258463203907013, 0.020391536876559258, -0.013800429180264473, 0.03926131874322891, 0.0022778792772442102, -0.0612887442111969, 0.05862566828727722, -0.09419672936201096, 0.06147896125912666, 0.0004704961902461946, 0.01712927222251892, 0.02082904241979122, 0.033687885850667953, -0.016739321872591972, -0.05409844219684601, 0.03172862157225609, -0.04009828343987465, -0.00497899716719985, -0.044967904686927795, -0.015807244926691055, -0.034810181707143784, 0.018232544884085655, 0.02257906273007393, 0.03186177834868431, -0.03283189609646797, 0.006862170994281769, 0.012288183905184269, 0.009872395545244217, -0.009254181757569313, 0.010576208122074604, -0.0398319773375988, -0.01873662695288658, 0.0028342714067548513, -0.01156534906476736, -0.06684315204620361, 0.047516848891973495, 0.023682335391640663, -0.011793612502515316, 0.013220259919762611, 0.011546327732503414, -0.015959421172738075, -0.022179601714015007, 0.027600858360528946, -0.0592343732714653, -0.029636207967996597, -0.02685900218784809, -0.0053499252535402775, -0.03789173811674118, -0.0648648738861084, -0.017119761556386948, -0.01600697636604309, 0.008402949199080467, -0.0663866251707077, -0.02670682594180107, -0.0157026257365942, -0.007832290604710579, -0.018223034217953682, 0.0038234132807701826, -0.07513672858476639, -0.02579377219080925, 0.001170444767922163, 0.024652455002069473, 0.005173972342163324, -0.004132519941776991, -0.08795752376317978, 0.005559166893362999, -0.04025046154856682, 0.02467147819697857, 0.028304671868681908, -0.0011793612502515316, 0.011308552697300911, -0.02640247531235218, 0.004389316309243441, -0.05154950171709061, 0.012202585116028786, 0.03334549069404602, 0.036598242819309235, 0.022845368832349777, 0.03144329413771629, 0.036331936717033386, -0.06490291655063629, -0.023967664688825607, 0.016178173944354057, 0.020448602735996246, 0.004734089598059654, 0.0398319773375988, -0.0459570474922657, -0.012991996482014656, 0.02343505062162876, 0.024481257423758507, 0.005288104061037302, -0.043940719217061996, 0.06147896125912666, -0.026668783277273178, 0.034296587109565735, -0.015103433281183243, -0.00814139749854803, 0.029084570705890656, -0.015598004683852196, 0.07228343188762665, 0.004249029327183962, 0.04203852266073227, -0.009235159493982792, -0.0005165649927221239, -0.01603550836443901, -0.0037663474213331938, 0.014618373475968838, -0.03157644718885422, 0.014295000582933426, -0.03697868436574936, -0.011137355118989944, -0.027410639449954033, 0.08149006217718124, 0.028628043830394745, 0.006096537224948406, -0.04367441311478615, 0.011508283205330372, 0.015388762578368187, -0.043940719217061996, 0.04340810328722, -0.025831816717982292, 0.004553380887955427, -0.020106207579374313, 0.03110089898109436, 0.04862011969089508, 0.0014409131836146116, 0.027296507731080055, -0.052424512803554535, 0.004520092159509659, 0.06775620579719543, 0.0010783071629703045, 0.012754221446812153, 0.023111676797270775, -0.007199810352176428, 0.010100658982992172, -0.01633986085653305, -0.021532854065299034, 0.07178886234760284, -0.0811857134103775, 0.0169770959764719, 0.014256956055760384, -0.030606327578425407, -0.011536816135048866, -0.034144412726163864, 0.028418803587555885, 0.0032860429491847754, -0.006415154784917831, -0.008640723302960396, -0.010785449296236038, 0.006534041836857796, 0.018812714144587517, 0.028685109689831734, -0.012449870817363262, -0.04104938358068466, -0.038120001554489136, 0.04827772453427315, 0.008797654882073402, 0.029750339686870575, -0.03207101672887802, 0.021057305857539177, 0.013924072496592999, -0.01961163617670536, -0.024595389142632484, -0.01488468050956726, 0.010015060193836689, -0.001960450317710638, 0.01779503934085369, -0.017661886289715767, -0.01151779480278492, -0.03709281608462334, -0.0012055165134370327, 0.032451458275318146, -0.0064484430477023125, -0.0227312371134758, 0.03345962241292, 0.008849965408444405, 0.019992075860500336, -0.0022505351807922125, -0.0024110330268740654, -0.03773956000804901, 0.011165888048708439, 0.05143536999821663, 0.004874376114457846, -0.007875089533627033, 0.02236982062458992, -0.006224935408681631, -0.026136167347431183, 0.045690737664699554, -0.023263853043317795, 0.053756047040224075, 0.06429421156644821, -0.05173972249031067, 0.022712215781211853, 0.02891337312757969, -0.001517001073807478, 0.020962195470929146, 0.03054926171898842, 0.022388841956853867, -0.02328287437558174, -0.018299121409654617, -0.026269322261214256, -0.044245071709156036, -0.041848305612802505, -0.022483952343463898, 0.008750099688768387, 0.019421417266130447, -0.005972894374281168, -0.029046528041362762, -0.04508203640580177, 0.010157724842429161, -0.005635254550725222, 0.033174291253089905, 0.025679640471935272, -0.06189744547009468, 0.02512800507247448, 0.06912578642368317, 0.030967745929956436, 0.06885948032140732, 0.015902355313301086, 0.013847984373569489, 0.023054610937833786, 0.0013850361574441195, -0.0038210353814065456, -0.0024443212896585464, 0.0038329241797327995, -0.00016451020201202482, 0.03079654648900032, -0.04591900110244751, 0.025983992964029312, -0.023758424445986748, 0.029712295159697533, 0.012468892149627209, -0.01535071898251772, 0.0006372355273924768, 0.053147345781326294, -0.021875249221920967, 0.03732107952237129, 0.01843227632343769, 0.0039161453023552895, 0.08445748686790466, 0.00836490560323, -0.004137275740504265, 0.019107555970549583, -0.010205280035734177, -0.04371245577931404, 0.005644765682518482, -0.009192360565066338, -0.04618531093001366, 0.012630579061806202, -0.0035975275095552206, -0.019744791090488434, 0.010509630665183067, 0.02124752476811409, 0.0360085628926754, -0.009710708633065224, 0.026212256401777267, -0.0005837362841702998, 0.02891337312757969, 0.00037419755244627595, -0.03713085874915123, 0.0055306339636445045, -0.019174132496118546, 0.05603868514299393, -0.01709122769534588, 0.005663787480443716, 0.05961481109261513, 0.0127637330442667, 0.044207025319337845, 0.015712136402726173, -0.028076408430933952, 0.017357535660266876, 0.020810021087527275, 0.07601173967123032, -0.029598163440823555, 0.05250059813261032, -0.001225727261044085, 0.008883253671228886, 0.03157644718885422, 0.016739321872591972, -0.014589840546250343, -0.002858049003407359, 0.019440438598394394, -0.02149481140077114, 0.033269401639699936, -0.020657844841480255, -0.029445989057421684, -0.021989380940794945, 0.02957914210855961, 0.005701831541955471, -0.03382103890180588, 0.04192439094185829, -0.002325434237718582, 0.01966870203614235, -0.006733772344887257, -0.07258778810501099, -0.02294047921895981, 0.01997305452823639, 0.020714910700917244, 0.012440359219908714, -0.014057225547730923, -0.025356268510222435, -0.004018388222903013, -0.011708013713359833, -0.024633433669805527, -0.030092734843492508, 0.010081636719405651, -0.016092574223876, -0.010623762384057045, -0.0006925180787220597, 0.0005236982251517475, -0.04622335359454155, 0.007014346309006214, 0.04127764701843262, 0.010309900157153606, -0.012269161641597748, 0.01879369281232357, 0.013648253865540028, 0.0038638347759842873, -0.016387416049838066, 0.017652375623583794, 0.010148214176297188, -0.03536181524395943, -0.014998812228441238, -0.0016121107619255781, 0.018089881166815758, -0.008854720741510391, -0.005906317383050919, 0.010281367227435112, 0.03971784561872482, 0.05021796375513077, 0.03248950093984604, 0.0016430214745923877, -0.005364191718399525, 0.01688198558986187, 0.022636128589510918, 0.04919077828526497, -0.02185622788965702, -0.03283189609646797, -0.00988190621137619, 0.03948958218097687, 0.010205280035734177, -0.0030530239455401897, -0.015559960156679153, 0.0043298727832734585, 0.020848063752055168, -0.026022035628557205, -0.042000479996204376, 0.001871284912340343, 0.02242688648402691, -0.02957914210855961, -0.003000713651999831, 0.04432115703821182, 0.002147103426977992, 0.0015681225340813398, -0.0623159296810627, -0.01090909168124199, 0.013400968164205551, -0.02160894311964512, 0.005516367498785257, 0.020258383825421333, -0.015721647068858147, -0.002376555697992444, -0.05828327313065529, -0.02130459062755108, 0.015816757455468178, -0.021570898592472076, 0.03800586983561516, -0.012649601325392723, -0.03313624858856201, 0.008421971462666988, -0.03619878366589546, -0.019839899614453316, -0.005031307693570852, -0.0037140368949621916, -0.01488468050956726, 0.051663633435964584, 0.012725688517093658, 0.04082112014293671, 0.07445193827152252, 0.030320998281240463, -0.007860823534429073, -0.003457240527495742, 0.02761988155543804, -0.019649680703878403, 0.03412539139389992, 0.03167155757546425, 0.053147345781326294, -0.09792502969503403, 0.001817785669118166, -0.0074233184568583965, 0.015417295508086681, 0.02339700609445572, -0.027087265625596046, -0.002239835448563099, 0.016539590433239937, 0.021285569295287132, 0.00383767974562943, 0.016767853870987892, 0.0015277009224519134, 0.02543235570192337, 0.009853373281657696, -0.0515875443816185, -0.0038543238770216703, 0.012830309569835663, 0.006110803689807653, -0.017205359414219856, 0.010110169649124146, -0.010452564805746078, 0.04907664656639099, 0.01776650734245777, -0.05698978155851364, 0.06593009829521179, -0.04926686733961105, -0.03591345250606537, 0.012535469606518745, -0.023777445778250694, 0.03739716485142708, 0.03372592851519585, 0.0022469686809927225, -0.03543790429830551, -0.020353494212031364, -0.015103433281183243, -0.004874376114457846, -0.015588493086397648, 0.027581837028265, 0.029712295159697533, -0.010357455350458622, 0.023834511637687683, -0.0038923679385334253, -0.029179681092500687, -0.03279385343194008, 0.06262028217315674, 0.004945708438754082, -0.047478802502155304, -0.03695966303348541, -0.034296587109565735, -0.015569471754133701, -0.0028509157709777355, -0.026174211874604225, 0.0013660142431035638, 0.0004963541869074106, 0.025508442893624306, 0.019269241020083427, -0.004094475880265236, 0.013419990427792072, 0.04610922187566757, -0.024481257423758507, 0.00480542192235589, -0.018679561093449593, 0.028513912111520767, -0.02737259492278099, 0.015150988474488258, 0.01631132699549198, 0.01371483039110899, -0.014009671285748482, 0.006833638064563274, -0.017481178045272827, -0.015559960156679153, 0.015445828437805176, 0.0030411353800445795, -0.006814615800976753, -0.005521122831851244, 0.022103512659668922, 0.03948958218097687, 0.03167155757546425, -0.03574225679039955, 0.0017036539502441883, -0.022388841956853867, 0.006239201873540878, 0.014209401793777943, 0.07859872281551361, -0.015588493086397648, 0.007475628983229399, 0.003138622734695673, 0.06292463093996048, 0.03180471062660217, 0.025603553280234337, -0.007965444587171078, 0.022617105394601822, -0.054973453283309937, 0.04310375452041626, 0.03694063797593117, -0.006990569178014994, -0.07133233547210693, -0.0449298620223999, -0.0018546407809481025, -0.009491955861449242, 0.006243957206606865, 0.024024730548262596, 0.030606327578425407, -0.034753113985061646, 0.0036094163078814745, -0.009316002950072289, 0.005825473926961422, 0.046451617032289505, 0.03441071882843971, 0.028418803587555885, 0.001421891269274056, 0.01529365312308073, 0.022997545078396797, -0.03998415172100067, -0.01547436136752367, -0.005468812305480242, -0.07890307158231735, -0.007594516035169363, 0.026516607031226158, -0.001552667235955596, 0.021666008979082108, 0.04447333514690399, 0.014038204215466976, -0.014456686563789845, 0.03125307336449623, 0.0034310854971408844, -0.011270509101450443, 0.008716811425983906, -0.019744791090488434, -0.03910914063453674, -0.06954427063465118, 0.0024443212896585464, -0.007038123905658722, 0.010756916366517544, -0.030777525156736374, 0.017661886289715767, -0.031081877648830414, -0.01970674656331539, -0.045538563281297684, -0.012440359219908714, 0.055582158267498016, 0.005678053945302963, -0.017994770780205727, -0.023454071953892708, -0.009044940583407879, 0.05904415249824524, -0.020771976560354233, 0.015112943947315216, 0.027334552258253098, 0.019839899614453316, -0.007604027166962624, -0.007261632010340691, -0.027562815696001053, -0.02879924140870571, -0.010062615387141705, 0.02685900218784809, -0.01567409187555313, -0.020087186247110367, 0.011631926521658897, 0.024728544056415558, -0.0064484430477023125, 0.029788384214043617, 0.013629231601953506, -0.05908219516277313, 0.014903702773153782, 0.0007073790184222162, -0.015816757455468178, 0.011736546643078327, 0.06269636750221252, -0.03336451202630997, 0.0046984232030808926, 0.018898313865065575, -0.05953872203826904, 0.004253785125911236, -0.027315529063344002, -0.005597210489213467, -0.008046287111938, 0.011356107890605927, -0.02849489077925682, -0.03825315460562706, 0.03294602781534195, -0.0014504241989925504, -0.012040898203849792, -0.014275978319346905, -0.016092574223876, -0.016292305663228035, 0.0010509630665183067, 0.0010503686498850584, -0.009054451249539852, -0.01639692671597004, 0.013838473707437515, 0.005231038201600313, -0.019411906599998474, -0.007546961307525635, -0.02625029906630516, -0.04641357436776161, -0.001499167992733419, 0.02343505062162876, 0.010576208122074604, 0.004570025019347668, 0.026440519839525223, -0.004912420175969601, -0.006681462284177542, 0.004945708438754082, -0.022084491327404976, -0.03834826499223709, -0.011327574960887432, 0.008150908164680004, -0.02685900218784809, -0.03422049805521965, 0.026269322261214256, 0.027657924219965935, -0.02216057851910591, 0.036179762333631516, -0.020905129611492157, -0.04504399374127388, 0.002401521895080805, 0.007965444587171078, -0.02073393203318119, 0.012792265973985195, -0.04401680827140808, -0.0052405488677322865, -0.009767774492502213, 0.008674012497067451, -0.01848934218287468, 0.015892844647169113, -0.0010664184810593724, -0.00892605260014534, 0.02415788546204567, 0.0042466516606509686, 0.03264167532324791, -0.008702545426785946, 0.01438059937208891, 0.019630659371614456, -0.030359042808413506, -0.04919077828526497, 0.029807405546307564, 0.009453912265598774, 0.01603550836443901, -0.017956726253032684, -0.005844496190547943, -0.0011811446165665984, 0.03385908156633377, -0.03034001961350441, -0.03336451202630997, 0.008355394005775452, -0.016996117308735847, -0.024937784299254417, -0.023111676797270775, 0.008864231407642365, -0.0383102186024189 ]
Session-based recommender systems (SBRSs) have shown superior performance over conventional methods. However, they show limited scalability on large-scale industrial datasets since most models learn one embedding per item. This leads to a large memory requirement (of storing one vector per item) and poor performance on sparse sessions with cold-start or unpopular items. Using one public and one large industrial dataset, we experimentally show that state-of-the-art SBRSs have low performance on sparse sessions with sparse items. We propose M2TRec, a Metadata-aware Multi-task Transformer model for session-based recommendations. Our proposed method learns a transformation function from item metadata to embeddings, and is thus, item-ID free (i.e., does not need to learn one embedding per item). It integrates item metadata to learn shared representations of diverse item attributes. During inference, new or unpopular items will be assigned identical representations for the attributes they share with items previously observed during training, and thus will have similar representations with those items, enabling recommendations of even cold-start and sparse items. Additionally, M2TRec is trained in a multi-task setting to predict the next item in the session along with its primary category and subcategories. Our multi-task strategy makes the model converge faster and significantly improves the overall performance. Experimental results show significant performance gains using our proposed approach on sparse items on the two datasets.
[ 0.0019939630292356014, -0.0016103486996144056, -0.04128480702638626, -0.02882617712020874, 0.03409905359148979, -0.05053313449025154, -0.062243249267339706, 0.0028734691441059113, -0.008142189122736454, 0.03275172784924507, 0.019095471128821373, -0.04008718207478523, 0.02654736116528511, -0.009514467790722847, 0.024434883147478104, 0.014388137497007847, 0.0026198055129498243, 0.0075683267787098885, -0.017964379861950874, -0.04071925953030586, 0.020110124722123146, -0.023885972797870636, 0.007776247803121805, -0.014537841081619263, 0.023852704092860222, 0.016492299735546112, -0.01949467882514, 0.004586738534271717, -0.05289511755108833, -0.004312282893806696, 0.020675670355558395, 0.005759413354098797, -0.0039005992002785206, -0.026746965944767, -0.049501847475767136, -0.033134300261735916, 0.10499182343482971, 0.03413232043385506, -0.019178638234734535, 0.021307751536369324, 0.013672889210283756, 0.003977530170232058, -0.05083254352211952, -0.003010696964338422, 0.0222725048661232, -0.01901230216026306, -0.015461009927093983, -0.023303793743252754, -0.0051813931204378605, -0.041318073868751526, -0.04078579694032669, -0.015494277700781822, -0.010121596977114677, 0.028842810541391373, -0.0461418442428112, 0.04760560765862465, 0.03459806367754936, 0.019827352836728096, 0.05086581036448479, 0.040253520011901855, -0.02120794914662838, 0.04374659061431885, 0.009872091934084892, -0.032352518290281296, -0.005318620707839727, 0.011294271796941757, 0.010221399366855621, -0.032701823860406876, -0.0022767356131225824, -0.028426967561244965, -0.07425276935100555, -0.027512114495038986, 0.0405861921608448, -0.011161202564835548, 0.04384639486670494, 0.0014336156891658902, 0.04291490837931633, 0.027146173641085625, -0.007522583939135075, -0.008666150271892548, 0.03892282396554947, 0.0501006580889225, 0.047372736036777496, 0.039954110980033875, 0.039388567209243774, -0.027295878157019615, -0.013647939078509808, -0.04534342512488365, 0.03330063819885254, 0.016226159408688545, -0.03110499121248722, -0.010055062361061573, -0.013639621436595917, 0.00047717883717268705, -0.06653474271297455, 0.02804439328610897, 0.003418222302570939, 0.03439846262335777, -0.0612119622528553, 0.010512488894164562, 0.011435658670961857, -0.049435313791036606, -0.004283173941075802, -0.023802803829312325, 0.04098540171980858, -0.007410306949168444, -0.01491209864616394, 0.031071724370121956, -0.03662737458944321, 0.03566262125968933, 0.07804524898529053, -0.05572284385561943, -0.01625942811369896, 0.0032581230625510216, -0.016899824142456055, -0.0075101088732481, -0.08922308683395386, -0.04926897585391998, -0.006507929414510727, -0.04467807710170746, 0.005385155789554119, -0.04085233062505722, -0.020592501387000084, -0.004172975663095713, -0.04015371575951576, 0.05429234728217125, -0.007801198400557041, 0.0275453832000494, 0.05761908367276192, 0.03260202333331108, -0.03506380692124367, -0.014221800491213799, -0.0009803478606045246, -0.09254982322454453, -0.022605178877711296, 0.03686024621129036, -0.013473285362124443, -0.0007017335738055408, -0.0009751498000696301, -0.05040006712079048, -0.032069746404886246, -0.04211648926138878, -0.04135134071111679, -0.005805156193673611, -0.012849521823227406, 0.010005162097513676, -0.06739969551563263, 0.07977515459060669, -0.023653101176023483, 0.050699472427368164, -0.044245604425668716, 0.013905760832130909, -0.030872119590640068, 0.00023365129891317338, -0.020160026848316193, 0.03992084413766861, -0.03296796232461929, -0.006324958987534046, -0.027013104408979416, 0.02162379026412964, 0.047572340816259384, 0.007011098321527243, -0.0006414364906959236, 0.041750550270080566, 0.07584960758686066, 0.008699417114257812, 0.02604835107922554, 0.02867647260427475, -0.04970145225524902, 0.048503827303647995, -0.031204793602228165, 0.05229630693793297, 0.026796866208314896, 0.020625770092010498, 0.04461154341697693, 0.014562791213393211, 0.0823034718632698, -0.029774297028779984, -0.020259829238057137, 0.003694757353514433, -0.004877828061580658, 0.03529667854309082, -0.02255527675151825, 0.029990535229444504, 0.05266224592924118, 0.0401204489171505, 0.04524362459778786, 0.009040407836437225, 0.012400412000715733, -0.017748141661286354, 0.02070893719792366, 0.04291490837931633, 0.04833748936653137, 0.04384639486670494, -0.0023869338911026716, -0.0019180718809366226, -0.07924287766218185, 0.0080631785094738, 0.034830935299396515, 0.023370327427983284, -0.027428947389125824, -0.039388567209243774, 0.0528285838663578, -0.007094266824424267, 0.04677392169833183, 0.011934668757021427, -0.0035388164687901735, -0.015419426374137402, -0.02270497940480709, -0.06048008054494858, 0.004424560349434614, -0.07451891154050827, -0.03692677989602089, -0.012816254049539566, 0.010479222051799297, 0.010845162905752659, 0.001241288729943335, 0.011784966103732586, -0.03275172784924507, 0.05209670215845108, 0.02769508585333824, 0.0018941608723253012, 0.045077286660671234, 0.002447230974212289, 0.037392523139715195, -0.015577445738017559, -0.019112104550004005, -0.011585361324250698, 0.01643408089876175, 0.0023495079949498177, 0.03795807063579559, -0.012550115585327148, -0.028693106025457382, -0.03872321918606758, 0.008321001194417477, 0.007106741890311241, 0.002075052121654153, -0.06127849593758583, -0.05036680027842522, -0.006008918862789869, -0.002228913828730583, 0.07372049242258072, 0.0013327740598469973, -0.023802803829312325, 0.03308439999818802, 0.02669706381857395, -0.02613152004778385, 0.054192546755075455, 0.011643579229712486, 0.02789469063282013, 0.002224755473434925, -0.0011518826941028237, -0.004802976734936237, 0.008138030767440796, 0.007426940370351076, 0.040386587381362915, 0.04461154341697693, -0.02683013491332531, -0.01536952517926693, -0.04531015828251839, 0.03849034756422043, 0.0009673527674749494, 0.009048724547028542, 0.014462988823652267, 0.008558031171560287, 0.04630817845463753, 0.05672086775302887, -0.0033080242574214935, 0.030406376346945763, 0.021756859496235847, 0.025632508099079132, -0.07644841820001602, -0.0328681617975235, -0.058184631168842316, -0.01600160449743271, -0.036261431872844696, -0.0012132193660363555, -0.056754134595394135, 0.06324127316474915, -0.002447230974212289, 0.03699331730604172, -0.023653101176023483, 0.005152284167706966, 0.028426967561244965, 0.007048523984849453, -0.030123604461550713, 0.045509763062000275, 0.01544437650591135, -0.019877253100275993, -0.014770712703466415, -0.027994493022561073, -0.05422581359744072, -0.053061455488204956, 0.015311307273805141, 0.08516446501016617, 0.04281510412693024, 0.030772317200899124, 0.03918896242976189, 0.035263411700725555, -0.0517972968518734, -0.008441595360636711, 0.022372307255864143, 0.03216954693198204, -0.023669734597206116, -0.008707733824849129, 0.0023411912843585014, -0.0027008946053683758, 0.054625023156404495, 0.012533482164144516, -0.05964839458465576, 0.01999368891119957, 0.002174854278564453, -0.002422280376777053, 0.010745360516011715, 0.010121596977114677, 0.029923999682068825, -0.009880408644676208, -0.0355960875749588, -0.03878975287079811, -0.05286185070872307, -0.03416559100151062, 0.019810719415545464, -0.07817832380533218, -0.014171900227665901, -0.02179012820124626, -0.033699847757816315, 0.007148326374590397, 0.0596151277422905, 0.01851329207420349, 0.023470129817724228, -0.006420602556318045, -0.04161747917532921, 0.001059877686202526, -0.007460207678377628, 0.010238032788038254, 0.0017756458837538958, -0.0018099528970196843, -0.008973873220384121, -0.0175152700394392, -0.05016719549894333, -0.02776162140071392, -0.008221198804676533, 0.03423212468624115, 0.046873725950717926, 0.011186153627932072, 0.006470503751188517, -0.05642145872116089, 0.0623430535197258, 0.01714932918548584, -0.0087576350197196, 0.0008925011497922242, -0.011626945808529854, 0.012624966911971569, 0.052129969000816345, 0.06663454324007034, -0.03968797251582146, 0.0038111931644380093, 0.012267342768609524, 0.0029088156297802925, 0.005925750359892845, -0.012450313195586205, -0.07950901240110397, -0.05232957378029823, 0.008108921349048615, -0.02854340337216854, -0.02134101837873459, -0.003052281215786934, -0.024800824001431465, 0.022804781794548035, 0.010662192478775978, -0.028909344226121902, -0.0035429750569164753, -0.009115259163081646, -0.0247675571590662, -0.049069371074438095, 0.025632508099079132, 0.029691128060221672, -0.014654276892542839, 0.003384954994544387, 0.05183056369423866, 0.022405574098229408, -0.046574316918849945, -0.03552955016493797, 0.0036323810927569866, -0.008558031171560287, 0.06653474271297455, 0.041384607553482056, -0.014421405270695686, -0.07385355979204178, 0.006944563705474138, 0.07385355979204178, -0.03792480379343033, -0.0004865352821070701, -0.08130545169115067, 0.0411517359316349, -0.021474087610840797, 0.017415467649698257, 0.0008192089735530317, 0.006428919266909361, 0.007451890967786312, -0.046075306832790375, 0.03188677504658699, -0.04314778000116348, 0.04980125278234482, -0.04278183728456497, -0.015095069073140621, 0.04587570205330849, -0.0007854218129068613, 0.04883649945259094, -0.003725945483893156, -0.006545355077832937, -0.0689299926161766, -0.008765951730310917, 0.021723592653870583, 0.019877253100275993, 0.014313286170363426, -0.04527689144015312, -0.019261807203292847, -0.013988928869366646, -0.02207290008664131, -0.01764833927154541, 0.008387535810470581, 0.05203016847372055, 0.019344976171851158, -0.013714473694562912, 0.04055292531847954, -0.0316871702671051, -0.002133270027115941, -0.015851901844143867, -0.0328182615339756, 0.06397315114736557, -0.010886747390031815, 0.03240241855382919, -0.044511742889881134, 0.008503971621394157, 0.018895866349339485, 0.0034514896105974913, -0.008616249077022076, -0.016142992302775383, -0.020908541977405548, -0.042881641536951065, 0.017531903460621834, -0.004545154515653849, 0.025931915268301964, 0.029641227796673775, -0.04008718207478523, -0.013415067456662655, 0.014113682322204113, -0.00918179377913475, -0.014371504075825214, -0.07737990468740463, -0.0022746564354747534, -0.04667412117123604, -0.03366657719016075, 0.0283937007188797, -0.04817115142941475, 0.04204995557665825, -0.018812697380781174, -0.02611488662660122, -0.02648082748055458, -0.023021019995212555, 0.028909344226121902, 0.00016451753617729992, -0.022255871444940567, 0.012142590247094631, 0.01771487481892109, -0.03273509070277214, 0.00017452373867854476, 0.0022850525565445423, -0.02285468392074108, 0.01437982078641653, 0.012325560674071312, 0.0036095096729695797, 0.03935530036687851, 0.01829705387353897, 0.032834894955158234, -0.005148125346750021, -0.07791218161582947, 0.016883190721273422, 0.02554934099316597, 0.0384238138794899, 0.021590523421764374, 0.028726374730467796, -0.02084200829267502, -0.004528520628809929, 0.05086581036448479, -0.013839226216077805, 0.021740226075053215, -0.020243193954229355, -0.023470129817724228, -0.03752559423446655, 0.015660613775253296, -0.005751096643507481, -0.0063623846508562565, -0.02184002846479416, -0.055257100611925125, -0.01601823791861534, -0.037259455770254135, 0.026281222701072693, -0.022804781794548035, -0.013972295448184013, 0.024717656895518303, 0.007963377051055431, 0.03137113153934479, 0.035762421786785126, 0.02967449463903904, 0.007651495281606913, -0.014296652749180794, -0.022022999823093414, 0.010412686504423618, 0.00841248594224453, 0.06344087421894073, 0.028061026707291603, 0.020259829238057137, -0.029192117974162102, 0.008333476260304451, 0.002162378979846835, -0.03123806044459343, -0.015144970268011093, -0.010529122315347195, -0.014670910313725471, 0.013173879124224186, -0.025066964328289032, 0.01906220242381096, -0.06091255694627762, 0.007992485538125038, 0.006383176892995834, 0.004956838209182024, 0.10379419475793839, -0.011976253241300583, -0.02327052503824234, 0.016558833420276642, -0.017398834228515625, -0.03636123612523079, 0.0032144596334546804, -0.005522383376955986, 0.05222977325320244, -0.012832888402044773, 0.0067366426810622215, -0.04041985422372818, -0.016999626532197, -0.012375461868941784, -0.0029711921233683825, 0.0038340643513947725, -0.0014824771787971258, 0.015011901035904884, 0.011252688243985176, -0.024950528517365456, -0.010944965295493603, -0.0021062404848635197, -0.0059881266206502914, -0.03439846262335777, 0.006079611834138632, 0.003052281215786934, -0.04730620235204697, -0.0038902030792087317, -0.012475264258682728, -0.01145229209214449, 0.03075568377971649, -0.03265192359685898, -0.0014533682260662317, 0.023935873061418533, -0.015851901844143867, -0.019245173782110214, 0.029092315584421158, 0.020243193954229355, 0.023786170408129692, 0.04760560765862465, 0.013015858829021454, -0.01714932918548584, 0.00370099488645792, 0.035263411700725555, -0.01829705387353897, -0.008874070830643177, -0.0017299032770097256, 0.047006793320178986, 0.002102081896737218, -0.03330063819885254, -0.004603372421115637, 0.00674080103635788, 0.044578276574611664, -0.022089533507823944, 0.013423384167253971, 0.043447185307741165, 0.029375087469816208, 0.032352518290281296, -0.0445450097322464, -0.035828959196805954, 0.00306891486980021, -0.004299807827919722, 0.040885597467422485, 0.059748198837041855, 0.008558031171560287, -0.04261550307273865, -0.03962143883109093, -0.041251540184020996, -0.008857437409460545, -0.014263384975492954, 0.05422581359744072, -0.023852704092860222, 0.0066576325334608555, 0.048071350902318954, 0.020758839324116707, 0.006453869864344597, -0.022505376487970352, -0.04041985422372818, 0.05708680674433708, -0.005672086495906115, 0.0029670335352420807, -0.0007220059051178396, -0.016359228640794754, -0.016467347741127014, 0.048636894673109055, 0.003690598998218775, 0.030289940536022186, 0.028626572340726852, 0.08696090430021286, -0.02702973783016205, -0.027944590896368027, -0.05079927295446396, 0.05089907720685005, -0.017132695764303207, 0.058617107570171356, 0.012857838533818722, -0.021008344367146492, 0.01829705387353897, 0.03449826315045357, 0.004586738534271717, 0.0035741631872951984, 0.006520404480397701, -0.03922222927212715, 0.015876851975917816, 0.02461785450577736, -0.06141156703233719, 0.009763972833752632, -0.011261004954576492, 0.05948205664753914, 0.0161263570189476, 0.03128796070814133, 0.027878057211637497, -0.026464194059371948, 0.017132695764303207, 0.006162780337035656, 0.06693395227193832, 0.017565172165632248, 0.004690699279308319, -0.013656255789101124, 0.008462387137115002, 0.04264876991510391, 0.02526656724512577, -0.027927957475185394, 0.01046258769929409, 0.00491109536960721, 0.03459806367754936, -0.004744758829474449, 0.002788221463561058, 0.0017652498790994287, 0.003767529735341668, 0.040952131152153015, -0.024218644946813583, 0.02262181229889393, 0.008765951730310917, -0.002149903913959861, -0.02376953698694706, 0.04368005692958832, -0.011809916235506535, -0.02440161630511284, 0.0025262408889830112, -0.0019430223619565368, -0.0003261761739850044, 0.022721614688634872, -0.013805958442389965, -0.06806503981351852, 0.024883992969989777, 0.01801428198814392, -0.04318104684352875, -0.0026509936433285475, -0.008907338604331017, 0.0030460436828434467, -0.054192546755075455, 0.007547534536570311, -0.019694283604621887, -0.0272626094520092, 0.003906836733222008, 0.03479766845703125, -0.02619805373251438, 0.00380911398679018, 0.015186554752290249, -0.030439643189311028, 0.05116521567106247, -0.03958817198872566, -0.022887950763106346, 0.033117666840553284, 0.03095528855919838, -0.006462186574935913, 0.015743782743811607, -0.043380651623010635, 0.004894461948424578, 0.025948548689484596, -0.02277151495218277, -0.029474889859557152, -0.006932088173925877, -0.026430925354361534, 0.014720811508595943, 0.016999626532197, 0.04298144206404686, 0.011011499911546707, -0.0300404354929924, -0.03200320899486542, 0.014138632453978062, 0.005031690001487732, -0.02411884441971779, -0.01536952517926693, 0.002141586970537901, 0.014113682322204113, 0.021657058969140053, 0.0023723794147372246, 0.02782815508544445, -0.032635290175676346, 0.025216666981577873, -0.016991309821605682, 0.021756859496235847, 0.0522630400955677, -0.030572714284062386, -0.023969139903783798, 0.017007943242788315, 0.025100231170654297, 0.005709512624889612, 0.023969139903783798, -0.0012215363094583154, 0.034331925213336945, -0.06713355332612991, -0.021174680441617966, -0.0059382254257798195, 0.012541798874735832, 0.013473285362124443, -0.028576672077178955, 0.0137726916000247, -0.018030915409326553, -0.028776274994015694, 0.005942384246736765, -0.025599241256713867, -0.031421031802892685, -0.031570736318826675, 0.012283976189792156, 0.044245604425668716, 0.022505376487970352, 0.055057499557733536, 0.010088330134749413, 0.023935873061418533, 0.023386960849165916, -0.028127562254667282, 0.016567150130867958, -0.008616249077022076, -0.06314147263765335, 0.025516072288155556, -0.02767845243215561, 0.004337233491241932, 0.03250221908092499, -0.08370070159435272, 0.02925865165889263, 0.017814677208662033, -0.03196994215250015, 0.024717656895518303, 0.06350740790367126, 0.025599241256713867, -0.05529037117958069, -0.008029911667108536, -0.004848719108849764, -0.05941552296280861, 0.008479021489620209, -0.00008550754137104377, 0.041251540184020996, -0.048071350902318954, 0.03599529340863228, 0.019461411982774734, 0.020725572481751442, 0.03416559100151062, -0.06906305998563766, 0.029874099418520927, -0.01440477091819048, 0.05745274946093559, 0.04777194559574127, 0.043380651623010635, -0.026514094322919846, 0.017847944051027298, 0.008067336864769459, -0.017165962606668472, 0.03123806044459343, -0.0031416872516274452, 0.016916457563638687, 0.023087555542588234, 0.015885168686509132, 0.003946342039853334, 0.04105193540453911, -0.015544178895652294, 0.030057068914175034, -0.008287733420729637, -0.006112879142165184, -0.016642002388834953, 0.05771888792514801, -0.0075433761812746525, 0.047439269721508026, 0.053493931889534, -0.03852361440658569, -0.024933893233537674, -0.007281395606696606, -0.006715850438922644, -0.002438914030790329, 0.01821388490498066, 0.008990506641566753, 0.001806834014132619, -0.0009501992608420551, 0.016242792829871178, 0.01828042045235634, -0.011618629097938538, -0.04161747917532921, 0.0014575266977772117, -0.006981989368796349, -0.03356677666306496, 0.01771487481892109, -0.0344649963080883, -0.016384180635213852, -0.02105824463069439, -0.024285180494189262, -0.005094066262245178, 0.01504516787827015, 0.0048362440429627895, 0.04471134394407272, 0.032918062061071396, 0.012891106307506561, -0.00928991287946701, -0.02283805049955845, -0.02648082748055458, -0.01533625740557909, 0.014255068264901638, 0.0009096546564251184, 0.009589319117367268, 0.019378243014216423, 0.08263614773750305, 0.026381025090813637, 0.017049526795744896, -0.033633310347795486, -0.025848746299743652, 0.0014970316551625729, 0.01576041616499424, -0.0003599633346311748, 0.0405861921608448, -0.002447230974212289, 0.05652126297354698, 0.021041611209511757, 0.05901631340384483, 0.026164786890149117, -0.038889557123184204, -0.028210729360580444, 0.015253089368343353, 0.02880954183638096, 0.061677705496549606, 0.027944590896368027, 0.02055923454463482, 0.06320800632238388, -0.006266741082072258, -0.04098540171980858, 0.004915254190564156, 0.025100231170654297, 0.010953282006084919, 0.006853078491985798, -0.047006793320178986, 0.003757133614271879, -0.025582607835531235, 0.0009839864214882255, 0.0023349535185843706, -0.03772519901394844, 0.0478384792804718, -0.0006944563356228173, 0.030057068914175034, 0.026946570724248886, -0.005301987286657095, 0.0384238138794899, -0.02283805049955845, 0.04570936784148216, -0.0063623846508562565, 0.026813499629497528, -0.007015256676822901, 0.021257849410176277, -0.008017436601221561, -0.030589347705245018, -0.021008344367146492, -0.003139608073979616, -0.030140237882733345, 0.0036635692231357098, 0.03802460432052612, 0.011161202564835548, -0.05099887773394585, 0.013182195834815502, -0.0011820312356576324, -0.010080013424158096, 0.01986061967909336, -0.027811521664261818, 0.031354498118162155, 0.011443975381553173, -0.035196878015995026, -0.06766583025455475, -0.02626458927989006, 0.030589347705245018, 0.003680202877148986, -0.0013701998395845294, -0.015120020136237144, 0.041817083954811096, -0.025432905182242393, -0.023752901703119278, -0.02533310279250145, 0.012508531101047993, 0.0087576350197196, -0.012209124863147736, -0.0177980437874794, 0.0032227765768766403, -0.019228540360927582, 0.0400206483900547, 0.001435694983229041, -0.01758180558681488, 0.04973471909761429, 0.05352719873189926, 0.07445237785577774, -0.005160600878298283, 0.010770311579108238, 0.013306948356330395, 0.015527545474469662, 0.02335369400680065, 0.0035180244594812393, -0.06946226954460144, -0.00016061901987995952, -0.022388940677046776, -0.011976253241300583, 0.039255496114492416, 0.02426854707300663, -0.023237258195877075, 0.008158822543919086, -0.021241215988993645, 0.017964379861950874, -0.020891908556222916, 0.011643579229712486, -0.02014339342713356, 0.04710659757256508, -0.016600416973233223, -0.03258538991212845, -0.017024576663970947, -0.024035675451159477, -0.0018827252788469195, -0.014479623176157475, -0.06826464086771011, -0.008154664188623428, -0.04504401981830597, -0.023520030081272125, -0.010479222051799297, 0.03539648279547691, -0.02290458418428898, 0.016525566577911377, -0.004881986416876316, 0.028493503108620644, -0.03328400477766991, 0.021008344367146492, -0.004416243638843298, 0.003711391007527709, -0.04767214134335518, 0.007214860990643501, -0.03082221932709217, 0.005439214874058962, -0.049568381160497665, 0.03749232739210129, -0.03529667854309082, -0.027512114495038986, 0.014953683130443096, 0.005609710235148668, 0.016592100262641907, 0.009647537022829056, 0.025166764855384827, -0.02305428683757782, 0.002777825342491269, 0.03762539476156235, 0.040253520011901855, -0.005069115664809942, 0.044944215565919876, 0.03243568539619446, 0.011477243155241013, -0.013756057247519493, 0.0022933692671358585, -0.004466144368052483, -0.03912242874503136, -0.016142992302775383, 0.002777825342491269, -0.038689952343702316, 0.051131948828697205, -0.014446355402469635, -0.06756602972745895, 0.0013504473026841879, -0.03679371252655983, 0.024218644946813583, -0.01682497188448906, 0.010761993937194347, -0.06287533044815063, -0.04128480702638626, -0.011843184009194374, 0.06703375279903412, 0.004715649876743555, -0.0406859926879406, 0.032918062061071396, -0.02676359936594963, -0.03765866160392761, 0.02120794914662838, 0.02070893719792366, -0.01650061644613743, -0.06497117131948471, -0.008362585678696632, 0.0035637670662254095, -0.014462988823652267, 0.005435056518763304, 0.0010432439157739282, -0.009980211034417152, -0.026497460901737213, 0.036760445684194565, -0.008641199208796024, 0.019195273518562317, -0.018163984641432762 ]
Machine programming (MP) is an emerging field at the intersection of deterministic and probabilistic computing, and it aims to assist software and hardware engineers, among other applications. Along with powerful compute resources, MP systems often rely on vast amount of open-source code to learn interesting properties about code and programming and solve problems in the areas of debugging, code recommendation, auto-completion, etc. Unfortunately, several of the existing MP systems either do not consider quality of code repositories or use atypical quality measures than those typically used in software engineering community to select them. As such, impact of quality of code repositories on the performance of these systems needs to be studied. In this preliminary paper, we evaluate impact of different quality repositories on the performance of a candidate MP system. Towards that objective, we develop a framework, named GitRank, to rank open-source repositories on quality, maintainability, and popularity by leveraging existing research on this topic. We then apply GitRank to evaluate correlation between the quality measures used by the candidate MP system and the quality measures used by our framework. Our preliminary results reveal some correlation between the quality measures used in GitRank and ControlFlag's performance, suggesting that some of the measures used in GitRank are applicable to ControlFlag. But it also raises questions around right quality measures for code repositories used in MP systems. We believe that our findings also generate interesting insights towards code quality measures that affect performance of MP systems.
[ -0.020937960594892502, 0.008462831377983093, -0.03367602825164795, -0.019009720534086227, 0.002273959806188941, 0.04113578796386719, -0.023080449551343918, 0.04343409463763237, -0.01933109387755394, 0.000025753994123078883, 0.07027363777160645, -0.0145007548853755, 0.0610414557158947, -0.05788615345954895, -0.03225419670343399, 0.037318259477615356, 0.0271317008882761, -0.009694762527942657, -0.0458492636680603, -0.038486890494823456, -0.009285741485655308, -0.05313372611999512, -0.030131185427308083, 0.03540949895977974, 0.005487693008035421, -0.003744486253708601, -0.005546124652028084, 0.005025110207498074, -0.04877083748579025, 0.0297026876360178, 0.015679122880101204, 0.013653497211635113, -0.02352842316031456, -0.0182988028973341, -0.01632186956703663, -0.030481774359941483, 0.048147570341825485, -0.004160810727626085, 0.0018478967249393463, 0.028865167871117592, -0.0535622239112854, -0.02132750302553177, -0.005249097943305969, 0.017412591725587845, 0.010868261568248272, 0.0039830817840993404, -0.007883385755121708, -0.04179801046848297, -0.03737669438123703, -0.06910500675439835, 0.04144742339849472, 0.022515609860420227, 0.008998453617095947, -0.008005117997527122, -0.010858523659408092, -0.018590960651636124, 0.027404380962252617, 0.013147090561687946, 0.06427466869354248, -0.0281834676861763, -0.020996391773223877, 0.042577099055051804, -0.05652275308966637, -0.009329564869403839, 0.012182970531284809, -0.030929747968912125, -0.03714296594262123, -0.00949999038130045, 0.027053792029619217, -0.003440155414864421, -0.01148179266601801, -0.014588401652872562, -0.00020892309839837253, 0.028826214373111725, 0.011968721635639668, 0.0007839561440050602, 0.07101377099752426, 0.018444880843162537, -0.020314689725637436, 0.02572934329509735, 0.010069698095321655, 0.03887643665075302, -0.0014169642236083746, 0.015766771510243416, 0.0023202181328088045, -0.010965648107230663, 0.05184823274612427, -0.07709064334630966, -0.00405125180259347, 0.01698409393429756, -0.0292352344840765, 0.012075846083462238, 0.0458492636680603, 0.05582157522439957, 0.001358532696031034, 0.009573030285537243, -0.005258836317807436, -0.01686723157763481, -0.02132750302553177, 0.01548435166478157, -0.07533770054578781, -0.01605892740190029, 0.01737363636493683, -0.035351067781448364, 0.021639138460159302, -0.046978939324617386, -0.04370677471160889, -0.026742156594991684, 0.0514586865901947, 0.14342989027500153, -0.04744638875126839, 0.036733947694301605, -0.01596154272556305, -0.017519716173410416, -0.0245607141405344, 0.015893371775746346, -0.06462525576353073, -0.04440795257687569, 0.014929252676665783, -0.03833107277750969, -0.02876778319478035, 0.04230441898107529, -0.031845174729824066, -0.016146576032042503, -0.038389503955841064, 0.056444842368364334, -0.009972311556339264, -0.0460829883813858, 0.008998453617095947, 0.00884750485420227, -0.05441921949386597, 0.028105558827519417, -0.008409269154071808, -0.037571463733911514, 0.03307223692536354, -0.015240887179970741, 0.0661834329366684, 0.007683744188398123, -0.018590960651636124, -0.04238232597708702, -0.03521472588181496, -0.02025625854730606, -0.01909736730158329, 0.01747102290391922, 0.06135309115052223, -0.023840058594942093, -0.001738337567076087, 0.1061895415186882, -0.023547900840640068, 0.0544971264898777, -0.04510913044214249, 0.025826729834079742, -0.018230631947517395, 0.0006877876585349441, 0.053172677755355835, 0.012475128285586834, 0.004360451828688383, 0.04312245920300484, -0.008019725792109966, -0.009685023687779903, 0.00942695140838623, -0.029176803305745125, -0.0030116576235741377, 0.06357348710298538, 0.010001528076827526, 0.03539001941680908, -0.03170883655548096, -0.019175276160240173, -0.0734289363026619, 0.03342282772064209, 0.03690924122929573, -0.02366476319730282, 0.015143501572310925, 0.012591991573572159, 0.016954878345131874, 0.013195783831179142, 0.04261605069041252, 0.02839771658182144, -0.036870285868644714, -0.010946170426905155, -0.0706242248415947, 0.0535622239112854, -0.006997174117714167, 0.007157860789448023, 0.08951707929372787, 0.016243960708379745, 0.06076877564191818, 0.031124521046876907, 0.006198609713464975, 0.01944795623421669, -0.02259351871907711, 0.003009223146364093, 0.03202047199010849, 0.025456663221120834, 0.014364413917064667, -0.015912849456071854, -0.08390765637159348, 0.009339303709566593, -0.012144017033278942, -0.0034109398256987333, -0.03595485910773277, -0.04133055731654167, -0.014072257094085217, -0.009285741485655308, 0.01990566961467266, 0.03572113439440727, 0.011121464893221855, 0.029994845390319824, 0.021853387355804443, -0.04510913044214249, -0.02294410765171051, 0.0015618257457390428, -0.013263953849673271, -0.005176058504730463, 0.043044548481702805, -0.025924116373062134, 0.007109167519956827, 0.05804197117686272, -0.03400714322924614, -0.022866200655698776, 0.02095743641257286, 0.006334950216114521, 0.036753423511981964, -0.024599667638540268, -0.037084534764289856, -0.024249078705906868, -0.04031774401664734, 0.02981954999268055, -0.008414138108491898, 0.03258530795574188, -0.006276518572121859, 0.008613779209554195, -0.003352508181706071, 0.00489120464771986, 0.011666825972497463, 0.030111707746982574, -0.017548931762576103, -0.005195535719394684, -0.044797495007514954, 0.05418549105525017, -0.028495103120803833, -0.003544845385476947, -0.03653917461633682, -0.003737182356417179, 0.08756936341524124, 0.02726804092526436, -0.028962554410099983, 0.07561038434505463, 0.004399406258016825, 0.012932841666042805, -0.036149632185697556, 0.010468980297446251, 0.01932135410606861, 0.005341614596545696, -0.014257289469242096, 0.05321163311600685, 0.021756000816822052, -0.026488954201340675, -0.0017517281230539083, -0.05157555267214775, 0.01852278970181942, 0.009339303709566593, -0.03085184097290039, 0.056912295520305634, -0.024833394214510918, -0.025359278544783592, 0.004523572977632284, 0.05056273937225342, -0.03831159695982933, -0.0024236906319856644, 0.012893888168036938, -0.03213733434677124, -0.030014321208000183, -0.018211156129837036, 0.023138880729675293, -0.025476140901446342, -0.005005632992833853, 0.010761137120425701, -0.003264860948547721, -0.01945769414305687, 0.03961656615138054, 0.060846686363220215, -0.01339055597782135, 0.008457961492240429, -0.013254215009510517, -0.056912295520305634, -0.0039611696265637875, -0.007401325274258852, -0.03375393897294998, 0.012767286039888859, -0.00914453249424696, -0.0007936947513371706, 0.003737182356417179, 0.0551983043551445, 0.04713475704193115, -0.010274208150804043, -0.0219897273927927, 0.04425213485956192, 0.027521243318915367, 0.026995360851287842, -0.027754969894886017, 0.001031072810292244, 0.0035034562461078167, -0.048381295055150986, 0.022768814116716385, 0.009514598175883293, -0.039674997329711914, 0.049316197633743286, -0.012504343874752522, 0.0022398747969418764, 0.051069144159555435, -0.02294410765171051, -0.05204300209879875, -0.03461093455553055, 0.014315721578896046, 0.05126391723752022, 0.03889591246843338, 0.001969628967344761, -0.05656170845031738, -0.0150266382843256, 0.061314135789871216, 0.005439000204205513, -0.07903836667537689, 0.08118085563182831, 0.013380817137658596, -0.05091332644224167, -0.07416906952857971, 0.04518703743815422, -0.031962040811777115, -0.03784414380788803, 0.024034829810261726, -0.024833394214510918, -0.01239721942692995, -0.0954381451010704, -0.000549317104741931, -0.0701567754149437, -0.03527315706014633, 0.07681796699762344, 0.03772728145122528, 0.0297026876360178, -0.045031219720840454, -0.014481277205049992, 0.005755504127591848, -0.0030993048567324877, 0.022301360964775085, -0.042343370616436005, -0.02212606742978096, 0.015338272787630558, -0.023840058594942093, -0.0017395549220964313, 0.0011528050526976585, -0.008224235847592354, 0.02841719426214695, -0.01409173384308815, 0.02107430063188076, -0.013166568242013454, 0.026352614164352417, -0.041408468037843704, 0.04031774401664734, 0.02247665636241436, 0.02121064066886902, -0.04347304627299309, -0.005906452424824238, 0.018961027264595032, -0.012406958267092705, 0.02271038293838501, -0.0037615287583321333, -0.047796979546546936, 0.02502816542983055, -0.004265500698238611, -0.014919513836503029, 0.024210125207901, 0.037298783659935, 0.0008996019023470581, -0.04378468170762062, 0.035935383290052414, -0.010439763776957989, 0.04101892560720444, -0.06762474030256271, 0.0295858234167099, -0.0003432851517572999, 0.027423858642578125, 0.01840592734515667, -0.032916419208049774, -0.01676010712981224, -0.00614504748955369, 0.0018235502066090703, 0.009792148135602474, 0.0023823014926165342, -0.008550478145480156, 0.012377742677927017, 0.0018588525708764791, -0.01252382155507803, 0.0010815917048603296, 0.0032259065192192793, 0.003457197919487953, -0.00760096637532115, -0.05157555267214775, 0.01234852708876133, -0.03529263660311699, 0.02202868089079857, -0.0032429490238428116, -0.03862323239445686, 0.050952281802892685, -0.049783650785684586, -0.031845174729824066, 0.013312647119164467, -0.0293520987033844, 0.031046612188220024, -0.02013939619064331, -0.015192193910479546, 0.0016799060394987464, -0.003505890956148505, 0.04810861498117447, 0.025086596608161926, -0.00931982696056366, -0.035935383290052414, 0.0533284954726696, -0.026488954201340675, -0.013020489364862442, 0.027443334460258484, -0.014081995002925396, 0.05948328226804733, 0.019506387412548065, 0.003337900387123227, 0.028027649968862534, 0.03203994780778885, 0.029079416766762733, 0.013721667230129242, -0.06933873146772385, 0.039188068360090256, 0.014861081726849079, 0.009723978117108345, -0.017432069405913353, 0.023002540692687035, 0.002904533175751567, -0.015873895958065987, 0.014753957279026508, -0.01923370733857155, 0.05219881981611252, 0.0026269834488630295, 0.020412076264619827, 0.04238232597708702, -0.03463041037321091, -0.062482766807079315, 0.01019629929214716, -0.043512001633644104, -0.07323416322469711, -0.03692871704697609, 0.01701330952346325, -0.013663236051797867, 0.04464167729020119, -0.09091943502426147, 0.022515609860420227, 0.032195765525102615, 0.00346206733956933, 0.04822547733783722, -0.004832773469388485, 0.026469476521015167, -0.043278276920318604, 0.029546869918704033, 0.016925662755966187, 0.03227367252111435, 0.015795987099409103, -0.010585842654109001, 0.047212664037942886, -0.014802650548517704, -0.03316962346434593, 0.012689377181231976, 0.009655808098614216, 0.01402356382459402, -0.058392561972141266, 0.0330917164683342, -0.02633313648402691, 0.008891329169273376, -0.005580209661275148, 0.05289999768137932, -0.06575493514537811, 0.010819569230079651, 0.0031626056879758835, 0.050601691007614136, 0.026255227625370026, -0.03129981458187103, 0.04534285515546799, 0.01721782051026821, 0.004652609582990408, 0.039636045694351196, -0.02224292978644371, 0.02469705417752266, 0.02563195861876011, -0.048615019768476486, 0.020801618695259094, 0.0193505696952343, -0.013244477100670338, 0.000267811119556427, 0.04288873076438904, -0.04386259242892265, 0.007026389706879854, 0.08421929180622101, -0.019272660836577415, 0.006485898047685623, -0.025067120790481567, -0.022398747503757477, 0.1036185547709465, -0.0354289747774601, 0.0465504415333271, -0.02609940990805626, 0.0022483959328383207, -0.04787488654255867, 0.006612499710172415, -0.015922587364912033, 0.014929252676665783, 0.0007334372494369745, -0.026703203096985817, -0.007708090823143721, -0.0022557000629603863, 0.0544971264898777, -0.01204663049429655, 0.025320323184132576, 0.0358964279294014, 0.01666272059082985, -0.005346483550965786, 0.026625294238328934, 0.052471499890089035, -0.03028700314462185, -0.0016494729788973927, -0.010176822543144226, -0.008477439172565937, 0.03387080132961273, -0.04460272192955017, -0.027891309931874275, 0.048731882125139236, -0.021639138460159302, -0.061314135789871216, -0.01792873628437519, -0.05648379772901535, 0.020548416301608086, 0.01760736294090748, -0.05796406418085098, -0.04448585957288742, -0.005068934056907892, 0.03410452604293823, -0.030442818999290466, 0.006846225820481777, -0.035584792494773865, 0.01664324291050434, -0.0174807608127594, -0.01152074709534645, 0.0451480858027935, 0.005935668013989925, -0.021950772032141685, -0.012260879389941692, 0.010809830389916897, -0.011744734831154346, 0.00022094417363405228, -0.022496134042739868, -0.013069182634353638, -0.0608077310025692, -0.006515114102512598, -0.022554565221071243, 0.0256124809384346, -0.0005645336350426078, 0.008087895810604095, -0.0037761367857456207, -0.012494605965912342, -0.015591476112604141, -0.026118887588381767, 0.02715117670595646, -0.019389525055885315, -0.009855449199676514, 0.0027195001021027565, 0.018104031682014465, -0.002760889008641243, 0.020684756338596344, -0.009300349280238152, -0.012036892585456371, 0.021483320742845535, -0.04542076587677002, -0.02726804092526436, 0.027170654386281967, -0.04109683260321617, -0.011111726984381676, 0.0034498940221965313, 0.024599667638540268, 0.06271649152040482, 0.009933358058333397, -0.01885390281677246, -0.01840592734515667, -0.03564322367310524, 0.019399262964725494, 0.002370128408074379, 0.028728827834129333, -0.032098378986120224, 0.004002558998763561, -0.012903626076877117, -0.005784720182418823, -0.004219242371618748, -0.03015066124498844, 0.057029157876968384, -0.015883633866906166, 0.007951555773615837, -0.017509978264570236, 0.029079416766762733, -0.02156122960150242, -0.02257404290139675, 0.023080449551343918, 0.0014997422695159912, -0.018931811675429344, 0.0011661956086754799, 0.012144017033278942, -0.008940021507441998, -0.0008612562087364495, 0.05457503721117973, 0.009655808098614216, -0.018581222742795944, -0.040239837020635605, 0.03975290805101395, -0.0030871317721903324, -0.011773950420320034, 0.0013159264344722033, 0.028358763083815575, 0.008964368142187595, 0.048731882125139236, -0.023450514301657677, -0.014637094922363758, 0.04810861498117447, -0.0256124809384346, -0.009378258138895035, 0.018328018486499786, -0.008954629302024841, -0.05878210440278053, -0.003744486253708601, -0.02376214973628521, -0.03342282772064209, -0.021366458386182785, 0.0036957934498786926, 0.028611965477466583, 0.03909068554639816, -0.020061487331986427, -0.01117015816271305, -0.007114036940038204, -0.039421796798706055, -0.02156122960150242, 0.062249042093753815, -0.019409000873565674, 0.028358763083815575, 0.006261910777539015, 0.004004993475973606, 0.03912963718175888, -0.017159387469291687, 0.01862017624080181, 0.012514082714915276, 0.005146842449903488, 0.05009528622031212, -0.004470010753720999, -0.029624778777360916, 0.004825469106435776, -0.026820065453648567, -0.007070213556289673, 0.019253185018897057, 0.02222345396876335, 0.01701330952346325, 0.03143615648150444, -0.002361607039347291, -0.0017249470110982656, 0.009631461463868618, -0.02680058777332306, 0.021853387355804443, -0.029488438740372658, 0.09629514068365097, 0.017305467277765274, 0.0009081231546588242, -0.02376214973628521, 0.010741660371422768, -0.0019404132617637515, -0.02004200965166092, -0.03463041037321091, 0.0774022787809372, -0.0219897273927927, 0.045615535229444504, 0.03182569891214371, -0.02272985875606537, 0.02177547849714756, 0.0027268039993941784, 0.0135074183344841, -0.020528938621282578, -0.0068949186243116856, 0.0022094417363405228, -0.05204300209879875, -0.025690389797091484, -0.04869293048977852, -0.024521758779883385, 0.013137352652847767, 0.05184823274612427, 0.018308540806174278, 0.023353129625320435, -0.004903377965092659, -0.011803166009485722, 0.009748324751853943, -0.030579159036278725, -0.0004939289065077901, -0.02130802534520626, -0.042577099055051804, -0.0007413498242385685, 0.023353129625320435, 0.017276251688599586, -0.01036185584962368, -0.0011217633727937937, 0.011627871543169022, 0.026294181123375893, 0.0007096994668245316, 0.010566365905106068, -0.015299318358302116, 0.03979186341166496, 0.0006537025910802186, -0.03143615648150444, 0.015503828413784504, -0.013410032726824284, 0.005935668013989925, 0.02633313648402691, -0.014364413917064667, 0.017441807314753532, -0.024969734251499176, -0.042109645903110504, -0.020061487331986427, 0.01617579162120819, -0.015065592713654041, 0.026722678914666176, -0.048264432698488235, -0.005219881888478994, 0.008949760347604752, -0.028378238901495934, -0.07650633156299591, 0.00030676546157337725, -0.028202945366501808, 0.04417422413825989, 0.024891825392842293, 0.05348431318998337, -0.00010172257316298783, 0.0015484351897612214, 0.03948022797703743, 0.008078156970441341, 0.005872367415577173, 0.00884263589978218, -0.006597891915589571, -0.003345204284414649, 0.01746128499507904, 0.011228589341044426, -0.03521472588181496, 0.03283851221203804, 0.018951287493109703, -0.0071042985655367374, 0.023255743086338043, -0.06614447385072708, -0.04261605069041252, 0.01618552953004837, 0.019983578473329544, 0.009392865933477879, 0.0591716468334198, 0.007586358580738306, -0.022768814116716385, 0.0387011393904686, 0.044096317142248154, 0.012075846083462238, 0.017178865149617195, -0.04207069054245949, -0.036052245646715164, -0.008793942630290985, 0.03611067682504654, -0.0023835189640522003, 0.017860567197203636, 0.010507933795452118, 0.019282400608062744, -0.04783593490719795, 0.06446944177150726, 0.005848020780831575, -0.010439763776957989, -0.041525330394506454, -0.025456663221120834, 0.050134241580963135, -0.007630181964486837, 0.021717047318816185, -0.06976722925901413, 0.013546372763812542, 0.03517577052116394, 0.020645802840590477, 0.04764116182923317, -0.0025685520377010107, -0.025651434436440468, 0.052705228328704834, -0.07475338876247406, -0.01234852708876133, 0.01130649819970131, 0.01071244478225708, 0.08344020694494247, -0.01792873628437519, 0.007411064114421606, 0.013819053769111633, -0.05819778889417648, -0.01060532033443451, 0.0117544736713171, 0.019632989540696144, 0.006997174117714167, 0.050367966294288635, -0.03817525506019592, -0.034396685659885406, -0.009918749332427979, -0.04039565473794937, -0.0274822898209095, 0.048498157411813736, 0.03131929412484169, 0.02574882097542286, -0.002034147037193179, 0.017665794119238853, 0.032896943390369415, -0.015912849456071854, 0.017159387469291687, 0.025963069871068, 0.018201416358351707, 0.0054682157933712006, -0.048615019768476486, -0.04078519716858864, -0.0041462029330432415, -0.05278313532471657, 0.0304038655012846, 0.007084821350872517, -0.010985124856233597, 0.023353129625320435, 0.016146576032042503, 0.0036519698332995176, 0.0015642603393644094, -0.012893888168036938, -0.04043461009860039, -0.013945654965937138, -0.01793847605586052, 0.030773932114243507, 0.01899024285376072, 0.03305276110768318, -0.027326472103595734, 0.03375393897294998, -0.02793026529252529, -0.024638622999191284, -0.02331417426466942, -0.021522274240851402, -0.04993946850299835, 0.014072257094085217, 0.012738070450723171, 0.03052072785794735, 0.020412076264619827, 0.03190360590815544, 0.06980618089437485, -0.003907607402652502, 0.05578261986374855, -0.003588669002056122, 0.0060914852656424046, 0.00544386962428689, 0.000427584775025025, -0.006276518572121859, -0.009519468061625957, -0.01944795623421669, 0.028378238901495934, -0.029722163453698158, -0.026995360851287842, 0.02724856324493885, 0.0011047208681702614, -0.006330080796033144, -0.03470832109451294, -0.05745765566825867, 0.0005870541208423674, -0.0505237840116024, -0.0002854623016901314, 0.03934388607740402, 0.00949512142688036, 0.012913364917039871, 0.03443564102053642, 0.009587638080120087, -0.024716531857848167, 0.004358017351478338, 0.012260879389941692, 0.017071740701794624, 0.03981133922934532, -0.04308350384235382, 0.029293665662407875, -0.034260343760252, 0.03903225064277649, -0.0244438499212265, -0.02933262102305889, -0.014715003781020641, -0.014773434959352016, -0.024210125207901, 0.013780099339783192, 0.010264469310641289, -0.015348011627793312, -0.016818538308143616, 0.03868166357278824, 0.015065592713654041, 0.015815462917089462, -0.010322901420295238, -0.012611468322575092, -0.006495636887848377, -0.005911321844905615, -0.044291090220212936, -0.04133055731654167, 0.02387901209294796, 0.02668372541666031, -0.01747102290391922, 0.022866200655698776, -0.022048158571124077, 0.026469476521015167, -0.03922702372074127, -0.0017918997909873724, -0.010391071438789368, -0.016497164964675903, -0.041759055107831955, 0.011296759359538555, -0.002042668405920267, -0.053172677755355835, 0.005852890200912952, 0.010098913684487343, 0.01737363636493683, 0.010089174844324589, 0.005263705737888813, -0.0013500114437192678, 0.010215776972472668, -0.016828276216983795, 0.015581737272441387, -0.02200920507311821, 0.017139911651611328, 0.0692218691110611, -0.012718592770397663, -0.02574882097542286, -0.009232179261744022, 0.00029261407325975597, 0.02921575866639614, 0.00561916409060359, -0.04787488654255867, 0.01204663049429655, 0.002438298426568508, -0.03770780563354492, -0.038272641599178314, -0.04775802418589592, 0.049316197633743286, 0.04242128133773804, -0.023489469662308693, 0.018259849399328232, 0.02771601639688015, 0.021970249712467194, 0.05391281098127365, 0.028611965477466583, 0.01402356382459402, -0.003681185422465205, -0.02808608114719391, 0.03492256999015808, -0.0189999807626009, -0.009222440421581268, 0.03924649953842163, -0.011803166009485722, -0.04690102860331535, 0.0021948337089270353, 0.019077889621257782, 0.0049447668716311455, 0.015182455070316792, -0.06419675797224045, -0.03133876994252205, -0.005229620728641748, -0.03694819658994675, -0.035799041390419006, -0.038954343646764755, -0.01384826935827732, 0.014403368346393108, 0.03850637003779411, -0.057808246463537216, 0.005852890200912952, 0.03609120100736618, 0.02294410765171051, -0.010819569230079651, -0.007230900228023529, -0.010839045979082584, 0.0038978690281510353, 0.013234738260507584, 0.04413527250289917, -0.056912295520305634, -0.0365976057946682, 0.04900456592440605, 0.026878496631979942, -0.004871727433055639, 0.017130171880126, 0.008759858086705208, -0.02341156080365181, 0.012747809290885925, 0.011209112592041492, -0.028456147760152817, 0.03821421042084694, -0.02317783422768116, -0.00037189223803579807, 0.010926693677902222, -0.008423876948654652, -0.01169604156166315, -0.015503828413784504, -0.005171189084649086, -0.028514578938484192, -0.028378238901495934, -0.01229009497910738, -0.014101472683250904, 0.029391052201390266, 0.024969734251499176, 0.022145545110106468, 0.026060456410050392, -0.03480570763349533, 0.023840058594942093, -0.02317783422768116, -0.0446806326508522, 0.00259046396240592, 0.026722678914666176, 0.025125551968812943, 0.01605892740190029, -0.07751914113759995, -0.01152074709534645, 0.014588401652872562, -0.04238232597708702, -0.0033841587137430906, -0.010030743665993214, -0.00856021698564291, 0.00090690579963848 ]
EEG signals are complex and low-frequency signals. Therefore, they are easily influenced by external factors. EEG artifact removal is crucial in neuroscience because artifacts have a significant impact on the results of EEG analysis. The removal of ocular artifacts is the most challenging among these artifacts. In this study, a novel ocular artifact removal method is presented by developing bidirectional long-short term memory (BiLSTM)-based deep learning (DL) models. We created a benchmarking dataset to train and test proposed DL models by combining the EEGdenoiseNet and DEAP datasets. We also augmented the data by contaminating ground-truth clean EEG signals with EOG at various SNR levels. The BiLSTM network is then fed to features extracted from augmented signals using highly-localized time-frequency (TF) coefficients obtained by wavelet synchrosqueezed transform (WSST). We also compare the WSST-based DL model results with traditional TF analysis (TFA) methods namely short-time Fourier transformation (STFT) and continuous wavelet transform (CWT) as well as augmented raw signals. The best average MSE value of 0.3066 was obtained by the first time-proposed BiLSTM-based WSST-Net model. Our results demonstrated the WSST-Net model significantly improves artifact removal performance compared to traditional TF and raw signal methods. Also, the proposed EOG removal approach reveals that it outperforms many conventional and DL-based ocular artifact removal methods in the literature.
[ 0.0045977490954101086, -0.023051729425787926, -0.022367915138602257, -0.004291832447052002, 0.006478237919509411, 0.026092901825904846, 0.01247060764580965, 0.023519601672887802, -0.017500240355730057, 0.005627969279885292, 0.007171049248427153, -0.06755362451076508, -0.03915734961628914, -0.022097988054156303, 0.03940927982330322, 0.015673736110329628, 0.027568500488996506, -0.0748596340417862, 0.0006753787747584283, -0.03179734945297241, -0.011327918618917465, -0.004483030643314123, -0.009258481673896313, -0.0812658965587616, -0.0005586917977780104, 0.04433993995189667, 0.08025816828012466, 0.019272757694125175, -0.07079274207353592, 0.023753538727760315, 0.05582081526517868, 0.018678918480873108, 0.008057308383286, -0.014387086033821106, -0.05790824815630913, -0.025319112464785576, 0.03915734961628914, 0.029943855479359627, 0.024617303162813187, 0.03348889201879501, 0.006482736673206091, 0.014809971675276756, -0.041856613010168076, -0.015592758543789387, -0.01021222211420536, -0.020676376298069954, -0.014854959212243557, -0.03854551538825035, 0.02328566648066044, 0.0014373590238392353, -0.012335644103586674, -0.0513940192759037, 0.033452898263931274, -0.021630115807056427, -0.034244686365127563, -0.004282834939658642, 0.06593406200408936, 0.026848696172237396, 0.05409328639507294, -0.017104346305131912, 0.03696194663643837, 0.06949709355831146, -0.03611617535352707, -0.0042648399248719215, -0.04095685854554176, -0.05189788341522217, 0.03246317058801651, -0.012632563710212708, -0.02335764653980732, -0.014863956719636917, -0.07324007898569107, 0.008525180630385876, 0.020784346386790276, 0.013388358056545258, -0.018292024731636047, 0.01659148745238781, 0.004993641749024391, 0.06823743879795074, 0.010689091868698597, -0.012362636625766754, 0.01616860181093216, 0.028306299820542336, -0.022044003009796143, 0.027568500488996506, 0.05056624487042427, -0.009609386324882507, 0.0040196566842496395, -0.059959691017866135, 0.03087959997355938, -0.008637649938464165, 0.02490522526204586, 0.025157157331705093, -0.006802149582654238, 0.01882288046181202, -0.01963265985250473, -0.018319016322493553, 0.005771929863840342, -0.012596573680639267, -0.04995441064238548, -0.010626109316945076, 0.009330461733043194, 0.012983468361198902, -0.033075001090765, 0.018301021307706833, 0.0067886533215641975, -0.04376409575343132, -0.011318921111524105, 0.011318921111524105, 0.012794519774615765, 0.1644032746553421, -0.06776956468820572, 0.001125818700529635, 0.006451244931668043, 0.044879790395498276, -0.017851144075393677, -0.027496520429849625, -0.017284298315644264, -0.012641561217606068, 0.003958923276513815, 0.015520777553319931, -0.012938480824232101, 0.10286001861095428, -0.017617207020521164, 0.054633136838674545, 0.0005353543674573302, 0.06618599593639374, 0.02868419699370861, 0.027766447514295578, 0.034928496927022934, 0.04945054650306702, -0.026002926751971245, -0.030411727726459503, 0.00009665339894127101, -0.005200585350394249, -0.010122246108949184, 0.014459067024290562, -0.029925858601927757, 0.028882144019007683, -0.0030996568966656923, -0.0376097708940506, -0.03087959997355938, -0.017140338197350502, -0.030537692829966545, 0.01699637621641159, 0.025301117449998856, 0.010068261064589024, 0.03782571107149124, 0.06514228135347366, -0.055532895028591156, 0.01615060679614544, -0.047866977751255035, 0.047759007662534714, 0.00824175775051117, 0.025912951678037643, 0.006770658306777477, -0.0173832718282938, 0.01729329489171505, -0.05668457970023155, -0.028360284864902496, -0.04541964456439018, 0.01240762509405613, -0.044771820306777954, 0.0633067786693573, -0.01804909110069275, 0.007607430685311556, 0.026038916781544685, -0.009582393802702427, 0.014207134954631329, -0.06845337897539139, 0.05654061958193779, -0.025786984711885452, -0.009726353920996189, -0.04757905751466751, 0.0029736910946667194, 0.03249916061758995, 0.004620243329554796, 0.0557488352060318, -0.024653293192386627, -0.07054080814123154, -0.0021076765842735767, -0.01963265985250473, 0.01963265985250473, 0.015241853892803192, 0.0010279703419655561, 0.00943843275308609, -0.02490522526204586, 0.06467440724372864, -0.015934664756059647, 0.02420341596007347, -0.024599308148026466, 0.011102980002760887, -0.01014923956245184, 0.08875185996294022, -0.060715485364198685, 0.029206056147813797, -0.044016025960445404, -0.014594029635190964, -0.0011252564145252109, -0.003704742295667529, -0.0078008780255913734, -0.04437592998147011, -0.03172536939382553, 0.0038801943883299828, -0.010023273527622223, -0.005515499506145716, -0.04005710408091545, 0.051645949482917786, -0.04344018176198006, -0.025930946692824364, -0.005533494986593723, 0.021432170644402504, 0.005677455570548773, -0.07781083136796951, 0.02118023857474327, 0.009951293468475342, -0.0033943266607820988, 0.03530639410018921, -0.02870219200849533, 0.02859422191977501, 0.028954124078154564, 0.015772709622979164, 0.03008781559765339, 0.0051241060718894005, -0.03496449068188667, 0.011138970032334328, 0.01397319883108139, -0.02047842927277088, 0.02037045918405056, 0.018678918480873108, -0.020730361342430115, 0.014261120930314064, 0.007976329885423183, 0.03248116374015808, -0.020064542070031166, 0.010833052918314934, 0.025013195350766182, 0.06546619534492493, -0.028378279879689217, 0.019020825624465942, -0.09717356413602829, -0.025858966633677483, -0.05970775708556175, -0.0688132792711258, -0.024383367970585823, -0.014225129969418049, 0.019092805683612823, 0.015142880380153656, 0.05268966779112816, 0.019182782620191574, 0.030735639855265617, -0.01470200065523386, 0.03413671255111694, -0.043260231614112854, 0.056072745472192764, -0.01952468790113926, -0.012092710472643375, 0.008984056301414967, -0.018444983288645744, 0.01396420132368803, -0.012083712965250015, 0.01616860181093216, 0.003776722587645054, -0.030447717756032944, 0.024581313133239746, -0.034334659576416016, -0.006991098169237375, 0.058520082384347916, 0.0406329482793808, 0.04200057312846184, -0.06564614176750183, -0.03237319365143776, -0.01650151051580906, 0.005897895433008671, 0.026110896840691566, 0.028396274894475937, 0.021396180614829063, 0.02330366149544716, -0.022313930094242096, 0.006113837007433176, 0.032859060913324356, -0.028378279879689217, 0.02260185219347477, 0.061471279710531235, 0.05823215842247009, -0.019776619970798492, 0.004201856907457113, 0.02792840264737606, -0.04664331302046776, -0.014764983206987381, 0.034388646483421326, -0.00890307780355215, -0.009636378847062588, -0.08796007186174393, -0.009492417797446251, 0.051034118980169296, 0.012866499833762646, -0.027766447514295578, -0.0061408295296132565, 0.007503958884626627, -0.08256153762340546, -0.02101828344166279, 0.011912759393453598, -0.015736719593405724, 0.022817792370915413, -0.047003213316202164, -0.01400019135326147, 0.013658284209668636, 0.0782427191734314, -0.003050170373171568, -0.011471879668533802, 0.007661415729671717, -0.021522145718336105, 0.007751391269266605, -0.04739910736680031, -0.0033515882678329945, 0.05448917672038078, 0.026056911796331406, 0.0015835692174732685, 0.016564493998885155, 0.00037396076368167996, -0.022097988054156303, 0.04984644055366516, -0.059851717203855515, 0.0842890739440918, 0.007656916975975037, -0.022079993039369583, 0.07442775368690491, 0.01648351550102234, -0.038149621337652206, -0.0028634711634367704, -0.000251509714871645, 0.006104839500039816, -0.014405081048607826, 0.010032271035015583, 0.012920484878122807, 0.042612407356500626, -0.06859733909368515, 0.008552173152565956, 0.01669945754110813, -0.02398747391998768, 0.027568500488996506, -0.025481069460511208, -0.08817601203918457, -0.03008781559765339, -0.024383367970585823, -0.014009188860654831, -0.011912759393453598, -0.0008626403287053108, -0.0352524109184742, -0.03775373101234436, 0.0009633004665374756, -0.007854863069951534, -0.008480193093419075, 0.023753538727760315, 0.009110021404922009, -0.04369211569428444, 0.0332549549639225, -0.013874226249754429, 0.001782640116289258, 0.013748260214924812, -0.014180142432451248, -0.014513052068650723, -0.03370483219623566, 0.01723930984735489, -0.03987715393304825, -0.00012413811055012047, 0.0014204885810613632, -0.025463072583079338, 0.011138970032334328, 0.0209822915494442, 0.027460530400276184, -0.0016769188223406672, -0.03714189678430557, 0.001133691635914147, -0.02411344088613987, -0.005942883435636759, 0.009609386324882507, 0.044016025960445404, 0.03375881537795067, 0.05823215842247009, -0.017761169001460075, -0.032103266566991806, -0.014558039605617523, 0.003020928241312504, 0.012821512296795845, 0.028918134048581123, -0.00881310272961855, 0.025157157331705093, 0.00582141662016511, 0.04009309411048889, -0.002151539782062173, -0.057620324194431305, -0.010590119287371635, -0.01092302892357111, 0.052257783710956573, 0.028216324746608734, 0.012371635064482689, 0.07694707065820694, 0.06327079236507416, -0.016987379640340805, -0.07680311053991318, 0.004163617268204689, -0.0013473834842443466, -0.04999040067195892, -0.034424636512994766, 0.03679998964071274, -0.053013578057289124, -0.0008362100343219936, 0.07946638017892838, -0.01467500813305378, 0.02024449221789837, 0.01839999482035637, 0.009870314970612526, -0.03563030809164047, 0.025481069460511208, -0.011022001504898071, -0.03093358501791954, 0.051034118980169296, 0.030609672889113426, -0.0219180379062891, -0.05337348207831383, 0.010617111809551716, -0.00507012102752924, -0.00865564588457346, 0.009969288483262062, 0.04981045052409172, 0.029188059270381927, -0.050998128950595856, -0.022943759337067604, -0.01817505620419979, 0.009060535579919815, 0.012110705487430096, 0.022241950035095215, -0.03248116374015808, -0.034370649605989456, -0.03602619841694832, 0.015826694667339325, 0.026218866929411888, -0.03847353532910347, 0.010671096853911877, 0.011822784319519997, 0.01581769809126854, 0.022277940064668655, -0.04581553861498833, -0.05661259964108467, -0.038761455565690994, -0.027388550341129303, 0.043656125664711, -0.022115983068943024, -0.005407528951764107, -0.026074906811118126, 0.05276164785027504, -0.043980035930871964, 0.028306299820542336, -0.0003531539405230433, -0.002894962439313531, -0.008489190600812435, -0.06039157137274742, 0.055496904999017715, -0.04822688177227974, -0.019938576966524124, 0.050242334604263306, 0.02270982228219509, 0.01966864988207817, 0.036638032644987106, 0.0025732999201864004, -0.061471279710531235, -0.06568213552236557, 0.007279019802808762, 0.052473727613687515, 0.01320840697735548, 0.010392173193395138, -0.028126349672675133, 0.056144725531339645, 0.028036372736096382, 0.053877342492341995, -0.043404191732406616, -0.05366140231490135, 0.010995008982717991, 0.02402346581220627, 0.038797445595264435, 0.009096525609493256, 0.007445474620908499, 0.03775373101234436, -0.023141704499721527, 0.010518139228224754, 0.015268846414983273, 0.05340947210788727, 0.0034573094453662634, -0.052473727613687515, -0.017617207020521164, 0.005511000752449036, 0.04239646717905998, 0.015016915276646614, 0.026038916781544685, -0.0077558900229632854, -0.010725082829594612, -0.0117148132994771, 0.05801621824502945, 0.01965065486729145, 0.022925764322280884, 0.056072745472192764, -0.032103266566991806, 0.009168505668640137, -0.006239802576601505, 0.02629084885120392, -0.01088703889399767, 0.006163323298096657, -0.01021222211420536, 0.0018141315085813403, 0.05135802924633026, -0.008507185615599155, -0.008435205556452274, -0.03901338577270508, 0.015169873833656311, 0.03647607937455177, -0.05862805247306824, 0.015286841429769993, 0.007782883010804653, 0.03249916061758995, 0.01549378503113985, 0.016114616766572, -0.037249866873025894, 0.08198569715023041, -0.05823215842247009, 0.026668746024370193, 0.03717788681387901, 0.026020921766757965, 0.014135154895484447, -0.019920581951737404, -0.03973319008946419, 0.01089603640139103, -0.012182686477899551, -0.026236863806843758, -0.01666346751153469, -0.009708358906209469, 0.004827186930924654, 0.03832957521080971, -0.012695546261966228, -0.006734667811542749, -0.00732850655913353, 0.011336916126310825, -0.019740629941225052, -0.015826694667339325, 0.01636654883623123, -0.026542779058218002, 0.07212437689304352, -0.04164067283272743, -0.01885887049138546, 0.0352524109184742, -0.005762932356446981, -0.003068165387958288, -0.025355102494359016, 0.00888508278876543, -0.01965065486729145, -0.016114616766572, -0.004674228373914957, -0.0013496328610926867, -0.02258385717868805, -0.029619943350553513, -0.0015565765788778663, -0.030339747667312622, 0.003988164942711592, -0.007422980852425098, 0.014621023088693619, 0.0007001220365054905, 0.014306108467280865, 0.042504437267780304, 0.011192955076694489, 0.00407814048230648, -0.027334563434123993, -0.008574667386710644, 0.018570948392152786, 0.0063612693920731544, -0.006010365206748247, 0.0367639996111393, 0.05358942225575447, -0.008669141680002213, 0.010644104331731796, 0.042648397386074066, 0.03937328979372978, -0.005506501998752356, 0.047003213316202164, 0.03487451374530792, 0.0055424924939870834, -0.031959306448698044, -0.01699637621641159, -0.03631412237882614, -0.0074319783598184586, -0.008417210541665554, 0.03365084528923035, 0.05866404250264168, 0.004213104024529457, -0.017869139090180397, -0.062299054116010666, 0.0015801951522007585, -0.01174180582165718, 0.03471255674958229, 0.05949181690812111, -0.05110609903931618, 0.014495057053864002, 0.06244301423430443, 0.03408272936940193, 0.06525024771690369, 0.04505974426865578, -0.028918134048581123, 0.01891285553574562, 0.018301021307706833, 0.007458970881998539, -0.009636378847062588, 0.013748260214924812, 0.023879503831267357, 0.0249412152916193, -0.0017399017233401537, 0.02118023857474327, -0.014872954227030277, 0.0040826392360031605, 0.01579970121383667, -0.0021200482733547688, -0.01389222126454115, 0.02035246416926384, -0.005915890913456678, 0.03926531970500946, -0.007530951406806707, 0.045635584741830826, 0.04671529307961464, 0.0033223461359739304, -0.0162045918405056, 0.009312466718256474, -0.0389414057135582, -0.018660923466086388, 0.0020705617498606443, -0.0023213685490190983, -0.013055448420345783, -0.017194323241710663, 0.020154517143964767, 0.0077558900229632854, -0.023969478905200958, 0.029008109122514725, 0.015241853892803192, -0.0015813198406249285, 0.03167138621211052, -0.02719060331583023, -0.011165962554514408, -0.010680094361305237, -0.024257401004433632, -0.02022649720311165, 0.030285760760307312, 0.03532439097762108, 0.04963050037622452, 0.027316568419337273, 0.019092805683612823, 0.055352941155433655, 0.023591581732034683, -0.022205960005521774, -0.06341475248336792, 0.04739910736680031, -0.00014663198089692742, 0.032229233533144, 0.01688840612769127, -0.013766255229711533, 0.0349464938044548, 0.0038509524893015623, -0.047075193375349045, 0.005200585350394249, -0.06521426141262054, -0.0036147667560726404, -0.032697103917598724, 0.01875089854001999, 0.010284202173352242, -0.03370483219623566, -0.07413983345031738, -0.06791352480649948, -0.000007635618203494232, 0.03840155526995659, -0.06251499801874161, 0.05963577702641487, 0.02575099468231201, 0.007139557972550392, -0.02864820696413517, -0.023681558668613434, -0.025157157331705093, -0.001637554494664073, -0.0019490948179736733, -0.010779067873954773, -0.006122834514826536, -0.015628749504685402, 0.009119019843637943, -0.019902586936950684, -0.007958334870636463, 0.011804788373410702, -0.0188948605209589, -0.013694275170564651, -0.012605571188032627, 0.03782571107149124, -0.0017961363773792982, -0.04120878875255585, 0.017185324802994728, 0.020856326445937157, 0.022421900182962418, -0.02630884386599064, 0.010752075351774693, 0.0019727132748812437, 0.0014272367116063833, 0.05801621824502945, -0.002550806151703, 0.019740629941225052, -0.01821104623377323, -0.05808819830417633, -0.005582981277257204, 0.0052815633825957775, 0.013478333130478859, 0.006959606893360615, 0.015646744519472122, 0.04423196613788605, 0.002521564019843936, -0.015025912784039974, 0.017320288345217705, -0.021630115807056427, 0.04959451034665108, 0.0005215768469497561, 0.06902921944856644, -0.0007001220365054905, -0.06280291825532913, -0.0033200967591255903, 0.0574403740465641, -0.004975646734237671, -0.039481259882450104, -0.028774172067642212, 0.00224938802421093, 0.04246844723820686, -0.010509141720831394, -0.01089603640139103, 0.019920581951737404, 0.013262392021715641, -0.051609959453344345, 0.011057991534471512, 0.044123996049165726, 0.0024585812352597713, -0.010842050425708294, -0.04192859306931496, -0.00946542527526617, 0.004242346156388521, 0.008228261955082417, 0.001784889493137598, 0.028036372736096382, -0.016897402703762054, 0.0513940192759037, -0.06240702420473099, -0.011453884653747082, -0.0020075789652764797, -0.03242718055844307, 0.05945582687854767, -0.025157157331705093, -0.0038801943883299828, 0.014216132462024689, 0.009330461733043194, -0.032229233533144, 0.015259848907589912, 0.0026947669684886932, -0.0032121262047439814, 0.0018714909674599767, 0.050242334604263306, -0.007139557972550392, 0.05074619501829147, 0.05484908074140549, -0.0188948605209589, 0.008003323338925838, 0.02173808589577675, 0.008367723785340786, 0.05941983684897423, 0.004377309232950211, 0.06352271884679794, -0.07007294148206711, -0.03233720362186432, 0.028918134048581123, 0.03597221523523331, -0.0374298170208931, -0.054813090711832047, -0.028918134048581123, -0.029709918424487114, 0.012785522267222404, -0.01893085055053234, 0.02103627845644951, -0.036440085619688034, 0.012749532237648964, 0.021324198693037033, -0.03159940242767334, -0.03840155526995659, 0.021648110821843147, -0.013775252737104893, -0.011417893692851067, 0.05020634084939957, -0.01841798983514309, 0.011363908648490906, 0.007121562957763672, -0.017212318256497383, 0.05736839398741722, -0.04581553861498833, -0.01648351550102234, 0.015655741095542908, 0.007625425700098276, -0.03940927982330322, 0.013442343100905418, -0.013784250244498253, -0.0341007225215435, -0.02252987213432789, -0.06107538565993309, 0.021324198693037033, 0.005308555904775858, -0.003191881813108921, -0.001991833094507456, 0.0007259899866767228, -0.005938384681940079, 0.043296221643686295, 0.00024757327628321946, -0.06438648700714111, 0.03672800958156586, 0.005785426124930382, -0.035828255116939545, -0.003992663696408272, -0.04124477878212929, -0.01314542442560196, -0.021522145718336105, -0.03329094499349594, -0.006478237919509411, 0.04322424158453941, 0.028414269909262657, 0.014917941763997078, 0.022961754351854324, -0.006806648336350918, 0.02951197139918804, 0.016564493998885155, 0.008925572037696838, -0.04380008578300476, 0.06240702420473099, -0.029044099152088165, -0.028522241860628128, -0.0016690460033714771, -0.004926159977912903, 0.01400019135326147, 0.01778816059231758, 0.0015779457753524184, 0.009285474196076393, 0.009645376354455948, -0.004845181945711374, 0.005960878450423479, 0.0026272854302078485, 0.024455348029732704, 0.019776619970798492, 0.016474518924951553, 0.02497720532119274, -0.00582591537386179, 0.015718724578619003, -0.01472899317741394, 0.00880410522222519, -0.016384543851017952, 0.02641681395471096, 0.015844689682126045, 0.00942043773829937, 0.029116079211235046, -0.004314326215535402, -0.0077603887766599655, 0.011201952584087849, 0.01671745255589485, -0.009978285990655422, -0.01961466483771801, 0.011975741945207119, -0.029386006295681, -0.015259848907589912, -0.01594366319477558, -0.008511684834957123, -0.019812610000371933, 0.01472899317741394, -0.006041856482625008, -0.014944934286177158, -0.022061998024582863, 0.00024841679260134697, 0.01546679250895977, -0.04210854694247246, 0.019866595044732094, -0.0037182385567575693, 0.06553817540407181, -0.022151974961161613, 0.05110609903931618, 0.03825759142637253, -0.027442535385489464, -0.03768175095319748, 0.018390996381640434, -0.023897498846054077, -0.021648110821843147, 0.041064828634262085, 0.0078053767792880535, 0.001764644985087216, 0.0009424936142750084, 0.029098084196448326, -0.002813984639942646, -0.03473055362701416, -0.010617111809551716, -0.00511060981079936, 0.01246161013841629, -0.025301117449998856, -0.01048214826732874, -0.041136808693408966, 0.0060373577289283276, -0.03233720362186432, -0.013532319106161594, -0.007895352318882942, 0.00867364089936018, -0.022799797356128693, -0.027388550341129303, -0.05143000930547714, 0.01651950553059578, -0.052545707672834396, 0.044879790395498276, 0.00255980365909636, 0.00658170972019434, -0.03309299796819687, 0.03161739930510521, 0.007130560465157032, 0.011093982495367527, 0.013370363041758537, -0.01199373695999384, 0.054705120623111725, -0.04059695824980736, -0.02173808589577675, -0.042540427297353745, 0.0044897785410285, 0.014279115945100784, 0.035918228328228, -0.0015970655949786305, 0.05182590335607529, 0.040309034287929535, 0.007715401239693165, 0.05639665946364403, 0.00662219850346446, -0.026578769087791443, 0.06701377034187317, -0.011561854742467403, 0.03786170110106468, 0.008579166606068611, 0.018696913495659828, -0.036602042615413666, 0.012308651581406593, -0.001636429806239903, -0.04991842061281204, 0.032103266566991806, -0.05297758802771568, 0.0039026883896440268, -0.00657721096649766, -0.02558903954923153, -0.02265583723783493, -0.001663422561250627, 0.008034814149141312, -0.04146072268486023, -0.00973535142838955, -0.021468160673975945, -0.021252218633890152, -0.01170581579208374, -0.012983468361198902, -0.025373097509145737, -0.0024315884802490473, -0.004678727127611637, 0.006109338253736496, -0.002780243754386902, 0.010095253586769104, -0.034208692610263824, -0.014845961704850197, -0.04743509739637375, -0.006343274377286434, 0.012848504818975925, 0.00823276024311781, -0.04761504754424095, 0.0024900727439671755, -0.017599212005734444, 0.014054177328944206, -0.008205767720937729, 0.0009964789496734738, 0.0055424924939870834, -0.013595301657915115, 0.029583953320980072, 0.0034910503309220076, -0.014953931793570518, 0.006446746177971363, 0.017041364684700966, -0.007225034758448601, 0.028108354657888412, -0.006752663291990757, -0.032841067761182785, 0.007742393761873245, -0.029925858601927757, -0.01810307614505291, 0.013370363041758537, -0.004226600285619497, -0.060751475393772125, 0.01668146252632141, -0.04887470602989197, 0.0031041556503623724, 0.007796379271894693, -0.005187089089304209, 0.006401758641004562, 0.008412711322307587, 0.015565766021609306, 0.02629084885120392, -0.019362732768058777, 0.011327918618917465, 0.006761660799384117, -0.008300242014229298, -0.010473150759935379, 0.027262583374977112, 0.035684291273355484, -0.06237103417515755, -0.011534862220287323, -0.005587480030953884, -0.000632640381809324, -0.011273933574557304, -0.014531047083437443, -0.0050791185349226, -0.0031176519114524126, -0.011795790866017342, -0.0009762344416230917, -0.032877057790756226, 0.00584840914234519, -0.055532895028591156 ]
In the past few years, Convolutional Neural Networks (CNN) have demonstrated promising performance in various real-world cybersecurity applications, such as network and multimedia security. However, the underlying fragility of CNN structures poses major security problems, making them inappropriate for use in security-oriented applications including such computer networks. Protecting these architectures from adversarial attacks necessitates using security-wise architectures that are challenging to attack. In this study, we present a novel architecture based on an ensemble classifier that combines the enhanced security of 1-Class classification (known as 1C) with the high performance of conventional 2-Class classification (known as 2C) in the absence of attacks.Our architecture is referred to as the 1.5-Class (SPRITZ-1.5C) classifier and constructed using a final dense classifier, one 2C classifier (i.e., CNNs), and two parallel 1C classifiers (i.e., auto-encoders). In our experiments, we evaluated the robustness of our proposed architecture by considering eight possible adversarial attacks in various scenarios. We performed these attacks on the 2C and SPRITZ-1.5C architectures separately. The experimental results of our study showed that the Attack Success Rate (ASR) of the I-FGSM attack against a 2C classifier trained with the N-BaIoT dataset is 0.9900. In contrast, the ASR is 0.0000 for the SPRITZ-1.5C classifier.
[ -0.026045970618724823, -0.0028100190684199333, -0.034090593457221985, -0.048474445939064026, 0.11837824434041977, 0.027940848842263222, -0.028216468170285225, 0.012213354930281639, -0.034021686762571335, 0.03405613824725151, 0.012153062969446182, -0.07800009846687317, 0.016399314627051353, -0.05729424208402634, -0.06132516637444496, 0.02344481833279133, 0.011205623857676983, -0.04571825638413429, 0.009138483554124832, -0.06545944511890411, 0.04771649092435837, -0.007734550628811121, -0.028061432763934135, 0.014771440997719765, -0.02132599987089634, 0.052780985832214355, 0.033866651356220245, 0.025632541626691818, -0.07345239073038101, 0.028819384053349495, 0.022721318528056145, 0.007054117042571306, -0.0001773757248884067, -0.016442378982901573, -0.005658796988427639, -0.06556280702352524, 0.014082394540309906, 0.09067856520414352, -0.0335049033164978, 0.040412597358226776, 0.03696736320853233, -0.06470149755477905, 0.020395785570144653, 0.022204533219337463, 0.04906013235449791, -0.02365153282880783, -0.047888755798339844, -0.03817319497466087, -0.008522648364305496, -0.010551029816269875, -0.0019530170829966664, -0.04278980940580368, 0.04158397763967514, 0.01142095122486353, -0.00012684114335570484, 0.03576153144240379, 0.003856508992612362, 0.010714678093791008, 0.051196180284023285, 0.02508130483329296, 0.014926477335393429, 0.01737259328365326, -0.03517584130167961, 0.006916307378560305, -0.006533025298267603, -0.0034495405852794647, 0.07855133712291718, -0.04354776069521904, 0.0403781458735466, -0.01250620000064373, -0.10142768919467926, -0.003460307139903307, -0.029353395104408264, -0.02465065009891987, -0.012230581603944302, 0.01028402429074049, 0.06304778158664703, 0.029646240174770355, 0.0035421312786638737, 0.04175623878836632, -0.00228892732411623, 0.05326332151889801, -0.013953198678791523, -0.01974119246006012, 0.05884459987282753, -0.005839671939611435, -0.056467387825250626, -0.07510610669851303, 0.06821563839912415, -0.027406837791204453, -0.042238570749759674, 0.041549522429704666, 0.029491204768419266, -0.035589270293712616, 0.0035227518528699875, 0.010723290964961052, -0.008419291116297245, -0.0382765494287014, -0.037553053349256516, -0.03924121707677841, -0.002158654620870948, 0.02306584268808365, -0.008729361928999424, 0.031765058636665344, 0.01605479046702385, 0.009939500130712986, -0.05281544104218483, 0.04568380489945412, -0.004106288310140371, 0.11824043840169907, 0.010990296490490437, 0.027544647455215454, -0.016829969361424446, 0.01623566634953022, -0.017605146393179893, -0.02487459033727646, -0.05422798544168472, -0.02552918531000614, -0.044030092656612396, 0.02726902812719345, -0.018035801127552986, 0.053849007934331894, -0.029043324291706085, 0.02871602587401867, -0.052298653870821, 0.04513256624341011, 0.02471955493092537, 0.022497378289699554, 0.0012510506203398108, 0.04303097352385521, -0.0003386019088793546, -0.029939085245132446, 0.02266964130103588, -0.055261556059122086, 0.006395215634256601, 0.03948238492012024, 0.003787604160606861, -0.007540756370872259, 0.024995174258947372, -0.0006524412310682237, 0.047647587954998016, -0.010051470249891281, 0.0010211889166384935, 0.004435739014297724, 0.046372853219509125, -0.022325117141008377, 0.02952565625309944, 0.04210076108574867, -0.020981475710868835, 0.011188398115336895, -0.02313474752008915, 0.0730389654636383, 0.02728625386953354, 0.05732869729399681, 0.012273646891117096, -0.01409100741147995, 0.03283308073878288, -0.014409692026674747, 0.03343599662184715, -0.0364505760371685, 0.04806101694703102, -0.02552918531000614, -0.019172728061676025, 0.0010077309561893344, 0.060084883123636246, 0.05191968008875847, 0.02478845976293087, 0.04330659285187721, -0.060394953936338425, 0.049473561346530914, 0.019344989210367203, 0.026097647845745087, 0.013350281864404678, 0.03910340741276741, 0.001940097426995635, 0.025598090142011642, 0.010671612806618214, -0.05295324698090553, -0.02666611224412918, 0.02630436234176159, -0.03164447471499443, -0.001981009729206562, 0.019017692655324936, -0.059947073459625244, 0.007613967638462782, 0.010077309794723988, 0.052574273198843, -0.01581362448632717, 0.033728841692209244, 0.0004185421275906265, -0.005223836284130812, 0.00219418341293931, 0.056398481130599976, -0.06218647584319115, 0.024598971009254456, -0.038689978420734406, 0.00789389293640852, -0.02923281118273735, -0.02351372316479683, -0.005473615601658821, -0.022996937856078148, -0.030266381800174713, 0.015193482860922813, -0.024237222969532013, 0.011007523164153099, 0.02720012329518795, 0.00394694646820426, 0.006851709447801113, -0.02146380953490734, -0.029939085245132446, -0.04737196862697601, 0.017320914193987846, -0.034848544746637344, 0.038311004638671875, -0.013057437725365162, -0.01148985605686903, 0.00388019485399127, -0.015538006089627743, -0.03403891250491142, 0.019930679351091385, 0.018931562080979347, 0.05140289291739464, -0.007540756370872259, -0.028285373002290726, -0.05333222448825836, -0.030610905960202217, -0.03286753222346306, 0.023789342492818832, -0.0003781682753469795, 0.0001795290008885786, -0.05946474149823189, -0.029353395104408264, 0.022342342883348465, -0.008191044442355633, 0.037794217467308044, -0.0363127663731575, 0.006326311267912388, -0.038621075451374054, -0.02961178682744503, -0.0007762543391436338, -0.011059201322495937, 0.0130402110517025, -0.05581279471516609, -0.03214403614401817, -0.01824251562356949, 0.003720852779224515, 0.011343433521687984, 0.0660451352596283, -0.008303014561533928, 0.03731188550591469, -0.02465065009891987, 0.04120500013232231, 0.011369273066520691, 0.0035227518528699875, -0.033935558050870895, 0.00120152544695884, 0.004222564864903688, -0.07048948854207993, 0.014823120087385178, -0.02606319636106491, 0.07586405426263809, -0.008785347454249859, -0.028819384053349495, 0.07868915051221848, -0.02191169001162052, -0.01322969887405634, 0.017407044768333435, 0.04303097352385521, 0.004487417638301849, -0.011799926869571209, 0.018638717010617256, -0.04196295142173767, -0.048784516751766205, 0.00670959334820509, 0.015357131138443947, -0.010611320845782757, 0.04978363215923309, 0.000673435628414154, 0.014564727433025837, 0.04203185811638832, 0.06559725850820541, -0.028302598744630814, 0.005676023196429014, -0.03445234149694443, 0.009741399437189102, -0.03955128788948059, -0.0925389900803566, 0.04127390310168266, -0.06184195354580879, -0.042238570749759674, -0.009396876208484173, -0.014797280542552471, -0.059705909341573715, -0.05670855566859245, 0.06246209517121315, 0.014306334778666496, 0.0424797385931015, -0.03257468715310097, 0.000123611229355447, -0.0005824599065817893, -0.0501970611512661, -0.01262678299099207, 0.006731125991791487, 0.03169615566730499, -0.07827571779489517, 0.0025580863002687693, 0.0220839511603117, 0.03700181469321251, 0.013178020715713501, -0.029336169362068176, -0.055192649364471436, -0.005129092372953892, -0.03562372177839279, 0.004849167075008154, -0.033797748386859894, 0.023479269817471504, 0.029852954670786858, -0.012290872633457184, 0.000675588904414326, 0.01751040294766426, 0.027165671810507774, 0.03329818695783615, -0.04075711965560913, 0.04981808736920357, -0.02509853057563305, -0.028061432763934135, 0.016519898548722267, 0.012135837227106094, -0.0850972831249237, -0.017536241561174393, -0.013970424421131611, 0.005301353987306356, -0.030335286632180214, -0.019258858636021614, -0.009104031138122082, 0.016735224053263664, -0.02847485989332199, 0.07772447913885117, -0.011498468928039074, -0.02871602587401867, 0.0045046438463032246, -0.01721755787730217, -0.07241882383823395, 0.0024181236512959003, -0.045167017728090286, -0.01578778587281704, 0.014797280542552471, -0.03207512944936752, -0.03676064684987068, -0.043065425008535385, 0.0010018094908446074, 0.00817381776869297, 0.006920614279806614, 0.001132620731368661, 0.017493177205324173, -0.011179784312844276, 0.015684427693486214, -0.0003089944366365671, 0.0068904682993888855, -0.015098738484084606, -0.015891142189502716, -0.005912883207201958, -0.018552586436271667, 0.024995174258947372, -0.03464182838797569, -0.01884543150663376, -0.02065417915582657, -0.030938202515244484, 0.03285030648112297, 0.04671737551689148, -0.029112229123711586, 0.05205748602747917, -0.03171338140964508, 0.025150209665298462, -0.042238570749759674, -0.006481346674263477, 0.03321205824613571, -0.02494349516928196, -0.0008397758356295526, 0.03796647861599922, -0.013858454301953316, -0.015615523792803288, -0.006576090585440397, -0.006042079534381628, -0.00480610178783536, 0.04533928260207176, 0.03496912494301796, -0.012411455623805523, -0.04303097352385521, 0.0110764279961586, -0.004780262243002653, -0.02590816095471382, -0.053228866308927536, 0.0011358506744727492, 0.051265083253383636, -0.014254656620323658, -0.03066258318722248, -0.01563275046646595, 0.035003580152988434, -0.04189404845237732, -0.03669174388051033, 0.048405539244413376, -0.003322497708722949, -0.013350281864404678, -0.040963832288980484, 0.017613759264349937, -0.016020338982343674, -0.032815854996442795, -0.026028743013739586, 0.00017858693900052458, -0.006395215634256601, -0.044340163469314575, 0.03262636810541153, 0.0241166390478611, 0.008871478028595448, 0.027544647455215454, -0.006657915189862251, 0.0008774580783210695, 0.0038694285321980715, -0.0055080680176615715, -0.013109115883708, 0.037484146654605865, 0.043513305485248566, -0.04265199974179268, 0.005964561365544796, 0.020171845331788063, -0.018294192850589752, -0.022704092785716057, 0.021308772265911102, 0.02871602587401867, 0.05553717538714409, -0.007988636381924152, 0.03488299623131752, -0.05216084420681, -0.01730368845164776, -0.05615731701254845, 0.010585482232272625, -0.02590816095471382, -0.027320707216858864, -0.013953198678791523, -0.0069852122105658054, 0.07944709807634354, -0.00788097269833088, -0.00041961876559071243, -0.016183987259864807, -0.05340112745761871, 0.008285787887871265, -0.025046851485967636, -0.008940382860600948, -0.002203873125836253, -0.009767238982021809, 0.0011336973402649164, -0.05877569317817688, -0.02645939774811268, 0.059637002646923065, 0.005396097898483276, -0.03979245573282242, -0.03879333660006523, 0.029749596491456032, 0.019086597487330437, -0.018294192850589752, 0.07841353118419647, -0.0461316853761673, -0.024013282731175423, -0.006102371029555798, 0.05529600754380226, -0.055571626871824265, -0.05946474149823189, -0.00595164205878973, -0.010551029816269875, 0.012333937920629978, -0.030025215819478035, 0.020309654995799065, 0.00915570929646492, 0.003740232205018401, -0.01670077256858349, -0.01860426366329193, -0.034624602645635605, -0.013849841430783272, -0.011954962275922298, 0.023841019719839096, 0.032953664660453796, 0.02847485989332199, -0.008036009036004543, 0.03655393421649933, 0.021825557574629784, -0.0007552599417977035, -0.0649082139134407, -0.02983572706580162, -0.055192649364471436, 0.013289990834891796, -0.007601047866046429, -0.032591916620731354, 0.004496030509471893, -0.026218231767416, -0.049542468041181564, 0.02751019410789013, -0.03562372177839279, 0.09412379562854767, 0.05688081681728363, -0.017226170748472214, -0.036795102059841156, 0.006843096110969782, 0.04633839800953865, -0.005107559729367495, -0.02387547306716442, 0.002471955493092537, 0.03264359384775162, -0.0039189537055790424, 0.04620058834552765, 0.0045175631530582905, 0.02365153282880783, 0.00011890094901900738, -0.006093757692724466, -0.025356922298669815, -0.013531156815588474, -0.04971472918987274, -0.03479686379432678, 0.023548174649477005, 0.028750479221343994, 0.002723888261243701, -0.013083276338875294, -0.015529393218457699, 0.012936853803694248, -0.017501790076494217, 0.03689845651388168, 0.051437344402074814, -0.020481916144490242, -0.0443057119846344, -0.02487459033727646, -0.02501240000128746, 0.015314065851271152, -0.025511959567666054, -0.032367974519729614, 0.015288226306438446, -0.0036390286404639482, -0.015339905396103859, 0.04499475657939911, -0.042169664055109024, -0.017519015818834305, -0.017407044768333435, 0.06215202435851097, -0.0006556711159646511, -0.025649767369031906, 0.0017269236268475652, 0.03279862925410271, 0.030335286632180214, -0.036140505224466324, 0.00788097269833088, -0.03272972255945206, -0.020533595234155655, 0.00262699113227427, 0.0007827141089364886, -0.007114408537745476, -0.027527419850230217, -0.009775851853191853, 0.00915570929646492, 0.02780303917825222, 0.017880765721201897, -0.0074890777468681335, 0.007269443944096565, 0.028216468170285225, 0.02916390635073185, 0.017183104529976845, 0.04382338002324104, -0.013307216577231884, 0.011799926869571209, 0.04606277868151665, 0.027923623099923134, 0.014228817075490952, 0.018173610791563988, -0.021946141496300697, -0.020774761214852333, -0.003763918299227953, 0.013858454301953316, -0.014254656620323658, 0.04447797313332558, -0.019500024616718292, 0.026648886501789093, 0.03765640780329704, -0.03111046366393566, -0.0009883515303954482, -0.013126341626048088, 0.009138483554124832, 0.030042441561818123, 0.021084832027554512, 0.00734696164727211, -0.008264255709946156, -0.028819384053349495, -0.048922326415777206, 0.026321588084101677, 0.009035126306116581, -0.023530948907136917, -0.005568359512835741, -0.04558044672012329, 0.012747365981340408, 0.02403050847351551, 0.01786353811621666, 0.05863788351416588, -0.050300419330596924, 0.01657157577574253, 0.010318475775420666, 0.011610439047217369, 0.020447464659810066, -0.012833497487008572, 0.02148103527724743, 0.03496912494301796, 0.036278314888477325, 0.0020316115114837885, -0.035830434411764145, 0.020516369491815567, -0.013221086002886295, 0.05260872468352318, -0.028612669557332993, 0.00808338075876236, 0.03548591211438179, 0.0423419289290905, -0.019344989210367203, -0.03202345222234726, 0.023841019719839096, 0.04778539761900902, -0.017346754670143127, 0.04819882661104202, 0.03097265399992466, 0.010861100628972054, 0.01171379629522562, 0.02840595506131649, -0.002747574122622609, -0.0034473873674869537, -0.03555481508374214, -0.03202345222234726, -0.002540860092267394, -0.016494058072566986, -0.029370620846748352, -0.062048666179180145, -0.003955559339374304, 0.012377003207802773, 0.03503803163766861, 0.005374565254896879, 0.03247133269906044, -0.009147096425294876, 0.011808539740741253, -0.03576153144240379, 0.026958957314491272, -0.005671716760843992, 0.01944834738969803, -0.05185077339410782, -0.007088569458574057, 0.04210076108574867, 0.05092056095600128, 0.03931012004613876, 0.009698334150016308, -0.0018991853576153517, 0.011326206848025322, -0.016218440607190132, 0.007510610390454531, 0.04974918067455292, -0.006731125991791487, -0.005775073543190956, -0.025288019329309464, 0.0005668486701324582, -0.017338139936327934, -0.020516369491815567, -0.002616224577650428, -0.0027066620532423258, -0.005663103424012661, 0.017269236966967583, 0.031833961606025696, 0.040722668170928955, 0.049232397228479385, -0.011972188949584961, -0.04165288060903549, -0.0281820148229599, 0.07138524949550629, 0.02780303917825222, -0.04816437140107155, 0.04544263705611229, 0.03285030648112297, -0.013281377963721752, -0.0423419289290905, -0.024909043684601784, 0.022497378289699554, -0.008798266761004925, 0.012290872633457184, -0.008638924919068813, -0.01815638318657875, 0.029181133955717087, 0.04647620767354965, 0.0020843667443841696, -0.017157265916466713, -0.006864629220217466, -0.011842992156744003, 0.029181133955717087, -0.01333305612206459, 0.01069745235145092, 0.014711149968206882, -0.014823120087385178, 0.0012413609074428678, 0.010232345201075077, 0.007717324420809746, -0.006769884843379259, 0.02787194401025772, -0.03820764645934105, -0.008763814345002174, -0.005335806403309107, 0.05915467068552971, 0.024461163207888603, 0.0016870880499482155, -0.0011433870531618595, 0.008871478028595448, -0.012962693348526955, 0.05477922409772873, 0.021825557574629784, 0.005912883207201958, 0.07104072719812393, 0.02744128927588463, 0.02599429152905941, 0.014237429946660995, -0.020481916144490242, 0.048853419721126556, 0.02132599987089634, 0.023375913500785828, -0.031024333089590073, -0.072625532746315, -0.03651948273181915, 0.014263269491493702, 0.015805011615157127, 0.0021511181257665157, -0.0890248492360115, -0.004106288310140371, 0.05870679020881653, -0.015150416642427444, -0.008570020087063313, 0.008798266761004925, -0.021205415949225426, -0.01951725222170353, 0.05908576399087906, 0.01390151958912611, 0.024151090532541275, 0.015589684247970581, 0.03955128788948059, -0.02577035129070282, -0.007067036349326372, -0.0302147027105093, 0.023754889145493507, -0.039826907217502594, -0.010947231203317642, -0.010981683619320393, -0.009276293218135834, 0.015538006089627743, 0.005465002730488777, -0.012333937920629978, 0.03669174388051033, -0.06063612177968025, -0.04013697803020477, 0.0003353720239829272, 0.026321588084101677, -0.00002479626527929213, -0.04489140212535858, -0.008802573196589947, -0.01690748706459999, 0.060015980154275894, 0.02651107683777809, 0.010163440369069576, 0.021446581929922104, -0.02930171601474285, -0.00566741032525897, -0.004399133380502462, 0.027182897552847862, -0.009973952546715736, 0.00763119338080287, 0.04068821668624878, 0.05205748602747917, -0.017587920650839806, -0.04685518518090248, 0.007148860953748226, 0.022325117141008377, 0.00035367481177672744, 0.009439941495656967, 0.008109220303595066, -0.03844881430268288, -0.020671404898166656, -0.0028487779200077057, 0.05491703376173973, -0.008380532264709473, -0.01174824871122837, 0.0068904682993888855, -0.04227302223443985, -0.021722201257944107, 0.027251802384853363, -0.014668084681034088, -0.007433092687278986, -0.027096766978502274, 0.0016235666116699576, 0.0015998806338757277, 0.021670522168278694, -0.05340112745761871, 0.04568380489945412, -0.000013457945897243917, -0.05298770219087601, 0.051437344402074814, -0.005736314691603184, -0.0041364342905581, 0.0221528559923172, -0.014263269491493702, -0.03600269556045532, -0.05350448563694954, -0.020516369491815567, -0.028957193717360497, -0.036278314888477325, 0.007148860953748226, -0.04919794201850891, -0.037484146654605865, 0.025977065786719322, -0.030989881604909897, -0.0028595442418009043, -0.0036002695560455322, 0.021756652742624283, -0.00042392528848722577, -0.02683837339282036, 0.014823120087385178, -0.015606910921633244, -0.04775094613432884, -0.03720852732658386, -0.048784516751766205, 0.00012401497224345803, 0.047647587954998016, 0.02282467670738697, 0.04378892481327057, -0.017312301322817802, -0.011601826176047325, 0.02856099046766758, -0.01393597200512886, 0.037932027131319046, -0.020361334085464478, 0.019723964855074883, -0.007941264659166336, 0.027458516880869865, -0.01594282127916813, -0.013505318202078342, 0.0012026020558550954, 0.0384143590927124, 0.014530275017023087, -0.022032272070646286, -0.006537331733852625, -0.01415991224348545, -0.028371503576636314, -0.006119597237557173, 0.005357339046895504, -0.03464182838797569, 0.004321615677326918, 0.03765640780329704, 0.03128272667527199, 0.04440906643867493, -0.014616405591368675, 0.025150209665298462, 0.0033332640305161476, 0.008212576620280743, -0.021274320781230927, -0.037484146654605865, -0.011911896988749504, 0.006666528061032295, 0.030938202515244484, 0.015503553673624992, 0.007545062806457281, 0.00856571365147829, -0.0012984225759282708, -0.016046177595853806, 0.020085714757442474, -0.03486577048897743, 0.0038457426708191633, -0.019620608538389206, -0.01770850270986557, 0.0461316853761673, -0.005008508916944265, -0.021808331832289696, 0.0024375030770897865, -0.003085637930780649, 0.0005625421181321144, 0.013281377963721752, 0.018173610791563988, 0.0150728989392519, 0.05050713196396828, -0.02328978292644024, 0.033194832503795624, 0.01793244294822216, 0.04447797313332558, -0.025150209665298462, 0.0027066620532423258, -0.0629444271326065, -0.013798162341117859, 0.01390151958912611, -0.01336750853806734, 0.00281647895462811, 0.017811860889196396, -0.023462044075131416, -0.02532247081398964, 0.0038651220966130495, -0.017966896295547485, -0.031299952417612076, 0.0030318060889840126, -0.041411712765693665, 0.0222217608243227, 0.011386498808860779, 0.0034495405852794647, 0.03696736320853233, 0.023479269817471504, -0.019465573132038116, -0.009017900563776493, -0.017045296728610992, -0.003828516462817788, -0.030231930315494537, -0.036657292395830154, 0.006627769209444523, -0.014788667671382427, 0.034538473933935165, -0.017424272373318672, -0.024977946653962135, 0.02766522951424122, 0.013384734280407429, 0.08268561959266663, 0.0241855438798666, -0.05198858305811882, 0.04137726128101349, -0.0005824599065817893, -0.007713017985224724, -0.012049706652760506, -0.031610023230314255, 0.00979307759553194, 0.020740309730172157, 0.0013016525190323591, 0.006868935655802488, 0.018879882991313934, 0.016115082427859306, 0.03669174388051033, 0.020774761214852333, -0.0055037615820765495, 0.014892024919390678, -0.02992185764014721, -0.0401025265455246, -0.02509853057563305, 0.015271000564098358, 0.004732890520244837, -0.0031459294259548187, 0.022032272070646286, -0.04482249543070793, 0.02365153282880783, -0.02177388034760952, -0.009517459198832512, 0.016158148646354675, -0.07813791185617447, -0.019603382796049118, 0.02403050847351551, -0.009448554366827011, -0.06353011727333069, -0.008178124204277992, -0.020309654995799065, -0.001455611432902515, -0.01637347601354122, 0.04702744632959366, 0.022945258766412735, -0.013841228559613228, -0.05619176849722862, -0.008914543315768242, -0.019121048972010612, -0.0011240076273679733, -0.021567165851593018, 0.006903388071805239, -0.014831732958555222, 0.04485694691538811, -0.017002230510115623, -0.05178187042474747, -0.009810304269194603, -0.02186001092195511, -0.0008214730187319219, 0.00011042244295822456, 0.036140505224466324, -0.03321205824613571, 0.0007692562066949904, 0.00896622147411108, 0.021567165851593018, -0.006136823445558548, 0.017760181799530983, -0.03388387709856033, -0.010869713500142097, -0.05477922409772873, 0.05939583480358124, 0.028767704963684082, -0.09529517590999603, -0.0022480152547359467, -0.01145540364086628, 0.011507081799209118, 0.0011907590087503195, -0.013918746262788773, 0.012876562774181366, -0.0027604938950389624, -0.020240750163793564, 0.017829086631536484, 0.009241840802133083, 0.018432002514600754, -0.00489653879776597, -0.00941410195082426, 0.008238416165113449, 0.049921441823244095, -0.022187307476997375, 0.040205880999565125, 0.0402403362095356, -0.005223836284130812, -0.03148943930864334, -0.00642536161467433, -0.01922440715134144, -0.02969791740179062, 0.031024333089590073, 0.011464016512036324, 0.02043023891746998, 0.02251460589468479, -0.07813791185617447, 0.029629014432430267, -0.04089492931962013, -0.002997353672981262, 0.03247133269906044, 0.025890935212373734, -0.008643231354653835, 0.0032040677033364773 ]
As recommender systems become increasingly central for sorting and prioritizing the content available online, they have a growing impact on the opportunities or revenue of their items producers. For instance, they influence which recruiter a resume is recommended to, or to whom and how much a music track, video or news article is being exposed. This calls for recommendation approaches that not only maximize (a proxy of) user satisfaction, but also consider some notion of fairness in the exposure of items or groups of items. Formally, such recommendations are usually obtained by maximizing a concave objective function in the space of randomized rankings. When the total exposure of an item is defined as the sum of its exposure over users, the optimal rankings of every users become coupled, which makes the optimization process challenging. Existing approaches to find these rankings either solve the global optimization problem in a batch setting, i.e., for all users at once, which makes them inapplicable at scale, or are based on heuristics that have weak theoretical guarantees. In this paper, we propose the first efficient online algorithm to optimize concave objective functions in the space of rankings which applies to every concave and smooth objective function, such as the ones found for fairness of exposure. Based on online variants of the Frank-Wolfe algorithm, we show that our algorithm is computationally fast, generating rankings on-the-fly with computation cost dominated by the sort operation, memory efficient, and has strong theoretical guarantees. Compared to baseline policies that only maximize user-side performance, our algorithm allows to incorporate complex fairness of exposure criteria in the recommendations with negligible computational overhead.
[ -0.01630367338657379, -0.02219732105731964, -0.022537166252732277, -0.022823352366685867, -0.029083676636219025, -0.012127142399549484, -0.08449649065732956, 0.04185473918914795, -0.09236661344766617, 0.04811506345868111, -0.038742464035749435, 0.000991031643934548, 0.011375903151929379, -0.015006891451776028, -0.016732951626181602, 0.04446618631482124, 0.04414422810077667, 0.03482528775930405, 0.030121102929115295, -0.04317834973335266, -0.006251380778849125, -0.03920751437544823, 0.027330785989761353, 0.05705838277935982, -0.0006265913834795356, 0.046612583100795746, -0.0019775917753577232, -0.0291731096804142, -0.006984733045101166, 0.004637111444026232, 0.06503582745790482, 0.021070461720228195, -0.0351293608546257, -0.012824720703065395, -0.07075954973697662, -0.010678323917090893, 0.07058068364858627, 0.0067074899561703205, 0.010794587433338165, 0.025202276185154915, -0.02169649489223957, 0.023091653361916542, -0.022644486278295517, 0.009775049053132534, 0.009712445549666882, -0.024772996082901955, -0.013209284283220768, -0.000863030378241092, 0.037883903831243515, -0.04936712607741356, 0.020390769466757774, -0.054053425788879395, -0.023037992417812347, -0.018137052655220032, -0.06439190357923508, 0.015167870558798313, 0.02062329649925232, -0.022716032341122627, 0.033036623150110245, 0.00381656177341938, 0.0044202362187206745, 0.004900939296931028, -0.08785917609930038, -0.014595498330891132, 0.021964794024825096, -0.0024705922696739435, 0.0091400733217597, 0.03291141986846924, -0.0034767156466841698, 0.021177781745791435, -0.08056142926216125, 0.053946107625961304, 0.02439737692475319, 0.021571287885308266, -0.0297097098082304, 0.016187408939003944, 0.05784539505839348, -0.0267941877245903, -0.03085445426404476, 0.007096524350345135, -0.011957218870520592, 0.026418568566441536, 0.001817729789763689, 0.03652451932430267, 0.07093841582536697, -0.06042107194662094, 0.04307103157043457, -0.05995601788163185, 0.008737623691558838, -0.018512673676013947, -0.03673915937542915, 0.009739276021718979, 0.020211903378367424, 0.010973453521728516, 0.03312605619430542, -0.0038322126492857933, -0.012601138092577457, 0.0024124605115503073, -0.013620676472783089, 0.038313183933496475, 0.01717117428779602, -0.029763368889689445, 0.023395726457238197, -0.018655765801668167, -0.005312331952154636, -0.00018683154485188425, -0.009363655932247639, -0.002566732931882143, -0.004545442294329405, 0.12520648539066315, 0.01825331710278988, 0.037311531603336334, -0.029334090650081635, 0.05315909534692764, -0.06678871810436249, 0.04339298978447914, -0.06496427953243256, -0.045253198593854904, 0.04153277724981308, 0.012690571136772633, -0.004945656284689903, -0.022966446354985237, 0.024880316108465195, 0.02037288248538971, -0.0416758731007576, 0.0489378497004509, -0.00909088458865881, -0.008321759290993214, 0.07734183222055435, 0.009046168066561222, -0.0016779904253780842, 0.016715064644813538, -0.020569635555148125, -0.045968666672706604, -0.007118883077055216, 0.02005092427134514, 0.056342918425798416, 0.01796713098883629, -0.034181371331214905, -0.026275474578142166, -0.02094525657594204, -0.036846477538347244, -0.07154656201601028, -0.021750153973698616, 0.00785223487764597, 0.009327882900834084, 0.007677840534597635, -0.01216291543096304, -0.027581200003623962, 0.009041696786880493, -0.037883903831243515, 0.04185473918914795, -0.031122753396630287, 0.018870405852794647, 0.053659919649362564, -0.015972770750522614, 0.0038970517925918102, -0.02618604153394699, 0.007445313967764378, -0.00986448209732771, 0.03698957338929176, 0.0013113142922520638, -0.03221384063363075, 0.0503687784075737, 0.04407268017530441, 0.04003030061721802, 0.046827223151922226, 0.006336342543363571, -0.0865713357925415, 0.05222899094223976, -0.015552434138953686, -0.016258956864476204, -0.04446618631482124, 0.02640068158507347, -0.0010681678541004658, 0.06750418245792389, 0.06793346256017685, -0.021535515785217285, -0.04854434356093407, -0.02511284314095974, -0.0250055231153965, 0.0517997108399868, 0.0003971393161918968, 0.013584903441369534, 0.03444967046380043, 0.010329535230994225, 0.07093841582536697, 0.022501394152641296, 0.004330802708864212, 0.018727311864495277, 0.008630303665995598, 0.021285101771354675, 0.05995601788163185, 0.004976957570761442, 0.04353608191013336, -0.04199783131480217, -0.003004955593496561, -0.0626390129327774, 0.034574877470731735, -0.009265279397368431, -0.03677493333816528, -0.012091368436813354, 0.04235556349158287, -0.0413181409239769, 0.03192765265703201, 0.015230474062263966, 0.05641446262598038, -0.054303839802742004, -0.0492955818772316, -0.030800795182585716, -0.02475511096417904, -0.03156992048025131, -0.07244089245796204, 0.006573340389877558, -0.023288406431674957, -0.032857757061719894, -0.006533095613121986, 0.031158527359366417, -0.0002076527161989361, -0.04940290004014969, -0.032750438898801804, 0.030800795182585716, 0.06403417140245438, -0.009211619384586811, 0.03995875269174576, -0.014058899134397507, 0.007856707088649273, 0.026829959824681282, 0.02418273687362671, -0.0029110508039593697, -0.05097692459821701, -0.014523952268064022, -0.027616972103714943, 0.0017897819634526968, 0.02654377371072769, 0.005057447589933872, -0.04818660765886307, -0.02454047091305256, -0.002754542510956526, -0.015606094151735306, -0.03641720116138458, -0.024701450020074844, 0.023968098685145378, 0.04886630177497864, 0.03282198682427406, 0.006577812135219574, -0.03300085291266441, 0.032535798847675323, 0.024415263906121254, 0.006492850370705128, -0.03591637313365936, -0.055484358221292496, -0.00616194773465395, 0.0288153775036335, -0.02550634928047657, 0.04063844680786133, 0.038277409970760345, -0.06070725619792938, 0.006381059065461159, -0.04364340379834175, 0.06281787902116776, 0.00636764382943511, 0.022250980138778687, 0.046719904989004135, 0.019120818004012108, 0.01261008158326149, 0.07612553983926773, -0.027938932180404663, 0.0006646004621870816, 0.039100196212530136, 0.019102931022644043, -0.02650800161063671, 0.021177781745791435, -0.0434645377099514, 0.027581200003623962, -0.01524836104363203, 0.010508401319384575, -0.04317834973335266, 0.08170617371797562, -0.00268076010979712, 0.011858842335641384, 0.023037992417812347, 0.027760066092014313, -0.008429079316556454, -0.01109866052865982, -0.045754026621580124, 0.038742464035749435, -0.055698998272418976, -0.0445377342402935, -0.004265963565558195, -0.00708758132532239, -0.04124659299850464, -0.004771261475980282, 0.038635142147541046, 0.061887774616479874, 0.054089199751615524, -0.024629903957247734, -0.021571287885308266, 0.02432583086192608, -0.019192365929484367, -0.010714097879827023, 0.010195384733378887, 0.04117504507303238, 0.0002526487805880606, -0.012672685086727142, 0.006372115574777126, -0.02888692356646061, 0.05981292575597763, -0.014720705337822437, 0.02058752253651619, 0.0485801137983799, 0.009283166378736496, 0.0208379365503788, -0.03287564590573311, 0.0104189682751894, 0.028511304408311844, 0.046075984835624695, 0.0005245816428214312, 0.03194554150104523, -0.05748766288161278, 0.0104189682751894, -0.018727311864495277, -0.047363825142383575, -0.007351409178227186, -0.06339025497436523, -0.019961491227149963, -0.02799259126186371, 0.037311531603336334, -0.00817419495433569, 0.027438106015324593, -0.03394884243607521, -0.01641099341213703, -0.008728680200874805, -0.03720421344041824, -0.00019619408703874797, 0.018154939636588097, -0.023717684671282768, 0.030836567282676697, 0.024594129994511604, -0.030156875029206276, -0.0025868553202599287, -0.023878665640950203, 0.015078437514603138, 0.02450469695031643, 0.03162357956171036, -0.0026271003298461437, -0.05094115063548088, 0.018780972808599472, 0.07662636786699295, -0.025059182196855545, 0.0010771111119538546, -0.004185474012047052, 0.03205285966396332, 0.06017065793275833, 0.07269130647182465, -0.011295413598418236, 0.017654113471508026, 0.029226770624518394, -0.026168154552578926, 0.011062887497246265, 0.028475532308220863, -0.016876045614480972, -0.05290868133306503, 0.04925980791449547, -0.054590027779340744, -0.0203013364225626, -0.03067558817565441, 0.06285365670919418, 0.016929704695940018, 0.004051323980093002, -0.08199235796928406, -0.009095356799662113, -0.0022771928925067186, 0.03673915937542915, -0.01620529592037201, -0.007718085311353207, 0.014738591387867928, -0.031051207333803177, -0.04185473918914795, 0.026812074705958366, -0.027026712894439697, -0.01339709386229515, 0.02899424359202385, 0.008031101897358894, -0.00306755886413157, -0.00033481555874459445, -0.0067879799753427505, 0.010740927420556545, 0.014792251400649548, -0.009399429894983768, -0.002048020251095295, -0.07201161235570908, 0.019317571073770523, -0.014032069593667984, -0.0145865548402071, -0.01756468042731285, -0.012404385022819042, 0.008415664546191692, 0.021750153973698616, -0.033966731280088425, 0.0010944388341158628, -0.06378375738859177, 0.02550634928047657, 0.08363793045282364, -0.019389118999242783, 0.009408372454345226, -0.005030617583543062, -0.054124973714351654, 0.06725376844406128, 0.010901907458901405, 0.02543480321764946, -0.05380301550030708, -0.02985280193388462, 0.04257020354270935, 0.020319223403930664, 0.05086960643529892, -0.05856085941195488, -0.0255421232432127, 0.03529034182429314, -0.05280136317014694, -0.04160432517528534, 0.03341224417090416, 0.08199235796928406, 0.01599065586924553, -0.02618604153394699, 0.028439758345484734, 0.01972896419465542, -0.053981881588697433, -0.022215208038687706, -0.047184959053993225, 0.0409604050219059, 0.03949370235204697, -0.004681827966123819, -0.03214229270815849, 0.03344801813364029, 0.048150837421417236, 0.00020094522915314883, 0.009953915141522884, 0.00703392131254077, -0.003622044576331973, 0.007297749165445566, 0.005924949422478676, -0.022107888013124466, 0.0431068018078804, -0.014881684444844723, -0.002861862536519766, 0.004346453584730625, -0.007096524350345135, -0.02561366930603981, 0.0057729133404791355, -0.08950474858283997, -0.022519279271364212, -0.03174878656864166, -0.05784539505839348, 0.03192765265703201, -0.019961491227149963, 0.05330218747258186, -0.026490114629268646, 0.009891312569379807, -0.04536052048206329, 0.014649158343672752, 0.034396007657051086, 0.011000283993780613, -0.015498774126172066, -0.004829392768442631, 0.027652746066451073, -0.0246477909386158, -0.015096324495971203, 0.003966362681239843, -0.03720421344041824, -0.006121702492237091, -0.013897919096052647, -0.007038393057882786, 0.007476615719497204, 0.022286754101514816, 0.008133949711918831, 0.0024951864033937454, -0.09351135790348053, 0.04138968512415886, -0.05841776728630066, 0.01634838990867138, 0.0064302473329007626, 0.034467555582523346, -0.019764738157391548, 0.009846595115959644, -0.024093303829431534, 0.004185474012047052, -0.012932040728628635, -0.009381542913615704, -0.027062486857175827, -0.027312899008393288, 0.04224824532866478, -0.03502204269170761, 0.02996012195944786, -0.02216154709458351, 0.0007652128115296364, 0.011706805787980556, -0.047292277216911316, 0.034288689494132996, 0.0033202075865119696, 0.039350610226392746, 0.07340677082538605, 0.01514104101806879, -0.011322243139147758, 0.017546793445944786, -0.00892543327063322, -0.004335274454206228, -0.0024929505307227373, -0.030299969017505646, -0.009470975957810879, 0.0398872084915638, 0.028225118294358253, 0.0160174872726202, -0.0007847763481549919, 0.004031201358884573, -0.013468639925122261, 0.05018991231918335, -0.04800774157047272, 0.04110350087285042, 0.012520648539066315, 0.013763769529759884, 0.013209284283220768, -0.026311248540878296, 0.0688277930021286, -0.02543480321764946, 0.02126721478998661, 0.03459276258945465, -0.01720694825053215, 0.04135391116142273, 0.0008339646155945957, 0.033537451177835464, 0.04350030794739723, -0.025416916236281395, -0.010105951689183712, 0.018977725878357887, -0.013227170333266258, 0.03099754825234413, 0.0018020790303125978, -0.015069494023919106, -0.02511284314095974, -0.005710309837013483, 0.08492577075958252, 0.013423923403024673, -0.00903275329619646, -0.034646421670913696, 0.02421851083636284, 0.017126457765698433, -0.07862967252731323, -0.0161337498575449, 0.047363825142383575, 0.03174878656864166, 0.008563228882849216, -0.029119450598955154, -0.034646421670913696, -0.017412643879652023, -0.0029110508039593697, -0.02564944140613079, -0.0017338861944153905, -0.020927369594573975, -0.014550781808793545, -0.03248213976621628, -0.03081868216395378, 0.021285101771354675, -0.00885835848748684, -0.0003141341148875654, -0.018441125750541687, 0.05147775262594223, 0.08735834807157516, -0.0306040421128273, 0.0017875460907816887, -0.012475932016968727, -0.012520648539066315, -0.020748503506183624, -0.032070744782686234, -0.02903001755475998, 0.008107120171189308, -0.016724009066820145, -0.033859409391880035, -0.006287154275923967, -0.0008976857643574476, 0.0023923381231725216, -0.01796713098883629, 0.037812355905771255, -0.0250055231153965, 0.016893932595849037, 0.01630367338657379, -0.015284134075045586, -0.04031648859381676, 0.007092053070664406, -0.03266100585460663, -0.03280409798026085, 0.045038558542728424, -0.02421851083636284, 0.01221657544374466, -0.07676946371793747, 0.02019401639699936, 0.008590059354901314, 0.009766105562448502, 0.006904243025928736, -0.06714645028114319, 0.06271056085824966, -0.02115989476442337, -0.009712445549666882, -0.005455425474792719, -0.039529476314783096, 0.02992434985935688, 0.04797196760773659, 0.013924749568104744, 0.015203644521534443, 0.038456276059150696, -0.0032307743094861507, 0.015597150661051273, 0.056521784514188766, -0.03659606724977493, 0.018333805724978447, -0.008102647960186005, 0.029369862750172615, -0.009462032467126846, 0.00196194089949131, -0.0055269720032811165, 0.032893531024456024, -0.015105267986655235, 0.04056689888238907, 0.0590616874396801, 0.02429005689918995, 0.05197857692837715, -0.018798859789967537, -0.04206937924027443, 0.017573624849319458, 0.0035393189173191786, -0.017913470044732094, 0.03176667168736458, -0.02496974915266037, -0.02632913365960121, -0.009166902862489223, -0.001379507128149271, 0.005097692366689444, 0.02507706917822361, -0.006756678223609924, 0.0145865548402071, -0.019228138029575348, 0.01244910154491663, 0.009479919448494911, 0.10803531110286713, -0.0012822485296055675, 0.03455698862671852, 0.013352377340197563, -0.03985143452882767, 0.04332144185900688, 0.00278808013536036, -0.028046252205967903, 0.018459012731909752, 0.014201992191374302, 0.038348957896232605, -0.008004271425306797, -0.021750153973698616, 0.02098102867603302, 0.017537850886583328, 0.019317571073770523, -0.008563228882849216, 0.029477182775735855, -0.005312331952154636, 0.0056655933149158955, 0.016232125461101532, -0.0017942535923793912, 0.01713540218770504, 0.02963816374540329, 0.05791694298386574, 0.023020105436444283, 0.03212440758943558, -0.02838609740138054, -0.014112559147179127, -0.038563597947359085, 0.034181371331214905, 0.019442778080701828, -0.028904810547828674, -0.013200340792536736, 0.07820039242506027, -0.006398945581167936, 0.025631556287407875, 0.004031201358884573, 0.0033157358411699533, 0.0157760176807642, -0.01695653423666954, -0.0009507867507636547, -0.024415263906121254, 0.0056655933149158955, 0.04138968512415886, 0.005983081180602312, -0.002177698537707329, -0.03142682835459709, -0.045682478696107864, -0.002450469648465514, 0.006412360351532698, 0.01980051025748253, 0.023252632468938828, 0.005839988123625517, 0.013978409580886364, 0.005817629862576723, 0.002296197460964322, -0.009900255128741264, 0.03273255005478859, -0.008196553215384483, 0.024916090071201324, -0.018924064934253693, 0.03550498187541962, -0.020319223403930664, 0.012145028449594975, -0.06861314922571182, -0.003935060929507017, 0.022036340087652206, 0.01284260768443346, -0.04940290004014969, 0.027974706143140793, 0.046719904989004135, -0.012028765864670277, 0.0354870930314064, -0.010714097879827023, -0.009560409002006054, 0.02860073745250702, 0.013593846932053566, 0.010821416974067688, 0.03625622019171715, -0.06138695031404495, -0.003892580047249794, -0.011501110158860683, 0.011769409291446209, 0.036703385412693024, 0.0052810306660830975, 0.0007858942844904959, 0.02949506975710392, -0.00541518023237586, -0.039135970175266266, -0.004306208807975054, -0.004713129717856646, 0.05233630910515785, -0.009685616008937359, 0.022912785410881042, 0.014023126102983952, 0.011653145775198936, 0.009292109869420528, -0.005589575041085482, 0.029584502801299095, 0.023771345615386963, -0.0009038342977873981, 0.00510216411203146, 0.04253442957997322, 0.02600717544555664, 0.02899424359202385, -0.025166502222418785, 0.008777868933975697, 0.0013191397301852703, 0.004214539658278227, -0.008281514048576355, -0.06940016150474548, 0.010794587433338165, -0.028869036585092545, -0.01752890832722187, 0.014684931375086308, -0.009596182964742184, 0.015758130699396133, 0.05319486930966377, 0.02098102867603302, 0.003300085198134184, 0.04199783131480217, -0.012547478079795837, -0.055198170244693756, 0.04829392954707146, -0.00353037565946579, -0.05276558920741081, 0.02044443041086197, -0.025023410096764565, 0.009381542913615704, -0.053516827523708344, -0.02650800161063671, 0.01720694825053215, 0.03126584738492966, 0.019675305113196373, -0.0220900010317564, 0.03437812253832817, -0.004968014545738697, 0.037740811705589294, 0.007472143974155188, 0.02001515030860901, -0.032750438898801804, -0.005661121569573879, 0.0057460833340883255, -0.02144608087837696, 0.04350030794739723, 0.04911671578884125, -0.02148185484111309, -0.019603757187724113, -0.03199920058250427, 0.009050640277564526, 0.015597150661051273, -0.010275875218212605, 0.008482739329338074, -0.001277776900678873, -0.026347020640969276, -0.037490397691726685, 0.03509358689188957, 0.016366275027394295, 0.01428248267620802, 0.05240785703063011, -0.0175020769238472, -0.018995612859725952, 0.003405169118195772, -0.010982397012412548, -0.004306208807975054, 0.030299969017505646, -0.0104189682751894, 0.07079531997442245, -0.01802973262965679, -0.006694075185805559, 0.00019353903189767152, -0.025023410096764565, -0.014398745261132717, 0.037812355905771255, -0.026525886729359627, -0.027813725173473358, 0.0024258755147457123, -0.027616972103714943, -0.008545342832803726, -0.029298316687345505, -0.0031122753862291574, -0.011125490069389343, -0.017054911702871323, 0.016974421218037605, 0.02055175043642521, -0.013754826039075851, 0.03681070730090141, 0.05255094915628433, -0.045968666672706604, -0.020319223403930664, -0.03063981421291828, 0.022894900292158127, 0.019335458055138588, -0.0019898887258023024, 0.009792936034500599, 0.05101269856095314, 0.05022568628191948, -0.011626316234469414, -0.023002220317721367, 0.011590543203055859, 0.015686582773923874, 0.02436160482466221, -0.028439758345484734, 0.027151919901371002, 0.022465620189905167, -0.023234745487570763, 0.009703502058982849, 0.04017339274287224, 0.020033037289977074, -0.0322674997150898, 0.004223483148962259, -0.012297064997255802, 0.014506065286695957, -0.015963826328516006, -0.032893531024456024, -0.006671716924756765, 0.0158386193215847, 0.005245257169008255, -0.03634565323591232, -0.027241352945566177, 0.021785927936434746, -0.00020220287842676044, -0.002515308791771531, -0.039171744138002396, -0.013817429542541504, -0.0641772672533989, 0.008290457539260387, 0.08134844154119492, -0.028976356610655785, 0.054124973714351654, 0.026597434654831886, -0.004333038814365864, 0.015176814049482346, 0.00096755544655025, 0.029083676636219025, -0.008840472437441349, 0.016893932595849037, 0.020605409517884254, -0.010606777854263783, -0.06067148223519325, 0.03609523922204971, -0.06764727085828781, -0.03595214709639549, -0.015856506302952766, 0.00018431624630466104, -0.034896835684776306, 0.03017476201057434, 0.02461201697587967, -0.013164566829800606, -0.017654113471508026, 0.005093220621347427, -0.012458045035600662, 0.0026628735940903425, 0.03192765265703201, -0.011760465800762177, 0.0019764737226068974, 0.008867301978170872, -0.009506748989224434, -0.008344117552042007, -0.039565250277519226, 0.04414422810077667, 0.03384152427315712, 0.02482665702700615, 0.0012464752653613687, 0.06203087046742439, -0.01860210672020912, 0.024737223982810974, -0.017287438735365868, 0.015042664483189583, -0.03130162134766579, 0.0001579054951434955, -0.01081247441470623, -0.019246025010943413, -0.002035723300650716, -0.0023163198493421078, -0.03140893951058388, 0.01278894767165184, -0.005741611588746309, 0.03149837255477905, 0.030586155131459236, -0.0065420386381447315, 0.007753858808428049, 0.0061574759893119335, 0.032500024884939194, -0.0326252318918705, -0.015284134075045586, -0.016124805435538292, 0.010159611701965332, 0.010427911765873432, -0.016250012442469597, -0.0034990739077329636, 0.05212166905403137, -0.04375072196125984, -0.005026145838201046, 0.003456593258306384, -0.00013030697300564498, 0.01969319023191929, -0.0008054577629081905, 0.037633489817380905, 0.03960102051496506, 0.012422272004187107, -0.0329829640686512, 0.013710109516978264, -0.0028640981763601303, -0.012422272004187107, 0.05169238895177841, -0.037812355905771255, 0.00975716207176447, 0.002562261186540127, -0.019335458055138588, 0.0028327966574579477, -0.014157275669276714, -0.023628251627087593, 0.012824720703065395, 0.004239133559167385, 0.04357185587286949, -0.012064538896083832, -0.005656649824231863, -0.023037992417812347, -0.027116145938634872, -0.0398872084915638, -0.0004460480995476246, -0.011089717037975788, -0.02824300527572632, -0.028117798268795013, 0.03673915937542915, -0.0018512672977522016, -0.015203644521534443, 0.022215208038687706, 0.022447733208537102, 0.02967393584549427, 0.014997947961091995, 0.01849478669464588, -0.023520931601524353, -0.014362972229719162, 0.012493818067014217, 0.04482392221689224, 0.036882251501083374, 0.005679008085280657, 0.006881884764879942, 0.02992434985935688, -0.02062329649925232, -0.00734693743288517, -0.007302220910787582, -0.027438106015324593, 0.006846111733466387, -0.02015824429690838, -0.003156991908326745, 0.010141724720597267, -0.04264175146818161, -0.010955567471683025, 0.019120818004012108, -0.0011447450378909707, -0.02087370865046978, -0.01430036872625351, 0.004181002266705036, -0.034539103507995605, -0.034252915531396866, -0.01591016724705696, 0.008509568870067596, 0.038026995956897736, -0.02593562938272953, 0.05677219480276108, -0.008178666234016418, -0.023342065513134003, 0.022859126329421997, -0.02269814722239971, 0.024129077792167664, -0.003402933245524764, 0.01695653423666954, -0.030478835105895996, -0.011501110158860683, -0.012010878883302212, 0.013710109516978264, 0.024951864033937454, -0.037132665514945984, 0.04897361993789673, -0.02597140148282051, 0.03539765998721123, -0.04385804384946823 ]
In recent years, with the large-scale deployment of space spacecraft entities and the increase of satellite onboard capabilities, delay/disruption tolerant network (DTN) emerged as a more robust communication protocol than TCP/IP in the case of excessive network dynamics. DTN node buffer management is still an active area of research, as the current implementation of the DTN core protocol still relies on the assumption that there is always enough memory available in different network nodes to store and forward bundles. In addition, the classical queuing theory does not apply to the dynamic management of DTN node buffers. Therefore, this paper proposes a centralized approach to automatically manage cognitive DTN nodes in low earth orbit (LEO) satellite constellation scenarios based on the advanced reinforcement learning (RL) strategy advantage actor-critic (A2C). The method aims to explore training a geosynchronous earth orbit intelligent agent to manage all DTN nodes in an LEO satellite constellation scenario. The goal of the A2C agent is to maximize delivery success rate and minimize network resource consumption cost while considering node memory utilization. The intelligent agent can dynamically adjust the radio data rate and perform drop operations based on bundle priority. In order to measure the effectiveness of applying A2C technology to DTN node management issues in LEO satellite constellation scenarios, this paper compares the trained intelligent agent strategy with the other two non-RL policies, including random and standard policies. Experiments show that the A2C strategy balances delivery success rate and cost, and provides the highest reward and the lowest node memory utilization.
[ -0.029552916064858437, -0.008496230468153954, -0.018938446417450905, -0.0077932546846568584, 0.0372065044939518, 0.015214071609079838, -0.0052420576103031635, 0.03715064004063606, -0.07292326539754868, 0.043314483016729355, 0.02383599989116192, -0.06227155029773712, 0.0024254992604255676, -0.04718783125281334, 0.0006570030236616731, 0.01403158251196146, 0.019329506903886795, 0.007462716195732355, 0.026573415845632553, -0.05106118321418762, 0.009795106016099453, -0.038696255534887314, 0.0425696074962616, 0.03076333738863468, -0.010344451293349266, 0.017588360235095024, 0.025847163051366806, 0.0019355111289769411, -0.07932918518781662, 0.05839819833636284, 0.06312815845012665, 0.03707615286111832, -0.029497049748897552, -0.014459885656833649, -0.016554847359657288, -0.04685263708233833, 0.03037227876484394, 0.019664699211716652, 0.015865838155150414, 0.0017958470853045583, -0.007532548625022173, -0.0064478241838514805, -0.07932918518781662, -0.029143234714865685, 0.058733392506837845, 0.007313741371035576, -0.034878771752119064, -0.017020393162965775, 0.0225883349776268, -0.041787486523389816, -0.03698304295539856, -0.05690845102071762, 0.06849125772714615, -0.05370548740029335, -0.06707599759101868, 0.06729945540428162, 0.0443573072552681, 0.021768972277641296, 0.041899219155311584, 0.0009974341373890638, 0.03828657418489456, 0.007597724907100201, -0.025828540325164795, 0.009580954909324646, 0.011312789283692837, -0.02040957473218441, -0.0046927123330533504, 0.025679565966129303, 0.017066948115825653, -0.03268139064311981, -0.06551175564527512, -0.007197354920208454, -0.0573553740978241, -0.03456220030784607, 0.017672158777713776, -0.015102340839803219, 0.013947783969342709, 0.036424387246370316, 0.005367755424231291, -0.013361195102334023, 0.009152651764452457, 0.052886124700307846, -0.01977643184363842, -0.0049766963347792625, 0.05255093052983284, -0.013147043995559216, 0.025195397436618805, -0.06994376331567764, 0.09862145036458969, 0.0016713133081793785, -0.03422700613737106, 0.024282924830913544, -0.03446909040212631, -0.02880804054439068, 0.019459858536720276, -0.008612616918981075, -0.0006273243925534189, -0.018649807199835777, -0.0464802011847496, -0.016610711812973022, -0.04718783125281334, -0.03659198433160782, 0.002930617658421397, 0.032830365002155304, 0.04398486763238907, -0.03543742746114731, -0.03770929574966431, -0.027243802323937416, 0.010242030955851078, 0.14733627438545227, -0.007644279859960079, 0.049943868070840836, -0.03918042406439781, 0.04130331799387932, -0.06323988735675812, -0.03517672047019005, -0.009916148148477077, -0.02854733355343342, -0.03491601720452309, -0.024580875411629677, -0.0051536038517951965, 0.02052130550146103, -0.053109586238861084, -0.03698304295539856, 0.006494379136711359, 0.055679406970739365, -0.02029784396290779, 0.017150746658444405, 0.03227170929312706, -0.012960825115442276, -0.07128453999757767, -0.01836116798222065, -0.0721411406993866, 0.019087422639131546, -0.04424557462334633, 0.021377911791205406, -0.03215997666120529, 0.01988816261291504, 0.0036894590593874454, -0.007760666310787201, 0.010679645463824272, -0.0510239377617836, 0.030018461868166924, 0.024711228907108307, 0.01964607834815979, 0.05664774402976036, -0.005121015477925539, 0.022011056542396545, -0.0693851038813591, -0.02294215001165867, 0.007718767039477825, 0.07225287705659866, 0.002767676254734397, 0.001124295755289495, -0.0037104086950421333, 0.007490649353712797, -0.01026996411383152, -0.015335113741457462, -0.02435741201043129, -0.005479486659169197, 0.016554847359657288, -0.016322072595357895, 0.0087336590513587, 0.005656394641846418, 0.013677767477929592, 0.024022219702601433, 0.029552916064858437, 0.0009724110132083297, -0.1038355752825737, 0.035791244357824326, -0.027523132041096687, -0.03128474950790405, -0.04301653057336807, 0.04014876112341881, 0.008114482276141644, 0.017569739371538162, 0.05471106991171837, -0.05266266316175461, 0.00685284985229373, 0.055940113961696625, -0.04007427394390106, -0.00487893121317029, 0.025735430419445038, 0.06424546986818314, 0.047523025423288345, 0.0027048273477703333, 0.041415050625801086, -0.028268005698919296, 0.014376087114214897, 0.01894775778055191, 0.0031657188665121794, -0.01798873208463192, 0.02934807538986206, -0.030390899628400803, -0.00282354187220335, -0.04551186412572861, -0.024580875411629677, 0.022886283695697784, 0.009553021751344204, -0.03709477558732033, -0.029180478304624557, -0.062048088759183884, -0.009152651764452457, -0.007849120534956455, 0.0059636556543409824, -0.02243935875594616, 0.05575389415025711, -0.010996216908097267, 0.02629408799111843, -0.006582832895219326, -0.051359131932258606, -0.03212273493409157, 0.005921756383031607, 0.005349133629351854, -0.01901293359696865, 0.0024511043448001146, 0.01694590598344803, -0.009785795584321022, -0.001494405441917479, -0.033724214881658554, 0.08066996186971664, 0.02195519022643566, -0.0030120883602648973, -0.038435548543930054, -0.06648009270429611, -0.01345430500805378, 0.013985028490424156, 0.030688850209116936, -0.033742837607860565, -0.04715058580040932, -0.023314587771892548, 0.049794893711805344, 0.02999984100461006, 0.002001851564273238, 0.017765268683433533, -0.035269830375909805, 0.026554793119430542, 0.033761460334062576, -0.06309091299772263, 0.023649781942367554, -0.0148695670068264, 0.0016782964812591672, -0.021024096757173538, -0.036908555775880814, 0.03378008306026459, 0.008854701183736324, -0.036927178502082825, 0.029925353825092316, 0.05832371115684509, -0.008929189294576645, -0.029813621193170547, -0.04540013149380684, 0.05944102630019188, -0.030186058953404427, -0.019441237673163414, 0.004350535571575165, -0.0024976590648293495, -0.047634758055210114, -0.0025744743179529905, -0.014776458032429218, 0.04499045014381409, -0.020335087552666664, 0.0372065044939518, 0.032215844839811325, -0.01790493354201317, 0.005847268737852573, 0.03161994367837906, 0.010940351523458958, -0.004287686664611101, -0.023444941267371178, -0.08543716371059418, -0.017066948115825653, 0.009366802871227264, 0.0038477450143545866, 0.009115408174693584, 0.002937600715085864, -0.012728051282465458, 0.007113556377589703, 0.005097738467156887, 0.022253140807151794, 0.04703885689377785, -0.060409363359212875, 0.004478560760617256, -0.02143377810716629, -0.10100504755973816, -0.03709477558732033, -0.039366643875837326, -0.008691759780049324, 0.014767146669328213, 0.03236481919884682, -0.04960867390036583, -0.006815606262534857, 0.028286628425121307, -0.002776987152174115, 0.10040915012359619, -0.005819336045533419, -0.013929162174463272, -0.008207591250538826, 0.01689935103058815, -0.017569739371538162, -0.00720201013609767, 0.007067001424729824, 0.025065043941140175, 0.046889882534742355, 0.002091469243168831, -0.014050204306840897, -0.04949694499373436, -0.01288633793592453, -0.015754105523228645, 0.00560983968898654, 0.020353710278868675, -0.008505541831254959, -0.00478582177311182, -0.0867779403924942, 0.0037476522848010063, 0.019180530682206154, 0.0219365693628788, 0.010409628041088581, -0.04372416436672211, -0.008850046433508396, 0.026070624589920044, 0.04085639491677284, -0.08908704668283463, 0.02232762798666954, -0.010418939404189587, 0.032606903463602066, 0.06428271532058716, 0.0662938728928566, -0.05333305150270462, 0.0541151687502861, -0.06376130133867264, -0.022793175652623177, -0.0398135706782341, -0.03567951172590256, -0.016517603769898415, 0.016033435240387917, -0.05512075126171112, -0.005544663406908512, -0.010009258054196835, 0.012588387355208397, 0.02806316502392292, -0.04201095178723335, -0.024189814925193787, -0.009068853221833706, -0.006880783010274172, -0.03048400953412056, -0.01977643184363842, -0.005586562678217888, -0.014850945211946964, -0.0181190837174654, 0.001011400599963963, -0.013165665790438652, -0.02374288998544216, 0.009869594126939774, 0.08707588911056519, -0.020186113193631172, -0.0015130273532122374, 0.0036987699568271637, -0.06398475915193558, -0.05918031930923462, 0.013687077909708023, -0.01855669915676117, -0.0778394341468811, 0.0018051579827442765, -0.00970199704170227, 0.020577171817421913, -0.015688929706811905, -0.018016664311289787, 0.003482290543615818, 0.041526779532432556, 0.022532468661665916, 0.03405940905213356, 0.015316491946578026, -0.03264414519071579, 0.01733696646988392, 0.003691786667332053, 0.015605131164193153, -0.018156327307224274, -0.0064478241838514805, 0.05195503309369087, 0.025158153846859932, 0.006126597058027983, 0.005986932665109634, 0.01626620814204216, -0.00994408130645752, 0.0515081062912941, 0.01912466622889042, -0.008705726824700832, 0.034394603222608566, 0.015772728249430656, -0.002749054227024317, 0.021638618782162666, -0.04800719395279884, -0.0339662991464138, -0.006699219346046448, -0.03327729180455208, 0.013677767477929592, -0.004681074060499668, 0.05188054218888283, -0.0667780414223671, -0.0085707176476717, -0.006364025641232729, 0.007341674063354731, 0.0032565004657953978, 0.006452479865401983, 0.028770796954631805, -0.02374288998544216, 0.0015595820732414722, -0.03610781580209732, 0.017150746658444405, 0.010577225126326084, -0.05307234451174736, 0.01862187497317791, -0.0297391340136528, 0.021768972277641296, 0.01912466622889042, -0.005619150586426258, 0.023184234276413918, -0.04107985645532608, -0.0065642111003398895, -0.010409628041088581, 0.021657241508364677, 0.038956962525844574, 0.03128474950790405, 0.019180530682206154, 0.0077932546846568584, 0.03013019450008869, -0.052997857332229614, -0.018109774217009544, -0.015446845442056656, 0.05519523844122887, 0.05229022353887558, -0.027243802323937416, -0.011061393655836582, -0.042532362043857574, 0.017187990248203278, -0.03517672047019005, 0.019813675433397293, -0.010493426583707333, -0.00020222192688379437, 0.006080042105168104, -0.05143361911177635, -0.04003703221678734, -0.007853776216506958, -0.0019657716620713472, -0.037187885493040085, 0.01321222074329853, -0.02310974709689617, -0.016741065308451653, -0.03929215669631958, -0.04733680561184883, 0.032327573746442795, -0.03595884144306183, 0.002930617658421397, 0.0230725035071373, 0.016750376671552658, -0.02549334615468979, -0.06741118431091309, 0.02910599112510681, 0.020633038133382797, 0.02296077273786068, 0.008291389793157578, -0.024301547557115555, -0.04960867390036583, -0.009823039174079895, 0.0015421240823343396, -0.0034939292818307877, -0.0336311049759388, 0.014683348126709461, 0.028919771313667297, 0.012066975235939026, -0.06491585820913315, 0.01621965318918228, -0.007984128780663013, 0.009999946691095829, 0.0010102366795763373, -0.0020099985413253307, -0.11128432303667068, -0.017085570842027664, -0.011564183980226517, 0.0018202882492914796, 0.02053992822766304, 0.04681539535522461, 0.0261637344956398, 0.00778394378721714, -0.0009671736625023186, -0.027262425050139427, 0.01798873208463192, 0.02357529290020466, -0.0832025408744812, 0.0632026419043541, -0.0049999733455479145, -0.019031556323170662, 0.0028933738358318806, -0.010586535558104515, -0.014878878369927406, -0.0036987699568271637, -0.007067001424729824, 0.043314483016729355, 0.03072609379887581, 0.005004629027098417, -0.012011109851300716, 0.008780214004218578, 0.017606982961297035, -0.06562348455190659, 0.01542822364717722, 0.03292347490787506, 0.027709349989891052, -0.047634758055210114, 0.0006925009656697512, -0.014776458032429218, 0.06443168967962265, 0.008794180117547512, 0.02754175290465355, -0.02053992822766304, 0.052364714443683624, -0.01453437376767397, 0.00014082793495617807, 0.023631159216165543, 0.046629175543785095, -0.0025605077389627695, 0.009096786379814148, -0.023780133575201035, -0.03366835042834282, -0.019292263314127922, -0.017253167927265167, 0.061675649136304855, 0.01797010935842991, 0.0160055011510849, -0.01774664781987667, -0.04007427394390106, 0.06383578479290009, -0.005851924419403076, -0.0318434052169323, -0.045996032655239105, -0.007122867275029421, 0.053779974579811096, -0.0052420576103031635, -0.025847163051366806, 0.02119169384241104, 0.01990678533911705, 0.06033487617969513, 0.004269064869731665, 0.04454352334141731, -0.021340668201446533, -0.0012895648833364248, 0.06584694981575012, -0.03554916009306908, 0.0020006876438856125, -0.0284356027841568, -0.0007018119213171303, -0.007863086648285389, -0.015232693403959274, -0.0007262531435117126, -0.013156354427337646, -0.043575186282396317, -0.008365876972675323, -0.028268005698919296, -0.03813759982585907, 0.007932919077575207, -0.019161909818649292, 0.020130246877670288, -0.01938537135720253, -0.009599576704204082, -0.007760666310787201, -0.00487893121317029, 0.001556090428493917, 0.007416161708533764, 0.010093056596815586, 0.023910487070679665, 0.019739188253879547, -0.06055833771824837, -0.024953313171863556, -0.008496230468153954, 0.036182302981615067, 0.002469726139679551, 0.004455283749848604, 0.021024096757173538, -0.019040867686271667, -0.004192249849438667, 0.007923607714474201, -0.03378008306026459, 0.05113567039370537, 0.010809998027980328, 0.0237242691218853, 0.009134029969573021, 0.010698267258703709, -0.009832349605858326, 0.030204681679606438, -0.034897394478321075, -0.013128422200679779, -0.019608834758400917, -0.02525126188993454, -0.007467371877282858, -0.025046421214938164, -0.0015025525353848934, 0.030074328184127808, -0.00433424161747098, -0.003414786420762539, -0.04796994850039482, 0.0014140986604616046, 0.057988520711660385, 0.012541832402348518, 0.014413331635296345, -0.032569658011198044, 0.01008374523371458, 0.010958973318338394, 0.018891891464591026, 0.005502764135599136, 0.003971114754676819, -0.019236396998167038, 0.014450575225055218, 0.05188054218888283, 0.02651754952967167, -0.005786747671663761, 0.010884486138820648, 0.005991588346660137, 0.010949662886559963, -0.010921729728579521, -0.003214601194486022, 0.012616320513188839, -0.028863906860351562, 0.022606955841183662, -0.04156402498483658, -0.01013961061835289, 0.013901229947805405, -0.006354714743793011, -0.06383578479290009, -0.040372226387262344, -0.029050124809145927, -0.028230762109160423, 0.009492500685155392, -0.008519507944583893, 0.009999946691095829, -0.010670334100723267, -0.027653483673930168, -0.01805390790104866, 0.013770876452326775, -0.0018854648806154728, -0.007472027558833361, -0.052252981811761856, 0.05214124917984009, 0.01875222846865654, 0.03610781580209732, -0.0010591191239655018, 0.0033449542243033648, -0.031173018738627434, 0.025809919461607933, 0.044953204691410065, 0.0451766699552536, -0.007853776216506958, 0.032346196472644806, 0.027578996494412422, 0.0420854389667511, -0.015120962634682655, -0.015577198937535286, 0.006024176720529795, 0.0020099985413253307, 0.024189814925193787, 0.06595867872238159, -0.0030795924831181765, 0.005432932171970606, 0.019832296296954155, 0.021526888012886047, 0.01685279607772827, -0.022420737892389297, 0.05284888297319412, 0.05269990488886833, 0.023947730660438538, 0.04625673592090607, -0.09683375060558319, 0.00004389961395645514, -0.025288505479693413, 0.006326782051473856, 0.03914318233728409, -0.025362994521856308, -0.03381732478737831, 0.030037084594368935, -0.028137654066085815, -0.06286744773387909, -0.03614506125450134, -0.05463658273220062, -0.03955286368727684, -0.0020681919995695353, -0.0689009353518486, -0.00797947309911251, -0.02016749046742916, 0.010921729728579521, -0.009152651764452457, 0.01332395151257515, -0.01579134911298752, -0.01256976556032896, 0.061563920229673386, 0.0009049067157320678, -0.0018191244453191757, 0.038845229893922806, -0.0015432878863066435, -0.0043272580951452255, 0.008431053720414639, -0.026126490905880928, -0.01026996411383152, -0.021396534517407417, 0.019683321937918663, -0.0014757836470380425, -0.04238338768482208, 0.03366835042834282, -0.007067001424729824, 0.0003945509670302272, -0.03111715242266655, -0.00701579125598073, -0.004418039694428444, 0.019478481262922287, -0.027616240084171295, 0.023146990686655045, 0.039850812405347824, 0.015651686117053032, -0.01842634566128254, -0.033463507890701294, -0.011322099715471268, -0.03683406859636307, -0.02459949627518654, -0.007872398011386395, 0.048416875302791595, -0.0541151687502861, -0.04491596296429634, 0.029627403244376183, 0.021787593141198158, 0.01678762026131153, -0.032569658011198044, 0.00012737071665469557, -0.013873296789824963, 0.0029725166969001293, -0.030148815363645554, -0.008929189294576645, -0.0022253140341490507, -0.004548393189907074, 0.0023801084607839584, 0.03046538680791855, 0.0324951708316803, -0.002316095633432269, 0.026871366426348686, -0.02472984977066517, 0.04044671356678009, 0.00845898687839508, 0.012327681295573711, 0.0031703743152320385, -0.0014199180295690894, 0.02422705851495266, -0.029497049748897552, -0.004990662448108196, -0.020074380561709404, -0.01785837858915329, 0.017653537914156914, -0.011629360727965832, -0.054785557091236115, 0.02217865362763405, 0.0184449665248394, 0.0037918793968856335, 0.044841475784778595, 0.031303372234106064, 0.0261637344956398, 0.038956962525844574, 0.01491612195968628, 0.03236481919884682, -0.003584710881114006, -0.05653601139783859, -0.018258748576045036, 0.011275545693933964, 0.019161909818649292, -0.007709456142038107, 0.02182483673095703, -0.0019843934569507837, 0.029292209073901176, -0.07679661363363266, 0.02677825652062893, 0.020986853167414665, 0.026256844401359558, -0.02741139940917492, -0.00013857294106855989, -0.0064990343526005745, -0.014971987344324589, 0.0586589053273201, -0.038100358098745346, 0.03186202794313431, 0.0012744346167892218, 0.01256045512855053, 0.012858404777944088, -0.02270006574690342, -0.01724385656416416, 0.0008065599831752479, 0.00886401254683733, 0.02893839403986931, 0.015884459018707275, -0.0002825287519954145, 0.05344478040933609, -0.009445945732295513, 0.003547467291355133, 0.025325750932097435, -0.0044808886013925076, -0.0035940217785537243, 0.03854728117585182, -0.011526940390467644, -0.0510239377617836, 0.005400343798100948, 0.023295965045690536, 0.006969236768782139, -0.015418912284076214, -0.016014812514185905, -0.030781960114836693, 0.03059574030339718, 0.012402168475091457, 0.0053956881165504456, -0.025940271094441414, 0.03175029531121254, 0.008496230468153954, 0.004401745740324259, -0.03264414519071579, 0.016145166009664536, -0.02970189042389393, -0.008175003342330456, -0.02575405314564705, 0.00994408130645752, 0.005991588346660137, 0.004215526860207319, -0.054897285997867584, -0.027597619220614433, 0.014497130177915096, -0.015037164092063904, 0.0398135706782341, -0.0023242428433150053, 0.026089247316122055, 0.012932891957461834, -0.006368681322783232, -0.010996216908097267, -0.06089353188872337, 0.04119158908724785, -0.01518613938242197, 0.029254965484142303, -0.01459954958409071, 0.03970183804631233, -0.0013407750520855188, -0.0031005421187728643, -0.01886395923793316, 0.007779288105666637, -0.05828646942973137, 0.011266234330832958, -0.025307128205895424, -0.002593096112832427, 0.004934797063469887, -0.014962676912546158, 0.0004815500578843057, 0.025828540325164795, 0.051992274820804596, 0.010996216908097267, -0.008417087607085705, 0.015549265779554844, -0.0006360534462146461, 0.021899325773119926, -0.04033498093485832, -0.015456155873835087, 0.04681539535522461, 0.014506440609693527, 0.025065043941140175, -0.02459949627518654, 0.017886310815811157, 0.0342828705906868, -0.010903107933700085, -0.022513847798109055, -0.013035312294960022, -0.029310831800103188, 0.010167543776333332, -0.02204830013215542, -0.004457611124962568, 0.021787593141198158, -0.0023754530120640993, -0.04461801424622536, 0.03098680078983307, -0.0012930564116686583, 0.03925491124391556, -0.03458082303404808, -0.015847215428948402, -0.016340695321559906, -0.025214018300175667, 0.02078201249241829, 0.0591430738568306, -0.05739261955022812, -0.014441263861954212, -0.05538145452737808, -0.02882666327059269, -0.02400359697639942, -0.016582779586315155, 0.07608897984027863, -0.04260684922337532, -0.02525126188993454, 0.0007472027209587395, 0.03854728117585182, -0.01648036018013954, -0.03996254503726959, -0.00004619098035618663, 0.052737150341272354, -0.004920830484479666, -0.03508361428976059, -0.03013019450008869, -0.03111715242266655, 0.03063298389315605, -0.02474847249686718, -0.017476629465818405, -0.009152651764452457, 0.010856552980840206, -0.062308795750141144, 0.004308636300265789, 0.0038640389684587717, 0.009804417379200459, -0.015325803309679031, -0.02882666327059269, 0.004711334593594074, -0.025102287530899048, -0.07422679662704468, 0.019962649792432785, -0.02553059160709381, 0.01620103046298027, -0.03888247534632683, -0.03124750591814518, 0.03240206092596054, 0.0028212140314280987, 0.0008810474537312984, -0.03452495485544205, 0.021731728687882423, 0.01537235826253891, -0.03521396592259407, 0.010940351523458958, 0.0225883349776268, 0.01824943721294403, 0.005879857111722231, 0.004585636779665947, -0.022606955841183662, -0.03273725509643555, -0.015949636697769165, -0.020875122398138046, 0.007043724413961172, -0.045474618673324585, -0.014804390259087086, -0.0002652162220329046, -0.009972014464437962, 0.014506440609693527, -0.011499008163809776, -0.01065171230584383, 0.04297928884625435, 0.016405871137976646, 0.03970183804631233, -0.060148656368255615, 0.024394655600190163, 0.010316519066691399, -0.07467371970415115, -0.023146990686655045, -0.03504636883735657, -0.025158153846859932, -0.06249501183629036, -0.011722470633685589, 0.035921595990657806, -0.005875201430171728, 0.02191794663667679, 0.005083771888166666, -0.007760666310787201, -0.025940271094441414, 0.06688977777957916, -0.022923527285456657, -0.007192699238657951, -0.029552916064858437, 0.03364972770214081, 0.02027922123670578, -0.05348202586174011, -0.026964474469423294, -0.009729929268360138, -0.02119169384241104, 0.01803528517484665, -0.03191789239645004, 0.001879645511507988, -0.019683321937918663, 0.0007023938233032823, 0.03279312327504158, 0.017364898696541786, 0.0040339636616408825, -0.03024192526936531, -0.0030749370343983173, 0.00043615922913886607, 0.008012061938643456, 0.01589377038180828, -0.009110752493143082, 0.006033487617969513, -0.039366643875837326, -0.004155005794018507, -0.018919825553894043, 0.016694510355591774, -0.04621949419379234, 0.01378018781542778, -0.006084697786718607, -0.04823065549135208, -0.00851485226303339, 0.010856552980840206, -0.01774664781987667, 0.008170347660779953, 0.01224388275295496, 0.05322131887078285, 0.008561407215893269, 0.004632191266864538, 0.04245787486433983, 0.05418965592980385, -0.025307128205895424, 0.07482269406318665, -0.014245734550058842, 0.027113450691103935, -0.016452426090836525, -0.013929162174463272, 0.02106134034693241, 0.008580029010772705, -0.020390953868627548, 0.017327655106782913, 0.007430128287523985, -0.025418858975172043, 0.019664699211716652, 0.013742944225668907, -0.01319359801709652, 0.0336311049759388 ]
Artificial intelligence (AI) has been widely applied in drug discovery with a major task as molecular property prediction. Despite booming techniques in molecular representation learning, key elements underlying molecular property prediction remain largely unexplored, which impedes further advancements in this field. Herein, we conduct an extensive evaluation of representative models using various representations on the MoleculeNet datasets, a suite of opioids-related datasets and two additional activity datasets from the literature. To investigate the predictive power in low-data and high-data space, a series of descriptors datasets of varying sizes are also assembled to evaluate the models. In total, we have trained 62,820 models, including 50,220 models on fixed representations, 4,200 models on SMILES sequences and 8,400 models on molecular graphs. Based on extensive experimentation and rigorous comparison, we show that representation learning models exhibit limited performance in molecular property prediction in most datasets. Besides, multiple key elements underlying molecular property prediction can affect the evaluation results. Furthermore, we show that activity cliffs can significantly impact model prediction. Finally, we explore into potential causes why representation learning models can fail and show that dataset size is essential for representation learning models to excel.
[ -0.012932448647916317, 0.01496161799877882, -0.0284457765519619, 0.011361478827893734, 0.027136635035276413, -0.02176915481686592, 0.00496071157976985, 0.010370271280407906, 0.0238637812435627, 0.03738534450531006, 0.01107159722596407, -0.013428051955997944, 0.02670648880302906, -0.03459874168038368, -0.04974738135933876, 0.021507326513528824, 0.009163991548120975, -0.001496161799877882, -0.048101603984832764, -0.037086110562086105, -0.0016598044894635677, -0.046044379472732544, -0.0024452893994748592, 0.005811653565615416, 0.036637261509895325, 0.0038292391691356897, 0.02623893693089485, 0.012876342982053757, -0.0757431909441948, 0.06781353056430817, 0.04279022663831711, 0.019450103864073753, 0.01404521893709898, 0.012633216567337513, -0.040433771908283234, -0.013661827892065048, 0.025603068992495537, -0.0016562978271394968, 0.013007257133722305, 0.04024675115942955, 0.0524778738617897, 0.024574458599090576, -0.01290439534932375, 0.009425819851458073, 0.010519887320697308, -0.030877038836479187, -0.016195951029658318, -0.030559105798602104, -0.0075836703181266785, 0.027192741632461548, -0.060482341796159744, -0.038226936012506485, 0.04312686249613762, -0.014774598181247711, -0.0555076040327549, 0.03459874168038368, 0.01742093451321125, 0.008514096029102802, -0.0013640787219628692, 0.03564605489373207, -0.03695519641041756, -0.009855966083705425, -0.03701130300760269, -0.02809043787419796, -0.0008632152457721531, 0.01061339769512415, 0.002431262983009219, -0.02384507842361927, 0.008327075280249119, 0.018066154792904854, -0.05644270405173302, -0.0037520932964980602, 0.03749755397439003, 0.009430495090782642, -0.01948750764131546, -0.019786739721894264, 0.018094206228852272, 0.05229085683822632, -0.008013816550374031, -0.008687089197337627, 0.057938866317272186, 0.060818977653980255, 0.0057321698404848576, 0.013437403365969658, 0.06358687579631805, 0.024911094456911087, 0.020104674622416496, -0.061155613511800766, -0.014007815159857273, 0.004378611221909523, -0.062427353113889694, 0.028950730338692665, -0.012876342982053757, 0.02223670482635498, -0.003908722661435604, 0.00498408917337656, 0.026220235973596573, 0.020085971802473068, -0.008584228344261646, -0.006120237056165934, 0.044997066259384155, 0.0038385901134461164, 0.028932029381394386, 0.014512769877910614, 0.009500627405941486, -0.10622748732566833, -0.04473523795604706, -0.009612839668989182, -0.014344451017677784, 0.1654755026102066, -0.00013295968528836966, 0.002237229375168681, -0.026519468054175377, -0.001975401071831584, -0.023527145385742188, 0.011726167984306812, -0.0910414457321167, -0.032167479395866394, 0.006751430220901966, -0.06762651354074478, 0.027024421840906143, 0.031587716192007065, -0.04978478327393532, -0.026556871831417084, -0.04035896435379982, 0.13338282704353333, -0.011913188733160496, -0.013381296768784523, 0.002473342465236783, 0.028258755803108215, -0.04035896435379982, 0.07088066637516022, -0.010809768922626972, 0.01496161799877882, 0.02167564444243908, 0.012427493929862976, 0.013895602896809578, 0.021731751039624214, -0.03852616623044014, -0.03097054921090603, -0.022386321797966957, -0.04234137758612633, -0.0477275624871254, -0.036730773746967316, 0.029380878433585167, 0.017261967062950134, -0.007873551920056343, 0.07944618910551071, 0.010351569391787052, 0.006101534701883793, -0.0577518455684185, 0.01595282554626465, 0.054385483264923096, -0.023209210485219955, -0.01650453545153141, -0.008046545088291168, -0.01386754959821701, -0.0011910850880667567, -0.011155756190419197, -0.019468804821372032, 0.06474640220403671, -0.06583111733198166, 0.03693649545311928, 0.04308946058154106, 0.031007952988147736, 0.05139315873384476, 0.03287815675139427, 0.012623865157365799, -0.10592825710773468, 0.07260125130414963, 0.034804463386535645, -0.0017661722376942635, -0.00968764815479517, 0.02489239163696766, -0.010463781654834747, 0.023807674646377563, 0.005797626916319132, 0.030315978452563286, -0.010117794387042522, -0.005143056157976389, -0.019281785935163498, 0.019300486892461777, 0.02016078121960163, 0.0019333215896040201, 0.036263223737478256, 0.005115003325045109, 0.06167927011847496, 0.016233354806900024, 0.017495742067694664, 0.05019623041152954, 0.01777627319097519, 0.006064130924642086, 0.015045776963233948, 0.01868331991136074, -0.008616956882178783, -0.03517850488424301, -0.04275282472372055, 0.00956608448177576, -0.006218422669917345, -0.04215436056256294, -0.029511792585253716, -0.05202902853488922, -0.000416996655985713, 0.027491973713040352, 0.030933145433664322, -0.027248846367001534, -0.004399650730192661, -0.01685052178800106, 0.02489239163696766, 0.014793300069868565, -0.003950802143663168, -0.014868107624351978, -0.05606866255402565, -0.036973897367715836, -0.003586112754419446, -0.005619957577437162, -0.021170688793063164, 0.03841395303606987, -0.056106068193912506, -0.02373286709189415, 0.005998673848807812, 0.016205303370952606, 0.06815017014741898, -0.03716091811656952, 0.048550449311733246, -0.010360920801758766, 0.026276342570781708, -0.01743028499186039, -0.007494835648685694, -0.04151849076151848, 0.05116873234510422, -0.00865436065942049, -0.012296579778194427, 0.04065819829702377, 0.0005791782750748098, -0.011314723640680313, 0.024219119921326637, -0.08011946827173233, -0.022292811423540115, 0.033439215272665024, 0.01661674678325653, 0.020123375579714775, -0.03532811999320984, -0.016326865181326866, 0.07368596643209457, -0.029436983168125153, 0.007391974329948425, 0.044548217207193375, 0.06515784561634064, 0.05000920966267586, 0.013222330249845982, -0.044211581349372864, 0.009912071749567986, 0.014868107624351978, -0.010781715624034405, -0.03573956713080406, 0.055320583283901215, -0.007116119842976332, -0.03659985959529877, -0.02751067467033863, 0.04731611907482147, 0.005760223139077425, 0.023414932191371918, 0.05090690404176712, 0.00032027214183472097, 0.04881227761507034, 0.047390926629304886, 0.0009502965258434415, 0.04619399458169937, 0.032859452068805695, 0.005844382103532553, -0.02650076523423195, -0.021488623693585396, 0.060482341796159744, -0.0410696417093277, -0.06672881543636322, 0.0348418690264225, -0.01948750764131546, 0.033308301120996475, -0.015045776963233948, 0.02348973974585533, -0.03220488131046295, 0.013848847709596157, 0.03413119167089462, -0.008897487074136734, -0.07566838711500168, 0.017607953399419785, -0.01663544960319996, -0.06029532104730606, -0.023471038788557053, -0.012997905723750591, -0.025733983144164085, -0.0627639889717102, 0.0008766573155298829, -0.02259204350411892, 0.009271527640521526, -0.01926308311522007, 0.028520584106445312, 0.04686727002263069, -0.049934402108192444, -0.06100599840283394, -0.005535798612982035, 0.050383247435092926, 0.006209071725606918, 0.0030040123965591192, -0.009584786370396614, 0.07372337579727173, 0.10480613261461258, -0.012530354782938957, -0.021974876523017883, -0.004488485399633646, -0.01244619581848383, 0.018430843949317932, -0.01767341047525406, -0.006251151207834482, 0.0244248416274786, 0.01403586845844984, -0.03815212473273277, -0.02773509919643402, 0.014568875543773174, 0.008172784000635147, 0.008434612303972244, -0.07275086641311646, 0.02741716429591179, -0.03602009639143944, -0.0018561757169663906, -0.02489239163696766, 0.03912463039159775, -0.08677738159894943, 0.0122124208137393, -0.026051918044686317, 0.00250607100315392, -0.0310827624052763, 0.019076062366366386, 0.03401897847652435, -0.05000920966267586, -0.03168122470378876, 0.01707494631409645, -0.030128957703709602, 0.004750313702970743, -0.03179343789815903, -0.0236019529402256, -0.02670648880302906, -0.00473161181434989, 0.01973063312470913, -0.0460817851126194, -0.022872572764754295, 0.0017603278392925858, 0.03805861622095108, -0.018056802451610565, 0.0009970515966415405, -0.0030414164066314697, -0.04058339074254036, 0.040171943604946136, 0.01175422128289938, -0.0002834525366779417, -0.05588164180517197, -0.010351569391787052, -0.005633984226733446, 0.05131835117936134, 0.007887577638030052, -0.0627639889717102, 0.020347800105810165, -0.0038572922348976135, -0.06033272668719292, 0.020927563309669495, -0.03998492285609245, 0.02397599257528782, 0.03759106621146202, 0.016326865181326866, -0.001263555372133851, 0.03083963505923748, -0.01336259488016367, 0.02820265106856823, -0.01844954490661621, 0.02807173691689968, -0.007200278807431459, 0.02225540764629841, -0.022554639726877213, 0.029156453907489777, 0.01524214819073677, 0.014110676012933254, -0.0223489161580801, 0.03327089920639992, -0.049822188913822174, 0.03222358599305153, 0.05146796628832817, -0.0057321698404848576, -0.0029829726554453373, 0.0410696417093277, 0.029418282210826874, -0.0087759243324399, 0.03667466714978218, -0.029736215248703957, 0.036151010543107986, 0.01060404721647501, 0.0258087906986475, 0.014484716579318047, 0.044436004012823105, -0.02704312466084957, -0.011034193448722363, 0.0032331121619790792, -0.00005734799924539402, -0.0061623165383934975, -0.007784716784954071, 0.007162874564528465, -0.013558966107666492, -0.054759521037340164, 0.012100208550691605, -0.017813676968216896, -0.001593178603798151, 0.004355233628302813, 0.00584905780851841, -0.00681688729673624, 0.015064478851854801, 0.021021073684096336, -0.006625191308557987, -0.02290997840464115, -0.021713048219680786, 0.022105790674686432, 0.006321283522993326, -0.009047103114426136, 0.027922119945287704, -0.013091416098177433, -0.0513557530939579, 0.020216885954141617, -0.008453314192593098, -0.027361059561371803, -0.035234611481428146, -0.03454263508319855, 0.004696545656770468, 0.04413677379488945, 0.032485414296388626, -0.04578255116939545, -0.05573202669620514, -0.014400557614862919, -0.025603068992495537, 0.017626656219363213, -0.0458199568092823, 0.00026007500127889216, -0.006092183757573366, 0.026519468054175377, -0.026295043528079987, 0.004806419834494591, -0.01134277693927288, -0.008313048630952835, -0.031138867139816284, -0.024854987859725952, -0.05012141913175583, -0.03646894544363022, -0.025827493518590927, 0.043052054941654205, -0.07372337579727173, -0.06455938518047333, 0.06639218330383301, 0.02075924538075924, 0.011950592510402203, -0.02075924538075924, 0.06594333052635193, -0.07144172489643097, 0.003705338342115283, 0.014540822245180607, 0.010791067034006119, 0.014578226953744888, -0.017177807167172432, 0.04514668136835098, -0.020366502925753593, -0.027005720883607864, 0.029848428443074226, 0.03923684358596802, 0.03413119167089462, -0.0172900203615427, -0.019188275560736656, -0.024686669930815697, 0.02831486240029335, -0.006438171491026878, -0.02268555387854576, -0.05423586443066597, 0.050271037966012955, 0.030315978452563286, 0.0502336323261261, -0.0034458476584404707, -0.03229839354753494, -0.019749335944652557, 0.010772365145385265, 0.01261451467871666, 0.03072742372751236, -0.014559525065124035, 0.026968317106366158, 0.0035884506069123745, -0.03119497373700142, -0.03790900111198425, -0.021189391613006592, -0.010856524109840393, 0.007326517254114151, -0.039723094552755356, 0.03334570676088333, -0.04578255116939545, 0.038245636969804764, 0.0616418682038784, 0.035814374685287476, -0.08505679666996002, -0.023246614262461662, 0.051542773842811584, -0.001123874681070447, 0.02257334068417549, 0.019637124612927437, -0.045483317226171494, -0.006433495786041021, -0.0074247028678655624, 0.005185135640203953, -0.022386321797966957, -0.041668105870485306, 0.0074293785728514194, -0.030559105798602104, 0.04103223606944084, -0.006274528801441193, 0.002251256024464965, 0.018617862835526466, 0.035365525633096695, 0.0033523375168442726, 0.029436983168125153, -0.0048952545039355755, 0.021021073684096336, -0.05995868518948555, -0.0140919741243124, 0.03424340486526489, -0.03878799453377724, 0.024967201054096222, 0.018169015645980835, -0.037534959614276886, 0.01267062034457922, -0.029867129400372505, -0.034561336040496826, -0.013231680728495121, 0.033532727509737015, 0.02053482085466385, 0.011230564676225185, 0.0040069082751870155, 0.015326307155191898, -0.028408372774720192, 0.043052054941654205, -0.0075789946131408215, 0.017944591119885445, 0.00006162170029710978, 0.05352518707513809, 0.042603205889463425, -0.04092002660036087, -0.0198428463190794, 0.022180598229169846, 0.02853928692638874, 0.030241170898079872, 0.029081644490361214, -0.03027857467532158, 0.0023786635138094425, -0.03768457472324371, 0.01696273498237133, -0.04817641153931618, -0.028576690703630447, 0.007088066544383764, -0.005568527150899172, 0.013493509031832218, -0.03196175768971443, 0.023527145385742188, -0.007106768433004618, -0.04956036061048508, 0.006181018427014351, 0.08198966830968857, 0.005774249322712421, -0.000758600770495832, -0.011146405711770058, -0.029025539755821228, -0.04641842097043991, 0.025397347286343575, 0.01614919677376747, 0.03998492285609245, 0.02027299255132675, -0.05124354362487793, 0.003335973247885704, -0.008892811834812164, 0.019898952916264534, -0.004867201205343008, 0.00013734298408962786, 0.007939008995890617, 0.020572224631905556, 0.005629308987408876, 0.010463781654834747, -0.044884853065013885, -0.002816992113366723, 0.004184577614068985, -0.0019298149272799492, 0.05101911723613739, -0.016710257157683372, -0.017458338290452957, -0.016719607636332512, 0.001105757080949843, 0.0019403347978368402, 0.011585903353989124, 0.030877038836479187, -0.04275282472372055, 0.003153628669679165, 0.022180598229169846, 0.05700376629829407, 0.05262749269604683, 0.0010671841446310282, 0.019749335944652557, 0.03934905678033829, 0.06624256074428558, -0.019169572740793228, 0.01536371186375618, 0.004825121723115444, 0.017720166593790054, 0.0013196615036576986, -0.06721507012844086, 0.009444521740078926, 0.003448185510933399, 0.04185512661933899, 0.034318212419748306, -0.017944591119885445, -0.011642009019851685, 0.0010408844100311399, -0.035365525633096695, 0.0766034871339798, 0.0004614139616023749, 0.01537306234240532, 0.04058339074254036, 0.003134926548227668, -0.026201533153653145, 0.0026019189972430468, -0.027585484087467194, -0.01993635669350624, -0.012679971754550934, -0.03050299920141697, -0.01524214819073677, 0.013250382617115974, -0.039162036031484604, -0.015503976494073868, 0.02534124068915844, 0.026799999177455902, -0.05057026818394661, -0.04473523795604706, 0.030933145433664322, -0.002299180021509528, -0.001969556789845228, 0.01891709677875042, 0.05831290781497955, -0.035028889775276184, -0.009201395325362682, 0.035945288836956024, 0.007181576918810606, 0.01169811561703682, 0.018945148214697838, 0.018543055281043053, 0.03848876431584358, -0.017177807167172432, -0.024256523698568344, -0.009650243446230888, 0.021469922736287117, 0.04780237004160881, 0.030203767120838165, 0.01731807366013527, 0.05648010969161987, -0.040059734135866165, 0.007139496970921755, 0.05408624932169914, 0.0010911461431533098, -0.0011653697583824396, 0.04095742851495743, -0.003985868766903877, 0.07372337579727173, -0.0005639828741550446, -0.047428328543901443, -0.04279022663831711, 0.01683182083070278, 0.03592658415436745, -0.011127703823149204, -0.014924214221537113, 0.017794974148273468, -0.015485274605453014, -0.028614094480872154, -0.05064507573843002, 0.008116677403450012, -0.02453705295920372, 0.014363153837621212, -0.014746544882655144, -0.004993440117686987, -0.007812770083546638, 0.027323655784130096, -0.02511681616306305, 0.032279692590236664, 0.014288345351815224, -0.016719607636332512, -0.0024452893994748592, 0.006410118192434311, -0.005316049791872501, 0.023770270869135857, -0.035702161490917206, -0.05745261535048485, 0.0021273549646139145, 0.008818003349006176, -0.015962176024913788, 0.01881423406302929, -0.03564605489373207, -0.0033920793794095516, -0.00239152112044394, 0.002669713692739606, 0.0308209341019392, -0.015550731681287289, -0.002756210509687662, 0.004383286461234093, 0.010547940619289875, 0.046044379472732544, 0.008504744619131088, 0.04574514552950859, 0.03815212473273277, -0.0009964671917259693, 0.0008036025101318955, 0.001718248357065022, 0.04009713605046272, -0.010463781654834747, 0.01615854725241661, 0.008383181877434254, 0.017794974148273468, -0.03321479260921478, -0.02764158882200718, -0.007976412773132324, -0.010230006650090218, 0.014774598181247711, -0.009986880235373974, -0.003950802143663168, 0.023545846343040466, -0.014886810444295406, -0.0238637812435627, 0.028389669954776764, -0.007092742249369621, 0.026987018063664436, 0.012885693460702896, 0.0438375398516655, -0.017860431224107742, -0.03841395303606987, 0.026108022779226303, -0.01175422128289938, 0.023452335968613625, -0.03209267184138298, 0.016130493953824043, 0.04641842097043991, 0.005372155923396349, 0.0006890526274219155, 0.01139888260513544, 0.007817445322871208, 0.024331331253051758, -0.025883600115776062, 0.06527005881071091, -0.02487369067966938, -0.05217864364385605, 0.018589811399579048, 0.04697947949171066, 0.0359639897942543, -0.024948498234152794, 0.004070027731359005, -0.025771386921405792, 0.002322557382285595, 0.014204186387360096, 0.033196091651916504, 0.06732728332281113, 0.0013021283084526658, -0.03671206906437874, 0.0018164339708164334, -0.0021519013680517673, -0.008892811834812164, -0.005026168655604124, -0.01042637787759304, 0.060706764459609985, -0.030858337879180908, -0.0006212578155100346, 0.015625540167093277, -0.04200474172830582, -0.01135212741792202, -0.026201533153653145, 0.06265177577733994, -0.0036281924694776535, 0.027435867115855217, 0.050383247435092926, 0.0621655248105526, -0.02062833122909069, 0.008850731886923313, 0.007611723151057959, -0.048550449311733246, -0.0014587577898055315, -0.003590788459405303, -0.01673831045627594, -0.05962204933166504, 0.004479134455323219, -0.01961842179298401, 0.024163013324141502, -0.004100418649613857, -0.024144310504198074, -0.018169015645980835, 0.03229839354753494, 0.0037146892864257097, 0.06848680973052979, -0.04473523795604706, 0.043725330382585526, 0.059435028582811356, -0.04611918702721596, -0.02165694162249565, 0.009393091313540936, 0.00864968542009592, -0.0059004882350564, 0.0018152650445699692, 0.0552457757294178, 0.010968736372888088, 0.0069290995597839355, 0.017112350091338158, 0.0008649685187265277, -0.013241032138466835, -0.027230145409703255, 0.012090858072042465, -0.026519468054175377, -0.0048204464837908745, -0.011604605242609978, -0.001388625125400722, 0.011267968453466892, -0.01834668405354023, -0.007317166309803724, -0.03699260205030441, 0.022853871807456017, 0.01821576990187168, 0.03946126624941826, 0.0037123514339327812, 0.015055128373205662, 0.021974876523017883, -0.026743892580270767, 0.029193857684731483, -0.05745261535048485, 0.016654150560498238, -0.007382623385637999, 0.03407508507370949, 0.0052786460146307945, 0.00013135248445905745, -0.02625763975083828, -0.027061827480793, -0.05116873234510422, 0.0010426377411931753, -0.024050801992416382, 0.0014797975309193134, 0.004675505682826042, -0.0014295357977971435, -0.00024444126756861806, 0.05752742290496826, -0.02567787654697895, -0.05184200778603554, -0.015653593465685844, 0.04275282472372055, -0.03153160959482193, -0.0014459001831710339, 0.04215436056256294, 0.008621632121503353, -0.033401813358068466, 0.010585344396531582, 0.025864897295832634, 0.016541939228773117, 0.01570969820022583, 0.01569099724292755, 0.022554639726877213, -0.01478394865989685, -0.04252839833498001, -0.041555892676115036, -0.019637124612927437, -0.07189057767391205, -0.0032868804410099983, -0.011819678358733654, 0.012081506662070751, 0.011006140150129795, 0.006980529986321926, 0.04585735872387886, -0.003181681502610445, 0.016944032162427902, -0.025715280324220657, -0.03476706147193909, -0.014063920825719833, -0.06149224936962128, 0.05479692667722702, 0.02820265106856823, 0.018084855750203133, -0.04095742851495743, 0.00702260946854949, -0.024106906726956367, -0.028726307675242424, -0.04724130779504776, -0.015064478851854801, 0.0060080247931182384, -0.0035346823278814554, 0.038021210581064224, 0.019468804821372032, -0.02913775108754635, 0.020441310480237007, -0.007826796732842922, -0.01937529630959034, 0.014896160922944546, 0.03299036622047424, -0.04323907569050789, -0.05363740026950836, 0.009351011365652084, 0.013428051955997944, 0.0005403131362982094, 0.0001843902573455125, -0.029380878433585167, 0.05640530213713646, 0.021114584058523178, 0.014148079790174961, -0.04050857946276665, 0.003847941057756543, -0.011857082135975361, 0.04024675115942955, 0.01673831045627594, -0.0003214410098735243, -0.008579553104937077, 0.009313607588410378, -0.008397208526730537, -0.03175603598356247, 0.005358129274100065, 0.014232239685952663, 0.014886810444295406, -0.04252839833498001, 0.031812138855457306, -0.0671776682138443, 0.0075041865929961205, -0.009351011365652084, -0.01536371186375618, -0.018832936882972717, 0.04286503419280052, 0.0410696417093277, 0.018608512356877327, 0.041219256818294525, -0.05401144176721573, -0.013512210920453072, 0.003410781268030405, -0.000005109268386149779, 0.004829797428101301, -0.02558436617255211, 0.04376273229718208, -0.022049684077501297, 0.019880250096321106, 0.0041822399944067, -0.027192741632461548, 0.0419299341738224, 0.047764964401721954, -0.025266433134675026, -0.003335973247885704, -0.0006960658938623965, 0.03703000396490097, 0.0075041865929961205, 0.014531471766531467, -0.03867578133940697, 0.0036913116928189993, -0.008154082112014294, 0.009168666787445545, 0.006092183757573366, -0.0056573618203401566, -0.039835307747125626, 0.02945568598806858, 0.007789392489939928, -0.007186252158135176, -0.004004570655524731, -0.005895812530070543, 0.004027948249131441, -0.022386321797966957, -0.04514668136835098, -0.03497278317809105, 0.008803976699709892, -0.03645024076104164, 0.01605568639934063, 0.03848876431584358, 0.024798881262540817, -0.003679622896015644, 0.010847172699868679, -0.016130493953824043, 0.026051918044686317, -0.013512210920453072, 0.01261451467871666, 0.0019450103864073753, 0.018758129328489304, -0.011137054301798344, -0.01880488358438015, 0.0003436496772337705, 0.004829797428101301, -0.02292867936193943, -0.04851304739713669, 0.01478394865989685, 0.05068248137831688, -0.002795952372252941, -0.0022383984178304672, -0.03278464451432228, -0.04596957191824913, -0.004427704028785229, -0.018589811399579048, 0.023003488779067993, 0.0025621771346777678, 0.030222468078136444, -0.0060828328132629395, -0.020834052935242653, 0.0023681435268372297, 0.045445915311574936, 0.06272658705711365, 0.007256384938955307, 0.039723094552755356, -0.015157989226281643, -0.0158219113945961, -0.002015142934396863, 0.051093924790620804, 0.007677180226892233, -0.04563293606042862, 0.023807674646377563, 0.017794974148273468, -0.011436286382377148, -0.005086950026452541, -0.012408792041242123, -0.012221772223711014, -0.04185512661933899, 0.02074054256081581, -0.022610744461417198, 0.023714164271950722, -0.005872434936463833 ]
Deep reinforcement learning (DRL) algorithms have recently gained wide attention in the wireless networks domain. They are considered promising approaches for solving dynamic radio resource management (RRM) problems in next-generation networks. Given their capabilities to build an approximate and continuously updated model of the wireless network environments, DRL algorithms can deal with the multifaceted complexity of such environments. Nevertheless, several challenges hinder the practical adoption of DRL in commercial networks. In this article, we first discuss two key practical challenges that are faced but rarely tackled when developing DRL-based RRM solutions. We argue that it is inevitable to address these DRL-related challenges for DRL to find its way to RRM commercial solutions. In particular, we discuss the need to have safe and accelerated DRL-based RRM solutions that mitigate the slow convergence and performance instability exhibited by DRL algorithms. We then review and categorize the main approaches used in the RRM domain to develop safe and accelerated DRL-based solutions. Finally, a case study is conducted to demonstrate the importance of having safe and accelerated DRL-based RRM solutions. We employ multiple variants of transfer learning (TL) techniques to accelerate the convergence of intelligent radio access network (RAN) slicing DRL-based controllers. We also propose a hybrid TL-based approach and sigmoid function-based rewards as examples of safe exploration in DRL-based RAN slicing.
[ -0.011762448586523533, -0.026810968294739723, -0.037579167634248734, -0.025260616093873978, 0.007195652462542057, 0.01823347993195057, -0.03505142405629158, 0.005822243634611368, -0.04991457238793373, 0.019480502232909203, 0.017289787530899048, -0.01809866726398468, 0.02591782994568348, -0.043847981840372086, -0.00103742943610996, -0.005952843930572271, 0.03596141189336777, 0.007667498663067818, -0.03383810445666313, -0.03761287406086922, 0.01637979969382286, 0.019008655101060867, -0.0018663196824491024, 0.054464519023895264, -0.010439594276249409, 0.01295891497284174, -0.009243127889931202, -0.0027067954652011395, -0.12436514347791672, 0.052678242325782776, 0.03599511459469795, 0.010068858042359352, -0.023069903254508972, -0.01737404614686966, -0.053689341992139816, -0.001600906252861023, 0.019076062366366386, 0.05348712205886841, -0.017070716246962547, 0.03461327776312828, 0.00002817384483932983, -0.02591782994568348, -0.04674646258354187, -0.051161594688892365, -0.00477322842925787, -0.011442267335951328, -0.0647440180182457, -0.006757509894669056, -0.0034440550953149796, -0.034141432493925095, -0.005034429021179676, -0.07603462040424347, 0.055475614964962006, 0.0016999096842482686, -0.039095815271139145, 0.027737807482481003, 0.062283679842948914, -0.018789583817124367, 0.007119819987565279, -0.016059618443250656, 0.031647391617298126, -0.0065173739567399025, -0.03016444481909275, 0.000045124230382498354, 0.011863558553159237, -0.049880869686603546, 0.006374134682118893, -0.004769015591591597, 0.016607295721769333, -0.015503513626754284, -0.11256898939609528, 0.018115518614649773, -0.05695855990052223, -0.0040507144294679165, 0.036298442631959915, 0.00621404405683279, -0.039533961564302444, 0.030686846002936363, -0.005754836834967136, -0.0021928204223513603, -0.01867162249982357, 0.018115518614649773, -0.0726642981171608, -0.07333835959434509, 0.04209541156888008, 0.04846533015370369, 0.04509500414133072, -0.057059671729803085, 0.04209541156888008, -0.01439973060041666, -0.034579575061798096, 0.017272936180233955, -0.010557555593550205, -0.00943692121654749, -0.0009705494740046561, 0.005160816479474306, 0.01328752189874649, -0.02320471592247486, -0.045566849410533905, 0.022446392104029655, -0.01259660441428423, -0.00439827935770154, -0.015823695808649063, 0.0046636927872896194, 0.005750623997300863, -0.0321529395878315, -0.049071989953517914, 0.03916322439908981, -0.00857748743146658, 0.11769188940525055, 0.011416989378631115, -0.004103375598788261, -0.015697307884693146, 0.0508582666516304, -0.06683362275362015, -0.028411874547600746, -0.02204195223748684, -0.06949618458747864, -0.02591782994568348, 0.03377069532871246, 0.01680951565504074, 0.054161187261343, -0.05156603455543518, -0.017829040065407753, -0.039331741631031036, 0.06191294640302658, 0.01961531490087509, -0.002430849941447377, 0.02318786457180977, -0.0011385392863303423, -0.008695448748767376, -0.011796151287853718, -0.01562147494405508, -0.03380440175533295, 0.02283397875726223, 0.04917310178279877, -0.002032729797065258, -0.005877011455595493, -0.001107995631173253, -0.01946365088224411, 0.03916322439908981, -0.03238886222243309, 0.016902200877666473, 0.025092100724577904, 0.04795978218317032, 0.06629437208175659, -0.02355859987437725, 0.019008655101060867, -0.009167294949293137, -0.0009278937359340489, -0.024889880791306496, 0.07967457920312881, -0.04014061763882637, 0.04209541156888008, 0.03535475209355354, 0.0367702916264534, -0.02126677706837654, -0.02505839616060257, 0.017694227397441864, -0.008762856014072895, 0.03066999465227127, -0.022210467606782913, -0.01160235796123743, 0.08439303934574127, 0.016480909660458565, 0.06224997714161873, 0.038522861897945404, 0.008623829111456871, -0.08277527987957001, 0.047353122383356094, -0.062148869037628174, -0.0208117812871933, -0.06073332950472832, 0.03045092336833477, 0.04135393723845482, 0.009091462939977646, 0.0036652327980846167, -0.02189028635621071, 0.016758961603045464, 0.015233887359499931, -0.053891561925411224, 0.03697251155972481, 0.00549363624304533, 0.03707361966371536, 0.030990175902843475, 0.008362628519535065, 0.038320641964673996, 0.001626183744519949, -0.024451738223433495, -0.02371026575565338, -0.003947497811168432, 0.06248589977622032, 0.04158985987305641, -0.03262478485703468, 0.036736585199832916, -0.07387761026620865, -0.020289380103349686, 0.007389446254819632, 0.05119529739022255, 0.014307047240436077, -0.04030913487076759, 0.023642858490347862, 0.016902200877666473, 0.0013365461491048336, -0.01674211025238037, -0.023137308657169342, 0.037444356828927994, 0.021671215072274208, 0.008282583206892014, -0.03087221458554268, 0.00390536873601377, 0.04644313454627991, -0.02563135325908661, 0.02699633501470089, -0.030922768637537956, -0.017272936180233955, 0.01461880188435316, -0.04846533015370369, -0.052813056856393814, -0.023069903254508972, 0.010995698161423206, 0.05864372476935387, 0.024401182308793068, -0.028563538566231728, 0.005042854696512222, -0.06315996497869492, 0.00815619621425867, -0.0010943036759272218, -0.07239466905593872, -0.010734498500823975, -0.031495723873376846, 0.03703991696238518, 0.01737404614686966, 0.013582426123321056, 0.020221974700689316, 0.023861929774284363, 0.03223719820380211, 0.030147593468427658, -0.041825782507658005, 0.012217442505061626, -0.04266836494207382, -0.015082222409546375, -0.020727524533867836, -0.023171011358499527, 0.050588637590408325, -0.025597648695111275, 0.010650239884853363, 0.046712759882211685, 0.05402637645602226, -0.0038147910963743925, -0.02175547368824482, -0.04229763150215149, 0.011779299937188625, 0.009563309140503407, -0.051532331854104996, 0.03029925748705864, -0.002380294958129525, -0.059486307203769684, 0.0249909907579422, -0.01867162249982357, 0.08513451367616653, 0.00010729758650995791, 0.008312074467539787, 0.018840139731764793, -0.00818568654358387, 0.02155325375497341, 0.007566388696432114, 0.052947867661714554, -0.022581204771995544, 0.003064892953261733, -0.05082456395030022, -0.024873027577996254, -0.033214591443538666, -0.01752571202814579, 0.013085302896797657, -0.04883606731891632, -0.010279503650963306, -0.0034693325869739056, 0.018401997163891792, 0.026861522346735, 0.009622289799153805, -0.021704919636249542, 0.012175314128398895, -0.02514265477657318, -0.04202800244092941, -0.04617350921034813, -0.033854953944683075, 0.01565517857670784, -0.035860300064086914, 0.010565981268882751, -0.03338310867547989, -0.004478324670344591, 0.010827181860804558, 0.000794660416431725, 0.08459526300430298, 0.021502699702978134, -0.00014784686209168285, -0.05021790415048599, 0.015604623593389988, -0.0001286254555452615, -0.010245800018310547, 0.018772732466459274, 0.019446799531579018, 0.03282700479030609, -0.014863151125609875, -0.015056945383548737, -0.03080480732023716, 0.019413094967603683, -0.011012550443410873, -0.006845980882644653, 0.016632573679089546, -0.00317021575756371, -0.029355566948652267, -0.041252829134464264, -0.047353122383356094, 0.032051827758550644, 0.0270805936306715, 0.02226102352142334, -0.037511762231588364, -0.02972630225121975, 0.04984716698527336, 0.01959846355021, -0.0808204934000969, 0.03683769702911377, 0.02082863450050354, -0.02635597251355648, 0.06909174472093582, 0.015916379168629646, -0.0885048434138298, 0.013590851798653603, -0.0210308525711298, 0.049510132521390915, -0.08621301501989365, -0.022581204771995544, 0.010068858042359352, 0.012032074853777885, -0.04758904501795769, 0.004343511536717415, -0.023238418623805046, -0.03136091306805611, -0.02448544092476368, 0.005089196842163801, -0.005278777796775103, -0.010919866152107716, -0.023541748523712158, -0.014096401631832123, -0.05220639705657959, -0.008274157531559467, -0.01873902976512909, 0.02419896237552166, 0.000857327482663095, -0.004033862613141537, 0.03353477269411087, -0.0015398190589621663, 0.06990062445402145, -0.024434885010123253, -0.03161368519067764, -0.006521586794406176, -0.040241729468107224, -0.0003307135484647006, 0.03316403925418854, -0.04566795751452446, -0.05968852713704109, -0.006845980882644653, -0.037511762231588364, 0.016362948343157768, -0.021923990920186043, -0.01198994554579258, 0.011593932285904884, 0.04647683724761009, -0.005548404064029455, 0.0278557687997818, 0.043982792645692825, -0.04860014468431473, -0.016110172495245934, 0.027670402079820633, 0.0022728657349944115, -0.01803125999867916, -0.055677834898233414, 0.05025160685181618, 0.011838280595839024, 0.033939212560653687, -0.029102791100740433, 0.015006390400230885, 0.022665463387966156, 0.029271308332681656, 0.04489278420805931, -0.03784879669547081, -0.0004865912487730384, -0.0000010984837217620225, 0.03828693926334381, -0.036365851759910583, -0.05072345212101936, -0.0433761365711689, 0.0009637034381739795, -0.03051832877099514, -0.007178801111876965, 0.012857805006206036, -0.002767882775515318, -0.080146424472332, -0.01772793009877205, -0.015318145975470543, -0.011947816237807274, 0.043847981840372086, -0.017424602061510086, 0.007532685529440641, -0.010026728734374046, -0.08196640014648438, 0.004718460608273745, -0.014888428151607513, 0.006449967157095671, -0.020710671320557594, -0.008998778648674488, -0.040545057505369186, 0.023963039740920067, 0.02433377504348755, -0.002112775109708309, 0.013085302896797657, -0.010186819359660149, -0.0664965957403183, 0.010287929326295853, 0.03154627978801727, 0.05625079199671745, -0.00390536873601377, -0.010169968008995056, 0.031697943806648254, -0.0008157249540090561, -0.04142134264111519, -0.005392526276409626, -0.009841361083090305, 0.02908593975007534, 0.03365273401141167, 0.029540933668613434, -0.05796965956687927, -0.04897088184952736, -0.0018842245917767286, 0.0033008160535246134, 0.07718053460121155, -0.03781509026885033, 0.03230460360646248, 0.029035385698080063, -0.05844150483608246, -0.033079780638217926, 0.021384738385677338, 0.02699633501470089, -0.008164621889591217, 0.027754660695791245, -0.03002963215112686, -0.031647391617298126, -0.0032123448327183723, -0.03707361966371536, -0.0018284035613760352, -0.08230343461036682, 0.009479050524532795, 0.05493636429309845, -0.02131733112037182, -0.02756929211318493, -0.03297866880893707, -0.03818582743406296, -0.0036673392169177532, 0.0017862743698060513, 0.02318786457180977, 0.049071989953517914, -0.035523269325494766, 0.0031807480845600367, -0.00001532940223114565, -0.06487883627414703, -0.04860014468431473, -0.004528879653662443, -0.008274157531559467, 0.00033203006023541093, -0.04745423421263695, 0.031495723873376846, 0.005186093971133232, -0.00004571667159325443, -0.014256492257118225, 0.01767737604677677, -0.1288139820098877, -0.022867683321237564, -0.025243764743208885, 0.044117607176303864, 0.033130332827568054, 0.04489278420805931, 0.009217849932610989, -0.00402333028614521, -0.018924398347735405, 0.007330465596169233, 0.022143062204122543, 0.0073852334171533585, -0.026052644476294518, 0.007667498663067818, -0.005211371462792158, -0.02655819244682789, 0.0033008160535246134, -0.055037472397089005, -0.01435760222375393, 0.02168806828558445, -0.043342430144548416, 0.0372084341943264, 0.003286070888862014, -0.001455560908652842, -0.0031491511035710573, 0.03491660952568054, -0.030265554785728455, 0.0036062521394342184, -0.012857805006206036, 0.019160320982336998, 0.016708405688405037, -0.026676153764128685, 0.002630963223055005, -0.0011954136425629258, 0.08547154814004898, -0.020778078585863113, -0.035152532160282135, 0.01259660441428423, 0.048296816647052765, -0.00723356893286109, -0.026457082480192184, -0.00450781499966979, 0.05338601395487785, 0.019649017602205276, 0.0007219876861199737, -0.011619209311902523, 0.02404729835689068, -0.05035271495580673, -0.012335404753684998, 0.054599329829216, 0.0012048926437273622, 0.013868903741240501, 0.012074204161763191, -0.027956878766417503, 0.01658201962709427, -0.017829040065407753, -0.066934734582901, -0.0744168683886528, -0.007785459980368614, 0.035860300064086914, 0.04192689433693886, -0.036601774394512177, -0.002835289342328906, -0.016607295721769333, 0.081898994743824, -0.011113660410046577, 0.01767737604677677, 0.035523269325494766, 0.007857079617679119, 0.00732625275850296, -0.023069903254508972, -0.001367089687846601, -0.008564848452806473, 0.0006466818740591407, 0.010557555593550205, -0.06265442073345184, 0.002784734359011054, -0.013093728572130203, -0.01339705754071474, 0.03223719820380211, -0.04057876020669937, -0.06258700788021088, -0.003970669116824865, 0.007469491567462683, -0.029187049716711044, 0.013843626715242863, -0.003433522768318653, 0.021367887035012245, -0.04317391663789749, 0.02571561001241207, 0.03993839770555496, 0.0052745649591088295, 0.02162066102027893, 0.00912516564130783, -0.01184670627117157, -0.013135857880115509, -0.029557785019278526, 0.006639548111706972, -0.013506594114005566, -0.006639548111706972, -0.015958508476614952, -0.0008520613191649318, 0.012857805006206036, -0.016143877059221268, -0.039399147033691406, 0.027198554947972298, 0.00879655871540308, 0.028277060016989708, -0.015200183726847172, -0.009504327550530434, 0.011813003569841385, 0.01996919885277748, -0.03380440175533295, -0.038253236562013626, -0.0028710991609841585, -0.03916322439908981, 0.0034019257873296738, -0.009934044443070889, -0.01853680983185768, 0.029760004952549934, -0.0011259005405008793, 0.002373975468799472, -0.05520598962903023, 0.005830669309943914, 0.058407802134752274, -0.003107022028416395, 0.004752163775265217, 0.007642221171408892, 0.0014861044473946095, 0.018991803750395775, 0.01996919885277748, 0.015023241750895977, -0.03882618993520737, 0.014804170466959476, 0.02268231473863125, 0.08149455487728119, -0.03294496610760689, 0.0017999663250520825, 0.01909291371703148, -0.001564043341204524, 0.01702016219496727, 0.016531463712453842, 0.020508451387286186, -0.004141291603446007, -0.027518736198544502, 0.018924398347735405, -0.0051229000091552734, -0.00883026234805584, 0.060935549437999725, 0.012267997488379478, -0.01759311743080616, -0.017247658222913742, -0.01185513287782669, -0.019210875034332275, -0.03388866037130356, -0.006433115806430578, -0.02721540629863739, -0.003216557903215289, -0.029338713735342026, -0.0066058449447155, 0.0315968357026577, -0.010919866152107716, 0.006525799632072449, -0.04991457238793373, 0.03596141189336777, 0.002984847640618682, 0.06059851497411728, -0.012259571813046932, 0.0002276288578286767, 0.00840475782752037, 0.038522861897945404, 0.03409087657928467, 0.02419896237552166, 0.0058601596392691135, 0.04610610008239746, -0.0003528313245624304, 0.047218311578035355, -0.050083089619874954, -0.05520598962903023, 0.04947642982006073, -0.008821836672723293, 0.004908041562885046, 0.05486895889043808, 0.009554882533848286, 0.045196112245321274, -0.03102387860417366, -0.004206591751426458, 0.03397291526198387, -0.01012783870100975, 0.04509500414133072, 0.03166424110531807, 0.01831773854792118, 0.036601774394512177, -0.0750909298658371, -0.016758961603045464, -0.0026120049878954887, 0.0210308525711298, 0.0011259005405008793, -0.010574407875537872, 0.026693006977438927, 0.05898075923323631, -0.02355859987437725, -0.027164852246642113, -0.01260503102093935, -0.03774768486618996, 0.002717327792197466, 0.007696988992393017, 0.005948630627244711, -0.010043581016361713, -0.023946188390254974, -0.002027463633567095, -0.030349813401699066, 0.030400367453694344, -0.01091144047677517, -0.0019368859939277172, 0.008636468090116978, -0.040612466633319855, 0.0029869540594518185, 0.07165319472551346, -0.01723923347890377, -0.045701660215854645, 0.025884127244353294, 0.0011343263322487473, -0.007376807741820812, -0.02347434125840664, 0.04640943184494972, 0.0004879077896475792, 0.024586550891399384, 0.05780114233493805, 0.0190423596650362, 0.002329739974811673, -0.04084838926792145, -0.0013523445231840014, 0.012908359989523888, 0.019514204934239388, -0.002182288095355034, 0.010085709393024445, 0.03950025513768196, -0.005304055288434029, 0.001814711606130004, 0.021098259836435318, 0.004394066520035267, -0.0030501477885991335, 0.005531552713364363, 0.02397989109158516, 0.01554564293473959, -0.06808064877986908, -0.004478324670344591, 0.007802311796694994, 0.00698079401627183, 0.004924893379211426, -0.038455452769994736, 0.0007467385148629546, -0.02131733112037182, -0.030636291950941086, -0.029743153601884842, -0.003399819368496537, 0.016025913879275322, 0.011593932285904884, -0.02018827013671398, 0.051801957190036774, 0.02190713956952095, -0.011905687861144543, 0.014087975025177002, 0.006159276235848665, 0.027383923530578613, -0.023592302575707436, 0.0007541111554019153, 0.0033640097826719284, 0.008097215555608273, -0.0008120386628434062, -0.01532657165080309, -0.059216681867837906, 0.012562901712954044, -0.03080480732023716, 0.04482537508010864, -0.018789583817124367, -0.012689288705587387, 0.044623155146837234, 0.034714389592409134, 0.009285256266593933, 0.010953569784760475, 0.01185513287782669, -0.02677726373076439, 0.06626066565513611, 0.0017631034133955836, -0.013017895631492138, 0.028816312551498413, -0.03190016373991966, -0.021654363721609116, 0.003880091244354844, 0.007996105588972569, -0.0008262572227977216, 0.07124875485897064, 0.006845980882644653, 0.051734551787376404, -0.036669179797172546, 0.008539571426808834, -0.016135450452566147, -0.00572955934330821, -0.005021790508180857, -0.006690103095024824, 0.05402637645602226, -0.021418441087007523, 0.0012733524199575186, 0.015857398509979248, 0.053183794021606445, -0.01845255121588707, 0.04816200211644173, -0.02514265477657318, -0.016118599101901054, -0.004625776782631874, 0.015208610333502293, 0.00890609435737133, 0.009040907956659794, -0.02210935950279236, 0.03532104939222336, 0.04199429973959923, -0.011501247994601727, 0.013304374180734158, 0.02411470375955105, -0.04020802676677704, -0.025226913392543793, 0.016177579760551453, -0.0002817384374793619, -0.00009544876957079396, 0.03468068689107895, -0.03919692710042, 0.010978846810758114, -0.0139278843998909, -0.05028530955314636, -0.019851237535476685, 0.01476204115897417, 0.029675748199224472, 0.03505142405629158, -0.04064616933465004, -0.021384738385677338, -0.008181474171578884, -0.03683769702911377, 0.017896447330713272, 0.05523969233036041, -0.017037013545632362, -0.013767793774604797, 0.008813410066068172, -0.039736177772283554, -0.03703991696238518, 0.021283628419041634, -0.057565219700336456, -0.0010010930709540844, -0.0012691395822912455, -0.012731418013572693, 0.030063334852457047, 0.021367887035012245, 0.013978439383208752, 0.05999185889959335, -0.01880643703043461, 0.01953105628490448, -0.04216281697154045, 0.0010390093084424734, 0.03375384584069252, 0.020997149869799614, -0.012984192930161953, 0.014559821225702763, 0.006112934555858374, 0.009883490391075611, -0.03115869127213955, 0.0043119145557284355, -0.07347317039966583, -0.010220522992312908, -0.014391304925084114, -0.008914520032703876, 0.0031301931012421846, -0.008813410066068172, 0.02606949582695961, 0.007402085233479738, 0.04475796967744827, 0.03778138756752014, -0.029203901067376137, 0.0090830372646451, 0.03828693926334381, 0.03311348333954811, -0.004954383708536625, -0.018907545134425163, 0.002890057163313031, 0.02541228197515011, 0.022378984838724136, -0.02750188484787941, 0.01357400044798851, -0.025614500045776367, 0.00189791654702276, -0.03703991696238518, 0.011147363111376762, -0.01566360518336296, 0.028748907148838043, 0.030568884685635567, -0.030855363234877586, 0.02721540629863739, 0.004853273741900921, -0.006702742073684931, 0.011366434395313263, -0.006740658078342676, 0.04324132204055786, -0.03990469500422478, 0.03505142405629158, 0.008320500142872334, -0.005523126572370529, -0.006563715636730194, 0.04388168454170227, -0.009925618767738342, -0.006184553727507591, -0.028344467282295227, -0.031124988570809364, -0.05581264942884445, 0.005670578684657812, 0.03319774195551872, -0.01680951565504074, -0.019295133650302887, 0.016910625621676445, 0.029119642451405525, -0.0344616137444973, 0.0014850512379780412, 0.00549363624304533, 0.017845893278717995, -0.0026499212253838778, -0.03124294988811016, -0.014778892509639263, -0.06784472614526749, 0.06241849437355995, 0.019076062366366386, -0.035590674728155136, 0.005468358751386404, 0.02534487470984459, -0.05271194502711296, -0.01593323051929474, -0.031108137220144272, 0.02456969954073429, -0.009841361083090305, 0.026052644476294518, 0.009714973159134388, 0.0012354362988844514, -0.045701660215854645, 0.01357400044798851, 0.006660612765699625, 0.02478877082467079, 0.001981121487915516, -0.04597128927707672, 0.020289380103349686, -0.008615403436124325, 0.02104770578444004, -0.006251960527151823, -0.0034756518434733152, 0.004769015591591597, -0.013548722490668297, 0.016860071569681168, 0.0367702916264534, 0.023811375722289085, -0.0017820615321397781, 0.017829040065407753, 0.0254291333258152, -0.006500522140413523, 0.025395428761839867, -0.016110172495245934, 0.012621882371604443, -0.04984716698527336, 0.020137716084718704, 0.001099569839425385, -0.0012933637481182814, 0.039736177772283554, -0.009512754157185555, 0.017542563378810883, 0.03417513519525528, -0.0011690829414874315, 0.04199429973959923, -0.036163631826639175, -0.013304374180734158, 0.014551395550370216, -0.07077690958976746, -0.008383693173527718, -0.0198175348341465, -0.028260208666324615, -0.035219937562942505, -0.02721540629863739, 0.052678242325782776, -0.02822650596499443, 0.013734091073274612, 0.009723399765789509, -0.007039774674922228, -0.010978846810758114, 0.051599737256765366, 0.006782787386327982, -0.006740658078342676, -0.06676621735095978, 0.021856583654880524, 0.025530243292450905, -0.011484396643936634, 0.012175314128398895, 0.015604623593389988, -0.015191758051514626, 0.017795337364077568, 0.022564353421330452, -0.04849903658032417, 0.00024500713334418833, 0.02406414970755577, 0.002746818121522665, 0.023878781124949455, -0.0025951534043997526, -0.03338310867547989, 0.009807657450437546, -0.03193386644124985, 0.03196757286787033, -0.02569875866174698, 0.00770120183005929, 0.008333138190209866, 0.0019347795750945807, -0.008349990472197533, -0.00757481437176466, 0.019008655101060867, -0.02333952859044075, -0.027535587549209595, 0.04152245447039604, -0.024401182308793068, -0.0029785283841192722, 0.01873902976512909, -0.014222788624465466, 0.01774478331208229, 0.03511882945895195, 0.08614560961723328, 0.023642858490347862, 0.01242808811366558, 0.0012828315375372767, 0.023996742442250252, 0.026322269812226295, 0.02463710494339466, 0.007010284345597029, 0.004705822095274925, -0.000777808774728328, -0.026878373697400093, 0.030552033334970474, 0.0027826279401779175, -0.04364576190710068, 0.026962632313370705, 0.01457667350769043, -0.042466145008802414, 0.024300072342157364, -0.005000725854188204, 0.03707361966371536, -0.007098755799233913 ]
Operating under real world conditions is challenging due to the possibility of a wide range of failures induced by execution errors and state uncertainty. In relatively benign settings, such failures can be overcome by retrying or executing one of a small number of hand-engineered recovery strategies. By contrast, contact-rich sequential manipulation tasks, like opening doors and assembling furniture, are not amenable to exhaustive hand-engineering. To address this issue, we present a general approach for robustifying manipulation strategies in a sample-efficient manner. Our approach incrementally improves robustness by first discovering the failure modes of the current strategy via exploration in simulation and then learning additional recovery skills to handle these failures. To ensure efficient learning, we propose an online algorithm called Meta-Reasoning for Skill Learning (MetaReSkill) that monitors the progress of all recovery policies during training and allocates training resources to recoveries that are likely to improve the task performance the most. We use our approach to learn recovery skills for door-opening and evaluate them both in simulation and on a real robot with little fine-tuning. Compared to open-loop execution, our experiments show that even a limited amount of recovery learning improves task success substantially from 71% to 92.4% in simulation and from 75% to 90% on a real robot.
[ 0.013331466354429722, 0.01885237917304039, -0.024125494062900543, -0.04119373485445976, 0.02101316675543785, 0.03714969381690025, -0.031162923201918602, 0.0140847684815526, -0.03316511958837509, 0.010045681148767471, 0.03703074902296066, 0.04765627533197403, 0.05197785049676895, -0.04678403213620186, -0.017375510185956955, 0.02684134617447853, 0.013718029484152794, 0.0049485014751553535, -0.02846689336001873, -0.05197785049676895, 0.007369476370513439, -0.023986728861927986, -0.04353293776512146, 0.04325540363788605, -0.004628843627870083, -0.0022091083228588104, 0.04182809591293335, -0.01256825216114521, -0.10094249248504639, 0.006284126080572605, 0.017048418521881104, 0.027158526703715324, -0.03157922253012657, 0.017742250114679337, 0.00395235838368535, 0.00479486770927906, 0.019447091966867447, 0.05118490383028984, -0.024938266724348068, 0.048211339861154556, -0.0035385380033403635, -0.03580167889595032, -0.045594606548547745, -0.0404602587223053, 0.02809024229645729, -0.010556142777204514, -0.06870909035205841, -0.026286281645298004, -0.050629839301109314, 0.029735613614320755, -0.01656273566186428, -0.04785451292991638, 0.07469586282968521, -0.04028184339404106, -0.021409641951322556, 0.008286324329674244, 0.04262104630470276, 0.0008840149966999888, 0.011715831235051155, 0.019219117239117622, -0.008563856594264507, 0.0006715292693115771, -0.049757592380046844, -0.004710616543889046, 0.0503523051738739, -0.06997781246900558, 0.036277446895837784, -0.04270033910870552, -0.011210326105356216, -0.03296688199043274, -0.02900213561952114, -0.04868711158633232, -0.03270917385816574, -0.024621088057756424, 0.009768148884177208, 0.03566291183233261, 0.029874378815293312, 0.013053934089839458, -0.020993342623114586, -0.022916246205568314, 0.03599991649389267, 0.03986554592847824, 0.012895343825221062, -0.031975697726011276, 0.05840074270963669, -0.10118038207292557, 0.026781875640153885, -0.06878838688135147, 0.07005710154771805, -0.006323773879557848, -0.06188972294330597, 0.00770152360200882, -0.0014991705538704991, 0.020358983427286148, 0.00016447511734440923, 0.03270917385816574, -0.02206382527947426, 0.0008679082384333014, -0.044762011617422104, -0.0035880974028259516, -0.012558341026306152, -0.01281604915857315, 0.022499946877360344, 0.004849383141845465, 0.01839643344283104, -0.012855696491897106, -0.03792281821370125, -0.00760736083611846, -0.0007037428440526128, 0.12774419784545898, -0.03887435793876648, -0.002215303247794509, 0.0006334304925985634, 0.042422808706760406, -0.030449267476797104, -0.0420263335108757, -0.024700382724404335, -0.06458575278520584, 0.026286281645298004, -0.040599025785923004, 0.012637635692954063, 0.06906592100858688, 0.016295116394758224, -0.04924217611551285, -0.07322890311479568, 0.039350129663944244, 0.01009028498083353, 0.013618910685181618, 0.012518692761659622, 0.027911828830838203, 0.0256320983171463, -0.01581934653222561, -0.017464715987443924, 0.0012972161639481783, 0.026187162846326828, 0.00813269056379795, -0.014035209082067013, 0.01375767681747675, -0.04456377401947975, -0.014887630008161068, 0.03996466472744942, -0.017345774918794632, -0.043929412961006165, 0.013698206283152103, 0.03290741145610809, -0.0026861170772463083, -0.04262104630470276, 0.07267384231090546, -0.07005710154771805, 0.05586330592632294, -0.048211339861154556, 0.04928182438015938, -0.05415846407413483, 0.019863389432430267, 0.028209185227751732, 0.031440455466508865, -0.02567174658179283, 0.034612253308296204, -0.03171798586845398, 0.015611196868121624, 0.08841388672590256, -0.0281695369631052, -0.0039721825160086155, 0.0915856882929802, 0.04753733426332474, 0.01881273090839386, 0.024541793391108513, -0.014302830211818218, -0.029021957889199257, 0.04499989375472069, -0.04860781505703926, -0.016542913392186165, 0.015234545804560184, 0.031361158937215805, 0.05447564274072647, 0.0035360599867999554, 0.07005710154771805, 0.021925058215856552, -0.01898123323917389, -0.03744705021381378, -0.03528626263141632, 0.002225215081125498, 0.017702601850032806, -0.0019340538419783115, 0.08492491394281387, 0.010942705906927586, -0.021191580221056938, -0.0467047356069088, 0.05130384489893913, -0.005892607383430004, 0.007919585332274437, 0.012627723626792431, -0.01718718372285366, 0.04702191799879074, 0.016701502725481987, -0.04006378352642059, -0.042184922844171524, 0.028566012158989906, 0.008563856594264507, 0.026960289105772972, -0.013529703952372074, -0.04325540363788605, -0.029537376016378403, -0.01980391889810562, 0.028704779222607613, 0.0033080868888646364, 0.028229009360074997, -0.022499946877360344, 0.02014092169702053, -0.07061216980218887, 0.01635458692908287, -0.03415630757808685, -0.049004290252923965, -0.040182724595069885, -0.04008360579609871, -0.0034443752374500036, -0.01394600234925747, -0.0011943804565817118, -0.02002197876572609, 0.010992265306413174, -0.007746127434074879, -0.01818828284740448, 0.03366071358323097, 0.0010698626283556223, 0.008038527332246304, 0.04262104630470276, 0.019883213564753532, 0.007409123703837395, 0.05467388033866882, -0.005022840574383736, -0.014451508410274982, -0.0429382249712944, 0.055665068328380585, -0.005144261289387941, 0.07747118175029755, 0.04131267964839935, -0.024541793391108513, -0.0131728770211339, 0.012082571163773537, -0.03679286688566208, 0.04595143347978592, 0.008236764930188656, -0.0061800517141819, -0.010268698446452618, 0.0360395647585392, 0.012429486028850079, -0.01702859438955784, 0.06581482291221619, 0.004658579360693693, 0.016334762796759605, -0.07489410042762756, 0.0208149291574955, -0.009669030085206032, 0.016681678593158722, 0.007414079736918211, 0.07081040740013123, 0.03413648530840874, -0.0004091744194738567, 0.021746644750237465, 0.00593225471675396, 0.05764744058251381, 0.009703721851110458, 0.03952854126691818, 0.029537376016378403, -0.0031891444232314825, 0.03703074902296066, -0.02513650432229042, 0.01723674312233925, 0.0007223276188597083, 0.03853735327720642, 0.016870005056262016, -0.06629059463739395, -0.007612316869199276, 0.004802301526069641, 0.009069361723959446, -0.051502082496881485, 0.04333470016717911, -0.005292939022183418, -0.011636536568403244, 0.0362972728908062, 0.049004290252923965, -0.011943805031478405, 0.025295095518231392, 0.00032987946178764105, 0.007379387971013784, -0.04198668524622917, -0.030389796942472458, 0.03423560410737991, -0.09475748986005783, 0.012003275565803051, -0.007329828571528196, -0.00909414142370224, -0.04277963563799858, 0.032312698662281036, 0.040182724595069885, 0.014451508410274982, -0.003186666639521718, -0.0014050076715648174, -0.0033948158379644156, -0.007602405268698931, 0.004931156057864428, -0.008311104029417038, -0.018158547580242157, 0.0041159046813845634, -0.03712986782193184, 0.029973497614264488, -0.004480165895074606, -0.013430585153400898, -0.04872675985097885, -0.04002413526177406, 0.040678318589925766, 0.002241321839392185, -0.01661229506134987, -0.000287134520476684, -0.04159021005034447, 0.044841304421424866, 0.004760175943374634, 0.026980113238096237, -0.033938247710466385, -0.009490616619586945, 0.022797303274273872, 0.008558901026844978, -0.05181926116347313, 0.005302851088345051, 0.033184945583343506, -0.007022560574114323, -0.008692710660398006, 0.016711413860321045, -0.04246245697140694, -0.03588097169995308, -0.01179512683302164, 0.03203516826033592, -0.021032990887761116, 0.002971083391457796, -0.03966730833053589, 0.005124437157064676, -0.061572544276714325, 0.04753733426332474, -0.0420263335108757, -0.04448447749018669, -0.03542502596974373, -0.039766427129507065, -0.023074835538864136, 0.007210886105895042, 0.0010165863204747438, -0.03653515502810478, 0.015888730064034462, 0.015492254868149757, -0.020755458623170853, -0.02285677380859852, 0.0010463219368830323, -0.018763171508908272, -0.007651964668184519, 0.003640134586021304, 0.04206598177552223, -0.017286302521824837, -0.020616691559553146, 0.02142946608364582, -0.0013789890799671412, -0.016513178125023842, 0.04079725965857506, -0.06351526826620102, -0.02642504870891571, 0.04785451292991638, -0.011319356970489025, -0.0060016377829015255, -0.03134133666753769, 0.012340279296040535, 0.007141503039747477, 0.062286198139190674, -0.002489118603989482, 0.000467096921056509, 0.06363420933485031, -0.04432588815689087, -0.017742250114679337, 0.0008189683430828154, 0.013688294216990471, -0.036396391689777374, 0.0013096060138195753, 0.05292939022183418, -0.003845806000754237, 0.014362300746142864, -0.053999874740839005, -0.009014846757054329, 0.007602405268698931, 0.06625094264745712, 0.03960783779621124, -0.0008394115720875561, -0.009579823352396488, 0.04535672068595886, 0.019427267834544182, 0.00042435197974555194, -0.02900213561952114, 0.01394600234925747, 0.028189361095428467, -0.02023012936115265, -0.0025820424780249596, -0.033363357186317444, 0.025691570714116096, 0.02709905616939068, -0.02626645751297474, 0.024898620322346687, 0.0010717210825532675, 0.049797240644693375, -0.014173975214362144, -0.011755479499697685, 0.04884570091962814, -0.0536033995449543, -0.007305048871785402, 0.0029017003253102303, 0.007270357571542263, -0.017216920852661133, 0.021667350083589554, 0.025037385523319244, 0.005580383352935314, 0.008127734065055847, -0.0013566873967647552, 0.04424659162759781, 0.02001206763088703, -0.06430821865797043, -0.024006551131606102, -0.01848563924431801, 0.02418496459722519, 0.009892047382891178, -0.039429422467947006, 0.03300653025507927, -0.017553923651576042, -0.021151931956410408, -0.012964727357029915, -0.050788428634405136, 0.014847982674837112, 0.016364499926567078, 0.015284105204045773, -0.00959469098597765, 0.043929412961006165, -0.00577366491779685, -0.008177293464541435, 0.04880605265498161, -0.02293607033789158, 0.005263203755021095, 0.009485661052167416, -0.010813850909471512, -0.07616281509399414, -0.0476166270673275, 0.010075417347252369, -0.04587214067578316, -0.03530608490109444, -0.021905235946178436, 0.05625978112220764, -0.04053955152630806, -0.05471352860331535, 0.06541834771633148, -0.0619293712079525, 0.01697903499007225, 0.03964748606085777, 0.003746687201783061, 0.044762011617422104, -0.056576959788799286, -0.02142946608364582, -0.011041824705898762, 0.013450409285724163, 0.030112264677882195, -0.0027455883100628853, -0.0263457540422678, 0.013965826481580734, 0.03540520370006561, -0.053246572613716125, -0.01722683198750019, 0.016830356791615486, 0.027455883100628853, -0.0025795644614845514, -0.03748669475317001, -0.03869594633579254, -0.01021913904696703, 0.04262104630470276, 0.007577625568956137, -0.0059768580831587315, -0.049043938517570496, 0.014213623479008675, -0.03964748606085777, -0.014887630008161068, 0.04190739244222641, -0.008365618996322155, -0.04369152709841728, 0.008365618996322155, -0.002049279399216175, 0.08611433953046799, -0.042184922844171524, 0.017464715987443924, -0.031777460128068924, 0.006323773879557848, -0.05863862857222557, -0.03009244054555893, 0.0009180870838463306, 0.025988925248384476, -0.031103450804948807, -0.07366502285003662, -0.04262104630470276, 0.03661445155739784, -0.014610097743570805, 0.06359456479549408, -0.06874873489141464, 0.019080352038145065, 0.0008902099216356874, -0.02555280365049839, 0.006061109248548746, 0.03449331223964691, 0.01727639138698578, 0.05538753420114517, -0.03687215968966484, -0.002227693097665906, 0.0337003618478775, -0.06208796054124832, 0.009956474415957928, 0.003340300638228655, 0.02793165296316147, 0.007319916971027851, 0.006621129810810089, 0.06002629175782204, 0.01481824740767479, 0.040559377521276474, 0.047378744930028915, 0.004970803391188383, 0.029953673481941223, -0.040301669389009476, 0.06395139545202255, 0.006968045141547918, -0.023530781269073486, -0.00794932059943676, 0.009555043652653694, -0.02434355579316616, 0.03770475834608078, -0.04095585271716118, -0.032986707985401154, 0.024541793391108513, -0.024066023528575897, 0.08960331231355667, 0.05031265690922737, -0.007785774767398834, -0.04515848308801651, -0.017207007855176926, 0.014154152013361454, 0.0030107307247817516, -0.00028527603717520833, -0.0067549399100244045, -0.005639854818582535, 0.01955612190067768, -0.015710314735770226, 0.03958801180124283, 0.006611218210309744, -0.01914973556995392, -0.005496132653206587, -0.012647547759115696, 0.010427288711071014, -0.01198345236480236, -0.04010343179106712, -0.015868905931711197, 0.01764313131570816, 0.011319356970489025, -0.05836109817028046, -0.007998879998922348, 0.02097351849079132, -0.019694887101650238, 0.05328621715307236, 0.02551315538585186, -0.048250988125801086, 0.002144681056961417, 0.04337434843182564, -0.011180590838193893, 0.020378807559609413, -0.02668275684118271, 0.03459243103861809, 0.0015759875532239676, -0.035226788371801376, 0.035563793033361435, 0.025711392983794212, 0.008182249963283539, -0.07580599188804626, -0.05082807317376137, -0.015343576669692993, 0.019734535366296768, -0.009084230288863182, -0.0077659511007368565, 0.041471268981695175, -0.017048418521881104, 0.007433903403580189, -0.0193182360380888, -0.03417612984776497, 0.009133788757026196, 0.006878838408738375, -0.038101233541965485, 0.00467096921056509, -0.044762011617422104, 0.05768708884716034, -0.01826757751405239, -0.0070671639405190945, 0.018673965707421303, -0.023629900068044662, 0.025156328454613686, -0.03383912891149521, -0.010972441174089909, 0.03266952559351921, 0.012310544028878212, 0.020695986226201057, 0.0015896162949502468, -0.008102954365313053, 0.0015004094457253814, 0.03524661436676979, -0.023253249004483223, 0.015799522399902344, 0.01468939334154129, 0.019784094765782356, 0.03300653025507927, -0.03703074902296066, 0.03070697747170925, -0.006125536281615496, 0.02164752595126629, 0.028248833492398262, 0.017008770257234573, -0.019427267834544182, 0.018079252913594246, 0.03009244054555893, 0.009797884151339531, 0.001090305857360363, -0.05257256329059601, 0.04880605265498161, -0.021191580221056938, -0.02005171589553356, 0.00038594348006881773, 0.03326423838734627, -0.012597988359630108, -0.012290719896554947, -0.015700403600931168, -0.03992501646280289, 0.02396690472960472, 0.020497748628258705, 0.03149992600083351, 0.03913206607103348, 0.031024156138300896, -0.007661876268684864, -0.07144476473331451, -0.0061453599482774734, 0.02596910297870636, 0.05166067183017731, -0.014768688008189201, 0.0007000258774496615, 0.036812689155340195, -0.030726799741387367, 0.03992501646280289, -0.007443815004080534, -0.03633692115545273, 0.008722446858882904, 0.012042922899127007, 0.03853735327720642, 0.02456161566078663, -0.015591373667120934, 0.0005163465393707156, -0.006393156945705414, -0.001185707631520927, -0.01956603303551674, 0.02388761006295681, -0.01681053265929222, -0.041471268981695175, 0.0015512078534811735, 0.05380163714289665, 0.006740072276443243, 0.039270833134651184, 0.057290613651275635, -0.001171459211036563, 0.07271348685026169, 0.01864422857761383, 0.0009756998042576015, -0.02775323949754238, 0.03262988105416298, -0.020795105025172234, 0.002264862647280097, -0.005882695317268372, 0.019090263172984123, 0.008791829459369183, -0.03966730833053589, -0.014154152013361454, -0.002859574742615223, -0.003471632953733206, -0.008861212991178036, -0.0026068221777677536, -0.008306147530674934, -0.018882114440202713, 0.034810490906238556, -0.02301536500453949, -0.006472451612353325, -0.054911766201257706, 0.016870005056262016, -0.0027133747935295105, 0.0074785067699849606, 0.013787413015961647, 0.005506044253706932, -0.0059768580831587315, -0.06886768341064453, 0.0390329472720623, -0.032114461064338684, -0.029081430286169052, -0.044682715088129044, -0.0383787639439106, 0.02896248735487461, 0.04789416119456291, 0.038557179272174835, -0.006249434780329466, -0.011904156766831875, 0.03001314587891102, 0.01805942878127098, 0.011616712436079979, 0.022539595142006874, -0.012072659097611904, -0.021746644750237465, 0.02933913841843605, 0.02555280365049839, 0.0020059149246662855, -0.027792885899543762, 0.003744209185242653, 0.058242153376340866, 0.0003515616699587554, 0.00495345750823617, 0.016721326857805252, -0.051422785967588425, -0.043057169765233994, 0.015829257667064667, 0.01689974032342434, 0.00447520986199379, 0.018872203305363655, -0.015670668333768845, 0.016959210857748985, -0.06418927758932114, -0.029477905482053757, 0.00215831003151834, 0.006735116243362427, 0.003159408923238516, 0.017216920852661133, 0.025612274184823036, -0.00882156565785408, 0.025988925248384476, 0.008345795795321465, 0.015561637468636036, 0.05507035553455353, -0.010476848110556602, 0.02755500189960003, -0.0006969284149818122, 0.0031693207565695047, 0.027118878439068794, 0.03151974827051163, -0.002061669249087572, 0.07885884493589401, -0.012786313891410828, 0.024046199396252632, 0.0075974492356181145, -0.062286198139190674, -0.0288831926882267, 0.024581439793109894, 0.007438859436661005, 0.03762546181678772, -0.008048439398407936, 0.014154152013361454, 0.04686332494020462, 0.029933851212263107, -0.007835334166884422, 0.025414036586880684, -0.004601586144417524, -0.031162923201918602, 0.02771359123289585, 0.04404835402965546, -0.008935552090406418, 0.013906355015933514, -0.011854597367346287, 0.03453296050429344, -0.05435670167207718, -0.01179512683302164, 0.007423991337418556, 0.009639294818043709, 0.025493333116173744, -0.06819367408752441, -0.00055134785361588, -0.043850116431713104, -0.0006771046901121736, -0.026405224576592445, 0.05748885124921799, 0.0005166562623344362, 0.006100756581872702, -0.01748454011976719, -0.003020642790943384, 0.02214311994612217, -0.007240621838718653, 0.01972462423145771, -0.008395355194807053, -0.0115473298355937, 0.03873559087514877, 0.00977806095033884, -0.048964641988277435, -0.025195976719260216, 0.01527419313788414, 0.004849383141845465, -0.014927278272807598, 0.005089745856821537, -0.02388761006295681, -0.007468594703823328, 0.007364520337432623, -0.04932146891951561, 0.01705832965672016, 0.0029636493418365717, -0.032728999853134155, -0.024997739121317863, 0.01939753256738186, 0.010694908909499645, 0.022817127406597137, -0.033323708921670914, -0.043176110833883286, -0.01619599759578705, -0.017177272588014603, 0.03568273410201073, 0.02581051178276539, -0.006809455342590809, -0.006764851976186037, -0.01002585794776678, -0.03354177251458168, 0.006596350111067295, 0.015918465331196785, -0.018951497972011566, -0.02626645751297474, -0.02093387208878994, -0.01981383003294468, 0.034394193440675735, -0.021488936617970467, 0.0062196990475058556, 0.033858951181173325, -0.028189361095428467, -0.0020777760073542595, -0.019338060170412064, 0.005605163052678108, -0.002586998278275132, 0.0012018143897876143, -0.02509685792028904, 0.03088539093732834, -0.02676205150783062, -0.0043637012131512165, -0.01709797792136669, 0.014263182878494263, -0.024244436994194984, -0.03243164345622063, -0.011696008034050465, 0.03867612034082413, -0.009099097922444344, 0.00361535488627851, 0.008226852864027023, 0.0402025505900383, 0.0221827682107687, -0.01129953283816576, -0.05415846407413483, 0.0019340538419783115, 0.032610055059194565, 0.07287207245826721, -0.017831455916166306, -0.02858583629131317, -0.009847443550825119, 0.004066345281898975, -0.006234566681087017, -0.011854597367346287, 0.05673554912209511, 0.018535198643803596, -0.007498330436646938, -0.039766427129507065, -0.03151974827051163, -0.08175311237573624, 0.0034939346369355917, -0.0004032892466057092, -0.024700382724404335, 0.023709194734692574, -0.008182249963283539, 0.016671767458319664, 0.007250533904880285, -0.029319314286112785, 0.013351290486752987, -0.0001818208838813007, 0.03536555543541908, 0.03536555543541908, 0.05300868675112724, -0.028823720291256905, -0.013034110888838768, -0.04107479378581047, 0.02135016955435276, -0.04381047189235687, -0.000581393192987889, -0.02775323949754238, -0.04040078818798065, 0.02105281502008438, -0.006412980612367392, -0.017157448455691338, 0.019843565300107002, 0.012974639423191547, -0.025949278846383095, 0.013698206283152103, -0.030231207609176636, 0.011349092237651348, -0.0024346034042537212, -0.019169557839632034, -0.002705940743908286, -0.00990195944905281, -0.005520912352949381, 0.017742250114679337, -0.005511000286787748, -0.009480704553425312, 0.033363357186317444, -0.0004887791583314538, -0.005530823953449726, -0.012399750761687756, 0.012042922899127007, 0.010516495443880558, 0.023629900068044662, 0.013410761952400208, -0.033145297318696976, -0.02688099443912506, 0.03179728239774704, 0.010238963179290295, 0.01602749526500702, -0.0031891444232314825, 0.003102415706962347, 0.021964706480503082, -0.02355060540139675, 0.032649703323841095, 0.013658558018505573, -0.002237604930996895, 0.03096468560397625, 0.002921523991972208, -0.06581482291221619, 0.005530823953449726, 0.007508242502808571, 0.04888534918427467, -0.016840269789099693, 0.00813269056379795, -0.004430606495589018, 0.0005817029159516096, -0.04246245697140694, -0.020874399691820145, -0.007319916971027851, -0.002762933960184455, -0.003199056489393115, 0.010417376644909382, 0.0019365318585187197, -0.010100197046995163, 0.04860781505703926, 0.035266436636447906, -0.020091362297534943, -0.05518929660320282, -0.03326423838734627, -0.04912323132157326, 0.02551315538585186, -0.02559245191514492, -0.019754359498620033, 0.0016936910105869174, -0.011081472039222717, 0.006333685480058193, -0.018822643905878067, 0.07473550736904144, -0.03383912891149521, 0.016285203397274017, -0.05181926116347313, -0.014976836740970612, -0.043929412961006165, 0.020577045157551765, -0.06204831227660179, -0.057369910180568695, -0.03451313450932503, 0.005501088220626116, 0.019952597096562386, 0.03233252465724945, -0.012845785357058048, 0.03621797636151314, -0.0009732218459248543, 0.02210347168147564, -0.052334677428007126, -0.03409683704376221, -0.030984509736299515, 0.018327049911022186, 0.036733392626047134, -0.06105712428689003, 0.029735613614320755, 0.007850201800465584, -0.03574220836162567, -0.031936049461364746, -0.006472451612353325, 0.009599647484719753, -0.016513178125023842, -0.0378633476793766, -0.01597793586552143, 0.010144799947738647, 0.02384796179831028, 0.004197677597403526, -0.03100433200597763, -0.011249973438680172, 0.004698226694017649, 0.004433084279298782, 0.02123122848570347, -0.013936090283095837, -0.018584758043289185, -0.010665173642337322, 0.01930832490324974, 0.04412765055894852, 0.017335861921310425, -0.026286281645298004, 0.067916139960289, -0.01438212487846613, 0.011884333565831184, 0.02230170927941799, -0.013331466354429722, -0.0061701396480202675, 0.023074835538864136, 0.02351095899939537, -0.012439398095011711, 0.004021741915494204, -0.03835894167423248, 0.022460300475358963, -0.015383224003016949, -0.041114442050457, 0.028863368555903435, -0.03104398027062416, 0.03679286688566208, -0.01877308450639248 ]
With the advances of the Internet of Things (IoT) and 5G/6G wireless communications, the paradigms of mobile computing have developed dramatically in recent years, from centralized mobile cloud computing to distributed fog computing and mobile edge computing (MEC). MEC pushes compute-intensive assignments to the edge of the network and brings resources as close to the endpoints as possible, addressing the shortcomings of mobile devices with regard to storage space, resource optimisation, computational performance and efficiency. Compared to cloud computing, as the distributed and closer infrastructure, the convergence of MEC with other emerging technologies, including the Metaverse, 6G wireless communications, artificial intelligence (AI), and blockchain, also solves the problems of network resource allocation, more network load as well as latency requirements. Accordingly, this paper investigates the computational paradigms used to meet the stringent requirements of modern applications. The application scenarios of MEC in mobile augmented reality (MAR) are provided. Furthermore, this survey presents the motivation of MEC-based Metaverse and introduces the applications of MEC to the Metaverse. Particular emphasis is given on a set of technical fusions mentioned above, e.g., 6G with MEC paradigm, MEC strengthened by blockchain, etc.
[ -0.05117302015423775, 0.0053049735724925995, -0.045635778456926346, -0.028039246797561646, 0.03272174671292305, 0.01575697958469391, -0.033297766000032425, 0.005365362856537104, -0.03753431513905525, 0.0500209778547287, 0.0491662360727787, -0.011520433239638805, 0.017930995672941208, 0.018878644332289696, 0.000015396748494822532, 0.039057984948158264, 0.02521488256752491, -0.04061881825327873, -0.028373710811138153, -0.0023075705394148827, 0.010563493706285954, 0.004001956898719072, -0.01775447279214859, -0.04340601712465286, 0.019696224480867386, 0.006103971507400274, 0.04701079800724983, -0.005318909417837858, -0.020941173657774925, 0.06525767594575882, 0.004724306520074606, 0.005625501740723848, -0.011037318035960197, -0.021145569160580635, -0.02623685635626316, -0.006294430233538151, 0.04496685042977333, -0.013564380817115307, 0.006155069917440414, 0.03251735121011734, 0.0038835008163005114, 0.016518814489245415, -0.01353650912642479, 0.06165289878845215, 0.016295839101076126, -0.005476851016283035, -0.028689594939351082, -0.061690058559179306, -0.015561874955892563, -0.0456729419529438, -0.0076926760375499725, -0.06306508183479309, 0.04333169385790825, 0.034208253026008606, -0.013954589143395424, -0.030603472143411636, 0.12873154878616333, 0.015283155255019665, -0.006034291349351406, 0.0022924733348190784, 0.046862147748470306, -0.018748575821518898, -0.054591987282037735, -0.03794310241937637, -0.009197765029966831, -0.04452089965343475, -0.06797055155038834, 0.027333157137036324, 0.015729106962680817, -0.05173046141862869, -0.032164305448532104, 0.04299722984433174, 0.04024719074368477, -0.053439944982528687, 0.020829686895012856, -0.03790593892335892, 0.0037093006540089846, 0.054889287799596786, 0.019603317603468895, -0.014707133173942566, 0.02252058871090412, 0.027649039402604103, -0.010582075454294682, -0.04143639653921127, 0.05247371271252632, -0.0000794062070781365, -0.010256901383399963, -0.07220710068941116, 0.05968327447772026, 0.05481496453285217, -0.04950070008635521, 0.03322344273328781, -0.0009116471628658473, -0.019714806228876114, 0.04753107577562332, 0.020662453025579453, -0.005639437586069107, 0.01079576089978218, -0.028763920068740845, 0.0030891483183950186, 0.013527218252420425, 0.02396993339061737, 0.04671349748969078, -0.03857487067580223, 0.03950393572449684, -0.009587973356246948, 0.01780092716217041, 0.014335506595671177, 0.0100339250639081, 0.05975760146975517, -0.00947648473083973, -0.021944565698504448, -0.004327130503952503, 0.00946719478815794, -0.03151395916938782, 0.01757795177400112, -0.012068582698702812, -0.03177409619092941, -0.05024395138025284, 0.05280817672610283, -0.0017907769652083516, 0.006052872631698847, -0.020030688494443893, -0.07135235518217087, -0.05195343494415283, 0.07395374774932861, -0.02058812789618969, -0.05173046141862869, 0.023208098486065865, -0.039169471710920334, -0.008840073831379414, 0.03528597205877304, 0.0009128085221163929, -0.019491828978061676, 0.048943258821964264, 0.03056631051003933, -0.004712693393230438, 0.04875744506716728, 0.010907248593866825, -0.020532384514808655, 0.05176762118935585, -0.003546713851392269, -0.06752460449934006, -0.03547178581357002, 0.03450555354356766, 0.02800208516418934, -0.031216656789183617, 0.05303115397691727, -0.060463692992925644, -0.01311842817813158, -0.043889131397008896, 0.005151677411049604, 0.01912020333111286, -0.03086361102759838, 0.045524291694164276, -0.005411816295236349, 0.06414280086755753, -0.0069261956959962845, -0.039355285465717316, 0.0076926760375499725, 0.067227303981781, -0.043480344116687775, 0.01945466734468937, 0.04756823927164078, 0.018962260335683823, -0.009727333672344685, 0.010461295954883099, -0.006823998410254717, -0.02458311803638935, 0.03274032846093178, -0.03753431513905525, -0.014010332524776459, -0.044706713408231735, 0.007251369301229715, 0.011408944614231586, 0.03610355034470558, 0.0610954575240612, -0.032480187714099884, -0.02099691890180111, 0.027128761634230614, -0.03983839973807335, -0.055929843336343765, 0.033706557005643845, 0.01302552130073309, 0.002392347902059555, 0.019008714705705643, -0.004519911948591471, -0.04898042231798172, 0.010210447944700718, -0.06908543407917023, 0.015357480384409428, 0.00751150818541646, 0.032684583216905594, -0.03368797525763512, 0.05020679160952568, -0.09000802785158157, 0.01732710190117359, 0.021349962800741196, -0.015413224697113037, -0.035657599568367004, -0.0444837361574173, 0.00848238356411457, -0.009996762499213219, 0.012207943014800549, 0.07164966315031052, 0.008045721799135208, -0.011148805730044842, -0.019083039835095406, 0.03759005665779114, 0.00823153555393219, -0.017512915655970573, 0.022502006962895393, 0.0008140950812958181, -0.032684583216905594, -0.012886161915957928, 0.009337125346064568, 0.025382114574313164, -0.043666157871484756, -0.0628049373626709, 0.02657132036983967, 0.05782514065504074, -0.025233464315533638, 0.007446473464369774, -0.04035867750644684, 0.01956615410745144, -0.022279031574726105, 0.027110179886221886, 0.020829686895012856, -0.019018005579710007, -0.02365405112504959, 0.010136122815310955, 0.0395410992205143, -0.007019102573394775, -0.005081997253000736, 0.04478103667497635, -0.02097833715379238, -0.0006067969952709973, -0.007181689143180847, -0.028540942817926407, 0.05537240207195282, -0.04786553978919983, 0.04032151401042938, -0.05745351314544678, -0.021740172058343887, 0.06165289878845215, -0.037106942385435104, -0.04340601712465286, 0.03805459290742874, 0.00704697472974658, -0.0010782985482364893, -0.00944396760314703, 0.00663353968411684, -0.008812202140688896, 0.009114149026572704, 0.02090401202440262, 0.0013692127540707588, 0.022966541349887848, -0.03192274644970894, 0.011808443814516068, -0.0019800744485110044, 0.028986895456910133, -0.009165247902274132, -0.01008966937661171, -0.013815228827297688, 0.02933994121849537, 0.01648165099322796, 0.05867988243699074, 0.058717045933008194, -0.040581654757261276, -0.03259167820215225, 0.000028071619453839958, -0.07599769532680511, -0.014242599718272686, 0.020012106746435165, -0.009541519917547703, -0.008719295263290405, -0.027426062151789665, -0.021647265180945396, 0.012486662715673447, 0.009183828718960285, 0.0605008527636528, -0.02675713412463665, 0.05801095440983772, -0.008463801816105843, -0.03417108952999115, 0.018915807828307152, 0.005054125562310219, -0.004317839629948139, -0.0444837361574173, 0.0069401320070028305, -0.01023832056671381, -0.034617044031620026, -0.0264598336070776, 0.031346727162599564, 0.02499190717935562, -0.022390518337488174, 0.011734118685126305, 0.03346499800682068, 0.007232788018882275, -0.009207055903971195, -0.011808443814516068, 0.0009284865227527916, 0.02344965562224388, 0.029042640700936317, -0.03712552413344383, 0.016723209992051125, -0.006800771690905094, 0.05165613442659378, -0.00031356015824712813, -0.06217317655682564, 0.064848892390728, -0.04407494515180588, 0.01218936126679182, -0.021126987412571907, 0.008668196387588978, 0.017968159168958664, 0.0316997729241848, -0.03902082145214081, -0.06878813356161118, -0.03872352093458176, 0.06648404896259308, 0.01502301637083292, -0.07982545346021652, -0.0014807007974013686, -0.0014505061553791165, -0.023431073874235153, 0.027649039402604103, 0.015534003265202045, -0.011641211807727814, -0.016611721366643906, -0.01435408741235733, -0.0028406227938830853, 0.01977054961025715, -0.0018999424064531922, 0.0013169527519494295, -0.0153388986364007, 0.015812722966074944, 0.05154464766383171, -0.017940286546945572, 0.008988725021481514, -0.0033423190470784903, -0.057787977159023285, -0.06351102888584137, 0.017819508910179138, -0.02725883014500141, -0.018265461549162865, -0.011808443814516068, 0.016044989228248596, 0.009857403114438057, 0.019213108345866203, 0.0010481039062142372, -0.006261912640184164, -0.00221350253559649, -0.033390674740076065, 0.03872352093458176, 0.028745338320732117, 0.005021607968956232, -0.053254131227731705, -0.028782501816749573, 0.009146666154265404, -0.025790905579924583, -0.04641619697213173, 0.01635158248245716, 0.047382425516843796, -0.03526739031076431, -0.023338166996836662, -0.0407303050160408, -0.01984487473964691, -0.011037318035960197, 0.0024341559037566185, 0.018674250692129135, -0.004603527951985598, -0.013313532806932926, -0.052436552941799164, 0.005095933564007282, 0.03300046548247337, 0.02933994121849537, -0.009653007611632347, -0.02304086647927761, 0.04433508589863777, 0.0011677213478833437, 0.05998057499527931, 0.010544911958277225, -0.01358296163380146, 0.04808851704001427, 0.035676177591085434, 0.03913230821490288, -0.0442235991358757, 0.015088050626218319, 0.08770394325256348, -0.02387702651321888, -0.03392953425645828, -0.044297922402620316, 0.022706402465701103, 0.020532384514808655, -0.029154127463698387, -0.017048383131623268, 0.0079249432310462, -0.019380340352654457, -0.020253663882613182, -0.02120131254196167, 0.014530610293149948, 0.07514294981956482, 0.07503146678209305, -0.011604049243032932, -0.029079802334308624, 0.029172709211707115, -0.031439632177352905, 0.014632808044552803, -0.04210532456636429, 0.002043947810307145, -0.08413632214069366, 0.00216821045614779, -0.06265629082918167, 0.022056054323911667, 0.019324596971273422, -0.06299075484275818, 0.037385664880275726, -0.013610834255814552, -0.03824040666222572, -0.05466631427407265, -0.025790905579924583, 0.057081885635852814, -0.012979068793356419, -0.011696956120431423, 0.0430343896150589, 0.019789131358265877, -0.04455806314945221, -0.03300046548247337, 0.0465276837348938, 0.010665691457688808, -0.07885922491550446, 0.07324765622615814, -0.037385664880275726, 0.03654950112104416, -0.0264598336070776, 0.03920663520693779, 0.06971719861030579, -0.02419290877878666, 0.0203651525080204, -0.001772195682860911, 0.01435408741235733, -0.01471642404794693, -0.01847914606332779, -0.0491662360727787, -0.014837202616035938, -0.025084814056754112, 0.0003974665596615523, -0.00704697472974658, -0.047382425516843796, -0.053365617990493774, 0.028225060552358627, -0.07112938165664673, -0.01147397980093956, 0.02088543027639389, -0.008751812390983105, 0.027723364531993866, -0.015097341500222683, -0.011492560617625713, -0.030176101252436638, 0.03838905692100525, 0.04641619697213173, 0.05518658831715584, -0.038649193942546844, 0.023746956139802933, -0.009095567278563976, -0.08636608719825745, -0.016704628244042397, -0.0101825762540102, -0.0336136519908905, 0.020922591909766197, -0.03365081176161766, 0.02839229255914688, 0.01934317871928215, 0.023486817255616188, -0.03983839973807335, 0.015403933823108673, -0.07662945985794067, -0.003811498172581196, -0.007265305146574974, 0.009829530492424965, 0.056561607867479324, 0.004961218684911728, -0.01496727205812931, -0.05124734342098236, 0.008250116370618343, 0.014456285163760185, 0.0019173623295500875, -0.01116738747805357, 0.006526696961373091, 0.017856670543551445, 0.0016305128810927272, 0.02541927807033062, -0.055632542818784714, -0.0073117585852742195, -0.05503793805837631, -0.011929222382605076, 0.04396345838904381, -0.03794310241937637, 0.03697687387466431, -0.0732848197221756, -0.02666422724723816, 0.027816271409392357, 0.020420895889401436, -0.04812568053603172, 0.006238685920834541, 0.0561528205871582, -0.009425386786460876, -0.044706713408231735, 0.0030055323150008917, 0.02789059653878212, 0.049240559339523315, -0.02285505272448063, 0.020327989012002945, 0.02933994121849537, 0.05165613442659378, 0.002394670620560646, -0.016388744115829468, -0.01600782759487629, 0.04518982768058777, 0.008742522448301315, 0.0024062839802354574, 0.03075212426483631, 0.02757471427321434, 0.006833289284259081, 0.01689044199883938, -0.00009428580233361572, 0.008185082115232944, 0.037218429148197174, -0.025066232308745384, -0.056858912110328674, -0.0006155070150271058, -0.052027761936187744, -0.004872957244515419, 0.018488436937332153, 0.02757471427321434, 0.0046871439553797245, 0.017940286546945572, -0.03168119117617607, -0.011455398052930832, 0.006057518068701029, 0.050466928631067276, 0.030176101252436638, -0.004715016111731529, -0.0017152902437373996, 0.04385197162628174, 0.047605402767658234, -0.03108658827841282, 0.018850773572921753, 0.01163192093372345, -0.004937991965562105, -0.028671013191342354, -0.011251003481447697, -0.037088360637426376, -0.04537564143538475, 0.021665846928954124, 0.06733878701925278, -0.03764580190181732, -0.02584664896130562, -0.015840595588088036, 0.01682540588080883, -0.0010051345452666283, 0.01915736496448517, 0.023412492126226425, -0.03645659610629082, 0.0036187167279422283, 0.0013610833557322621, 0.06098397076129913, 0.002547966782003641, 0.0077948737889528275, 0.028280803933739662, -0.013452893123030663, -0.020550966262817383, -0.013963880017399788, 0.02244626358151436, 0.03220146894454956, -0.006749672815203667, 0.022371938452124596, -0.02344965562224388, 0.022279031574726105, 0.011083771474659443, 0.004150607623159885, 0.016537396237254143, 0.04805135354399681, 0.022093217819929123, 0.0264598336070776, -0.028578106313943863, -0.010284774005413055, -0.0039206636138260365, -0.023839863017201424, 0.041324906051158905, -0.004761469084769487, -0.05834541842341423, -0.020327989012002945, 0.05072706937789917, -0.02829938568174839, 0.023208098486065865, -0.0039160181768238544, 0.014725714921951294, -0.030696379020810127, 0.010201158002018929, 0.05303115397691727, 0.00046540459152311087, 0.011929222382605076, -0.0033771591261029243, 0.011650502681732178, 0.035434622317552567, 0.03491434454917908, 0.008775039575994015, -0.005147031974047422, 0.013127719052135944, -0.003544391365721822, 0.017215615138411522, 0.0126538947224617, -0.01791241578757763, -0.06566646695137024, 0.000022500846171169542, -0.010461295954883099, -0.01619364134967327, -0.02759329415857792, 0.014484156854450703, 0.011028027161955833, -0.025344952940940857, 0.014883656054735184, -0.04548712819814682, 0.0006607990362681448, 0.020142177119851112, -0.0003736591897904873, -0.03166260942816734, -0.020012106746435165, -0.011362491175532341, -0.006173651199787855, -0.0021519518923014402, -0.023691212758421898, 0.01650952361524105, -0.027128761634230614, -0.0520649254322052, -0.00561156589537859, 0.005221357569098473, -0.0031193429604172707, -0.03404102101922035, 0.036512341350317, -0.0017431622836738825, 0.06362251937389374, -0.0013192753540351987, 0.0070794918574392796, -0.010368390008807182, 0.004503652919083834, 0.003435225924476981, 0.016974058002233505, 0.033390674740076065, 0.006206168793141842, 0.005983192473649979, 0.01671391911804676, -0.022260449826717377, -0.016862569376826286, 0.01857205294072628, -0.00032430249848403037, -0.028578106313943863, 0.0060760993510484695, 0.023078028112649918, 0.011120934039354324, -0.02612536959350109, 0.00857064500451088, -0.020346570760011673, -0.038128916174173355, 0.0034677432850003242, 0.010173285380005836, -0.028652431443333626, 0.03417108952999115, -0.010219738818705082, 0.002829009434208274, 0.015979954972863197, 0.012282268144190311, -0.01095370203256607, -0.012477371841669083, 0.0021635652519762516, 0.0023691211827099323, -0.00820830836892128, 0.005495432298630476, -0.010517040267586708, -0.0025897747837007046, -0.008733231574296951, -0.007283886428922415, -0.03190416842699051, -0.01203142013400793, -0.006981940008699894, 0.019807711243629456, -0.003019468393176794, -0.004612818360328674, 0.03149537742137909, 0.005955320782959461, 0.051804784685373306, 0.03898365795612335, 0.006610312964767218, 0.03766438364982605, -0.013703741133213043, -0.0000378159384126775, 0.024861836805939674, -0.06875097006559372, 0.00928602647036314, -0.025382114574313164, -0.003704655449837446, 0.036883965134620667, -0.017475754022598267, 0.031123749911785126, 0.014456285163760185, 0.008779685012996197, -0.01363870594650507, 0.009392868727445602, 0.019789131358265877, -0.01409394945949316, 0.008877236396074295, 0.035434622317552567, 0.0386863574385643, -0.05771365389227867, -0.04340601712465286, 0.03004603274166584, -0.016946185380220413, 0.04582159221172333, 0.01224510557949543, -0.0175965316593647, -0.021015498787164688, -0.032777488231658936, 0.000995843904092908, 0.045226991176605225, 0.012876871041953564, -0.02172159031033516, -0.04675066098570824, 0.011864188127219677, 0.007297822739928961, -0.006563859526067972, -0.02666422724723816, 0.025363534688949585, -0.010108251124620438, -0.0030589536763727665, 0.003198313759639859, 0.03305621072649956, -0.0042899674735963345, 0.041733697056770325, -0.01224510557949543, 0.012012838385999203, -0.0037998848129063845, -0.041845183819532394, 0.007674094755202532, -0.022780727595090866, 0.014372669160366058, 0.027518969029188156, -0.05827109143137932, 0.02746322564780712, 0.013257788494229317, -0.019018005579710007, 0.02437872253358364, -0.06001773849129677, -0.013313532806932926, -0.014121821150183678, 0.03450555354356766, 0.03106800653040409, 0.039355285465717316, 0.030900774523615837, 0.05210208520293236, 0.027518969029188156, 0.003398063126951456, 0.03426399827003479, 0.01791241578757763, 0.016286548227071762, -0.02787201479077339, -0.0239885151386261, 0.014948691241443157, 0.01800532266497612, -0.006271203514188528, -0.002947465516626835, 0.027091598138213158, -0.026942947879433632, 0.006057518068701029, 0.008519546128809452, -0.009745914489030838, -0.02655274048447609, -0.023523980751633644, -0.038649193942546844, -0.00845915637910366, 0.017819508910179138, -0.016797535121440887, 0.04143639653921127, -0.022929377853870392, 0.008779685012996197, -0.03056631051003933, -0.062321826815605164, 0.025437859818339348, 0.05979476496577263, 0.02973014861345291, -0.005383944138884544, 0.0366424098610878, 0.024322979152202606, 0.05908867344260216, -0.010414843447506428, -0.02428581565618515, 0.03194132819771767, -0.039057984948158264, -0.0039624716155231, 0.051916275173425674, -0.023078028112649918, 0.020643873140215874, -0.00026463897665962577, -0.060575179755687714, -0.019008714705705643, -0.033910952508449554, -0.034208253026008606, -0.011864188127219677, 0.022873634472489357, 0.014158983714878559, 0.07023748010396957, -0.00827798806130886, 0.05864271894097328, -0.0019394276896491647, 0.0407303050160408, -0.03482143580913544, 0.04288573935627937, 0.005820605903863907, -0.0500209778547287, 0.031755514442920685, -0.029191290959715843, 0.05173046141862869, 0.03920663520693779, -0.00485902139917016, -0.02365405112504959, 0.07848759740591049, -0.026199694722890854, 0.015617619268596172, 0.014781458303332329, 0.027407482266426086, -0.009615845046937466, -0.05689607188105583, 0.01373161282390356, -0.025475021451711655, 0.026106787845492363, -0.002603710861876607, 0.055929843336343765, 0.00484044011682272, 0.025400696322321892, -0.04318304359912872, 0.04333169385790825, -0.00566266430541873, -0.01594279333949089, -0.06912259757518768, -0.01564549095928669, 0.02685004100203514, -0.028763920068740845, -0.00674038240686059, -0.003718591295182705, 0.005727699026465416, 0.0002075884403893724, 0.04589591920375824, 0.047270938754081726, 0.006591731682419777, 0.0018987810472026467, 0.01712270826101303, -0.04221681132912636, 0.006489534396678209, -0.03034333325922489, -0.019398922100663185, 0.03660524636507034, 0.012886161915957928, 0.014335506595671177, -0.006721801124513149, -0.01702980138361454, -0.01872999407351017, 0.02099691890180111, -0.015952084213495255, -0.029247034341096878, -0.016249384731054306, -0.00674038240686059, 0.03392953425645828, -0.006210814230144024, -0.017540788277983665, 0.01655597612261772, -0.0036767832934856415, 0.04210532456636429, 0.06507186591625214, 0.014010332524776459, 0.01702980138361454, 0.01714129000902176, 0.023208098486065865, 0.023226680234074593, 0.039578262716531754, -0.05693323537707329, -0.06206168606877327, -0.08212953805923462, 0.02449021115899086, -0.017243485897779465, 0.0029776603914797306, 0.029507173225283623, 0.031049424782395363, -0.0015561875188723207, 0.04898042231798172, -0.006577795371413231, -0.03418967127799988, 0.027909178286790848, 0.008635679259896278, 0.034635625779628754, 0.0010051345452666283, -0.031049424782395363, -0.045115500688552856, -0.02090401202440262, 0.029581498354673386, -0.0034932924900203943, -0.04128774628043175, -0.07306184619665146, -0.0059228031896054745, -0.002273891819640994, -0.0015155408764258027, -0.02149861492216587, -0.022056054323911667, -0.026775715872645378, -0.003249412402510643, -0.004273708909749985, -0.038017429411411285, -0.02233477495610714, 0.024750350043177605, 0.02428581565618515, 0.038537707179784775, 0.03166260942816734, -0.04693647474050522, -0.032350119203329086, -0.02357972413301468, 0.00947648473083973, -0.03210856020450592, -0.008180436678230762, 0.0151252131909132, 0.013378567062318325, -0.018627796322107315, 0.005030898842960596, 0.032758910208940506, -0.017104126513004303, 0.016435198485851288, -0.048534467816352844, -0.03913230821490288, -0.005713763181120157, -0.027723364531993866, 0.028875406831502914, -0.035843413323163986, -0.021034080535173416, 0.033074792474508286, 0.035750504583120346, 0.0048311492428183556, -0.0063176569528877735, 0.02625543810427189, 0.030213264748454094, 0.019714806228876114, 0.05277101695537567, -0.0035258098505437374, -0.01662101224064827, 0.06852799654006958, -0.060760993510484695, 0.006173651199787855, 0.0179588682949543, -0.0008663551416248083, -0.03333492949604988, -0.025066232308745384, 0.030120357871055603, 0.007711257319897413, 0.010136122815310955, -0.022371938452124596, -0.0022042118944227695, 0.009364997036755085, 0.005741635337471962, 0.009067695587873459, -0.0239885151386261, -0.038537707179784775, 0.009360351599752903, 0.036475177854299545, 0.0026501640677452087, -0.022186124697327614, 0.02614394947886467, 0.02437872253358364, -0.016816115006804466, -0.0013819874729961157, -0.025958137586712837, 0.0009900372242555022, -0.016741789877414703, 0.03744140639901161, -0.018627796322107315, 0.05303115397691727, 0.04154788330197334, -0.015171666629612446, 0.012282268144190311, 0.043777644634246826, -0.023746956139802933, -0.0017838089261204004, 0.04868311807513237, -0.006122552789747715, 0.0055372403003275394, 0.0000803497969172895, 0.026478415355086327, -0.04938920959830284, 0.0016641916008666158, 0.010628528892993927, 0.009885274805128574, -0.03457988053560257, -0.034338321536779404, -0.0005931513151153922, -0.03489576280117035, -0.014205437153577805, 0.031346727162599564, -0.011037318035960197, 0.012170779518783092, 0.004389842506498098, 0.03283323347568512, -0.041213419288396835, 0.020736780017614365, -0.008863301016390324, 0.012375175021588802, 0.035750504583120346, 0.01245879102498293, 0.01945466734468937, 0.033892370760440826, -0.054480500519275665, 0.019677642732858658, -0.010321936570107937, -0.04165937379002571, 0.003314447123557329, -0.04355466738343239, -0.0004282419104129076, 0.009165247902274132 ]
Smart meter measurements, though critical for accurate demand forecasting, face several drawbacks including consumers' privacy, data breach issues, to name a few. Recent literature has explored Federated Learning (FL) as a promising privacy-preserving machine learning alternative which enables collaborative learning of a model without exposing private raw data for short term load forecasting. Despite its virtue, standard FL is still vulnerable to an intractable cyber threat known as Byzantine attack carried out by faulty and/or malicious clients. Therefore, to improve the robustness of federated short-term load forecasting against Byzantine threats, we develop a state-of-the-art differentially private secured FL-based framework that ensures the privacy of the individual smart meter's data while protect the security of FL models and architecture. Our proposed framework leverages the idea of gradient quantization through the Sign Stochastic Gradient Descent (SignSGD) algorithm, where the clients only transmit the `sign' of the gradient to the control centre after local model training. As we highlight through our experiments involving benchmark neural networks with a set of Byzantine attack models, our proposed approach mitigates such threats quite effectively and thus outperforms conventional Fed-SGD models.
[ -0.02974548377096653, -0.037816837430000305, -0.02511715330183506, -0.04549309238791466, 0.06389352679252625, -0.02180582843720913, -0.011975332163274288, 0.026471788063645363, -0.061899203807115555, 0.04052610322833061, 0.0017873630858957767, -0.025625141337513924, -0.029594969004392624, -0.022125672549009323, -0.056706443428993225, 0.002542288741096854, 0.008014911785721779, -0.08594393730163574, 0.05290594696998596, -0.05843736231327057, -0.0025893247220665216, -0.04218176752328873, 0.0030126473866403103, 0.010347891598939896, -0.015126735903322697, 0.050083793699741364, 0.0006596780731342733, 0.0049905055202543736, -0.04342351481318474, 0.07902026176452637, 0.03947250172495842, 0.026095500215888023, -0.04184310883283615, -0.029030539095401764, -0.03977353125810623, -0.009924568235874176, 0.039246730506420135, 0.04846575856208801, -0.014741041697561741, 0.0031913837883621454, -0.04865390434861183, 0.006025294773280621, -0.025738026946783066, 0.041203420609235764, 0.023066390305757523, -0.018485097214579582, -0.038870442658662796, -0.049143075942993164, -0.03685730695724487, 0.026189571246504784, -0.02682925947010517, -0.10904795676469803, -0.017657265067100525, -0.015107921324670315, -0.000034615459298947826, 0.0004906429094262421, 0.07954706251621246, 0.03433618322014809, 0.029049353674054146, 0.010940543375909328, 0.01733742095530033, 0.00033072096994146705, -0.016979949548840523, -0.009999825619161129, -0.006773164961487055, 0.052454400807619095, 0.009369545616209507, 0.020733410492539406, -0.03023465722799301, -0.022125672549009323, -0.0715697780251503, 0.0392843596637249, 0.0159075316041708, -0.02983955480158329, -0.0048588053323328495, 0.0002132782683474943, -0.001989617245271802, 0.022633660584688187, 0.024797311052680016, 0.0025540476199239492, 0.02539937011897564, 0.04549309238791466, 0.008687525056302547, 0.010206783190369606, 0.08654599636793137, 0.0023047577124089003, -0.04703586921095848, -0.08632022887468338, 0.059641484171152115, 0.0018097050487995148, 0.02831559255719185, -0.008071355521678925, -0.007478703279048204, -0.015418358147144318, 0.001197650795802474, 0.0434611439704895, -0.009811682626605034, -0.029406825080513954, -0.054072435945272446, -0.008320645429193974, -0.04342351481318474, 0.04105290770530701, -0.012417469173669815, 0.00950594898313284, 0.013123007491230965, -0.047224011272192, -0.016697732731699944, 0.039811160415410995, 0.06204972043633461, 0.09196453541517258, -0.013819138519465923, 0.011627267114818096, -0.0052633136510849, 0.07834294438362122, -0.041692595928907394, 0.012680870480835438, 0.01255857665091753, -0.025060711428523064, -0.019698621705174446, -0.021843457594513893, -0.0016297928523272276, 0.03446788340806961, -0.0049575804732739925, 0.02389422245323658, -0.041165791451931, 0.01710224151611328, 0.03610473498702049, -0.02673518843948841, 0.025643955916166306, 0.028390850871801376, 0.011091058142483234, 0.02756301872432232, -0.005714857950806618, -0.06596310436725616, 0.00825949851423502, 0.0006196975591592491, 0.03606710582971573, 0.00237648724578321, -0.005333867389708757, -0.010978171601891518, 0.02767590619623661, 0.0069613088853657246, 0.017375050112605095, 0.033470723778009415, -0.0003727592702489346, 0.025060711428523064, -0.028165077790617943, 0.03157047554850578, -0.01454349048435688, 0.009868125431239605, -0.04617040976881981, 0.0866212546825409, 0.06013065576553345, 0.004303782247006893, 0.026885703206062317, -0.014750448986887932, 0.008104280568659306, -0.03665034845471382, -0.0030808495357632637, -0.03721477836370468, 0.027807606384158134, 0.024214064702391624, 0.07017751783132553, 0.03202201798558235, 0.019115377217531204, 0.02803337760269642, 0.05196522921323776, 0.030272286385297775, -0.06487186998128891, 0.06400641053915024, 0.004082713276147842, 0.0026010836008936167, -0.00575719028711319, 0.005437346640974283, -0.005780708510428667, 0.05034719407558441, 0.04109053686261177, -0.04827761650085449, -0.0245527233928442, 0.012925457209348679, -0.012727905996143818, 0.033752940595149994, 0.011834224686026573, 0.02803337760269642, 0.01760082319378853, 0.06438269466161728, 0.047224011272192, -0.0008595805265940726, 0.034975871443748474, -0.01170252449810505, 0.018221694976091385, 0.0030338135547935963, 0.03390345349907875, -0.044815775007009506, 0.03354598209261894, -0.047186385840177536, 0.01917182095348835, -0.00011001983511960134, 0.027073847129940987, 0.008094873279333115, -0.009454209357500076, -0.0039110323414206505, 0.0016591902822256088, 0.023612005636096, 0.029199868440628052, 0.054260578006505966, 0.057760048657655716, 0.04571886360645294, -0.02842848002910614, -0.04161733761429787, -0.03587896004319191, 0.01100639346987009, -0.06829608231782913, -0.012050589546561241, 0.00928017683327198, -0.0021848161704838276, 0.033188510686159134, -0.015550058335065842, -0.0028832987882196903, -0.0271114744246006, 0.026471788063645363, 0.036876123398542404, -0.004553072154521942, -0.01724334992468357, -0.05354563519358635, 0.010319669730961323, -0.014148389920592308, 0.06197446212172508, -0.007902026176452637, -0.01670714095234871, -0.02709265984594822, -0.011740152724087238, 0.0033607129007577896, 0.014590526930987835, 0.032812222838401794, 0.007309373933821917, 0.009651760570704937, 0.03021584264934063, -0.048390503972768784, -0.021203769370913506, -0.03179624676704407, 0.006857829634100199, -0.012107032351195812, -0.027882862836122513, 0.012492726556956768, -0.020074909552931786, -0.06272703409194946, 0.1286148875951767, 0.02020660974085331, 0.03529571741819382, -0.0566311851143837, -0.05553995445370674, 0.003962771967053413, 0.006476839073002338, -0.026396529749035835, -0.0425204262137413, 0.008711042813956738, -0.004108583088964224, -0.017403271049261093, 0.014383568428456783, 0.06961308419704437, 0.007662143092602491, -0.015634723007678986, 0.07108060270547867, -0.019905580207705498, 0.04496629163622856, 0.08511611074209213, 0.027638277038931847, 0.06814556568861008, 0.010630106553435326, -0.027036217972636223, -0.042821455746889114, -0.030667386949062347, -0.03439262881875038, -0.038004983216524124, -0.03204083442687988, -0.046885356307029724, -0.025606326758861542, -0.0029797223396599293, 0.033019181340932846, 0.044326603412628174, -0.013828545808792114, 0.029312754049897194, -0.025060711428523064, 0.001057719113305211, 0.00523979589343071, 0.001913183950819075, -0.015126735903322697, -0.05222862958908081, -0.024722052738070488, -0.05343274772167206, 0.012370433658361435, -0.022219745442271233, 0.011561417020857334, 0.02069578319787979, 0.0189648624509573, 0.0313447043299675, -0.008301830850541592, 0.0007225885638035834, 0.039133843034505844, -0.02765709161758423, -0.015559465624392033, -0.001986089628189802, 0.03117537498474121, 0.005536121781915426, -0.03258645161986351, -0.013583959080278873, 0.03354598209261894, 0.00878630019724369, -0.006688500754535198, 0.014430604875087738, -0.06897339969873428, -0.04677246883511543, -0.07759036868810654, -0.05437346547842026, 0.041504450142383575, -0.0007872628630138934, 0.041504450142383575, -0.03695137798786163, -0.05644304305315018, 0.007676254026591778, 0.06573732942342758, -0.08165426552295685, 0.0346372127532959, -0.013311151415109634, -0.06569970399141312, 0.03211609274148941, 0.038306012749671936, -0.011730745434761047, -0.010968764312565327, -0.005423235706984997, -0.00540912477299571, -0.06434506922960281, -0.05817396193742752, 0.001347577665001154, -0.014703412540256977, -0.051438428461551666, 0.03002769872546196, -0.017629044130444527, -0.0005535534000955522, -0.0023800150956958532, -0.01794888824224472, -0.06287755072116852, 0.008029023185372353, 0.021467171609401703, 0.030291099101305008, -0.03170217573642731, 0.017685486003756523, 0.0641569271683693, 0.014797484502196312, 0.0010459601180627942, 0.002855077153071761, 0.021203769370913506, 0.002972666872665286, 0.041316308081150055, -0.028597809374332428, 0.00041538552613928914, -0.07055380195379257, -0.032925110310316086, -0.03217253461480141, 0.020413566380739212, -0.02607668563723564, -0.011900074779987335, 0.03902095556259155, -0.009059108793735504, -0.05324460566043854, -0.007445778232067823, -0.03209727630019188, -0.0009277825010940433, 0.02871069498360157, -0.03883281350135803, 0.04654669761657715, -0.02795812115073204, -0.02135428413748741, -0.0379297249019146, 0.005592565052211285, -0.019472850486636162, -0.01204118225723505, 0.004101527854800224, 0.04665958136320114, -0.034242112189531326, 0.034712471067905426, 0.034524329006671906, -0.010263226926326752, 0.02775116264820099, 0.02577565610408783, 0.00276100542396307, 0.031871505081653595, 0.005837151315063238, 0.05411006510257721, 0.02248314581811428, -0.012238733470439911, 0.00818894524127245, -0.04635855183005333, 0.07736460119485855, -0.01672595553100109, 0.014327125623822212, -0.029500897973775864, 0.03798616677522659, -0.030065327882766724, -0.003111422760412097, 0.02908698096871376, -0.014233053661882877, 0.019679807126522064, -0.025738026946783066, 0.04549309238791466, -0.004553072154521942, -0.04127867892384529, -0.010075083002448082, -0.0002588442584965378, -0.0379297249019146, -0.0672801062464714, 0.03313206508755684, -0.03853178396821022, -0.016170931980013847, 0.028353221714496613, -0.10822013020515442, 0.009905753657221794, -0.024157622829079628, -0.017487935721874237, -0.028466107323765755, 0.03032872825860977, 0.07021514326334, 0.033847011625766754, -0.006768461782485247, 0.039510130882263184, -0.014609340578317642, -0.002064874628558755, 0.0018214640440419316, -0.0003583545330911875, 0.04379980266094208, 0.016199152916669846, 0.029895998537540436, -0.0481647290289402, -0.04624566808342934, 0.0365186482667923, 0.0029844259843230247, -0.02135428413748741, 0.009454209357500076, 0.008607564494013786, -0.0017732522683218122, -0.03871992602944374, -0.01793007366359234, 0.014900963753461838, -0.019792694598436356, -0.024533908814191818, 0.01293486449867487, -0.04195599630475044, 0.009990418329834938, -0.01175896730273962, -0.05478737875819206, -0.008894482627511024, -0.045869380235672, -0.006180513184517622, 0.024759681895375252, -0.03794853761792183, 0.041128162294626236, -0.02351793460547924, 0.06837134063243866, -0.022426702082157135, 0.005578454118221998, 0.08014912158250809, 0.010583071038126945, 0.0027233767323195934, 0.009981011040508747, 0.014722227118909359, -0.024044737219810486, -0.05599150061607361, -0.0034994687885046005, 0.026302458718419075, -0.013668623752892017, -0.013668623752892017, -0.015333693474531174, 0.03273696452379227, -0.026302458718419075, 0.02173057198524475, -0.03732766583561897, -0.042558055371046066, -0.0015098514268174767, -0.025286482647061348, -0.013442851603031158, 0.011420308612287045, 0.046132780611515045, -0.06754350662231445, 0.0365186482667923, 0.03078027255833149, 0.005583157762885094, -0.04184310883283615, -0.03459958732128143, -0.0005091633065603673, -0.04417608678340912, -0.04891730472445488, 0.0014404734829440713, -0.03021584264934063, -0.014675191603600979, 0.005649007856845856, 0.006274585146456957, 0.04872915893793106, 0.0930933952331543, 0.008823929354548454, 0.027882862836122513, 0.0016662456328049302, 0.014571712352335453, 0.024025922641158104, -0.03456195816397667, -0.049067817628383636, -0.014853927306830883, -0.0008431179448962212, 0.004292022902518511, 0.027243174612522125, 0.035465046763420105, 0.015757016837596893, 0.010329077020287514, -0.047186385840177536, -0.019397592172026634, 0.022125672549009323, -0.0011811882723122835, -0.06855948269367218, 0.0035441527143120766, 0.02304757572710514, 0.02786404825747013, 0.008132501505315304, -0.011928296647965908, 0.034618400037288666, -0.04696061089634895, 0.023743707686662674, 0.0269045177847147, 0.0050657629035413265, 0.024157622829079628, -0.027901677414774895, -0.03241712227463722, 0.05809870734810829, -0.06724248081445694, -0.03559674695134163, 0.0071118236519396305, 0.032812222838401794, -0.021674128249287605, 0.02208804339170456, -0.011937703937292099, -0.047637928277254105, -0.037158336490392685, 0.03540860116481781, 0.0007472823490388691, 0.0007602172554470599, 0.019905580207705498, 0.02295350469648838, 0.03401634097099304, -0.024496281519532204, 0.010799435898661613, -0.01994320936501026, 0.022050416097044945, 0.03777921199798584, 0.01298190001398325, 0.02180582843720913, -0.04571886360645294, 0.008626378141343594, -0.00828301627188921, -0.022351445630192757, -0.028071006760001183, 0.003497116966173053, -0.0017179851420223713, 0.019096562638878822, -0.020074909552931786, -0.001839102478697896, 0.009590613655745983, -0.02652822993695736, -0.017450308427214622, 0.043009597808122635, -0.004682420752942562, 0.021881086751818657, 0.016340261325240135, -0.02030068077147007, -0.04161733761429787, -0.009618835523724556, -0.0144964549690485, 0.014759855344891548, 0.03397871181368828, 0.009261362254619598, 0.03958538919687271, 0.015399543568491936, -0.0013734473614022136, -0.03779802471399307, 0.028071006760001183, 0.027318432927131653, 0.0402250736951828, -0.004292022902518511, -0.00019931449787691236, -0.021279027685523033, 0.00902147963643074, -0.004948173649609089, -0.004682420752942562, 0.03973590210080147, 0.015314878895878792, 0.0036217619199305773, -0.013395815156400204, 0.001999024534597993, 0.026208385825157166, -0.0009430691716261208, 0.04289671406149864, -0.06859710812568665, -0.015060885809361935, 0.027261989191174507, 0.006302806548774242, 0.02889883890748024, -0.01430831104516983, 0.014186018146574497, 0.021787013858556747, 0.03189031779766083, -0.019867951050400734, -0.03126944601535797, 0.047073498368263245, 0.005188056267797947, 0.04598226770758629, -0.07597233355045319, 0.025098340585827827, 0.028767136856913567, -0.0008801586809568107, -0.02220093086361885, -0.023066390305757523, 0.0018626204691827297, 0.0245527233928442, -0.03211609274148941, 0.03448669984936714, -0.013348779641091824, 0.026979774236679077, 0.05298120155930519, -0.01719631440937519, -0.019698621705174446, 0.008367680944502354, -0.03617998957633972, -0.017610229551792145, -0.02295350469648838, -0.016885876655578613, -0.01926589198410511, -0.03864467144012451, -0.02720554731786251, -0.013245300389826298, 0.03713952377438545, 0.022991133853793144, 0.012266954407095909, 0.025324111804366112, -0.00030308737768791616, -0.008593453094363213, 0.029895998537540436, -0.006862533278763294, -0.025531070306897163, -0.0224643312394619, -0.00006460082659032196, 0.047449786216020584, 0.02617075853049755, 0.0050657629035413265, 0.011693117208778858, 0.014599934220314026, 0.035182829946279526, -0.013358186930418015, -0.012972492724657059, 0.006721425801515579, 0.005540825426578522, 0.0022377315908670425, 0.04221939668059349, 0.00562078645452857, 0.01935996301472187, -0.018955456092953682, 0.03695137798786163, 0.012549170292913914, -0.023066390305757523, 0.053131718188524246, 0.003666446078568697, 0.02786404825747013, 0.061447661370038986, 0.004442537669092417, 0.025813285261392593, -0.03939724341034889, 0.05268017202615738, 0.015794644132256508, -0.030140584334731102, 0.046320922672748566, 0.04180547967553139, -0.007332892157137394, -0.03755343705415726, -0.03700782358646393, 0.04331062734127045, -0.012361026369035244, 0.0035229865461587906, -0.026208385825157166, -0.019341150298714638, -0.022332631051540375, -0.000545028131455183, -0.008922704495489597, -0.004176785238087177, -0.004426075145602226, -0.058399736881256104, 0.017139870673418045, -0.008640489540994167, -0.0170552060008049, -0.02558751218020916, 0.009082626551389694, 0.006853125989437103, -0.014411790296435356, 0.021316656842827797, -0.015239621512591839, -0.01171193178743124, -0.01614271104335785, 0.009294288232922554, 0.009181401692330837, -0.020432380959391594, 0.015145549550652504, 0.026471788063645363, -0.010423148982226849, -0.02955733984708786, -0.0034077486488968134, 0.002885650610551238, -0.009101441130042076, 0.028578994795680046, 0.027055032551288605, -0.02605787105858326, -0.013659216463565826, -0.014957406558096409, -0.015662943944334984, 0.04899256303906441, 0.014806891791522503, 0.004287319257855415, -0.0060770343989133835, -0.010394927114248276, 0.0015110273379832506, 0.007671550381928682, -0.017911259084939957, -0.004915248136967421, -0.014806891791522503, 0.009350731037557125, 0.07394038885831833, -0.03629287704825401, -0.040827132761478424, -0.00025487563107162714, 0.040940020233392715, -0.0036829086020588875, -0.008725154213607311, 0.03172098845243454, -0.03183387592434883, -0.008645192719995975, 0.025154782459139824, 0.01872968301177025, -0.0035582634154707193, -0.019962022081017494, 0.021655313670635223, 0.032059647142887115, 0.024627981707453728, -0.00601588748395443, -0.03700782358646393, 0.03335784003138542, 0.025568699464201927, -0.034975871443748474, 0.025813285261392593, -0.03713952377438545, -0.04041321948170662, 0.02078985422849655, 0.003290159162133932, -0.021843457594513893, 0.030008884146809578, 0.0009889291832223535, 0.02182464301586151, 0.05565284192562103, 0.0061005521565675735, 0.03190913423895836, 0.04139156639575958, -0.01750675030052662, -0.024232879281044006, -0.016810620203614235, 0.031589288264513016, -0.04236990958452225, 0.020620524883270264, 0.02605787105858326, 0.03237949311733246, -0.06347960978746414, -0.013659216463565826, 0.017139870673418045, 0.03853178396821022, -0.0100562684237957, 0.02523004077374935, 0.0034712471533566713, -0.008433531038463116, -0.00562078645452857, -0.005225684959441423, 0.028917651623487473, -0.04696061089634895, -0.008499381132423878, 0.022163301706314087, -0.07089246064424515, 0.022633660584688187, 0.033583611249923706, -0.037534624338150024, 0.04812709987163544, 0.003207846311852336, -0.012313990853726864, 0.028654251247644424, -0.04101527854800224, -0.01275612786412239, 0.042068880051374435, -0.05271780118346214, -0.020470010116696358, 0.051325540989637375, -0.02983955480158329, -0.016509590670466423, -0.01401668880134821, -0.028748324140906334, -0.020846297964453697, 0.0012970140669494867, -0.06502238661050797, -0.021279027685523033, -0.03126944601535797, 0.0030526279006153345, 0.01204118225723505, 0.005343274679034948, -0.031006045639514923, -0.017958294600248337, -0.0392843596637249, -0.009002665057778358, 0.06291517615318298, 0.0003066150820814073, -0.04936884716153145, -0.0014134278753772378, -0.029726669192314148, -0.016199152916669846, -0.0045883492566645145, 0.006288695614784956, -0.014044910669326782, -0.03883281350135803, 0.013922617770731449, 0.00894151907414198, 0.0306109432131052, -0.008546417579054832, -0.004426075145602226, -0.05640541389584541, 0.022596031427383423, -0.03685730695724487, 0.012426876462996006, -0.04278382658958435, 0.05956622585654259, -0.0015627667307853699, 0.004562479443848133, 0.012605613097548485, 0.017657265067100525, 0.022878246381878853, -0.015747608616948128, -0.012897235341370106, -0.020526453852653503, -0.0004115638439543545, -0.007906729355454445, 0.03371531143784523, 0.049632247537374496, 0.008875668980181217, 0.058211591094732285, 0.06261415034532547, 0.01473163440823555, -0.055690471082925797, -0.002530529862269759, -0.009755238890647888, 0.02142954245209694, 0.014186018146574497, -0.034975871443748474, -0.031231816858053207, 0.010075083002448082, 0.028089821338653564, -0.02803337760269642, 0.034411441534757614, -0.017440900206565857, 0.015390136279165745, -0.03388464078307152, -0.014364754781126976, -0.06242600455880165, -0.0038734038826078176, -0.034618400037288666, 0.024778496474027634, 0.03288748115301132, 0.04733689874410629, -0.0006473311805166304, -0.017610229551792145, 0.03320732340216637, 0.004143860191106796, -0.058776021003723145, 0.02406354993581772, 0.034524329006671906, 0.021015627309679985, -0.02803337760269642, 0.03264289349317551, -0.009110847488045692, -0.010498406365513802, -0.014628155156970024, -0.010968764312565327, -0.04955699294805527, -0.016199152916669846, 0.004651847295463085, -0.022125672549009323, -0.019049527123570442, 0.025832099840044975, -0.030159398913383484, -0.030648572370409966, -0.022520774975419044, -0.012257547117769718, 0.024101179093122482, 0.0034289148170500994, -0.004844694398343563, 0.013094785623252392, 0.006537985987961292, 0.03597303107380867, 0.04673483967781067, 0.001763845095410943, -0.011269793845713139, 0.008127798326313496, 0.01199414674192667, -0.0326993353664875, -0.01576642319560051, 0.019209448248147964, 0.01841924712061882, 0.009661167860031128, -0.01025381963700056, -0.013715659268200397, -0.009999825619161129, 0.002010783413425088, 0.018221694976091385, 0.02255840227007866, 0.05305645987391472, -0.024439837783575058, 0.015230214223265648, -0.017986515536904335, -0.017534971237182617, 0.035051129758358, 0.022878246381878853, -0.021598871797323227, 0.030102957040071487, -0.005813633557409048, 0.019491665065288544, 0.06336672604084015, -0.008565232157707214, -0.00044831063132733107, 0.03284985199570656, -0.037835653871297836, 0.024496281519532204, -0.032925110310316086, 0.0024223471991717815, -0.03350835293531418, -0.03958538919687271, -0.030648572370409966, -0.01246450562030077, 0.019181227311491966, -0.03917147219181061, 0.04334825649857521, 0.000012521462849690579, -0.021768201142549515, 0.02464679628610611, -0.039133843034505844, -0.013480479829013348, 0.002544640563428402, 0.014477640390396118, -0.03373412415385246, -0.030911972746253014, -0.03456195816397667, -0.005634896922856569, -0.005484382156282663, 0.056894589215517044, 0.004694179631769657, 0.006759054493159056, -0.04052610322833061, -0.015032663941383362, 0.0007431667181663215, 0.024816123768687248, -0.05072348192334175, -0.017403271049261093, -0.020131351426243782, -0.0031396441627293825, -0.017469121143221855, -0.03236067667603493, 0.01724334992468357, 0.012850199826061726, -0.0075116283260285854, 0.01586049422621727, 0.011420308612287045, -0.01444941945374012, 0.0014839817304164171, 0.008405310101807117, 0.012257547117769718, -0.013377001509070396, 0.022069230675697327, 0.038099054247140884, -0.03277459368109703, -0.02880476601421833, 0.010592477396130562, 0.00512690981850028, -0.015070292167365551, -0.00029985368018969893, 0.01520199328660965, 0.002041356638073921, 0.05185234174132347, -0.056894589215517044, -0.0170552060008049, -0.04530495032668114, -0.02918105386197567, -0.06347960978746414, -0.025361740961670876, 0.024778496474027634, 0.004515443462878466, 0.009764646179974079, 0.005799522623419762, -0.0014087242307141423, 0.027149103581905365, -0.009049701504409313, 0.01741267926990986, -0.001975506544113159, -0.027920491993427277, 0.039698272943496704, -0.04236990958452225, -0.025907356292009354, 0.027600647881627083, 0.034411441534757614, -0.06137240305542946, 0.002514067105948925, -0.032906293869018555, 0.010046862065792084, -0.02191871590912342, -0.04428897425532341, 0.039698272943496704, -0.0060770343989133835, 0.011815410107374191, -0.010122119449079037 ]
How might we design Reinforcement Learning (RL)-based recommenders that encourage aligning user trajectories with the underlying user satisfaction? Three research questions are key: (1) measuring user satisfaction, (2) combatting sparsity of satisfaction signals, and (3) adapting the training of the recommender agent to maximize satisfaction. For measurement, it has been found that surveys explicitly asking users to rate their experience with consumed items can provide valuable orthogonal information to the engagement/interaction data, acting as a proxy to the underlying user satisfaction. For sparsity, i.e, only being able to observe how satisfied users are with a tiny fraction of user-item interactions, imputation models can be useful in predicting satisfaction level for all items users have consumed. For learning satisfying recommender policies, we postulate that reward shaping in RL recommender agents is powerful for driving satisfying user experiences. Putting everything together, we propose to jointly learn a policy network and a satisfaction imputation network: The role of the imputation network is to learn which actions are satisfying to the user; while the policy network, built on top of REINFORCE, decides which items to recommend, with the reward utilizing the imputed satisfaction. We use both offline analysis and live experiments in an industrial large-scale recommendation platform to demonstrate the promise of our approach for satisfying user experiences.
[ 0.024031994864344597, -0.0056862966157495975, -0.03651750087738037, -0.03985624387860298, -0.009668443351984024, 0.005438499618321657, -0.05265475809574127, -0.007773010991513729, -0.05202874541282654, -0.022936468943953514, -0.007381752133369446, -0.042429860681295395, 0.007116565480828285, -0.036691393703222275, 0.008138186298310757, 0.04058659449219704, 0.023040805011987686, 0.03926501050591469, 0.003932152409106493, -0.027840247377753258, 0.029753070324659348, -0.036726173013448715, 0.008172964677214622, 0.04778575897216797, 0.03217018023133278, 0.015111289918422699, 0.012424645014107227, -0.0013063701335340738, -0.09299790114164352, 0.023336423560976982, 0.008164269849658012, 0.0339786671102047, -0.008868535980582237, 0.041942957788705826, -0.05787154659628868, -0.020623693242669106, 0.07407835870981216, -0.015180847607553005, -0.01424182578921318, 0.07254810631275177, -0.027214232832193375, 0.0017313208663836122, -0.008807674050331116, -0.0435427725315094, 0.005751506425440311, -0.03554370254278183, 0.0025801353622227907, 0.03128332644701004, -0.006073208525776863, -0.023823322728276253, -0.013528864830732346, -0.033317871391773224, -0.008381635881960392, -0.02265824005007744, -0.03545675426721573, 0.005999303888529539, -0.002599698258563876, -0.049594245851039886, 0.09251100569963455, 0.04517736658453941, -0.012572454288601875, 0.034309063106775284, -0.07084395736455917, 0.007194817531853914, 0.033404819667339325, -0.08346857875585556, 0.0013389750383794308, 0.006229712162166834, -0.007286110892891884, -0.010485739447176456, -0.045699045062065125, 0.02707511931657791, -0.022606072947382927, -0.015832945704460144, -0.010590075515210629, 0.013207162730395794, 0.015954669564962387, 0.03545675426721573, -0.0007613247144035995, 0.015380823984742165, 0.054324131458997726, 0.013833177275955677, -0.013450613245368004, 0.005290690343827009, 0.041560396552085876, -0.029109666123986244, 0.08611174672842026, -0.06427080184221268, 0.04298631474375725, 0.010016229003667831, -0.05543704703450203, 0.009146764874458313, 0.012589843943715096, -0.03916067257523537, 0.01469394750893116, 0.03234407305717468, 0.026936005800962448, -0.004616855643689632, -0.034343842417001724, 0.02935311570763588, 0.012894156388938427, -0.07007882744073868, -0.0333004854619503, -0.00831207912415266, 0.011363898403942585, -0.03493507578969002, -0.04966380074620247, 0.007886041887104511, -0.047577086836099625, 0.08047761768102646, -0.010085786692798138, -0.018380476161837578, -0.042360302060842514, 0.012668095529079437, -0.08312079310417175, -0.050915829837322235, -0.03964757174253464, -0.05296776816248894, 0.018658705055713654, -0.03239624202251434, 0.020154183730483055, 0.03989102318882942, 0.05418501794338226, 0.0076034655794501305, -0.005955830682069063, 0.06900069117546082, -0.01985856518149376, 0.009311962872743607, 0.07853002101182938, 0.04298631474375725, -0.0016454611904919147, -0.006121028680354357, -0.03707395866513252, -0.02180616557598114, -0.011059585958719254, 0.025231854990124702, 0.014824367128312588, -0.004486436024308205, 0.02128448709845543, -0.013807093724608421, -0.02980523742735386, -0.06809644401073456, -0.020571526139974594, 0.0030170411337167025, 0.027596797794103622, 0.034378618001937866, -0.03368304669857025, 0.035387199372053146, -0.04350799694657326, 0.0008124057203531265, -0.036239273846149445, 0.04062137380242348, -0.04211685061454773, 0.02410155162215233, 0.059471361339092255, -0.04218640923500061, -0.05129839479923248, -0.04594249650835991, 0.028987940400838852, -0.03416994959115982, 0.036726173013448715, -0.008438151329755783, -0.044307902455329895, 0.08312079310417175, 0.04987247288227081, 0.04444701597094536, -0.0063514369539916515, -0.010511823929846287, -0.04201251640915871, 0.041977737098932266, -0.08778111636638641, 0.010285763069987297, -0.0455947108566761, 0.044794801622629166, 0.07122651487588882, -0.02032807655632496, 0.08235566318035126, -0.053767673671245575, -0.03556109219789505, 0.014128795824944973, -0.04493391513824463, 0.028744490817189217, -0.006090597715228796, 0.05015070363879204, 0.03561325743794441, -0.013302803970873356, 0.040551815181970596, -0.04368188977241516, 0.012868071906268597, -0.04208207502961159, -0.016867607831954956, 0.0634361207485199, 0.00684703141450882, 0.03029213659465313, 0.007425225339829922, 0.010946555994451046, -0.04253419488668442, -0.022919079288840294, 0.020049847662448883, -0.0058558424934744835, -0.03843032196164131, -0.019162993878126144, -0.010963945649564266, -0.007442614529281855, 0.019632505252957344, 0.017380591481924057, 0.042951539158821106, -0.008333815261721611, 0.0018095726845785975, -0.07039183378219604, 0.020710639655590057, -0.05074193701148033, -0.02653605118393898, -0.01938905380666256, -0.01761534810066223, -0.008007766678929329, -0.024414557963609695, 0.028257591649889946, 0.010772663168609142, -0.021180151030421257, -0.04921168088912964, 0.03349176421761513, 0.042325522750616074, -0.025510083884000778, 0.0089641772210598, 0.004199512768536806, -0.010207511484622955, 0.0037582595832645893, -0.029613954946398735, -0.0242058876901865, 0.0017356681637465954, 0.0711221843957901, -0.017380591481924057, 0.028188033029437065, -0.029144443571567535, 0.011989912949502468, -0.017841408029198647, -0.02366681955754757, -0.023440757766366005, -0.021945279091596603, -0.02457106113433838, -0.03606538102030754, 0.015728609636425972, 0.021145371720194817, 0.019510779529809952, 0.0035104623530060053, -0.028170645236968994, 0.08958960324525833, 0.022414790466427803, 0.018380476161837578, -0.030605144798755646, -0.024918848648667336, -0.00925979483872652, 0.024379780516028404, -0.007894735783338547, 0.09884070605039597, 0.04611638933420181, -0.023492926731705666, 0.012728957459330559, -0.05644562467932701, 0.0021736607886850834, 0.03363088145852089, 0.05961047485470772, 0.007899083197116852, -0.005342858377844095, 0.000887397036422044, 0.05022025853395462, -0.013128911145031452, 0.06879201531410217, 0.030466029420495033, 0.028709711506962776, -0.024936236441135406, -0.012372476980090141, 0.00037223941762931645, -0.0321006216108799, -0.07275677472352982, -0.006190585903823376, -0.05818455293774605, 0.02272779680788517, -0.019041268154978752, -0.011303036473691463, -0.010372709482908249, 0.009598886594176292, 0.0004523931711446494, -0.03354393318295479, -0.035787150263786316, -0.023492926731705666, 0.015928586944937706, -0.0647229254245758, -0.01991073228418827, 0.006334047764539719, -0.010937861166894436, -0.024414557963609695, 0.02597959339618683, 0.08117318898439407, 0.02417110837996006, -0.02231045439839363, 0.047159746289253235, 0.00851205550134182, 0.0094771608710289, 0.025840479880571365, 0.03498724475502968, 0.03606538102030754, -0.0010487913386896253, -0.023597262799739838, -0.0019986811093986034, -0.015615579672157764, 0.04931601509451866, -0.056549958884716034, 0.02471017651259899, 0.018293529748916626, 0.033422209322452545, -0.03163111209869385, -0.02987479418516159, -0.009016345255076885, 0.061801522970199585, 0.03686528652906418, -0.037630416452884674, -0.016311150044202805, -0.024831900373101234, -0.0502898171544075, 0.022988636046648026, -0.08277300745248795, 0.010250984691083431, -0.014607001096010208, -0.008342510089278221, 0.04789009690284729, -0.014728725887835026, 0.0064253415912389755, 0.028692323714494705, -0.0009151112171821296, 0.02658822014927864, -0.03376999497413635, -0.023492926731705666, -0.014824367128312588, -0.026257822290062904, -0.035787150263786316, 0.04444701597094536, -0.014485275372862816, -0.02220611833035946, -0.012642011046409607, -0.03881288692355156, 0.00003009161628142465, 0.016302457079291344, 0.010572685860097408, -0.013154995627701283, -0.04124738648533821, 0.03589148819446564, -0.0015432991785928607, 0.017824018374085426, 0.0009987971279770136, 0.012850683182477951, 0.010633548721671104, 0.014433108270168304, 0.0717134177684784, -0.04131694510579109, 0.0070383138954639435, 0.01843264326453209, -0.023545093834400177, 0.05411545932292938, 0.04489913955330849, -0.07915603369474411, -0.07964292913675308, 0.06065383180975914, -0.061349403113126755, 0.023475537076592445, -0.0427776463329792, 0.009807557798922062, 0.06959192454814911, 0.004390794783830643, -0.02650127373635769, 0.02222350798547268, 0.06072339043021202, 0.007551297545433044, 0.0009694527252577245, 0.006999187637120485, 0.008651169948279858, -0.005616739392280579, -0.07199164479970932, 0.03943890333175659, -0.021580103784799576, -0.024066772311925888, -0.023145141080021858, 0.011894271709024906, -0.045281700789928436, 0.029179222881793976, 0.006829642225056887, -0.028188033029437065, 0.011937744915485382, 0.01935427635908127, -0.002166053047403693, -0.006294921971857548, -0.005960178095847368, -0.007416530512273312, -0.015485160052776337, -0.04041270166635513, 0.04222118854522705, 0.015241709537804127, -0.003727828385308385, -0.009424993768334389, -0.009207626804709435, -0.020223740488290787, 0.030918151140213013, 0.059993039816617966, 0.013763620518147945, -0.012755041942000389, 0.036169715225696564, -0.011224784888327122, 0.005847147665917873, -0.0028866215143352747, 0.008651169948279858, 0.036795731633901596, -0.01612856425344944, 0.0012509417720139027, 0.014633084647357464, 0.0013781009474769235, -0.050428930670022964, -0.014146184548735619, 0.04413400962948799, -0.055228374898433685, -0.045699045062065125, 0.014798282645642757, 0.0333004854619503, -0.0013346277410164475, -0.07261765748262405, -0.0002833910402841866, -0.034343842417001724, -0.003412647405639291, -0.004319063853472471, -0.08611174672842026, 0.00745565677061677, 0.0570368617773056, 0.03992580249905586, -0.08778111636638641, -0.0007955598412081599, 0.025005795061588287, -0.01855436898767948, 0.03305703401565552, -0.014363550581037998, -0.045281700789928436, -0.045246925204992294, -0.08325990289449692, -0.05206352472305298, 0.020501969382166862, 0.05693252384662628, -0.016658935695886612, 0.021962668746709824, -0.06451425701379776, 0.015824250876903534, 0.005412415601313114, -0.05929746851325035, 0.02410155162215233, -0.03776952996850014, -0.03853465989232063, 0.053802452981472015, -0.03514374792575836, 0.013581032864749432, -0.025718754157423973, 0.01565905287861824, -0.03180500492453575, -0.023927658796310425, 0.014433108270168304, 0.030153023079037666, -0.03401344642043114, -0.01066832710057497, 0.00046326147275976837, -0.009311962872743607, -0.01664154790341854, -0.0069904932752251625, 0.024327611550688744, -0.02886621654033661, -0.028327148407697678, 0.018728261813521385, -0.042395081371068954, 0.007551297545433044, 0.03446556627750397, 0.0099466722458601, -0.08186876028776169, 0.03929978609085083, -0.02789241634309292, 0.010798746719956398, 0.021041037514805794, 0.07574773579835892, -0.04121261090040207, 0.006781821604818106, -0.01845003291964531, 0.049559466540813446, 0.03408300131559372, 0.0017617520643398166, -0.027196845039725304, -0.033456988632678986, -0.023319033905863762, -0.023023415356874466, 0.01843264326453209, -0.05022025853395462, -0.012224668636918068, 0.020554136484861374, -0.040099695324897766, 0.027857637032866478, -0.013876650482416153, 0.006794863846153021, 0.028657544404268265, 0.002434500027447939, 0.01570252515375614, 0.0015096074203029275, 0.015476465225219727, 0.032483186572790146, -0.008072976022958755, -0.048516109585762024, 0.003745217574760318, 0.012468118220567703, 0.03651750087738037, 0.00875550601631403, -0.006034082267433405, -0.01399837527424097, 0.01232030987739563, -0.003416994819417596, -0.02512751892209053, 0.0540459044277668, 0.019597725942730904, -0.0029931310564279556, 0.02886621654033661, -0.011424761265516281, 0.015806861221790314, -0.07866913080215454, -0.01945861242711544, 0.00782083161175251, 0.00047412977437488735, 0.07136563211679459, 0.04980291798710823, -0.022901689633727074, 0.044307902455329895, 0.005316774360835552, -0.06068861111998558, -0.01422443613409996, 0.009120680391788483, -0.009198932908475399, 0.015293877571821213, 0.023510316386818886, -0.03780430927872658, -0.03891722485423088, 0.03728263080120087, -0.0033822162076830864, 0.02464061975479126, 0.021145371720194817, -0.013250636868178844, 0.024431947618722916, -0.055193595588207245, 0.010259679518640041, 0.008429456502199173, 0.02897055074572563, -0.0097119165584445, 0.0029844362288713455, -0.024397168308496475, 0.003395258216187358, 0.005373289342969656, 0.008690295740962029, 0.000752086634747684, -0.004912473261356354, -0.03458729013800621, -0.03156155347824097, -0.006829642225056887, -0.018310919404029846, -0.0045994664542376995, 0.023579873144626617, -0.0045994664542376995, 0.013172384351491928, 0.042325522750616074, -0.011311731301248074, -0.03592626750469208, -0.036726173013448715, 0.011407371610403061, -0.03034430555999279, -0.020084626972675323, -0.02093670144677162, -0.00201607053168118, -0.013841872103512287, -0.03738696500658989, 0.004908126313239336, 0.007516519166529179, 0.03561325743794441, -0.04169951006770134, -0.010772663168609142, 0.04980291798710823, -0.014024459756910801, 0.0028127171099185944, -0.02700556255877018, -0.03077903762459755, 0.013772315345704556, -0.027631577104330063, 0.000041469371353741735, 0.046707622706890106, 0.0003252339956816286, -0.020588915795087814, -0.04938557371497154, -0.008851147256791592, 0.02799675054848194, -0.004712496884167194, 0.021580103784799576, -0.06451425701379776, -0.001887824386358261, 0.04326454550027847, 0.0017813150770962238, 0.031074654310941696, -0.028796657919883728, -0.007299153134226799, 0.059958260506391525, 0.00593844149261713, 0.02370159700512886, 0.0444817952811718, -0.04611638933420181, -0.015146068297326565, 0.05783676728606224, -0.017293645069003105, -0.0029626996256411076, -0.04942035302519798, 0.0303964726626873, -0.013363666832447052, 0.00030404081917367876, -0.018849987536668777, 0.012172500602900982, -0.031978897750377655, 0.06197541579604149, -0.0032300599850714207, -0.012841988354921341, 0.025927426293492317, 0.029144443571567535, -0.0019508606055751443, 0.0006950280512683094, 0.022988636046648026, -0.03561325743794441, 0.027127286419272423, 0.015389518812298775, -0.026309991255402565, -0.005542835220694542, -0.010059702210128307, 0.01803269051015377, 0.05255042389035225, 0.04514258727431297, 0.005990609060972929, -0.0052124387584626675, 0.04938557371497154, -0.0007183948764577508, 0.09550195932388306, -0.013450613245368004, 0.01652851700782776, -0.02945745177567005, -0.0058558424934744835, 0.03836076706647873, 0.0058558424934744835, -0.020049847662448883, 0.02137143351137638, -0.012120332568883896, 0.043334104120731354, -0.027266401797533035, 0.008955482393503189, -0.0063818683847785, -0.01747623272240162, -0.00032659253338351846, 0.00925979483872652, 0.018623925745487213, 0.00950324535369873, -0.01046835072338581, -0.008125144056975842, -0.003351785009726882, 0.0016932818107306957, 0.051889631897211075, 0.0030170411337167025, 0.00745565677061677, 0.010485739447176456, -0.01542429719120264, -0.020658472552895546, -0.024240665137767792, 0.039578016847372055, 0.037699975073337555, -0.01251159142702818, -0.020762808620929718, 0.014937397092580795, 0.02517968788743019, 0.0023236435372382402, 0.0097119165584445, -0.007751274388283491, -0.00003224829561077058, -0.021093204617500305, 0.0013813615078106523, -0.0106944115832448, 0.022432180121541023, 0.003438731422647834, -0.027770690619945526, 0.024814512580633163, -0.010833526030182838, 0.01283329352736473, -0.007686064578592777, 0.0069122412241995335, 0.019041268154978752, 0.029283558949828148, -0.03410039097070694, -0.04514258727431297, 0.002869232324883342, -0.030952930450439453, 0.0017237130086869001, 0.005690644029527903, 0.015206931158900261, -0.009738000109791756, 0.015111289918422699, 0.004929862916469574, 0.0036343608517199755, 0.023423369973897934, -0.031022487208247185, 0.035300251096487045, 0.01748492754995823, 0.0020138968247920275, -0.035821929574012756, 0.0342395044863224, -0.006655749399214983, 0.01649373769760132, 0.06305355578660965, -0.028692323714494705, -0.015389518812298775, 0.003571324748918414, 0.008912009187042713, -0.02317991852760315, 0.07373057305812836, -0.03418733924627304, -0.00852944515645504, 0.008316426537930965, 0.021997448056936264, 0.021423600614070892, -0.017719682306051254, -0.017145836725831032, 0.03556109219789505, 0.005390678998082876, -0.029961740598082542, -0.0038973737973719835, -0.03230929374694824, 0.03137027472257614, -0.06023648753762245, 0.0011455191997811198, 0.02222350798547268, -0.035752374678850174, 0.019302107393741608, -0.010581380687654018, 0.005512403789907694, -0.011598654091358185, 0.003260491183027625, 0.012111637741327286, 0.03444817662239075, 0.04229074344038963, 0.003388737328350544, -0.020154183730483055, 0.03891722485423088, -0.02990957349538803, 0.042812421917915344, -0.0014117927057668567, -0.07553905993700027, 0.03738696500658989, 0.006134070921689272, 0.013920123688876629, 0.013441918417811394, -0.03383955359458923, 0.0078121367841959, 0.07060050219297409, -0.028257591649889946, 0.001219423720613122, 0.025336191058158875, -0.032865751534700394, -0.022814743220806122, 0.03891722485423088, -0.0017095842631533742, -0.06166240945458412, -0.00337352161295712, 0.011511707678437233, 0.0061471126973629, -0.057175975292921066, -0.017789240926504135, -0.025788312777876854, 0.010781357996165752, 0.015267794020473957, -0.012694179080426693, 0.024014605209231377, -0.021562715992331505, -0.009885809384286404, 0.010703105479478836, 0.03648272156715393, -0.02408416196703911, 0.01605031080543995, 0.01891954429447651, -0.014320077374577522, 0.015267794020473957, -0.005047240294516087, 0.01846742257475853, 0.018676094710826874, -0.044829580932855606, -0.005234175361692905, 0.0624970942735672, 0.0024692786391824484, -0.02848365157842636, -0.011450844816863537, 0.0018845639424398541, -0.04500347375869751, 0.017641430720686913, 0.00020962241978850216, 0.002417110837996006, 0.036656614392995834, -0.05870623141527176, -0.004851610865443945, 0.03222234919667244, -0.009094596840441227, -0.01661546342074871, 0.04086482524871826, 0.04406445100903511, 0.041942957788705826, 0.014059238135814667, -0.01996290124952793, 0.014215742237865925, -0.03825642913579941, 0.003829990280792117, 0.04079526662826538, 0.01544168684631586, -0.018832597881555557, -0.016485042870044708, -0.007025271654129028, -0.03919545188546181, -0.010807441547513008, -0.04305587336421013, -0.028048919513821602, -0.03258752450346947, -0.0013313672970980406, 0.029300948604941368, -0.016937164589762688, 0.01544168684631586, 0.05063760280609131, -0.02933572605252266, -0.012355088256299496, 0.007260027341544628, 0.005034198518842459, 0.010990029200911522, -0.01347669679671526, 0.009251100942492485, 0.03870855271816254, -0.014841755852103233, -0.016093784943223, -0.011616043746471405, -0.052306972444057465, -0.020188961178064346, -0.00876420084387064, 0.0016454611904919147, 0.01843264326453209, -0.030413862317800522, -0.00006537964509334415, 0.005873231682926416, 0.025005795061588287, 0.023127751424908638, -0.010868304409086704, -0.008594654500484467, 0.018293529748916626, -0.006903546862304211, 0.04472524672746658, -0.0036669657565653324, -0.023492926731705666, 0.00378216989338398, 0.013320193625986576, -0.026814280077815056, -0.009225016459822655, 0.017824018374085426, -0.03467423841357231, -0.002070412039756775, -0.059436582028865814, -0.00016438310558442026, -0.041560396552085876, 0.04413400962948799, 0.02175399847328663, -0.06110595166683197, 0.0009879288263618946, 0.004586424212902784, 0.03309181332588196, 0.025527473539114, -0.0025236201472580433, 0.03443078696727753, -0.024258054792881012, 0.010381404310464859, -0.01016403827816248, 0.01092047244310379, 0.01305935438722372, 0.03606538102030754, -0.039125893265008926, -0.03776952996850014, -0.016432875767350197, -0.000953150272835046, -0.025840479880571365, 0.0031865867786109447, 0.03559587150812149, -0.000872724805958569, -0.005103755742311478, 0.015285182744264603, 0.007364362943917513, -0.015354740433394909, 0.013894040137529373, -0.017415370792150497, 0.00969452690333128, 0.0010743318125605583, -0.014650474302470684, -0.027127286419272423, -0.07588684558868408, 0.0001672360231168568, 0.02173660881817341, -0.002836627420037985, -0.037699975073337555, 0.03599582239985466, -0.03302225470542908, -0.00898156687617302, -0.009303268045186996, 0.03870855271816254, -0.03559587150812149, 0.01185079850256443, 0.0063036163337528706, -0.024953626096248627, -0.022832132875919342, -0.011389982886612415, 0.001544386032037437, 0.03648272156715393, 0.03267446905374527, 0.013172384351491928, 0.056097839027643204, -0.01134650968015194, -0.004447310231626034, 0.0021312744356691837, 0.04169951006770134, -0.025527473539114, 0.008707685396075249, 0.0068687680177390575, 0.031144212931394577, 0.015502548776566982, 0.0031018140725791454, 0.025857869535684586, 0.03453512489795685, -0.033317871391773224, -0.020728029310703278, -0.025753533467650414, 0.02843148447573185, -0.02797936275601387, -0.03032691590487957, -0.007094828877598047, -0.01938905380666256, 0.0021899633575230837, 0.007233943324536085, -0.007938208989799023, 0.02839670516550541, -0.01135520450770855, 0.007986029610037804, -0.03752608224749565, 0.005295037757605314, -0.015763388946652412, 0.04660328850150108, -0.0026018719654530287, -0.013624506071209908, -0.020641082897782326, -0.026379548013210297, -0.017624041065573692, 0.023336423560976982, -0.02408416196703911, -0.00782083161175251, -0.0179283544421196, -0.009964060969650745, -0.08235566318035126, 0.033909108489751816, -0.042812421917915344, -0.008651169948279858, -0.0023975479416549206, 0.01938905380666256, 0.0019454264547675848, 0.002921400126069784, -0.00412343442440033, -0.0013194121420383453, 0.013189774006605148, -0.0052602593787014484, 0.02279735542833805, -0.007907778024673462, -0.0029670470394194126, 0.056167397648096085, -0.02611870877444744, 0.018693482503294945, 0.025892646983265877, -0.019597725942730904, 0.009085902012884617, -0.05108972266316414, 0.009172848425805569, 0.011294341646134853, -0.0175892636179924, -0.002401895122602582, -0.03964757174253464, -0.05926268920302391, -0.004084308631718159, -0.027562018483877182, -0.026379548013210297, -0.02897055074572563, -0.006260143127292395, 0.008603349328041077, 0.01760665327310562, 0.01649373769760132, -0.061905860900878906, 0.022919079288840294, 0.023006025701761246, 0.011702990159392357, 0.018293529748916626, -0.02276257611811161, 0.04893345385789871, -0.035821929574012756, -0.005794979631900787, 0.05220263823866844, -0.009998839348554611, 0.0322745144367218, -0.027266401797533035, 0.007833873853087425, -0.022153951227664948, 0.004751622676849365, -0.01616334170103073, -0.014702641405165195, 0.026240432634949684, -0.04274286702275276, 0.026292601600289345, -0.012433339841663837, 0.06712264567613602, -0.014833061024546623 ]
In this paper three customised Artificial Intelligence (AI) frameworks, considering Deep Learning (convolutional neural networks), Machine Learning algorithms and data reduction techniques are proposed, for a problem of long-term summer air temperature prediction. Specifically, the prediction of average air temperature in the first and second August fortnights, using input data from previous months, at two different locations, Paris (France) and C\'ordoba (Spain), is considered. The target variable, mainly in the first August fortnight, can contain signals of extreme events such as heatwaves, like the mega-heatwave of 2003, which affected France and the Iberian Peninsula. Thus, an accurate prediction of long-term air temperature may be valuable also for different problems related to climate change, such as attribution of extreme events, and in other problems related to renewable energy. The analysis carried out this work is based on Reanalysis data, which are first processed by a correlation analysis among different prediction variables and the target (average air temperature in August first and second fortnights). An area with the largest correlation is located, and the variables within, after a feature selection process, are the input of different deep learning and ML algorithms. The experiments carried out show a very good prediction skill in the three proposed AI frameworks, both in Paris and C\'ordoba regions.
[ -0.01540983933955431, -0.02235071174800396, -0.020012538880109787, -0.01916564255952835, 0.032347775995731354, 0.0038087342400103807, -0.036711134016513824, 0.015299375168979168, -0.048714976757764816, 0.02444954216480255, 0.01598978042602539, -0.07228080183267593, 0.01679064892232418, 0.0237867534160614, -0.030506694689393044, 0.01678144372999668, 0.030248943716287613, -0.041203368455171585, 0.039325468242168427, -0.06672073900699615, -0.016901114955544472, -0.010052296333014965, -0.006485204212367535, 0.002754715969786048, 0.012390468269586563, 0.033415600657463074, 0.014001413248479366, -0.004110211040824652, -0.05261806771159172, 0.07747264951467514, 0.12902288138866425, 0.01679064892232418, 0.013080873526632786, -0.01389094814658165, -0.04403863474726677, -0.046358395367860794, 0.015170498751103878, 0.08844548463821411, 0.00839532446116209, 0.05055605620145798, 0.0014153302181512117, -0.04043011739850044, 0.010153556242585182, -0.037742141634225845, -0.002247268334031105, -0.060497887432575226, -0.04587971419095993, -0.061565715819597244, -0.015087650157511234, 0.008703705854713917, -0.03382064029574394, -0.05412775278091431, -0.0012185648083686829, 0.038699500262737274, -0.048089008778333664, 0.03229254484176636, 0.031003786250948906, 0.0383681058883667, 0.041976623237133026, 0.03422567620873451, 0.00208042049780488, 0.03133518248796463, -0.030874911695718765, -0.04746304079890251, 0.01995730772614479, -0.05567425861954689, 0.03094855509698391, -0.021061955019831657, 0.016155477613210678, 0.037742141634225845, -0.02448636293411255, 0.020712150260806084, -0.04352313280105591, -0.03400474786758423, -0.002393404021859169, 0.0024371296167373657, 0.021908851340413094, 0.014645791612565517, 0.0013370843371376395, 0.012399673461914062, 0.02921793982386589, 0.031813863664865494, 0.006558847613632679, 0.007143390364944935, 0.05836223438382149, 0.0211724191904068, -0.04672661051154137, -0.08778269588947296, 0.027947593480348587, -0.028242167085409164, -0.06686802208423615, 0.03402315825223923, -0.05935641750693321, -0.008740527555346489, -0.0317954495549202, 0.05644751340150833, -0.005339132156223059, 0.013126900419592857, -0.03728187084197998, -0.015483482740819454, -0.05913548916578293, -0.006549641955643892, 0.03343401104211807, 0.020270289853215218, 0.029567744582891464, -0.04970915988087654, -0.04035647213459015, 0.0006449533393606544, -0.030322587117552757, 0.10855007916688919, -0.031684987246990204, -0.021190831437706947, -0.016045011579990387, -0.03691365197300911, -0.020159825682640076, -0.005969701800495386, -0.019994128495454788, -0.018871070817112923, 0.023105554282665253, 0.007640481926500797, 0.05037194862961769, 0.03118789568543434, 0.039325468242168427, 0.022700516507029533, 0.018070200458168983, 0.032587114721536636, 0.02671406976878643, -0.030727624893188477, 0.05051923543214798, 0.03282645717263222, -0.013927769847214222, 0.04510645940899849, -0.03481482341885567, 0.002987152198329568, -0.017922913655638695, 0.04970915988087654, -0.021651100367307663, 0.050040554255247116, 0.02737685851752758, -0.04591653496026993, -0.013854127377271652, -0.04974598065018654, 0.003346162848174572, 0.014848310500383377, 0.04481188580393791, -0.007387333549559116, -0.02104354463517666, 0.08844548463821411, -0.02194567397236824, -0.03426249697804451, -0.06944553554058075, 0.0330289751291275, -0.03122471645474434, 0.006545039359480143, 0.030451463535428047, -0.00001576784416101873, 0.018806632608175278, 0.0047545889392495155, -0.033673353493213654, -0.011018863879144192, -0.009329672902822495, -0.019460216164588928, 0.04613746330142021, 0.012243181467056274, 0.0014659599401056767, -0.025480547919869423, -0.016634156927466393, -0.0019826130010187626, -0.10405784100294113, 0.04050375893712044, 0.008372311480343342, -0.03409679979085922, -0.001207058085128665, 0.03720822557806969, -0.017784832045435905, 0.060497887432575226, 0.005730361677706242, 0.022663693875074387, -0.024007683619856834, 0.07320134341716766, -0.050077375024557114, 0.03162975236773491, 0.03862585872411728, 0.018199075013399124, 0.03558807447552681, 0.034962110221385956, 0.07909279316663742, -0.006080166436731815, 0.037484388798475266, -0.02459682896733284, 0.00013858442252967507, -0.012335236184298992, 0.021872030571103096, -0.008514994755387306, 0.002736305119469762, -0.044222742319107056, 0.029457280412316322, 0.006669312249869108, -0.0357353612780571, 0.03792624920606613, -0.04945140704512596, -0.08424782007932663, -0.03240300714969635, 0.05147659778594971, -0.007626673672348261, 0.04698435962200165, 0.041976623237133026, -0.0028283591382205486, 0.05353860557079315, 0.004418591968715191, -0.027947593480348587, -0.02275574952363968, -0.05372271314263344, 0.0019158738432452083, -0.0031505480874329805, -0.0022069946862757206, 0.04646885767579079, 0.009352685883641243, -0.038294464349746704, -0.009407918900251389, 0.009104140102863312, 0.004901875276118517, 0.009536794386804104, 0.017389001324772835, -0.016827471554279327, 0.01302564051002264, 0.0155479209497571, -0.04532738775014877, -0.03752120956778526, -0.020675327628850937, 0.018162254244089127, -0.014249959029257298, -0.007078952621668577, -0.02432066574692726, 0.02527802810072899, 0.04282351955771446, 0.036582257598638535, -0.011589598841965199, -0.024283844977617264, -0.04403863474726677, 0.015695206820964813, -0.02273733727633953, -0.02461523935198784, -0.06403276324272156, 0.05199209973216057, -0.055085111409425735, 0.0017053002957254648, 0.09838731586933136, 0.02155904658138752, 0.051108378916978836, 0.026787713170051575, -0.030248943716287613, 0.014783872291445732, 0.06307540088891983, -0.05884091556072235, -0.027155930176377296, 0.04473824426531792, 0.046358395367860794, 0.001688040210865438, -0.01957068033516407, 0.011967020109295845, -0.0023772944696247578, 0.017389001324772835, 0.05438550189137459, -0.013522732071578503, 0.02949410118162632, 0.059577349573373795, 0.01078872848302126, 0.04061422497034073, -0.03597470372915268, -0.02419179119169712, 0.01275868434458971, -0.03660067170858383, -0.02964138798415661, 0.020270289853215218, -0.026382675394415855, 0.050740163773298264, -0.0343361422419548, -0.009412521496415138, 0.024762526154518127, -0.0006777475937269628, 0.00396292470395565, 0.08351138979196548, -0.008004095405340195, -0.01957068033516407, -0.010641442611813545, -0.05147659778594971, -0.04433320462703705, -0.04691071808338165, -0.07555792480707169, 0.0074057443998754025, 0.016192298382520676, -0.06362772732973099, 0.016422433778643608, 0.005900661461055279, -0.019515447318553925, 0.017508670687675476, -0.05011419579386711, 0.005546253640204668, 0.04311809316277504, -0.020601684227585793, 0.015501893125474453, 0.04308127239346504, 0.02432066574692726, 0.011617214418947697, 0.01955226995050907, 0.029438868165016174, 0.04219755157828331, -0.03877314552664757, 0.023179197683930397, 0.04797854274511337, 0.03862585872411728, -0.006600271910429001, -0.048604510724544525, 0.005569267086684704, 0.04786808043718338, 0.02391562983393669, 0.003979034256190062, -0.036177221685647964, -0.005136613268405199, 0.025370081886649132, -0.01163562573492527, -0.0568525493144989, 0.03877314552664757, -0.01957068033516407, -0.07121297717094421, -0.013108489103615284, 0.033249903470277786, 0.026474731042981148, -0.004961710423231125, -0.06097656860947609, 0.013927769847214222, -0.024541595950722694, -0.0000832801015349105, 0.041571587324142456, -0.010162761434912682, -0.04945140704512596, -0.0025222795084118843, -0.05055605620145798, -0.011423901654779911, -0.02179838716983795, -0.04381770268082619, -0.01640402339398861, -0.013246570713818073, -0.019791610538959503, -0.019147232174873352, -0.008561021648347378, 0.0056521156802773476, -0.06436415761709213, 0.040246009826660156, 0.0008733622962608933, -0.030046425759792328, 0.011819733306765556, 0.015796465799212456, 0.012206360697746277, 0.0015649179695174098, -0.0198468416929245, -0.06038742512464523, 0.0025683066342025995, 0.010632236488163471, -0.0011466476134955883, -0.02724798396229744, -0.02919952943921089, 0.014378834515810013, -0.028794491663575172, 0.004556673113256693, 0.012197154574096203, -0.03376540541648865, 0.01448009442538023, 0.02724798396229744, 0.012639014050364494, 0.06664709746837616, -0.03056192770600319, 0.04716847091913223, -0.028094880282878876, 0.02141175977885723, 0.0008871704339981079, 0.01691952534019947, 0.025738298892974854, 0.012436495162546635, -0.006554244551807642, 0.05195527896285057, 0.010457334108650684, 0.044885531067848206, -0.014599764719605446, 0.0317586287856102, 0.017103632912039757, 0.004413989372551441, -0.01730615273118019, 0.016229121014475822, 0.027818718925118446, -0.030377820134162903, 0.0000036363128401717404, -0.0780617892742157, 0.02260846272110939, -0.027671432122588158, 0.014222342520952225, 0.04352313280105591, 0.040908798575401306, -0.025554189458489418, -0.03649020567536354, 0.012823122553527355, 0.0000787493190728128, 0.010862371884286404, -0.018999945372343063, 0.032605525106191635, 0.03450183942914009, -0.05247078090906143, 0.022148191928863525, 0.031666576862335205, -0.003026275197044015, -0.0008693349664099514, -0.018963124603033066, -0.010853166691958904, -0.0073459092527627945, 0.010273226536810398, -0.002692579524591565, 0.04031965136528015, -0.03479641303420067, 0.013752867467701435, -0.03150087967514992, 0.03126153722405434, -0.007263060659170151, 0.02299508824944496, 0.004860450979322195, 0.05644751340150833, 0.014921952970325947, 0.03665590286254883, 0.00873592495918274, -0.020951490849256516, -0.0022668298333883286, 0.007893630303442478, 0.034446608275175095, 0.009757723659276962, -0.03884678706526756, 0.030856501311063766, -0.030064836144447327, 0.007612865883857012, 0.014185521751642227, -0.02606969326734543, -0.04996691271662712, -0.024817759171128273, 0.01210510078817606, -0.004048074595630169, -0.02025187946856022, -0.04790490120649338, 0.022958267480134964, 0.022810980677604675, -0.028278987854719162, -0.043964989483356476, -0.027671432122588158, 0.034059979021549225, -0.026769302785396576, -0.041350655257701874, 0.022019317373633385, -0.0012507836800068617, 0.03612199053168297, -0.0018479840364307165, 0.0740850567817688, -0.014434067532420158, 0.0009285947307944298, 0.04385452717542648, 0.026124924421310425, -0.007000706624239683, 0.003465833142399788, -0.01614627242088318, -0.03030417673289776, -0.06793585419654846, 0.03240300714969635, 0.05873045325279236, 0.005500226281583309, 0.01123058795928955, -0.02500186674296856, 0.0713602602481842, 0.03267917037010193, -0.008017903193831444, -0.027837129309773445, -0.06108703464269638, 0.00946315098553896, -0.006135398987680674, 0.035514432936906815, -0.0030792062170803547, 0.030893322080373764, -0.006922460626810789, -0.02141175977885723, 0.05607929825782776, -0.01876980997622013, -0.040246009826660156, 0.0007876370218582451, 0.022958267480134964, 0.011746089905500412, 0.011782911606132984, 0.044222742319107056, -0.04853086918592453, -0.020159825682640076, 0.016321174800395966, 0.02340012602508068, 0.05121884495019913, 0.08108115941286087, 0.021651100367307663, 0.008561021648347378, -0.018355567008256912, -0.001562616671435535, 0.04293398559093475, 0.017757216468453407, 0.042234376072883606, 0.04654250293970108, -0.0026902782265096903, 0.0008112258510664105, -0.004002047702670097, 0.04046693816781044, -0.013237365521490574, -0.004103307146579027, -0.005969701800495386, 0.008050122298300266, 0.0502246618270874, 0.04337584599852562, 0.021724743768572807, 0.006545039359480143, 0.007718727923929691, 0.03347083553671837, -0.012077484279870987, -0.008077738806605339, 0.032476652413606644, -0.011129328981041908, 0.021743154153227806, -0.014599764719605446, -0.03334195911884308, 0.10170125961303711, 0.003339258721098304, -0.04444367066025734, 0.010052296333014965, -0.029825495555996895, -0.05147659778594971, -0.004791410639882088, -0.011746089905500412, -0.008878608234226704, 0.025296438485383987, 0.03520144894719124, -0.03516462817788124, -0.04112972691655159, 0.032310955226421356, 0.0015706713311374187, 0.02233229950070381, 0.026622015982866287, 0.009104140102863312, 0.021338116377592087, -0.006692325696349144, -0.025811942294239998, -0.029567744582891464, -0.0004913381999358535, -0.006190631538629532, 0.008409133180975914, 0.0016558213392272592, -0.02711910754442215, 0.01706681214272976, -0.02025187946856022, -0.02579353004693985, -0.03744756802916527, -0.002028640126809478, 0.019662734121084213, -0.009094934910535812, 0.005062969867140055, -0.0009625396342016757, -0.017821654677391052, -0.03461230546236038, 0.013596375472843647, 0.04565878212451935, 0.006660107057541609, 0.00027127162320539355, -0.02194567397236824, -0.017029989510774612, -0.019810020923614502, 0.03253188356757164, 0.016293557360768318, 0.039656862616539, 0.03625086322426796, -0.05386999994516373, 0.0015338497469201684, 0.0018146145157516003, 0.027873951941728592, -0.015962162986397743, 0.007898232899606228, 0.009472356177866459, 0.06174982339143753, -0.017757216468453407, -0.0006391999777406454, -0.017389001324772835, -0.0344097837805748, -0.004480728413909674, -0.01052177231758833, 0.008676089346408844, -0.01903676800429821, 0.015465072356164455, -0.03521985933184624, 0.006692325696349144, 0.001493576099164784, -0.019018355756998062, 0.021908851340413094, -0.06451144069433212, -0.01270345225930214, 0.04506963863968849, 0.007654290180653334, 0.05180799216032028, -0.03599311411380768, 0.033415600657463074, 0.02220342494547367, 0.022682106122374535, 0.029788674786686897, 0.021853620186448097, 0.006959282327443361, -0.015253347344696522, -0.01601739600300789, -0.007313690148293972, 0.05236031487584114, 0.038036711513996124, 0.021374939009547234, 0.021853620186448097, -0.036692723631858826, -0.01942339353263378, -0.014664201997220516, -0.010549387894570827, 0.0184936486184597, -0.005868442356586456, 0.013909359462559223, 0.09094934910535812, 0.008275654166936874, -0.014157905243337154, -0.02063850685954094, -0.029659798368811607, -0.02419179119169712, -0.011055685579776764, -0.0310958418995142, -0.005606088787317276, 0.048346761614084244, 0.008869403041899204, 0.013375446200370789, 0.003095315769314766, 0.019091999158263206, -0.015492687933146954, -0.015262553468346596, -0.04293398559093475, -0.003376080421730876, 0.0291074737906456, 0.016836676746606827, 0.01865934580564499, -0.07121297717094421, -0.004460016265511513, 0.05828859284520149, 0.03672954440116882, 0.03216366842389107, 0.012685040943324566, 0.00899367593228817, 0.05604247376322746, 0.03730028122663498, -0.0648060142993927, 0.04311809316277504, 0.014259164221584797, 0.011055685579776764, 0.02393404021859169, -0.03387587144970894, 0.005504829343408346, 0.003827145090326667, -0.011396285146474838, 0.02936522662639618, 0.006232055835425854, 0.04193980246782303, 0.005316118244081736, 0.015023212879896164, 0.010880783200263977, 0.02487299032509327, -0.048714976757764816, -0.06513740867376328, 0.006374739576131105, 0.02312396466732025, -0.0013946180697530508, 0.01336624100804329, 0.06403276324272156, 0.008225024677813053, -0.054422322660684586, -0.05129249021410942, 0.010199583135545254, -0.015326990745961666, 0.02750573493540287, -0.04639521613717079, -0.006678517442196608, 0.004308127332478762, 0.025554189458489418, -0.0079350546002388, -0.01866855099797249, -0.006591066252440214, 0.0007565687992610037, 0.011506750248372555, -0.002533786231651902, -0.04418592154979706, 0.019736377522349358, -0.02194567397236824, 0.05398046597838402, -0.00430122297257185, -0.0092698372900486, -0.009895805269479752, -0.019994128495454788, -0.030746035277843475, 0.030874911695718765, 0.0066647096537053585, 0.000087954722403083, 0.010595415718853474, -0.003737392369657755, -0.07511606067419052, 0.0031597535125911236, 0.03332354873418808, -0.005352939944714308, 0.008211216889321804, 0.03356288745999336, 0.0423448383808136, -0.0060571529902517796, -0.02765302173793316, -0.005104394163936377, -0.00905351061373949, 0.014148700051009655, 0.041350655257701874, 0.002139104763045907, -0.01098204217851162, -0.06274400651454926, -0.004763794597238302, 0.025719886645674706, 0.025204384699463844, -0.0050123403780162334, -0.08115480840206146, 0.0014417957281693816, 0.008758937940001488, 0.017232509329915047, -0.023105554282665253, 0.008317078463733196, 0.030727624893188477, -0.044370029121637344, 0.01772039569914341, 0.04208708927035332, -0.019091999158263206, 0.047536686062812805, 0.020583273842930794, -0.05320721119642258, 0.02050963044166565, 0.020123004913330078, -0.02023346908390522, 0.018963124603033066, -0.033526066690683365, -0.031243126839399338, 0.014130288735032082, 0.02356582321226597, 0.006158412434160709, -0.036029934883117676, 0.08093387633562088, -0.0741586983203888, -0.02986231818795204, 0.023179197683930397, -0.008565624244511127, -0.00717100640758872, -0.014636585488915443, 0.022534819319844246, 0.0008750883280299604, 0.050298307090997696, -0.02087784744799137, 0.024412721395492554, 0.0436704158782959, -0.01890789158642292, 0.022111371159553528, 0.045437853783369064, 0.041350655257701874, 0.011267409659922123, 0.00833088718354702, 0.005569267086684704, 0.06093974784016609, -0.01783085986971855, 0.028002826496958733, 0.006324109621345997, 0.03122471645474434, -0.005334529094398022, 0.01760072447359562, -0.03105901926755905, -0.01783085986971855, -0.013762072660028934, -0.031648166477680206, 0.02977026253938675, -0.025701476261019707, 0.03954639658331871, -0.02803964912891388, -0.0728331208229065, 0.01611865498125553, 0.027708254754543304, -0.01971796713769436, -0.019515447318553925, 0.011156944558024406, -0.03777896240353584, 0.01997571811079979, -0.014369629323482513, 0.014130288735032082, 0.014222342520952225, -0.0008210066007450223, -0.0068764337338507175, 0.04790490120649338, -0.026622015982866287, -0.014001413248479366, 0.0006461039884015918, -0.04856768995523453, 0.004860450979322195, -0.04142430052161217, -0.024026094004511833, 0.053906820714473724, 0.0020366946700960398, 0.026143336668610573, 0.013522732071578503, -0.0020539548713713884, 0.028518328443169594, 0.017260124906897545, -0.0042966203764081, -0.037484388798475266, 0.040282830595970154, -0.025830352678894997, -0.09072842448949814, -0.05305992439389229, -0.017932118847966194, 0.003698269370943308, -0.008961456827819347, -0.04481188580393791, 0.011055685579776764, -0.0013428376987576485, 0.006121590733528137, 0.01341226790100336, -0.015363812446594238, 0.021466992795467377, -0.009564410895109177, -0.05571107938885689, -0.020656917244195938, -0.017748011276125908, 0.01838318444788456, -0.03448342904448509, 0.049414586275815964, -0.00040676360367797315, 0.028610382229089737, 0.008119163103401661, 0.04116654768586159, -0.007718727923929691, -0.014047440141439438, 0.020988311618566513, -0.0025821146555244923, -0.027008643373847008, 0.0036384342238307, 0.004340345971286297, 0.0647691935300827, 0.03069080412387848, 0.009693286381661892, 0.020067771896719933, 0.010273226536810398, -0.01890789158642292, 0.034078389406204224, 0.027966005727648735, 0.02540690451860428, 0.012915176339447498, -0.03910453990101814, 0.0001933134044520557, 0.012905971147119999, -0.0070743500255048275, -0.01183814462274313, 0.013458294793963432, -0.0291074737906456, -0.0043104286305606365, -0.030911732465028763, -0.03251347318291664, -0.03503575176000595, 0.001227770233526826, 0.0002971618087030947, -0.005320721305906773, 0.024946633726358414, 0.042528945952653885, 0.011810528114438057, 0.026364265009760857, 0.037373922765254974, 0.027303216978907585, -0.06440097838640213, 0.018696166574954987, 0.013596375472843647, 0.029843905940651894, 0.006779776886105537, 0.030985375866293907, -0.0007732536178082228, -0.03105901926755905, 0.00604794779792428, -0.02273733727633953, -0.008708308450877666, -0.01892630197107792, 0.03584582731127739, 0.021632689982652664, 0.005656718276441097, 0.04985644668340683, 0.007843000814318657, -0.015060034580528736, 0.003956020809710026, 0.012979613617062569, 0.005320721305906773, 0.017039194703102112, -0.018042583018541336, 0.004255196079611778, -0.007691111881285906, 0.04017236456274986, -0.028481507673859596, -0.0032172873616218567, -0.013522732071578503, -0.021264472976326942, 0.010917603969573975, -0.016744622960686684, -0.014167110435664654, -0.008809567429125309, -0.029843905940651894, -0.0011639076983556151, -0.06042424589395523, -0.03452024981379509, -0.010484950616955757, 0.03137200325727463, -0.03321308270096779, 0.0634804368019104, 0.019625913351774216, -0.023878807201981544, 0.029678208753466606, -0.03807353600859642, 0.021724743768572807, -0.0001737519196467474, 0.052875816822052, -0.016983963549137115, -0.036950476467609406, -0.0015890821814537048, 0.03676636889576912, 0.06502694636583328, 0.008234229870140553, 0.03678477928042412, -0.010264021344482899, 0.014268370345234871, 0.001839929260313511, 0.0028927968814969063, 0.0008100752020254731, -0.040135543793439865, -0.002687976695597172, -0.004239086527377367, -0.00746557954698801, 0.010595415718853474, -0.024431131780147552, 0.05265488848090172, 0.024670472368597984, 0.008561021648347378, 0.013439883477985859, 0.0018445319728925824, 0.023713110014796257, 0.023768343031406403, -0.011414695531129837, -0.003005563048645854, -0.0006863776361569762, -0.021264472976326942, -0.04205026850104332, 0.025738298892974854, 0.035514432936906815, -0.004446208011358976, 0.020178236067295074, -0.04414909705519676, -0.013513526879251003, -0.02789236232638359, 0.013458294793963432, -0.0029181118588894606, -0.01515208836644888, -0.017821654677391052, -0.02577511966228485, 0.017619134858250618, -0.017637547105550766, -0.017241714522242546, -0.04282351955771446, -0.009016688913106918, 0.012740273959934711, -0.001296810689382255, -0.008708308450877666, 0.0010845111683011055, 0.01625673659145832, 0.018217487260699272, 0.02748732455074787, 0.01427757553756237, -0.009140961803495884, -0.006163015495985746, -0.033802229911088943, -0.0158516988158226, 0.004434701520949602, -0.0410192608833313, 0.006660107057541609, 0.004013554193079472, 0.029291583225131035, 0.01572282239794731, -0.01031004823744297, -0.019994128495454788, 0.012620603665709496, 0.01704839989542961, -0.014176315627992153, 0.03385746106505394, 0.021779976785182953, 0.012261592783033848, 0.0022909939289093018, 0.004842040594667196, 0.05372271314263344, -0.03056192770600319, 0.046763431280851364, 0.029273170977830887, 0.0064483825117349625, 0.0039030895568430424, 0.014249959029257298, 0.03799989074468613, -0.022313889116048813, -0.024265434592962265, 0.024652061983942986, 0.0049525052309036255, 0.04326537996530533, -0.03026735410094261, -0.022645283490419388, 0.023510592058300972, -0.06568973511457443, 0.00700991228222847, -0.0158885195851326, -0.0034819424618035555, 0.010061502456665039 ]
Polar codes are widely used state-of-the-art codes for reliable communication that have recently been included in the 5th generation wireless standards (5G). However, there remains room for the design of polar decoders that are both efficient and reliable in the short blocklength regime. Motivated by recent successes of data-driven channel decoders, we introduce a novel $\textbf{C}$ur$\textbf{RI}$culum based $\textbf{S}$equential neural decoder for $\textbf{P}$olar codes (CRISP). We design a principled curriculum, guided by information-theoretic insights, to train CRISP and show that it outperforms the successive-cancellation (SC) decoder and attains near-optimal reliability performance on the Polar(32,16) and Polar(64,22) codes. The choice of the proposed curriculum is critical in achieving the accuracy gains of CRISP, as we show by comparing against other curricula. More notably, CRISP can be readily extended to Polarization-Adjusted-Convolutional (PAC) codes, where existing SC decoders are significantly less reliable. To the best of our knowledge, CRISP constructs the first data-driven decoder for PAC codes and attains near-optimal performance on the PAC(32,16) code.
[ 0.016003046184778214, 0.00002116175710398238, -0.045738812536001205, -0.0034377940464764833, 0.02100515179336071, 0.06212947517633438, -0.03497782349586487, 0.02015608735382557, -0.03387034684419632, 0.030049549415707588, 0.0034124143421649933, -0.07298275083303452, -0.0028217597864568233, -0.07774490863084793, -0.029957260936498642, -0.005735809449106455, 0.06482433527708054, 0.012975942343473434, -0.01350199431180954, -0.056259844452142715, 0.002100745914503932, -0.04500049352645874, 0.019140899181365967, -0.007032480556517839, 0.04005376249551773, 0.05548461154103279, 0.02227875217795372, -0.0023072443436831236, -0.10668697953224182, 0.03339044004678726, 0.04463133588433266, 0.04629255086183548, 0.005537386517971754, -0.030529456213116646, -0.015163210220634937, -0.05803180858492851, 0.04909816011786461, 0.027391605079174042, -0.04049675166606903, -0.014184937812387943, -0.009404327720403671, 0.0038184893783181906, 0.0775972381234169, 0.029606560245156288, 0.009625823237001896, -0.01967618055641651, -0.042711708694696426, 0.008970566093921661, 0.02102361060678959, -0.04308086633682251, 0.02163272351026535, -0.030178755521774292, 0.035070113837718964, -0.022555621340870857, 0.018707137554883957, 0.025176649913191795, 0.0022807109635323286, 0.022869406268000603, 0.04887666553258896, 0.006044980138540268, -0.03327969089150429, -0.010419514961540699, -0.009436629712581635, -0.04093974456191063, 0.029329689219594002, -0.00994883757084608, 0.012865194119513035, -0.024955155327916145, 0.004621410276740789, -0.03263366222381592, -0.05832713842391968, -0.05507853627204895, 0.0009177064057439566, 0.044668249785900116, 0.011000940576195717, 0.030344877392053604, 0.04732619598507881, 0.0635322779417038, 0.06825751811265945, -0.011859236285090446, 0.028222212567925453, -0.038023386150598526, -0.0304371677339077, -0.022426415234804153, 0.08461126685142517, -0.031821515411138535, 0.018051879480481148, -0.07420098036527634, 0.07648976147174835, 0.018744053319096565, 0.0237553883343935, 0.0014477957738563418, 0.00233493116684258, 0.013649657368659973, -0.0010832512052729726, 0.0009603904327377677, -0.030732493847608566, -0.01884557120501995, -0.022832490503787994, -0.013142063282430172, 0.003043255303055048, 0.07239209860563278, 0.0049421172589063644, -0.00823224801570177, -0.02617337927222252, -0.03064020536839962, -0.05555844306945801, 0.03403646871447563, 0.00900748185813427, 0.12381596118211746, 0.018974777311086655, 0.022407956421375275, 0.006367994472384453, 0.01651064120233059, -0.05098086968064308, -0.06128041073679924, -0.05245750769972801, -0.07685892283916473, -0.036528293043375015, -0.022426415234804153, -0.033501189202070236, 0.027576183900237083, -0.01147161889821291, 0.030141839757561684, -0.03403646871447563, 0.003310895524919033, 0.007900004275143147, 0.04300703480839729, 0.03772806003689766, -0.026247210800647736, -0.024585995823144913, -0.017516598105430603, -0.002208032878115773, -0.022407956421375275, 0.10144492238759995, 0.00933972466737032, 0.018753282725811005, -0.042748622596263885, -0.0201745443046093, 0.015190896578133106, 0.025379687547683716, -0.0032347566448152065, 0.06504583358764648, -0.0037884952034801245, 0.032264504581689835, 0.042305633425712585, -0.01544930785894394, 0.10270006209611893, -0.025398146361112595, 0.02999417670071125, -0.017922673374414444, 0.06585798412561417, -0.004356077406555414, 0.03879861906170845, 0.04677245765924454, 0.028129922226071358, -0.006146498955786228, -0.007037095259875059, 0.006677165161818266, -0.027594642713665962, 0.02035912312567234, 0.054081808775663376, -0.014286456629633904, -0.017507370561361313, 0.004344541113823652, 0.03449791669845581, -0.007120156195014715, 0.011074773035943508, -0.05013180524110794, 0.03508857265114784, 0.023847676813602448, 0.020063797011971474, -0.015467765741050243, 0.003380113048478961, 0.01906706765294075, -0.0013059002812951803, 0.012680615298449993, -0.058659378439188004, -0.05629676207900047, 0.02203879877924919, -0.055595360696315765, 0.01774732396006584, 0.0026833252049982548, 0.021983424201607704, 0.0360114686191082, 0.04688320308923721, 0.06947574019432068, -0.011979212984442711, 0.004312239587306976, -0.015070919878780842, 0.027262398973107338, 0.0011103613069280982, 0.016123022884130478, -0.03490399196743965, 0.047879934310913086, -0.004586801864206791, -0.0010192252229899168, 0.036565206944942474, -0.022241834551095963, 0.03798647224903107, 0.00038386776577681303, -0.0006483356701210141, -0.010871735401451588, -0.009155145846307278, -0.006234174128621817, 0.012680615298449993, 0.020931320264935493, 0.05330657213926315, -0.006875588092952967, -0.020894404500722885, -0.013123605400323868, -0.03920469433069229, 0.002124971942976117, -0.030510999262332916, 0.006954034324735403, -0.02205725573003292, -0.03150773048400879, -0.03756193816661835, -0.06829443573951721, 0.0042799380607903, 0.04057058319449425, 0.01201612874865532, 0.056001435965299606, -0.022334124892950058, -0.058659378439188004, -0.059213120490312576, -0.025250481441617012, 0.034590207040309906, 0.015070919878780842, -0.009367411956191063, 0.017913445830345154, 0.01866099238395691, 0.02253716252744198, -0.0018907866906374693, 0.0042084138840436935, 0.019620805978775024, -0.005343577824532986, -0.02633950114250183, -0.017267417162656784, 0.008601406589150429, -0.04186264052987099, 0.03383342921733856, -0.011517764069139957, -0.056001435965299606, -0.03809721767902374, 0.0037261995021253824, -0.003647753270342946, 0.03427642211318016, -0.004789839033037424, 0.03383342921733856, -0.02637641690671444, 0.01564311608672142, -0.000009256015800929163, 0.002355696400627494, -0.022574078291654587, 0.032024551182985306, 0.05378647893667221, -0.04437292367219925, 0.017221271991729736, -0.006044980138540268, 0.05596451833844185, 0.026044173166155815, 0.004835984203964472, 0.0237553883343935, -0.0342395044863224, 0.002992495894432068, -0.03045562468469143, 0.046587876975536346, 0.01339124608784914, -0.009288965724408627, 0.0142679987475276, -0.00047183147398754954, -0.003684669267386198, -0.04263787716627121, 0.024106089025735855, 0.002376461634412408, 0.03366731107234955, -0.041456565260887146, 0.017341248691082, 0.050242554396390915, 0.03195071965456009, 0.006727924570441246, 0.020839029923081398, -0.015504681505262852, 0.003896935610100627, -0.062277138233184814, -0.05718274414539337, -0.006972492206841707, -0.031618475914001465, -0.06283088028430939, -0.011148604564368725, 0.011407015845179558, -0.04378226771950722, 0.02253716252744198, 0.02654253877699375, -0.02078365720808506, 0.005860400386154652, -0.053048159927129745, 0.024733658879995346, 0.040607500821352005, 0.0311016533523798, 0.04119815304875374, -0.020635994151234627, -0.02595188468694687, -0.045517317950725555, -0.0237553883343935, 0.013575825840234756, 0.009893463924527168, -0.03770960122346878, -0.016593702137470245, 0.0381341353058815, -0.006681779399514198, -0.018937861546874046, 0.0074893152341246605, 0.009939608164131641, 0.004512969870120287, 0.006547959521412849, 0.005749653093516827, -0.05799489468336105, 0.011490076780319214, 0.038060303777456284, 0.027613099664449692, -0.05419255420565605, 0.012966712936758995, 0.029625017195940018, -0.005546615459024906, 0.045517317950725555, 0.026893239468336105, -0.04607105627655983, 0.013428161852061749, -0.007886161096394062, -0.04045983776450157, 0.006894045975059271, 0.013114376924932003, 0.03488553315401077, 0.008610635995864868, -0.04821217805147171, 0.035679224878549576, -0.0655626580119133, -0.059693027287721634, -0.016676761209964752, -0.039130862802267075, 0.008199946023523808, -0.01777501031756401, -0.03136006370186806, -0.047510776668787, -0.021337395533919334, -0.003892321139574051, -0.022610994055867195, -0.0285359974950552, 0.0010446049273014069, 0.01797804795205593, 0.030178755521774292, -0.015144751407206059, 0.07242901623249054, -0.053011246025562286, -0.02637641690671444, -0.013271269388496876, 0.03466403856873512, 0.0029025133699178696, 0.04278554022312164, -0.05633367598056793, -0.0334458127617836, -0.00911823008209467, -0.04367152228951454, -0.02938506379723549, -0.04311778396368027, -0.03702665865421295, 0.03172922506928444, -0.004965189844369888, 0.0036708256229758263, 0.057773396372795105, -0.04954114928841591, -0.03281824290752411, 0.027963802218437195, -0.02358926646411419, 0.018993236124515533, 0.02425375208258629, -0.03920469433069229, 0.04440983757376671, 0.010779445990920067, 0.020303750410676003, -0.028369875624775887, 0.024475248530507088, 0.02872057817876339, 0.03854021057486534, -0.0034077998716384172, 0.01062255259603262, -0.021558891981840134, 0.004621410276740789, 0.035051655024290085, -0.033962637186050415, 0.00010584483243292198, -0.011194749735295773, 0.056887418031692505, -0.0005364342941902578, 0.004443752579391003, 0.037155862897634506, 0.007636978756636381, -0.03401800990104675, -0.03663903847336769, -0.018725594505667686, -0.03152618557214737, 0.0018665606621652842, 0.004653711803257465, 0.039758432656526566, -0.03154464438557625, -0.03536543995141983, -0.021983424201607704, 0.042527128010988235, 0.023626182228326797, -0.04141965135931969, 0.026690201833844185, 0.05363881587982178, 0.03470095619559288, 0.049614980816841125, -0.019417768344283104, 0.020229918882250786, -0.04226871579885483, 0.014314143918454647, -0.010170333087444305, 0.04644021391868591, 0.05330657213926315, -0.022887863218784332, 0.042121052742004395, 0.0158369243144989, 0.025859594345092773, -0.009385869838297367, 0.02532431297004223, 0.03435025364160538, -0.03145235404372215, 0.03558693826198578, -0.0011178598506376147, -0.046587876975536346, -0.050611712038517, -0.022795574739575386, -0.05363881587982178, 0.039093948900699615, -0.01781192608177662, -0.006386452354490757, -0.015440079383552074, -0.016141481697559357, 0.0022841719910502434, -0.0033962635789066553, 0.002729470143094659, 0.0025541195645928383, -0.02999417670071125, 0.014203395694494247, -0.028462165966629982, 0.007553917821496725, -0.05230984464287758, -0.01340047549456358, -0.033519644290208817, -0.04869208484888077, 0.05806872621178627, -0.04437292367219925, -0.052605170756578445, -0.02488132379949093, 0.009298195131123066, -0.0263210441917181, -0.008933650329709053, 0.034165672957897186, -0.027816137298941612, -0.07298275083303452, -0.005048250779509544, 0.013206666335463524, -0.03756193816661835, -0.036528293043375015, -0.029255857691168785, 0.0038254112005233765, -0.01187769416719675, -0.06906966865062714, 0.0227402001619339, 0.007544688880443573, 0.04407759755849838, 0.033981095999479294, 0.027262398973107338, -0.02977268025279045, -0.025841137394309044, -0.0617603175342083, 0.0021907284390181303, -0.04954114928841591, 0.014360289089381695, 0.02504744380712509, -0.005292818415910006, -0.010225706733763218, 0.04518507421016693, -0.014092648401856422, 0.0403490886092186, -0.00248720939271152, -0.0017281259642913938, 0.001253987313248217, -0.045960307121276855, -0.05168227478861809, -0.017461225390434265, -0.01969463750720024, 0.000772350060287863, -0.019122440367937088, 0.02100515179336071, -0.002055754652246833, 0.0025333543308079243, -0.05825330317020416, 0.04260095953941345, 0.05098086968064308, -0.05290049687027931, -0.005288204178214073, 0.06969723850488663, 0.041936472058296204, -0.02574884705245495, 0.07634209841489792, 0.029828054830431938, 0.08446360379457474, -0.018688678741455078, 0.014507952146232128, 0.015744635835289955, 0.01739662140607834, 0.006188029423356056, -0.02979113906621933, -0.005869629792869091, 0.03383342921733856, 0.02209417149424553, 0.0285359974950552, 0.006714080926030874, 0.01584615372121334, -0.08749070763587952, 0.04780610278248787, 0.030714036896824837, -0.029735764488577843, -0.009155145846307278, 0.017830384895205498, -0.0068479012697935104, 0.044668249785900116, -0.01608610711991787, -0.04632946476340294, -0.01113937608897686, -0.019214730709791183, 0.03540235757827759, 0.050870124250650406, -0.004427602048963308, 0.033095113933086395, -0.031138569116592407, 0.04651404544711113, -0.012366829439997673, 0.027576183900237083, -0.029698848724365234, -0.02595188468694687, -0.019214730709791183, -0.03935236111283302, -0.01652909815311432, 0.012459119781851768, -0.03754347935318947, 0.010659469291567802, -0.016824426129460335, 0.01180386170744896, -0.029274316504597664, -0.006049594841897488, -0.02785305306315422, -0.0022391807287931442, -0.016206083819270134, -0.026524079963564873, -0.01241297461092472, 0.018033422529697418, -0.009390484541654587, 0.019436227157711983, 0.011148604564368725, 0.009515075944364071, 0.028554456308484077, 0.046403296291828156, -0.040386006236076355, 0.004459903109818697, -0.04655096307396889, -0.038023386150598526, -0.007978450506925583, 0.01674136519432068, 0.038687873631715775, 0.005832713562995195, 0.022758658975362778, 0.015947673469781876, -0.009395099245011806, 0.005934232380241156, -0.02333085425198078, -0.0043837642297148705, -0.019602347165346146, 0.02803763374686241, 0.03667595610022545, -0.033778056502342224, -0.019546974450349808, 0.0005776762845925987, 0.038724787533283234, -0.044483669102191925, -0.024604452773928642, 0.022186461836099625, 0.0005773879238404334, 0.03172922506928444, -0.05961919203400612, 0.010613324120640755, 0.03370422497391701, 0.007443170063197613, 0.010807132348418236, -0.05651825666427612, -0.013631199486553669, 0.04333927854895592, 0.013944984413683414, -0.008929035626351833, -0.059693027287721634, -0.0004328967188484967, 0.03134160861372948, -0.011619282886385918, 0.05533694848418236, 0.01511706504970789, -0.03728506714105606, 0.009902692399919033, 0.03905703127384186, -0.03497782349586487, 0.017516598105430603, -0.03754347935318947, 0.009192061610519886, 0.01424031239002943, 0.005934232380241156, 0.023700013756752014, 0.013695802539587021, -0.012376058846712112, 0.0544140487909317, 0.004254558589309454, 0.0067832982167601585, 0.014452578499913216, 0.007253976073116064, -0.055595360696315765, 0.004053828306496143, -0.04522198811173439, 0.00984731875360012, 0.027114735916256905, -0.03252291679382324, -0.04780610278248787, -0.045369651168584824, -0.015800008550286293, 0.0195100586861372, 0.0313231498003006, 0.0019265490118414164, -0.008624479174613953, -0.03302128240466118, -0.0009459701832383871, 0.007014022674411535, 0.01093633845448494, -0.006769455038011074, 0.06216639280319214, -0.011342412792146206, 0.0019277026876807213, 0.056038349866867065, 0.04009067639708519, 0.017645804211497307, 0.03839254751801491, 0.0016081492649391294, 0.060542091727256775, -0.027336230501532555, -0.0016600623494014144, 0.059065453708171844, -0.008661394938826561, -0.05186685174703598, 0.005389722995460033, 0.03339044004678726, 0.004480668343603611, -0.010244164615869522, -0.00003136410305160098, 0.01995304971933365, 0.004199184477329254, 0.038244880735874176, 0.003959231078624725, -0.042527128010988235, 0.04688320308923721, -0.03152618557214737, -0.017101295292377472, -0.002390305045992136, 0.024549080058932304, 0.01691671460866928, -0.03798647224903107, 0.001236682990565896, -0.006017293315380812, 0.008089198730885983, -0.0027917656116187572, -0.025859594345092773, 0.0008184949401766062, 0.03935236111283302, -0.013446619734168053, -0.002434142865240574, -0.019030151888728142, 0.015781551599502563, -0.04994722455739975, -0.03854021057486534, -0.005223601125180721, -0.03730352595448494, 0.011600824072957039, 0.037192780524492264, 0.003996147308498621, 0.01564311608672142, -0.008306079544126987, -0.012043815106153488, -0.022131087258458138, 0.043191615492105484, -0.006487971171736717, -0.015698490664362907, -0.010880963876843452, -0.009150531142950058, -0.016649074852466583, 0.023183191195130348, 0.09251126646995544, 0.013178979977965355, -0.009865776635706425, -0.020709825679659843, -0.009450472891330719, 0.024050714448094368, 0.030178755521774292, 0.019362393766641617, 0.029514269903302193, 0.05227292701601982, 0.04566498100757599, 0.02059907652437687, 0.019989965483546257, 0.020839029923081398, 0.03691590949892998, 0.02550889365375042, 0.05655517429113388, -0.015153980813920498, -0.039758432656526566, -0.005703507922589779, 0.03219067305326462, 0.016556784510612488, -0.020746741443872452, -0.0055835312232375145, -0.008056897670030594, -0.015763092786073685, -0.024512164294719696, -0.02013762854039669, -0.010345683433115482, 0.04429909214377403, -0.010677927173674107, 0.009039782918989658, 0.06190798059105873, 0.016178397461771965, 0.045517317950725555, 0.011997670866549015, -0.023718472570180893, -0.02011916972696781, -0.002789458492770791, 0.024715201929211617, -0.013944984413683414, 0.009875006042420864, 0.04603413864970207, -0.0109271090477705, -0.022555621340870857, 0.016215313225984573, -0.014987858943641186, 0.023663097992539406, -0.03942619264125824, -0.06962340325117111, 0.003340889699757099, -0.020894404500722885, -0.04186264052987099, 0.009422785602509975, -0.019343936815857887, 0.021964965388178825, 0.02979113906621933, -0.014987858943641186, 0.001828491105698049, 0.0017546593444421887, -0.008827516809105873, 0.005855786148458719, 0.022574078291654587, 0.022758658975362778, -0.056887418031692505, 0.04153039678931236, 0.051534608006477356, 0.07870472222566605, -0.024715201929211617, -0.0211897324770689, -0.003008646657690406, 0.024604452773928642, 0.02827758714556694, -0.0012632162543013692, 0.03187688812613487, 0.014692531898617744, 0.009884234517812729, 0.02528739720582962, 0.012883652001619339, -0.06061592325568199, 0.009588907472789288, 0.016879798844456673, -0.005546615459024906, -0.008296851068735123, -0.02253716252744198, 0.026228753849864006, -0.0034262577537447214, 0.007950764149427414, -0.0006956341676414013, 0.05315890908241272, -0.012348371557891369, -0.013049773871898651, 0.044040679931640625, -0.0278715118765831, -0.039500024169683456, 0.004035370424389839, 0.003866941435262561, -0.013741947710514069, 0.01821800135076046, 0.005449711345136166, 0.014212625101208687, -0.051977600902318954, -0.040164507925510406, -0.01255140919238329, 0.022389499470591545, 0.017064379528164864, -0.006437211763113737, -0.00610958319157362, 0.001791575225070119, -0.013538910076022148, -0.030492540448904037, -0.0045083556324243546, -0.0034216432832181454, -0.01995304971933365, -0.011850006878376007, -0.007406254298985004, -0.005334348883479834, 0.0211897324770689, 0.024124545976519585, -0.0355684794485569, -0.006358765531331301, 0.017885757610201836, -0.004111509304493666, 0.009288965724408627, -0.010511805303394794, 0.008144572377204895, 0.06120657920837402, -0.03957385569810867, 0.014000358991324902, -0.006663321517407894, 0.022020339965820312, -0.04843367263674736, 0.07180144637823105, -0.02054370380938053, 0.018900945782661438, -0.0009701962699182332, -0.013132834807038307, 0.004859056789427996, -0.04968881234526634, -0.008827516809105873, 0.0032439855858683586, -0.05035329982638359, 0.005380493588745594, 0.012376058846712112, -0.021595807746052742, 0.011277810670435429, 0.01776578091084957, 0.03649137541651726, 0.029237400740385056, -0.025601183995604515, 0.03641754388809204, 0.031157027930021286, 0.01714744046330452, 0.008702925406396389, -0.0399060994386673, 0.03089861571788788, 0.056259844452142715, -0.019011693075299263, -0.011766945943236351, -0.013871152885258198, -0.031858429312705994, -0.008970566093921661, -0.025453519076108932, 0.003991532605141401, -0.04116123914718628, 0.049208905547857285, -0.008167644962668419, -0.04031217470765114, 0.03497782349586487, -0.019140899181365967, -0.038281798362731934, 0.002457215217873454, -0.028185296803712845, -0.015716947615146637, 0.038687873631715775, 0.013409703969955444, -0.009662739001214504, 0.03196917846798897, 0.005777339916676283, 0.04806451499462128, -0.002729470143094659, 0.02868366241455078, -0.01190538052469492, -0.06545190513134003, -0.026634829118847847, -0.0071339993737638, 0.03514394536614418, -0.044483669102191925, 0.04673554003238678, -0.019030151888728142, -0.00931665301322937, -0.0006962110055610538, 0.014000358991324902, -0.04477899894118309, -0.010650239884853363, -0.019030151888728142, -0.03593763709068298, 0.01910398341715336, -0.03920469433069229, -0.0134927649050951, -0.01210841815918684, 0.03839254751801491, -0.03357502073049545, -0.011397787369787693, -0.043708436191082, -0.021780386567115784, -0.0142679987475276, -0.03514394536614418, 0.011933067813515663, 0.06541499495506287, 0.006446440704166889, 0.006940191145986319, 0.0031909188255667686, 0.014914027415215969, -0.01542162150144577, 0.007812329102307558, -0.006118812132626772, -0.013418933376669884, -0.0008052282501012087, 0.017645804211497307, 0.027576183900237083, 0.03876170516014099, -0.040607500821352005, 0.011831548996269703, 0.042748622596263885, -0.01886403001844883, 0.02851754054427147, 0.0005462400731630623, 0.010078043676912785, 0.01778423972427845, -0.010557950474321842, -0.049614980816841125, -0.008532189764082432, 0.007563146762549877, -0.014424891211092472, -0.07634209841489792, -0.012089960277080536, -0.008513731881976128, -0.004219949711114168, 0.02934814803302288, -0.0530850775539875, -0.00909977126866579, 0.02187267690896988, 0.0028563684318214655, 0.001066523720510304, -0.038023386150598526, -0.07527153939008713, -0.009893463924527168, -0.05814255774021149, -0.02848062478005886, -0.0010244165314361453, -0.014083418995141983, 0.0038853995501995087, -0.01969463750720024, -0.0007694659871049225, -0.004743694327771664, -0.05851171538233757, 0.020100712776184082, -0.005052865017205477, -0.028000717982649803, -0.04931965470314026, -0.045738812536001205, -0.05386031046509743, -0.028849782422184944, 0.01563388854265213, 0.0075216167606413364, -0.0050990101881325245, -0.010557950474321842, 0.023275481536984444, -0.005274360533803701, 0.042933203279972076, 0.013695802539587021, -0.022795574739575386, 0.012486806139349937, 0.011886922642588615, 0.03359347581863403, -0.02310935966670513, -0.01864253357052803, -0.013686573132872581, 0.026265669614076614, -0.0526420883834362, 0.05537386238574982, -0.002434142865240574, -0.0295511856675148, -0.004688320681452751, -0.034608665853738785, 0.001837720163166523, 0.024549080058932304, 0.009252049960196018, 0.009325881488621235, 0.025656556710600853, -0.008781371638178825, -0.006677165161818266, -0.03298436477780342, -0.002741006202995777, -0.014784821309149265, 0.023220106959342957, 0.02120818942785263, 0.021521974354982376, -0.008227633312344551, 0.034368712455034256, 0.017738094553351402, 0.006012678612023592, -0.04160422831773758, 0.016187626868486404, -0.01904860883951187, -0.019140899181365967, 0.009325881488621235, -0.03599300980567932, 0.005809641443192959, -0.0012401437852531672, -0.06478741765022278, 0.043413110077381134, 0.023829219862818718, 0.011480847373604774, 0.022001881152391434, -0.033132027834653854, 0.03534698486328125, -0.02122664824128151 ]
Due to its distributed nature, federated learning is vulnerable to poisoning attacks, in which malicious clients poison the training process via manipulating their local training data and/or local model updates sent to the cloud server, such that the poisoned global model misclassifies many indiscriminate test inputs or attacker-chosen ones. Existing defenses mainly leverage Byzantine-robust federated learning methods or detect malicious clients. However, these defenses do not have provable security guarantees against poisoning attacks and may be vulnerable to more advanced attacks. In this work, we aim to bridge the gap by proposing FLCert, an ensemble federated learning framework, that is provably secure against poisoning attacks with a bounded number of malicious clients. Our key idea is to divide the clients into groups, learn a global model for each group of clients using any existing federated learning method, and take a majority vote among the global models to classify a test input. Specifically, we consider two methods to group the clients and propose two variants of FLCert correspondingly, i.e., FLCert-P that randomly samples clients in each group, and FLCert-D that divides clients to disjoint groups deterministically. Our extensive experiments on multiple datasets show that the label predicted by our FLCert for a test input is provably unaffected by a bounded number of malicious clients, no matter what poisoning attacks they use.
[ -0.017261728644371033, -0.010686703957617283, -0.026959430426359177, -0.01779285818338394, 0.034230418503284454, -0.008530132472515106, -0.03586043789982796, 0.02745393104851246, -0.026629764586687088, 0.01967012882232666, -0.026648078113794327, -0.019084053114056587, -0.03926699608564377, -0.04615337401628494, -0.021556556224822998, 0.026739653199911118, -0.0022080817725509405, -0.052563562989234924, 0.01014641672372818, -0.06230705603957176, 0.0022046477533876896, -0.08600644767284393, -0.0005946596502326429, 0.028406303375959396, 0.050585564225912094, 0.05476134270429611, 0.024468613788485527, -0.013635391369462013, -0.05439504608511925, 0.06739857792854309, 0.05915690213441849, 0.02630009688436985, -0.031538140028715134, -0.007701386231929064, -0.033094897866249084, -0.015274569392204285, 0.02670302428305149, 0.06937658041715622, -0.027820227667689323, 0.05860745906829834, -0.0494866743683815, -0.013324039056897163, -0.0011858852813020349, 0.05175771191716194, 0.02194116823375225, -0.00973433256149292, -0.003241725033149123, -0.022344093769788742, -0.03126341477036476, -0.016126208007335663, -0.008603392168879509, -0.02351624332368374, -0.012792909517884254, -0.04216074198484421, 0.018369775265455246, 0.016080422326922417, 0.04651967063546181, -0.035988643765449524, 0.024377040565013885, -0.027930116280913353, -0.03628167882561684, -0.0010473793372511864, 0.008841484785079956, 0.008269146084785461, -0.0079165855422616, 0.05084197223186493, 0.027893487364053726, 0.015714125707745552, 0.016932060942053795, -0.00916657317429781, -0.03164802864193916, 0.02111699990928173, 0.0006387297180481255, -0.042600296437740326, -0.008172993548214436, 0.03012789599597454, 0.007843326777219772, -0.0033653501886874437, -0.009716018103063107, 0.028333043679594994, 0.026996061205863953, 0.027911802753806114, 0.01811336725950241, 0.037948329001665115, 0.06340594589710236, -0.04992622882127762, -0.06501764804124832, -0.08432148396968842, 0.010201361030340195, -0.028186524286866188, 0.004070471040904522, 0.01904742419719696, -0.026849541813135147, 0.016703125089406967, 0.005576866213232279, 0.022344093769788742, -0.02835135906934738, -0.026886172592639923, -0.05292985960841179, 0.005883639212697744, -0.047691818326711655, 0.060731980949640274, -0.04175781458616257, 0.04091533273458481, -0.020750703290104866, -0.015805698931217194, -0.0061858342960476875, 0.0606953501701355, 0.019029108807444572, 0.1551632434129715, 0.008498081937432289, -0.00927188340574503, -0.039816442877054214, 0.07318606227636337, -0.0035736814606934786, -0.050182636827230453, -0.08593318611383438, -0.024798281490802765, -0.011428454890847206, -0.013433928601443768, -0.048424411565065384, 0.03479817882180214, 0.006716964300721884, 0.035164475440979004, -0.04465155676007271, 0.03140993416309357, 0.02020125836133957, 0.0009088735096156597, -0.014303882606327534, 0.04212411120533943, 0.014715966768562794, -0.005865324754267931, 0.040842071175575256, -0.07249010354280472, 0.02776528336107731, 0.008864378556609154, -0.0006965359207242727, 0.010897324420511723, -0.01594305969774723, 0.0042925383895635605, 0.0331498421728611, 0.02320489101111889, -0.01371780876070261, 0.029047321528196335, -0.01573243923485279, -0.040036220103502274, -0.019084053114056587, 0.049450043588876724, 0.02058587037026882, 0.028864173218607903, -0.024193892255425453, 0.03606190159916878, 0.07846073806285858, 0.021922852843999863, 0.027582135051488876, -0.0513547845184803, 0.055970124900341034, -0.03254545480012894, 0.03809484839439392, -0.06813117116689682, 0.02131846360862255, -0.035567402839660645, 0.05868071690201759, 0.01626357063651085, 0.025237837806344032, 0.05113500729203224, 0.0238092802464962, 0.0013278252445161343, -0.07179413735866547, 0.0582045316696167, 0.02556750364601612, -0.012499871663749218, 0.0009615286253392696, 0.012655547820031643, -0.009917480871081352, 0.04941341280937195, 0.054321788251399994, -0.032985009253025055, -0.025530874729156494, -0.02289353869855404, -0.005086944438517094, 0.04875408113002777, 0.008534710854291916, -0.02692280150949955, 0.002279051812365651, 0.029175525531172752, 0.051611192524433136, 0.05051230266690254, 0.07413843274116516, -0.0005471555632539093, 0.029376989230513573, 0.012673863209784031, 0.06648283451795578, -0.017527293413877487, 0.043552666902542114, 0.007335089612752199, -0.0013953611487522721, -0.012756279669702053, 0.0438823364675045, -0.021666444838047028, 0.004752698820084333, -0.022179260849952698, 0.00041236987453885376, -0.039486777037382126, 0.03675786405801773, -0.019084053114056587, -0.004354351200163364, 0.020549239590764046, -0.0009924349142238498, -0.0008979990379884839, -0.022838594391942024, -0.028644395992159843, -0.02565907873213291, 0.015659179538488388, 0.023790964856743813, -0.013635391369462013, -0.002582391258329153, -0.0197617020457983, -0.02919384092092514, 0.03272860124707222, 0.047801706939935684, 0.039413515478372574, -0.024212205782532692, -0.01211526058614254, -0.053589195013046265, -0.024084001779556274, 0.008383614011108875, 0.03635494038462639, -0.01071417611092329, -0.03032935969531536, -0.04897385835647583, -0.018195783719420433, -0.03479817882180214, 0.035988643765449524, 0.00476185604929924, 0.0028571137227118015, -0.038973961025476456, 0.00714278407394886, 0.013708651065826416, -0.018882591277360916, 0.0025755229871720076, 0.001987159252166748, -0.019706757739186287, -0.026318412274122238, 0.008195886388421059, 0.037838440388441086, -0.05589686334133148, 0.07366225123405457, -0.0004003507492598146, 0.020787332206964493, -0.06915680319070816, -0.0031890699174255133, -0.01759139448404312, 0.004981634207069874, -0.032765232026576996, 0.02153824083507061, 0.02300342731177807, -0.04300322383642197, 0.04461492970585823, -0.07358898967504501, 0.07227032631635666, 0.04212411120533943, -0.038461145013570786, 0.01656576432287693, -0.0071656773798167706, -0.015494346618652344, 0.02846124768257141, -0.017957691103219986, 0.057325419038534164, 0.05912027508020401, -0.07358898967504501, -0.035787180066108704, -0.061757609248161316, -0.02445029839873314, 0.02908395230770111, 0.00019645517750177532, -0.0021783201955258846, -0.019029108807444572, -0.015393615700304508, 0.030897120013833046, 0.020421035587787628, -0.0426369272172451, -0.00937719363719225, -0.02007305435836315, 0.012756279669702053, -0.018864275887608528, -0.031538140028715134, -0.0003391105274204165, -0.07303954660892487, 0.015485189855098724, -0.029798230156302452, 0.0061308895237743855, -0.04963319003582001, -0.03780180960893631, 0.04238051921129227, 0.0418677031993866, 0.02216094546020031, 0.062380313873291016, -0.0020237888675183058, 0.020457666367292404, -0.053259529173374176, -0.06820443272590637, 0.007000843994319439, 0.018012635409832, 0.018974164500832558, -0.023845909163355827, -0.01428556814789772, 0.006021000444889069, -0.018681127578020096, -0.004574128892272711, -0.029541822150349617, -0.057728346437215805, -0.00393539946526289, -0.06446820497512817, -0.03595201298594475, -0.049559932202100754, -0.03045756369829178, 0.018772700801491737, 0.006002685986459255, -0.019413720816373825, 0.011730649508535862, 0.02639167197048664, -0.07073187828063965, 0.0007755185943096876, 0.026556504890322685, -0.059266794472932816, 0.0136170769110322, 0.053149640560150146, -0.08336911350488663, -0.0035393410362303257, -0.024395354092121124, -0.005682176444679499, -0.0532228983938694, -0.03393738344311714, -0.028424616903066635, -0.01738993264734745, -0.06996265053749084, 0.025091318413615227, -0.0006032447563484311, -0.018360618501901627, -0.01506394799798727, -0.03569560497999191, -0.04432189092040062, 0.04523763060569763, 0.015869801864027977, 0.020878907293081284, -0.004903796128928661, -0.03313152864575386, 0.04109847918152809, -0.024670077487826347, 0.0008745332015678287, 0.030878804624080658, 0.013076789677143097, -0.015915587544441223, 0.03734394162893295, -0.05662945657968521, 0.016941217705607414, 0.00351873692125082, -0.03126341477036476, 0.0019413720583543181, -0.006460556760430336, -0.0312817320227623, -0.02990811876952648, -0.014505346305668354, -0.006048473063856363, 0.004917532205581665, -0.021922852843999863, 0.01728004217147827, -0.02360781654715538, 0.052124008536338806, -0.05084197223186493, 0.030622396618127823, 0.013891799375414848, 0.021684760227799416, 0.0006885231705382466, -0.018067581579089165, 0.01490827277302742, -0.024725021794438362, -0.040036220103502274, 0.031135212630033493, 0.032875120639801025, 0.004370376467704773, 0.04300322383642197, 0.008603392168879509, 0.016025476157665253, -0.003392822341993451, -0.0037087532691657543, -0.025237837806344032, -0.04413874074816704, 0.008800276555120945, 0.02857113629579544, 0.0057325419038534164, 0.03820473700761795, 0.0015636286698281765, 0.010201361030340195, 0.0075640249997377396, -0.011318565346300602, -0.011941269971430302, 0.01935877650976181, -0.09391845017671585, 0.007106154225766659, 0.025750651955604553, -0.02423052117228508, -0.024285465478897095, -0.01582401432096958, -0.031208472326397896, 0.03673955053091049, 0.020329462364315987, 0.021611500531435013, 0.002726620528846979, -0.001413675956428051, -0.03097037971019745, 0.04128162935376167, -0.01103468518704176, 0.01647419109940529, 0.034303680062294006, -0.027783598750829697, -0.022215889766812325, -0.02538435533642769, 0.050182636827230453, 0.03582381084561348, 0.0008138652774505317, 0.09545689821243286, 0.0022149498108774424, 0.00921235978603363, 0.03250882402062416, 0.020439350977540016, -0.035164475440979004, 0.0019688443280756474, 0.0014228334184736013, 0.03249051049351692, 0.013131733983755112, -0.010961426421999931, -0.04600685462355614, -0.02807663567364216, 0.005883639212697744, 0.015173837542533875, -0.025530874729156494, 0.005238041747361422, -0.026904486119747162, -0.0017467769794166088, 0.024486929178237915, 0.013296566903591156, 0.0032623291481286287, -0.040439147502183914, -0.03459671512246132, 0.007646441925317049, -0.013690335676074028, -0.03219747170805931, 0.022747019305825233, -0.048424411565065384, 0.015073105692863464, -0.06355246156454086, 0.007115311920642853, 0.028717655688524246, -0.011584130115807056, -0.003923952579498291, -0.034523457288742065, 0.0563364215195179, -0.0017147260950878263, -0.020769018679857254, 0.05278334394097328, -0.0024244256783276796, 0.007444978691637516, -0.0075182379223406315, 0.015146365389227867, -0.015759911388158798, -0.0676916167140007, 0.0010061709908768535, -0.023845909163355827, -0.0009661073563620448, -0.019834961742162704, 0.00574627798050642, -0.027801914140582085, 0.025237837806344032, 0.013223308138549328, 0.011510871350765228, -0.06717880070209503, 0.005810379981994629, -0.004331457428634167, 0.00927188340574503, 0.011483399197459221, 0.015402772463858128, -0.01696869172155857, 0.07846073806285858, 0.0022962219081819057, 0.01278375182300806, -0.03448682650923729, 0.02412063255906105, -0.029285414144396782, -0.01092479657381773, -0.08168414235115051, 0.0021428351756185293, -0.006959635764360428, 0.045933596789836884, -0.012911955825984478, -0.026135263964533806, -0.026355041190981865, 0.09985245764255524, -0.0011389534920454025, 0.038900699466466904, -0.018452191725373268, 0.015549291856586933, 0.05490786209702492, 0.003301248187199235, -0.044358521699905396, -0.02474333718419075, -0.013085946440696716, -0.00018958711007144302, 0.030604083091020584, -0.03280186280608177, 0.03510953113436699, -0.008177571929991245, -0.0381314791738987, -0.023040058091282845, 0.03985307365655899, -0.0005998107371851802, -0.0006358680548146367, -0.016309356316924095, -0.005503606516867876, 0.011153732426464558, 0.021391723304986954, -0.0501093789935112, -0.04402885213494301, -0.0253660399466753, 0.019322145730257034, 0.014715966768562794, 0.030311044305562973, -0.03575054928660393, -0.075017549097538, 0.00801731739193201, 0.07021906226873398, -0.035787180066108704, -0.004697754047811031, 0.005279249977320433, 0.0008934203651733696, -0.016932060942053795, -0.030109582468867302, -0.010650074109435081, -0.017976006492972374, -0.028516191989183426, 0.07183076441287994, 0.001148683251813054, 0.005260935053229332, -0.029175525531172752, 0.04476144537329674, 0.044578298926353455, -0.035475827753543854, -0.00011868868750752881, -0.0350179560482502, 0.03263702988624573, 0.015622550621628761, -0.04256366565823555, 0.04128162935376167, -0.011666547507047653, -0.0399995893239975, 0.060512199997901917, 0.024889854714274406, -0.021373407915234566, -0.00714278407394886, -0.01050355564802885, -0.017334988340735435, -0.010787435807287693, 0.0037636978086084127, 0.03532930836081505, -0.031190156936645508, -0.03199600800871849, 0.04608011618256569, -0.019285516813397408, 0.021666444838047028, 0.06183087080717087, -0.05977960675954819, 0.024981429800391197, -0.008694966323673725, -0.00649260776117444, -0.037545401602983475, -0.02921215444803238, 0.0376552939414978, 0.02807663567364216, -0.030182842165231705, -0.037508774548769, -0.02814989537000656, -0.008269146084785461, 0.01584232784807682, 0.024468613788485527, 0.008846063166856766, -0.018589552491903305, -0.0012465531472116709, 0.003752250922843814, -0.058570828288793564, 0.02164812944829464, 0.02060418389737606, -0.03283849358558655, -0.01582401432096958, 0.017454033717513084, 0.03985307365655899, 0.030311044305562973, -0.016932060942053795, 0.04640978202223778, -0.030311044305562973, -0.0112819354981184, -0.016602395102381706, -0.02269207499921322, 0.0272341538220644, 0.03849777579307556, 0.008607970550656319, -0.01676722802221775, -0.016226939857006073, 0.03333299234509468, 0.014248938299715519, 0.062270425260066986, 0.024688392877578735, 0.015393615700304508, 0.021483296528458595, 0.017215941101312637, 0.020384406670928, 0.03747214376926422, -0.012270936742424965, 0.012399140745401382, 0.009670230560004711, 0.052124008536338806, -0.050475675612688065, 0.03609853237867355, 0.03137330710887909, 0.034120529890060425, 0.02692280150949955, 0.021043740212917328, -0.045933596789836884, -0.019432036206126213, -0.04717900604009628, -0.03820473700761795, 0.015778226777911186, -0.026574820280075073, -0.029889803379774094, -0.05303975194692612, -0.039486777037382126, 0.03210590034723282, 0.017737913876771927, 0.009780120104551315, 0.0181316826492548, 0.017417404800653458, -0.0033653501886874437, 0.014816698618233204, 0.017344145104289055, -0.016483347862958908, 0.004118547774851322, -0.005091522820293903, -0.01511889323592186, 0.042197369039058685, 0.011858852580189705, 0.005457819439470768, 0.0028754284139722586, 0.024358725175261497, 0.023882539942860603, -0.033168159425258636, -0.055457308888435364, -0.000013834493984177243, -0.011886325664818287, 0.009670230560004711, 0.004109390079975128, 0.013919271528720856, 0.0350179560482502, 0.002157716080546379, -0.010375351645052433, -0.0035004219971597195, -0.038790810853242874, 0.02113531529903412, 0.03769192099571228, 0.03912048041820526, 0.042820073664188385, -0.01616283878684044, 0.02609863318502903, -0.014688494615256786, 0.04058566689491272, 0.021831277757883072, -0.004233015235513449, 0.028442932292819023, 0.029138896614313126, 0.007577761076390743, -0.01999979466199875, -0.07802117615938187, 0.00885979924350977, 0.007760909385979176, -0.02258218638598919, -0.01594305969774723, -0.00659791799262166, 0.0011046131839975715, -0.0012305276468396187, -0.03456008434295654, -0.0387541837990284, 0.022344093769788742, -0.039926331490278244, -0.0011961873387917876, -0.029670026153326035, -0.048204634338617325, 0.013214150443673134, -0.02952350676059723, -0.00973433256149292, -0.03791169822216034, 0.027673710137605667, -0.024798281490802765, 0.011886325664818287, -0.07567688077688217, 0.017728757113218307, -0.014523660764098167, -0.053186267614364624, 0.0059385839849710464, 0.00097412004834041, 0.006744436454027891, 0.01144676934927702, -0.012179362587630749, 0.03333299234509468, -0.014642707072198391, -0.016822172328829765, 0.012966900132596493, -0.013754437677562237, -0.01159328781068325, -0.0013014976866543293, -0.017866117879748344, 0.026281781494617462, 0.023369723930954933, 0.02794843167066574, -0.022600501775741577, -0.040219370275735855, -0.03424873203039169, -0.011858852580189705, -0.011748963966965675, 0.0015899562276899815, -0.01438629999756813, 0.015027319081127644, 0.09472430497407913, -0.026977745816111565, -0.003972028847783804, 0.0009077287977561355, -0.02518289163708687, -0.00603473698720336, 0.014294725842773914, 0.010668388567864895, 0.017225097864866257, 0.03417547419667244, 0.032563768327236176, 0.01319583598524332, 0.016327671706676483, -0.020750703290104866, 0.027930116280913353, 0.030567452311515808, -0.024725021794438362, -0.004072760697454214, -0.00864460039883852, 0.0015006714966148138, 0.008456872776150703, -0.03320479020476341, 0.07366225123405457, -0.032563768327236176, -0.08058525621891022, 0.00047332391841337085, 0.02651987597346306, 0.021519925445318222, -0.003937688656151295, 0.010073157027363777, -0.026116948574781418, 0.020237887278199196, -0.0010668388567864895, -0.006868061609566212, 0.057728346437215805, -0.04161129519343376, -0.04080544412136078, -0.017124366015195847, 0.017472349107265472, -0.021098684519529343, 0.03280186280608177, -0.019926536828279495, -0.009010897018015385, -0.023552872240543365, -0.014248938299715519, 0.009853378869593143, 0.03606190159916878, -0.010979740880429745, 0.03776518255472183, 0.03780180960893631, -0.01263723336160183, -0.0019734229426831007, -0.015888115391135216, -0.004693175200372934, 0.010732490569353104, 0.013488872908055782, 0.0426369272172451, -0.03853440284729004, -0.027618765830993652, 0.03820473700761795, -0.004061313811689615, -0.00405902462080121, 0.0018852829234674573, -0.009358878247439861, 0.05651956796646118, 0.0051922546699643135, -0.04274681583046913, 0.0650542825460434, -0.000682227429933846, -0.05113500729203224, 0.04380907490849495, -0.018772700801491737, -0.016071263700723648, -0.0007400336326099932, -0.013543817214667797, -0.026062004268169403, 0.029889803379774094, -0.014239780604839325, -0.02619020827114582, 0.002064997097477317, 0.01387348398566246, 0.01253650151193142, 0.02018294297158718, 0.006982529070228338, -0.03181286156177521, -0.027930116280913353, 0.01946866512298584, 0.04274681583046913, 0.00745413638651371, -0.034413568675518036, -0.009587814100086689, -0.021098684519529343, -0.0007171400939114392, 0.021043740212917328, -0.039816442877054214, 0.018076738342642784, 0.0096885459497571, -0.003960581962019205, 0.015952218323946, 0.0031455722637474537, -0.016803856939077377, -0.011291093192994595, -0.019230572506785393, 0.023681076243519783, -0.09164741635322571, 0.030384304001927376, -0.006895533762872219, 0.017362460494041443, -0.004945004358887672, -0.013781909830868244, -0.005920269060879946, 0.006858904380351305, -0.01030209194868803, -0.024193892255425453, -0.020878907293081284, -0.005897375755012035, -0.01428556814789772, -0.013031002134084702, 0.02701437473297119, 0.024505244567990303, -0.005755435675382614, 0.017069421708583832, 0.0569591224193573, 0.008168414235115051, 0.012563973665237427, -0.02712426520884037, 0.007197728380560875, 0.030384304001927376, -0.00792116392403841, -0.0016334539977833629, -0.04981634020805359, 0.02195948176085949, 0.014789225533604622, -0.008603392168879509, 0.0370325893163681, 0.015695810317993164, -0.02483491040766239, -0.011117102578282356, -0.04648303985595703, -0.07087839394807816, 0.032050952315330505, -0.02597043104469776, -0.02701437473297119, 0.06849746406078339, -0.009010897018015385, 0.009615286253392696, 0.00455581396818161, 0.015274569392204285, -0.023168260231614113, -0.033094897866249084, 0.021812964230775833, 0.004633652046322823, 0.012362510897219181, -0.018919220194220543, 0.012408297508955002, -0.04908374696969986, 0.03322310373187065, -0.009253568015992641, -0.03529267758131027, -0.07410180568695068, -0.029450248926877975, 0.02930372953414917, 0.012353353202342987, 0.02620852366089821, 0.0426369272172451, -0.01418483629822731, -0.004674860741943121, -0.002346587600186467, -0.009789276868104935, -0.01728920079767704, 0.00020604184828698635, -0.03168465569615364, -0.0022206732537597418, -0.0006793657667003572, 0.04750867187976837, 0.025091318413615227, 0.029322044923901558, -0.006309459451586008, 0.01490827277302742, 0.02650156058371067, -0.0034088478423655033, -0.052966490387916565, -0.0059294262900948524, -0.010347879491746426, 0.005288407206535339, -0.005695912521332502, -0.014880799688398838, -0.000962673278991133, 0.018278202041983604, 0.025750651955604553, 0.0055814445950090885, 0.04556730017066002, -0.01102552842348814, 0.031519822776317596, -0.0034408988431096077, -0.05076871067285538, 0.03192275017499924, 0.03300332650542259, -0.019798332825303078, 0.01614452339708805, -0.007101575843989849, 0.008768225088715553, -0.0063827186822891235, 0.04413874074816704, 0.009056683629751205, 0.03498132526874542, -0.012417455203831196, -0.022289149463176727, -0.06054883077740669, -0.0036950171925127506, -0.01294858567416668, 0.001838351134210825, 0.006552130915224552, 0.006817695684731007, 0.004743541125208139, -0.0209338515996933, 0.008708702400326729, -0.016748912632465363, -0.0007623548153787851, 0.021831277757883072, -0.054211899638175964, 0.00022378434368874878, 0.045310892164707184, 0.014880799688398838, -0.053589195013046265, 0.024523558095097542, -0.020274518057703972, 0.029688341543078423, -0.023552872240543365, 0.05043904483318329, -0.0011240727035328746, 0.019138997420668602, -0.01677638478577137, -0.008429400622844696, -0.01438629999756813, 0.03172128647565842, -0.005476134363561869, -0.014715966768562794, -0.000471893057692796, -0.009194045327603817, -0.01967012882232666, -0.030164526775479317, 0.02890080399811268, 0.021684760227799416, 0.02525615133345127, 0.02556750364601612, 0.011987056583166122, -0.02225251868367195, -0.0085392901673913, 0.019706757739186287, 0.02122688852250576, 0.02597043104469776, -0.01852545142173767, 0.04142814874649048, -0.05029252544045448, -0.05025589466094971, 0.021043740212917328, 0.034303680062294006, -0.035787180066108704, 0.002133677713572979, 0.030713971704244614, 0.020475981757044792, 0.021080370992422104, -0.034944698214530945, -0.03289343789219856, -0.0014571737265214324, -0.02805832028388977, -0.05457819625735283, -0.004500869661569595, 0.0003745955182239413, -0.027252469211816788, 0.0588272362947464, -0.01749982126057148, 0.04238051921129227, 0.012335038743913174, -0.013076789677143097, 0.06219716742634773, -0.0028136158362030983, -0.017554765567183495, -0.002077588578686118, -0.03985307365655899, -0.007486186921596527, 0.014239780604839325, 0.016730597242712975, -0.05168445408344269, -0.03706921637058258, -0.05153793469071388, 0.0395234040915966, 0.004354351200163364, -0.0007068379782140255, 0.024779966101050377, -0.017005320638418198, -0.0029807386454194784, 0.022289149463176727 ]
Multi-Agent Reinforcement Learning (MARL) -- where multiple agents learn to interact in a shared dynamic environment -- permeates across a wide range of critical applications. While there has been substantial progress on understanding the global convergence of policy optimization methods in single-agent RL, designing and analysis of efficient policy optimization algorithms in the MARL setting present significant challenges, which unfortunately, remain highly inadequately addressed by existing theory. In this paper, we focus on the most basic setting of competitive multi-agent RL, namely two-player zero-sum Markov games, and study equilibrium finding algorithms in both the infinite-horizon discounted setting and the finite-horizon episodic setting. We propose a single-loop policy optimization method with symmetric updates from both agents, where the policy is updated via the entropy-regularized optimistic multiplicative weights update (OMWU) method and the value is updated on a slower timescale. We show that, in the full-information tabular setting, the proposed method achieves a finite-time last-iterate linear convergence to the quantal response equilibrium of the regularized problem, which translates to a sublinear last-iterate convergence to the Nash equilibrium by controlling the amount of regularization. Our convergence results improve upon the best known iteration complexities, and lead to a better understanding of policy optimization in competitive Markov games.
[ -0.032592590898275375, -0.005146913230419159, -0.04237036779522896, -0.01680329069495201, 0.005703703034669161, 0.04711439833045006, -0.038495469838380814, 0.035815633833408356, -0.04211686924099922, 0.04725925624370575, -0.03333497792482376, 0.011407406069338322, 0.01662222109735012, -0.05080822482705116, -0.033751439303159714, 0.04088559374213219, -0.017355553805828094, 0.02096789889037609, 0.0060251024551689625, -0.040342383086681366, 0.005758024286478758, 0.014576130546629429, 0.018106995150446892, 0.08278518170118332, -0.008664196357131004, 0.021601643413305283, -0.01191440224647522, 0.021619752049446106, -0.050735797733068466, 0.028011519461870193, 0.010900410823523998, 0.012973661534488201, -0.002478394890204072, 0.03023868054151535, -0.014322632923722267, 0.0011384772369638085, 0.03929217904806137, -0.018288064748048782, -0.007564196828752756, 0.05819588154554367, -0.057181887328624725, 0.0088497931137681, -0.02449876256287098, -0.03324444219470024, 0.001187139772810042, 0.011751439422369003, 0.00929794181138277, -0.01702962815761566, 0.00006174768350319937, -0.007921810261905193, 0.062106989324092865, -0.0396905317902565, 0.03795225918292999, -0.01328148040920496, -0.007564196828752756, -0.04816460609436035, 0.046426333487033844, -0.010529217310249805, 0.06475061178207397, 0.029043618589639664, 0.04975802078843117, -0.02516872249543667, -0.06427983194589615, 0.0016386830247938633, 0.008102879859507084, -0.0795259177684784, 0.024136623367667198, 0.010674073360860348, 0.03414979204535484, -0.02984032593667507, -0.051496293395757675, 0.010348147712647915, -0.006722221616655588, -0.02674403041601181, 0.0011384772369638085, 0.0031641973182559013, 0.05537118762731552, 0.021384360268712044, 0.05653003603219986, 0.018288064748048782, -0.0226699560880661, 0.04171851649880409, 0.0002444444107823074, 0.04026995599269867, 0.023050203919410706, -0.06348311901092529, 0.03759011998772621, -0.06044114753603935, 0.013544031418859959, 0.008021398447453976, -0.047150611877441406, -0.00090591557091102, -0.03440329059958458, 0.01285596564412117, -0.01778106763958931, -0.02051522396504879, 0.004685184918344021, 0.028971191495656967, -0.039219748228788376, -0.011389299295842648, 0.0297497920691967, -0.0015311726601794362, -0.018577776849269867, 0.0003434670506976545, -0.0055543202906847, 0.0189037024974823, -0.04591933637857437, 0.0045403288677334785, 0.008627982810139656, 0.1623835265636444, 0.0018661521608009934, 0.034475717693567276, -0.032320983707904816, 0.05200328677892685, -0.07011028379201889, -0.006889711134135723, -0.07239176332950592, -0.05200328677892685, 0.012312755919992924, 0.02163785882294178, -0.06916871666908264, 0.027160491794347763, 0.04577448219060898, -0.050772011280059814, -0.04095802083611488, 0.008120986633002758, -0.01502880547195673, 0.08003291487693787, 0.021963784471154213, 0.005486419424414635, -0.01872263289988041, -0.03626830875873566, -0.041501231491565704, -0.032719340175390244, 0.003358847461640835, -0.004807407036423683, 0.005115225911140442, -0.062251847237348557, -0.019700409844517708, 0.015119340270757675, -0.005074485205113888, -0.05450205132365227, -0.007731686811894178, 0.03300905227661133, -0.006129217799752951, -0.03650370240211487, 0.0082658426836133, 0.012013990432024002, -0.027178598567843437, 0.005884773097932339, -0.03950946033000946, 0.03445760905742645, -0.03668477013707161, 0.05595061182975769, 0.01648641750216484, -0.0037753083743155003, 0.0008182097808457911, -0.029242796823382378, 0.015544855035841465, -0.01426831167191267, 0.0679374411702156, -0.00549999950453639, -0.008021398447453976, 0.08271274715662003, 0.04494155943393707, 0.027739915996789932, 0.001835596514865756, -0.008908641524612904, -0.01442222110927105, 0.05747159942984581, -0.04892509803175926, -0.06804608553647995, -0.02656296081840992, -0.031868308782577515, 0.06163620948791504, 0.024245265871286392, 0.055841971188783646, -0.0264724250882864, 0.003150617005303502, 0.02866337262094021, 0.014132509008049965, -0.047947321087121964, -0.02100411430001259, 0.047911107540130615, 0.07438353449106216, 0.009388476610183716, 0.03558024391531944, -0.061925921589136124, -0.00527366204187274, 0.008795472793281078, -0.011769546195864677, 0.07865678519010544, 0.015119340270757675, -0.035544030368328094, 0.029586829245090485, -0.018958022817969322, -0.015454319305717945, 0.010800821706652641, -0.008967489004135132, 0.0035648145712912083, 0.008618929423391819, -0.05352427437901497, 0.014386006630957127, -0.014431274496018887, 0.014358846470713615, -0.04389135539531708, 0.008347324095666409, -0.01361645944416523, 0.022597528994083405, -0.00790822971612215, -0.020134977996349335, -0.04273250699043274, -0.02449876256287098, -0.05251028388738632, -0.023394236341118813, -0.025820573791861534, -0.013625512830913067, 0.02993086166679859, -0.020641973242163658, -0.009067077189683914, -0.03692016005516052, 0.0013489710399881005, 0.014023867435753345, 0.004300411324948072, 0.03625020384788513, -0.014096295461058617, -0.011271604336798191, -0.05298106372356415, -0.001178086269646883, -0.01975473016500473, 0.0354716032743454, 0.05366913229227066, -0.02920658141374588, 0.02544032782316208, -0.03543538972735405, -0.00041787547525018454, 0.019609874114394188, 0.042442794889211655, 0.06015143543481827, -0.025965429842472076, -0.02984032593667507, -0.06178106367588043, 0.006504937540739775, 0.016948146745562553, -0.015037858858704567, -0.04787489399313927, -0.007559670135378838, 0.05667489394545555, 0.0453399121761322, 0.019428804516792297, -0.05609546974301338, -0.07872921228408813, -0.012548146769404411, -0.008012345060706139, -0.016296295449137688, 0.0425514355301857, 0.01241234503686428, -0.03476542979478836, 0.006351028103381395, -0.05366913229227066, 0.08271274715662003, 0.06819093972444534, 0.0028111108113080263, 0.05156872048974037, 0.025512754917144775, 0.005223867949098349, 0.037336621433496475, 0.01290123350918293, -0.006962139159440994, 0.032683126628398895, -0.015544855035841465, -0.003440328873693943, -0.03224855661392212, -0.02777612954378128, 0.026599174365401268, -0.011851027607917786, -0.040740735828876495, -0.0016873455606400967, -0.02404608763754368, 0.02212674729526043, 0.07025513797998428, -0.014078187756240368, 0.05786995217204094, -0.013625512830913067, 0.015789298340678215, -0.043565429747104645, -0.01262962818145752, -0.035634566098451614, -0.06583703309297562, -0.013154731132090092, -0.006278600078076124, 0.021474895998835564, 0.0009608023683540523, 0.024516871199011803, 0.0631934106349945, 0.011706171557307243, -0.005744443740695715, 0.022995883598923683, 0.032139915972948074, -0.0207868292927742, 0.0359242781996727, 0.03586995601654053, 0.0012731479946523905, 0.010855142958462238, -0.05211193114519119, -0.0011248970404267311, 0.015128393657505512, 0.03090863861143589, -0.016178598627448082, -0.0037956787273287773, -0.007183949928730726, -0.013879011385142803, 0.004492797888815403, 0.002937859855592251, 0.003915637731552124, -0.0005918723763898015, 0.08387159556150436, -0.004411316476762295, -0.03458435833454132, -0.020134977996349335, 0.046426333487033844, -0.014938270673155785, -0.03467489406466484, -0.0013048353139311075, -0.01590699516236782, -0.003060081973671913, 0.020189298316836357, 0.025675717741250992, -0.035272423177957535, 0.053596705198287964, -0.025748146697878838, -0.02786666341125965, 0.000739557552151382, -0.016586007550358772, 0.041682299226522446, -0.025657610967755318, -0.008555554784834385, -0.010628805495798588, -0.0017077159136533737, -0.01388806477189064, -0.008044032379984856, -0.04501398652791977, 0.0406683087348938, 0.03503703325986862, -0.005291769281029701, -0.021764608100056648, -0.06688723713159561, -0.054900407791137695, 0.03309958428144455, -0.005622221622616053, 0.0009291151654906571, 0.022742385044693947, 0.060803286731243134, 0.020533330738544464, 0.04479670524597168, -0.024172836914658546, -0.03197695314884186, -0.0024738681968301535, 0.016767077147960663, 0.027305347844958305, 0.0064551434479653835, -0.040378596633672714, -0.019193414598703384, -0.033841971307992935, -0.06460575759410858, 0.0011667694197967649, -0.00105246901512146, 0.054936621338129044, -0.008297530002892017, 0.016857611015439034, 0.005830452311784029, 0.029170367866754532, 0.015535800717771053, 0.02324938029050827, -0.005097119137644768, 0.041501231491565704, -0.0073061720468103886, -0.009515225887298584, -0.04856295883655548, 0.04899752512574196, -0.020171191543340683, 0.031922630965709686, 0.010601645335555077, 0.01733744703233242, 0.028609050437808037, 0.04019752889871597, 0.010728394612669945, -0.07333333045244217, 0.06764773279428482, -0.02279670536518097, 0.031469956040382385, -0.019790945574641228, 0.019682303071022034, 0.044144853949546814, 0.010692180134356022, 0.0011554525699466467, 0.038821395486593246, 0.00112829206045717, 0.012865019962191582, 0.049830447882413864, 0.03619588166475296, -0.05468312278389931, 0.02346666529774666, 0.014730039983987808, 0.02145678922533989, 0.029912754893302917, 0.009144032374024391, -0.01444938126951456, 0.04258764907717705, -0.04179094359278679, -0.005251028575003147, 0.010882304050028324, -0.029369544237852097, -0.02114897035062313, 0.034511931240558624, 0.007011933717876673, -0.08082962036132812, -0.030727569013834, -0.0058032916858792305, -0.03929217904806137, -0.04649876058101654, -0.054900407791137695, 0.09799505025148392, 0.01001316774636507, -0.012195060960948467, 0.003200411330908537, 0.049794234335422516, -0.03425843268632889, -0.00423250999301672, 0.013046089559793472, 0.04856295883655548, -0.017283126711845398, 0.07286254316568375, -0.05269135534763336, 0.021293824538588524, -0.00918024592101574, -0.021348146721720695, -0.004820987116545439, 0.02154732309281826, -0.011054320260882378, 0.04439834877848625, -0.02091357856988907, 0.004510905127972364, 0.003469752846285701, 0.010004114359617233, -0.04030616953969002, -0.003313580062240362, -0.025567075237631798, -0.0007706789765506983, -0.00008805940888123587, -0.028500409796833992, 0.015843620523810387, -0.027124278247356415, -0.012240327894687653, 0.061129212379455566, 0.027069956064224243, 0.027975305914878845, -0.03152427822351456, 0.033570367842912674, -0.007446501404047012, 0.04562962427735329, 0.0006179011543281376, 0.033045265823602676, -0.04323950409889221, -0.016151439398527145, 0.008664196357131004, -0.018795059993863106, -0.015879834070801735, -0.02482469007372856, -0.013580245897173882, -0.0359242781996727, -0.0851752981543541, 0.021692179143428802, -0.009524279274046421, 0.045086417347192764, 0.05178600549697876, 0.025874894112348557, -0.0632658377289772, 0.017500409856438637, -0.017183538526296616, 0.07431110739707947, -0.021493002772331238, -0.02410040982067585, 0.004490534774959087, -0.013951439410448074, 0.02558518387377262, 0.042261723428964615, 0.01997201517224312, -0.001078497851267457, 0.03597859665751457, 0.014440327882766724, -0.01702962815761566, -0.015291356481611729, 0.003680246649309993, 0.00904897041618824, -0.00046116250450722873, 0.018487241119146347, -0.05363291874527931, 0.05710946023464203, -0.009134978987276554, 0.03798847272992134, -0.029279010370373726, -0.008048558607697487, 0.027884772047400475, -0.014213990420103073, 0.03816954419016838, 0.023502878844738007, 0.02750452421605587, -0.030202466994524002, 0.016341563314199448, 0.033534154295921326, 0.05674732103943825, 0.009795883670449257, -0.012394237332046032, 0.0075506167486310005, 0.011724279262125492, 0.0368296280503273, -0.014150615781545639, 0.05222057178616524, 0.029260903596878052, 0.014060080982744694, -0.026454318314790726, 0.02145678922533989, -0.00046370879863388836, -0.04084938019514084, 0.046788472682237625, -0.010646912269294262, -0.07112427055835724, 0.07691851258277893, -0.008188888430595398, -0.014902056194841862, 0.041501231491565704, -0.02844608761370182, -0.026399997994303703, -0.027739915996789932, -0.04881645739078522, 0.028609050437808037, 0.024172836914658546, 0.014358846470713615, 0.01594320870935917, 0.003202674677595496, 0.08676871657371521, -0.0033158434089273214, 0.03032921627163887, -0.030582712963223457, -0.018432920798659325, 0.02109464816749096, -0.02011687122285366, 0.006595472805202007, 0.050953082740306854, -0.004920575767755508, 0.015934154391288757, 0.000932510185521096, -0.03002139739692211, -0.019682303071022034, 0.011208229698240757, 0.005409464705735445, -0.005916460417211056, -0.0274139903485775, -0.03755390644073486, 0.02015308476984501, -0.007767900358885527, 0.03431275486946106, -0.036376953125, -0.04323950409889221, -0.010800821706652641, 0.03378765285015106, 0.06026007607579231, 0.01236707717180252, 0.02893497608602047, -0.011941562406718731, -0.03371522203087807, 0.018387652933597565, -0.013824690133333206, -0.028554730117321014, 0.016477365046739578, -0.06366419047117233, 0.038097117096185684, -0.006029629148542881, -0.015363784506917, -0.01599752902984619, 0.001087551354430616, 0.07123291492462158, 0.028102055191993713, 0.010230451822280884, -0.04142880439758301, -0.01872263289988041, 0.002092489507049322, 0.016730863600969315, -0.04399999603629112, 0.015282303094863892, 0.040523454546928406, -0.0057716043666005135, 0.011787652969360352, -0.021112754940986633, -0.025060079991817474, 0.012231274507939816, -0.0444345623254776, 0.06931357085704803, -0.06942221522331238, -0.0193563774228096, -0.03911110758781433, -0.002319958759471774, -0.023846911266446114, -0.019899586215615273, 0.0022701644338667393, 0.04704197123646736, 0.04562962427735329, -0.014739093370735645, 0.014078187756240368, 0.012430451810359955, 0.022869134321808815, 0.05109793692827225, -0.01720164529979229, 0.06475061178207397, -0.04874403029680252, -0.0292971171438694, -0.004259670618921518, 0.013652673922479153, -0.039219748228788376, -0.0002815071784425527, -0.018469134345650673, 0.024227159097790718, 0.03302715718746185, 0.013761315494775772, -0.0012369340984150767, -0.014748146757483482, -0.012466665357351303, -0.007736213505268097, -0.03816954419016838, 0.019519340246915817, -0.005821398459374905, 0.003539917292073369, -0.022959668189287186, -0.0012052467791363597, -0.03005761094391346, 0.006513991393148899, 0.012756377458572388, -0.005495472811162472, 0.018523454666137695, -0.0585942342877388, 0.013643620535731316, 0.04048724099993706, 0.037879832088947296, -0.01370699517428875, -0.004268724005669355, 0.014467488043010235, -0.0007836933364160359, 0.02333991602063179, 0.017808228731155396, 0.0007140946108847857, -0.006251439917832613, 0.012113579548895359, 0.05468312278389931, -0.024987652897834778, -0.016368722543120384, -0.010511110536754131, 0.00884526688605547, 0.0047078183852136135, 0.01399670634418726, 0.023955553770065308, -0.047947321087121964, 0.011099587194621563, -0.00309176929295063, 0.02373826876282692, 0.00016013372805900872, 0.04494155943393707, 0.026001643389463425, -0.01571687124669552, 0.02324938029050827, -0.052292998880147934, 0.0016975307371467352, 0.021040327847003937, -0.009469958022236824, 0.014684772118926048, -0.014232097193598747, 0.02996707521378994, 0.040921807289123535, -0.02683456614613533, -0.012122632935643196, -0.0019283948931843042, 0.0212395042181015, -0.006151851266622543, -0.06399011611938477, -0.02965925633907318, -0.015979422256350517, 0.02185514196753502, -0.025911109521985054, -0.061129212379455566, -0.011470780707895756, 0.009415636770427227, -0.07036378234624863, 0.013734155334532261, -0.029007405042648315, -0.005165020003914833, 0.036847732961177826, -0.011860080994665623, -0.003578394651412964, -0.002826954470947385, -0.0359242781996727, -0.006047735922038555, -0.018613990396261215, 0.040342383086681366, 0.0350189283490181, 0.03293662145733833, -0.02544032782316208, 0.007455554790794849, 0.013362961821258068, 0.016993414610624313, -0.002639094367623329, 0.032502055168151855, 0.010339093394577503, 0.01711110956966877, 0.019700409844517708, 0.03853168338537216, -0.02674403041601181, 0.05218435823917389, -0.024571191519498825, -0.023937446996569633, 0.015164608135819435, 0.05989793688058853, -0.003908847458660603, 0.020533330738544464, -0.022380245849490166, 0.004395472817122936, 0.023267487064003944, 0.022452672943472862, -0.010837036184966564, -0.017618104815483093, -0.0113530857488513, -0.01957366056740284, -0.024716047570109367, -0.036576129496097565, -0.005567900836467743, -0.013607406057417393, 0.018758846446871758, 0.025856787338852882, 0.017210697755217552, 0.011298764497041702, -0.01733744703233242, 0.007663785479962826, 0.031651027500629425, 0.012575307860970497, -0.004843621049076319, -0.0040559666231274605, 0.00310308625921607, 0.00014966561866458505, 0.03224855661392212, 0.011325924657285213, -0.01962798275053501, 0.031198350712656975, -0.001399897038936615, -0.014893002808094025, -0.00844238605350256, -0.044724274426698685, 0.001519855810329318, -0.02531357854604721, 0.04483291879296303, 0.017844442278146744, -0.017953084781765938, 0.036883946508169174, 0.028391767293214798, 0.020660080015659332, -0.01594320870935917, 0.009958846494555473, -0.02118518389761448, -0.03233909234404564, 0.023810697719454765, 0.017237858846783638, -0.02620082162320614, 0.013679834082722664, 0.049432095140218735, 0.012638682499527931, -0.005495472811162472, -0.011244443245232105, -0.0020970162004232407, -0.004648970905691385, -0.01589794084429741, 0.0018423866713419557, 0.02154732309281826, -0.007980657741427422, 0.0111086405813694, 0.018577776849269867, 0.016676541417837143, 0.00416687224060297, 0.005748970899730921, 0.02933333069086075, -0.0203341543674469, 0.02880822867155075, 0.019646089524030685, -0.003752674674615264, -0.0311802439391613, -0.05653003603219986, 0.02038847655057907, 0.017437035217881203, 0.033534154295921326, -0.018976129591464996, 0.031234566122293472, -0.018396705389022827, -0.006604526191949844, -0.024842796847224236, 0.0472954697906971, 0.00024076644331216812, 0.01917530782520771, -0.05504526197910309, -0.0062333326786756516, -0.0025440326426178217, -0.015101233497262001, 0.017265019938349724, 0.0017258229199796915, 0.019718516618013382, 0.039799172431230545, -0.035598352551460266, -0.00846954621374607, 0.020678186789155006, 0.01572592370212078, -0.024788474664092064, 0.05729053169488907, -0.0043207816779613495, -0.011099587194621563, -0.008990122936666012, -0.0022373455576598644, -0.02516872249543667, 0.01613333262503147, -0.018577776849269867, 0.013335801661014557, 0.019139092415571213, -0.03759011998772621, -0.008329217322170734, -0.006450616754591465, 0.019917692989110947, 0.06634403020143509, -0.013824690133333206, 0.0016771603841334581, -0.018976129591464996, 0.03309958428144455, 0.018523454666137695, 0.03708312287926674, 0.02790287882089615, 0.041682299226522446, -0.0030329215805977583, 0.011624690145254135, 0.006079423241317272, -0.01115390844643116, -0.003988065291196108, -0.01377036888152361, -0.015888888388872147, 0.02194567769765854, -0.031741559505462646, 0.0030148145742714405, 0.01877695322036743, 0.004363785497844219, 0.07021892070770264, -0.01599752902984619, 0.025186829268932343, -0.011280657723546028, 0.007641151547431946, 0.05327077582478523, 0.01863209716975689, 0.02750452421605587, -0.03373333066701889, 0.031288884580135345, 0.03907489404082298, -0.05707324668765068, 0.01643209718167782, 0.0396905317902565, 0.02194567769765854, -0.03643127158284187, -0.008655142970383167, -0.07394896447658539, 0.05424855649471283, 0.023013990372419357, -0.005907407030463219, 0.05062715709209442, -0.00808477308601141, 0.020044442266225815, 0.042804934084415436, -0.029061725363135338, 0.03574320673942566, -0.032357197254896164, -0.005423044785857201, -0.022416459396481514, -0.018613990396261215, -0.06167242303490639, 0.00003777005986194126, 0.007618518080562353, -0.03194073960185051, -0.05598682537674904, 0.004295884631574154, -0.01066501997411251, 0.004716872237622738, 0.0019453702261671424, -0.033045265823602676, 0.013163784518837929, 0.0013716048561036587, 0.05124279484152794, -0.034964606165885925, -0.050011519342660904, 0.04389135539531708, 0.0226699560880661, 0.005463785491883755, -0.034023042768239975, 0.04461563378572464, -0.0040559666231274605, 0.06362798064947128, -0.0032366253435611725, -0.003730040742084384, 0.011018105782568455, 0.033353082835674286, 0.013679834082722664, -0.003121193265542388, 0.006839917041361332, 0.054139912128448486, -0.024534977972507477, -0.012466665357351303, -0.00009633487206883729, -0.022832920774817467, -0.012874073348939419, 0.0021524690091609955, 0.06413497775793076, 0.03498271480202675, 0.008365431800484657, 0.03134320676326752, 0.04360164329409599, 0.00557695422321558, 0.007690945640206337, -0.048273246735334396, 0.016459258273243904, -0.023321809247136116, 0.013018929399549961, -0.016604114323854446, 0.02525925636291504, -0.00636008195579052, -0.015445265918970108, -0.02822880446910858, 0.01411440223455429, 0.0027228393591940403, 0.03481975197792053, -0.0023041150998324156, 0.003082715906202793, -0.051858432590961456, -0.021257610991597176, 0.02261563576757908, 0.015608228743076324, 0.02898929826915264, -0.016830451786518097, 0.004680658224970102, 0.02105843462049961, -0.019790945574641228, -0.0026345676742494106, 0.002516872249543667, -0.012638682499527931, 0.045448556542396545, -0.0236115213483572, -0.030981067568063736, 0.034693002700805664, -0.020189298316836357, -0.02951440028846264, -0.012240327894687653, 0.06652509421110153, 0.014657611958682537, 0.0010219134856015444, -0.1001678928732872, -0.010511110536754131, -0.02096789889037609, 0.04117530584335327, 0.011986830271780491, 0.02181892842054367, -0.0415736585855484, 0.03436707705259323, 0.015798352658748627, -0.0032049380242824554, -0.008148147724568844, 0.032320983707904816, 0.021112754940986633, 0.003551234258338809, -0.04403620958328247, 0.0099407397210598, -0.02956872247159481, 0.004257407039403915, 0.06141892448067665, -0.020098764449357986, 0.030093824490904808, -0.0158164594322443, -0.00292880623601377, 0.004685184918344021, -0.01411440223455429, 0.016468310728669167, 0.01043868251144886, 0.006038682535290718, -0.030039504170417786, 0.0698929950594902, 0.009515225887298584, -0.04294979199767113, 0.010628805495798588, 0.007482715416699648, -0.031107816845178604, -0.027395881712436676, 0.03722798079252243, -0.04371028393507004, 0.004721398930996656, 0.0027454730588942766, -0.037879832088947296, 0.053198348730802536, 0.003972222097218037, -0.014820574782788754, 0.005187653936445713, 0.03400493413209915, -0.019700409844517708, -0.029043618589639664, -0.009596707299351692, 0.027178598567843437, 0.006599999498575926, 0.009723455645143986, -0.03036542981863022, 0.043203286826610565, -0.026689710095524788, -0.028102055191993713, -0.010275719687342644, -0.015345677733421326, -0.0027454730588942766, -0.046969544142484665, 0.0012708846479654312, -0.020008228719234467 ]
Bayesian optimization (BO) is a popular method for efficiently inferring optima of an expensive black-box function via a sequence of queries. Existing information-theoretic BO procedures aim to make queries that most reduce the uncertainty about optima, where the uncertainty is captured by Shannon entropy. However, an optimal measure of uncertainty would, ideally, factor in how we intend to use the inferred quantity in some downstream procedure. In this paper, we instead consider a generalization of Shannon entropy from work in statistical decision theory (DeGroot 1962, Rao 1984), which contains a broad class of uncertainty measures parameterized by a problem-specific loss function corresponding to a downstream task. We first show that special cases of this entropy lead to popular acquisition functions used in BO procedures such as knowledge gradient, expected improvement, and entropy search. We then show how alternative choices for the loss yield a flexible family of acquisition functions that can be customized for use in novel optimization settings. Additionally, we develop gradient-based methods to efficiently optimize our proposed family of acquisition functions, and demonstrate strong empirical performance on a diverse set of sequential decision making tasks, including variants of top-$k$ optimization, multi-level set estimation, and sequence search.
[ -0.009914758615195751, -0.0011670497478917241, -0.030423620715737343, -0.027761323377490044, 0.03495870530605316, 0.009331807494163513, -0.0435514934360981, 0.020490501075983047, -0.06958691775798798, 0.016836728900671005, 0.035142309963703156, -0.020472140982747078, -0.002701312769204378, -0.002139017451554537, 0.00014415990153793246, 0.06158166751265526, 0.05019805580377579, -0.030056405812501907, 0.021335091441869736, -0.03323280066251755, 0.02438296191394329, -0.04270690307021141, -0.00863869208842516, 0.05702822282910347, -0.011135742999613285, 0.034352801740169525, -0.0159278754144907, 0.0011934431968256831, -0.08218233287334442, 0.059855762869119644, 0.037786245346069336, 0.03852067142724991, -0.03819018229842186, 0.016900990158319473, -0.03707018122076988, -0.007119347341358662, 0.022455092519521713, -0.008964594453573227, 0.01032787375152111, 0.02285902574658394, -0.014716072008013725, -0.0034816409461200237, -0.02891804464161396, 0.02862427569925785, 0.02094951830804348, -0.0019198368536308408, -0.020086565986275673, 0.008872791193425655, 0.01833312213420868, -0.042045921087265015, -0.008721315301954746, -0.020563943311572075, 0.0391816571354866, -0.019756074994802475, -0.0034632801543921232, 0.008243937976658344, 0.07395675033330917, 0.019535746425390244, 0.04244985431432724, -0.00358491949737072, 0.013972464948892593, -0.015560662373900414, -0.044983625411987305, -0.029560668393969536, 0.03929182142019272, -0.05038166046142578, 0.05442100763320923, 0.018149515613913536, 0.01725902408361435, -0.0014229514636099339, -0.04244985431432724, 0.015285252593457699, -0.008836069144308567, 0.05948854982852936, -0.03334296494722366, 0.03925509750843048, 0.03315936028957367, -0.031708866357803345, 0.005402625538408756, 0.01473443303257227, 0.046525921672582626, 0.040209852159023285, -0.011071479879319668, -0.020784271880984306, 0.030919358134269714, -0.020086565986275673, 0.03826362267136574, -0.0509692020714283, 0.013182956725358963, -0.005067543126642704, -0.024089191108942032, 0.0007407380035147071, 0.007064265199005604, 0.041788872331380844, 0.009230824187397957, 0.05765248462557793, -0.012026234529912472, 0.02568656951189041, -0.02493378147482872, -0.026953455060720444, 0.027522634714841843, -0.03363673761487007, -0.037290509790182114, -0.007238691672682762, 0.01593705639243126, -0.05680789425969124, -0.019223615527153015, -0.009988200850784779, -0.018984926864504814, 0.12852464616298676, -0.00537967449054122, 0.05302559584379196, -0.011603939346969128, 0.029009848833084106, -0.03380198031663895, 0.004718690644949675, -0.042560018599033356, -0.045497726649045944, 0.023721978068351746, -0.03929182142019272, -0.006894429214298725, 0.046048544347286224, 0.0275777168571949, -0.05684461444616318, -0.06988068670034409, 0.024327879771590233, -0.05177707225084305, 0.013173776678740978, 0.047590840607881546, -0.017589515075087547, -0.029927881434559822, 0.024327879771590233, -0.010291151702404022, -0.006297707557678223, -0.02285902574658394, 0.033526573330163956, 0.04002624750137329, -0.0052236090414226055, -0.02280394360423088, -0.00982295535504818, -0.0061049205251038074, -0.05038166046142578, -0.018360663205385208, 0.027687881141901016, 0.01377049833536148, -0.006674101110547781, 0.01275148056447506, 0.03694165498018265, -0.06620855629444122, 0.02096787840127945, 0.007986889220774174, 0.11280792206525803, -0.020068205893039703, 0.0035275425761938095, 0.03826362267136574, -0.006086559966206551, -0.014036727137863636, 0.01537705585360527, 0.023556731641292572, 0.0019611483439803123, 0.034334439784288406, 0.012935088016092777, -0.04898625239729881, 0.044469527900218964, 0.07175347208976746, 0.026659684255719185, -0.005944265052676201, -0.030974440276622772, -0.11963808536529541, 0.0304787028580904, -0.01525771152228117, -0.029836079105734825, -0.015450499020516872, 0.09488791227340698, -0.03180066868662834, 0.03582165390253067, 0.07564593851566315, 0.014936399646103382, -0.010052463039755821, -0.02091279625892639, -0.014082629233598709, 0.04399215057492256, -0.0008417216595262289, 0.012430169619619846, 0.03429771959781647, -0.010107545182108879, 0.0701744556427002, -0.008055740967392921, 0.03578493371605873, 0.020086565986275673, 0.01179672684520483, 0.009584266692399979, 0.009304266422986984, 0.014642629772424698, 0.0493534654378891, -0.007261642720550299, -0.08431217074394226, -0.020784271880984306, -0.04961051419377327, -0.0017591811483725905, 0.0159278754144907, -0.10876857489347458, -0.0008009839802980423, 0.049977727234363556, 0.013779678381979465, 0.03925509750843048, 0.020508861169219017, -0.02867935597896576, -0.012255743145942688, -0.018755417317152023, 0.009767873212695122, -0.011741644702851772, -0.06874232739210129, -0.0057973796501755714, -0.05008789151906967, -0.02280394360423088, 0.03398558869957924, 0.025943618267774582, -0.0699908509850502, -0.022216403856873512, -0.02495214156806469, -0.0014436071505770087, 0.0676039606332779, -0.00873508583754301, -0.01806689240038395, 0.014257055707275867, 0.0008824593969620764, 0.007036724593490362, 0.04924330115318298, -0.025613125413656235, -0.028018372133374214, 0.03844723105430603, 0.030680669471621513, -0.030148210003972054, -0.006834757048636675, 0.01220066100358963, -0.014348858967423439, 0.013513448648154736, 0.02335476502776146, -0.016139023005962372, -0.0361337848007679, 0.003938362468034029, -0.0010540168732404709, -0.0024373780470341444, 0.04267018288373947, 0.013109513558447361, -0.027412470430135727, 0.04061378911137581, -0.03692329674959183, 0.017057057470083237, -0.05618363246321678, -0.019700992852449417, 0.022234763950109482, 0.021408533677458763, -0.03582165390253067, -0.027981651946902275, 0.04795805364847183, -0.021022960543632507, 0.030184932053089142, -0.08592790365219116, 0.039695754647254944, 0.04803149774670601, 0.04909641668200493, 0.04377182200551033, 0.018507549539208412, -0.02787148766219616, 0.08306363970041275, 0.01138361170887947, -0.04002624750137329, 0.05431084334850311, 0.04766428470611572, -0.03642755746841431, 0.008487217128276825, -0.01061246357858181, -0.007798691745847464, -0.035105589777231216, 0.006201314274221659, -0.026843290776014328, -0.01773640140891075, 0.03158034011721611, 0.003169509582221508, 0.005246559623628855, 0.01831476204097271, -0.008918692357838154, 0.0005846723797731102, -0.045497726649045944, 0.02625574916601181, -0.039401985704898834, -0.02280394360423088, -0.02598033845424652, -0.023942304775118828, -0.0011831152951344848, 0.045975103974342346, 0.034334439784288406, 0.05038166046142578, 0.033251162618398666, -0.054751500487327576, 0.00003311732871225104, 0.049500349909067154, -0.028697717934846878, -0.02787148766219616, 0.019847877323627472, -0.00729377381503582, 0.000012327105650911108, -0.016910171136260033, -0.010180988349020481, -0.004539674147963524, 0.031947556883096695, -0.00543934665620327, 0.004998690914362669, 0.0033416408114135265, 0.03954887017607689, -0.03429771959781647, -0.03666624426841736, 0.021830828860402107, 0.04637903720140457, 0.06022297590970993, 0.020086565986275673, -0.018746238201856613, -0.03903477266430855, -0.00728918332606554, 0.028257060796022415, -0.09569577872753143, 0.0005777871119789779, -0.03075411170721054, 0.005870822351425886, -0.03187411278486252, 0.06128789484500885, -0.0028940995689481497, 0.0018544270424172282, -0.057175107300281525, -0.027724603191018105, -0.05357641726732254, -0.02974427491426468, -0.029505586251616478, -0.01990295946598053, -0.0016467220848426223, 0.05596330389380455, -0.015064924955368042, -0.036758050322532654, -0.013706235215067863, -0.012843284755945206, 0.015597383491694927, -0.020765909925103188, 0.0016536072362214327, -0.033269524574279785, -0.06308723986148834, 0.0036881982814520597, -0.015101646073162556, 0.0050537725910544395, 0.0009461479494348168, 0.007564593572169542, 0.007128527853637934, -0.033251162618398666, 0.023024272173643112, 0.02441968210041523, -0.014504924416542053, 0.012108857743442059, -0.03136001527309418, 0.07792265713214874, 0.04373510181903839, -0.023501649498939514, -0.04531411826610565, 0.009602626785635948, -0.06202232092618942, 0.04858231544494629, 0.011016398668289185, 0.01128262747079134, 0.013715416193008423, -0.03341640904545784, -0.05361313745379448, 0.0361337848007679, 0.05699149891734123, 0.025558043271303177, 0.003304919460788369, 0.010419677011668682, -0.014165252447128296, -0.02491542138159275, -0.06833839416503906, 0.06988068670034409, 0.011778365820646286, -0.004211477469652891, -0.027706241235136986, -0.016010498628020287, 0.018782958388328552, -0.02436460182070732, -0.020068205893039703, -0.00806492194533348, 0.022161321714520454, 0.05254821851849556, -0.03819018229842186, -0.002685246989130974, -0.009703611023724079, -0.027724603191018105, 0.01377049833536148, 0.000714918365702033, 0.014771154150366783, -0.03455476835370064, -0.05207084119319916, -0.010695086792111397, 0.00617377320304513, -0.013164595700800419, 0.03637247532606125, 0.02919345535337925, -0.05489838495850563, 0.0051180352456867695, 0.006834757048636675, 0.005476067773997784, -0.024584928527474403, 0.02656788006424904, 0.006568527314811945, -0.04083411768078804, -0.05100592225790024, 0.03635411337018013, -0.004714100621640682, 0.0195908285677433, -0.0009834431111812592, 0.006361970212310553, 0.025319354608654976, 0.013862301595509052, -0.059819042682647705, -0.0038947558496147394, 0.049757398664951324, 0.015386235900223255, 0.012191480956971645, -0.024768535047769547, -0.0010970496805384755, 0.028991488739848137, -0.01299935020506382, -0.012136398814618587, 0.06272003054618835, 0.052621662616729736, -0.009685249999165535, -0.04428591951727867, 0.02414427325129509, -0.03022165223956108, -0.04219280555844307, 0.008689183741807938, -0.01167738251388073, -0.013339022174477577, 0.03740067407488823, -0.008271479047834873, -0.011392791755497456, 0.027944929897785187, 0.03497706353664398, -0.023703616112470627, -0.0019967223051935434, -0.010428857058286667, -0.04182559251785278, 0.02177574671804905, -0.08049315214157104, -0.011622300371527672, 0.006609838921576738, 0.0022411486133933067, 0.03866755962371826, -0.03136001527309418, 0.08394495397806168, -0.026200667023658752, 0.06683281809091568, -0.03815345838665962, 0.0271003395318985, 0.024217715486884117, 0.04913313686847687, -0.05640396103262901, -0.025099027901887894, 0.026145584881305695, 0.0023685256019234657, -0.036960016936063766, -0.011236726306378841, -0.024474764242768288, 0.017589515075087547, -0.03150689974427223, 0.02331804297864437, -0.00035659852437675, 0.02333640307188034, 0.009721971116960049, -0.023226240649819374, -0.02921181544661522, 0.010309512726962566, 0.0007854921277612448, -0.01128262747079134, -0.04593838006258011, 0.030148210003972054, -0.06767740845680237, 0.024841977283358574, 0.012044595554471016, 0.02654951997101307, 0.039108213037252426, -0.010419677011668682, 0.025337716564536095, -0.0906282365322113, -0.07219412922859192, -0.036243949085474014, 0.01697443425655365, 0.0236301738768816, -0.008142954669892788, -0.005485248286277056, -0.052952155470848083, 0.05309903994202614, -0.000017338634279440157, -0.0039773788303136826, -0.04211936146020889, -0.01798427104949951, -0.02576001174747944, 0.00979541428387165, -0.028220340609550476, 0.026145584881305695, 0.04645248129963875, 0.033581655472517014, 0.004094427917152643, 0.029009848833084106, -0.002806886564940214, 0.0008497544913552701, -0.01102557871490717, 0.022142959758639336, 0.017727220430970192, 0.006986232474446297, -0.018948204815387726, 0.0931987315416336, 0.03130493313074112, 0.02649443782866001, 0.027706241235136986, 0.0159278754144907, 0.03600526228547096, -0.048215102404356, 0.04615870863199234, 0.032535094767808914, 0.006348199676722288, 0.039401985704898834, 0.016845909878611565, -0.021041320636868477, 0.05309903994202614, -0.06477642059326172, -0.042045921087265015, -0.006389510817825794, 0.004211477469652891, 0.03130493313074112, 0.05541248247027397, -0.012779021635651588, -0.024456404149532318, -0.0360419824719429, 0.055889859795570374, 0.03626231104135513, -0.003408198244869709, 0.015973778441548347, -0.009207872673869133, 0.04105444252490997, -0.03319608047604561, 0.013715416193008423, 0.05005117133259773, -0.0027104930486530066, 0.022987551987171173, -0.023556731641292572, -0.0045236083678901196, -0.03852067142724991, -0.011567218229174614, -0.032755423337221146, -0.00875803641974926, -0.031433455646038055, -0.044653136283159256, 0.006150822155177593, 0.0021516403649002314, -0.028789520263671875, -0.014835416339337826, 0.0005247133667580783, -0.05948854982852936, 0.00967606995254755, 0.01826886087656021, -0.0278164055198431, 0.018948204815387726, -0.00952918455004692, -0.0002523156872484833, -0.03973247483372688, -0.006577707827091217, -0.0034288540482521057, 0.012310825288295746, -0.012246563099324703, 0.002616394544020295, -0.0161665640771389, -0.016616400331258774, -0.0008658200385980308, -0.030643947422504425, -0.004255083855241537, 0.012127218768000603, 0.02280394360423088, -0.05383346602320671, -0.04715018346905708, 0.004149510059505701, 0.029560668393969536, 0.007660986855626106, -0.041495099663734436, 0.04142165929079056, 0.03293903172016144, -0.016533777117729187, -0.006568527314811945, -0.005104264710098505, 0.018590172752738, 0.005829510744661093, -0.050014447420835495, -0.02598033845424652, 0.040760673582553864, -0.014780334196984768, 0.01326557993888855, 0.009428201243281364, -0.023483289405703545, 0.015817711129784584, 0.046856414526700974, -0.0033393457997590303, -0.028293782845139503, 0.0079409871250391, 0.001797050004824996, 0.018590172752738, 0.029854439198970795, -0.040944281965494156, 0.013981645926833153, 0.002806886564940214, -0.07380986958742142, 0.0025750831700861454, 0.016855088993906975, 0.025080665946006775, 0.056146908551454544, -0.004367542918771505, -0.011952792294323444, 0.025007223710417747, 0.021830828860402107, 0.024346239864826202, -0.005315412301570177, -0.04777444899082184, 0.005590822082012892, 0.0013793448451906443, -0.027522634714841843, 0.026072142645716667, -0.018204597756266594, -0.02067410759627819, -0.019719352945685387, -0.0028688537422567606, 0.028514111414551735, 0.028000012040138245, 0.002402951940894127, -0.02146361581981182, -0.06778757274150848, 0.000633442890830338, -0.04810493811964989, 0.04560788720846176, -0.01075934898108244, 0.005333772860467434, -0.018121974542737007, 0.010520660318434238, 0.03470165282487869, 0.01473443303257227, -0.04836198687553406, 0.016607221215963364, 0.01218230091035366, 0.045240674167871475, 0.00682098651304841, -0.03552788496017456, -0.013513448648154736, -0.009878037497401237, -0.017920007929205894, 0.01805771328508854, 0.07175347208976746, -0.03448132798075676, -0.007009183522313833, 0.021628862246870995, 0.012173119932413101, 0.013926563784480095, 0.008748856373131275, 0.028183618560433388, 0.033600013703107834, 0.042302969843149185, -0.008721315301954746, 0.03719870373606682, -0.001083279144950211, 0.05203412100672722, 0.03371017798781395, -0.010860332287847996, -0.0562937967479229, 0.06551084667444229, -0.014862957410514355, -0.034921981394290924, 0.008551479317247868, 0.009712791070342064, 0.010483939200639725, -0.03075411170721054, -0.03481181710958481, -0.012549513950943947, 0.037015099078416824, 0.030001325532794, -0.02146361581981182, 0.021426893770694733, -0.05508199334144592, -0.017148859798908234, 0.03163542225956917, -0.02656788006424904, 0.04883936420083046, 0.004066886845976114, -0.029083291068673134, 0.014064268209040165, 0.035931818187236786, -0.02893640659749508, -0.004023280460387468, 0.001344918622635305, 0.0016272137872874737, -0.015799351036548615, 0.02787148766219616, -0.00676131434738636, 0.006986232474446297, 0.017993450164794922, -0.025007223710417747, -0.012430169619619846, -0.0006018854910507798, 0.021867550909519196, -0.03475673496723175, 0.027687881141901016, -0.008978364989161491, 0.013513448648154736, 0.03079083375632763, -0.008702954277396202, 0.00045098381815478206, -0.007743610069155693, 0.02913837321102619, 0.015597383491694927, 0.03527083620429039, -0.034664932638406754, 0.030368538573384285, 0.060076091438531876, 0.03826362267136574, 0.02788984775543213, -0.005503608845174313, -0.0011601644800975919, 0.00979541428387165, 0.0034472146071493626, -0.035417720675468445, -0.004819674417376518, 0.023005912080407143, -0.002820656867697835, -0.0013586891582235694, 0.02654951997101307, -0.020600665360689163, -0.017607877030968666, 0.03668460622429848, -0.023979026824235916, 0.02251017466187477, 0.018103614449501038, -0.01695607230067253, 0.03211279958486557, 0.03207607939839363, 0.027430832386016846, 0.03288394957780838, 0.03427935764193535, 0.08078692108392715, -0.030845915898680687, 0.019958041608333588, -0.009157381020486355, -0.022969190031290054, -0.009777053259313107, 0.008533118292689323, -0.012118037790060043, 0.03710690140724182, -0.0339488685131073, 0.014376400038599968, 0.035950180143117905, 0.03483017906546593, 0.0009312299080193043, 0.00797311868518591, -0.004362952895462513, -0.01191607117652893, 0.035913459956645966, 0.025099027901887894, -0.02227148599922657, -0.006348199676722288, 0.021794108673930168, -0.00996065977960825, -0.09878037124872208, 0.0033600013703107834, 0.02598033845424652, 0.013228857889771461, 0.026843290776014328, -0.0032085259445011616, 0.03819018229842186, -0.027779683470726013, 0.04105444252490997, -0.01275148056447506, 0.04560788720846176, -0.027981651946902275, -0.020068205893039703, 0.0042596738785505295, 0.009226233698427677, 0.017378367483615875, 0.01990295946598053, -0.04186231270432472, -0.024089191108942032, -0.005935084540396929, 0.009331807494163513, 0.013834760524332523, 0.0047737727873027325, 0.018691156059503555, 0.0010620496468618512, -0.03877772018313408, -0.0013839349849149585, 0.044689856469631195, 0.01721312291920185, -0.021812468767166138, 0.030552145093679428, -0.03288394957780838, -0.030937718227505684, -0.007472790312021971, -0.029854439198970795, 0.01907672919332981, 0.023189518600702286, 0.015000662766397, 0.017626237124204636, -0.03225968778133392, -0.0015365580329671502, 0.021794108673930168, -0.015542302280664444, 0.0005052051274105906, 0.023777060210704803, -0.012714759446680546, 0.00835410226136446, -0.001692623714916408, -0.002701312769204378, 0.00458557577803731, -0.016350170597434044, -0.016139023005962372, 0.03444460406899452, -0.027118699625134468, -0.017837384715676308, -0.009249184280633926, 0.005131805315613747, 0.04744395613670349, 0.015101646073162556, -0.012136398814618587, -0.015175088308751583, -0.03932854160666466, 0.05970887839794159, -0.03628067299723625, -0.005632133688777685, 0.0007986888522282243, 0.06014953553676605, 0.0029973783530294895, -0.0058662318624556065, -0.001582459663040936, 0.010502299293875694, 0.03165378421545029, -0.008358691819012165, 0.008055740967392921, 0.050565268844366074, -0.014504924416542053, -0.02014164812862873, 0.006366560235619545, 0.02893640659749508, 0.022914107888936996, -0.02654951997101307, -0.0013059022603556514, -0.018149515613913536, -0.017718041315674782, 0.033783622086048126, -0.04825182631611824, 0.02197771519422531, -0.026439355686306953, 0.051593463867902756, -0.02072918973863125, -0.014890498481690884, 0.008546888828277588, 0.021812468767166138, 0.05486166477203369, -0.05464133620262146, -0.017093777656555176, -0.08181511610746384, 0.0030318046920001507, 0.034352801740169525, -0.02787148766219616, 0.03973247483372688, 0.009712791070342064, 0.022436730563640594, 0.004193116445094347, 0.012375087477266788, 0.0488760881125927, -0.06705314666032791, 0.00045012315968051553, -0.01034623384475708, -0.00823016744107008, -0.051850516349077225, 0.06745707988739014, 0.01138361170887947, -0.006407871842384338, -0.029579030349850655, -0.002848197938874364, 0.006017707753926516, 0.02834886498749256, 0.02150033786892891, -0.029266897588968277, -0.04061378911137581, 0.03029509447515011, -0.017598696053028107, 0.00036118869320489466, -0.031084604561328888, 0.031415097415447235, -0.003222296480089426, 0.0188747625797987, -0.001559508848004043, 0.02888132445514202, 0.008266888558864594, 0.0233914852142334, 0.007082626223564148, 0.014238694682717323, -0.001377049833536148, 0.027155421674251556, -0.014165252447128296, -0.003141968511044979, -0.01497312169522047, 0.03664788603782654, -0.044469527900218964, 0.0028918045572936535, -0.0040049199014902115, -0.019700992852449417, -0.05948854982852936, 0.018929844722151756, 0.018250498920679092, 0.029542308300733566, -0.010823611170053482, 0.039144936949014664, 0.07002757489681244, -0.01206295657902956, -0.009758693166077137, 0.00039762313826940954, 0.03371017798781395, 0.028312142938375473, -0.012127218768000603, -0.00784459337592125, 0.023758698254823685, 0.01232000533491373, 0.021022960543632507, 0.0034931162372231483, 0.01830558106303215, 0.0004750821681227535, -0.018177056685090065, -0.009464922361075878, 0.02333640307188034, -0.00035286901402287185, 0.04222952574491501, -0.005852461792528629, 0.020361976698040962, 0.005632133688777685, -0.028018372133374214, 0.03958559036254883, 0.009657708927989006, -0.01750689372420311, -0.0021091813687235117, 0.015055743977427483, 0.01194361224770546, -0.01828722096979618, -0.014936399646103382, -0.010364594869315624, 0.05387018620967865, 0.005145575851202011, 0.023979026824235916, -0.05445772781968117, 0.05783608928322792, 0.029230177402496338, 0.023171158507466316, -0.047370512038469315, -0.01699279434978962, 0.019205253571271896, 0.006729183252900839, -0.05199740082025528, 0.009731152094900608, -0.04792133346199989, 0.005632133688777685, 0.00708721624687314, -0.023244600743055344, 0.007550823036581278, 0.020894436165690422, 0.027522634714841843, 0.0004174182249698788, 0.014403941109776497, -0.007477380335330963, 0.00038758214213885367, 0.002430492779240012, 0.05445772781968117, -0.017598696053028107, -0.009905578568577766, -0.018709516152739525, -0.01885640248656273, -0.0015170498518273234, -0.0016742630396038294, 0.023501649498939514, -0.0344262458384037, 0.0067245932295918465, 0.0005181150045245886, -0.012420988641679287, -0.0055311499163508415, -0.06764068454504013, -0.00195655832067132, 0.032535094767808914, -0.014247874729335308, 0.011392791755497456, -0.0014963940484449267, -0.0051180352456867695, 0.009639348834753036, -0.01206295657902956, 0.0010207381565123796, 0.01350426860153675, 0.025521323084831238, 0.0050537725910544395, 0.07212068885564804, 0.02728394605219364, 0.0225836168974638, 0.01986623741686344, -0.005609182640910149, -0.017910826951265335, -0.007358036004006863, 0.05757904052734375, -0.04593838006258011, 0.03760264068841934, -0.03958559036254883, -0.021022960543632507, 0.004333116579800844, -0.023244600743055344, 0.030423620715737343, -0.029780996963381767, -0.03800657391548157, -0.0019037713063880801 ]
In many complex sequential decision-making tasks, online planning is crucial for high performance. For efficient online planning, Monte Carlo Tree Search (MCTS) employs a principled mechanism for trading off exploration for exploitation. MCTS outperforms comparison methods in many discrete decision-making domains such as Go, Chess, and Shogi. Following, extensions of MCTS to continuous domains have been proposed. However, the inherent high branching factor and the resulting explosion of search tree size are limiting existing methods. To address this problem, we propose Continuous Monte Carlo Graph Search (CMCGS), a novel extension of MCTS to online planning in environments with continuous state and action spaces. CMCGS takes advantage of the insight that, during planning, sharing the same action policy between several states can yield high performance. To implement this idea, at each time step, CMCGS clusters similar states into a limited number of stochastic action bandit nodes, which produce a layered directed graph instead of an MCTS search tree. Experimental evaluation shows that CMCGS outperforms comparable planning methods in several complex continuous DeepMind Control Suite benchmarks and a 2D navigation task with limited sample budgets. Furthermore, CMCGS can be parallelized to scale up and it outperforms the Cross-Entropy Method (CEM) in continuous control with learned dynamics models.
[ 0.0665011778473854, -0.004730477463454008, -0.04842105507850647, -0.03927119821310043, 0.022563552483916283, -0.001144304289482534, -0.052373796701431274, 0.0486406534910202, -0.07964037358760834, 0.010403390042483807, 0.0011608884669840336, -0.0029965790454298258, 0.00225658412091434, 0.0066290730610489845, -0.007411385886371136, 0.040222782641649246, 0.024009231477975845, 0.013660740107297897, -0.015911605209112167, -0.026790788397192955, 0.008610017597675323, -0.014228031039237976, -0.024411825463175774, 0.04322393611073494, 0.016634443774819374, -0.015197916887700558, 0.00914985965937376, -0.000050824608479160815, -0.044468317180871964, 0.07356487214565277, 0.027925370261073112, 0.07005131989717484, -0.026717590168118477, 0.008660341612994671, -0.012434658594429493, -0.037111829966306686, 0.05145880952477455, 0.003856665687635541, 0.009460954926908016, 0.019470900297164917, 0.03090822510421276, 0.0003333979984745383, -0.024302026256918907, -0.013404544442892075, 0.012791503220796585, -0.028108367696404457, -0.03508055955171585, -0.0033259738702327013, 0.012407209724187851, 0.022984446957707405, 0.01616780087351799, -0.012535307556390762, 0.03378128260374069, -0.04670088365674019, -0.029828540980815887, -0.02803516946732998, 0.044431716203689575, 0.030926525592803955, 0.0483112558722496, 0.06855074316263199, 0.016103751957416534, -0.021008078008890152, -0.09581732749938965, -0.007685882039368153, 0.03336038812994957, -0.07649282366037369, -0.0007382792537100613, -0.01722918450832367, 0.04812826216220856, -0.06646458059549332, -0.04915304481983185, 0.047542668879032135, -0.023624936118721962, -0.020166290923953056, 0.059986479580402374, -0.007846004329621792, 0.014346979558467865, -0.0033259738702327013, -0.014658074826002121, -0.009762899950146675, 0.06770896166563034, 0.02591240219771862, -0.022234158590435982, -0.011071329936385155, 0.11192107945680618, -0.05010462924838066, 0.05599714070558548, -0.0615602545440197, 0.01674424298107624, 0.0025459483731538057, -0.03244540095329285, 0.005252019502222538, 0.04424871876835823, 0.002719795797020197, -0.00904921069741249, -0.006107531022280455, 0.010119744576513767, 0.007617258001118898, -0.009936747141182423, 0.021227674558758736, 0.009753749705851078, -0.059657081961631775, -0.0062264795415103436, -0.001027071732096374, 0.0304507315158844, -0.012269961647689342, -0.019416002556681633, -0.0036942558363080025, 0.013258146122097969, 0.11074990034103394, -0.001995813101530075, 0.054057370871305466, -0.007315312512218952, 0.03544655442237854, -0.056912124156951904, -0.01829056814312935, -0.023021046072244644, -0.0453467033803463, 0.05123921111226082, -0.057570915669202805, 0.010522338561713696, 0.06009627506136894, 0.0031132397707551718, -0.04318733513355255, -0.06082826480269432, 0.03253690153360367, -0.033708080649375916, -0.014337829314172268, 0.013935236260294914, 0.013596691191196442, -0.0022977583575993776, 0.0009836099343374372, 0.001221506274305284, 0.010339341126382351, 0.038246411830186844, -0.013688189908862114, 0.03110952116549015, 0.018565064296126366, 0.006738871335983276, -0.003902415046468377, -0.041284166276454926, -0.04604209214448929, -0.033378686755895615, -0.0013438855530694127, 0.03517206013202667, 0.012434658594429493, -0.03303099423646927, 0.03480606526136398, -0.05069022253155708, 0.05090981721878052, -0.03744122385978699, 0.042345549911260605, 0.022618452087044716, 0.028675658628344536, -0.008225723169744015, 0.007704181596636772, -0.06423201411962509, -0.013303895480930805, 0.008971436880528927, -0.042345549911260605, 0.06357322633266449, 0.00248189945705235, 0.009126984514296055, 0.0486406534910202, 0.0486406534910202, 0.03131081908941269, -0.029737042263150215, -0.0048402757383883, -0.041979555040597916, 0.02787047252058983, -0.03389107808470726, 0.014969170093536377, -0.001828828128054738, 0.06770896166563034, 0.03974698856472969, 0.020294388756155968, 0.05570434406399727, -0.0007840285543352365, 0.009058360941708088, 0.03239050135016441, -0.0469936765730381, -0.06038907170295715, 0.04977523535490036, 0.048604052513837814, 0.0651835948228836, 0.023240642622113228, 0.05255679413676262, 0.013642440550029278, 0.028309665620326996, -0.001895164605230093, -0.008399571292102337, 0.0552651509642601, 0.06415881216526031, -0.03799021616578102, 0.04552970081567764, -0.005833035334944725, -0.049921631813049316, 0.02181326411664486, -0.01203206554055214, 0.012919601052999496, -0.05222739651799202, -0.030157936736941338, 0.02399093098938465, 0.02578430436551571, 0.04948243871331215, 0.024100730195641518, 0.04688388109207153, -0.02578430436551571, -0.0094335051253438, -0.04970203712582588, -0.0162958987057209, 0.012910451740026474, -0.04904324561357498, -0.044395118951797485, -0.02733978070318699, -0.023917732760310173, 0.012132713571190834, 0.06463460624217987, -0.025637906044721603, -0.06624498218297958, 0.037313126027584076, 0.012782353907823563, 0.027559377253055573, -0.016323348507285118, -0.017046188935637474, 0.06291443109512329, 0.04084497317671776, -0.0008589430362917483, -0.020111391320824623, -0.036782436072826385, -0.008898238651454449, 0.04523690417408943, 0.0075623588636517525, 0.031329117715358734, 0.03650793805718422, -0.0025894101709127426, 0.05006803199648857, 0.012590206228196621, 0.01952579990029335, -0.009072085842490196, 0.009245933033525944, -0.011098779737949371, -0.05497235432267189, 0.011602021753787994, 0.07217409461736679, 0.006299678236246109, -0.000914414064027369, 0.0012272249441593885, 0.03978358954191208, 0.005119346547871828, -0.01662529446184635, -0.020568883046507835, -0.04589569568634033, -0.04282134026288986, 0.017796477302908897, 0.047249872237443924, 0.04670088365674019, -0.015005769208073616, 0.01952579990029335, -0.05841270089149475, 0.06675737351179123, 0.009570753201842308, -0.02644309401512146, 0.01773242838680744, -0.024741219356656075, 0.029737042263150215, 0.043406933546066284, 0.03919799625873566, -0.050360824912786484, 0.011794168502092361, -0.07554123550653458, -0.09669571369886398, -0.02280144952237606, 0.009195609018206596, 0.011775868944823742, -0.03617854416370392, 0.045127104967832565, -0.01731153391301632, 0.015014919452369213, 0.020971477031707764, 0.009488403797149658, -0.01669849269092083, 0.006688547320663929, -0.015774358063936234, -0.02558300644159317, -0.013377094641327858, 0.004032800439745188, -0.028712259605526924, -0.06986832618713379, -0.0027152206748723984, -0.01681744121015072, -0.0536181777715683, -0.00682579493150115, 0.011098779737949371, 0.054167166352272034, 0.02422882802784443, -0.04739627242088318, 0.007644707337021828, 0.01451167743653059, -0.0022897522430866957, -0.0233321413397789, 0.016927240416407585, 0.01711023785173893, -0.01299280021339655, -0.024466723203659058, 0.008815889246761799, 0.0029897165950387716, 0.033049292862415314, -0.013047699816524982, -0.05914469063282013, -0.002066724468022585, -0.05314238369464874, -0.03835621103644371, -0.009058360941708088, -0.0072741382755339146, 0.03475116565823555, 0.08300752192735672, 0.01818077079951763, -0.06145045533776283, -0.04571269825100899, 0.013148347847163677, -0.01817162148654461, -0.04051557928323746, -0.017741577699780464, -0.038868602365255356, 0.016671044752001762, -0.035995546728372574, 0.016305049881339073, -0.020202890038490295, 0.031164420768618584, 0.00432788347825408, -0.03758762404322624, -0.05072681978344917, -0.05471615865826607, 0.005101046524941921, -0.0007520040962845087, -0.010805984027683735, 0.04589569568634033, -0.0453467033803463, -0.013111748732626438, 0.007333612535148859, -0.021062975749373436, -0.05281298980116844, 0.011556272394955158, 0.0201845895498991, -0.016716793179512024, 0.0018700024811550975, 0.013779688626527786, 0.013541791588068008, -0.015417513437569141, 0.0008720959885977209, -0.012288261204957962, -0.007059116382151842, -0.017787326127290726, 0.07517524808645248, -0.013743088580667973, 0.017009587958455086, 0.008738115429878235, -0.02710188366472721, 0.01592075452208519, 0.0152253657579422, -0.051715005189180374, -0.029096553102135658, 0.03138401731848717, -0.010842583142220974, 0.025839202105998993, -0.022289058193564415, -0.004163186065852642, -0.038246411830186844, -0.006505549885332584, -0.012288261204957962, -0.006542149465531111, 0.01117197796702385, -0.014987469650804996, -0.03094482421875, 0.007763655856251717, -0.021996261551976204, 0.015627959743142128, -0.07261328399181366, 0.0372399277985096, 0.01295620109885931, 0.04637148603796959, -0.009561602957546711, 0.014099933207035065, -0.019452601671218872, 0.09523173421621323, 0.04761586710810661, -0.019781995564699173, 0.032646697014570236, 0.03643473982810974, 0.02115447446703911, -0.05142220854759216, -0.018812110647559166, 0.03478776663541794, 0.005965708289295435, -0.019635599106550217, 0.04735967144370079, -0.03206110745668411, 0.009223057888448238, -0.033708080649375916, 0.03110952116549015, -0.002459024777635932, -0.0277972724288702, 0.06273143738508224, -0.023807933554053307, 0.029773643240332603, -0.005915384273976088, -0.029096553102135658, -0.03659943863749504, 0.004307296127080917, 0.0032664998434484005, -0.07905478775501251, -0.003689680714160204, 0.013614990748465061, 0.015078968368470669, 0.02902335487306118, -0.013431993313133717, 0.007832279428839684, 0.004154036287218332, -0.025235312059521675, -0.04080837219953537, 0.00038515188498422503, 0.06086486577987671, 0.02329554222524166, -0.02832796424627304, 0.025491507723927498, 0.015810957178473473, -0.017540279775857925, -0.06946573406457901, -0.028785457834601402, 0.008710666559636593, 0.001256961957551539, 0.007361061871051788, -0.0463348887860775, 0.00012230788706801832, -0.00017513403145130724, -0.006345427595078945, 0.024448424577713013, 0.005682062823325396, -0.05325218290090561, -0.006711422000080347, -0.009726300835609436, -0.03647134080529213, -0.0193611029535532, 0.02009309083223343, -0.020825080573558807, -0.03535505756735802, 0.0026557466480880976, -0.011556272394955158, 0.0061395554803311825, -0.055484745651483536, 0.04194295406341553, 0.02087997831404209, -0.010449139401316643, 0.014465928077697754, 0.0020758742466568947, 0.011446474120020866, -0.001023640506900847, -0.011940566822886467, 0.0010293591767549515, 0.07202769070863724, -0.000883533270098269, -0.016305049881339073, -0.05914469063282013, 0.031530413776636124, 0.025637906044721603, -0.024796118959784508, -0.0233321413397789, 0.0016366811469197273, -0.02770577371120453, 0.024668021127581596, -0.030304335057735443, 0.025802602991461754, 0.02124597318470478, -0.0018219657940790057, 0.01203206554055214, -0.00919103343039751, -0.06437841057777405, 0.020276088267564774, -0.04384612664580345, 0.03136571869254112, 0.009003461338579655, -0.004108286928385496, -0.02783387154340744, 0.012818953022360802, 0.002630584640428424, 0.02439352497458458, -0.04670088365674019, -0.022417156025767326, 0.0390515998005867, 0.014767873100936413, -0.02852926217019558, -0.020532283931970596, -0.007049966603517532, 0.020459085702896118, 0.03184150904417038, 0.01764092966914177, -0.061377257108688354, 0.031329117715358734, 0.04428531974554062, 0.012297411449253559, -0.027614274993538857, 0.026845688000321388, 0.003573019988834858, -0.03078012727200985, 0.0060709319077432156, 0.03568445146083832, 0.0033991727977991104, 0.005302343517541885, -0.0028501811902970076, -0.008564268238842487, 0.056180138140916824, -0.006889844313263893, 0.00011437324428698048, 0.018473565578460693, 0.008976012468338013, 0.03171341121196747, 0.00828519742935896, 0.04743286967277527, 0.02022118866443634, 0.028785457834601402, -0.006327127572149038, 0.0018299719085916877, 0.008747265674173832, -0.03570275008678436, 0.029828540980815887, 0.004032800439745188, -0.029810242354869843, 0.07217409461736679, -0.04146716371178627, -0.021355772390961647, 0.03290289267897606, 0.007498309947550297, -0.026058798655867577, -0.013011099770665169, -0.04040578007698059, 0.03185981139540672, 0.011409875005483627, 0.00994589738547802, -0.015216216444969177, -0.02443012408912182, 0.028986753895878792, -0.03167681396007538, 0.038868602365255356, -0.012306560762226582, 0.008298922330141068, -0.010751084424555302, -0.010540638118982315, 0.03425707295536995, 0.010915782302618027, 0.004407944623380899, -0.010540638118982315, -0.00040287975571118295, -0.019672198221087456, -0.022234158590435982, -0.04249194636940956, 0.01854676567018032, -0.05881529673933983, 0.0317683108150959, -0.04183315858244896, 0.028419462963938713, -0.0017373295268043876, 0.04607869312167168, -0.0004323308530729264, -0.010696185752749443, -0.024576522409915924, 0.01568285934627056, 0.029462547972798347, 0.01518876664340496, -0.010613837279379368, -0.02587580308318138, -0.01088833250105381, 0.002141067059710622, -0.04849425330758095, 0.035995546728372574, 0.014886821620166302, 0.01915980502963066, 0.007068266160786152, -0.032811395823955536, -0.02320404350757599, 0.043699730187654495, -0.002209691097959876, 0.05083661898970604, 0.024045830592513084, 0.023917732760310173, -0.029169751331210136, -0.024466723203659058, -0.012334010563790798, -0.030359232798218727, -0.0317683108150959, -0.0017258921870961785, 0.0058925095945596695, -0.011693520471453667, -0.013962685130536556, 0.02340533956885338, -0.020294388756155968, -0.01322154700756073, -0.03312249109148979, 0.0536181777715683, -0.0658789873123169, 0.042711544781923294, 0.033671483397483826, -0.016488047316670418, -0.01870231330394745, -0.015481562353670597, -0.006505549885332584, 0.04380952566862106, 0.03861240670084953, -0.0030286035034805536, -0.02660779096186161, -0.0039115650579333305, 0.003785754321143031, 0.030231134966015816, -0.04560289904475212, 0.016680194064974785, 0.024082429707050323, 0.0028112942818552256, 0.00537096755579114, -0.00225658412091434, -0.04289454221725464, 0.03949079290032387, -0.009140709415078163, 0.026296695694327354, -0.017942873761057854, -0.0007399948663078249, 0.0012638242915272713, -0.01625015027821064, -0.0047808014787733555, -0.0073519120924174786, 0.033872779458761215, 0.052703190594911575, -0.00536181777715683, -0.015554760582745075, -0.02832796424627304, -0.016176952049136162, -0.027852172031998634, -0.01992839388549328, 0.036654338240623474, -0.019672198221087456, 0.01060468703508377, -0.053435180336236954, -0.02508891373872757, 0.009154434315860271, 0.052995987236499786, 0.0061487057246267796, 0.027907071635127068, -0.02787047252058983, -0.0004065968678332865, 0.009735450148582458, 0.012251662090420723, -0.0004832269623875618, 0.03897840157151222, 0.008628317154943943, 0.049262844026088715, -0.019287902861833572, -0.02227075770497322, -0.023753035813570023, -0.001221506274305284, -0.004799101036041975, -0.02680908888578415, 0.00982694886624813, -0.025637906044721603, -0.0055585396476089954, 0.0282913651317358, 0.014813622459769249, 0.03524525836110115, 0.03623344376683235, 0.02435692586004734, -0.0400397852063179, 0.09025420993566513, -0.01140072476118803, 0.005384692456573248, -0.0005981720751151443, 0.027559377253055573, -0.0030789277516305447, -0.03220750391483307, -0.04194295406341553, 0.022160960361361504, -0.020038191229104996, -0.04520030692219734, 0.0228380486369133, -0.03024943545460701, -0.04000318422913551, 0.013459443114697933, -0.005526515189558268, -0.0009189890115521848, 0.004227234981954098, -0.004684728104621172, 0.00669312197715044, 0.04146716371178627, -0.04000318422913551, 0.005146795883774757, -0.001287842751480639, -0.004945498891174793, 0.004149461165070534, 0.053398579359054565, -0.06986832618713379, 0.006912718992680311, 0.01952579990029335, -0.013001950457692146, -0.0774444118142128, 0.005064447410404682, 0.016735093668103218, 0.044797711074352264, 0.03967379033565521, 0.025326810777187347, -0.015655409544706345, 0.0004932346055284142, -0.03606874495744705, 0.008998886682093143, -0.024009231477975845, 0.042345549911260605, -0.028748858720064163, 0.027284881100058556, 0.033378686755895615, -0.037477824836969376, 0.01592075452208519, -0.03799021616578102, 0.0188670102506876, 0.05050722509622574, -0.0032482000533491373, 0.004627541173249483, 0.00073541997699067, -0.048238057643175125, -0.028144966810941696, 0.03187811002135277, -0.0004946643020957708, -0.02115447446703911, 0.01727493479847908, -0.006734296679496765, 0.02660779096186161, -0.10613837093114853, -0.032518599182367325, 0.01620440185070038, 0.01748538203537464, 0.01346859335899353, 0.01801607385277748, 0.021337471902370453, -0.016195250675082207, 0.020404186099767685, -0.00826689787209034, 0.00747086014598608, 0.020806780084967613, -0.004348470829427242, 0.018885308876633644, 0.015591360628604889, 0.008916538208723068, -0.009817799553275108, 0.006688547320663929, -0.03745952621102333, 0.029444247484207153, 0.010439989157021046, 0.014584875665605068, -0.04681067913770676, -0.044029124081134796, 0.02181326411664486, 0.04417552053928375, 0.020074792206287384, 0.008166249841451645, -0.01788797602057457, 0.017567729577422142, -0.011181128211319447, 0.036416441202163696, 0.029993239790201187, 0.0006713709444738925, -0.008170824497938156, -0.04450491443276405, -0.002310339594259858, 0.02534511126577854, -0.023917732760310173, 0.022215858101844788, 0.008440745063126087, 0.0314389169216156, -0.02713848277926445, -0.004343895707279444, -0.013258146122097969, 0.010138044133782387, 0.04629828780889511, -0.06020607426762581, -0.016058003529906273, -0.015088118612766266, 0.024265427142381668, 0.0020209751091897488, 0.092669777572155, -0.05387437343597412, 0.022362256422638893, -0.012864702381193638, -0.028144966810941696, -0.005293193738907576, 0.014667225070297718, -0.006555874366313219, 0.00039487361209467053, -0.009708001278340816, 0.03140231594443321, 0.0473230741918087, -0.0013210109900683165, 0.0031384017784148455, -0.020459085702896118, -0.031987909227609634, -0.01418228168040514, -0.011290926486253738, 0.0009916160488501191, -0.007049966603517532, 0.008916538208723068, 0.020568883046507835, -0.0645614042878151, -0.010165493935346603, 0.029663844034075737, 0.03123762086033821, 0.006080081686377525, 0.005457891151309013, -0.0014731273986399174, -0.02475951984524727, 0.019781995564699173, 0.013743088580667973, -0.016753392294049263, -0.006208179518580437, -0.00601603277027607, -0.016872340813279152, -0.03676413372159004, -0.019251303747296333, -0.020843379199504852, 0.0004334745754022151, -0.009364881552755833, -0.03548315539956093, -0.028931856155395508, 0.005526515189558268, -0.034202173352241516, 0.01219676248729229, -0.0017647790955379605, 0.026022199541330338, 0.08395911008119583, -0.05632653459906578, 0.012004615738987923, -0.04413892328739166, 0.06145045533776283, -0.006569599267095327, -0.029297849163413048, 0.02038588747382164, 0.032683297991752625, 0.022197559475898743, -0.004520030692219734, -0.036983732134103775, 0.002238284330815077, 0.015408363193273544, -0.030835026875138283, -0.003296236740425229, -0.016844891011714935, -0.024173928424715996, -0.011473923921585083, 0.0005741536733694375, 0.04677408188581467, 0.012846402823925018, 0.011528822593390942, -0.010687035508453846, 0.005110196303576231, 0.05043402686715126, 0.04318733513355255, -0.050983015447854996, -0.002285177353769541, 0.0053252181969583035, -0.021227674558758736, -0.028803756460547447, 0.02038588747382164, 0.05596053972840309, 0.051678404211997986, 0.012581056915223598, -0.022783149033784866, 0.014639775268733501, -0.03418387472629547, 0.017704978585243225, 0.035922348499298096, -0.05449656397104263, 0.05120261386036873, -0.014731273986399174, 0.02181326411664486, -0.020404186099767685, -0.015326014719903469, -0.017366433516144753, -0.040918171405792236, 0.020330987870693207, -0.016963839530944824, 0.020696982741355896, -0.03564785048365593, 0.04776226729154587, 0.03138401731848717, -0.014173132367432117, -0.0549357570707798, 0.023716434836387634, -0.03376298025250435, -0.01989179477095604, 0.029206350445747375, -0.035300157964229584, -0.04194295406341553, 0.011226877570152283, 0.03345188498497009, -0.017183436080813408, 0.0026214346289634705, 0.002088455483317375, -0.018061822280287743, -0.0282913651317358, -0.04194295406341553, -0.030999723821878433, -0.009762899950146675, -0.019104907289147377, -0.04315073788166046, 0.032976094633340836, -0.013011099770665169, 0.05127581208944321, -0.038173213601112366, 0.0079832524061203, -0.031201019883155823, -0.004362195264548063, -0.0023949756287038326, -0.00880216434597969, -0.012315711006522179, -0.03831961005926132, -0.08849743753671646, -0.004863150417804718, 0.012626806274056435, 0.0019100331701338291, -0.009122409857809544, -0.00011365841055521742, 0.020477386191487312, -0.047213274985551834, 0.004520030692219734, 0.03791701793670654, -0.00021802399714943022, 0.040991369634866714, -0.015051518566906452, -0.03777061775326729, 0.02230735681951046, 0.024814419448375702, -0.0032870869617909193, 0.009817799553275108, -0.02750447764992714, -0.003874965477734804, -0.03605044633150101, 0.008632892742753029, -0.0004732192901428789, -0.031219320371747017, -0.010613837279379368, -0.005288618616759777, 0.06946573406457901, 0.01037594024091959, -0.011867367662489414, 0.018034372478723526, 0.00562716368585825, 0.00982694886624813, -0.0026122848503291607, 0.0078597292304039, -0.02611369825899601, -0.00562716368585825, -0.07861559092998505, -0.06020607426762581, -0.050946418195962906, -0.026168597862124443, -0.0024498747661709785, 0.009072085842490196, 0.08293432742357254, 0.028309665620326996, -0.010293591767549515, -0.0400397852063179, -0.008962287567555904, 0.007996977306902409, 0.018738912418484688, -0.04223575070500374, -0.002096461597830057, 0.006624498404562473, 0.01751282997429371, 0.02378963492810726, -0.04139396548271179, -0.0052703190594911575, 0.03224410489201546, -0.03368978202342987, 0.05489915609359741, -0.007114015519618988, -0.0006462088203988969, -0.01899510808289051, -0.001797947334125638, 0.03433027118444443, -0.014081633649766445, 0.007077416405081749, -0.027742372825741768, 0.018400367349386215, -0.03742292523384094, 0.029078252613544464, 0.011867367662489414, -0.006221904419362545, 0.022252457216382027, -0.018043523654341698, 0.03469626605510712, 0.021849865093827248, -0.04461471363902092, -0.052044399082660675, 0.005929108709096909, 0.006199029739946127, -0.019434301182627678, 0.028547560796141624, -0.017220035195350647, 0.025107214227318764, -0.0655129924416542, -0.017183436080813408, 0.021758366376161575, 0.017220035195350647, -0.01613120175898075, 0.02353343926370144, 0.06708677113056183, -0.016606993973255157, 0.02701038494706154, -0.028474362567067146, 0.002404125640168786, 0.014310380443930626, -0.010504039004445076, 0.009126984514296055, 0.011656920425593853, -0.05497235432267189, 0.01021124329417944, 0.00043919324525631964, -0.04626169055700302, -0.0026397344190627337, -0.03048733063042164, -0.0279619712382555, 0.02071528136730194 ]
News recommendation is one of the most challenging tasks in recommender systems, mainly due to the ephemeral relevance of news to users. As social media, and particularly microblogging applications like Twitter or Weibo, gains popularity as platforms for news dissemination, personalized news recommendation in this context becomes a significant challenge. We revisit news recommendation in the microblogging scenario, by taking into consideration social interactions and observations tracing how the information that is up for recommendation spreads in an underlying network. We propose a deep-learning based approach that is diffusion and influence-aware, called Influence-Graph News Recommender (IGNiteR). It is a content-based deep recommendation model that jointly exploits all the data facets that may impact adoption decisions, namely semantics, diffusion-related features pertaining to local and global influence among users, temporal attractiveness, and timeliness, as well as dynamic user preferences. To represent the news, a multi-level attention-based encoder is used to reveal the different interests of users. This news encoder relies on a CNN for the news content and on an attentive LSTM for the diffusion traces. For the latter, by exploiting previously observed news diffusions (cascades) in the microblogging medium, users are mapped to a latent space that captures potential influence on others or susceptibility of being influenced for news adoptions. Similarly, a time-sensitive user encoder enables us to capture the dynamic preferences of users with an attention-based bidirectional LSTM. We perform extensive experiments on two real-world datasets, showing that IGNiteR outperforms the state-of-the-art deep-learning based news recommendation methods.
[ -0.015962928533554077, -0.0009548056987114251, -0.032628629356622696, -0.013268975540995598, -0.005178749095648527, 0.007868519052863121, -0.016849758103489876, 0.018506288528442383, -0.021652022376656532, 0.013335905969142914, 0.00990571640431881, -0.0353727787733078, 0.006914759054780006, -0.05163689702749252, -0.03624287620186806, 0.027290919795632362, 0.026788940653204918, -0.007236862555146217, 0.0355735719203949, -0.006872927770018578, 0.039589401334524155, -0.031072493642568588, -0.0066135721281170845, 0.005471569951623678, 0.012164621613919735, 0.014105606824159622, -0.0019922286737710238, -0.0022693630307912827, -0.07576534897089005, 0.06893843412399292, 0.017284806817770004, -0.003252404974773526, 0.06083984300494194, 0.0008345399401150644, -0.061576079577207565, -0.022338060662150383, 0.107289619743824, 0.07128100097179413, 0.010482992976903915, -0.03416803106665611, 0.014005211181938648, -0.005078352987766266, -0.02804388850927353, -0.013879716396331787, -0.017987577244639397, -0.02026321552693844, -0.0031080860644578934, -0.021702220663428307, -0.027625571936368942, -0.037347231060266495, 0.0770370289683342, -0.023927660658955574, -0.03671139106154442, 0.006216172128915787, -0.05033174902200699, 0.07556455582380295, 0.016766095533967018, -0.046148594468832016, 0.016305947676301003, 0.020530937239527702, 0.010842744261026382, 0.03771534934639931, -0.015812335535883904, 0.00006555792060680687, 0.027307651937007904, -0.05946776643395424, 0.03707950934767723, -0.04313671961426735, 0.023375483229756355, -0.03130675107240677, -0.036577530205249786, 0.038920097053050995, 0.034971196204423904, -0.04035910218954086, -0.015402385964989662, -0.02163529023528099, 0.004379766061902046, -0.010541556403040886, -0.02263924852013588, 0.020146086812019348, 0.05812915787100792, 0.05625510215759277, -0.0223045963793993, -0.002168967155739665, 0.02138430066406727, -0.012884125113487244, 0.04531196132302284, -0.05695787072181702, 0.010943139903247356, -0.0069063929840922356, -0.016925055533647537, -0.007115550804883242, -0.04665057361125946, -0.07971424609422684, -0.01939311809837818, 0.05003056302666664, 0.033214271068573, 0.017150945961475372, -0.07810791581869125, 0.0012946872739121318, 0.007161565590649843, -0.0009098367299884558, 0.07342278212308884, 0.014967337250709534, 0.003842230187729001, -0.019677571952342987, -0.01454065553843975, 0.029566556215286255, 0.004463429097086191, 0.08513562381267548, 0.026822404935956, -0.020982718095183372, -0.019878365099430084, 0.04209929704666138, -0.045010775327682495, 0.022154001519083977, -0.019694305956363678, -0.01937638595700264, 0.031156156212091446, -0.01542748510837555, 0.008562923409044743, 0.05454837158322334, -0.033532191067934036, 0.03366605192422867, -0.028579331934452057, 0.05709173157811165, -0.021785883232951164, -0.02884705364704132, 0.04367216303944588, 0.016322679817676544, -0.059534698724746704, 0.03875277191400528, -0.016849758103489876, -0.007847603410482407, -0.009261510334908962, 0.010324032977223396, 0.055251143872737885, 0.018623417243361473, -0.009479034692049026, -0.04604819789528847, 0.03704604133963585, -0.028880519792437553, -0.017719855532050133, -0.023024098947644234, 0.008617304265499115, 0.04541235789656639, 0.0009642178192734718, 0.013729122467339039, -0.014080507680773735, -0.010215270332992077, -0.050298284739255905, 0.04109533876180649, -0.0123821459710598, 0.03902049362659454, -0.002208707155659795, -0.0018813750939443707, 0.0027985323686152697, -0.029717151075601578, -0.0002485057048033923, -0.00675998255610466, 0.048926208168268204, -0.0022923701908439398, -0.024178650230169296, 0.0223045963793993, -0.00791035033762455, 0.02322489023208618, 0.03821732476353645, 0.0018458182457834482, -0.052105408161878586, 0.03741415962576866, -0.015469316393136978, -0.0077890390530228615, 0.0032733206171542406, 0.03167486935853958, -0.004785532131791115, 0.015285257250070572, 0.05103452131152153, -0.10862823575735092, -0.08045048266649246, 0.006002830807119608, -0.07476139068603516, 0.0022170734591782093, -0.014222735539078712, -0.0007906167884357274, 0.03574089705944061, 0.06204459071159363, 0.10963219404220581, 0.00675998255610466, 0.030051803216338158, 0.024379441514611244, 0.00046537627349607646, 0.009253144264221191, 0.043638698756694794, -0.03885316476225853, 0.0012936413986608386, 0.017042184248566628, 0.02546706236898899, -0.038685839623212814, -0.0007869565160945058, -0.034184761345386505, -0.028010422363877296, -0.03741415962576866, 0.03298001363873482, -0.014264566823840141, -0.017067281529307365, 0.023927660658955574, 0.049394723027944565, -0.0004577942891046405, -0.054012928158044815, -0.0353727787733078, 0.01971103809773922, -0.028445471078157425, -0.032946549355983734, 0.016732629388570786, -0.01566174067556858, 0.023174691945314407, 0.015795603394508362, -0.018656881526112556, -0.0036163395270705223, 0.009152748622000217, -0.0020696171559393406, 0.0023927660658955574, 0.07201723754405975, 0.027525175362825394, -0.02714032493531704, -0.0314406119287014, -0.02896418236196041, -0.007245228625833988, -0.025969041511416435, -0.0050239721313118935, 0.03269555792212486, -0.022689446806907654, -0.0011796504259109497, 0.010223636403679848, -0.007328891661018133, -0.015502781607210636, -0.016088424250483513, -0.060438260436058044, -0.031223086640238762, 0.01177977118641138, -0.013503232039511204, 0.011495316401124, -0.04738680645823479, 0.03821732476353645, 0.0005276007577776909, -0.015519513748586178, 0.0005589743959717453, 0.05792836472392082, 0.007901984266936779, 0.002739968243986368, -0.06401903927326202, -0.047721460461616516, -0.00529587734490633, 0.03413456305861473, -0.014448625966906548, 0.02998487278819084, 0.06508993357419968, 0.013419569469988346, -0.002604015404358506, -0.054247185587882996, 0.05474916473031044, -0.020129352807998657, 0.0020549760665744543, 0.03985712304711342, -0.008567106910049915, 0.0005197573336772621, 0.08118671923875809, 0.010976605117321014, 0.07208416610956192, 0.02657141536474228, 0.011595712043344975, -0.026621613651514053, -0.019192326813936234, -0.06867071241140366, -0.06867071241140366, -0.0059986477717757225, 0.031022295355796814, -0.05133570730686188, 0.006299835164099932, 0.0002737353788688779, 0.014331497251987457, -0.020213017240166664, -0.002378124976530671, -0.02556745894253254, -0.039823658764362335, -0.018958069384098053, -0.006964957341551781, -0.013361005112528801, -0.011930365115404129, 0.0119387311860919, -0.015301990322768688, 0.024161918088793755, -0.04367216303944588, 0.032143380492925644, 0.05397946387529373, 0.02827814407646656, -0.038685839623212814, 0.010441160760819912, 0.05618816986680031, -0.04109533876180649, -0.030286060646176338, 0.03798307105898857, 0.0682021975517273, 0.03651059791445732, -0.028880519792437553, -0.015536246821284294, 0.01982816681265831, 0.07697010040283203, -0.01947678066790104, -0.05893232300877571, 0.0037690249737352133, 0.03878623619675636, -0.01633104681968689, -0.015209960751235485, 0.02376033365726471, 0.016791194677352905, 0.011712840758264065, -0.01746886596083641, 0.057292524725198746, -0.041630782186985016, 0.002399040851742029, -0.02330855280160904, -0.03207645192742348, 0.03878623619675636, -0.0644540935754776, 0.004429963883012533, 0.017954111099243164, 0.039388611912727356, 0.052674319595098495, 0.021334102377295494, -0.03721337020397186, -0.06147568300366402, 0.009027253836393356, -0.016648966819047928, 0.010466259904205799, 0.01628921553492546, -0.013310806825757027, 0.059768952429294586, -0.03651059791445732, -0.04470958560705185, -0.03758148476481438, -0.02354281023144722, 0.0016994077013805509, -0.009278243407607079, 0.013578529469668865, -0.040593359619379044, -0.025400131940841675, 0.051871150732040405, 0.07596614211797714, 0.001831177156418562, 0.0009647406986914575, -0.004798081703484058, 0.023275088518857956, 0.0036644458305090666, 0.06592655926942825, -0.035171989351511, -0.023241622373461723, -0.011562246829271317, -0.017092380672693253, 0.03052031621336937, -0.024245580658316612, -0.054113324731588364, -0.026286961510777473, 0.07128100097179413, -0.09450589120388031, -0.009085818193852901, -0.06147568300366402, 0.01935965195298195, -0.0034699290990829468, 0.020664798095822334, -0.013578529469668865, 0.004919392988085747, -0.051536500453948975, 0.05056600645184517, 0.003720918670296669, -0.00830356776714325, 0.012591304257512093, -0.01311838161200285, -0.0030704375822097063, 0.046115126460790634, -0.0024952534586191177, -0.04470958560705185, 0.01266660075634718, -0.005425555165857077, -0.007780672982335091, 0.01697525382041931, 0.022722911089658737, 0.02714032493531704, -0.011060268618166447, 0.023358751088380814, 0.0058313217014074326, -0.030921900644898415, -0.0324278362095356, -0.04698522388935089, 0.009219679050147533, -0.010089775547385216, -0.013143480755388737, -0.030603980645537376, 0.03433535620570183, -0.012942689470946789, -0.05709173157811165, -0.012733531184494495, 0.043638698756694794, -0.003959358669817448, -0.024948351085186005, 0.004655854310840368, -0.010374230332672596, -0.053678277879953384, 0.03697911277413368, -0.04865848645567894, -0.009704925119876862, 0.002790166065096855, -0.06388518214225769, -0.010006112977862358, 0.008910125121474266, 0.019125396385788918, -0.048390764743089676, 0.007174115162342787, 0.023392217233777046, -0.0034009069204330444, -0.015051000751554966, 0.06160954385995865, 0.04869195446372032, 0.020999450236558914, -0.045445822179317474, 0.001828039763495326, 0.010959872975945473, -0.022555584087967873, 0.004865012131631374, -0.011930365115404129, 0.009035619907081127, -0.012775362469255924, 0.06826912611722946, -0.009596163406968117, -0.012206453830003738, -0.026303693652153015, 0.02703993022441864, 0.021936478093266487, -0.05722559243440628, 0.015042634680867195, -0.01531872246414423, -0.03600861877202988, -0.030587246641516685, 0.02183608151972294, -0.004772982560098171, -0.006383498199284077, 0.0479557178914547, -0.031139424070715904, -0.036577530205249786, -0.056489359587430954, -0.06314894556999207, -0.01848955638706684, -0.013494865968823433, -0.03231070935726166, 0.02342568151652813, 0.0026186564937233925, 0.003787849098443985, -0.0063082012347877026, 0.0328126884996891, -0.0138546172529459, -0.01627248339354992, 0.048625022172927856, -0.0004371399409137666, -0.02183608151972294, -0.007897801697254181, -0.004176882561296225, 0.011445119045674801, 0.0017632008530199528, -0.00928660947829485, 0.002057067584246397, 0.030269326642155647, -0.0021961575839668512, 0.028897251933813095, -0.03075457364320755, 0.021099846810102463, 0.01951024681329727, -0.001953534549102187, -0.0982540026307106, 0.036878716200590134, 0.009520865976810455, 0.03788267448544502, 0.06492260098457336, 0.04290246218442917, 0.01812143810093403, -0.004597289953380823, -0.03378317877650261, -0.01131962426006794, -0.007257778197526932, 0.007337258197367191, -0.007956365123391151, -0.018221834674477577, 0.02175241895020008, -0.02061459980905056, 0.0005710009718313813, -0.025165874511003494, -0.04869195446372032, 0.0059484499506652355, -0.0028654627967625856, 0.05802876129746437, 0.006944041233509779, 0.011662643402814865, 0.025885378941893578, 0.020447272807359695, 0.027006464079022408, 0.015887631103396416, 0.008634037338197231, 0.03999098390340805, 0.03771534934639931, -0.02806062065064907, 0.0446091927587986, -0.017937378957867622, -0.012373779900372028, -0.015611543320119381, -0.013260609470307827, 0.016766095533967018, -0.00835376512259245, -0.023040831089019775, 0.011645910330116749, 0.029014380648732185, 0.03865237534046173, 0.014122339896857738, 0.013135114684700966, -0.0353727787733078, 0.04069375619292259, -0.07161565870046616, 0.05575312301516533, 0.009780222550034523, 0.0048901112750172615, 0.045211564749479294, 0.016933420673012733, -0.03254496678709984, 0.028094084933400154, 0.01835569553077221, 0.001679537701420486, 0.0077555738389492035, -0.003927984740585089, -0.0034050901886075735, 0.00243459758348763, 0.0058313217014074326, -0.00867586862295866, -0.022906970232725143, -0.015067732892930508, -0.036443669348955154, 0.036209411919116974, 0.006994239054620266, -0.017954111099243164, 0.005505035165697336, -0.057392921298742294, -0.00986388511955738, 0.019342919811606407, -0.0043755825608968735, 0.02961675450205803, 0.0053837234154343605, -0.04698522388935089, -0.03597515448927879, 0.007119733840227127, -0.014105606824159622, 0.0036184312775731087, -0.03018566407263279, -0.013888082467019558, 0.008742799051105976, 0.017092380672693253, -0.014833476394414902, -0.05528460815548897, 0.014549021609127522, -0.013260609470307827, 0.009612895548343658, 0.018305497244000435, 0.03470347449183464, 0.019209058955311775, -0.0324278362095356, 0.006287285592406988, -0.017954111099243164, 0.0060488455928862095, 0.032595161348581314, 0.0042919195257127285, 0.002063342370092869, -0.008215721696615219, 0.05990281328558922, 0.0049570417031645775, 0.0001124223563238047, 0.010934773832559586, 0.025718051940202713, 0.051067985594272614, 0.013787686824798584, -0.021484697237610817, -0.006354216020554304, -0.02759210579097271, -0.0028278145473450422, -0.012005661614239216, 0.023375483229756355, 0.037782277911901474, -0.011361455544829369, -0.01992856152355671, -0.05635549873113632, -0.014908772893249989, 0.0025287186726927757, 0.030838236212730408, 0.017084015533328056, -0.06462141871452332, -0.00021687056869268417, 0.021116578951478004, -0.0028759208507835865, 0.027525175362825394, -0.04798918217420578, -0.00009863101149676368, 0.02232132852077484, 0.0007519225473515689, 0.00883482862263918, 0.0019817708525806665, -0.033749714493751526, 0.0011378187919035554, 0.0567905455827713, -0.027424780651926994, 0.02059786766767502, 0.027508443221449852, 0.06987546384334564, -0.006128325592726469, -0.03150754049420357, -0.02715705893933773, 0.02826141193509102, -0.0461820587515831, 0.11230941116809845, 0.039154354482889175, -0.0066805025562644005, 0.021484697237610817, -0.023024098947644234, 0.002323743887245655, -0.00009300989040639251, 0.010800912976264954, -0.03324773535132408, 0.030620712786912918, -0.020681530237197876, -0.00012902426533401012, -0.02355954237282276, -0.041396524757146835, 0.008650769479572773, 0.053644809871912, 0.051536500453948975, 0.035305850207805634, 0.0026604882441461086, 0.039154354482889175, -0.004043021705001593, 0.05742638558149338, 0.00602374691516161, 0.03952247276902199, -0.024161918088793755, -0.003402998670935631, 0.03483733534812927, 0.04531196132302284, 0.004831546917557716, 0.017987577244639397, -0.02232132852077484, 0.03391703963279724, 0.03945554047822952, -0.019091930240392685, 0.027759432792663574, 0.007998197339475155, 0.019761236384510994, 0.016197185963392258, 0.01984489895403385, -0.030838236212730408, 0.03336486220359802, -0.016080057248473167, 0.008211538195610046, -0.008717699907720089, 0.003595423884689808, 0.003927984740585089, 0.003660262795165181, 0.05260738730430603, 0.008726066909730434, -0.042433951050043106, -0.041865039616823196, 0.08460017293691635, 0.02939923107624054, -0.03247803449630737, 0.017836984246969223, 0.031156156212091446, -0.02949962578713894, -0.029683684930205345, -0.046115126460790634, 0.02309102937579155, 0.008759532123804092, -0.03932167962193489, -0.029934674501419067, -0.023375483229756355, 0.01542748510837555, 0.002806898672133684, 0.04644978046417236, 0.06000320985913277, 0.002627022797241807, -0.03527238219976425, 0.001737056183628738, 0.007391639053821564, 0.024847954511642456, -0.027843095362186432, -0.025734784081578255, 0.006094860378652811, -0.0224049910902977, -0.0038526880089193583, 0.009027253836393356, 0.003771116491407156, -0.0199452955275774, 0.008525274693965912, 0.008337032981216908, 0.014892040751874447, -0.007529683411121368, 0.0262367632240057, -0.07482831925153732, -0.028077352792024612, -0.009671459905803204, 0.011495316401124, -0.02896418236196041, 0.043203651905059814, 0.02578498236835003, 0.03145734593272209, 0.029215171933174133, 0.0005309995613060892, 0.020547669380903244, 0.013720756396651268, 0.00911928340792656, -0.015109565109014511, 0.009847152978181839, -0.06023746728897095, -0.028679726645350456, -0.016314314678311348, 0.00543810473755002, 0.0285960640758276, -0.029650220647454262, 0.004563824739307165, 0.026655079796910286, -0.018087971955537796, -0.010842744261026382, -0.010457893833518028, -0.002367667155340314, 0.018757278099656105, 0.002896836493164301, 0.02434597723186016, 0.0396897979080677, -0.047252945601940155, 0.028412004932761192, -0.03533931449055672, -0.014833476394414902, 0.019644107669591904, 0.018523020669817924, 0.005404639523476362, -0.02084885723888874, 0.04497730731964111, -0.012139523401856422, -0.013729122467339039, -0.009830419905483723, 0.012925956398248672, 0.03818386048078537, -0.0587649941444397, -0.08540334552526474, 0.01278372947126627, 0.026621613651514053, 0.008575472980737686, 0.02027994766831398, 0.015829067677259445, 0.017987577244639397, 0.030470119789242744, -0.029800813645124435, -0.022003408521413803, 0.029148241505026817, -0.022622516378760338, -0.060873307287693024, -0.0036686290986835957, -0.026554683223366737, -0.03932167962193489, 0.007358173839747906, -0.0028319975826889277, 0.058196086436510086, -0.026002507656812668, -0.023726869374513626, -0.008901759050786495, 0.026738742366433144, -0.0161135233938694, -0.025851912796497345, -0.009361905977129936, -0.042969394475221634, 0.0052163973450660706, -0.03277922049164772, 0.006073944736272097, -0.033281199634075165, 0.005262412130832672, -0.01458248682320118, -0.023743601515889168, 0.008433245122432709, 0.003923801705241203, -0.05759371072053909, -0.011394920758903027, -0.015870898962020874, 0.009085818193852901, 0.03600861877202988, 0.021032916381955147, 0.030453385785222054, 0.0035640501882880926, 0.008374680764973164, 0.01019017118960619, 0.03597515448927879, -0.04765452817082405, 0.009043985977768898, 0.03875277191400528, -0.013561796396970749, -0.031474076211452484, -0.03393377363681793, -0.028679726645350456, 0.02083212323486805, 0.008759532123804092, 0.021668756380677223, 0.0246638972312212, -0.028780123218894005, 0.008809729479253292, -0.00455964170396328, -0.008320299908518791, -0.06813526898622513, 0.0008162385784089565, -0.028763391077518463, -0.014833476394414902, -0.0005689093959517777, -0.07148179411888123, -0.0100228451192379, -0.008504359051585197, 0.007617529947310686, -0.011378188617527485, 0.022371526807546616, 0.021350836381316185, 0.05163689702749252, -0.015385652892291546, -0.0068310960195958614, 0.044776517897844315, -0.019443316385149956, -0.024613698944449425, -0.03279595449566841, 0.025600923225283623, 0.00594426691532135, -0.012097691185772419, 0.04956204816699028, 0.03477040305733681, 0.02344241365790367, 0.01925925724208355, 0.008801363408565521, -0.013176945969462395, -0.030369723215699196, 0.021802617236971855, -0.06007014214992523, 0.012147889472544193, 0.013386104255914688, -0.005454837344586849, 0.0011597804259508848, 0.024914884939789772, 0.0509006604552269, -0.02523280493915081, 0.008893392980098724, -0.019125396385788918, 0.01902499981224537, 0.0005955770611763, 0.06418636441230774, -0.040827617049217224, 0.08366315066814423, 0.005793672986328602, -0.0522727370262146, 0.005956816021353006, 0.000041374041757080704, -0.009027253836393356, -0.008337032981216908, -0.03436882048845291, 0.03771534934639931, 0.03118962235748768, 0.010834378190338612, -0.01177140511572361, -0.04434146732091904, 0.0617099404335022, 0.01746886596083641, -0.002792257582768798, 0.03607555106282234, 0.004020014312118292, 0.026788940653204918, -0.023526078090071678, 0.045010775327682495, 0.017987577244639397, 0.026989731937646866, 0.003062071278691292, 0.04879234731197357, -0.015854166820645332, -0.025868644937872887, 0.004040929954499006, -0.02232132852077484, -0.039355143904685974, 0.0005181886372156441, 0.009110917337238789, 0.007249411661177874, -0.042065832763910294, -0.046349383890628815, -0.011478584259748459, -0.0318421944975853, 0.014122339896857738, -0.014348230324685574, -0.0043086521327495575, 0.007563148625195026, -0.00273160170763731, 0.05789490044116974, -0.023057563230395317, 0.05628856644034386, -0.03477040305733681, -0.0010426519438624382, -0.05260738730430603, 0.03754802048206329, -0.02637062408030033, -0.0416642464697361, 0.0010070952121168375, 0.02073172852396965, -0.02703993022441864, 0.00912764947861433, 0.031022295355796814, -0.014214369468390942, -0.025533992797136307, 0.022555584087967873, 0.02521607279777527, 0.02049747109413147, 0.06187726557254791, -0.027525175362825394, 0.0434379056096077, -0.0316414013504982, 0.010909674689173698, 0.0328126884996891, 0.03774881362915039, -0.0041580586694180965, 0.008521092124283314, -0.023676671087741852, 0.01790391467511654, -0.028545865789055824, -0.005613797344267368, 0.013980112038552761, 0.005576149094849825, -0.06237924471497536, 0.02951635979115963, -0.0006813317886553705, -0.015385652892291546, -0.019225791096687317, 0.019694305956363678, -0.03018566407263279, -0.0006682593957521021, 0.0022149819415062666, -0.0059819151647388935, 0.02804388850927353, 0.002277729334309697, -0.0049403090961277485, 0.03607555106282234, -0.036778319627046585, 0.011696108616888523, 0.004229172132909298, 0.006667952984571457, 0.0017077740048989654, -0.0032795954030007124, -0.02904784493148327, -0.014055409468710423, 0.03651059791445732, 0.0353727787733078, 0.027910025790333748, -0.006195256020873785, -0.008265919052064419, -0.022137269377708435, -0.0416642464697361, 0.01813817024230957, -0.019326187670230865, -0.00923641212284565, -0.05140263959765434, 0.04447533190250397, -0.00973839033395052, -0.04045949876308441, 0.012373779900372028, -0.0200456902384758, 0.00675998255610466, 0.032176848500967026, 0.0013668467290699482, -0.0068310960195958614, -0.023526078090071678, 0.02106638066470623, 0.006567557342350483, 0.05066640302538872, 0.046248987317085266, -0.027290919795632362, 0.01520159374922514, -0.08533640950918198, 0.04035910218954086, 0.01825529895722866, -0.030888434499502182, 0.05642242729663849, -0.048156507313251495, 0.01609678938984871, 0.021936478093266487, -0.019660839810967445, -0.036209411919116974, -0.0032775038853287697, 0.017301538959145546, -0.007328891661018133, -0.014967337250709534, 0.04317018389701843, -0.013729122467339039, -0.0012068409705534577, -0.02837854065001011, 0.06090677157044411, -0.04437493532896042, 0.01984489895403385, 0.07134793698787689, -0.013369371183216572, -0.008809729479253292, 0.022388258948922157, 0.034184761345386505, 0.018523020669817924, -0.02049747109413147, -0.00608649430796504, -0.011637544259428978, -0.021685488522052765, -0.021434498950839043, 0.017008718103170395, -0.003907069098204374, -0.032277241349220276, 0.018171636387705803, 0.001841635094024241, 0.01092640683054924, -0.03560703620314598 ]
A scalable and computationally efficient framework is designed to fingerprint real-world Bluetooth devices. We propose an embedding-assisted attentional framework (Mbed-ATN) suitable for fingerprinting actual Bluetooth devices. Its generalization capability is analyzed in different settings and the effect of sample length and anti-aliasing decimation is demonstrated. The embedding module serves as a dimensionality reduction unit that maps the high dimensional 3D input tensor to a 1D feature vector for further processing by the ATN module. Furthermore, unlike the prior research in this field, we closely evaluate the complexity of the model and test its fingerprinting capability with real-world Bluetooth dataset collected under a different time frame and experimental setting while being trained on another. Our study reveals a 9.17x and 65.2x lesser memory usage at a sample length of 100 kS when compared to the benchmark - GRU and Oracle models respectively. Further, the proposed Mbed-ATN showcases 16.9x fewer FLOPs and 7.5x lesser trainable parameters when compared to Oracle. Finally, we show that when subject to anti-aliasing decimation and at greater input sample lengths of 1 MS, the proposed Mbed-ATN framework results in a 5.32x higher TPR, 37.9% fewer false alarms, and 6.74x higher accuracy under the challenging real-world setting.
[ -0.0216722022742033, -0.012482219375669956, -0.03167009726166725, -0.08228570222854614, 0.04556616023182869, 0.04403112828731537, -0.0023921728134155273, 0.05134272202849388, 0.010144327767193317, 0.028014302253723145, -0.014714072458446026, -0.03811318427324295, 0.06192634999752045, -0.01494634710252285, 0.004953502211719751, 0.02716599591076374, 0.012845778837800026, -0.05332210287451744, -0.003317483002319932, -0.04673762992024422, 0.039466433227062225, -0.09064757078886032, -0.03336670994758606, -0.05756363272666931, -0.0037214383482933044, 0.030761197209358215, 0.004774246830493212, 0.001863243873231113, -0.06430968642234802, 0.008144749328494072, -0.006372395437210798, 0.011876286938786507, -0.04086007922887802, -0.018794020637869835, -0.0663294643163681, 0.003486639354377985, 0.058694709092378616, 0.01939995400607586, -0.009442456066608429, 0.002686302876099944, 0.010023141279816628, -0.04205174744129181, -0.047707121819257736, 0.008942561224102974, 0.012159055098891258, 0.0005882599507458508, -0.043707966804504395, -0.001633494277484715, -0.036497361958026886, 0.017380177974700928, -0.023853560909628868, -0.04976729676127434, -0.03516431152820587, 0.0020122025161981583, 0.029832100495696068, 0.041001465171575546, 0.06859161704778671, 0.07093455642461777, 0.0831340029835701, 0.046939607709646225, 0.012512516230344772, 0.009376812726259232, 0.011189562268555164, -0.017359979450702667, 0.018763724714517593, -0.04956531897187233, -0.034699760377407074, -0.004847463686019182, 0.0039057431276887655, -0.00997769646346569, -0.08410349488258362, -0.0094828512519598, 0.0349421352148056, 0.014098040759563446, -0.03171049430966377, 0.01897580176591873, 0.01921817474067211, 0.06681421399116516, 0.0661274865269661, 0.0031584256794303656, 0.029226167127490044, 0.04144581779837608, -0.043182823807001114, 0.0448390394449234, 0.06495601683855057, 0.02688322588801384, -0.03865852579474449, -0.08151818066835403, 0.019268669188022614, -0.00957879051566124, -0.06564273685216904, 0.042940448969602585, -0.028781816363334656, 0.018733428791165352, -0.01596633344888687, 0.05958341062068939, -0.07929643243551254, -0.014017249457538128, -0.0493229441344738, -0.026034921407699585, 0.007604458834975958, 0.0166732557117939, -0.02312644198536873, -0.015461389906704426, 0.020015986636281013, 0.0017079735407605767, -0.005261518061161041, 0.04213254153728485, 0.013855667784810066, 0.09775719046592712, -0.022964859381318092, -0.02490384504199028, -0.0036103506572544575, 0.01890510879456997, -0.005726066883653402, -0.023005256429314613, -0.025529976934194565, -0.04936334118247032, -0.059623803943395615, -0.0005286133964546025, 0.036012616008520126, 0.013673887588083744, -0.00936166476458311, 0.04063790664076805, -0.008074057288467884, 0.04431390017271042, 0.027044808492064476, -0.004463706165552139, -0.020743105560541153, -0.005402902606874704, 0.010543233714997768, 0.006559224333614111, 0.04114285111427307, -0.07101534307003021, 0.04180937632918358, 0.02488364838063717, 0.025327999144792557, 0.04431390017271042, 0.0043475693091750145, -0.0303572416305542, 0.041203442960977554, -0.008695138618350029, -0.06273426115512848, -0.018794020637869835, -0.007442876696586609, 0.0189152080565691, -0.03433620184659958, 0.07097495347261429, -0.03439679741859436, 0.023570792749524117, -0.057644423097372055, 0.03657815605401993, 0.040496520698070526, 0.001115295453928411, 0.00845781434327364, -0.019268669188022614, -0.03112475760281086, -0.02112686261534691, 0.016996420919895172, 0.023086046800017357, 0.008533556014299393, -0.08402270823717117, 0.04738396033644676, 0.011189562268555164, 0.040496520698070526, 0.019359558820724487, 0.05061560124158859, 0.03514411300420761, -0.05384724587202072, 0.04435429349541664, -0.0016928252298384905, 0.02936755120754242, 0.022581102326512337, -0.003971385769546032, -0.049161363393068314, 0.03851713985204697, 0.02492404356598854, -0.01990489847958088, -0.018794020637869835, -0.010694717057049274, 0.012401428073644638, 0.057402051985263824, 0.025247206911444664, 0.019490843638777733, 0.06907635927200317, 0.024015143513679504, 0.06794528663158417, 0.01346181146800518, -0.001644855597987771, -0.03221543878316879, 0.0032846617978066206, 0.023469803854823112, 0.026943819597363472, -0.021571213379502296, 0.04673762992024422, -0.05958341062068939, -0.0388605035841465, 0.03906248137354851, 0.013724382035434246, 0.01319923996925354, -0.0588562898337841, -0.03132673352956772, 0.039264459162950516, -0.0020879441872239113, 0.010119080543518066, -0.01431011687964201, 0.016622761264443398, -0.024338308721780777, -0.0017445820849388838, -0.02336881496012211, -0.021349038928747177, -0.007584261242300272, -0.04205174744129181, -0.02688322588801384, 0.07158087939023972, 0.015976432710886, 0.01665305905044079, -0.05263537913560867, -0.00778623903170228, 0.05728086456656456, 0.001705448841676116, 0.020783500745892525, 0.048959385603666306, 0.006276455707848072, -0.009730273857712746, 0.010432146489620209, 0.0002152324450435117, 0.0463336743414402, 0.0017193348612636328, 0.011179463937878609, 0.0027342725079506636, 0.023813165724277496, -0.025792546570301056, 0.011573320254683495, 0.01720849610865116, -0.0006854616804048419, 0.0283980593085289, -0.06806647032499313, 0.03888069838285446, 0.00885672029107809, -0.04714158549904823, -0.00647843349725008, -0.06923794001340866, -0.037749625742435455, 0.035729847848415375, -0.02639847993850708, -0.04904017597436905, 0.07889247685670853, -0.03855753690004349, 0.009760570712387562, 0.015380598604679108, -0.0018544073682278395, -0.007725645322352648, 0.01619860902428627, -0.055867020040750504, 0.028579838573932648, -0.031993262469768524, -0.03694171458482742, 0.05215063318610191, -0.02736797370016575, 0.014865555800497532, -0.014390908181667328, -0.010937090031802654, 0.033972643315792084, -0.029529133811593056, 0.006089626345783472, 0.038476742804050446, -0.008998104371130466, 0.011068375781178474, -0.0033376808278262615, 0.047707121819257736, -0.03536628931760788, 0.0022899217437952757, 0.019319163635373116, 0.03136713057756424, -0.011381440795958042, -0.03304354473948479, -0.027509357780218124, 0.030438033863902092, 0.022318530827760696, 0.028458653017878532, 0.032982952892780304, 0.024297913536429405, 0.008185144513845444, -0.03457857668399811, -0.027509357780218124, 0.001824110746383667, -0.02038964442908764, -0.03270018473267555, -0.01871323026716709, -0.04952492192387581, -0.05299893766641617, -0.04435429349541664, 0.02017756924033165, -0.027792125940322876, -0.02413633093237877, -0.02239932306110859, -0.007978118024766445, 0.023853560909628868, -0.05000966787338257, -0.04750514775514603, -0.009654532186686993, -0.0013671362539753318, -0.022257938981056213, -0.005811907351016998, 0.005695770028978586, -0.008296232670545578, 0.03613380342721939, -0.022358927875757217, 0.005377655383199453, 0.0323164239525795, -0.04411192238330841, -0.05477634072303772, -0.0403551384806633, 0.010684618726372719, 0.019985688850283623, -0.01085629966109991, -0.0373658686876297, -0.007861980237066746, -0.03653775900602341, -0.008513358421623707, 0.024459494277834892, -0.06693539768457413, 0.06269386410713196, 0.022581102326512337, -0.019581735134124756, 0.047424353659152985, 0.012684197165071964, -0.008245738223195076, 0.0044081625528633595, -0.009053648449480534, 0.005756363272666931, -0.06580432504415512, -0.011997473426163197, -0.027468962594866753, -0.007538816425949335, -0.053443290293216705, 0.05893708020448685, 0.021571213379502296, 0.009301071055233479, -0.033730268478393555, -0.010765409097075462, -0.010053438134491444, -0.051181137561798096, -0.042698077857494354, -0.024297913536429405, -0.04011276364326477, -0.0034487685188651085, -0.027327576652169228, -0.0607144832611084, 0.0012554173590615392, -0.05659414082765579, 0.015592675656080246, 0.0003515673743095249, -0.0313873291015625, -0.026580261066555977, -0.04960571229457855, -0.00635724700987339, -0.029448343440890312, -0.02314664050936699, -0.043505989015102386, -0.00998779572546482, 0.03629538416862488, 0.05178707093000412, -0.036012616008520126, -0.022055961191654205, -0.05114074423909187, 0.007064168807119131, -0.021227851510047913, 0.03387165442109108, -0.00772059615701437, 0.044717855751514435, -0.017784133553504944, -0.007190404925495386, -0.04972689971327782, 0.030539022758603096, 0.016309695318341255, -0.03191247209906578, 0.033225324004888535, 0.04386954754590988, 0.0013810222735628486, 0.025065427646040916, 0.05663453787565231, -0.000201977658434771, 0.04774751886725426, -0.0008596674306318164, 0.0031432772520929575, 0.029771506786346436, -0.03789100795984268, 0.09638374298810959, 0.008629495278000832, -0.06293623894453049, -0.016754046082496643, -0.02542898803949356, 0.03393224626779556, -0.02312644198536873, 0.0457681380212307, 0.04677802696824074, 0.01797601208090782, -0.028438454493880272, -0.03605301305651665, 0.019056592136621475, -0.02589353546500206, -0.028196081519126892, 0.007766040973365307, -0.0353056937456131, 0.008634544909000397, -0.010310960002243519, 0.018087100237607956, -0.04702039808034897, 0.02340921014547348, 0.0013456761371344328, -0.01295686699450016, -0.00797306839376688, 0.01381527166813612, -0.008063958026468754, -0.044717855751514435, -0.004276876803487539, -0.007801386993378401, -0.06123962625861168, -0.03956742212176323, 0.04653565213084221, 0.0378304161131382, -0.0000098967084340984, -0.010002943687140942, 0.024540286511182785, 0.010280663147568703, -0.020026085898280144, -0.039708808064460754, -0.02542898803949356, -0.006266356911510229, -0.024560483172535896, 0.01445150189101696, -0.015471489168703556, 0.004413211718201637, 0.012845778837800026, -0.015744158998131752, 0.013593096286058426, -0.04108225554227829, -0.010144327767193317, -0.005051966290920973, -0.023490002378821373, -0.01893540658056736, -0.0041253939270973206, -0.050979163497686386, -0.015229115262627602, 0.021510621532797813, 0.008690088987350464, 0.01595623604953289, -0.046172093600034714, -0.06467324495315552, 0.052433401346206665, -0.04077928885817528, -0.01692572794854641, 0.0607144832611084, -0.04083988443017006, 0.026499468833208084, -0.040254149585962296, -0.002736797323450446, -0.0765899270772934, -0.02813548780977726, 0.07481252402067184, 0.041486211121082306, -0.023954549804329872, 0.023833364248275757, 0.003203870728611946, -0.0189657025039196, -0.06374415010213852, 0.003224068321287632, 0.019228274002671242, 0.02886260859668255, -0.017370078712701797, 0.010826002806425095, 0.026034921407699585, -0.002115715993568301, -0.01968272216618061, -0.03655795753002167, -0.032801173627376556, 0.01716810092329979, 0.01746096834540367, -0.0018645062809810042, -0.0019263619324192405, 0.012522614561021328, -0.03205385431647301, 0.020510831847786903, 0.006640015635639429, -0.014087941497564316, 0.02038964442908764, -0.03756784647703171, -0.0015779504319652915, -0.02264169603586197, -0.027085203677415848, -0.05283735692501068, -0.01791541837155819, -0.04653565213084221, -0.04714158549904823, 0.02587333880364895, -0.010775508359074593, 0.022742684930562973, 0.038254570215940475, -0.04083988443017006, -0.025711756199598312, 0.009947399608790874, -0.010765409097075462, -0.02589353546500206, 0.01195707730948925, -0.021813588216900826, 0.04213254153728485, -0.010523036122322083, 0.036234792321920395, 0.02587333880364895, 0.02018766663968563, 0.03167009726166725, -0.0007403743802569807, 0.003160950494930148, 0.0008539867703802884, -0.02890300378203392, -0.01196717657148838, 0.004435934592038393, -0.0038729216903448105, 0.04306163638830185, 0.011310748755931854, -0.03439679741859436, 0.057684820145368576, -0.0439099445939064, 0.033265721052885056, 0.0167237501591444, -0.006200714036822319, 0.04051671922206879, -0.07097495347261429, -0.005579632706940174, 0.004642961546778679, -0.04758593812584877, -0.07602439075708389, -0.018804119899868965, 0.02866063080728054, 0.004640436731278896, 0.0306400116533041, -0.03304354473948479, -0.018561746925115585, 0.0037441609892994165, -0.008493160828948021, -0.00218009646050632, 0.03193266689777374, -0.05033283308148384, -0.00038028607377782464, 0.02866063080728054, -0.04710119217634201, 0.008387122303247452, -0.008281083777546883, 0.032720379531383514, 0.009311170317232609, -0.018359769135713577, 0.016107719391584396, -0.023550596088171005, -0.014047546312212944, 0.021470224484801292, -0.01195707730948925, 0.00746812392026186, 0.0283980593085289, -0.004453607369214296, 0.006094675976783037, 0.02118745632469654, -0.04455627128481865, 0.02140963263809681, -0.005574583541601896, 0.020864292979240417, 0.059664200991392136, 0.03928465396165848, 0.02066231518983841, 0.006867240648716688, -0.014663578011095524, -0.009583840146660805, -0.029286760836839676, -0.02815568633377552, 0.017824528738856316, 0.05845233425498009, -0.03112475760281086, 0.0024401426780968904, 0.03164989873766899, -0.014592885971069336, -0.003776982193812728, 0.01872332952916622, 0.0038501990493386984, 0.027085203677415848, 0.014653479680418968, -0.008876917883753777, -0.07477212697267532, 0.01071491464972496, -0.032740578055381775, -0.0020021034870296717, 0.05562464892864227, -0.011128969490528107, 0.005690720397979021, -0.030761197209358215, -0.03853733837604523, 0.007215652149170637, 0.03013506717979908, 0.0338110588490963, -0.027246786281466484, -0.015451290644705296, 0.030438033863902092, 0.07000545412302017, 0.0657639279961586, 0.011876286938786507, -0.039749205112457275, 0.008392171934247017, 0.012734691612422466, -0.05574583262205124, 0.033508092164993286, -0.02886260859668255, 0.012663999572396278, 0.04176897928118706, 0.002505785319954157, 0.0007328002247959375, 0.05162549018859863, 0.02789311483502388, -0.03383125737309456, 0.03318493068218231, -0.028761619701981544, 0.04528339207172394, -0.056149788200855255, 0.04702039808034897, 0.03017546236515045, 0.01719839870929718, 0.030316846445202827, -0.02512602135539055, -0.018016407266259193, -0.0001361771282972768, -0.021995367482304573, 0.0015034711686894298, 0.007377234287559986, -0.028741421177983284, 0.039486631751060486, -0.00996759720146656, 0.007907425053417683, -0.004711128771305084, -0.002327792579308152, -0.0016713651129975915, 0.027832521125674248, 0.021086467429995537, -0.008493160828948021, -0.055180296301841736, 0.028458653017878532, -0.011381440795958042, 0.006700608879327774, -0.03243761137127876, 0.01920807547867298, 0.04738396033644676, 0.03152871131896973, -0.02868082746863365, 0.004779296461492777, 0.01671365089714527, 0.02243971824645996, -0.03809298574924469, -0.018491053953766823, 0.01046244241297245, 0.027266984805464745, 0.01616831123828888, 0.02344960719347, 0.011765198782086372, 0.006826844997704029, 0.008791077882051468, 0.006190615240484476, 0.03562885895371437, 0.01530990656465292, -0.0303572416305542, -0.02114706113934517, -0.004090047441422939, 0.02963012270629406, -0.049403734505176544, -0.0493229441344738, -0.0736006572842598, -0.021571213379502296, 0.02864043228328228, -0.037002306431531906, 0.016865134239196777, -0.0009688615682534873, -0.015895642340183258, -0.04516220465302467, 0.018036605790257454, -0.006549125537276268, -0.029024189338088036, 0.006660213228315115, -0.00099663354922086, -0.01482516061514616, -0.03310414031147957, 0.02464127540588379, -0.07384303212165833, 0.003468966344371438, -0.02142982929944992, -0.009861559607088566, 0.04407152533531189, 0.01468377560377121, 0.013784975744783878, 0.01333052571862936, -0.028236476704478264, 0.002721648896113038, 0.021349038928747177, 0.0031180300284177065, -0.01282558124512434, 0.03552787005901337, -0.03510371595621109, -0.0001378339802613482, 0.001346938544884324, 0.011906582862138748, 0.019298965111374855, -0.04136502370238304, 0.031468119472265244, 0.04423310607671738, 0.003067535813897848, 0.018319373950362206, 0.03037744015455246, 0.019319163635373116, -0.00946770329028368, -0.0026812534779310226, -0.011563220992684364, 0.026943819597363472, -0.06047211214900017, 0.0663294643163681, -0.02387375943362713, -0.00020134648366365582, 0.033225324004888535, -0.07315631210803986, -0.026519667357206345, 0.036982107907533646, 0.0005062065320089459, 0.025812745094299316, 0.01594613678753376, 0.002361876191571355, 0.026701446622610092, -0.03267998620867729, -0.018238583579659462, 0.00023290548415388912, -0.0035775292199105024, 0.016541970893740654, 0.006473383866250515, 0.025832943618297577, -0.01084620039910078, -0.024701867252588272, 0.006796548143029213, -0.013744579628109932, -0.03607321158051491, -0.00659961998462677, 0.01134104561060667, -0.00038691345253027976, 0.004577318672090769, 0.012128758244216442, -0.07404500991106033, -0.02068251185119152, 0.017844727262854576, -0.05408961698412895, -0.0012989687966182828, -0.04536418244242668, -0.024075737223029137, 0.0011916682124137878, 0.03914327174425125, 0.009715125896036625, -0.01693582721054554, 0.03259919583797455, 0.00498379860073328, 0.009200082160532475, 0.01271449401974678, 0.00466820877045393, 0.04302124306559563, 0.02019776590168476, -0.04738396033644676, -0.0603509247303009, 0.014390908181667328, -0.035002727061510086, 0.044435083866119385, 0.01842036284506321, -0.001755943289026618, -0.027731532230973244, 0.01059372816234827, 0.016107719391584396, 0.006220912095159292, 0.0021384384017437696, -0.036982107907533646, -0.00566547317430377, -0.01644098199903965, 0.062774658203125, 0.000030789757147431374, 0.06956110894680023, 0.00015203552902676165, -0.004198610782623291, 0.029569528996944427, -0.026034921407699585, 0.005715967621654272, 0.009341467171907425, 0.025974327698349953, -0.016299597918987274, 0.053928036242723465, -0.009245526976883411, 0.06701618432998657, -0.002388385822996497, 0.015835048630833626, 0.006316851358860731, -0.05562464892864227, -0.00947275198996067, 0.0313873291015625, 0.0027140749152749777, -0.024055538699030876, 0.03585103526711464, -0.01019482221454382, -0.010765409097075462, -0.04964610934257507, 0.022035762667655945, -0.03140752762556076, -0.025247206911444664, -0.03243761137127876, -0.019561536610126495, 0.020228063687682152, 0.01795581355690956, 0.03787081316113472, 0.03716389089822769, -0.038739316165447235, 0.017572056502103806, 0.019753415137529373, -0.060391321778297424, -0.02417672611773014, -0.003633073065429926, 0.012290340848267078, 0.009144539013504982, 0.0196625255048275, -0.005559435114264488, 0.05223142355680466, 0.009104142896831036, 0.0196625255048275, 0.00617041764780879, 0.03152871131896973, -0.02637828327715397, -0.014885753393173218, 0.014512094669044018, -0.029508937150239944, 0.019581735134124756, -0.0339120477437973, 0.030781395733356476, 0.02020786516368389, 0.04083988443017006, 0.00678644934669137, 0.012189351953566074, -0.011017881333827972, 0.0024792756885290146, -0.007644854485988617, -0.0029968435410410166, 0.011401639319956303, 0.029731111600995064, 0.020308854058384895, 0.008836522698402405, 0.020076580345630646, 0.019309064373373985, 0.029529133811593056, 0.01866273581981659, -0.008649693801999092, 0.012552911415696144, 0.023570792749524117, 0.00579675892367959, -0.005503891035914421, -0.04225372523069382, 0.013381020165979862, 0.010563431307673454, -0.03837575390934944, -0.002653481438755989, 0.00741258030757308, 0.02666105143725872, -0.020076580345630646, -0.024075737223029137, -0.05606899783015251, -0.024782659485936165, 0.006453186273574829, -0.022278135642409325, -0.05206984281539917, 0.013158844783902168, 0.07040940970182419, 0.027933510020375252, -0.034295808523893356, 0.011310748755931854, 0.030741000548005104, -0.03815358132123947, 0.03092277981340885, 0.027226589620113373, 0.01383547019213438, 0.004703554790467024, 0.05647295340895653, -0.016834838315844536, 0.0014176307013258338, -0.025832943618297577, -0.006488532293587923, -0.032740578055381775, 0.002916052471846342, 0.052877750247716904, 0.041243840008974075, 0.0043829153291881084, 0.036739736795425415, -0.012179252691566944, -0.016824739053845406, -0.02866063080728054, -0.010134229436516762, -0.0019112136214971542, 0.0048828101716935635, -0.04152660816907883, -0.03257899731397629, -0.06471364200115204, 0.02488364838063717, 0.027489159256219864, -0.023045651614665985, -0.0038072788156569004, 0.008265935815870762, -0.062128327786922455, -0.03455837815999985, -0.02514621801674366, 0.017269089818000793, -0.007129811216145754, -0.0013658739626407623, 0.008139699697494507, 0.013754678890109062, -0.03011486865580082, 0.042213331907987595, -0.026297491043806076, 0.0368003286421299, 0.047424353659152985, -0.056190185248851776, 0.024257516488432884, -0.04075909033417702, -0.035750046372413635, 0.0026307590305805206, 0.026701446622610092, -0.031266141682863235, 0.02488364838063717, 0.00410772068426013, 0.029327156022191048, 0.014794863760471344, -0.01743067242205143, 0.024722065776586533, 0.03112475760281086, -0.017026716843247414, 0.03684072569012642, -0.018824318423867226, -0.01207826379686594, -0.014259622432291508, -0.03877970948815346, 0.00573111604899168, 0.017329683527350426, -0.003135703271254897, -0.03976939991116524, 0.01744077168405056, 0.03304354473948479, -0.03411402553319931, 0.04754554107785225, 0.009068797342479229, -0.03465936705470085, 0.02363138645887375, -0.006761202123016119, -0.026580261066555977, -0.03441699221730232, -0.012936669401824474, -0.029185771942138672, -0.008508308790624142, 0.035467278212308884, -0.00185314507689327, 0.02516641654074192, -0.013148745521903038, 0.004006731789559126, -0.027731532230973244, 0.031003570184111595, -0.021591411903500557, 0.0239141546189785, -0.0424153096973896, 0.0120984623208642, -0.03320512920618057, -0.031003570184111595, 0.046697236597537994, 0.03286176547408104, 0.031225746497511864, -0.010432146489620209, 0.0231668371707201, -0.026257095858454704, -0.014027348719537258, 0.01913738250732422, 0.01333052571862936, -0.010775508359074593, 0.046495258808135986, -0.00021838834800291806, 0.009119291789829731, -0.026782236993312836, 0.00944750476628542, -0.033003151416778564, -0.0523122139275074, 0.02070271037518978, -0.009452554397284985, -0.042940448969602585, 0.024580681696534157, -0.004337470047175884, -0.04189016669988632, -0.02413633093237877, -0.02415652759373188, -0.05215063318610191, -0.003751734970137477, -0.023712176829576492, -0.03237701952457428, -0.0502520427107811, -0.0029286760836839676, 0.051181137561798096, 0.007139910478144884, 0.01889500953257084, 0.031851876527071, 0.005407951772212982, -0.023772770538926125, 0.01866273581981659, -0.04330401122570038, -0.005102460738271475, -0.024701867252588272, 0.008927412331104279, -0.0031331784557551146, 0.014714072458446026, 0.00478939525783062, 0.0102301687002182, 0.013613294810056686, 0.014633281156420708, 0.028539443388581276, -0.008493160828948021, 0.025853140279650688, -0.026459073647856712 ]
In recent years, much work has been done on processing of wireless spectrum data involving machine learning techniques in domain-related problems for cognitive radio networks, such as anomaly detection, modulation classification, technology classification and device fingerprinting. Most of the solutions are based on labeled data, created in a controlled manner and processed with supervised learning approaches. However, spectrum data measured in real-world environment is highly nondeterministic, making its labeling a laborious and expensive process, requiring domain expertise, thus being one of the main drawbacks of using supervised learning approaches in this domain. In this paper, we investigate the use of self-supervised learning (SSL) for exploring spectrum activities in a real-world unlabeled data. In particular, we compare the performance of two SSL models, one based on a reference DeepCluster architecture and one adapted for spectrum activity identification and clustering, and a baseline model based on K-means clustering algorithm. We show that SSL models achieve superior performance regarding the quality of extracted features and clustering performance. With SSL models we achieve reduction of the feature vectors size by two orders of magnitude, while improving the performance by a factor of 2 to 2.5 across the evaluation metrics, supported by visual assessment. Additionally we show that adaptation of the reference SSL architecture to the domain data provides reduction of model complexity by one order of magnitude, while preserving or even improving the clustering performance.
[ 0.02767021395266056, -0.016561411321163177, -0.025404194369912148, -0.0114097585901618, 0.05608396604657173, 0.04967537894845009, -0.014835341833531857, 0.01348104141652584, -0.03710605576634407, -0.010312155820429325, -0.006426287814974785, -0.0523308701813221, -0.007262767292559147, -0.053747132420539856, 0.021509474143385887, -0.006390881258994341, 0.011613345704972744, -0.026519501581788063, -0.03930126130580902, -0.05318062752485275, 0.03682280331850052, -0.05024188384413719, -0.05413660407066345, -0.004007577896118164, -0.009869573637843132, 0.013773145154118538, 0.029953936114907265, 0.035034775733947754, -0.1380855143070221, 0.012259515933692455, 0.020801344886422157, -0.007236212491989136, -0.02519175596535206, 0.012232961133122444, -0.021102299913764, -0.013728886842727661, -0.004686940927058458, 0.019969290122389793, 0.019845368340611458, -0.003724325681105256, 0.02834293805062771, -0.04149646684527397, -0.008409054018557072, -0.011701862327754498, 0.030644362792372704, -0.05172896012663841, -0.07994797080755234, -0.036964431405067444, -0.041106995195150375, -0.04836533963680267, -0.030237188562750816, -0.04638257250189781, -0.014029842801392078, -0.03128167986869812, -0.04270029067993164, 0.025793666020035744, 0.04418736696243286, 0.00860378984361887, -0.002469606464728713, 0.011896598152816296, 0.017251837998628616, 0.011781527660787106, -0.045001715421676636, -0.003044962650164962, -0.002325767418369651, -0.012666691094636917, -0.020942971110343933, -0.06022652983665466, 0.0576772578060627, -0.003306085942313075, -0.06624564528465271, 0.006408584304153919, -0.008063839748501778, 0.02786494977772236, 0.013374821282923222, 0.04043427109718323, -0.03540654480457306, -0.0017614755779504776, -0.005306555889546871, -0.012755206786096096, 0.02890944294631481, -0.02011091634631157, 0.0013299583224579692, 0.01770327240228653, 0.04298354312777519, 0.028431454673409462, 0.0015656331088393927, -0.06089925393462181, 0.0542428232729435, -0.013675777241587639, -0.0357074998319149, 0.003405666910111904, 0.0004190696345176548, 0.06794515997171402, 0.0072760446928441525, 0.030219484120607376, -0.009444694966077805, -0.03923045098781586, -0.048400744795799255, 0.030892208218574524, -0.040611304342746735, -0.036999836564064026, -0.010179380886256695, -0.01469371560961008, 0.0006893211393617094, -0.029228100553154945, -0.04953375458717346, 0.055942337960004807, -0.0150389289483428, 0.1178329735994339, 0.044966310262680054, -0.0002466010337229818, 0.03126397728919983, -0.007824845612049103, -0.008488718420267105, 0.0008934619836509228, -0.019084127619862556, -0.0920570120215416, -0.013498744927346706, 0.010666221380233765, 0.024200372397899628, 0.0729374811053276, -0.015800170600414276, -0.010754737071692944, -0.07768195867538452, 0.08908285945653915, 0.02958216704428196, 0.029759200289845467, 0.002808181568980217, 0.009887277148663998, -0.019473599269986153, -0.03158263489603996, -0.006957385689020157, 0.012427696958184242, 0.00898441020399332, 0.05378253757953644, 0.03834528475999832, 0.033813249319791794, 0.0133217116817832, -0.03668117895722389, 0.000053455580200534314, 0.058066729456186295, -0.031635746359825134, 0.05148111283779144, 0.0393366701900959, 0.04337301477789879, -0.018145853653550148, 0.06543128937482834, -0.0882331058382988, -0.02037646621465683, 0.006616597529500723, 0.12066549807786942, -0.000026658637580112554, 0.033884063363075256, 0.009444694966077805, 0.025846775621175766, 0.003441073466092348, -0.048188306391239166, 0.017659014090895653, -0.024873096495866776, 0.05944758653640747, -0.07230015844106674, 0.04248785227537155, 0.057854291051626205, 0.029989341273903847, 0.04836533963680267, 0.0005947192548774183, -0.01785374991595745, -0.058845676481723785, 0.0548093281686306, -0.008568383753299713, -0.02326209843158722, 0.01966833509504795, -0.005682750139385462, 0.024572141468524933, 0.008621493354439735, -0.007815994322299957, -0.015056632459163666, -0.025333382189273834, -0.008267427794635296, -0.03390176594257355, 0.12264826893806458, 0.0036822804249823093, -0.00006407062755897641, 0.0490734688937664, 0.022837219759821892, 0.05994327738881111, -0.005200336221605539, -0.02814820222556591, -0.016393229365348816, -0.008316111750900745, 0.014879600144922733, 0.07116714864969254, -0.01420687511563301, -0.0038460358045995235, -0.007364560849964619, -0.0024651805870234966, 0.07888577878475189, 0.014906154945492744, -0.013596112839877605, -0.05909352004528046, -0.042594071477651596, 0.07407049089670181, -0.006324493791908026, 0.03174196556210518, 0.01613653264939785, 0.05293278023600578, 0.0075415936298668385, -0.01783604547381401, -0.02623624913394451, -0.06305905431509018, 0.010993731208145618, -0.040823742747306824, 0.05360550805926323, 0.037955813109874725, -0.030608955770730972, 0.02450132742524147, -0.01867695152759552, -0.04291272908449173, -0.020270245149731636, 0.04879021644592285, 0.008878191001713276, 0.03271564468741417, -0.004054049029946327, -0.05569449067115784, -0.019951587542891502, 0.025775963440537453, 0.011170764453709126, 0.013587260618805885, -0.003350344253703952, -0.016074569895863533, 0.003965532872825861, -0.021474068984389305, 0.002416496630758047, 0.005129523109644651, -0.009241107851266861, 0.05236627906560898, 0.04730314016342163, -0.00026942166732624173, -0.01913723722100258, -0.015118594281375408, -0.04362086206674576, -0.07860252261161804, -0.06228011101484299, 0.014259985648095608, -0.03301659971475601, 0.012082482688128948, 0.0601557157933712, 0.03784959390759468, 0.030715176835656166, -0.02906877174973488, -0.018623841926455498, -0.041885942220687866, -0.017756382003426552, -0.051020827144384384, 0.03128167986869812, 0.012392289936542511, -0.05842079594731331, 0.013728886842727661, -0.08448000997304916, 0.05629640445113182, -0.027971168980002403, -0.009267662651836872, 0.040823742747306824, -0.03338836878538132, 0.011232726275920868, 0.032396987080574036, 0.006280235480517149, -0.003750880714505911, -0.0017404528334736824, -0.030361110344529152, -0.0005687176017090678, -0.059058114886283875, 0.03161804378032684, -0.0021221796050667763, -0.036964431405067444, 0.029953936114907265, -0.027333851903676987, -0.030414219945669174, 0.04386870563030243, -0.020730530843138695, -0.02450132742524147, 0.03326444700360298, -0.014136062003672123, -0.017906859517097473, -0.02331520803272724, -0.021155409514904022, -0.03105153888463974, -0.020022399723529816, 0.025775963440537453, -0.029776902869343758, -0.06999873369932175, -0.014897302724421024, 0.030697472393512726, 0.006837888620793819, -0.015021226368844509, -0.009134887717664242, -0.02499702014029026, 0.019243456423282623, -0.010276748798787594, -0.03961992263793945, 0.016570262610912323, 0.03370703011751175, 0.036504145711660385, -0.03174196556210518, -0.005532272160053253, 0.018818577751517296, 0.01115306094288826, -0.03420272096991539, -0.037247683852910995, -0.022500857710838318, 0.012569323182106018, -0.00151362968608737, -0.02421807497739792, -0.03544194996356964, 0.021403254941105843, 0.03827447444200516, 0.031210867688059807, -0.00981646403670311, -0.04949834570288658, 0.01202052179723978, 0.056154776364564896, -0.08724172413349152, 0.030892208218574524, -0.018517622724175453, -0.013534151017665863, 0.05293278023600578, 0.04323139041662216, -0.047905053943395615, 0.021403254941105843, -0.039407484233379364, 0.045462001115083694, -0.0218635406345129, 0.029281212016940117, 0.04167350009083748, 0.01202052179723978, -0.0364687405526638, 0.08525895327329636, 0.01672959141433239, -0.005952725186944008, -0.0041115847416222095, -0.02131473831832409, -0.04510793462395668, -0.027298444882035255, 0.009772205725312233, -0.003376899054273963, -0.028449157252907753, -0.0026001681108027697, 0.0032994472421705723, 0.00946239847689867, 0.0008984410087577999, -0.018092744052410126, 0.005970428232103586, -0.03345918282866478, 0.012126740999519825, -0.03707065060734749, -0.0792398452758789, -0.013489892706274986, -0.004855122417211533, 0.005381794646382332, 0.012463103048503399, -0.05817294865846634, -0.05070216953754425, 0.00043843258754350245, -0.048400744795799255, 0.027758730575442314, -0.019013313576579094, 0.0035893383901566267, 0.012153295800089836, 0.03468070924282074, -0.013392524793744087, -0.0036402351688593626, 0.014233429916203022, -0.027971168980002403, -0.05937677249312401, 0.040823742747306824, 0.005036580841988325, -0.0036690030246973038, 0.003171098418533802, 0.034061092883348465, -0.008351518772542477, 0.042346224188804626, -0.013507596217095852, 0.007550445385277271, -0.0012823807774111629, 0.05739400535821915, -0.0157559122890234, 0.02906877174973488, -0.019031016156077385, 0.049108874052762985, 0.015092039480805397, -0.01019708439707756, -0.036026157438755035, -0.045497406274080276, 0.061253320425748825, 0.002967510838061571, -0.026271654292941093, 0.0050233034417033195, 0.026076918467879295, -0.0037575194146484137, -0.028449157252907753, 0.008634770289063454, -0.03469841182231903, 0.013419079594314098, -0.039655327796936035, 0.00734243169426918, -0.010276748798787594, -0.035760607570409775, -0.0038792293053120375, 0.010471485555171967, 0.02570515125989914, -0.018871687352657318, -0.018553027883172035, 0.08214318007230759, 0.012648987583816051, 0.0620676688849926, -0.03558357432484627, 0.012303773313760757, 0.01961522549390793, -0.011560236103832722, -0.0049259355291724205, 0.00648824917152524, 0.10735263675451279, -0.016570262610912323, -0.004390411544591188, 0.04270029067993164, -0.007028198800981045, -0.03326444700360298, 0.013764293864369392, -0.021704211831092834, 0.03082139603793621, 0.0683700367808342, -0.02182813361287117, -0.04245244711637497, -0.019703742116689682, -0.0011905450373888016, -0.028714707121253014, 0.00994923897087574, -0.037955813109874725, -0.03657495975494385, 0.0017935626674443483, -0.018305182456970215, -0.04415195807814598, -0.03225535899400711, -0.06557291746139526, -0.0073380060493946075, -0.015384143218398094, -0.0156585443764925, -0.004102732986211777, -0.00786910392343998, -0.07739870250225067, 0.020305652171373367, -0.11181386560201645, -0.009187998250126839, 0.07407049089670181, -0.03816825523972511, 0.00691312737762928, -0.035760607570409775, 0.021509474143385887, -0.008528551086783409, 0.03377784043550491, 0.03653955087065697, 0.011719565838575363, -0.013534151017665863, -0.03707065060734749, 0.04903806373476982, -0.030007045716047287, -0.04202756658196449, -0.004682515282183886, 0.030715176835656166, 0.025351084768772125, -0.07435373961925507, -0.007355709560215473, 0.059058114886283875, -0.00013187553850002587, 0.02671423740684986, -0.008121375925838947, -0.08448000997304916, -0.007501761429011822, -0.015065483748912811, 0.019792256876826286, 0.014419314451515675, -0.022925736382603645, -0.005434904247522354, 0.020217135548591614, 0.002209589583799243, 0.004554166458547115, 0.04542659595608711, 0.024448217824101448, -0.013781997375190258, 0.03101613186299801, 0.036504145711660385, -0.036220893263816833, 0.003047175705432892, 0.000016069521734607406, 0.004762180149555206, -0.0006196144968271255, -0.042062971740961075, 0.08759579062461853, 0.014463572762906551, -0.006705114152282476, -0.014118359424173832, 0.0387701652944088, -0.02813049778342247, -0.042558666318655014, -0.009480101987719536, 0.019827663898468018, -0.003914636094123125, -0.00522246491163969, 0.03561898320913315, 0.025174051523208618, 0.024873096495866776, 0.004748902749270201, -0.06851165741682053, 0.0014583070296794176, 0.05466770380735397, -0.03145871311426163, -0.016428636386990547, -0.0031157757621258497, 0.030750581994652748, 0.0027949039358645678, -0.009825315326452255, 0.005049858242273331, 0.03273335099220276, -0.05534042790532112, 0.011312390677630901, 0.05211843177676201, -0.015605433844029903, 0.016340119764208794, -0.038911789655685425, -0.026041513308882713, -0.026767347007989883, -0.046913668513298035, -0.06351933628320694, -0.0065988944843411446, 0.027581697329878807, 0.028466859832406044, 0.041815128177404404, -0.007307025138288736, -0.021155409514904022, -0.003779648570343852, 0.0322730652987957, 0.0004364962805993855, 0.0031069242395460606, -0.000373981602024287, 0.009630579501390457, 0.0132243437692523, -0.0065988944843411446, 0.037991221994161606, -0.019208049401640892, -0.002467393409460783, 0.008099246770143509, -0.044010333716869354, 0.009896128438413143, -0.045249562710523605, -0.032874975353479385, 0.011870043352246284, -0.0062935128808021545, -0.028024278581142426, -0.03291038051247597, -0.024412810802459717, 0.016242751851677895, 0.03422042354941368, -0.010878660716116428, 0.0165171530097723, -0.019933883100748062, 0.02136784791946411, 0.0601557157933712, 0.012082482688128948, 0.016809256747364998, -0.011144209653139114, 0.0015545685309916735, -0.02526256814599037, -0.017446573823690414, -0.028431454673409462, -0.0004270914359949529, 0.0364687405526638, -0.008639196865260601, 0.023102769628167152, 0.009860722348093987, 0.015322181396186352, -0.012312625534832478, 0.048613183200359344, 0.025652039796113968, 0.035778310149908066, 0.008904745802283287, 0.007253915537148714, -0.0078071425668895245, 0.026289358735084534, -0.02908647432923317, -0.02379319630563259, 0.03682280331850052, -0.03802662715315819, -0.010621963068842888, -0.0368582122027874, 0.010117419995367527, -0.011648752726614475, -0.026023808866739273, 0.03400798514485359, -0.03253861144185066, 0.03253861144185066, 0.030608955770730972, 0.0076743680983781815, 0.02035876177251339, 0.02959986962378025, -0.02232382632791996, 0.01274635549634695, -0.04422277212142944, 0.00410052016377449, 0.032131437212228775, 0.038663946092128754, 0.03011326491832733, 0.0256874468177557, -0.016888920217752457, 0.019827663898468018, 0.009958090260624886, 0.05512798950076103, 0.028254421427845955, 0.004346153233200312, -0.033335261046886444, 0.039442889392375946, -0.03466300666332245, 0.00838249921798706, -0.023686977103352547, 0.016508299857378006, 0.0070724571123719215, -0.005970428232103586, -0.021173112094402313, 0.008165634237229824, -0.013905920088291168, -0.03468070924282074, -0.004385985434055328, -0.018535325303673744, -0.006337771192193031, -0.041602689772844315, -0.009984645061194897, 0.015472658909857273, 0.03253861144185066, 0.0019562114030122757, -0.006408584304153919, 0.01785374991595745, 0.019243456423282623, -0.021509474143385887, 0.03255631774663925, -0.0011706288205459714, 0.022129088640213013, -0.06139494478702545, -0.008462163619697094, 0.048400744795799255, 0.029652979224920273, 0.04390411451458931, 0.026767347007989883, 0.007599129341542721, 0.017287245020270348, -0.051799774169921875, 0.002914401004090905, 0.04092996567487717, 0.033335261046886444, 0.012764059007167816, 0.03961992263793945, 0.031918998807668686, -0.012029373086988926, 0.01382625475525856, -0.004390411544591188, 0.007754032965749502, -0.005691601894795895, -0.007214083336293697, 0.022837219759821892, 0.0020768151152879, 0.027741026133298874, -0.015428401529788971, -0.03880557045340538, -0.024306591600179672, 0.015649691224098206, 0.0528973750770092, -0.040894556790590286, 0.014445869252085686, -0.007767310366034508, -0.004109371919184923, -0.029529057443141937, -0.028944849967956543, -0.003832758404314518, 0.0184291061013937, 0.0033547698985785246, -0.006178441923111677, -0.006227125879377127, -0.0063643259927630424, 0.02834293805062771, -0.03368932753801346, -0.036504145711660385, -0.04726773500442505, 0.00872771255671978, 0.029458243399858475, -0.021049190312623978, 0.03852231800556183, 0.022872626781463623, -0.030980724841356277, 0.025351084768772125, -0.007152121514081955, 0.030927615240216255, -0.0035672092344611883, 0.02230612188577652, 0.005611937027424574, 0.035512764006853104, 0.015578879043459892, 0.033848654478788376, 0.009878425858914852, 0.010887512005865574, -0.005049858242273331, -0.0016895559383556247, -0.029741495847702026, 0.03901800885796547, 0.010524595156311989, 0.023120472207665443, 0.061040882021188736, -0.009249959141016006, 0.005775692407041788, -0.011330094188451767, -0.00198829872533679, 0.006979514844715595, -0.03161804378032684, 0.030626660212874413, 0.00035987430601380765, -0.07191068679094315, -0.002648852067068219, 0.027493180707097054, -0.013401377014815807, 0.026979785412549973, 0.00014397739141713828, 0.0059305960312485695, 0.03172426298260689, -0.03947829455137253, -0.004859548062086105, 0.002573613077402115, 0.03749552741646767, -0.007112289313226938, -0.034114204347133636, 0.025634337216615677, -0.030467329546809196, -0.04146106168627739, 0.003020620672032237, -0.02326209843158722, 0.030042452737689018, 0.014729121699929237, -0.024572141468524933, 0.013622667640447617, 0.029210397973656654, 0.008767545223236084, -0.04687826335430145, -0.006386455148458481, 0.010285601019859314, -0.05431363731622696, 0.024377405643463135, -0.02890944294631481, 0.008386924862861633, 0.04241703823208809, 0.005846505519002676, 0.003901358461007476, 0.0022217605728656054, 0.029759200289845467, -0.01102913822978735, 0.013596112839877605, 0.015003522858023643, -0.014029842801392078, 0.004073965363204479, 0.00036125737824477255, -0.059022706001996994, -0.006112054456025362, 0.01580902189016342, -0.0009227830450981855, 0.07739870250225067, -0.023102769628167152, 0.05679209530353546, -0.07169824838638306, 0.025528118014335632, 0.013047311455011368, -0.006749372463673353, 0.007174250669777393, 0.0024718192871659994, -0.0015401846030727029, -0.03032570332288742, 0.020234839990735054, -0.03386635705828667, 0.05013566464185715, -0.032874975353479385, 0.0018345015123486519, 0.01864154450595379, -0.01456094067543745, -0.012914536520838737, 0.0310338344424963, 0.0007828165544196963, -0.01344563439488411, 0.002220654161646962, -0.030520441010594368, 0.030042452737689018, -0.005603085272014141, -0.026289358735084534, 0.045497406274080276, -0.04436440020799637, -0.04617013409733772, 0.008648048155009747, 0.0025868904776871204, -0.01795111782848835, 0.025616634637117386, -0.004735625348985195, -0.03880557045340538, -0.004806438460946083, -0.02694438025355339, -0.01963292807340622, 0.010152826085686684, 0.034061092883348465, 0.010577704757452011, 0.0051914844661951065, 0.019809961318969727, -0.004516547080129385, -0.02883862890303135, -0.015649691224098206, -0.002451903186738491, -0.028750112280249596, -0.030024748295545578, -0.013339415192604065, 0.0053242589347064495, -0.009550915099680424, -0.00908177811652422, -0.04677204415202141, 0.019473599269986153, -0.002084560226649046, -0.01888938993215561, 0.016437487676739693, 0.007191954180598259, 0.01961522549390793, 0.010409523732960224, 0.018853984773159027, 0.054172009229660034, -0.023722384124994278, 0.017641309648752213, 0.007165399380028248, 0.039690736681222916, 0.02713911607861519, -0.0025802517775446177, -0.013897067867219448, -0.007630110252648592, 0.02696208283305168, -0.032131437212228775, -0.0010057671461254358, -0.009187998250126839, -0.040398865938186646, 0.013489892706274986, 0.043974924832582474, -0.010577704757452011, 0.029971638694405556, 0.029174990952014923, 0.04652419686317444, 0.03006015531718731, -0.0412486232817173, 0.02423577941954136, -0.02591758966445923, 0.009382734075188637, -0.010825550183653831, -0.012861426919698715, 0.051551926881074905, -0.0001322213065577671, 0.0008270746911875904, 0.02182813361287117, 0.0015523555921390653, 0.0005803353851661086, 0.0026156583335250616, -0.0485069639980793, 0.006576765328645706, -0.052755750715732574, 0.027528587728738785, -0.011294687166810036, -0.012471955269575119, 0.0033260020427405834, 0.020004697144031525, 0.03485774248838425, -0.027528587728738785, 0.009426992386579514, -0.0008397989440709352, -0.035813719034194946, -0.009878425858914852, 0.029475947842001915, 0.028679300099611282, -0.003921274561434984, 0.05502176657319069, -0.009577469900250435, -0.019261159002780914, -0.032874975353479385, 0.02575826086103916, -0.019526708871126175, -0.016198493540287018, 0.029228100553154945, -0.005899615120142698, 0.014968115836381912, 0.02784724533557892, 0.02786494977772236, -0.02181043103337288, -0.008165634237229824, 0.018110446631908417, 0.006479397416114807, -0.019261159002780914, -0.022164495661854744, -0.0066697075963020325, -0.02474917285144329, 0.04022183269262314, 0.023722384124994278, -0.004045197740197182, 0.005532272160053253, -0.015003522858023643, -0.004051836207509041, -0.02984771504998207, -0.027794135734438896, 0.010657369159162045, -0.01674729585647583, 0.037955813109874725, 0.0046559604816138744, 0.012640136294066906, -0.014950413256883621, 0.024572141468524933, 0.005271149333566427, 0.05438445135951042, 0.020234839990735054, -0.0353357307612896, 0.023846305906772614, -0.030485033988952637, 0.0022140154615044594, 0.03434434533119202, 0.0011728417593985796, -0.008519699797034264, 0.00045890198089182377, -0.00820104032754898, 0.020093213766813278, 0.06773271411657333, 0.004007577896118164, 0.030608955770730972, 0.014968115836381912, 0.01395902968943119, 0.03816825523972511, -0.03738930821418762, -0.020217135548591614, 0.00242313533090055, 0.0023478963412344456, -0.02011091634631157, -0.023651570081710815, 0.01674729585647583, -0.012781762517988682, 0.051551926881074905, 0.0008265214855782688, -0.01105569303035736, 0.004281978588551283, -0.03011326491832733, -0.018747763708233833, -0.004200101364403963, 0.0035362285561859608, -0.008895893581211567, -0.060722220689058304, -0.036291707307100296, 0.005545550025999546, -0.023155879229307175, -0.0007429841789416969, 0.026749642565846443, 0.043266795575618744, -0.040611304342746735, 0.020500387996435165, 0.012188702821731567, 0.04762180149555206, -0.04266488552093506, -0.030007045716047287, -0.028219014406204224, 0.010436078533530235, 0.0175704974681139, -0.04578065872192383, -0.00007185038703028113, 0.013737739063799381, -0.0151362968608737, -0.02522716112434864, -0.013091569766402245, -0.02350994385778904, -0.0018865049351006746, -0.012781762517988682, -0.01029445230960846, 0.009922684170305729, -0.023474538698792458, -0.02181043103337288, 0.010241342708468437, -0.041106995195150375, 0.05236627906560898, -0.02402333915233612, -0.02545730397105217, 0.026519501581788063, 0.001647510682232678, -0.0070104957558214664, 0.0500294454395771, 0.02012861892580986, -0.044753871858119965, -0.015915241092443466, -0.0016054654261097312, -0.032627128064632416, -0.03328214958310127, 0.009789909236133099, -0.03198981285095215, -0.014401611872017384, 0.01640208065509796, 0.005775692407041788, 0.01991618052124977, -0.027705619111657143, -0.0015645265812054276, -0.05027729272842407, -0.027457773685455322, 0.015543472021818161, 0.013489892706274986, -0.0074707805179059505, -0.03540654480457306, 0.02156258560717106, 0.02448362484574318, 0.03583142161369324, 0.0029453819151967764, -0.0037730098702013493, 0.04464765265583992, -0.018623841926455498, -0.009798760525882244, -0.046913668513298035, 0.01867695152759552, 0.015304477885365486 ]
Prompt-based learning has emerged as a successful paradigm in natural language processing, where a single general-purpose language model can be instructed to perform any task specified by input prompts. Yet task specification in robotics comes in various forms, such as imitating one-shot demonstrations, following language instructions, and reaching visual goals. They are often considered different tasks and tackled by specialized models. We show that a wide spectrum of robot manipulation tasks can be expressed with multimodal prompts, interleaving textual and visual tokens. Accordingly, we develop a new simulation benchmark that consists of thousands of procedurally-generated tabletop tasks with multimodal prompts, 600K+ expert trajectories for imitation learning, and a four-level evaluation protocol for systematic generalization. We design a transformer-based robot agent, VIMA, that processes these prompts and outputs motor actions autoregressively. VIMA features a recipe that achieves strong model scalability and data efficiency. It outperforms alternative designs in the hardest zero-shot generalization setting by up to $2.9\times$ task success rate given the same training data. With $10\times$ less training data, VIMA still performs $2.7\times$ better than the best competing variant. Code and video demos are available at https://vimalabs.github.io/
[ -0.003349812002852559, -0.02664971724152565, -0.031168825924396515, -0.023599784821271896, 0.016532868146896362, 0.01582617498934269, -0.000940899655688554, 0.032396238297224045, -0.0443728044629097, 0.057502392679452896, 0.011195485480129719, -0.021237947046756744, 0.03219166770577431, -0.039537545293569565, -0.02575705572962761, 0.0532994344830513, 0.011502338573336601, 0.012850631959736347, -0.05110497400164604, -0.004960790276527405, -0.029309110715985298, -0.0037496506702154875, -0.05869261175394058, -0.018141521140933037, 0.03470228612422943, -0.0014703372726216912, 0.014812631532549858, -0.003775221761316061, -0.01997334137558937, 0.02722623012959957, 0.004272695630788803, 0.014431389980018139, 0.00887084100395441, 0.03247062489390373, 0.013278366066515446, 0.05653534084558487, 0.012580973096191883, 0.06836313009262085, -0.07059478759765625, 0.029476484283804893, 0.008238538168370724, -0.028286267071962357, 0.001764404703862965, -0.05162569135427475, -0.03979790583252907, -0.014422090724110603, -0.008419860154390335, -0.03492544963955879, 0.01047949492931366, 0.05032389238476753, 0.045005105435848236, -0.041657619178295135, 0.08435668051242828, 0.0072156949900090694, -0.002054985146969557, 0.04481913521885872, 0.015705294907093048, -0.024827197194099426, 0.07420263439416885, -0.030387746170163155, -0.02711464650928974, 0.018755227327346802, -0.05315065756440163, -0.03537178039550781, 0.016439881175756454, -0.030815480276942253, 0.06215168163180351, -0.005355979781597853, 0.02430647611618042, -0.011093201115727425, 0.01908067800104618, -0.01683042198419571, -0.0747605487704277, -0.052592743188142776, 0.009191642515361309, 0.0061556571163237095, 0.03427455201745033, -0.002259553875774145, 0.013455038890242577, -0.0012332235928624868, 0.035520561039447784, 0.013808384537696838, 0.0638626217842102, -0.03890524059534073, 0.09410158544778824, -0.062412042170763016, 0.006681026890873909, -0.05255554988980293, -0.0007775934063829482, -0.06523881107568741, 0.009791400283575058, 0.02642655186355114, -0.01674673520028591, 0.035297393798828125, -0.01694200560450554, 0.012925020419061184, -0.006230045575648546, -0.007476055063307285, -0.04180639609694481, -0.0015702969394624233, 0.032600805163383484, -0.042996615171432495, 0.03265659883618355, -0.03360505402088165, 0.03961193189024925, -0.019136467948555946, -0.0446331650018692, -0.006002230569720268, -0.05958527326583862, 0.0831664577126503, 0.004970088601112366, -0.023711368441581726, 0.01973157748579979, 0.006555495783686638, -0.010739854536950588, 0.0054815104231238365, -0.03938876837491989, -0.0775873139500618, 0.021275142207741737, -0.06996248662471771, -0.009819296188652515, 0.0399094857275486, -0.0029894921462982893, -0.05240677297115326, -0.04619532451033592, 0.04080215096473694, -0.013241171836853027, 0.010944423265755177, 0.02430647611618042, 0.041211288422346115, 0.022893093526363373, 0.0513281375169754, -0.025347918272018433, 0.045228272676467896, 0.061630960553884506, -0.01908067800104618, -0.02120075188577175, 0.016988497227430344, -0.02856522426009178, -0.01684901863336563, -0.05456404387950897, 0.01581687666475773, 0.013901370577514172, 0.016783928498625755, -0.014468584209680557, 0.007369121070951223, 0.013854878023266792, 0.11128535121679306, -0.0015121808974072337, 0.007671325001865625, -0.03648761287331581, -0.007271486334502697, -0.0021165884099900723, 0.03799397870898247, 0.030034400522708893, 0.005546600557863712, -0.008201343938708305, 0.057056061923503876, 0.02555248700082302, 0.016672346740961075, 0.09715151786804199, -0.058618221431970596, -0.019136467948555946, 0.02452964335680008, 0.05475001409649849, -0.003691534511744976, 0.04764590039849281, 0.029271915555000305, -0.023804353550076485, 0.044000860303640366, -0.025850040838122368, 0.033065736293792725, 0.0037543000653386116, -0.03747326135635376, 0.015203171409666538, 0.008052567020058632, -0.0005823232932016253, 0.014078043401241302, -0.03274958208203316, -0.011418650858104229, -0.02107057347893715, 0.0032173071522265673, 0.00577441556379199, 0.05839505419135094, 0.03237764164805412, 0.10287944227457047, 0.05344821512699127, -0.019452620297670364, 0.010544585064053535, -0.028806988149881363, -0.006188202183693647, 0.02252115122973919, -0.018336791545152664, 0.01215323805809021, -0.02086600475013256, -0.04560021683573723, -0.019898952916264534, 0.032080087810754776, 0.004465640988200903, 0.043442945927381516, -0.02899295836687088, -0.023134855553507805, 0.018597152084112167, 0.019341036677360535, 0.0032289305236190557, 0.025738457217812538, -0.052369579672813416, -0.027133243158459663, 0.0524439662694931, -0.057613976299762726, 0.013826982118189335, -0.05869261175394058, -0.018234506249427795, -0.04597215726971626, -0.013008707202970982, -0.045786187052726746, -0.029588067904114723, -0.025812845677137375, -0.030722495168447495, -0.052592743188142776, -0.014812631532549858, 0.0188389141112566, -0.012450792826712132, -0.03812415897846222, -0.053262241184711456, -0.036654986441135406, -0.0010542260715737939, -0.04013265296816826, -0.02811889350414276, 0.05906455218791962, -0.00396119337528944, 0.01153953280299902, 0.04697640612721443, -0.04649287834763527, 0.01773238368332386, -0.005514055490493774, 0.023488203063607216, -0.012478688731789589, -0.02798871323466301, 0.05687008798122406, 0.03157796338200569, -0.021275142207741737, 0.008847595192492008, -0.004470290150493383, 0.0714130625128746, 0.04191797971725464, 0.04448438808321953, 0.023729965090751648, 0.016979198902845383, -0.007290083449333906, -0.005011932458728552, 0.0031243213452398777, -0.036840956658124924, 0.04850137233734131, -0.0006020827568136156, 0.05512195825576782, 0.0524439662694931, -0.006485756486654282, -0.016123730689287186, 0.015593711286783218, -0.013324858620762825, 0.068325936794281, 0.04641849175095558, 0.03168954700231552, 0.024362267926335335, -0.025943025946617126, 0.018476270139217377, -0.004663235507905483, 0.03583671152591705, 0.005718624219298363, -0.02041967213153839, -0.021907445043325424, -0.03010878898203373, 0.009173044934868813, -0.018336791545152664, -0.038198549300432205, 0.004942193161696196, 0.04664165526628494, 0.034962642937898636, -0.031038645654916763, 0.051588498055934906, -0.015314754098653793, 0.03691534698009491, 0.023953130468726158, -0.0010205187136307359, -0.041992366313934326, 0.011827788315713406, 0.020010534673929214, -0.05954807996749878, 0.03780800849199295, -0.0019096949836239219, 0.014143133535981178, -0.010228433646261692, 0.0017992743523791432, 0.05422929301857948, -0.030610911548137665, -0.03935157135128975, -0.005737221334129572, 0.05266713351011276, 0.0017446452984586358, -0.030741091817617416, -0.015472830273211002, 0.008257134817540646, 0.0026431202422827482, -0.04139725863933563, 0.01460806280374527, -0.03157796338200569, 0.04247589409351349, -0.006099865771830082, -0.029625263065099716, 0.00020151757053099573, 0.009210239164531231, -0.033958397805690765, -0.030480731278657913, 0.014375598169863224, 0.06263520568609238, 0.034981243312358856, -0.011241978034377098, -0.03470228612422943, 0.0005919124814681709, 0.0005460007232613862, 0.002966245636343956, -0.08896877616643906, 0.04716237634420395, 0.032842569053173065, 0.032842569053173065, 0.03100145235657692, -0.014245417900383472, 0.011874280869960785, -0.03427455201745033, -0.0580231137573719, -0.07632271200418472, -0.009168395772576332, 0.008164149709045887, 0.010693361982703209, -0.02856522426009178, -0.018420478329062462, 0.013231873512268066, -0.0691814050078392, -0.03546476736664772, -0.05698167160153389, -0.019034184515476227, 0.01997334137558937, -0.04206675663590431, 0.01774168200790882, -0.048129428178071976, -0.006787960417568684, 0.036283042281866074, -0.02252115122973919, -0.02354399301111698, 0.0010757290292531252, -0.028751196339726448, 0.013176081702113152, -0.023395216092467308, 0.028955765068531036, -0.043331362307071686, -0.034497715532779694, -0.02252115122973919, -0.04738554358482361, 0.030406342819333076, -0.010358612984418869, -0.08100919425487518, -0.06389981508255005, 0.026724107563495636, -0.06073829531669617, -0.04597215726971626, -0.03946315497159958, -0.03287976235151291, -0.03581811487674713, -0.015779683366417885, 0.005662832409143448, -0.0063834721222519875, 0.009856490418314934, 0.009517092257738113, 0.00010482691141078249, -0.00470972852781415, -0.008754609152674675, -0.04716237634420395, -0.01782536879181862, 0.06620585918426514, -0.027133243158459663, 0.00993087887763977, -0.022056221961975098, -0.0030545820482075214, -0.01371539942920208, 0.09008460491895676, 0.05698167160153389, -0.06330469995737076, -0.03077828511595726, 0.008921983651816845, 0.0532994344830513, -0.009726310148835182, -0.07364472001791, -0.016458479687571526, 0.02555248700082302, -0.0005750588024966419, 0.052146412432193756, -0.053373824805021286, 0.03548336401581764, 0.001072242041118443, -0.025013169273734093, 0.011418650858104229, -0.017239559441804886, 0.028044505044817924, 0.02352539636194706, -0.004858505912125111, 0.017695190384984016, 0.02865821123123169, -0.005151411052793264, -0.0161795224994421, -0.0457489937543869, -0.051476914435625076, -0.020438268780708313, -0.0035985487047582865, 0.02800730988383293, -0.03412577137351036, 0.001369215315207839, -0.0018271701410412788, -0.007541144732385874, -0.0466044619679451, 0.04597215726971626, 0.021609889343380928, 0.03511142358183861, 0.03535318374633789, -0.006085917819291353, 0.033753830939531326, 0.0011913799680769444, 0.019564203917980194, -0.09045654535293579, -0.004565600771456957, 0.08829927444458008, 0.019117871299386024, 0.05099339038133621, -0.011316366493701935, 0.015974953770637512, 0.002757027745246887, -0.01449647918343544, 0.07275205850601196, -0.0065183015540242195, -0.02934630587697029, -0.01048879325389862, 0.004677183460444212, -0.00032545014983043075, -0.01333415787667036, -0.038756463676691055, -0.009744907729327679, -0.0011617408599704504, -0.02017791010439396, 0.013092394918203354, -0.00775501225143671, -0.025682665407657623, 0.027802741155028343, -0.06375103443861008, -0.027970116585493088, 0.05315065756440163, -0.009242784231901169, -0.001286690472625196, -0.008382665924727917, -0.045228272676467896, -0.06683816015720367, -0.0009751881589181721, 0.00852214451879263, -0.012897124513983727, -0.05865541473031044, 0.01751851662993431, 0.01726745441555977, -0.05631217360496521, 0.01014474593102932, 0.013919968158006668, 0.06698694080114365, 0.02865821123123169, -0.05315065756440163, 0.0012890150537714362, 0.008433808572590351, 0.02867680788040161, 0.03079688362777233, -0.032954152673482895, -0.00814090296626091, 0.03234044462442398, 0.004279669374227524, 0.02521773800253868, -0.028249073773622513, 0.027189034968614578, -0.04909648001194, -0.002229333622381091, -0.0004134960472583771, 0.025589680299162865, 0.0032405536621809006, -0.0014145458117127419, -0.0010158694349229336, -0.013259769417345524, -0.05534512177109718, -0.016802527010440826, 0.018662242218852043, -0.012934318743646145, -0.017220962792634964, -0.06601988524198532, -0.027821337804198265, 0.01628180593252182, -0.031503573060035706, -0.031150229275226593, -0.047348346561193466, 0.023822950199246407, 0.016235312446951866, 0.01850416511297226, 0.035855308175086975, 0.02095898985862732, 0.017565010115504265, 0.02164708450436592, -0.021386723965406418, 0.0004750991065520793, 0.00808976124972105, 0.011483740992844105, -0.009782101958990097, 0.018996989354491234, 0.007127358112484217, -0.0008711603004485369, -0.013929266482591629, 0.02811889350414276, 0.007834049873054028, -0.0018050860380753875, 0.028825584799051285, -0.01265536155551672, -0.0014401169028133154, -0.06397420167922974, 0.02296748198568821, 0.027393603697419167, 0.0005364115932025015, 0.031373392790555954, 0.0019422400509938598, -0.016904810443520546, 0.03401419147849083, -0.04448438808321953, -0.015565815381705761, 0.035725127905607224, -0.019694384187459946, 0.05374576896429062, 0.019210858270525932, 0.0017992743523791432, -0.015240365639328957, 0.009717011824250221, -0.020047729834914207, -0.017016394063830376, 0.02465982362627983, -0.008610481396317482, -0.01818801462650299, -0.008582585491240025, -0.049691587686538696, -0.0028430395759642124, 0.025347918272018433, 0.02017791010439396, 0.0033195915166288614, -0.014161731116473675, 0.04024423658847809, -0.02620338648557663, -0.04069056734442711, -0.009819296188652515, -0.04080215096473694, -0.03044353611767292, -0.004016984719783068, -0.0035846009850502014, 0.015919161960482597, -0.006085917819291353, 0.022669928148388863, 0.01761150173842907, -0.04236431047320366, 0.08562128245830536, 0.028509432449936867, -0.011864982545375824, -0.012469390407204628, -0.022576941177248955, 0.01371539942920208, -0.0016388739459216595, -0.013901370577514172, 0.008257134817540646, 0.04664165526628494, -0.005128164310008287, -0.03300994262099266, -0.03654340282082558, -0.01872733235359192, 0.019489815458655357, -0.027040258049964905, -0.01428261213004589, 0.035297393798828125, -0.012943617068231106, 0.015072991140186787, -0.017778877168893814, -0.02486439235508442, 0.047571513801813126, 0.008917334489524364, 0.029030153527855873, 0.007824751548469067, 0.02240956760942936, 0.006973932031542063, -0.005151411052793264, -0.009800698608160019, 0.010330718010663986, 0.01596565544605255, 0.044670358300209045, -0.059734050184488297, 0.0006160306511446834, 0.010507390834391117, 0.03423735499382019, 0.062374845147132874, -0.01906207948923111, 0.01917366310954094, 0.002840714994817972, -0.010302822105586529, 0.05155130475759506, 0.033735234290361404, -0.034944046288728714, 0.004993335343897343, 0.021275142207741737, -0.0033986293710768223, 0.07145025581121445, -0.015054394491016865, 0.024027518928050995, -0.0003577045863494277, -0.006104514934122562, -0.0069134910590946674, -0.0069646332412958145, -0.03219166770577431, 0.022056221961975098, -0.005114216823130846, -0.036822360008955, 0.0053978231735527515, -0.023153454065322876, -0.029699651524424553, -0.01816011779010296, 0.023265035822987556, 0.03336329013109207, 0.020270895212888718, -0.024697016924619675, -0.029643859714269638, 0.013668905943632126, -0.02832346223294735, 0.018820317462086678, 0.006216098088771105, 0.011251276358962059, 0.005737221334129572, -0.026296371594071388, -0.005328083876520395, 0.0238601453602314, 0.052146412432193756, -0.0038612335920333862, 0.029085945338010788, 0.024455254897475243, 0.025459500029683113, 0.020940393209457397, 0.010544585064053535, -0.004019309300929308, 0.015575114637613297, 0.027951518073678017, 0.04630690813064575, -0.007573689799755812, 0.015370545908808708, 0.0012727425200864673, -0.029829831793904305, -0.017202364280819893, 0.03397699445486069, 0.05768836289644241, -0.03702692687511444, 0.03241483494639397, -0.01861574873328209, 0.048798926174640656, -0.03645041584968567, -0.007378419861197472, -0.00504447752609849, -0.01782536879181862, 0.05586584284901619, 0.035743724554777145, -0.01716517098248005, -0.01662585325539112, -0.009293926879763603, 0.02953227609395981, -0.008336173370480537, 0.06207729130983353, 0.0169513039290905, 0.000808394921477884, -0.012469390407204628, 0.025236334651708603, 0.003084802534431219, -0.03704552724957466, -0.02298607863485813, 0.022707121446728706, -0.02151690423488617, 0.016663048416376114, -0.028788389638066292, 0.0020015183836221695, 0.020828809589147568, -0.020363880321383476, -0.0005756399477832019, -0.00925673171877861, -0.0023165077436715364, 0.008080461993813515, 0.021833056584000587, 0.00260825059376657, -0.0412856750190258, 0.05463843047618866, 0.006202150136232376, -0.040876537561416626, -0.046790432184934616, -0.04150884225964546, -0.02787712961435318, 0.02499457076191902, -0.009828594513237476, 0.016077237203717232, 0.007424912881106138, -0.010200537741184235, 0.006992529146373272, 0.008405912667512894, 0.03938876837491989, 0.016672346740961075, 0.027244826778769493, -0.017425531521439552, 0.05564267560839653, 0.031150229275226593, -0.022279387339949608, 0.004821311682462692, 0.028267670422792435, 0.01354802493005991, 0.031299006193876266, 0.028714001178741455, -0.006053372751921415, -0.023506799712777138, -0.018680838868021965, 0.039091210812330246, 0.009558935649693012, 0.012199731543660164, -0.019359635189175606, 0.05891577526926994, -0.06423456221818924, 0.0016028420068323612, 0.026073206216096878, 0.021349530667066574, 0.0018050860380753875, -0.019155066460371017, 0.025794249027967453, 0.007634130772203207, -0.03174533694982529, 0.03055511973798275, -0.032842569053173065, 0.036059875041246414, -0.005718624219298363, 0.016198119148612022, 0.03516721352934837, 0.010563181713223457, 0.03460929915308952, -0.0016063289949670434, -0.03760344162583351, 0.0655735582113266, -0.00669032521545887, 0.03983509913086891, -0.013018006458878517, -0.0477202907204628, 0.009224187582731247, 0.00560704106464982, -0.0058766999281942844, -0.013436442241072655, -0.01411523763090372, 0.05735361576080322, 0.04314539209008217, -0.016040043905377388, 0.004788766615092754, 0.014245417900383472, -0.042885031551122665, 0.019434023648500443, -0.019210858270525932, 0.007675974164158106, -0.010888632386922836, 0.0013575920602306724, 0.0059045953676104546, 0.10369771718978882, -0.01316678337752819, 0.01159532368183136, -0.004988685715943575, -0.011864982545375824, 0.009986670687794685, -0.031168825924396515, -0.02889997325837612, -0.047683097422122955, -0.013138887472450733, 0.017351143062114716, 0.009214888326823711, -0.026724107563495636, -0.005588443949818611, -0.029048750177025795, -0.014849825762212276, 0.034516312181949615, -0.0025896532461047173, 0.02830486372113228, -0.04206675663590431, -0.021442515775561333, 0.022242194041609764, 0.04136006534099579, -0.014515076763927937, -0.008503547869622707, -0.022725719958543777, -0.01064686942845583, -0.016969900578260422, 0.04794345796108246, 0.009098656475543976, 0.014728943817317486, 0.07576479762792587, -0.03369803726673126, -0.0034102527424693108, -0.017909057438373566, -0.006123112048953772, 0.0006747278966940939, 0.031206021085381508, 0.023915937170386314, 0.01648637466132641, -0.010544585064053535, 0.012925020419061184, 0.006411368027329445, -0.05222080275416374, -0.0019527008989825845, 0.009837892837822437, 0.0479806512594223, -0.038086965680122375, 0.04452158138155937, 0.007615533657371998, 0.02073582448065281, 0.045451439917087555, -0.03299134597182274, -0.0039309728890657425, 0.016914108768105507, 0.03241483494639397, 0.05307627096772194, 0.0010519013740122318, 0.0345907025039196, 0.026370760053396225, -0.0454886332154274, 0.010888632386922836, -0.04794345796108246, 0.04809223487973213, 0.007011126261204481, -0.0010495767928659916, -0.024008922278881073, 0.03297274932265282, -0.04958000406622887, -0.016663048416376114, -0.02830486372113228, -0.01500790100544691, 0.006216098088771105, -0.05876699835062027, -0.0027244826778769493, 0.03035055100917816, -0.042327117174863815, 0.013594517484307289, 0.0166072566062212, 0.02676130086183548, 0.05296468734741211, 0.0010292361257597804, -0.04303380846977234, 0.03611566871404648, 0.01015404425561428, 0.046678848564624786, 0.016337597742676735, -0.015668099746108055, -0.037882398813962936, 0.002123562153428793, -0.00902891717851162, -0.023674173280596733, 0.00630443450063467, -0.0003425944014452398, 0.00942875538021326, -0.029178930446505547, 0.011279172264039516, -0.0336422473192215, -0.008838295936584473, 0.013055200688540936, -0.05162569135427475, 0.0457489937543869, -0.012469390407204628, 0.01616092398762703, -0.013092394918203354, -0.0206428375095129, -0.03297274932265282, -0.021368127316236496, 0.02676130086183548, 0.019117871299386024, 0.015110185369849205, -0.02611040137708187, -0.03163375332951546, -0.041322872042655945, -0.010005267336964607, -0.013343456201255322, 0.0017783526564016938, -0.01650497131049633, -0.011855684220790863, 0.006639183033257723, -0.04853856563568115, -0.01283203437924385, 0.04507949575781822, -0.0161795224994421, -0.039649125188589096, -0.005025880411267281, -0.010498091578483582, 0.04381489008665085, 0.020233700051903725, -0.01427331380546093, -0.028583820909261703, -0.0014098965330049396, -0.02051265724003315, 0.026798496022820473, 0.029829831793904305, -0.00937296450138092, 0.059734050184488297, -0.027486590668559074, -0.043219778686761856, 0.021275142207741737, 0.04943122714757919, -0.014329105615615845, -0.039760708808898926, -0.015026498585939407, -0.014347702264785767, -0.025292126461863518, 0.046344101428985596, -0.0372500941157341, -0.026240581646561623, 0.018597152084112167, 0.019657189026474953, 0.03890524059534073, -0.017890458926558495, -0.006346277892589569, -0.0119300726801157, 0.02531072311103344, 0.0173790380358696, 0.0086476756259799, -0.06003160402178764, 0.018913302570581436, -0.020438268780708313, 0.02865821123123169, 0.03680376335978508, -0.019155066460371017, -0.026593927294015884, -0.01906207948923111, -0.004026283510029316, 0.005402472335845232, 0.0008432645699940622, -0.02744939550757408, 0.005523353815078735, -0.013176081702113152, 0.03736167773604393, 0.0005750588024966419, 0.03849610313773155, 0.05050986260175705, 0.028732599690556526, 0.0071831499226391315, 0.015491426922380924, -0.0045377048663794994, -0.0048817521892488, 0.003459070110693574, 0.007536495570093393, 0.00959612987935543, -0.0026407954283058643, -0.028918569907546043, -0.009912281297147274, 0.025347918272018433, 0.018643643707036972, 0.030257565900683403, -0.02296748198568821, -0.018206611275672913, -0.06959053874015808, 0.026742704212665558, 0.00869416818022728, -0.019155066460371017, 0.01696060225367546, 0.01048879325389862, 0.0026965870056301355, -0.003605522681027651, -0.002554783597588539, 0.00941480789333582, 0.024380866438150406, -0.01355732325464487, -0.046678848564624786, -0.03282397240400314, -0.043777693063020706, 0.004653937183320522, 0.052927494049072266, -0.08011652529239655, 0.051700081676244736, 0.030871272087097168, -0.03421875834465027, -0.021144961938261986, 0.023172050714492798, -0.02722623012959957, -0.018253104761242867, -0.015565815381705761, -0.046678848564624786, 0.007527197245508432, 0.01718376763164997, -0.017648696899414062, -0.020363880321383476, 0.013854878023266792, 0.00997737143188715, -0.018587853759527206, 0.00023377200704999268, -0.00577441556379199, -0.05646095052361488, -0.020140714943408966, -0.022837301716208458, 0.06010599434375763, 0.02421349100768566, 0.027691159397363663, 0.052927494049072266, 0.0035869255661964417, -0.01751851662993431, 0.05140252783894539, 0.02252115122973919, 0.0023316177539527416, -0.004175060428678989, -0.01785326562821865, 0.0036334185861051083, 0.025626875460147858, 0.00018742441898211837, -0.026593927294015884, -0.0029964661225676537, -0.013994356617331505, 0.035632140934467316, -0.0004652193747460842, 0.009837892837822437, -0.04452158138155937 ]
Determining the state of a mobile robot is an essential building block of robot navigation systems. In this paper, we address the problem of estimating the robots pose in an indoor environment using 2D LiDAR data and investigate how modern environment models can improve gold standard Monte-Carlo localization (MCL) systems. We propose a neural occupancy field to implicitly represent the scene using a neural network. With the pretrained network, we can synthesize 2D LiDAR scans for an arbitrary robot pose through volume rendering. Based on the implicit representation, we can obtain the similarity between a synthesized and actual scan as an observation model and integrate it into an MCL system to perform accurate localization. We evaluate our approach on self-recorded datasets and three publicly available ones. We show that we can accurately and efficiently localize a robot using our approach surpassing the localization performance of state-of-the-art methods. The experiments suggest that the presented implicit representation is able to predict more accurate 2D LiDAR scans leading to an improved observation model for our particle filter-based localization. The code of our approach will be available at: https://github.com/PRBonn/ir-mcl.
[ 0.014270578511059284, 0.010969651862978935, -0.03610957786440849, -0.026918048039078712, 0.0020562398713082075, 0.00682981638237834, -0.03052900731563568, 0.04610354080796242, -0.04814610257744789, 0.0063282945193350315, -0.029963655397295952, -0.0339575931429863, 0.023507699370384216, -0.001775843556970358, -0.02303353324532509, 0.019623184576630592, 0.01305780652910471, -0.01949552446603775, -0.04697892442345619, -0.08090004324913025, 0.041106559336185455, -0.01758062280714512, -0.02934359200298786, 0.009647457860410213, 0.03592720627784729, 0.014452950097620487, 0.017571503296494484, 0.00036331842420622706, -0.0537266731262207, 0.053872570395469666, 0.04683302715420723, -0.010531960055232048, -0.049678023904561996, 0.0424925833940506, -0.06040147691965103, 0.001967333722859621, 0.06452307105064392, 0.012547166086733341, 0.0063237352296710014, 0.07167203724384308, 0.043586812913417816, 0.024218948557972908, -0.009638339281082153, 0.01956847310066223, -0.0005984068266116083, -0.0677328109741211, -0.025185517966747284, -0.006050177849829197, -0.04391508176922798, 0.015720432624220848, 0.008990920148789883, -0.03386640548706055, 0.030200738459825516, -0.05361725017428398, -0.02006087638437748, 0.00931462924927473, 0.06744101643562317, 0.07243800163269043, 0.08119183778762817, -0.002149705309420824, 0.033684033900499344, 0.021629272028803825, -0.05281481519341469, -0.05478442832827568, -0.0054757073521614075, -0.010340469889342785, 0.0486932173371315, -0.03964758664369583, 0.03707614541053772, -0.03694848716259003, -0.025896767154335976, 0.03605486452579498, -0.012747774831950665, -0.000038041576772229746, 0.0062325494363904, 0.04077829048037529, -0.036146052181720734, 0.05048045888543129, 0.043477389961481094, 0.04424335062503815, 0.0981888696551323, 0.01737089455127716, -0.017079100012779236, 0.004472663626074791, 0.07542889565229416, -0.005188472103327513, 0.035544224083423615, -0.06955652683973312, 0.0332828164100647, -0.02184811793267727, -0.06605499237775803, 0.06517960876226425, -0.011015244759619236, 0.042857326567173004, 0.03822508826851845, -0.024218948557972908, 0.004814610350877047, -0.00761857395991683, -0.04555642604827881, 0.022066963836550713, 0.02733750268816948, 0.024510743096470833, 0.038042716681957245, 0.04522815719246864, 0.01303045079112053, -0.03404877707362175, -0.021428663283586502, -0.02186635509133339, 0.019367864355444908, 0.09315541386604309, 0.04934975504875183, -0.04362328723073006, -0.001655022264458239, -0.02314295619726181, -0.016723476350307465, 0.05981788784265518, -0.055623337626457214, -0.014398238621652126, -0.00883590430021286, -0.03240743279457092, 0.014525898732244968, -0.003800168400630355, 0.0861523449420929, -0.02137395180761814, -0.016085175797343254, 0.011316157877445221, 0.051501739770174026, -0.0498603954911232, 0.009100343100726604, -0.004372359253466129, -0.009902778081595898, -0.03888162598013878, 0.007103374227881432, -0.01186327263712883, 0.0413254052400589, 0.04333149269223213, -0.012528928928077221, -0.005074489861726761, 0.030784327536821365, -0.022869398817420006, -0.02989070676267147, -0.03461413085460663, -0.047088347375392914, 0.04989686980843544, 0.005279657896608114, 0.05412789061665535, -0.007445320952683687, 0.01634049601852894, -0.028395259752869606, -0.015556298196315765, -0.071963831782341, 0.0622616671025753, 0.019769081845879555, 0.03826156258583069, 0.047744885087013245, -0.0033784338738769293, -0.002997733186930418, 0.0027127775829285383, -0.04063239321112633, 0.010349588468670845, 0.055039748549461365, -0.046541232615709305, 0.005881484132260084, 0.0329727865755558, 0.045410528779029846, 0.03041958436369896, 0.06076622009277344, 0.012310083024203777, -0.044790465384721756, 0.019641421735286713, -0.05277834087610245, -0.0056261639110744, 0.016687002032995224, -0.02131924033164978, 0.011325276456773281, -0.0037636940833181143, 0.03204268962144852, -0.03218858689069748, -0.012793367728590965, -0.02737397700548172, -0.03344695270061493, -0.0013039569603279233, 0.03961111232638359, 0.04738014191389084, 0.019714370369911194, 0.0063282945193350315, 0.023343564942479134, -0.0026512271724641323, 0.06605499237775803, -0.02808522619307041, 0.016586696729063988, 0.006063855718821287, 0.007153526414185762, -0.02555026113986969, 0.012984857894480228, -0.05478442832827568, -0.03778739646077156, -0.033118683844804764, 0.01710645668208599, 0.061276860535144806, -0.028851188719272614, -0.01859278418123722, 0.020297959446907043, 0.009957489557564259, 0.04333149269223213, 0.0006844634190201759, 0.012848079204559326, -0.045994117856025696, -0.0250213835388422, -0.05967199057340622, -0.019057832658290863, -0.025130806490778923, -0.06915531307458878, -0.019276678562164307, -0.020297959446907043, 0.007773589808493853, 0.010568434372544289, -0.0260973758995533, 0.006565377581864595, -0.003412628546357155, 0.012118592858314514, 0.01634049601852894, 0.05051693320274353, -0.04610354080796242, -0.01371434424072504, 0.016121650114655495, 0.04697892442345619, -0.004677831660956144, 0.020845074206590652, -0.01312163658440113, -0.013896715827286243, 0.003866278100758791, 0.0389910489320755, 0.018136855214834213, 0.008867818862199783, 0.027811668813228607, 0.06605499237775803, -0.0677328109741211, 0.019696133211255074, 0.015474230982363224, -0.027720483019948006, 0.022650552913546562, -0.04931328073143959, 0.008471161127090454, 0.036966722458601, -0.017288828268647194, -0.024711351841688156, 0.0174073688685894, 0.020863311365246773, 0.01724323444068432, -0.037969768047332764, -0.02252289280295372, -0.009775117971003056, 0.01245598029345274, -0.052559494972229004, 0.01183591689914465, 0.03669316694140434, -0.01680554263293743, 0.03634665906429291, -0.0073450165800750256, 0.014307052828371525, 0.021574560552835464, 0.004955948330461979, 0.011106430552899837, -0.01616724207997322, 0.01791800931096077, 0.06036500260233879, 0.06649268418550491, 0.049021486192941666, 0.015784261748194695, -0.02130100317299366, -0.0977511778473854, 0.024109525606036186, 0.05175705999135971, 0.012693063355982304, -0.022212861105799675, 0.021465137600898743, -0.005193031392991543, 0.013194585219025612, 0.004128437023609877, 0.03156852349638939, 0.004340444225817919, -0.016012227162718773, 0.028449971228837967, -0.024839011952280998, -0.013440786860883236, 0.02863234281539917, -0.012756893411278725, -0.05106404796242714, 0.03155028820037842, -0.03815213963389397, 0.007924046367406845, -0.08308850228786469, 0.020243247970938683, 0.042893800884485245, 0.016851136460900307, -0.0034650603774935007, -0.031896792352199554, 0.038042716681957245, 0.01009426824748516, -0.02128276601433754, -0.0018784275744110346, 0.04876616597175598, 0.018319226801395416, 0.04818257689476013, 0.021118631586432457, 0.024510743096470833, 0.062407564371824265, -0.0500427670776844, -0.027647534385323524, 0.008302466943860054, -0.0021873193327337503, -0.031933266669511795, -0.022851161658763885, 0.03815213963389397, 0.04847437143325806, 0.02806698903441429, -0.00939213763922453, -0.031294967979192734, 0.030911987647414207, 0.01726147159934044, 0.025805581361055374, -0.06014615669846535, 0.036091338843107224, -0.007112492807209492, 0.012939264997839928, 0.041106559336185455, 0.0260973758995533, -0.055039748549461365, 0.02673567645251751, -0.03641960769891739, 0.00251444848254323, -0.050772253423929214, -0.016349613666534424, -0.03756855055689812, -0.01705174520611763, -0.04825552552938461, 0.05292423814535141, 0.006428598891943693, -0.056279875338077545, -0.030273687094449997, -0.07987876236438751, -0.00564440106973052, -0.004668713081628084, 0.006898205727338791, -0.06689390540122986, 0.03167794644832611, -0.004741661716252565, -0.0028609544970095158, -0.030893750488758087, 0.0010058933403342962, -0.07652312517166138, -0.02261407859623432, -0.024492505937814713, 0.04672360420227051, -0.003734058700501919, -0.045994117856025696, -0.011990932747721672, -0.041143033653497696, 0.02793932892382145, -0.01823716051876545, -0.06229814141988754, -0.03342871367931366, 0.02182988077402115, -0.035580698400735855, 0.05124641954898834, -0.027009233832359314, 0.007408846635371447, -0.008721921592950821, 0.029580675065517426, 0.04201841726899147, -0.011124667711555958, -0.030693141743540764, -0.06871762126684189, -0.028249360620975494, -0.0068754092790186405, 0.006524343974888325, 0.04993334412574768, 0.01820068620145321, 0.03961111232638359, 0.027793431654572487, 0.0249301977455616, -0.023525936529040337, 0.0016379249282181263, 0.009610983543097973, 0.11226795613765717, 0.03173265978693962, -0.05245007202029228, 0.013769055716693401, 0.04435277357697487, 0.011990932747721672, -0.06215224415063858, -0.03350166231393814, -0.0027902855072170496, 0.015118606388568878, -0.009784236550331116, 0.032608043402433395, -0.017398251220583916, 0.007650488987565041, -0.002637549303472042, -0.05861423537135124, -0.00023679813602939248, 0.0011289941612631083, -0.02006087638437748, -0.0028449969831854105, 0.015993990004062653, 0.029963655397295952, -0.0401582270860672, -0.0038206852041184902, -0.0004889838746748865, -0.001564976293593645, 0.022723501548171043, -0.012072999961674213, -0.030054841190576553, 0.024164237082004547, -0.023416513577103615, -0.03171442076563835, -0.0008753836737014353, -0.04398803040385246, -0.013176348060369492, -0.003624635748565197, -0.010440774261951447, 0.03455941751599312, 0.00435640150681138, -0.034267622977495193, 0.06740454584360123, -0.01818244904279709, 0.01521891076117754, -0.02308824472129345, -0.024802537634968758, 0.04037707298994064, -0.005156557075679302, 0.0680975541472435, -0.015838973224163055, 0.0334651879966259, 0.02976304665207863, 0.009492442011833191, 0.03607310354709625, -0.03707614541053772, -0.014525898732244968, -0.007718878332525492, 0.005548655986785889, 0.007454439532011747, -0.049532126635313034, 0.024018339812755585, 0.007358694449067116, -0.007572981063276529, -0.013778174296021461, -0.007682404015213251, -0.07980581372976303, -0.05861423537135124, 0.03640137240290642, -0.03651079535484314, -0.0249301977455616, 0.04909443482756615, 0.03342871367931366, -0.007226475048810244, -0.017553266137838364, -0.02496667206287384, -0.05493032559752464, 0.04096066206693649, 0.054383210837841034, -0.021100394427776337, 0.0048100510612130165, 0.041617199778556824, 0.006104889325797558, -0.013404312543570995, -0.015145962126553059, 0.00432448647916317, 0.004055488388985395, 0.03339223936200142, -0.025787344202399254, 0.013969664461910725, -0.008617058396339417, -0.004661873914301395, 0.06984832137823105, -0.057556480169296265, -0.06350179016590118, 0.05299718677997589, -0.036857299506664276, 0.0055395374074578285, -0.013003095053136349, -0.02002440206706524, -0.018246278166770935, 0.011316157877445221, -0.011781205423176289, 0.05540449172258377, -0.014772100374102592, -0.003877676324918866, -0.00311171542853117, 0.01122497208416462, 0.004855643957853317, -0.02130100317299366, -0.04329501837491989, 0.007518269587308168, -0.04847437143325806, -0.02870529145002365, -0.023854205384850502, 0.014434712938964367, 0.017079100012779236, 0.001934278872795403, -0.04209136590361595, -0.007089695893228054, 0.04194546863436699, -0.013905834406614304, 0.026425644755363464, 0.06620088964700699, -0.004969626199454069, -0.0035060939844697714, 0.013139873743057251, 0.0826508104801178, -0.02914298325777054, 0.03047429583966732, -0.013194585219025612, 0.03793329373002052, -0.009109461680054665, 0.010531960055232048, -0.03603662922978401, 0.01953199878334999, -0.004819169640541077, 0.03271746635437012, 0.027611060068011284, -0.008886056020855904, 0.02863234281539917, -0.030273687094449997, 0.05529506877064705, 0.012838960625231266, -0.037422653287649155, 0.09184233844280243, -0.004278893582522869, -0.0188207495957613, 0.01862925849854946, -0.05602455511689186, -0.0334651879966259, 0.008024350740015507, -0.026644490659236908, 0.04449867084622383, 0.028285834938287735, 0.018401294946670532, -0.016249310225248337, -0.013796411454677582, -0.011443817988038063, 0.010750805959105492, -0.020972734317183495, -0.0036018393002450466, -0.006943798623979092, 0.009209766052663326, -0.025294940918684006, -0.01308516226708889, 0.032589804381132126, -0.007039543706923723, 0.019933216273784637, -0.02500314638018608, 0.009018275886774063, -0.021629272028803825, -0.02248641848564148, -0.009538034908473492, -0.007901249453425407, 0.02383596822619438, -0.02987246960401535, 0.03288159891963005, -0.038589831441640854, -0.0364743210375309, 0.008908852934837341, 0.019714370369911194, -0.056316349655389786, -0.011753849685192108, 0.02730102837085724, -0.00501065980643034, 0.021519849076867104, 0.02126452885568142, 0.01733442023396492, -0.028997085988521576, -0.0038526002317667007, 0.017343539744615555, 0.00818848516792059, 0.027063945308327675, -0.004677831660956144, 0.02680862508714199, -0.02562320977449417, -0.018601903691887856, -0.0034627807326614857, 0.012027407065033913, 0.04971449822187424, -0.020352670922875404, -0.013294889591634274, -0.04978744685649872, -0.0249301977455616, 0.036857299506664276, 0.010431655682623386, 0.03510653227567673, 0.050881676375865936, 0.03341047838330269, -0.006971154361963272, 0.006155041512101889, -0.049568600952625275, 0.025769107043743134, 0.00862161722034216, 0.054419685155153275, -0.05795769765973091, -0.058140069246292114, 0.017680926248431206, -0.02854115702211857, 0.040450021624565125, 0.011379987932741642, -0.023471225053071976, 0.03490592539310455, -0.015519823879003525, 0.025750869885087013, -0.011197616346180439, -0.04325854405760765, 0.03113083355128765, 0.02739221416413784, -0.03209740296006203, 0.048948537558317184, 0.020370908081531525, 0.029726572334766388, 0.03184208273887634, 0.015082132071256638, -0.04427982494235039, 0.0225046556442976, -0.0064513953402638435, 0.019604947417974472, 0.03448646888136864, -0.054383210837841034, 0.024638403207063675, -0.0029133863281458616, 0.003980260342359543, -0.021556323394179344, 0.004212784115225077, -0.016705239191651344, -0.025149043649435043, 0.026535067707300186, 0.004370079375803471, -0.017753874883055687, 0.03594544157385826, -0.03964758664369583, 0.04686950147151947, 0.002883750945329666, -0.0042036655358970165, 0.05343487858772278, 0.05861423537135124, -0.01955023594200611, 0.030164264142513275, 0.012811604887247086, 0.00560336746275425, -0.07039543986320496, -0.0236718337982893, 0.07623133063316345, -0.0018168771639466286, -0.029070034623146057, 0.0173161830753088, 0.010851110331714153, 0.02310648187994957, -0.0022887636441737413, -0.010495485737919807, -0.0013153551844879985, -0.020535042509436607, -0.01846512407064438, -0.019367864355444908, 0.030346635729074478, -0.022887635976076126, -0.03470531478524208, -0.009784236550331116, 0.01581161841750145, -0.01364139560610056, -0.016741713508963585, 0.008229518309235573, -0.027829905971884727, 0.029051797464489937, -0.029015323147177696, 0.01652286760509014, -0.045301105827093124, -0.0068115792237222195, 0.042273737490177155, -0.007800945546478033, 0.03521595522761345, 0.004570688121020794, 0.03607310354709625, -0.0003601839125622064, 0.013139873743057251, 0.02927064336836338, 0.0125106917694211, -0.011161142028868198, -0.008015232160687447, -0.02195754088461399, 0.00824319664388895, 0.04245610907673836, -0.03246214613318443, -0.013595802709460258, -0.032626278698444366, -0.02682686224579811, -0.027063945308327675, 0.025076095014810562, 0.022705264389514923, -0.022759975865483284, 0.019896741956472397, 0.013851122930645943, 0.015510705299675465, -0.012383031658828259, -0.04803667962551117, 0.049678023904561996, -0.028267597779631615, 0.012282727286219597, 0.023307090625166893, 0.020954497158527374, 0.006606411188840866, -0.002341195475310087, 0.014535017311573029, 0.027611060068011284, -0.007080577313899994, -0.016349613666534424, 0.024510743096470833, 0.06040147691965103, 0.0075820996426045895, 0.046541232615709305, 0.00015743798576295376, -0.030291924253106117, 0.01310339942574501, 0.055076222866773605, 0.04278437793254852, 0.013504616916179657, 0.0005508192116394639, -0.020954497158527374, -0.009091224521398544, -0.007354135159403086, -0.026516830548644066, -0.02788461744785309, -0.009328307583928108, 0.007987876422703266, 0.0024734148755669594, -0.04241963475942612, -0.011006126180291176, 0.013623158447444439, 0.010267521254718304, -0.00880854856222868, 0.025860292837023735, 0.01643168181180954, 0.014945353381335735, -0.008462042547762394, 0.03521595522761345, -0.030893750488758087, 0.06233461573719978, -0.00037585647078230977, -0.011033481918275356, -0.005981788504868746, -0.025677921250462532, 0.07094255089759827, -0.03227977454662323, -0.01654110476374626, 0.06470544636249542, 0.001527362153865397, 0.004071446135640144, -0.0727662667632103, -0.003373874584212899, 0.013431668281555176, 0.02252289280295372, -0.004905796144157648, 0.012793367728590965, -0.04880264028906822, 0.04158072546124458, 0.036839064210653305, 0.011653545312583447, 0.037459127604961395, 0.049605075269937515, -0.023507699370384216, -0.00563072320073843, 0.005858687683939934, -0.004851084668189287, 0.013550209812819958, 0.039793483912944794, 0.02675391361117363, 0.025349652394652367, -0.016212835907936096, -0.007554743904620409, 0.009820710867643356, -0.004506858065724373, 0.011088193394243717, -0.04303969815373421, -0.00885414145886898, -0.027665771543979645, 0.04555642604827881, 0.07094255089759827, 0.047197770327329636, -0.024601928889751434, 0.06667505949735641, -0.02730102837085724, 0.005744705442339182, 0.009114020504057407, -0.018456006422638893, -0.00046818211558274925, -0.016103412955999374, -0.017416488379240036, -0.018419532105326653, 0.03244390711188316, 0.017416488379240036, -0.04570232331752777, -0.01823716051876545, -0.014389120042324066, -0.023452987894415855, 0.026407407596707344, 0.015911921858787537, -0.02553202398121357, 0.025769107043743134, -0.017380014061927795, 0.010386062785983086, -0.011188497766852379, 0.028267597779631615, 0.009601864963769913, -0.03218858689069748, 0.005348047241568565, 0.04088771343231201, -0.027173368260264397, 0.032553330063819885, 0.025185517966747284, -0.06408537924289703, 0.0064468360505998135, 0.0040167346596717834, 0.04435277357697487, -0.03667492792010307, -0.01460796594619751, -0.04796373099088669, -0.010240165516734123, 0.015930159017443657, -0.013176348060369492, -0.00432448647916317, -0.010522841475903988, -0.018036551773548126, 0.03342871367931366, -0.018000077456235886, 0.02071741409599781, 0.041763097047805786, 0.01729794591665268, -0.024601928889751434, 0.005744705442339182, -0.04241963475942612, 0.01002131961286068, -0.015455993823707104, 0.0225958414375782, 0.05234064906835556, -0.0027925651520490646, 0.0152280293405056, 0.011680901050567627, -0.03288159891963005, -0.004641357343643904, 0.0015079851727932692, 0.028832951560616493, -0.002382229082286358, 0.015364808030426502, 0.06277230381965637, 0.010969651862978935, 0.05365372449159622, 0.036273710429668427, -0.009182410314679146, -0.009829829446971416, 0.0005528139299713075, 0.04705187305808067, 0.019039595499634743, 0.013021332211792469, 0.004087403416633606, -0.008493957109749317, -0.015291859395802021, -0.018729563802480698, -0.03299102187156677, 0.020407382398843765, 0.01664140820503235, -0.011580596677958965, -0.024547217413783073, -0.03448646888136864, -0.043513864278793335, -0.020498568192124367, -0.026516830548644066, -0.0547114796936512, 0.06051089987158775, -0.0346323661506176, -0.010431655682623386, 0.0068708499893546104, 0.024145999923348427, 0.025276703760027885, 0.005803976207971573, -0.005448351614177227, 0.020225010812282562, -0.016349613666534424, -0.02855939418077469, 0.05525859445333481, -0.02441955730319023, -0.015766024589538574, -0.036219000816345215, 0.011945339851081371, -0.00803802814334631, -0.016860254108905792, 0.013814648613333702, -0.024091288447380066, -0.014927116222679615, 0.04325854405760765, 0.024474268779158592, 0.009647457860410213, 0.03572659566998482, -0.007034984417259693, 0.017699163407087326, -0.0009956349385902286, 0.0063282945193350315, -0.014051731675863266, -0.030200738459825516, 0.006351090967655182, 0.02806698903441429, -0.013759937137365341, -0.040486495941877365, 0.011544122360646725, -0.0027743279933929443, 0.0022522893268615007, 0.019258441403508186, 0.013422549702227116, 0.009756880812346935, 0.0389910489320755, 0.014197629876434803, -0.024747826159000397, -0.029088271781802177, 0.0292888805270195, -0.007003069389611483, 0.03906399756669998, 0.009702169336378574, 0.006788782775402069, 0.021045682951807976, -0.048912063241004944, 0.0006257625645957887, 0.027501637116074562, 0.0008354898891411722, -0.010504604317247868, 0.04263848066329956, -0.005680875387042761, 0.02500314638018608, 0.003943786025047302, 0.012756893411278725, 0.024601928889751434, 0.010203691199421883, -0.029398303478956223, -0.030146026983857155, 0.024528980255126953, 0.002692260779440403, -0.029580675065517426, -0.03581778332591057, -0.01242862455546856, 0.015063894912600517, -0.0022363318130373955, 0.016705239191651344, 0.02934359200298786, -0.010914940387010574, -0.017452962696552277, 0.017790349200367928, 0.007664166856557131, -0.03767797350883484, -0.009528916329145432, -0.02624327316880226, -0.013951427303254604, 0.05062635615468025, -0.012191541492938995, -0.019604947417974472, -0.036912012845277786, 0.05978141352534294, -0.003050165018066764, 0.009811592288315296, -0.043513864278793335, -0.027738720178604126, -0.023398276418447495, 0.02861410565674305, -0.05000629276037216, -0.018173329532146454, -0.02487548626959324, 0.0065106661058962345, -0.003227977314963937, -0.022322284057736397, 0.008867818862199783, 0.051939431577920914, -0.003877676324918866, -0.013322245329618454, -0.013176348060369492, -0.029489489272236824, -0.024547217413783073, 0.008767514489591122, 0.03304573521018028, -0.015383045189082623, 0.001167178270407021, 0.0056626382283866405, 0.03335576504468918, -0.00440883357077837, -0.012018288485705853, -0.03158676251769066, -0.02201225236058235, 0.04548347741365433, 0.003948345314711332, -0.03105788491666317, 0.02440132014453411, -0.04489988833665848, -0.028285834938287735, 0.016705239191651344, 0.01577514410018921, -0.030583718791604042, 0.018665732815861702, 0.01703350804746151, -0.0011261446634307504, -0.001221889746375382, -0.004212784115225077, 0.04989686980843544, 0.0013028171379119158, -0.004221902694553137, 0.044060979038476944, 0.03390287980437279, -0.016568459570407867, 0.025203755125403404, -0.03536185249686241, -0.03169618546962738, -0.015601891092956066, -0.00760033680126071, -0.026881573721766472, -0.02872352860867977, -0.029434777796268463, 0.024492505937814713, -0.000006732076599291759, 0.0017724239733070135, 0.03479650244116783, -0.04741661623120308, 0.05901545286178589, -0.033811695873737335 ]
Learning provides a powerful tool for vision-based navigation, but the capabilities of learning-based policies are constrained by limited training data. If we could combine data from all available sources, including multiple kinds of robots, we could train more powerful navigation models. In this paper, we study how a general goal-conditioned model for vision-based navigation can be trained on data obtained from many distinct but structurally similar robots, and enable broad generalization across environments and embodiments. We analyze the necessary design decisions for effective data sharing across robots, including the use of temporal context and standardized action spaces, and demonstrate that an omnipolicy trained from heterogeneous datasets outperforms policies trained on any single dataset. We curate 60 hours of navigation trajectories from 6 distinct robots, and deploy the trained GNM on a range of new robots, including an underactuated quadrotor. We find that training on diverse data leads to robustness against degradation in sensing and actuation. Using a pre-trained navigation model with broad generalization capabilities can bootstrap applications on novel robots going forward, and we hope that the GNM represents a step in that direction. For more information on the datasets, code, and videos, please check out our project page https://sites.google.com/view/drive-any-robot.
[ 0.0020878745708614588, -0.027773478999733925, -0.034573256969451904, -0.07070286571979523, 0.06714548915624619, -0.0021388265304267406, -0.026735911145806313, 0.039798155426979065, -0.06951707601547241, 0.011468835175037384, -0.03479559347033501, -0.011811602860689163, 0.01749970018863678, -0.050025612115859985, -0.054435279220342636, 0.012636099010705948, -0.022789446637034416, -0.007554794196039438, 0.0022905245423316956, 0.00008308652468258515, 0.012645363807678223, -0.051841359585523605, -0.05395355075597763, -0.001651308499276638, 0.045060109347105026, 0.006318049505352974, 0.019324708729982376, 0.0127565311267972, -0.06940590590238571, 0.026050375774502754, -0.01155221089720726, 0.01973232440650463, 0.01956557296216488, 0.013757043518126011, -0.001199688296765089, -0.03188669681549072, 0.012904755771160126, 0.045838285237550735, -0.0601048469543457, 0.0023704266641288996, 0.02555011957883835, 0.0013525444082915783, -0.01791658066213131, -0.024438438937067986, -0.012367443181574345, -0.013849684037268162, -0.016063779592514038, 0.026309767737984657, -0.0068044099025428295, -0.006563545670360327, 0.024197574704885483, -0.00533143337816, -0.00576220965012908, -0.017036501318216324, -0.021084869280457497, -0.003133548889309168, 0.05317537486553192, 0.012571251019835472, 0.04991444572806358, 0.02662474289536476, -0.0014764503575861454, 0.014340675435960293, -0.036407530307769775, 0.006438481621444225, 0.0010068812407553196, -0.05847438424825668, 0.0513966865837574, -0.000837234198115766, 0.02903338335454464, -0.01243229117244482, -0.0027815166395157576, 0.011811602860689163, -0.07537192106246948, -0.019120901823043823, 0.03774154558777809, -0.022900614887475967, 0.036222249269485474, 0.013914532028138638, 0.022733861580491066, -0.0042869169265031815, 0.027792006731033325, 0.017601605504751205, 0.005025721155107021, 0.008898074738681316, 0.09693852066993713, -0.017305156216025352, 0.03735245764255524, -0.0596972331404686, 0.04342964291572571, -0.052545420825481415, -0.016100836917757988, 0.05399060621857643, -0.005739049520343542, -0.022604165598750114, -0.003851508954539895, 0.020139941945672035, 0.01588776521384716, -0.021047813817858696, -0.04357786849141121, 0.00015546154463663697, -0.005933593492954969, 0.02404935099184513, 0.02408640645444393, -0.012728739529848099, 0.0008273912244476378, -0.013914532028138638, -0.016517717391252518, 0.014859460294246674, 0.01891709305346012, 0.09041666239500046, 0.021084869280457497, -0.044948939234018326, -0.05402766168117523, 0.03411005809903145, -0.03448061645030975, 0.009208418428897858, -0.060290127992630005, -0.08248668164014816, 0.06414395570755005, -0.07833640277385712, 0.03931642696261406, 0.054249998182058334, 0.015128116123378277, -0.05313831940293312, -0.005530609283596277, 0.022011270746588707, -0.033072490245103836, 0.022715333849191666, 0.03916820138692856, 0.01538750808686018, 0.01363661140203476, 0.030163591727614403, 0.01799069344997406, 0.005146153271198273, 0.02658768743276596, -0.02743997611105442, -0.038130633533000946, -0.0031636569183319807, -0.050766732543706894, -0.006952634081244469, -0.01969526894390583, -0.043911371380090714, -0.016934596002101898, 0.021937157958745956, -0.0002908028254751116, 0.011153859086334705, -0.008008730597794056, 0.08270901441574097, -0.02836637571454048, 0.009958802722394466, -0.07489019632339478, 0.0770765021443367, 0.015285603702068329, 0.02727322280406952, 0.0019686005543917418, 0.011496626771986485, -0.03092323988676071, 0.042392075061798096, 0.018018484115600586, -0.04850631579756737, 0.06721960008144379, -0.023456454277038574, -0.014275827445089817, 0.07407496124505997, 0.05717742443084717, 0.02473488636314869, 0.08293134719133377, 0.015952613204717636, 0.013571763411164284, 0.03170141577720642, -0.04928449168801308, -0.03325776755809784, -0.009162098169326782, 0.03524026647210121, 0.013525444082915783, 0.012895491905510426, 0.04550477862358093, 0.037222761660814285, -0.004002049099653959, -0.008453402668237686, -0.06510741263628006, -0.04817281290888786, 0.023789959028363228, 0.08463592827320099, 0.014535220339894295, 0.09975478053092957, 0.041391562670469284, 0.021196037530899048, 0.01020893082022667, -0.04969210922718048, 0.00383992912247777, -0.0255315899848938, -0.021103397011756897, 0.012969603762030602, 0.02812551148235798, -0.023771431297063828, -0.043281421065330505, -0.007425098214298487, -0.036407530307769775, 0.002918160753324628, -0.010357154533267021, -0.0512484610080719, 0.011894979514181614, 0.016508452594280243, -0.004323973320424557, 0.044948939234018326, -0.008606258779764175, 0.002121456665918231, 0.00489602517336607, -0.07285211235284805, -0.017036501318216324, -0.061290640383958817, -0.04813575744628906, -0.04702407494187355, -0.011709699407219887, -0.01666594110429287, 0.0028232047334313393, -0.018574325367808342, 0.022845029830932617, -0.029644807800650597, 0.013979380019009113, -0.005197105463594198, 0.02049197442829609, 0.018602117896080017, -0.018092596903443336, 0.025309255346655846, 0.05910433456301689, -0.008027258329093456, 0.0048404415138065815, 0.020010245963931084, -0.016008196398615837, 0.014590803533792496, 0.02910749614238739, -0.029255719855427742, 0.0025522327050566673, 0.021881574764847755, 0.034814123064279556, -0.014850196428596973, -0.034758538007736206, -0.006341209635138512, 0.019899077713489532, -0.023789959028363228, -0.0006224251701496542, 0.004831177182495594, 0.06451451033353806, 0.01831493340432644, -0.012043203227221966, 0.03616666421294212, 0.03329482674598694, -0.0016304644523188472, -0.0213072057813406, 0.00979205034673214, -0.02149248495697975, -0.014535220339894295, -0.018074069172143936, -0.004141008947044611, 0.00797167420387268, -0.009398330934345722, -0.008680370636284351, -0.03798241168260574, 0.01245081890374422, 0.0861181691288948, -0.009352010674774647, 0.05228602886199951, -0.04476366192102432, 0.020232580602169037, 0.03086765669286251, 0.0056417775340378284, 0.037204235792160034, -0.002934372751042247, -0.04946977272629738, -0.047505803406238556, -0.02916307933628559, 0.022826502099633217, 0.008129161782562733, -0.036314889788627625, 0.03770449012517929, 0.006971161812543869, 0.03411005809903145, 0.05221191793680191, 0.042206794023513794, -0.06173531338572502, -0.025883622467517853, -0.031052935868501663, -0.04461543634533882, -0.020769894123077393, -0.04350375756621361, 0.0032285049092024565, -0.016332436352968216, 0.024975750595331192, -0.016851220279932022, 0.026810023933649063, -0.0344620905816555, 0.007161073852330446, 0.0343509204685688, -0.006920210085809231, -0.01886150985956192, -0.025401894003152847, 0.059363726526498795, 0.01288622710853815, 0.0012552723055705428, -0.0018886985490098596, 0.002862576860934496, 0.0013791783712804317, 0.011385459452867508, 0.01363661140203476, -0.044911883771419525, 0.01800922118127346, -0.0255130622535944, -0.028625767678022385, 0.017323683947324753, 0.0427255779504776, -0.02832932025194168, -0.0257724542170763, -0.037130121141672134, 0.08078210055828094, 0.026717383414506912, 0.02734733559191227, -0.044133707880973816, 0.013766307383775711, 0.01372925192117691, -0.015072531998157501, -0.06288404762744904, 0.01418318785727024, 0.013349427841603756, 0.011626322753727436, -0.011042690835893154, 0.045875340700149536, -0.07325973361730576, -0.02903338335454464, -0.059474896639585495, -0.06340283155441284, 0.015415300615131855, 0.025364838540554047, 0.0171939879655838, -0.021251622587442398, -0.003348936792463064, 0.01153368316590786, 0.02564275823533535, -0.0597342886030674, 0.013099299743771553, -0.008050418458878994, 0.0014857144560664892, -0.033053960651159286, -0.015294868499040604, -0.07503841817378998, -0.008393186144530773, 0.046653516590595245, -0.022733861580491066, -0.02045491710305214, 0.0010468323016539216, 0.031127048656344414, 0.01762939617037773, 0.014025699347257614, -0.00010783877951325849, 0.011144595220685005, -0.011403987184166908, 0.0002664848288986832, -0.0073556178249418736, -0.01596187613904476, 0.04428193345665932, -0.037148650735616684, -0.029311303049325943, 0.0016154104378074408, -0.11353961378335953, 0.03490675985813141, -0.0008227592334151268, -0.045690059661865234, -0.010440531186759472, 0.024512549862265587, -0.0012460083235055208, 0.006443113554269075, 0.0006015811813995242, -0.03159024938941002, -0.04887687787413597, 0.0039047771133482456, 0.052656590938568115, 0.01460933219641447, -0.014136867597699165, 0.02805139869451523, 0.040613386780023575, 0.04958094283938408, -0.007471418008208275, -0.03572199493646622, 0.040687497705221176, 0.12109903991222382, 0.051767244935035706, 0.004444404970854521, 0.03092323988676071, 0.02479047141969204, 0.06584852933883667, -0.023382341489195824, -0.030460041016340256, 0.02916307933628559, 0.0256983432918787, 0.0008065472356975079, 0.05221191793680191, -0.0171939879655838, 0.013358691707253456, 0.018666965886950493, -0.01020893082022667, 0.016184212639927864, 0.012988131493330002, 0.0007579111843369901, 0.02645799145102501, -0.032071977853775024, -0.021863045170903206, -0.00576684158295393, -0.01670299656689167, -0.00917599443346262, -0.04724641144275665, -0.0010867832461372018, -0.02895927242934704, -0.005845585372298956, 0.022900614887475967, -0.019176485016942024, -0.02060314081609249, 0.014896515756845474, -0.03831591457128525, -0.07444552332162857, -0.010523906908929348, 0.03581463545560837, 0.04342964291572571, 0.061142414808273315, -0.05621396750211716, 0.019954660907387733, -0.001300434349104762, -0.004034473095089197, -0.02395671047270298, -0.028440488502383232, 0.04709818959236145, -0.0023565306328237057, 0.08219023048877716, -0.02141837403178215, 0.03516615182161331, -0.0021423005964607, 0.030589736998081207, 0.03798241168260574, -0.011413251049816608, -0.016860485076904297, -0.005442601628601551, -0.016888275742530823, -0.03831591457128525, -0.031275272369384766, -0.003837612923234701, -0.03927937150001526, -0.008532145991921425, -0.07400085031986237, -0.013942323625087738, -0.03318365663290024, -0.09997711330652237, 0.04109511524438858, -0.03336893767118454, -0.04198445752263069, 0.04672762751579285, -0.0034948450047522783, -0.022548582404851913, -0.01243229117244482, 0.019306180998682976, -0.043096140027046204, 0.0600677914917469, 0.04113217070698738, -0.025327783077955246, -0.05447233468294144, 0.03357274457812309, 0.012978867627680302, -0.048209868371486664, -0.052545420825481415, -0.004951609298586845, 0.008184745907783508, 0.019176485016942024, -0.03759332373738289, 0.015054004266858101, -0.04446721076965332, -0.023771431297063828, 0.007429730147123337, -0.01659182831645012, -0.05647335946559906, 0.038871753960847855, -0.002818572800606489, 0.037148650735616684, 0.010171874426305294, 0.05621396750211716, -0.024975750595331192, -0.0049191853031516075, -0.022789446637034416, 0.05480583757162094, -0.025086918845772743, -0.040539275854825974, -0.0004990981542505324, 0.017017971724271774, -0.031034408137202263, -0.018157444894313812, 0.013525444082915783, 0.006582073867321014, 0.0025916045997291803, -0.016906805336475372, -0.029459528625011444, 0.041465673595666885, 0.027569672092795372, -0.02908896841108799, -0.05847438424825668, 0.03414711356163025, 0.028718408197164536, 0.00665618572384119, 0.015572788193821907, 0.06418100744485855, 0.07148104161024094, 0.0005002561374567449, -0.009282530285418034, 0.016045251861214638, 0.054361168295145035, 0.03570346534252167, -0.04354081302881241, 0.0011632113019004464, 0.0299412552267313, 0.006424585822969675, -0.02145542949438095, 0.06736782938241959, -0.00033263559453189373, -0.011885715648531914, 0.02734733559191227, 0.0005321011412888765, 0.01548014860600233, -0.04509716480970383, 0.04454132542014122, -0.00383992912247777, -0.026087431237101555, 0.04861748591065407, -0.015989668667316437, -0.0025198087096214294, 0.045764170587062836, -0.06273582577705383, -0.03444356098771095, -0.032831624150276184, -0.023623205721378326, 0.0429849699139595, 0.00011949116014875472, 0.02920013666152954, -0.027514087036252022, -0.030385928228497505, 0.031330857425928116, -0.0014961364213377237, 0.013553235679864883, 0.023623205721378326, -0.0014706604415550828, -0.002039238577708602, -0.017434852197766304, -0.0013942323857918382, 0.0005254426505416632, -0.004970137495547533, 0.003606013022363186, 0.018324196338653564, 0.002702772617340088, -0.03231284022331238, -0.0689982920885086, -0.03238695114850998, -0.005558401346206665, -0.010560963302850723, -0.02047344483435154, 0.054324109107255936, -0.012256274931132793, -0.0511743500828743, 0.008263490162789822, 0.019936133176088333, -0.020918117836117744, 0.008726689964532852, 0.03675956279039383, -0.003557377029210329, 0.019157957285642624, -0.0025174927432090044, -0.025198087096214294, -0.0037310770712792873, 0.012580515816807747, 0.041502732783555984, -0.030478568747639656, -0.009690146893262863, -0.045060109347105026, -0.0513596311211586, -0.045653004199266434, -0.0257353987544775, -0.005854849703609943, 0.004984033294022083, 0.045727115124464035, -0.00011268790694884956, -0.0029667967464774847, -0.038130633533000946, -0.009379802271723747, 0.022826502099633217, -0.033016905188560486, -0.017620133236050606, 0.04020576924085617, 0.017907317727804184, -0.019157957285642624, -0.035425543785095215, -0.015897028148174286, 0.018574325367808342, 0.024253157898783684, 0.043948426842689514, -0.04698701947927475, 0.0007995992200449109, 0.016693731769919395, 0.029607752338051796, 0.005039617419242859, 0.0012587463716045022, -0.006308785639703274, 0.021084869280457497, 0.00945854652673006, -0.005424073431640863, -0.03581463545560837, -0.02651357464492321, 0.03566640987992287, 0.0016420444007962942, -0.006137401796877384, 0.033813610672950745, 0.028755463659763336, 0.03140496835112572, 0.016462132334709167, -0.0014984523877501488, -0.010051442310214043, -0.0012413763906806707, -0.016832692548632622, 0.02060314081609249, 0.011366930790245533, -0.016452867537736893, 0.007550162263214588, 0.0036361210513859987, -0.013534707948565483, 0.014414788223803043, 0.03609255328774452, -0.022715333849191666, 0.04476366192102432, -0.005873377434909344, -0.021937157958745956, 0.03070090338587761, 0.0016582563985139132, -0.00665155379101634, 0.001152789336629212, 0.0017902684630826116, 0.01448890008032322, -0.047505803406238556, 0.02408640645444393, -0.01657330058515072, 0.07407496124505997, -0.007151809986680746, -0.0012379023246467113, 0.010005122981965542, -0.02668032795190811, 0.006262465845793486, 0.029663335531949997, -0.016128627583384514, 0.012580515816807747, -0.004863601177930832, 0.03750068321824074, -0.0010995212942361832, -0.02139984630048275, -0.0032725089695304632, -0.0212886780500412, -0.03624077886343002, 0.025346310809254646, 0.003564324928447604, -0.044948939234018326, -0.019195012748241425, -0.01195056363940239, 0.03444356098771095, -0.017073556780815125, 0.05558401346206665, 0.03857530653476715, 0.00768449017778039, 0.06544091552495956, 0.02471635863184929, 0.022530054673552513, -0.014442579820752144, 0.022807974368333817, 0.012098787352442741, -0.020806949585676193, 0.021214565262198448, 0.026180071756243706, 0.005979913752526045, -0.031071463599801064, 0.02054755762219429, -0.006100345868617296, -0.009412226267158985, 0.00977352261543274, -0.0256983432918787, -0.012284067459404469, 0.0016177264042198658, -0.010987106710672379, -0.03561082482337952, 0.013664403930306435, -0.050840847194194794, -0.03222019970417023, -0.049136269837617874, 0.042317964136600494, 0.00811526644974947, -0.004039105027914047, 0.007198129780590534, 0.004808017518371344, 0.050840847194194794, 0.00031179157667793334, -0.014646387659013271, -0.021158982068300247, -0.012682419270277023, -0.017295893281698227, 0.03961287438869476, 0.007573321927338839, -0.008017994463443756, 0.0215110145509243, 0.017722036689519882, 0.0073139299638569355, -0.004064580891281366, -0.0021353524643927813, -0.01837051659822464, 0.01319193933159113, -0.023623205721378326, 0.033072490245103836, -0.006151297595351934, -0.011172386817634106, 0.004534729290753603, 0.01284917164593935, 0.030348872765898705, 0.025235142558813095, 0.009514130651950836, -0.03346157819032669, -0.0425403006374836, -0.03433239459991455, 0.05050734058022499, -0.043318476527929306, -0.0035295849665999413, -0.013784836046397686, 0.05050734058022499, -0.055954575538635254, 0.0037889769300818443, 0.028588712215423584, 0.04213268309831619, -0.028848104178905487, 0.03092323988676071, 0.0030108008068054914, -0.01871328428387642, -0.04480071738362312, 0.023289702832698822, -0.01630464382469654, 0.05402766168117523, -0.006086449604481459, -0.005827057640999556, 0.004914553370326757, 0.019899077713489532, 0.035462602972984314, -0.017740564420819283, -0.03411005809903145, 0.09063900262117386, 0.01590629294514656, 0.0024526447523385286, -0.041576843708753586, -0.014998420141637325, 0.003951096907258034, 0.03335040807723999, -0.02564275823533535, 0.010468322783708572, -0.007068433798849583, -0.00489139324054122, 0.033739496022462845, -0.01721251755952835, 0.040687497705221176, 0.061179473996162415, 0.003335040993988514, -0.028755463659763336, -0.015239284373819828, 0.01374777965247631, 0.0018574325367808342, -0.016906805336475372, 0.00884249061346054, 0.03942759335041046, 0.009504866786301136, -0.003601381089538336, -0.011691170744597912, -0.008184745907783508, 0.02060314081609249, -0.06662670522928238, 0.041391562670469284, -0.008680370636284351, 0.0005349961575120687, 0.03612960875034332, -0.006994321942329407, -0.012904755771160126, 0.034665897488594055, -0.027940232306718826, -0.015582052059471607, 0.005257321521639824, -0.001896804547868669, -0.013831155374646187, -0.029422471299767494, 0.00707769813016057, 0.03711159527301788, 0.039057034999132156, 0.005854849703609943, -0.02827373519539833, 0.02475341409444809, -0.014192451722919941, -0.04131745174527168, -0.014090548269450665, -0.029348360374569893, -0.01199688296765089, 0.00934737827628851, -0.01980643719434738, -0.003538849065080285, -0.0678495541214943, 0.009995859116315842, 0.020158469676971436, 0.009597506374120712, 0.025142502039670944, -0.003138180822134018, -0.01844462938606739, -0.007601113989949226, 0.02321559004485607, -0.04898804426193237, 0.008226433768868446, 0.03664839267730713, 0.00890270620584488, -0.01577659696340561, -0.025327783077955246, -0.021196037530899048, -0.012460083700716496, 0.032109033316373825, -0.028773991391062737, 0.01978790946304798, -0.0012946443166583776, -0.014090548269450665, 0.05469467118382454, -0.0021689345594495535, 0.010468322783708572, 0.05725153535604477, -0.057585038244724274, -0.008972186595201492, -0.007513105869293213, 0.015980403870344162, -0.0017717404989525676, -0.001424340414814651, -0.012348915450274944, 0.030348872765898705, 0.00847656186670065, -0.0016408864175900817, -0.0022650486789643764, -0.02301178313791752, -0.012052467092871666, -0.0007637012167833745, 0.005572297610342503, 0.032942794263362885, 0.024975750595331192, 0.03333188220858574, 0.028533127158880234, 0.03429533541202545, 0.045060109347105026, 0.02821815200150013, -0.0343879759311676, 0.0428367480635643, 0.009931011125445366, 0.041613899171352386, -0.013358691707253456, -0.016564035788178444, 0.06773838400840759, -0.022807974368333817, 0.009064826183021069, -0.009977330453693867, 0.01362734753638506, 0.010347890667617321, 0.012599043548107147, -0.04617178812623024, -0.01824082061648369, -0.022048326209187508, 0.013469859957695007, 0.03787124156951904, -0.0513225756585598, 0.05402766168117523, -0.02655063197016716, -0.0008424452389590442, -0.008462666533887386, -0.011153859086334705, -0.030422983691096306, -0.017527492716908455, -0.03168288990855217, 0.008657210506498814, 0.019491462036967278, -0.037167176604270935, 0.03946464881300926, -0.032016392797231674, -0.003865404985845089, -0.037241291254758835, 0.010885203257203102, -0.014674180187284946, -0.018704021349549294, -0.006934105884283781, -0.050989069044589996, -0.03138643875718117, 0.040465161204338074, 0.045838285237550735, -0.020732836797833443, -0.030422983691096306, 0.03994637727737427, 0.04131745174527168, 0.0004967821296304464, -0.0029691127128899097, -0.020844005048274994, 0.0048821293748915195, 0.0027629886753857136, -0.01023672241717577, 0.035388488322496414, 0.017842469736933708, 0.03246106579899788, -0.015211491845548153, -0.0017856365302577615, -0.00103583128657192, 0.056992143392562866, 0.03455473110079765, 0.03522173687815666, 0.015016947872936726, 0.014331411570310593, -0.008180114440619946, 0.017416324466466904, -0.038204748183488846, 0.040687497705221176, -0.001424340414814651, -0.030126536265015602, 0.020084356889128685, -0.03946464881300926, 0.005271217320114374, -0.004858969245105982, -0.017694244161248207, 0.004937713500112295, -0.03084912896156311, -0.01721251755952835, 0.01583218015730381, -0.023456454277038574, -0.002427168656140566, 0.036407530307769775, 0.00840708240866661, 0.027662310749292374, -0.01782394014298916, -0.020881062373518944, 0.03751920908689499, -0.04791342094540596, 0.01151515543460846, 0.019973188638687134, 0.06599675118923187, 0.002387796761468053, 0.0033836769871413708, 0.010950051248073578, 0.024605190381407738, -0.010598018765449524, 0.025012806057929993, 0.044837772846221924, 0.020751366391777992, 0.018342724069952965, -0.0017068925080820918, -0.03942759335041046, 0.044874828308820724, 0.005507449619472027, -0.04172506555914879, -0.021937157958745956, 0.07059169560670853, 0.0055676656775176525, 0.03662986680865288, -0.021659238263964653, -0.010023650713264942, -0.047616973519325256, 0.017907317727804184, -0.022715333849191666, -0.0028278366662561893, -0.0007115912158042192, 0.03531437739729881, -0.006517225876450539, -0.0007058011833578348, 0.0342026986181736, 0.009180626831948757, 0.003640752984210849, 0.01960262842476368, -0.030126536265015602, -0.017981428653001785, -0.044059596955776215, -0.008471930399537086, 0.05499111860990524, -0.025920679792761803, 0.03729687258601189, -0.016091572120785713, -0.02319706231355667, -0.018148180097341537, -0.016767844557762146, -0.01195056363940239, -0.01112606655806303, -0.01808333210647106, -0.002897316822782159, 0.026884134858846664, 0.04472660273313522, -0.016767844557762146, 0.013127091340720654, 0.06595969945192337, 0.020714309066534042, -0.014896515756845474, 0.04687585309147835, 0.00427996926009655, -0.018528005108237267, -0.033795081079006195, -0.039057034999132156, 0.024197574704885483, 0.04795047640800476, 0.0032516648061573505, 0.053508877754211426, 0.03360980004072189, -0.004113216884434223, 0.03086765669286251, 0.014868724159896374, -0.036351945251226425, 0.006350473500788212, -0.019862022250890732, 0.015878500416874886, 0.011932034976780415, -0.06462568044662476, 0.053434766829013824, -0.024253157898783684, -0.03596285730600357, 0.014572275802493095, -0.027792006731033325, -0.011718963272869587, -0.07051758468151093 ]
Recent years have seen growing interest among both researchers and practitioners in user-engaged approaches to algorithm auditing, which directly engage users in detecting problematic behaviors in algorithmic systems. However, we know little about industry practitioners' current practices and challenges around user-engaged auditing, nor what opportunities exist for them to better leverage such approaches in practice. To investigate, we conducted a series of interviews and iterative co-design activities with practitioners who employ user-engaged auditing approaches in their work. Our findings reveal several challenges practitioners face in appropriately recruiting and incentivizing user auditors, scaffolding user audits, and deriving actionable insights from user-engaged audit reports. Furthermore, practitioners shared organizational obstacles to user-engaged auditing, surfacing a complex relationship between practitioners and user auditors. Based on these findings, we discuss opportunities for future HCI research to help realize the potential (and the mitigate risks) of user-engaged auditing in industry practice.
[ -0.019193314015865326, -0.010951478965580463, -0.03347105532884598, -0.06510093808174133, 0.019575443118810654, 0.03710128366947174, -0.02494262345135212, 0.009553233161568642, 0.01264500617980957, 0.01212392095476389, 0.02329251915216446, -0.054436057806015015, 0.024855775758624077, -0.029267631471157074, -0.029406588524580002, 0.0015263460809364915, 0.03908140957355499, -0.017699535936117172, 0.03237677365541458, -0.023466214537620544, 0.008936615660786629, -0.003999330569058657, -0.050197895616292953, 0.035520657896995544, 0.01620575785636902, 0.03651072084903717, 0.0031221702229231596, 0.00668292073532939, -0.01961018145084381, 0.011394402012228966, 0.003921167925000191, 0.035538025200366974, -0.025915315374732018, -0.025220535695552826, -0.07114553451538086, 0.014164838939905167, 0.03974144905805588, -0.02824283018708229, -0.013270309194922447, 0.025463707745075226, -0.043319568037986755, 0.013278993777930737, 0.005493109114468098, 0.00011629432992776856, -0.022875649854540825, -0.03651072084903717, -0.018168512731790543, 0.0028963666409254074, -0.026523249223828316, 0.029632391408085823, 0.07218769937753677, 0.017169764265418053, 0.06492724269628525, -0.023066716268658638, -0.04359748214483261, -0.024143625050783157, -0.030205585062503815, -0.05638144537806511, 0.06833167374134064, 0.024873144924640656, 0.02601953223347664, 0.011012271977961063, -0.02233719639480114, 0.010638827458024025, 0.08108089119195938, -0.013678492978215218, -0.04707138612866402, 0.01961018145084381, 0.017517155036330223, 0.023917822167277336, -0.010977533645927906, -0.03119564801454544, 0.00646580196917057, 0.01818588189780712, 0.008463296107947826, -0.005488766822963953, 0.03442637622356415, -0.011463879607617855, -0.020773939788341522, -0.0034673893824219704, 0.021347133442759514, -0.020739199593663216, 0.002570688258856535, -0.022076653316617012, 0.03842136636376381, -0.013973774388432503, -0.016223127022385597, -0.08754235506057739, 0.02718329057097435, -0.002360082697123289, -0.02471681870520115, 0.03070930205285549, -0.027374355122447014, -0.010769098997116089, -0.03932458162307739, -0.052629631012678146, -0.03581593930721283, -0.048044078052043915, -0.027235398069024086, 0.0004469935956876725, 0.01300976611673832, -0.03783080354332924, 0.006539622321724892, 0.009587972424924374, 0.012766593135893345, -0.027495941147208214, -0.07705117017030716, 0.012453941628336906, -0.002722671488299966, 0.15021155774593353, -0.025498447939753532, 0.016874482855200768, -0.07642586529254913, -0.03215097263455391, -0.050302114337682724, 0.051344286650419235, -0.05026737600564957, -0.062356557697057724, -0.007594820111989975, 0.04029727354645729, -0.010942794382572174, 0.027044333517551422, 0.03235940635204315, 0.05426236242055893, 0.005831814371049404, 0.0371360220015049, 0.019766507670283318, 0.01809903420507908, 0.05130954459309578, 0.006804507225751877, 0.005106637254357338, 0.06061960756778717, 0.02080867812037468, -0.018411684781312943, 0.030900366604328156, -0.016214441508054733, 0.05481818690896034, 0.027131181210279465, 0.034461118280887604, 0.014981206506490707, 0.010517241433262825, 0.007021626457571983, -0.04595973715186119, -0.012836071662604809, -0.03215097263455391, 0.0033827130682766438, -0.06624732911586761, 0.04429226368665695, -0.049225203692913055, 0.018481163308024406, -0.043076395988464355, 0.04196474701166153, -0.027131181210279465, -0.002852942794561386, 0.09747771918773651, -0.03451322391629219, 0.009596657007932663, 0.01163757499307394, -0.03154303878545761, 0.026453770697116852, 0.03946353867650032, -0.033141035586595535, 0.01477277185767889, 0.03129986673593521, 0.0801776796579361, -0.013148722238838673, -0.028677068650722504, -0.025446338579058647, 0.015797574073076248, 0.06805375963449478, 0.004385802429169416, -0.06169651448726654, -0.006591730751097202, 0.006361584644764662, 0.0020040078088641167, 0.01744767650961876, 0.044987041503190994, 0.021017111837863922, -0.03720549866557121, -0.07538369297981262, -0.046619776636362076, -0.0021386214066296816, 0.02836441807448864, 0.021451350301504135, -0.00904951710253954, 0.031994644552469254, 0.0610017366707325, -0.03887297213077545, 0.0010741959558799863, -0.0031026294454932213, 0.013635069131851196, -0.02872917801141739, 0.0005159288411960006, -0.007499287836253643, -0.03644124045968056, -0.0420689657330513, 0.014069306664168835, -0.015372020192444324, 0.025845836848020554, -0.038247670978307724, -0.03783080354332924, -0.05481818690896034, -0.014460121281445026, -0.010786468163132668, -0.03783080354332924, -0.0056841736659407616, -0.005888265557587147, 0.016865799203515053, -0.03027506358921528, -0.045438650995492935, -0.028294939547777176, 0.006322503089904785, 0.020183375105261803, -0.014746718108654022, -0.03828240931034088, -0.0134092653170228, 0.009640080854296684, 0.05179589241743088, 0.010534610599279404, 0.00045242157648317516, -0.022997237741947174, 0.018515901640057564, 0.004090520553290844, 0.023344628512859344, 0.036232806742191315, -0.013965089805424213, 0.0009493525139987469, 0.043423786759376526, 0.03793501853942871, 0.015259118750691414, -0.04866937920451164, 0.0062530250288546085, -0.053150713443756104, 0.034825876355171204, 0.043805915862321854, -0.04623764753341675, -0.003172107506543398, 0.024369429796934128, -0.0005949058686383069, -0.015441498719155788, -0.02282354235649109, -0.035155896097421646, -0.01901961863040924, -0.023605169728398323, 0.08302628248929977, -0.03897719085216522, -0.030327172949910164, 0.06166177615523338, -0.014729348011314869, 0.036337025463581085, -0.00018862207070924342, 0.03807397559285164, -0.03908140957355499, -0.006309476215392351, 0.02732224576175213, 0.09039095044136047, 0.03644124045968056, 0.00010923796071438119, 0.016049431636929512, -0.027009595185518265, 0.033853184431791306, 0.022424044087529182, -0.05110111087560654, 0.03821293264627457, -0.05186536908149719, -0.043528001755476, 0.027096442878246307, 0.007672983221709728, 0.02447364665567875, -0.037622369825839996, 0.0368928499519825, -0.012653691694140434, -0.013183461502194405, -0.024543123319745064, -0.031959906220436096, -0.0022688929457217455, -0.014451435767114162, -0.022979868575930595, -0.006213943939656019, 0.02763489820063114, -0.017091602087020874, -0.018620120361447334, 0.11220706254243851, -0.01571941003203392, 0.006600415334105492, -0.06287764012813568, -0.0060272216796875, -0.03998462110757828, 0.0007479747291654348, 0.017169764265418053, -0.02138187177479267, -0.034808509051799774, -0.02256299927830696, 0.038838233798742294, 0.05051054805517197, 0.018585380166769028, -0.0067958226427435875, 0.04766194894909859, 0.011889432556927204, -0.008628305979073048, 0.004418370313942432, -0.02553318627178669, -0.01294028852134943, 0.05836156755685806, 0.02893761172890663, 0.040714140981435776, -0.00694346334785223, 0.03675389289855957, 0.02233719639480114, -0.03619806841015816, 0.015024630352854729, 0.002134279115125537, -0.03003189153969288, -0.004173025954514742, -0.04067940264940262, 0.023674648255109787, 0.031056692823767662, 0.04682821035385132, 0.014260371215641499, -0.0053802072070539, -0.01755189523100853, -0.016605256125330925, -0.14326375722885132, -0.0016891852719709277, 0.005532190203666687, 0.00409269193187356, -0.017091602087020874, -0.00997878611087799, -0.00019201455870643258, -0.01928016170859337, -0.020721830427646637, 0.04505652189254761, -0.042485833168029785, 0.01797744818031788, 0.0006936949794180691, -0.022424044087529182, -0.03998462110757828, 0.015571770258247852, 0.03460007160902023, 0.017291352152824402, -0.04762721061706543, -0.02070446126163006, -0.09949257969856262, -0.002505552489310503, -0.007985634729266167, -0.026210596784949303, 0.013122668489813805, -0.0063529000617563725, -0.04043623059988022, 0.015363335609436035, 0.0009634652524255216, 0.009370853193104267, 0.008398160338401794, -0.003732274519279599, 0.010204589925706387, -0.002174446126446128, 0.01765611208975315, -0.0017868888098746538, 0.008841082453727722, 0.006887012626975775, 0.08344314992427826, -0.06805375963449478, -0.03828240931034088, 0.019592812284827232, -0.004737535025924444, -0.0007843421190045774, -0.022406673058867455, -0.025932684540748596, 0.026175858452916145, -0.019940203055739403, -0.033158402889966965, 0.05672883614897728, -0.012714484706521034, -0.006279079709202051, -0.001723924302496016, -0.004053610377013683, -0.019888093695044518, 0.019123835489153862, -0.06558728963136673, 0.017352145165205002, -0.035034310072660446, -0.027964917942881584, 0.000031176921766018495, 0.01901961863040924, -0.0005048015154898167, 0.06986019015312195, 0.006691605318337679, 0.03048349730670452, 0.06388507783412933, 0.03967197239398956, -0.02007915824651718, 0.022771432995796204, -0.0016490182606503367, -0.02824283018708229, 0.02991030365228653, 0.008211437612771988, 0.020513396710157394, -0.029927672818303108, 0.021816110238432884, -0.021798741072416306, -0.011950225569307804, 0.008059455081820488, -0.03842136636376381, 0.06457985192537308, 0.025116318836808205, -0.05599931627511978, -0.013218200765550137, 0.05756257101893425, 0.016639994457364082, -0.016283920034766197, -0.040957316756248474, 0.031143540516495705, -0.018863292410969734, 0.02895498089492321, 0.01761268824338913, -0.026557987555861473, -0.03072667121887207, 0.016171017661690712, 0.05179589241743088, -0.051240067929029465, 0.009075571782886982, 0.03070930205285549, 0.021937696263194084, -0.04092257469892502, 0.010326175950467587, -0.02468208037316799, -0.004401000682264566, -0.038004498928785324, 0.035746462643146515, -0.024386798962950706, 0.04540391266345978, 0.01809903420507908, -0.05676357448101044, -0.012601583264768124, 0.03915088623762131, -0.009127680212259293, 0.03845610469579697, 0.025376860052347183, -0.03223782032728195, -0.007399413269013166, -0.02850337326526642, -0.006969517562538385, -0.04554286599159241, 0.021208176389336586, -0.06426720321178436, -0.05391497164964676, -0.06207864359021187, 0.015693357214331627, -0.047210339456796646, -0.020409179851412773, -0.050163157284259796, -0.01650972291827202, -0.08802869915962219, -0.014381958171725273, 0.044639650732278824, -0.05853526294231415, 0.035989634692668915, -0.048287250101566315, 0.013487428426742554, -0.029354479163885117, -0.002038746839389205, 0.07006862014532089, 0.04842620715498924, -0.014755402691662312, 0.02186821959912777, -0.020148636773228645, -0.07413309067487717, -0.003417452098801732, 0.023935191333293915, -0.011307554319500923, 0.028920242562890053, -0.01785586029291153, -0.01035223063081503, 0.018932770937681198, 0.0034196232445538044, 0.0037105625960975885, 0.0423121377825737, 0.007998661138117313, -0.031595148146152496, -0.045091260224580765, 0.01431247964501381, 0.044639650732278824, -0.004155656322836876, -0.0296497605741024, 0.0062052588909864426, -0.02186821959912777, 0.08587487787008286, 0.022128760814666748, -0.0020637153647840023, -0.08914034813642502, -0.07962185144424438, 0.0052238814532756805, 0.009318744763731956, -0.010543295182287693, -0.013643753714859486, -0.008901876397430897, -0.014529598876833916, -0.0423121377825737, -0.008432899601757526, -0.014208262786269188, -0.002562003443017602, 0.025741619989275932, 0.0029549887403845787, -0.040227796882390976, 0.04123522713780403, -0.03560750558972359, -0.0420689657330513, 0.006478828843683004, 0.046619776636362076, 0.036232806742191315, 0.006357242353260517, -0.0014243002515286207, 0.011854693293571472, -0.009014777839183807, 0.004476992413401604, 0.0019388720393180847, -0.01181126944720745, 0.003228558460250497, 0.0036779947113245726, 0.001901961863040924, 0.0018086007330566645, -0.014738033525645733, -0.008636991493403912, 0.024768928065896034, -0.03925510123372078, 0.03227255865931511, 0.0017597489058971405, 0.0001998851221287623, 0.016631310805678368, 0.010065633803606033, -0.02812124416232109, 0.003812608541920781, -0.031977277249097824, -0.024838406592607498, 0.03475639969110489, -0.01638813689351082, 0.011151228100061417, 0.015172271057963371, 0.012271561659872532, -0.004420541226863861, -0.04408382624387741, 0.049919985234737396, 0.008832397870719433, 0.02185084857046604, -0.0032676400151103735, 0.026141120120882988, 0.05280332267284393, -0.034322161227464676, -0.0062052588909864426, -0.005488766822963953, -0.04783564433455467, 0.022059284150600433, -0.038942452520132065, -0.02068709209561348, 0.02753068134188652, -0.01690053753554821, 0.0029918989166617393, -0.010143796913325787, 0.0427984856069088, -0.01763005740940571, -0.017169764265418053, -0.02398729883134365, 0.029493436217308044, -0.03866453841328621, 0.01164625957608223, -0.003376199398189783, 0.035051681101322174, 0.0688527524471283, -0.028433894738554955, 0.013070560060441494, -0.014373273588716984, 0.015493607148528099, -0.06065434589982033, -0.01818588189780712, -0.029337109997868538, 0.007182294502854347, 0.02363990992307663, -0.0364065021276474, 0.004036240745335817, -0.02198980562388897, -0.016014693304896355, 0.04102679342031479, 0.012158660218119621, 0.04140892252326012, -0.001612108084373176, 0.023188302293419838, 0.015372020192444324, -0.0182032510638237, -0.014529598876833916, 0.005866553634405136, -0.001545886741951108, 0.01985335536301136, -0.020756570622324944, -0.0031938194297254086, -0.024317320436239243, -0.01683974452316761, 0.0005471397307701409, 0.029823455959558487, 0.013539536856114864, -0.031230386346578598, 0.030535606667399406, 0.04766194894909859, 0.03463481366634369, 0.03084825724363327, 0.008489349856972694, -0.029979782178997993, -0.013157407753169537, -0.046758733689785004, 0.012410517781972885, 0.03015347756445408, 0.02363990992307663, -0.005184799898415804, 0.04682821035385132, -0.049711551517248154, 0.04054044559597969, -0.014850934967398643, 0.0121152363717556, -0.030552975833415985, -0.010126426815986633, 0.011203336529433727, -0.015415444038808346, -0.020027050748467445, 0.0732993483543396, 0.0183248370885849, 0.026384292170405388, -0.003727931994944811, -0.020530765876173973, 0.0017065547872334719, 0.004646345041692257, 0.032793644815683365, -0.0430416576564312, 0.01712634228169918, -0.014051937498152256, 0.01928016170859337, -0.02363990992307663, 0.012314985506236553, 0.021086590364575386, 0.08518009632825851, 0.02610637992620468, -0.024612601846456528, -0.012306300923228264, 0.029528174549341202, -0.009535863064229488, 0.12408781051635742, -0.019662290811538696, 0.029962413012981415, 0.031977277249097824, -0.0183248370885849, 0.027513310313224792, -0.01856801100075245, 0.023136192932724953, 0.007099789101630449, 0.00863264873623848, 0.01588442176580429, -0.02600216306746006, 0.002262379275634885, 0.015293858014047146, 0.025272643193602562, -0.040714140981435776, 0.017803752794861794, 0.04787038266658783, -0.005323756020516157, 0.01222813781350851, 0.003801752580329776, 0.017751643434166908, 0.017135025933384895, 0.012506050057709217, -0.038143452256917953, 0.013747970573604107, 0.09664397686719894, -0.017925338819622993, -0.013435319066047668, -0.03300207853317261, 0.017360830679535866, -0.010829892009496689, -0.017942707985639572, -0.037900280207395554, 0.0020278908777981997, -0.012697115540504456, 0.017604002729058266, 0.031734101474285126, -0.026766421273350716, 0.0077120643109083176, -0.021190807223320007, -0.045681823045015335, -0.016709472984075546, -0.047001905739307404, 0.04220791906118393, 0.011420455761253834, -0.03239414468407631, -0.024543123319745064, 0.022076653316617012, 0.00779891200363636, 0.010612773708999157, 0.008120248094201088, -0.0047809588722884655, -0.018394315615296364, -0.06867905706167221, -0.006513568107038736, -0.01726529747247696, -0.0021679324563592672, -0.01123807579278946, -0.0031199990771710873, 0.013661122880876064, -0.013452689163386822, -0.00034766169846989214, 0.0048634642735123634, 0.009813775308430195, 0.025932684540748596, -0.007646929007023573, -0.014972521923482418, 0.004481334704905748, 0.006478828843683004, 0.015267803333699703, 0.010386969894170761, 0.028989719226956367, 0.06947805732488632, -0.002222212264314294, 0.006743714213371277, 0.015771519392728806, -0.019193314015865326, -0.03095247410237789, 0.014034567400813103, -0.05957743525505066, -0.06444089859724045, 0.024438906461000443, -0.006535280030220747, -0.017725588753819466, 0.0008152815862558782, -0.01210655178874731, 0.05499188229441643, 0.0023991642519831657, 0.01797744818031788, 0.016162334010004997, -0.013096613809466362, 0.023848343640565872, -0.03807397559285164, 0.043805915862321854, -0.02412625588476658, 0.0209128949791193, -0.02117343805730343, -0.014538283459842205, 0.018811184912919998, -0.06485776603221893, 0.02555055543780327, -0.021086590364575386, -0.010716990567743778, 0.022493520751595497, -0.010725675150752068, -0.01612759381532669, 0.015649933367967606, 0.010065633803606033, 0.031056692823767662, -0.027339616790413857, -0.019940203055739403, -0.0053671798668801785, 0.02365727908909321, -0.005962085910141468, 0.017091602087020874, 0.008385132998228073, -0.04015831649303436, 0.038490843027830124, 0.005979455541819334, 0.020634982734918594, 0.033036816865205765, 0.017499785870313644, -0.06683789193630219, 0.012862125411629677, -0.0005666803917847574, 0.03935931995511055, -0.022302456200122833, -0.036823369562625885, 0.04099205508828163, -0.005449685268104076, 0.002811690093949437, -0.02563740313053131, 0.02198980562388897, -0.011463879607617855, -0.034078989177942276, -0.018376946449279785, -0.040123578161001205, 0.005236908793449402, -0.013991143554449081, 0.009275320917367935, -0.02683589980006218, 0.03142145276069641, 0.014008513651788235, -0.009614026173949242, -0.004915572702884674, 0.036475978791713715, -0.021451350301504135, -0.008658703416585922, -0.003165594069287181, 0.018168512731790543, -0.00957928691059351, -0.04884307458996773, -0.017135025933384895, 0.0121760293841362, -0.0011409600265324116, -0.020617613568902016, 0.025567924603819847, 0.004893860779702663, 0.01035223063081503, -0.01879381388425827, -0.02409151755273342, -0.027495941147208214, -0.031247757375240326, -0.03925510123372078, 0.0432848297059536, 0.03416583687067032, 0.048877812922000885, 0.022736694663763046, -0.015424128621816635, -0.009006093256175518, -0.019644921645522118, -0.05221275985240936, -0.045924995094537735, 0.033974770456552505, 0.030639823526144028, 0.008537116460502148, -0.00282037490978837, -0.059403739869594574, -0.0019312729127705097, -0.03960249200463295, -0.022875649854540825, 0.015858367085456848, -0.01582362689077854, -0.02529001235961914, -0.02329251915216446, 0.017890600487589836, -0.015971269458532333, 0.04835672676563263, 0.02838178724050522, 0.024317320436239243, 0.013461373746395111, 0.044848088175058365, 0.010899370536208153, -0.033384207636117935, 0.009466385468840599, 0.035642243921756744, 0.017282666638493538, -0.0009716072236187756, 0.03206412494182587, -0.009648765437304974, 0.0025728594046086073, 0.029024459421634674, -0.03347105532884598, -0.0010769099462777376, -0.021451350301504135, 0.0067306868731975555, 0.02541160024702549, 0.015293858014047146, -0.006999914534389973, -0.011368347331881523, 0.020166005939245224, -0.017769012600183487, 0.0009325257851742208, 0.033627379685640335, -0.02494262345135212, -0.011837324127554893, -0.01381744910031557, -0.03831714764237404, -0.03359264135360718, -0.021364502608776093, 0.02775648422539234, -0.00863264873623848, 0.0007425467483699322, -0.06457985192537308, -0.0012538618175312877, -0.018967509269714355, -0.040714140981435776, 0.022771432995796204, 0.004450938198715448, 0.014486175030469894, -0.003295865375548601, 0.03425268456339836, 0.004889518488198519, -0.007516657467931509, 0.005497451405972242, -0.0031069719698280096, -0.017378199845552444, 0.03499957174062729, -0.022528260946273804, -0.05207380652427673, 0.03213360160589218, -0.04245109483599663, 0.009344798512756824, -0.005011104978621006, 0.0183248370885849, -0.01596258394420147, 0.006244340445846319, 0.01305318996310234, 0.0034500197507441044, -0.023587800562381744, 0.02469944953918457, 0.010239329189062119, -0.03182094916701317, -0.015684671700000763, -0.017030809074640274, 0.02421310357749462, -0.010195905342698097, -0.005189142655581236, 0.019349638372659683, -0.025932684540748596, -0.008580540306866169, 0.032689426094293594, -0.024612601846456528, -0.018481163308024406, 0.0011952397180721164, -0.007108473684638739, -0.023952560499310493, -0.03678863123059273, 0.0023709386587142944, -0.06214812397956848, 0.023709386587142944, -0.029701869934797287, -0.05721518024802208, 0.00945770088583231, 0.014989891089498997, 0.003975447732955217, 0.05707622319459915, 0.04227739945054054, -0.025915315374732018, 0.006565676536411047, -0.022893020883202553, -0.0009759495733305812, 0.01035223063081503, 0.0077598304487764835, -0.03803923726081848, 0.022875649854540825, -0.027721745893359184, 0.01865485869348049, -0.0004925885586999357, 0.03084825724363327, 0.026905378326773643, 0.05151798203587532, -0.026158489286899567, 0.038942452520132065, -0.010326175950467587, -0.04915572702884674, 0.009197157807648182, -0.04259004816412926, -0.0011214192491024733, 0.0023817946203052998, 0.0607585608959198, -0.014920412562787533, 0.047106124460697174, 0.024734187871217728, -0.06412824988365173, 0.01418220903724432, -0.050892677158117294, 0.0038951137103140354, 0.039185624569654465, 0.04064466431736946, -0.03699706494808197, -0.0017792896833270788, -0.017586633563041687, -0.009231897071003914, -0.007816281169652939, 0.023500952869653702, -0.00015700413496233523, -0.012688430026173592, -0.004112232476472855, 0.0005748223629780114, -0.009605341590940952, 0.027026964351534843, -0.018342208117246628, -0.018272729590535164, -0.03991514444351196, 0.03225518763065338, -0.005102294962853193, 0.009301374666392803, -0.04373643919825554, 0.008428556844592094, 0.0213992428034544, -0.035746462643146515, 0.01393903512507677, -0.031039321795105934, 0.038490843027830124, 0.008211437612771988, -0.01643156073987484, -0.0484609454870224, -0.016987385228276253, -0.0019692687783390284, -0.03430479019880295, -0.01983598619699478, 0.020270222797989845, -0.00039189966628327966, -0.020304962992668152, 0.014581707306206226, -0.005923004355281591, -0.022893020883202553, -0.004481334704905748, -0.04529969394207001, -0.029979782178997993, 0.018620120361447334, 0.009362168610095978, 0.00665252422913909, -0.016049431636929512, 0.025567924603819847, 0.011394402012228966, 0.08059454709291458, 0.02374412678182125, 0.014130099676549435, -0.02577636018395424, 0.023813605308532715, 0.002972358139231801, 0.06155756115913391, -0.03369686007499695, -0.010239329189062119, -0.009674819186329842, 0.02636692300438881, 0.032342035323381424, 0.016422875225543976, 0.008784632198512554, 0.03272416442632675, -0.007160582579672337, -0.043528001755476, -0.01117728278040886, -0.0944901555776596, 0.027252769097685814, 0.02740909345448017, 0.030118737369775772, -0.007551396265625954 ]
We consider quantitative analyses of spectral data using laser-induced breakdown spectroscopy. We address the small size of training data available, and the validation of the predictions during inference on unknown data. For the purpose, we build robust calibration models using deep convolutional multitask learning architectures to predict the concentration of the analyte, alongside additional spectral information as auxiliary outputs. These secondary predictions can be used to validate the trustworthiness of the model by taking advantage of the mutual dependencies of the parameters of the multitask neural networks. Due to the experimental lack of training samples, we introduce a simulation-based data augmentation process to synthesise an arbitrary number of spectra, statistically representative of the experimental data. Given the nature of the deep learning model, no dimensionality reduction or data selection processes are required. The procedure is an end-to-end pipeline including the process of synthetic data augmentation, the construction of a suitable robust, homoscedastic, deep learning model, and the validation of its predictions. In the article, we compare the performance of the multitask model with traditional univariate and multivariate analyses, to highlight the separate contributions of each element introduced in the process.
[ 0.01133112795650959, -0.03525441139936447, -0.0338391549885273, -0.0447801798582077, 0.046993788331747055, -0.041586779057979584, -0.06550099700689316, 0.03832080215215683, -0.00755257299169898, 0.06383171677589417, 0.02968410588800907, -0.08484283834695816, -0.000045573426177725196, -0.03365771099925041, 0.010941024869680405, -0.004667626228183508, 0.008096902631223202, -0.0477195605635643, 0.036524515599012375, -0.00263319443911314, 0.05211048573255539, -0.07569810003042221, -0.04459873586893082, 0.02981111779808998, -0.05080409348011017, -0.011621437035501003, 0.03100864216685295, 0.01067793183028698, -0.06796862185001373, 0.0228074099868536, 0.06695254147052765, 0.00954391248524189, 0.021428441628813744, -0.018325762823224068, -0.022716687992215157, -0.05062265321612358, 0.029357509687542915, 0.013971125707030296, 0.006391336675733328, -0.0027942252345383167, 0.0376313179731369, -0.010351334698498249, 0.02716204710304737, 0.013526590541005135, -0.019922463223338127, -0.10160818696022034, -0.05000574514269829, -0.06535583734512329, -0.00795628409832716, -0.0027851529885083437, -0.005661027505993843, 0.012828033417463303, 0.02678101509809494, -0.009298963472247124, -0.008555046282708645, 0.028559159487485886, 0.007566181011497974, 0.09210056811571121, 0.01908782497048378, 0.03021029196679592, 0.0116123640909791, 0.031625550240278244, -0.033748432993888855, 0.0012905147159472108, 0.014878341928124428, -0.10726922005414963, 0.05849728733301163, -0.081141397356987, 0.033730290830135345, 0.014778547920286655, 0.0016091743018478155, 0.007720408029854298, 0.015558754093945026, -0.00974349956959486, 0.0040235030464828014, 0.0386836901307106, -0.025819366797804832, 0.00020284781930968165, -0.03933688625693321, 0.019577721133828163, -0.013816899619996548, 0.048191312700510025, 0.0046540177427232265, 0.044889047741889954, 0.07275871932506561, 0.02160988375544548, -0.04202224314212799, -0.04942512512207031, 0.0027783489786088467, -0.04757440462708473, -0.043437499552965164, 0.03666967153549194, 0.00023615965619683266, -0.0021546378266066313, 0.006028450094163418, 0.05472326651215553, 0.008636696264147758, -0.020521225407719612, -0.07932696491479874, -0.022879986092448235, -0.003352163126692176, -0.009471334517002106, 0.04463502764701843, -0.01723710261285305, 0.012383498251438141, -0.05871501937508583, -0.035853173583745956, 0.03901028633117676, -0.0006049996591173112, 0.13441312313079834, -0.0003501286555547267, -0.04869935289025307, -0.01778143271803856, -0.02387792430818081, -0.017309680581092834, -0.005152986850589514, -0.02400493435561657, -0.05766264721751213, -0.037195853888988495, -0.02226307988166809, 0.01055092178285122, 0.024313388392329216, 0.03861111029982567, -0.03138967230916023, -0.030663900077342987, 0.0790366530418396, -0.016012361273169518, -0.0535983182489872, 0.031244518235325813, 0.004542883951216936, -0.01750926859676838, -0.010260612703859806, -0.023533182218670845, -0.024839572608470917, -0.026073386892676353, 0.027143901214003563, 0.021791327744722366, 0.01127669494599104, 0.023261018097400665, -0.015985146164894104, -0.03251462057232857, -0.02768823131918907, -0.008568654768168926, 0.04775584861636162, 0.02982926182448864, 0.021029265597462654, -0.03060946613550186, 0.09260860830545425, -0.01946885511279106, -0.015749270096421242, -0.030282869935035706, 0.04459873586893082, 0.01160329207777977, 0.010342261753976345, -0.006382264196872711, 0.016193805262446404, 0.02188204973936081, 0.0028010292444378138, 0.00527546089142561, -0.037595029920339584, 0.004976079799234867, -0.05334429815411568, 0.027089469134807587, 0.019015247002243996, 0.09181025624275208, -0.0024154626298695803, 0.02667214907705784, -0.04655832424759865, -0.050695229321718216, 0.034800805151462555, 0.008042469620704651, -0.015604115091264248, 0.002177318325266242, -0.01946885511279106, 0.023623904213309288, 0.01593071222305298, 0.015885351225733757, 0.023006998002529144, -0.03434719517827034, -0.01245607528835535, -0.03246018663048744, -0.005352574400603771, 0.011367416009306908, 0.01694679446518421, 0.0384659580886364, -0.016747206449508667, 0.05392491817474365, -0.016275454312562943, 0.05450553447008133, 0.07032737880945206, -0.025946376845240593, -0.025547202676534653, 0.012192982248961926, -0.016847001388669014, 0.03169812634587288, -0.027996685355901718, -0.04721152037382126, -0.00371278147213161, -0.00289855501614511, -0.024458542466163635, -0.030301013961434364, -0.06441233307123184, -0.01404370367527008, -0.010823086835443974, 0.02213606983423233, 0.041042450815439224, -0.016348032280802727, 0.04626801609992981, 0.02295256406068802, -0.02239008992910385, 0.007139789871871471, 0.02360576018691063, -0.04292945936322212, -0.010197107680141926, 0.01331793051213026, -0.009435046464204788, 0.03988121449947357, -0.022371945902705193, 0.009013190865516663, 0.021410297602415085, 0.01437937282025814, 0.023006998002529144, 0.06724284589290619, -0.00523463636636734, -0.012047828175127506, 0.02213606983423233, 0.05211048573255539, -0.027397923171520233, -0.013662672601640224, 0.018743082880973816, 0.04300203546881676, -0.010687003843486309, -0.009362468495965004, -0.029647817835211754, -0.0021058751735836267, -0.004393193405121565, 0.010269684717059135, 0.00967092253267765, 0.037449873983860016, -0.02135586366057396, 0.029647817835211754, -0.025021016597747803, -0.034274619072675705, -0.05976738780736923, 0.020085761323571205, 0.0027125757187604904, 0.0017044320702552795, 0.024766996502876282, 0.020103905349969864, 0.024367820471525192, -0.04238513112068176, 0.007275871932506561, -0.0024245346430689096, -0.010777725838124752, -0.01568576507270336, 0.013962053693830967, 0.07058140635490417, -0.0011612364323809743, -0.04510677978396416, -0.08266551792621613, 0.05690058693289757, -0.007017315365374088, 0.010941024869680405, 0.028577303513884544, -0.009779788553714752, -0.022698543965816498, 0.07656902819871902, -0.04695750027894974, 0.048590488731861115, 0.027651943266391754, -0.021265141665935516, -0.03126266226172447, 0.0031185548286885023, -0.010641643777489662, 0.0015864939196035266, -0.05421522632241249, 0.07072655856609344, -0.01345401257276535, -0.014161641709506512, 0.007938140071928501, 0.00960741750895977, -0.021519163623452187, 0.043800387531518936, 0.0008975767996162176, 0.023025142028927803, -0.018153391778469086, -0.019124113023281097, 0.02295256406068802, -0.024549264460802078, -0.022898131981492043, 0.01046927273273468, -0.04452615976333618, -0.03565358743071556, 0.016701845452189445, -0.0039327810518443584, 0.019450711086392403, -0.07304903119802475, -0.04441729560494423, 0.005910512059926987, -0.02043050341308117, -0.035599153488874435, -0.018888236954808235, 0.04717523232102394, 0.03988121449947357, 0.0506589412689209, 0.03022843599319458, 0.05552161857485771, 0.05182017758488655, -0.02678101509809494, -0.018888236954808235, -0.010260612703859806, 0.049533993005752563, 0.004994223825633526, -0.020611947402358055, -0.03715956583619118, 0.01824411377310753, 0.05690058693289757, -0.0007580923265777528, 0.023388028144836426, -0.013308858498930931, 0.03603461757302284, 0.016112156212329865, -0.1351388841867447, 0.03483709320425987, 0.026091530919075012, -0.014288651756942272, -0.018452772870659828, 0.022589677944779396, -0.02612782083451748, -0.008963293395936489, -0.00440453365445137, 0.0030369055457413197, -0.06960161030292511, 0.03285936266183853, 0.01885194703936577, -0.021700605750083923, -0.019450711086392403, 0.033077094703912735, -0.01504164095968008, -0.0038239152636379004, -0.017400402575731277, 0.016084939241409302, -0.032823074609041214, 0.02043050341308117, 0.005012368317693472, -0.010659787803888321, -0.09928571432828903, 0.00797896459698677, -0.024766996502876282, 0.0437278114259243, 0.0009463396854698658, -0.009897726587951183, -0.029629673808813095, 0.0359438955783844, 0.034818947315216064, -0.010006592608988285, -0.01345401257276535, -0.0075162844732403755, -0.021301431581377983, -0.02375091426074505, 0.031190084293484688, -0.07268614321947098, -0.060674604028463364, -0.0034179361537098885, -0.036125339567661285, 0.07069026678800583, -0.005438759922981262, -0.042094822973012924, 0.012991332449018955, -0.026327406987547874, 0.01721895858645439, 0.06129151210188866, 0.030790910124778748, 0.02745235525071621, -0.045941416174173355, -0.029593385756015778, -0.048082444816827774, -0.03937317430973053, -0.05621110275387764, 0.044743891805410385, -0.03948203846812248, 0.0006860820576548576, 0.031081220135092735, 0.01141277700662613, 0.00576535752043128, 0.055340174585580826, -0.0033249466214329004, 0.02797854132950306, -0.008341850712895393, 0.015885351225733757, 0.0012893807142972946, -0.07413768768310547, 0.001910823630169034, -0.02705318108201027, -0.006345975678414106, 0.022498955950140953, 0.023388028144836426, 0.023025142028927803, 0.0586424395442009, -0.032841216772794724, -0.030446168035268784, 0.010895663872361183, -0.054940998554229736, 0.002255565719678998, 0.014760403893887997, 0.019124113023281097, -0.005511336959898472, -0.03407503291964531, 0.019323701038956642, -0.018443699926137924, -0.010632570832967758, -0.010913807898759842, 0.01232906524091959, -0.03024658001959324, 0.04485275596380234, 0.02278926596045494, -0.04191337898373604, -0.01073236484080553, -0.0054342239163815975, 0.03991750255227089, 0.020357927307486534, 0.010995457880198956, -0.0015320610255002975, -0.03171627223491669, 0.030827198177576065, 0.06459377706050873, 0.04993316903710365, -0.011204116977751255, -0.011966179125010967, -0.036125339567661285, 0.049098528921604156, 0.0024789676535874605, 0.010233395732939243, -0.012619374319911003, 0.013635456562042236, 0.01946885511279106, 0.04706636443734169, -0.014542671851813793, -0.010033808648586273, -0.014569888822734356, 0.014270507730543613, -0.04325605928897858, 0.0041096885688602924, -0.03411132097244263, -0.04151420295238495, -0.06825892627239227, -0.011902673169970512, -0.045143067836761475, -0.05131213366985321, 0.003919173032045364, -0.06902099400758743, 0.027470499277114868, -0.13281641900539398, -0.013136487454175949, 0.016202878206968307, -0.0005828862776979804, 0.033349260687828064, -0.0017067000735551119, 0.04060698673129082, -0.027252767235040665, -0.014070919714868069, 0.061581820249557495, -0.0716700628399849, 0.0020899989176541567, -0.02253524400293827, 0.02703503519296646, -0.07780284434556961, -0.009652777574956417, -0.0036447402089834213, 0.07290387898683548, 0.004681234247982502, -0.0317344143986702, -0.030137713998556137, 0.008437108248472214, 0.006114635616540909, -0.012501436285674572, -0.011993395164608955, -0.016402464359998703, -0.001198659068904817, -0.04438100382685661, 0.033984310925006866, -0.004184533841907978, -0.02373277023434639, -0.03178884834051132, 0.009135664440691471, 0.030536890029907227, 0.060275427997112274, 0.0004581440589390695, 0.0022374214604496956, 0.020376071333885193, -0.008359995670616627, -0.020122051239013672, -0.02162802964448929, -0.028849467635154724, 0.04398183152079582, -0.0016964938258752227, 0.026309262961149216, 0.004649481736123562, 0.02692617103457451, -0.024894006550312042, 0.03198843449354172, -0.023043286055326462, -0.04902595281600952, 0.007942675612866879, 0.025692356750369072, 0.0063777281902730465, 0.012292776256799698, -0.008990510366857052, -0.022353801876306534, -0.00669071776792407, 0.026708438992500305, -0.01392576564103365, 0.01490555889904499, -0.001754328841343522, 0.02239008992910385, 0.06332367658615112, 0.018888236954808235, 0.00040059254388324916, 0.03500039130449295, -0.0043954611755907536, 0.010768653824925423, -0.013889476656913757, -0.0009905664483085275, 0.014606176875531673, -0.03755874186754227, 0.04332863539457321, 0.03314967080950737, -0.010287828743457794, 0.05490471050143242, -0.02863173559308052, -0.03443791717290878, 0.020466791465878487, -0.06252532452344894, -0.04067956283688545, 0.015585970133543015, -0.010142674669623375, -0.006182676646858454, -0.00812411867082119, 0.017736071720719337, -0.007266799919307232, -0.04525193199515343, -0.007588861510157585, 0.005892367567867041, 0.01685607247054577, 0.011349271982908249, 0.0424577072262764, 0.0003161080530844629, -0.006423089187592268, 0.028867611661553383, -0.037849050015211105, -0.019523287191987038, -0.033077094703912735, 0.030700188130140305, 0.02600080892443657, -0.05240079388022423, -0.014996279962360859, 0.032151732593774796, -0.07304903119802475, -0.012065972201526165, 0.004531543701887131, 0.03803049400448799, 0.033077094703912735, -0.02413194440305233, 0.013599167577922344, -0.0228074099868536, -0.0336395688354969, 0.00222267908975482, 0.0639042928814888, -0.012147622182965279, 0.043147191405296326, 0.007616078015416861, -0.004663090221583843, 0.0114037049934268, -0.014796692878007889, 0.0068268002942204475, 0.01602143421769142, 0.052836257964372635, -0.010650715790688992, 0.017064731568098068, -0.014451950788497925, 0.034818947315216064, -0.0002808116842061281, -0.006935666315257549, 0.053634610027074814, -0.006967418827116489, 0.004790100269019604, -0.04325605928897858, -0.00656370772048831, -0.0016012361738830805, 0.0076886555179953575, -0.01145813800394535, 0.03365771099925041, -0.021773183718323708, -0.0074890679679811, -0.027125757187604904, 0.022771120071411133, 0.018724936991930008, -0.02026720531284809, 0.02043050341308117, -0.03803049400448799, -0.014760403893887997, 0.002828245749697089, -0.002723915968090296, 0.05679171904921532, -0.034655649214982986, 0.03458307310938835, 0.008192160166800022, 0.0031979363411664963, 0.028468437492847443, -0.003172987839207053, -0.018978958949446678, -0.011267622001469135, 0.037449873983860016, 0.02415008842945099, 0.029883693903684616, 0.014778547920286655, 0.013626383617520332, -0.021410297602415085, -0.007026387844234705, -0.013363291509449482, 0.02400493435561657, -0.006867624819278717, -0.008087830618023872, -0.0435100793838501, -0.005030512809753418, 0.008346387185156345, 0.017917515709996223, -0.012918755412101746, -0.025347614660859108, -0.00987958163022995, -0.05225564166903496, -0.004944327287375927, 0.022371945902705193, -0.004152781330049038, 0.017599990591406822, 0.007806593552231789, 0.003141235327348113, 0.07330305129289627, -0.00579711003229022, 0.009326180443167686, -0.0040212348103523254, 0.04060698673129082, -0.04020781069993973, 0.008600407280027866, 0.014560816809535027, 0.02955709584057331, -0.048191312700510025, 0.014842052944004536, 0.05113069340586662, 0.03331296890974045, 0.02852286957204342, 0.018271328881382942, -0.006282470654696226, 0.032260600477457047, 0.0036674204748123884, -0.010405766777694225, 0.01768163964152336, 0.020702669396996498, 0.002615049947053194, 0.03167998045682907, 0.03483709320425987, 0.011984323151409626, -0.0008788654813542962, -0.003064122051000595, -0.04307461529970169, -0.022734832018613815, 0.042602863162755966, 0.02944822981953621, 0.0014504115097224712, 0.0035517504438757896, 0.026708438992500305, -0.020049473270773888, -0.01854349486529827, 0.024567408487200737, 0.022879986092448235, 0.005629274994134903, 0.05330801010131836, 0.029919981956481934, -0.006645357236266136, -0.03238761052489281, -0.014451950788497925, -0.02941194176673889, 0.005289068911224604, 0.0024562871549278498, -0.04536079987883568, -0.011866385117173195, 0.05940450355410576, 0.03614348545670509, -0.010786797851324081, -0.04017152264714241, 0.001580823794938624, -0.01645689830183983, 0.03443791717290878, 0.0050032963044941425, -0.010659787803888321, -0.015948856249451637, -0.007693191524595022, -0.022607821971178055, 0.0006157728494144976, -0.018888236954808235, -0.00615999661386013, -0.013209064491093159, -0.04532451182603836, 0.024603696539998055, 0.021718749776482582, 0.011839168146252632, 0.006545563228428364, -0.016411537304520607, -0.027615653350949287, -0.008958757854998112, -0.01318184845149517, 0.04253028333187103, 0.02610967494547367, 0.03485523909330368, 0.03193400055170059, 0.01311834342777729, 0.008500613272190094, -0.013789682649075985, -0.0011612364323809743, 0.05007832124829292, 0.022898131981492043, 0.030155859887599945, -0.020757101476192474, -0.05751749128103256, -0.021664317697286606, 0.015531537123024464, 0.039990078657865524, -0.014778547920286655, -0.024821428582072258, 0.00372865772806108, 0.044489871710538864, -0.035726163536310196, 0.021374007686972618, 0.010968240909278393, 0.0005117265391163528, -0.03592575341463089, -0.022208647802472115, 0.02783338539302349, -0.005883295554667711, -0.026472562924027443, 0.01835297979414463, 0.006554635241627693, 0.02295256406068802, -0.03726843371987343, 0.00785195454955101, 0.014288651756942272, -0.005130306351929903, 0.04630430415272713, 0.03396616503596306, 0.009344324469566345, 0.03235132247209549, -0.048735640943050385, 0.06775088608264923, -0.027216479182243347, -0.051239557564258575, 0.027397923171520233, -0.0006605666130781174, -0.002952988026663661, -0.03073647804558277, 0.03022843599319458, -0.008450716733932495, 0.020503081381320953, 0.01511421799659729, -0.021392153576016426, 0.035472143441438675, -0.011648653075098991, -0.04710265249013901, 0.014642465859651566, 0.018888236954808235, -0.019033391028642654, 0.04180451110005379, 0.01595792919397354, 0.07348449528217316, -0.020793389528989792, 0.017400402575731277, 0.025166170671582222, 0.003871544264256954, 0.025148026645183563, -0.04122389480471611, -0.00705360434949398, -0.01681978441774845, 0.031879570335149765, -0.044489871710538864, 0.0002591235679574311, -0.007607006002217531, 0.0018201021011918783, -0.026327406987547874, -0.02228122390806675, 0.027633799239993095, 0.006926593836396933, -0.011176900938153267, -0.014606176875531673, 0.007611542008817196, -0.016729062423110008, 0.05541275069117546, 0.04670348018407822, -0.027506789192557335, 0.043836675584316254, -0.03167998045682907, -0.037195853888988495, 0.02467627450823784, -0.013481229543685913, -0.00046409768401645124, 0.04180451110005379, -0.003445152658969164, -0.0330045185983181, -0.0458325520157814, -0.04278430715203285, 0.0384659580886364, -0.02757936529815197, 0.025293180719017982, 0.02385978028178215, 0.0043092756532132626, 0.02211792580783367, -0.006604532245546579, -0.028159983456134796, -0.02307957410812378, 0.008545974269509315, 0.03512740135192871, -0.02770637534558773, -0.01060535479336977, 0.0159760732203722, -0.0032863898668438196, -0.012936899438500404, -0.005783502012491226, 0.035326991230249405, 0.012855250388383865, -0.01593071222305298, 0.03211544454097748, 0.03485523909330368, 0.009389685466885567, 0.036107197403907776, -0.009625561535358429, 0.037449873983860016, -0.03100864216685295, 0.03077276609838009, 0.00197319476865232, 0.02041235938668251, -0.028795035555958748, 0.03100864216685295, -0.018978958949446678, -0.02943008579313755, -0.04615914821624756, 0.030337302014231682, 0.02678101509809494, -0.03792162612080574, -0.0021138133015483618, 0.004758347757160664, -0.00809236615896225, 0.07348449528217316, 0.00742556294426322, 0.017981020733714104, 0.023569470271468163, 0.027670087292790413, 0.007611542008817196, 0.015613187104463577, -0.02346060425043106, 0.02890390157699585, -0.009525767527520657, 0.0030958745628595352, 0.05472326651215553, 0.0053298939019441605, -0.00011283499043202028, -0.00801978912204504, 0.016738135367631912, 0.010505560785531998, -0.010659787803888321, -0.030700188130140305, -0.008949685841798782, -0.040752142667770386, -0.0054160794243216515, -0.022317513823509216, 0.024349676445126534, 0.07141604274511337, 0.009380613453686237, 0.013444940559566021, 0.011058962903916836, 0.026164108887314796, -0.043945543467998505, 0.0038261832669377327, 0.012238343246281147, 0.010387622751295567, 0.04445358365774155, -0.010696076788008213, -0.03247833251953125, -0.0026195861864835024, -0.011694014072418213, 0.00286680250428617, 0.01881565898656845, -0.03115379624068737, 0.00015025764878373593, 0.023097718134522438, -0.011095250956714153, 0.00016244835569523275, 0.0338391549885273, -0.011875457130372524, -0.07058140635490417, -0.01885194703936577, -0.0233335942029953, -0.0014867001445963979, -0.005207419861108065, -0.026091530919075012, 0.0010790199739858508, -0.02545648068189621, 0.029647817835211754, -0.026091530919075012, 0.007588861510157585, -0.006935666315257549, 0.00784288253635168, 0.008205768652260303, -0.01233813725411892, -0.014941846951842308, 0.028377715498209, -0.032133590430021286, -0.004930718801915646, 0.00894514936953783, 0.0011215457925572991, 0.019868029281497, 0.017962876707315445, -0.010968240909278393, 0.04006265848875046, 0.021972771733999252, 0.004615461453795433, 0.024875862523913383, -0.0004978347569704056, -0.011684942059218884, -0.01426143478602171, 0.005193811375647783, -0.008024325594305992, 0.010759581811726093, 0.023242874071002007, 0.033984310925006866, 0.03062761202454567, 0.012846178375184536, 0.04311090335249901, 0.028159983456134796, 0.0048309252597391605, 0.006441233213990927, -0.03235132247209549, -0.02400493435561657, -0.001925565884448588, 0.014370300807058811, -0.007901851087808609, 0.008527830243110657, 0.02930307574570179, -0.04321976751089096, 0.03100864216685295, -0.03186142444610596, -0.035072971135377884, 0.06887583434581757, -0.01226556021720171, -0.00980700459331274, -0.000002706586656131549, 0.011494426056742668, -0.013145559467375278, 0.02507544867694378, -0.0023145347367972136, -0.018761226907372475, 0.01841648481786251, 0.02756122127175331, -0.02531132660806179, -0.005974017083644867, 0.021555451676249504, -0.0034973176661878824, -0.02438596449792385, 0.03140781819820404, -0.06230759248137474, -0.053380586206912994, -0.0676783099770546, -0.02106555551290512, -0.009398757480084896, -0.0010393293341621757, -0.002316802740097046, 0.03714142367243767, -0.01505978498607874, 0.00567009998485446, 0.00980700459331274, -0.051638733595609665, 0.009013190865516663, 0.019686587154865265, 0.024694418534636497, -0.032804928719997406, 0.008269273675978184, 0.009389685466885567, 0.008577726781368256, -0.05515873059630394, 0.021392153576016426, -0.02266225591301918, -0.0620172843337059, -0.003263709368184209, 0.007665975019335747, -0.05236450582742691, 0.003578966949135065, -0.031879570335149765, -0.051493577659130096, -0.002042369917035103, -0.005919584073126316, -0.003885152516886592, -0.014361228793859482, -0.003358967136591673, -0.032841216772794724, 0.011775663122534752, -0.02465813048183918, 0.062126148492097855, 0.04927997291088104, 0.014442878775298595, -0.010387622751295567, -0.00889071635901928, -0.06470264494419098, -0.022861842066049576, 0.01165772508829832, -0.048590488731861115, -0.014143496751785278, 0.020176483318209648, -0.007761232554912567, -0.01424329075962305, -0.0029348437674343586, 0.0006384532316587865, 0.05650141090154648, -0.035708021372556686, 0.03893771022558212, -0.04797358065843582, 0.003186596091836691, -0.012773601338267326 ]
Neural networks (NNs) are increasingly applied in safety-critical systems such as autonomous vehicles. However, they are fragile and are often ill-behaved. Consequently, their behaviors should undergo rigorous guarantees before deployment in practice. In this paper we propose a set-boundary reachability method to investigate the safety verification problem of NNs from a topological perspective. Given an NN with an input set and a safe set, the safety verification problem is to determine whether all outputs of the NN resulting from the input set fall within the safe set. In our method, the homeomorphism property of NNs is mainly exploited, which establishes a relationship mapping boundaries to boundaries. The exploitation of this property facilitates reachability computations via extracting subsets of the input set rather than the entire input set, thus controlling the wrapping effect in reachability analysis and facilitating the reduction of computation burdens for safety verification. The homeomorphism property exists in some widely used NNs such as invertible NNs. Notable representations are invertible residual networks (i-ResNets) and Neural ordinary differential equations (Neural ODEs). For these NNs, our set-boundary reachability method only needs to perform reachability analysis on the boundary of the input set. For NNs which do not feature this property with respect to the input set, we explore subsets of the input set for establishing the local homeomorphism property, and then abandon these subsets for reachability computations. Finally, some examples demonstrate the performance of the proposed method.
[ -0.01977192424237728, 0.016138119623064995, -0.02334698475897312, -0.03497851639986038, 0.0394095741212368, 0.022658826783299446, 0.021601414307951927, 0.029204711318016052, -0.013737962581217289, -0.011916864663362503, -0.009407609701156616, 0.01449325680732727, 0.03484424203634262, -0.016683610156178474, -0.021131454035639763, 0.001349039375782013, -0.004389098845422268, -0.03705976903438568, 0.0020183140877634287, -0.054750438779592514, 0.024068709462881088, 0.00579898152500391, -0.015794042497873306, 0.02207137644290924, -0.011413334868848324, 0.015416394919157028, 0.015836002305150032, -0.007154314778745174, -0.034055378288030624, 0.01846274733543396, -0.006856393069028854, -0.007397687528282404, -0.007267609238624573, 0.03588486835360527, -0.037764713168144226, -0.0064661577343940735, 0.02329663187265396, 0.03247765079140663, -0.05921506881713867, 0.021215375512838364, 0.05303844064474106, -0.029557181522250175, 0.0487416535615921, 0.0030820202082395554, -0.015198198147118092, 0.028684396296739578, 0.038738202303647995, -0.007145922631025314, -0.011144786141812801, 0.04427702724933624, -0.02329663187265396, -0.012470747344195843, 0.05233350023627281, -0.0013154707849025726, -0.0008937648381106555, -0.003533098613843322, 0.06921852380037308, 0.023884082213044167, 0.06743938475847244, -0.025243612006306648, 0.03739545866847038, -0.010104158893227577, -0.05908079445362091, 0.0045569417998194695, 0.00006048254726920277, -0.005727647803723812, 0.06834573298692703, -0.05877867713570595, 0.020074041560292244, -0.04431059584021568, -0.02675420045852661, 0.01957051269710064, -0.02205459214746952, -0.0466604009270668, 0.01667521893978119, 0.0195369441062212, -0.014308629557490349, 0.04736534133553505, -0.007498393300920725, 0.03450855612754822, 0.021735690534114838, 0.03712690621614456, -0.020527219399809837, 0.018580237403512, 0.04092016443610191, 0.0026435297913849354, 0.06787577271461487, -0.059517186135053635, 0.06841287016868591, -0.0722396969795227, -0.03467639908194542, -0.020611140877008438, -0.01852988451719284, -0.003719824133440852, 0.0599871464073658, 0.01737176813185215, 0.04323640093207359, 0.021618200466036797, -0.01096015889197588, 0.044579144567251205, 0.03783185034990311, 0.0012881963048130274, 0.012160236947238445, 0.02071184664964676, -0.001229451154358685, -0.020527219399809837, 0.003789059352129698, 0.04941302910447121, 0.000998142291791737, 0.13367030024528503, 0.03598557412624359, 0.0026519219391047955, -0.013175688683986664, 0.04948016628623009, -0.027123454958200455, -0.011455295607447624, -0.07049413025379181, -0.03598557412624359, 0.028231220319867134, -0.03470996767282486, -0.012437178753316402, 0.03355184942483902, 0.021366434171795845, 0.013461021706461906, -0.03338400647044182, 0.009407609701156616, 0.0059626284055411816, -0.03133631870150566, -0.05938291177153587, 0.003810039721429348, 0.035179927945137024, -0.0218699648976326, -0.010565727017819881, -0.02672063186764717, 0.00516117736697197, -0.02677098475396633, 0.04276643693447113, -0.00918941292911768, -0.03246086835861206, -0.029825730249285698, -0.0043471381068229675, -0.03460926190018654, -0.0013175688218325377, 0.04991655796766281, 0.01098533533513546, 0.007229844108223915, 0.010548942722380161, 0.01727106235921383, -0.04639185220003128, 0.00459470646455884, -0.08647280186414719, 0.048003144562244415, 0.02561286650598049, 0.06216910853981972, 0.10010166466236115, 0.002130559179931879, -0.0287851020693779, 0.036321260035037994, -0.011698668822646141, -0.06566024571657181, 0.06455247849225998, -0.06287404894828796, 0.00004553401595330797, 0.054750438779592514, 0.005568196997046471, 0.06921852380037308, 0.033988241106271744, 0.009575452655553818, -0.035213496536016464, 0.029657887294888496, -0.057100243866443634, -0.0045611378736793995, -0.03497851639986038, -0.012378433719277382, 0.021735690534114838, 0.004128941800445318, 0.05579106882214546, -0.027375219389796257, 0.02896972931921482, -0.008337609469890594, -0.0459890253841877, -0.0342400036752224, 0.024672945961356163, 0.05172926187515259, 0.012781256809830666, 0.11003797501325607, 0.057301655411720276, -0.033182594925165176, 0.052669186145067215, -0.003858294803649187, -0.0048548635095357895, 0.03118526004254818, 0.03793255612254143, -0.008610354736447334, 0.02297772839665413, -0.074320949614048, -0.03366933763027191, 0.002184059238061309, 0.021618200466036797, -0.005740236025303602, 0.00490941246971488, -0.011514040641486645, -0.007414471823722124, 0.013150512240827084, -0.004036628175526857, -0.006906746421009302, -0.0034344906453043222, 0.033115457743406296, 0.0052576870657503605, -0.027996240183711052, -0.013863845728337765, -0.03705976903438568, -0.03341757506132126, -0.04058447852730751, -0.07378385215997696, -0.0196208655834198, -0.03783185034990311, 0.0007904364028945565, -0.006667569745332003, 0.003717726096510887, 0.02880188636481762, -0.0007442795322276652, 0.031705573201179504, -0.020292239263653755, -0.016448630020022392, 0.014677884988486767, 0.006717922631651163, 0.03564988821744919, -0.05122573301196098, -0.01831168867647648, -0.059584323316812515, -0.027056317776441574, 0.01448486465960741, -0.003277137875556946, 0.03558275103569031, -0.006822824478149414, -0.01831168867647648, -0.0016910198610275984, -0.03826824203133583, 0.003799549536779523, -0.03348471224308014, 0.013570119626820087, 0.025680003687739372, 0.02314557321369648, 0.02907043695449829, -0.020208317786455154, -0.026401730254292488, 0.01972157135605812, 0.023565180599689484, -0.0059500401839613914, -0.036421965807676315, 0.011287452653050423, 0.027408787980675697, -0.014619139954447746, -0.05310557782649994, -0.01623043417930603, -0.046928949654102325, 0.037731144577264786, 0.015147845260798931, 0.011178354732692242, 0.028281573206186295, 0.06609664112329483, 0.026049258187413216, 0.01967121846973896, 0.00922298151999712, 0.016423454508185387, 0.016121335327625275, 0.06166557967662811, 0.031034201383590698, 0.002200843533501029, 0.04008094593882561, -0.04843953624367714, -0.004829687066376209, -0.05300487205386162, 0.039745260030031204, -0.021265728399157524, 0.032930828630924225, -0.009466354735195637, 0.03672408312559128, -0.013200865127146244, -0.048909496515989304, -0.06267263740301132, -0.008610354736447334, -0.041020870208740234, -0.03366933763027191, -0.060658518224954605, -0.042262908071279526, 0.0034827457275241613, -0.09459640830755234, 0.0010815394343808293, 0.006722118705511093, 0.010272001847624779, -0.096476249396801, 0.0207454152405262, 0.022323140874505043, 0.07458950579166412, -0.021047532558441162, -0.05196424201130867, 0.010112551040947437, -0.054851144552230835, -0.02329663187265396, -0.045653339475393295, 0.015156237408518791, 0.01948659121990204, 0.008073256351053715, -0.02883545495569706, 0.0013270099880173802, 0.009038354270160198, 0.00986917782574892, -0.0005984657909721136, -0.03850322216749191, 0.04004737734794617, -0.04266573116183281, -0.06858071684837341, -0.0006645540124736726, -0.03202447667717934, 0.020006904378533363, -0.01958729699254036, -0.02435404248535633, -0.023581964895129204, 0.02786196582019329, -0.006852196995168924, -0.03669051453471184, 0.025797493755817413, -0.025864630937576294, 0.03591843694448471, -0.01038109976798296, 0.023699454963207245, -0.06354542076587677, -0.032897260040044785, -0.00047913979506120086, -0.0062521579675376415, -0.07344816625118256, -0.08345162123441696, -0.00986917782574892, -0.02410227805376053, -0.014174355193972588, 0.045485496520996094, -0.0031932161655277014, -0.052568480372428894, 0.05186353623867035, -0.01042306050658226, -0.04196079075336456, -0.028231220319867134, -0.0034848437644541264, -0.050453655421733856, -0.02193710207939148, -0.04830526188015938, -0.017942434176802635, -0.01968800276517868, 0.0008350197458639741, 0.04038306698203087, -0.025847846642136574, 0.0064619616605341434, 0.050185106694698334, 0.013578511774539948, -0.028566906228661537, 0.02766055427491665, -0.011413334868848324, 0.0032037063501775265, 0.034340713173151016, -0.05901365727186203, -0.018009571358561516, 0.01049019768834114, -0.09029962122440338, -0.03224267065525055, -0.027324866503477097, 0.020023688673973083, 0.03009427897632122, 0.011757413856685162, -0.05229993164539337, 0.05746949836611748, -0.004084882792085409, -0.01633113995194435, 0.018043139949440956, -0.013813492842018604, 0.025814278051257133, -0.026217103004455566, -0.03157129883766174, 0.03900675103068352, -0.008446707390248775, 0.018043139949440956, -0.0018179513281211257, -0.013511374592781067, -0.027425572276115417, 0.07526087760925293, 0.017170356586575508, -0.01742212101817131, -0.02329663187265396, 0.024622593075037003, -0.038603927940130234, -0.0311181228607893, -0.03581773117184639, -0.05545538291335106, 0.06643232703208923, 0.03789898753166199, -0.04984942078590393, -0.07532801479101181, -0.012235766276717186, -0.03608627989888191, -0.03368612378835678, -0.011136393994092941, 0.017002511769533157, -0.021651769056916237, -0.04236361384391785, 0.04780173301696777, -0.019100552424788475, -0.013696001842617989, 0.027039533481001854, -0.01747247390449047, 0.04028236120939255, -0.02777804434299469, 0.05924863740801811, -0.004019843880087137, 0.03353506326675415, -0.012260942719876766, 0.0012388923205435276, -0.01975513994693756, -0.00975168775767088, -0.04749961569905281, -0.006151452194899321, 0.0004770417290274054, 0.014828943647444248, -0.026149965822696686, -0.046761106699705124, 0.011321021243929863, -0.016566120088100433, 0.029775377362966537, -0.0030988045036792755, -0.00028192406171001494, -0.019839061424136162, -0.003403020091354847, 0.01831168867647648, -0.03375326097011566, -0.026955612003803253, -0.01096015889197588, 0.023699454963207245, -0.03591843694448471, -0.036287691444158554, 0.018865572288632393, -0.003986275289207697, -0.0059584323316812515, -0.042128633707761765, -0.004294686950743198, -0.025780709460377693, -0.029187927022576332, -0.008497060276567936, -0.0463247150182724, -0.006910942494869232, -0.02546180784702301, 0.01573529653251171, 0.015156237408518791, -0.006390628404915333, -0.0459890253841877, 0.00114448054227978, -0.04723106697201729, -0.01042306050658226, -0.06562668085098267, 0.031923770904541016, -0.0067682755179703236, 0.057234518229961395, 0.05750306695699692, -0.005895491223782301, -0.06129632517695427, 0.017640316858887672, 0.021551061421632767, -0.026183534413576126, -0.025931768119335175, 0.017774591222405434, -0.02755984663963318, 0.039913102984428406, -0.028096945956349373, 0.018580237403512, -0.006600432563573122, 0.010532158426940441, 0.0019553727470338345, -0.02410227805376053, -0.03222588822245598, 0.013385492376983166, -0.021047532558441162, 0.05676455795764923, 0.07492519170045853, 0.007741766050457954, 0.028365494683384895, 0.013192472979426384, 0.039812397211790085, 0.06599593162536621, 0.008643923327326775, 0.0036715692840516567, -0.05864440277218819, -0.00546749122440815, -0.023363769054412842, -0.03608627989888191, -0.06085992977023125, 0.0023707847576588392, -0.027224160730838776, -0.013461021706461906, -0.017136787995696068, 0.09835609793663025, 0.05438118427991867, 0.0011287452653050423, -0.021316081285476685, 0.007578118704259396, 0.02764376997947693, 0.03853679075837135, 0.03669051453471184, -0.02665349468588829, 0.007099765818566084, 0.018009571358561516, -0.03331686928868294, -0.006692746188491583, -0.04061804711818695, 0.009323688223958015, -0.03242729976773262, 0.02421976812183857, -0.018748082220554352, 0.025629650801420212, -0.07982620596885681, -0.007364118937402964, 0.04061804711818695, 0.020577572286128998, 0.006239569745957851, 0.004514981061220169, 0.03618698567152023, -0.01685984618961811, 0.05585820600390434, -0.016918590292334557, -0.022642042487859726, -0.010523766279220581, 0.0350792221724987, 0.0009420197457075119, 0.04880879074335098, -0.043135691434144974, -0.021786043420433998, 0.003814235795289278, -0.01837882585823536, -0.05109145864844322, 0.015819218009710312, -0.031873416155576706, -0.01638149283826351, -0.060658518224954605, 0.053776949644088745, 0.02197067067027092, 0.001312323729507625, -0.03377004340291023, 0.045619770884513855, 0.013125335797667503, -0.025713572278618813, -0.003151255426928401, 0.017841728404164314, 0.01863059215247631, 0.03222588822245598, -0.0009467403287999332, 0.02435404248535633, 0.01556745357811451, -0.021383218467235565, -0.004309373442083597, 0.01748925819993019, 0.008518040180206299, -0.03611984848976135, -0.020309023559093475, 0.013905806466937065, -0.03511279076337814, -0.03009427897632122, -0.0009656227193772793, -0.06247122585773468, -0.018882356584072113, 0.0068731773644685745, -0.01854666881263256, 0.015408002771437168, -0.04239718243479729, 0.0015640885103493929, -0.00923137366771698, -0.0209132581949234, 0.014669492840766907, -0.030278906226158142, 0.01096015889197588, -0.019788708537817, 0.004235941916704178, -0.015282120555639267, -0.014560394920408726, -0.03319937735795975, -0.009541884064674377, 0.035213496536016464, 0.011497256346046925, -0.02677098475396633, -0.023884082213044167, -0.002213431755080819, 0.03843608498573303, -0.07317961752414703, -0.025159690529108047, 0.03803326189517975, 0.016498982906341553, -0.009600629098713398, -0.02193710207939148, -0.008887295611202717, 0.02421976812183857, 0.029523612931370735, -0.026821337640285492, -0.03313224017620087, 0.044444870203733444, -0.006881569512188435, 0.011186746880412102, 0.008744629099965096, 0.04719749838113785, -0.01732141524553299, -0.012453963048756123, 0.0018127061193808913, -0.025159690529108047, 0.000036387875297805294, -0.0290368665009737, 0.0003383088915143162, 0.04655969515442848, -0.015139453113079071, 0.011799374595284462, 0.028415847569704056, 0.006696942262351513, 0.006348667666316032, 0.004038725979626179, 0.01377153117209673, 0.00577800115570426, -0.02670384757220745, 0.017808159813284874, -0.0027064711321145296, -0.022490983828902245, 0.04877522215247154, 0.016121335327625275, -0.025998905301094055, 0.018899140879511833, -0.012688943184912205, -0.01728784665465355, 0.007326354272663593, 0.008291452191770077, -0.013972943648695946, 0.0014539414551109076, 0.00991113856434822, -0.05904722586274147, 0.015408002771437168, -0.0013584806583821774, 0.008018706925213337, -0.012202197685837746, -0.0015945100458338857, -0.01033913902938366, 0.03605271130800247, -0.003172235796228051, -0.009701334871351719, 0.021064316853880882, -0.019990120083093643, 0.029187927022576332, 0.02322949469089508, 0.005568196997046471, 0.0347435362637043, -0.0030295690521597862, 0.03460926190018654, -0.000719103030860424, -0.006260550115257502, 0.06421679258346558, -0.0021337061189115047, 0.005291255656629801, -0.0018347356235608459, -0.02190353348851204, 0.023917650803923607, -0.022272787988185883, 0.04729820415377617, 0.01092659030109644, -0.031000632792711258, 0.0342400036752224, 0.02752627804875374, 0.015844395384192467, 0.051527850329875946, -0.042330045253038406, -0.035314202308654785, -0.036489102989435196, 0.034038592129945755, 0.030950279906392097, -0.01829490438103676, -0.0022365101613104343, 0.03709333762526512, 0.07532801479101181, -0.019990120083093643, 0.006394824478775263, 0.014912865124642849, -0.0015441571595147252, 0.013427453115582466, -0.0463247150182724, -0.0019889415707439184, 0.03481067344546318, -0.0058535304851830006, 0.000814039318356663, 0.03011106327176094, -0.003407216165214777, -0.023984787985682487, -0.013393884524703026, -0.010204864665865898, 0.045619770884513855, 0.038603927940130234, 0.011925256811082363, -0.036522671580314636, 0.057100243866443634, -0.0196208655834198, -0.02789553441107273, 0.007041020784527063, -0.006831216625869274, 0.001845225808210671, 0.01696055196225643, 0.0098943542689085, 0.010792315006256104, 0.041121575981378555, 0.012890354730188847, -0.002145245438441634, 0.0055514127016067505, 0.05787232145667076, 0.005052079446613789, 0.011958825401961803, 0.028634043410420418, 0.028600474819540977, 0.038603927940130234, -0.028096945956349373, 0.003283431986346841, 0.005689883138984442, 0.021030748263001442, -0.021349649876356125, -0.008539021015167236, -0.0482381246984005, -0.02072863094508648, 0.021131454035639763, -0.021299296990036964, -0.01439255103468895, -0.007490001153200865, -0.002190353348851204, 0.039778828620910645, -0.026099612936377525, 0.002840745495632291, 0.016666825860738754, -0.029322201386094093, -0.015164629556238651, 0.021081101149320602, -0.0013962453231215477, -0.025763925164937973, 0.006856393069028854, -0.0068689812906086445, -0.015240158885717392, 0.04256502538919449, -0.007422863971441984, -0.003539392724633217, -0.0232462789863348, -0.06391467899084091, 0.02885223925113678, 0.003812137758359313, 0.0005533579387702048, 0.05679812654852867, 0.00490521639585495, 0.026099612936377525, -0.04729820415377617, -0.03823467344045639, 0.005870314780622721, 0.04511624202132225, -0.000853377569001168, -0.011933648958802223, -0.023548396304249763, -0.028499769046902657, 0.08419013023376465, -0.020392945036292076, 0.042095065116882324, 0.03284690901637077, -0.037529733031988144, -0.04535122215747833, -0.025629650801420212, 0.0027840984985232353, -0.013586903922259808, 0.010288786143064499, 0.008400550112128258, 0.015164629556238651, -0.022188866510987282, -0.0054884715937078, -0.014258276671171188, -0.00974329560995102, -0.037697575986385345, 0.034156084060668945, 0.02410227805376053, 0.0010825884528458118, 0.011799374595284462, 0.019100552424788475, 0.00516117736697197, -0.013821884989738464, -0.002895294688642025, -0.02205459214746952, -0.024555454030632973, 0.02769412286579609, 0.013024629093706608, -0.025243612006306648, -0.03920816257596016, -0.0109769431874156, 0.008501255884766579, 0.016205256804823875, -0.0022239219397306442, -0.04619043692946434, -0.01732141524553299, 0.005001726094633341, -0.03385396674275398, 0.010691609233617783, -0.02410227805376053, 0.009609021246433258, 0.009332080371677876, -0.025176474824547768, 0.008098432794213295, -0.05293773487210274, -0.003019078867509961, -0.012168629094958305, -0.020493650808930397, 0.012881962582468987, -0.04008094593882561, -0.022692395374178886, 0.029624318704009056, 0.019066983833909035, -0.01982227712869644, 0.03947671130299568, 0.07009130716323853, 0.02876831777393818, -0.012319688685238361, 0.0011088139144703746, -0.046928949654102325, -0.04189365357160568, -0.03501208499073982, -0.020443297922611237, -0.048909496515989304, 0.03377004340291023, -0.029691455885767937, 0.03432392701506615, 0.01164831593632698, -0.02192031778395176, 0.09278370440006256, -0.04770102724432945, 0.02767733857035637, -0.02997678890824318, 0.019855845719575882, -0.0011151080252602696, 0.003709333948791027, 0.01836204156279564, -0.033988241106271744, -0.0001796446304069832, 0.010691609233617783, 0.028550121933221817, 0.007313766051083803, -0.018261335790157318, 0.039879534393548965, -0.016070982441306114, -0.0014906571013852954, 0.00990274641662836, -0.024723298847675323, -0.0368247888982296, 0.010523766279220581, 0.028248004615306854, 0.020527219399809837, 0.00987756997346878, -0.02655278891324997, 0.026838121935725212, 0.03222588822245598, -0.006835412699729204, -0.021786043420433998, -0.0025134512688964605, -0.004821294918656349, 0.06421679258346558, 0.0033316868357360363, -0.004661844111979008, 0.017573179677128792, -0.004265314433723688, -0.011321021243929863, -0.009600629098713398, -0.039711691439151764, 0.01685984618961811, -0.007733373902738094, -0.015710121020674706, 0.06696942448616028, 0.022356709465384483, 0.024656161665916443, 0.03230980783700943, -0.0035855495370924473, 0.017774591222405434, -0.02898651361465454, 0.01680949330329895, 0.05646244063973427, 0.008534824475646019, -0.023733023554086685, -0.008404746651649475, 0.001994186546653509, 0.02661992609500885, -0.09694620966911316, -0.011698668822646141, -0.05414620414376259, -0.020560787990689278, 0.007435452193021774, -0.03481067344546318, -0.00914745219051838, 0.06267263740301132, 0.02418619953095913, -0.023397337645292282, 0.03655624017119408, -0.006432589143514633, -0.0059542362578213215, 0.016994120553135872, -0.03575059399008751, -0.041121575981378555, -0.048137418925762177, -0.01725427806377411, -0.01684306189417839, 0.019352316856384277, -0.002320431638509035, 0.018865572288632393, -0.0034848437644541264, -0.010708393529057503, -0.046828243881464005, -0.04726463556289673, -0.02755984663963318, -0.00581996189430356, 0.0648210272192955, -0.06693585216999054, 0.021567845717072487, 0.03450855612754822, -0.002177765127271414, 0.03961098566651344, -0.012881962582468987, -0.036321260035037994, 0.012235766276717186, 0.011698668822646141, -0.02651922032237053, -0.004250627942383289, 0.006155648268759251, 0.00923976581543684, 0.04286714270710945, -0.04088659584522247, 0.028264788910746574, -0.024991847574710846, 0.018160630017518997, -0.008627139031887054, 0.033115457743406296, 0.014929649420082569, -0.016398277133703232, -0.013377100229263306, -0.010053805075585842, -0.024857573211193085, -0.016549335792660713, -0.007082981523126364, 0.05052079260349274, 0.020057257264852524, -0.021064316853880882, -0.015743689611554146, -0.003537294687703252, 0.0036694712471216917, 0.00291417702101171, -0.01377992331981659, -0.0019994317553937435, 0.0030547454953193665, 0.0017550101038068533, -0.06284048408269882, 0.05864440277218819, -0.022507768124341965, -0.020241886377334595, -0.02665349468588829, 0.07049413025379181, 0.002303647343069315, -0.018093492835760117, -0.04629114642739296, -0.019385885447263718, -0.023783376440405846, 0.020409729331731796, -0.00922298151999712, -0.007414471823722124, 0.00918102078139782, 0.020426513627171516, 0.008383765816688538, -0.013242825865745544, 0.06962134689092636, 0.03444141894578934, 0.01868094503879547, 0.059483617544174194, 0.03695906326174736, -0.0778120905160904, -0.0016102453228086233, -0.004737373441457748, 0.008157177828252316, 0.010658040642738342, 0.012244158424437046, -0.014736630022525787, -0.03241051360964775, -0.013511374592781067, -0.009583844803273678, -0.008811766281723976, -0.030396396294236183, 0.013276394456624985, -0.007099765818566084, 0.009315296076238155, -0.013847061432898045, -0.005136000923812389, 0.0037869613151997328, 0.04310212284326553, 0.003396725980564952, -0.019134121015667915, -0.0031281770206987858, 0.004259020090103149, -0.03437428176403046, 0.03920816257596016, -0.01727106235921383, 0.018261335790157318, -0.016020629554986954, -0.005383569281548262, 0.021248944103717804, -0.001957471016794443, 0.02202102355659008, -0.014140786603093147, -0.010792315006256104, -0.03816753625869751, -0.025126121938228607, 0.012059531174600124, -0.060154989361763, 0.0097684720531106, -0.0418265163898468, 0.024790436029434204, -0.0015913629904389381, -0.0183284729719162, 0.01624721847474575, -0.010800707153975964, -0.004485608544200659, -0.01859702169895172 ]
Graphs emerge in almost every real-world application domain, ranging from online social networks all the way to health data and movie viewership patterns. Typically, such real-world graphs are big and dynamic, in the sense that they evolve over time. Furthermore, graphs usually contain multi-aspect information i.e. in a social network, we can have the "means of communication" between nodes, such as who messages whom, who calls whom, and who comments on whose timeline and so on. How can we model and mine useful patterns, such as communities of nodes in that graph, from such multi-aspect graphs? How can we identify dynamic patterns in those graphs, and how can we deal with streaming data, when the volume of data to be processed is very large? In order to answer those questions, in this thesis, we propose novel tensor-based methods for mining static and dynamic multi-aspect graphs. In general, a tensor is a higher-order generalization of a matrix that can represent high-dimensional multi-aspect data such as time-evolving networks, collaboration networks, and spatio-temporal data like Electroencephalography (EEG) brain measurements. The thesis is organized in two synergistic thrusts: First, we focus on static multi-aspect graphs, where the goal is to identify coherent communities and patterns between nodes by leveraging the tensor structure in the data. Second, as our graphs evolve dynamically, we focus on handling such streaming updates in the data without having to re-compute the decomposition, but incrementally update the existing results.
[ 0.01710658334195614, -0.0311465784907341, -0.04594907909631729, 0.0027081279549747705, 0.07711223512887955, -0.017007125541567802, -0.07048177719116211, 0.01663416251540184, -0.018697893247008324, 0.006986845750361681, 0.05025887489318848, -0.01765359565615654, -0.0012887953780591488, -0.03081505559384823, 0.010915392078459263, 0.026372648775577545, 0.02168159931898117, -0.02559356950223446, -0.028378361836075783, -0.04528603330254555, -0.019360939040780067, -0.021449534222483635, -0.026637867093086243, -0.037528395652770996, 0.06020456552505493, 0.01432179007679224, 0.041175149381160736, -0.0026521834079176188, -0.05954151973128319, 0.0331854447722435, -0.012995698489248753, 0.009962264448404312, 0.04578331485390663, -0.06259153038263321, -0.04687734320759773, -0.046479515731334686, 0.05377301946282387, 0.0325058214366436, 0.03547295182943344, 0.005051580723375082, 0.024051988497376442, 0.0022605720441788435, -0.06033717468380928, -0.003008570522069931, -0.0030313627794384956, -0.0146201616153121, 0.01922832988202572, -0.06975242495536804, 0.026206888258457184, -0.029687877744436264, -0.004013499245047569, -0.03021831437945366, -0.016990549862384796, -0.007857093587517738, -0.052347470074892044, 0.006129030138254166, 0.07764267176389694, -0.0011043857084587216, 0.07837202399969101, 0.04110884293913841, -0.0285606998950243, 0.014951684512197971, -0.02889222279191017, -0.013658744283020496, 0.016062285751104355, -0.06816111505031586, -0.008934542536735535, -0.008259064517915249, 0.012705616652965546, -0.026074279099702835, -0.02851097099483013, 0.0205378457903862, 0.02040523663163185, -0.02507971040904522, 0.025560418143868446, -0.026339497417211533, 0.05231431871652603, -0.021996546536684036, -0.025195742025971413, -0.04333004727959633, 0.013783065602183342, 0.040379494428634644, -0.030450381338596344, 0.023621007800102234, -0.018084576353430748, -0.019791919738054276, -0.003953410778194666, -0.06968612223863602, -0.01266417559236288, 0.05294421315193176, -0.056922487914562225, -0.027350641787052155, 0.01820060797035694, -0.012316077016294003, 0.0335998497903347, -0.011694471351802349, 0.05430345609784126, -0.018532130867242813, -0.016219759359955788, 0.07054807990789413, -0.03315229341387749, -0.01192653737962246, 0.018316641449928284, -0.047374624758958817, 0.031047122552990913, -0.007757636718451977, 0.004376102704554796, 0.04982789605855942, 0.027135152369737625, 0.08056007325649261, -0.016990549862384796, 0.01650984212756157, 0.009357234463095665, 0.07976441830396652, -0.057983361184597015, 0.00901742372661829, -0.037329480051994324, -0.05214855819940567, -0.021118011325597763, -0.018648164346814156, -0.025278624147176743, 0.02758270688354969, -0.049927353858947754, 0.029969673603773117, -0.06723284721374512, 0.06209424510598183, -0.02567645162343979, -0.033931370824575424, -0.03030119650065899, 0.036732740700244904, -0.008528427220880985, 0.05201594904065132, -0.00605858163908124, -0.06186217814683914, -0.014139452949166298, -0.009025711566209793, 0.08095789700746536, 0.016775060445070267, 0.02274247258901596, 0.017073430120944977, -0.009796502999961376, 0.03444523364305496, -0.01326091680675745, -0.05324258282780647, 0.001528113498352468, 0.025527264922857285, -0.01740495301783085, -0.003953410778194666, 0.009539572522044182, 0.03293680399656296, -0.0029505540151149035, 0.06103337183594704, -0.003213700372725725, 0.029174018651247025, -0.030566414818167686, -0.01994110457599163, -0.003464414505288005, -0.02244410291314125, 0.03021831437945366, 0.029041409492492676, 0.06816111505031586, -0.022891657426953316, 0.02771531604230404, 0.0557621568441391, -0.03610284626483917, -0.003922330681234598, 0.03361642360687256, -0.034478385001420975, -0.015879947692155838, 0.04362841695547104, 0.005689762067049742, 0.009796502999961376, -0.013907386921346188, 0.07565353065729141, -0.011901672929525375, 0.018532130867242813, 0.02809656783938408, -0.005163469817489386, -0.029555268585681915, 0.03845665976405144, 0.002960914047434926, 0.01485222764313221, 0.014114588499069214, 0.02766558900475502, 0.027549555525183678, 0.025809060782194138, 0.06706708669662476, -0.04528603330254555, 0.0172723438590765, 0.011719335801899433, 0.04051210358738899, 0.04074416682124138, 0.06782959401607513, -0.050391484051942825, 0.03514143079519272, -0.04986104741692543, 0.04452352970838547, 0.0012514990521594882, -0.02143295668065548, -0.02206285111606121, -0.059640973806381226, -0.06710024178028107, 0.060867611318826675, -0.03799252584576607, 0.0016503626247867942, 0.026256615296006203, 0.038290899246931076, -0.05516541376709938, 0.02945581264793873, -0.002409757347777486, 0.008395818062126637, -0.02932320348918438, -0.038257744163274765, -0.0032364926300942898, 0.017454681918025017, -0.010965120978653431, 0.012954258359968662, -0.03394794836640358, 0.024151446297764778, -0.005246350541710854, 0.018051423132419586, 0.0065434337593615055, 0.09647317230701447, 0.026720747351646423, -0.02567645162343979, -0.03739578649401665, -0.008383385837078094, 0.0009365523001179099, -0.05702194198966026, 0.024814492091536522, 0.01679992489516735, 0.044490378350019455, -0.005764354951679707, 0.015308070927858353, -0.009299217723309994, 0.00791511032730341, 0.051021378487348557, -0.022626439109444618, -0.013136596418917179, 0.020007409155368805, -0.00019528772099874914, -0.013940539211034775, -0.034909363836050034, 0.01419746968895197, 0.04349580779671669, 0.025278624147176743, -0.011760775931179523, 0.07631658017635345, 0.054767586290836334, 0.05035833269357681, -0.047208864241838455, -0.04051210358738899, 0.033583272248506546, 0.036135997623205185, -0.023786770179867744, 0.026886509731411934, -0.024764763191342354, -0.030317772179841995, -0.009266065433621407, -0.08128942549228668, 0.049330610781908035, 0.0006381816347129643, -0.08791988343000412, 0.03199196234345436, 0.006336232181638479, -0.0015612657880410552, 0.035108279436826706, 0.007268640212714672, 0.043097980320453644, -0.007426113821566105, -0.02614058367908001, -0.018598435446619987, 0.02418459765613079, -0.07625027000904083, -0.009216337464749813, -0.04455668106675148, 0.0015250054420903325, -0.03709741681814194, -0.01828349009156227, -0.05291105806827545, 0.0028200168162584305, -0.0427001528441906, 0.0005796471377834678, -0.03139522299170494, -0.04187134653329849, -0.01506771706044674, 0.011354660615324974, -0.03527403995394707, -0.04018057882785797, -0.041141994297504425, 0.001418296480551362, -0.02426747791469097, -0.013120019808411598, 0.026289768517017365, 0.024665305390954018, -0.04197080433368683, 0.0025630865711718798, -0.03106369823217392, 0.02948896400630474, -0.045518096536397934, -0.026124006137251854, 0.011860232800245285, -0.0025237184017896652, -0.005756066646426916, -0.049363765865564346, -0.01722261682152748, 0.0427001528441906, 0.04594907909631729, 0.0007718268316239119, -0.046744734048843384, -0.021018553525209427, 0.040711015462875366, -0.0020751263946294785, -0.020769910886883736, -0.004079803824424744, 0.029886791482567787, 0.02380334585905075, -0.00008216847345465794, 0.05430345609784126, -0.07419483363628387, 0.02105170674622059, 0.021416381001472473, -0.07963180541992188, 0.02350497618317604, -0.03882133588194847, -0.0029982104897499084, 0.00777421286329627, 0.02358785644173622, -0.02638922445476055, -0.006854236591607332, -0.03988220915198326, 0.013658744283020496, -0.014363231137394905, 0.008528427220880985, 0.012730480171740055, -0.029638150706887245, 0.02388622611761093, -0.0013944683596491814, -0.054933350533246994, 0.028278905898332596, -0.0014286566292867064, -0.021167738363146782, -0.025063132867217064, 0.0003566461382433772, -0.011039713397622108, -0.03398109972476959, -0.025693027302622795, 0.01317803654819727, 0.043131131678819656, -0.0029443379025906324, 0.0008086051675491035, 0.0146201616153121, -0.051286596804857254, -0.016053996980190277, 0.09070467203855515, -0.012025994248688221, 0.03046695701777935, -0.03288707509636879, 0.0060378615744411945, 0.010757919400930405, 0.02657156251370907, -0.024449815973639488, -0.013269205577671528, 0.00923291314393282, -0.040677864104509354, -0.0028179448563605547, -0.05897792801260948, -0.005055724643170834, -0.019045991823077202, 0.045252878218889236, -0.03640121594071388, 0.018615012988448143, -0.004782218020409346, -0.036765892058610916, 0.004657897166907787, -0.018813926726579666, 0.04299852252006531, -0.003920258488506079, -0.02779819816350937, 0.022079426795244217, -0.017935389652848244, -0.051949642598629, 0.07571983337402344, -0.005677330307662487, -0.05420399829745293, 0.012233195826411247, 0.032820768654346466, -0.02910771407186985, -0.0008531535277143121, 0.03215772286057472, 0.014388094656169415, -0.02554384246468544, 0.0004156986833550036, -0.04366156831383705, 0.04634690657258034, -0.03610284626483917, -0.005996420979499817, -0.03234006091952324, 0.03356669470667839, -0.007413681596517563, -0.056922487914562225, -0.07121112197637558, -0.028113143518567085, 0.04333004727959633, 0.051916491240262985, -0.037329480051994324, 0.01650984212756157, -0.043429505079984665, 0.06451436132192612, -0.017471257597208023, -0.01406486053019762, -0.033881641924381256, -0.03152783215045929, -0.024930523708462715, 0.01132979616522789, 0.029008256271481514, -0.05496650189161301, -0.014885379932820797, 0.0424349345266819, 0.00559030519798398, -0.010890528559684753, 0.008901390247046947, 0.05572900548577309, -0.01955985277891159, 0.0004783772164955735, 0.063652403652668, 0.00948155578225851, -0.05095507577061653, 0.00024139013839885592, -0.06875785440206528, 0.019493548199534416, -0.007363953161984682, 0.02619031071662903, 0.01220004353672266, -0.014073148369789124, -0.007409537676721811, -0.0179519671946764, 0.01200941763818264, -0.03785991668701172, -0.010832511819899082, -0.030582990497350693, -0.06544262915849686, -0.005436975974589586, -0.00878535769879818, 0.01022748276591301, 0.015589865855872631, -0.05112083628773689, -0.0541376955807209, -0.004342950414866209, -0.0225767120718956, -0.034644145518541336, -0.017388377338647842, -0.05483389273285866, -0.032356638461351395, -0.022328069433569908, -0.011437540873885155, 0.033633001148700714, 0.0026874076575040817, 0.04004796966910362, -0.06464697420597076, -0.0048816753551363945, 0.03984905779361725, -0.003974131308495998, -0.04061155766248703, -0.01960958167910576, 0.04518657550215721, -0.021267196163535118, -0.005192477721720934, -0.008143031969666481, 0.035970237106084824, 0.04807082563638687, -0.035970237106084824, -0.026256615296006203, 0.06424914300441742, 0.0022274197544902563, -0.013418390415608883, -0.0036861205007880926, -0.03441207855939865, 0.03474360331892967, -0.017023703083395958, -0.0026335353031754494, 0.03892079368233681, 0.05029202997684479, -0.012042569927871227, -0.044954508543014526, 0.028627004474401474, 0.02529519982635975, 0.013418390415608883, -0.013070291839540005, -0.019974255934357643, 0.015755627304315567, 0.03199196234345436, 0.011503845453262329, -0.00461645657196641, 0.014479263685643673, 0.022046275436878204, -0.034942515194416046, 0.002656327560544014, 0.01400684379041195, 0.04943006858229637, 0.011396100744605064, 0.055695850402116776, 0.06395076960325241, -0.007861237041652203, -0.00846626702696085, -0.0028179448563605547, 0.03911970555782318, -0.048899631947278976, -0.059342604130506516, -0.024035412818193436, -0.05831488221883774, 0.03199196234345436, -0.017421530559659004, -0.03497567027807236, -0.0030810912139713764, 0.015042852610349655, -0.02559356950223446, -0.029422659426927567, 0.036732740700244904, 0.03656698018312454, 0.02431720681488514, 0.01773647591471672, 0.005946692544966936, 0.039020247757434845, -0.07174155861139297, 0.03457784280180931, 0.00882679782807827, -0.019593005999922752, -0.002299940213561058, -0.050988227128982544, -0.03255555033683777, -0.013385238125920296, -0.03467729687690735, -0.009730198420584202, 0.04604853317141533, 0.010260635055601597, 0.021930241957306862, 0.002546510426327586, -0.023355789482593536, -0.04929745942354202, -0.010202618315815926, 0.03928546607494354, -0.05218170955777168, 0.019145449623465538, 0.02464872971177101, 0.005896964110434055, 0.02096882462501526, -0.06560838967561722, 0.0032924371771514416, -0.0017498194938525558, -0.04899908974766731, -0.002759928349405527, 0.041771888732910156, -0.04183819517493248, -0.009067151695489883, 0.06378500908613205, -0.0019601292442530394, -0.005710482597351074, 0.03003597818315029, -0.021449534222483635, 0.04263385012745857, 0.0297873355448246, 0.002546510426327586, 0.010824223980307579, -0.014578720554709435, -0.000639735662844032, 0.014827363193035126, 0.047507233917713165, 0.012863089330494404, -0.0053043668158352375, 0.001465952955186367, -0.034644145518541336, -0.039152856916189194, -0.0066263144835829735, -0.0031018115114420652, 0.03527403995394707, 0.05151866376399994, -0.009904247708618641, 0.020256051793694496, -0.014371518976986408, 0.022643016651272774, -0.01035180315375328, 0.05920999497175217, 0.011644742451608181, -0.011702759191393852, -0.010658462531864643, -0.044622987508773804, -0.019112296402454376, -0.029638150706887245, -0.045219726860523224, 0.009705333970487118, 0.023140300065279007, 0.02456584945321083, -0.003503782907500863, 0.0033193733543157578, -0.008155464194715023, 0.01662587560713291, -0.00874391756951809, 0.0688241571187973, -0.05543063208460808, -0.00019839574815705419, 0.03136206790804863, 0.0010847016237676144, 0.057651836425065994, -0.006008853204548359, -0.05324258282780647, 0.03366615250706673, -0.05566269904375076, -0.041606128215789795, 0.03237321227788925, -0.017670171335339546, -0.017454681918025017, 0.0794328972697258, -0.009755061939358711, 0.011321508325636387, 0.026488682255148888, 0.043860483914613724, 0.06106652319431305, -0.061464350670576096, -0.03081505559384823, 0.06136489287018776, -0.00040974162402562797, 0.055231720209121704, 0.007786644622683525, -0.006149750202894211, -0.013136596418917179, 0.045551251620054245, 0.02758270688354969, 0.021565565839409828, -0.008391673676669598, -0.012680752202868462, 0.023985683917999268, -0.03968329355120659, 0.023322638124227524, 0.01094854436814785, -0.0041295322589576244, -0.011172322556376457, 0.05257953703403473, 0.03255555033683777, 0.01045954879373312, 0.01735522598028183, 0.011263491585850716, -0.0006936081335879862, 0.04369472339749336, 0.0010909176198765635, 0.019957680255174637, -0.00901742372661829, -0.03785991668701172, 0.018830502405762672, 0.014073148369789124, 0.039186011999845505, 0.043727874755859375, 0.008250776678323746, 0.012108875438570976, -0.01160330232232809, -0.06942090392112732, -0.04654581844806671, 0.012357517145574093, -0.01487709116190672, 0.030483532696962357, -0.007695476058870554, -0.009746774099767208, 0.042368631809949875, 0.004550151992589235, 0.029008256271481514, -0.003137035761028528, 0.012365804985165596, 0.006008853204548359, 0.018449250608682632, 0.036765892058610916, 0.04137406125664711, 0.0030790192540735006, -0.00005607399361906573, 0.0006842840230092406, 0.010210906155407429, -0.027317488566040993, -0.01671704277396202, 0.01620318368077278, -0.020471541211009026, -0.012821649201214314, 0.01863158866763115, -0.06895677000284195, -0.028544124215841293, 0.017537562176585197, -0.036301761865615845, -0.009647317230701447, 0.0021321068052202463, -0.010981696657836437, -0.0063776723109185696, -0.03263843059539795, -0.017288921400904655, -0.028162872418761253, -0.008561579510569572, -0.025693027302622795, 0.02541123330593109, -0.008205192163586617, 0.038390353322029114, 0.01566445827484131, 0.0016337864799425006, -0.012258060276508331, 0.0034934228751808405, -0.0018420242704451084, 0.014984836801886559, 0.043595265597105026, -0.007683043833822012, 0.06809481233358383, 0.0018492763629183173, 0.025112861767411232, -0.029853640124201775, -0.02494710125029087, -0.0018731046002358198, -0.005681474227458239, 0.01372504886239767, 0.0005723950453102589, 0.01858185976743698, 0.026322919875383377, 0.012357517145574093, 0.008694188669323921, -0.04943006858229637, -0.011570150032639503, -0.0006666718982160091, -0.023538127541542053, 0.022692743688821793, -0.019576428458094597, -0.025195742025971413, -0.0050432924181222916, -0.020338932052254677, -0.006307223811745644, -0.0044175428338348866, -0.004894107114523649, 0.0527784489095211, -0.05228116735816002, 0.05566269904375076, 0.0007956550107337534, 0.018482403829693794, 0.02983706444501877, -0.019145449623465538, 0.027483250945806503, 0.012092298828065395, -0.015457256697118282, 0.027814773842692375, -0.016410384327173233, -0.00007588767039123923, 0.00358044751919806, 0.00731008080765605, 0.09242859482765198, -0.016750195994973183, 0.038390353322029114, -0.02703569456934929, 0.018565284088253975, -0.0089759835973382, -0.03217430040240288, 0.02015659399330616, -0.055099111050367355, -0.031677015125751495, 0.02168159931898117, 0.037031110376119614, 0.0112883560359478, -0.0010365271009504795, 0.010608733631670475, -0.0023289485834538937, 0.04545179381966591, -0.022046275436878204, 0.03272131457924843, 0.00194148113951087, 0.02771531604230404, 0.006315511651337147, -0.01803484745323658, -0.028461243957281113, -0.01820060797035694, -0.029057985171675682, 0.014926820062100887, 0.06434860080480576, -0.014172605238854885, -0.01607886143028736, 0.01833321712911129, 0.02146610990166664, -0.02779819816350937, -0.03381533920764923, 0.013617304153740406, -0.005776787176728249, -0.011338084004819393, -0.010128025896847248, 0.030118858441710472, -0.0011209618533030152, 0.020587574690580368, 0.006187046878039837, -0.019675886258482933, -0.006510281469672918, 0.035240888595581055, 0.003565943567082286, -0.004562584217637777, 0.027997111901640892, 0.01141267642378807, 0.05768498778343201, 0.018084576353430748, 0.005735346581786871, 0.0048568109050393105, -0.017968542873859406, -0.03361642360687256, 0.047838758677244186, -0.02695281431078911, 0.026339497417211533, -0.014595297165215015, 0.005859667900949717, -0.025096286088228226, -0.0060254293493926525, -0.02622346393764019, 0.004715913441032171, 0.03016858734190464, 0.01909572072327137, -0.025063132867217064, -0.012647599913179874, 0.04399309307336807, 0.011876808479428291, 0.03746208921074867, -0.05078931152820587, -0.04442407190799713, -0.012398957274854183, -0.026322919875383377, -0.0476066917181015, -0.02745009772479534, 0.01092368084937334, -0.018532130867242813, 0.03941807523369789, -0.03623545542359352, 0.016567857936024666, 0.004013499245047569, 0.043263740837574005, 0.022891657426953316, 0.030732175335288048, 0.051949642598629, -0.03769415616989136, 0.0427001528441906, -0.042202867567539215, 0.035970237106084824, -0.003234420670196414, 0.01871446892619133, 0.06769698113203049, 0.01595454104244709, 0.0048816753551363945, 0.010136313736438751, 0.001197626581415534, -0.0027930806390941143, -0.02478133887052536, -0.016493266448378563, -0.004367814399302006, -0.012498414143919945, 0.05151866376399994, -0.0025983110535889864, 0.00196738145314157, 0.0356387160718441, 0.05244692787528038, -0.008818509988486767, 0.004637177102267742, -0.0099954167380929, -0.04392678663134575, -0.01281336136162281, 0.02869330905377865, 0.0017042350955307484, 0.043429505079984665, 0.01641867309808731, -0.04989420250058174, 0.009730198420584202, -0.013700185343623161, -0.004956267774105072, -0.011578437872231007, -0.026621291413903236, -0.009216337464749813, -0.005743634887039661, 0.02995309606194496, 0.012473550625145435, -0.005888675805181265, 0.05589476600289345, 0.03759469836950302, 0.010658462531864643, 0.023322638124227524, 0.011628166772425175, -0.019062567502260208, -0.010011992417275906, 0.02745009772479534, -0.019510123878717422, 0.050524093210697174, -0.02507971040904522, 0.05436975881457329, -0.011876808479428291, -0.028245752677321434, -0.005805795080959797, 0.012755344621837139, -0.00882679782807827, 0.0027910086791962385, 0.019211754202842712, -0.008884814567863941, -0.0272014569491148, 0.01765359565615654, 0.0009557184530422091, -0.013667033053934574, 0.025361504405736923, -0.024831067770719528, -0.015929676592350006, 0.015896525233983994, -0.04545179381966591, 0.027052270248532295, -0.009191473014652729, 0.03217430040240288, 0.00855329167097807, -0.013086867518723011, 0.004429975058883429, 0.009183185175061226, 0.005184189882129431, -0.014454399235546589, -0.01368360873311758, -0.00452943192794919, -0.03892079368233681, -0.004185476806014776, -0.018863653764128685, -0.01781935803592205, -0.011238627135753632, 0.011470693163573742, -0.0011251058895140886, -0.0014151885407045484, 0.041473519057035446, -0.027334066107869148, 0.06169641762971878, 0.029207170009613037, 0.019526701420545578, 0.01573905162513256, -0.033284902572631836, 0.020488116890192032, -0.003344237571582198, -0.012647599913179874, 0.028162872418761253, 0.017090007662773132, -0.006717483513057232, 0.060237716883420944, -0.029505541548132896, -0.014951684512197971, 0.008201048709452152, -0.030052553862333298, 0.017421530559659004, 0.002360028913244605, 0.03283734619617462, -0.0012349229073151946, 0.021665023639798164, -0.01442953571677208, -0.002637679222971201, 0.017288921400904655, 0.01718946360051632, 0.018018271774053574, 0.06153065711259842, -0.03336778283119202, 0.008192759938538074, 0.0003760713152587414, -0.016642451286315918, -0.013335510157048702, -0.0003778843383770436, -0.02812972106039524, -0.004042507614940405, 0.026422377675771713, 0.0023579567205160856, 0.03184277564287186, 0.010998273268342018, -0.0025900229811668396, -0.01752098649740219, -0.03679904341697693, 0.020272627472877502, 0.04399309307336807, -0.01512573380023241, -0.017603866755962372, 0.023140300065279007, -0.013376950286328793, -0.030052553862333298, 0.0021445390302687883, -0.005586161278188229, -0.02812972106039524, -0.014396383427083492, 0.009092016145586967, -0.016866229474544525, 0.03742893785238266, -0.012340941466391087, 0.03653382509946823, 0.030665870755910873, 0.04594907909631729, -0.046612124890089035, 0.007973126135766506, -0.028229176998138428, 0.016866229474544525, 0.01578049175441265, -0.03187593072652817, 0.030699023976922035, -0.029223745688796043, -0.0011406460544094443, 0.03729632869362831, -0.015523561276495457, -0.06507795304059982, -0.023604432120919228, 0.04455668106675148, -0.001452484866604209, 0.009796502999961376, 0.005714626517146826, 0.034345775842666626, -0.0348099060356617, -0.03054983727633953, 0.03921916335821152, 0.03230690956115723, 0.0019052207935601473, 0.031246036291122437, -0.022129155695438385, -0.007111166603863239, 0.02423432655632496, 0.02643895335495472, -0.01592138782143593, -0.025494113564491272, -0.03315229341387749, -0.029969673603773117, -0.024383511394262314, -0.021151162683963776, 0.027599284425377846, 0.011843656189739704, -0.030732175335288048, -0.011462405323982239, -0.05393877997994423, -0.020189747214317322, -0.029207170009613037 ]
Federated learning (FL) has been proposed as a privacy-preserving approach in distributed machine learning. A federated learning architecture consists of a central server and a number of clients that have access to private, potentially sensitive data. Clients are able to keep their data in their local machines and only share their locally trained model's parameters with a central server that manages the collaborative learning process. FL has delivered promising results in real-life scenarios, such as healthcare, energy, and finance. However, when the number of participating clients is large, the overhead of managing the clients slows down the learning. Thus, client selection has been introduced as a strategy to limit the number of communicating parties at every step of the process. Since the early na\"{i}ve random selection of clients, several client selection methods have been proposed in the literature. Unfortunately, given that this is an emergent field, there is a lack of a taxonomy of client selection methods, making it hard to compare approaches. In this paper, we propose a taxonomy of client selection in Federated Learning that enables us to shed light on current progress in the field and identify potential areas of future research in this promising area of machine learning.
[ -0.04058695584535599, 0.013903114013373852, -0.03848700597882271, -0.05945029482245445, 0.026846768334507942, 0.015840137377381325, -0.003183867549523711, 0.01798534393310547, -0.03848700597882271, 0.046054065227508545, -0.04058695584535599, -0.04011627659201622, -0.010925169102847576, -0.023570124059915543, -0.06893627345561981, 0.01766854152083397, 0.023552021011710167, -0.07697401195764542, 0.037074971944093704, -0.05619175359606743, -0.015324200503528118, -0.03779909387230873, 0.011594980023801327, 0.024909745901823044, 0.03225956857204437, 0.0396818071603775, 0.008413375355303288, 0.01964177004992962, -0.052100472152233124, 0.060029592365026474, 0.05785723030567169, 0.034884508699178696, -0.029272573068737984, -0.03213284909725189, -0.02900102734565735, -0.040514543652534485, 0.010228202678263187, 0.04456961899995804, 0.046054065227508545, 0.03256732225418091, -0.02291841432452202, -0.01703493483364582, -0.012319101020693779, 0.0362965427339077, -0.0004884984809905291, -0.030177723616361618, -0.049783285707235336, -0.005657191853970289, -0.05756758153438568, -0.029761353507637978, 0.014464307576417923, -0.03177078813314438, 0.015306097455322742, -0.0010618548840284348, -0.011812216602265835, -0.009386412799358368, 0.07328099757432938, -0.019116781651973724, 0.010155790485441685, -0.0125453881919384, -0.0025661021936684847, -0.02349771186709404, 0.010418284684419632, -0.01275357324630022, 0.03721979632973671, 0.061369214206933975, 0.005756758153438568, 0.01451861672103405, -0.030105311423540115, -0.03130010887980461, -0.06585876643657684, 0.05593831092119217, 0.002034326083958149, 0.007109958678483963, -0.009983811527490616, 0.02186843939125538, -0.0034893557894974947, -0.0022040419280529022, 0.005046214908361435, 0.013016066513955593, 0.0013181256363168359, 0.020546920597553253, -0.001632665516808629, 0.025543352589011192, 0.042940348386764526, 0.03148113936185837, 0.007272885646671057, -0.07194137573242188, 0.028222598135471344, 0.03276645392179489, -0.012011349201202393, 0.01661856658756733, -0.018827134743332863, -0.021669307723641396, 0.026195060461759567, -0.025543352589011192, -0.006471827160567045, -0.02483733370900154, -0.03571724519133568, 0.00006647199916187674, -0.07186896353960037, 0.030485475435853004, -0.026701945811510086, 0.017949137836694717, -0.0011631186353042722, -0.041636932641267776, -0.0025887310039252043, 0.04427997022867203, 0.034721579402685165, 0.06835697591304779, 0.005308708641678095, -0.011205765418708324, -0.05101429298520088, 0.06314331293106079, -0.03303799778223038, 0.04518512263894081, -0.027552787214517593, -0.033164720982313156, -0.018130168318748474, -0.038414593786001205, 0.06267262995243073, -0.007309091743081808, -0.015459973365068436, -0.004089018329977989, -0.07885672897100449, 0.016853906214237213, 0.0436282642185688, -0.009237062186002731, -0.014373792335391045, 0.014011732302606106, 0.0355905257165432, 0.024493377655744553, 0.02056502364575863, -0.029182057827711105, 0.039174921810626984, 0.0191348847001791, 0.07501889020204544, 0.013477693311870098, 0.0020648748613893986, 0.006367735099047422, 0.017677592113614082, 0.016926318407058716, 0.013758290559053421, 0.039790425449609756, 0.048190221190452576, -0.010943271219730377, -0.037328414618968964, 0.019189193844795227, 0.000587782240472734, 0.030829431489109993, -0.034594859927892685, 0.031408727169036865, 0.02929067611694336, 0.03008720837533474, 0.05597451701760292, -0.03852321207523346, 0.05916064977645874, -0.054236628115177155, 0.03913871571421623, 0.03877665475010872, 0.002633988391608, 0.033001795411109924, 0.021035701036453247, 0.08370833098888397, 0.04619888961315155, 0.07382409274578094, 0.003407892305403948, -0.003527824766933918, -0.05945029482245445, 0.04326620325446129, 0.0003244399558752775, -0.022049469873309135, 0.012726418673992157, 0.05354871228337288, 0.0004644554283004254, 0.01645563915371895, 0.03113718330860138, -0.032621629536151886, -0.03320092707872391, 0.01592160016298294, -0.002674720250070095, 0.06332433968782425, 0.0012151647824794054, 0.03624223172664642, 0.05141256004571915, -0.010264408774673939, 0.026448503136634827, 0.046343713998794556, 0.03808873891830444, 0.01049069594591856, 0.047610923647880554, 0.047864366322755814, 0.033798325806856155, -0.017713798210024834, 0.04771954193711281, -0.0191348847001791, 0.05199185386300087, 0.0047203609719872475, 0.06176748126745224, -0.021633101627230644, -0.02715452015399933, -0.03005100227892399, -0.020999494940042496, 0.04268690571188927, 0.022212397307157516, 0.014618183486163616, 0.048986755311489105, 0.02824070118367672, -0.0168086476624012, -0.07306376099586487, -0.012617800384759903, -0.003340005874633789, -0.019352121278643608, 0.0044488157145679, -0.026448503136634827, -0.007761667016893625, 0.0422162264585495, 0.02353391796350479, 0.00925063993781805, -0.005820118822157383, 0.05391077324748039, 0.0006222911179065704, 0.039718013256788254, 0.004012080375105143, -0.046560950577259064, 0.013305715285241604, 0.013559157028794289, 0.0032924856059253216, 0.0028331216890364885, 0.0185012798756361, 0.00022317621915135533, 0.03913871571421623, 0.023570124059915543, 0.011287229135632515, 0.035862069576978683, -0.0343957245349884, 0.046560950577259064, -0.011739804409444332, -0.04442479461431503, -0.022719282656908035, -0.012165225110948086, 0.028059670701622963, -0.02014865353703499, -0.008436004631221294, 0.04018868878483772, -0.017532767727971077, -0.05829170346260071, 0.06643805652856827, -0.014763007871806622, 0.04735748469829559, -0.0634329617023468, 0.00023166199389379472, -0.008512942120432854, -0.014536719769239426, -0.038378387689590454, 0.007046598009765148, -0.01741509884595871, -0.04275931790471077, 0.036785323172807693, -0.037654269486665726, 0.081753209233284, 0.018573692068457603, -0.021307246759533882, 0.034594859927892685, -0.011929885484278202, -0.04152831435203552, 0.08356350660324097, -0.006738846655935049, 0.029978590086102486, -0.022013263776898384, -0.08146356046199799, 0.00001822676495066844, -0.033762119710445404, -0.039718013256788254, -0.00693345395848155, -0.019659873098134995, -0.006856516469269991, -0.032621629536151886, -0.017786210402846336, 0.04753851518034935, -0.017777159810066223, -0.014898779802024364, 0.01030061487108469, -0.02945360355079174, -0.03193371742963791, -0.040550749748945236, -0.06781388819217682, -0.03750944510102272, -0.07023969292640686, -0.01664572022855282, -0.06813973933458328, -0.01607547514140606, -0.01706209033727646, -0.03519225865602493, 0.03776288777589798, -0.028838099911808968, -0.012282894924283028, 0.053983185440301895, -0.0005139558925293386, 0.0032404393423348665, -0.010155790485441685, -0.0250907763838768, -0.019732285290956497, -0.004779195412993431, 0.0237511545419693, 0.015713416039943695, -0.046886805444955826, 0.005390172358602285, -0.02601402997970581, -0.019877109676599503, -0.011893680319190025, -0.081898033618927, 0.017885778099298477, -0.09609079360961914, -0.01726122386753559, -0.0001592499465914443, 0.023859770968556404, 0.02098139189183712, -0.023570124059915543, -0.09695973992347717, 0.008191613480448723, 0.05362112447619438, -0.0713258758187294, -0.033128514885902405, -0.05307803675532341, -0.0725206732749939, 0.03855941817164421, 0.05930547043681145, -0.05543142557144165, 0.04619888961315155, -0.033255234360694885, -0.033671606332063675, -0.09145642071962357, -0.0409490168094635, 0.004647948779165745, 0.026593327522277832, -0.03982663154602051, 0.016926318407058716, -0.014102247543632984, 0.004593639634549618, -0.026701945811510086, -0.02199516072869301, -0.04829883947968483, 0.03568103909492493, -0.0014855785993859172, 0.0357353501021862, -0.05220909044146538, 0.01608452759683132, 0.07690159976482391, -0.005820118822157383, 0.0009413567022420466, 0.011386795900762081, -0.0122285857796669, -0.052643563598394394, -0.0012298735091462731, 0.006747898180037737, 0.005209142342209816, -0.02194085158407688, 0.017940087243914604, -0.011187662370502949, 0.017469407990574837, -0.033961255103349686, -0.004801824223250151, 0.004143327008932829, -0.04120245948433876, -0.01592160016298294, 0.016256505623459816, -0.018809031695127487, -0.008449581451714039, 0.05086946859955788, -0.03725600242614746, 0.050036728382110596, -0.02009434439241886, 0.01061741728335619, -0.03101046197116375, 0.006069035269320011, -0.021470174193382263, -0.04981949180364609, -0.03050357848405838, 0.0362241305410862, 0.029526015743613243, 0.026593327522277832, 0.036405161023139954, 0.06176748126745224, 0.006634754594415426, -0.02282790094614029, -0.006091664079576731, -0.043157584965229034, -0.047647129744291306, 0.0527159757912159, 0.01951504871249199, 0.004027920309454203, 0.01929781213402748, -0.012654006481170654, 0.04797298461198807, 0.009558390825986862, 0.017460357397794724, 0.006589496973901987, -0.006598548498004675, -0.0635053738951683, -0.035608626902103424, 0.025543352589011192, -0.02253825217485428, 0.051340147852897644, -0.010861808434128761, -0.04768333584070206, -0.011133353225886822, 0.0409490168094635, 0.01926160603761673, 0.012038503773510456, 0.0006907430943101645, -0.003462201217189431, 0.01770474761724472, -0.003317377297207713, 0.011341538280248642, -0.009513133205473423, -0.057676199823617935, 0.0271002110093832, -0.022339118644595146, -0.026882974430918694, 0.00247558718547225, -0.005955891218036413, 0.03148113936185837, 0.027534684166312218, -0.03133631497621536, 0.04775574803352356, 0.021470174193382263, 0.012744521722197533, -0.002480112947523594, 0.028584659099578857, 0.03253111615777016, 0.04297655448317528, 0.007200473453849554, -0.04543856531381607, -0.03899389132857323, -0.02349771186709404, 0.003991714678704739, -0.011260074563324451, 0.011115250177681446, -0.02744416892528534, -0.018166374415159225, 0.024692511186003685, -0.045583389699459076, 0.006652857642620802, -0.053186655044555664, 0.021977057680487633, 0.008626085706055164, -0.012201431207358837, -0.02257445827126503, 0.007553482428193092, -0.01380354817956686, -0.022502046078443527, -0.09399084746837616, -0.014572925865650177, 0.0007789952796883881, -0.044786855578422546, 0.023479608818888664, -0.0032834340818226337, 0.012789779342710972, -0.0487695187330246, 0.0102191511541605, 0.03222336247563362, -0.006091664079576731, -0.025416631251573563, -0.03254921734333038, -0.007675677537918091, -0.036857735365629196, -0.08631516993045807, -0.0053811208344995975, 0.006888196803629398, 0.01817542500793934, -0.06144162639975548, 0.01716165617108345, 0.03584396839141846, -0.012101864442229271, 0.020365890115499496, -0.02387787401676178, -0.07114484161138535, -0.030413063243031502, -0.02362443320453167, 0.019496945664286613, 0.031209595501422882, 0.014944037422537804, 0.012554439716041088, 0.035355184227228165, 0.015016449615359306, -0.015740569680929184, 0.014753956347703934, -0.0115406708791852, -0.017885778099298477, 0.040767986327409744, 0.020293477922677994, -0.025489043444395065, -0.01891764998435974, -0.004098069854080677, -0.05376594886183739, -0.004697732161730528, -0.020800363272428513, 0.04359205812215805, 0.004385455045849085, 0.004263259470462799, 0.015188428573310375, 0.020130550488829613, -0.06249160319566727, -0.0263941939920187, -0.03267594054341316, -0.01792198419570923, -0.002871590433642268, 0.0003470687079243362, 0.026738150045275688, 0.014364740811288357, 0.0673070028424263, -0.033418163657188416, -0.03964560106396675, -0.003740535117685795, 0.026792459189891815, 0.016790544614195824, -0.04218002036213875, -0.01929781213402748, 0.007517276331782341, 0.011966091580688953, -0.001637191278859973, -0.00300510018132627, 0.003905725199729204, -0.04753851518034935, 0.0032110221218317747, 0.0027765496633946896, 0.02378736063838005, -0.014799213968217373, -0.03307420387864113, -0.010834653861820698, 0.005765809677541256, -0.056915875524282455, -0.02101759798824787, 0.03263973444700241, 0.016790544614195824, 0.01942453347146511, -0.03683963418006897, -0.016057372093200684, -0.045764416456222534, -0.05709690600633621, 0.07215861231088638, 0.015469024889171124, -0.012346255593001842, 0.036785323172807693, 0.035355184227228165, 0.042650699615478516, -0.04981949180364609, -0.010119584389030933, -0.0422162264585495, 0.015559540130198002, 0.02668384276330471, -0.006241013761609793, 0.017152605578303337, -0.011060941033065319, -0.05550383776426315, 0.018130168318748474, -0.030232032760977745, -0.02496405504643917, -0.025362322106957436, -0.005308708641678095, -0.0026634058449417353, 0.013477693311870098, -0.006358683574944735, -0.02295462042093277, -0.056879669427871704, -0.026629533618688583, 0.03365350142121315, -0.00837264396250248, 0.042288638651371, 0.04004386439919472, -0.03493881598114967, -0.04366447031497955, -0.02505457028746605, -0.016953472048044205, 0.04511271044611931, -0.005802015773952007, 0.044207558035850525, 0.03729220852255821, -0.013061324134469032, -0.006241013761609793, -0.017967240884900093, 0.031861305236816406, 0.009902348741889, 0.039609394967556, 0.05383836105465889, -0.05315044894814491, -0.0010641177650541067, 0.0016530314460396767, -0.04272311180830002, 0.044243764132261276, 0.020130550488829613, -0.02525370381772518, 0.0021848075557500124, 0.011640237644314766, -0.007114484440535307, 0.0037676896899938583, -0.007327194791287184, 0.041057635098695755, -0.04996431618928909, 0.03689394146203995, 0.024529583752155304, -0.012644954957067966, 0.04004386439919472, 0.035518113523721695, -0.004116172902286053, -0.013658723793923855, 0.027335550636053085, -0.011929885484278202, -0.020383993163704872, 0.04753851518034935, -0.017170708626508713, 0.01709829643368721, -0.005150307435542345, 0.011957040056586266, 0.04174555093050003, 0.010988528840243816, -0.011785062029957771, -0.017532767727971077, -0.0012773938942700624, 0.018347404897212982, -0.02429424412548542, 0.020583126693964005, 0.02311754785478115, 0.0052725025452673435, 0.036314643919467926, 0.0027901269495487213, -0.024565789848566055, 0.008481262251734734, 0.0164918452501297, -0.0263941939920187, 0.020908979699015617, -0.05253494530916214, -0.04920399188995361, -0.056119341403245926, -0.06390363723039627, 0.004969277419149876, 0.009730369783937931, -0.0008700760663487017, 0.028222598135471344, 0.015206531621515751, -0.015514282509684563, 0.02161499857902527, 0.0765395388007164, -0.017116399481892586, 0.007358875125646591, -0.0005184815963730216, -0.015903497114777565, 0.04934881627559662, 0.013350972905755043, 0.054019391536712646, 0.01403888687491417, -0.0038740448653697968, 0.022139985114336014, -0.025923514738678932, -0.0607537142932415, -0.00044210953637957573, -0.04833504557609558, -0.011278177611529827, 0.0005484647117555141, 0.013477693311870098, 0.038957685232162476, 0.014283278025686741, 0.01145920716226101, 0.013287612237036228, -0.02795105241239071, 0.02576058730483055, 0.023968389257788658, -0.010753190144896507, 0.09428049623966217, -0.024203728884458542, 0.020239168778061867, -0.03808873891830444, -0.000054697971791028976, 0.01955125480890274, 0.0015941966557875276, -0.0003153884317725897, 0.045004092156887054, 0.031535450369119644, -0.02572438307106495, -0.025832999497652054, -0.021090010181069374, -0.0008695103460922837, 0.005494264420121908, -0.03928354009985924, -0.013939320109784603, -0.022646870464086533, 0.02865707129240036, -0.025670073926448822, -0.010164842009544373, -0.01130533218383789, -0.012219534255564213, 0.031155286356806755, -0.059776149690151215, 0.020709848031401634, -0.02521749772131443, 0.016356073319911957, -0.02483733370900154, 0.00868944637477398, 0.003726957831531763, 0.040224894881248474, -0.01259064581245184, -0.017505614086985588, 0.027245035395026207, -0.01351389940828085, -0.023045135661959648, -0.005575728137046099, 0.01737889274954796, -0.043483439832925797, 0.014373792335391045, 0.026213163509964943, -0.01984090358018875, 0.004392243456095457, 0.014581977389752865, 0.016310814768075943, -0.05485213175415993, -0.018664207309484482, 0.014862573705613613, -0.005449007265269756, 0.027932949364185333, -0.02253825217485428, 0.04464203119277954, 0.004860659129917622, -0.006168602034449577, -0.002335288794711232, 0.010155790485441685, -0.04782816022634506, -0.02168741077184677, -0.021832235157489777, 0.011124301701784134, 0.03798012062907219, -0.019913315773010254, -0.034305211156606674, 0.03294748440384865, 0.023045135661959648, 0.019804697483778, 0.0016733972588554025, 0.02677435614168644, -0.012129019014537334, 0.00043645233381539583, 0.015459973365068436, -0.008657766506075859, -0.03158975765109062, 0.0005640219897031784, -0.004960225895047188, 0.03604310005903244, 0.025416631251573563, -0.022520149126648903, -0.05315044894814491, -0.0014878413639962673, 0.026973489671945572, -0.030974255874753, 0.050797056406736374, -0.027498478069901466, -0.0698414295911789, -0.0020049086306244135, 0.013568208552896976, 0.013233303092420101, 0.04120245948433876, 0.04004386439919472, -0.03705686703324318, 0.006182179320603609, -0.013097530230879784, 0.021977057680487633, 0.03874044865369797, 0.047936778515577316, -0.006449198350310326, -0.020782260224223137, -0.0015919337747618556, -0.02349771186709404, 0.012925551272928715, -0.0009334366186521947, 0.031861305236816406, -0.030775122344493866, -0.01971418224275112, 0.04015248268842697, 0.03265783563256264, -0.00740413274616003, -0.025145085528492928, -0.001766175264492631, 0.013378126546740532, 0.007241205312311649, 0.027969155460596085, -0.0185012798756361, -0.0009311737376265228, -0.0032562795095145702, 0.06288986653089523, -0.02094518579542637, 0.00803773757070303, 0.028512246906757355, 0.0003012454544659704, 0.001435795216821134, -0.01891764998435974, 0.004138801246881485, 0.03616981953382492, -0.027389859780669212, -0.02098139189183712, 0.023552021011710167, -0.020166756585240364, -0.03591638058423996, 0.017813365906476974, -0.015831084921956062, 0.004838030319660902, -0.008101098239421844, -0.03667670488357544, -0.011160507798194885, 0.006729795131832361, -0.079363614320755, 0.006937979720532894, 0.013088478706777096, 0.010264408774673939, 0.031191492453217506, -0.005761283915489912, 0.00796080008149147, -0.0008214242407120764, -0.015369458124041557, -0.02626747265458107, 0.04464203119277954, -0.05329527333378792, -0.03457675501704216, -0.010608365759253502, 0.008196139708161354, 0.01451861672103405, -0.0016281397547572851, -0.01706209033727646, -0.025995926931500435, -0.004991905763745308, -0.01573151908814907, 0.01034587249159813, 0.005363017786294222, 0.007825027219951153, -0.03034065105021, -0.05463489517569542, 0.015613849274814129, -0.03743703290820122, 0.01909867860376835, 0.008571776561439037, 0.03557242080569267, 0.05488833785057068, 0.03888527303934097, 0.017750004306435585, -0.01900816336274147, 0.005145781673491001, 0.010771293193101883, 0.011341538280248642, 0.006838413421064615, -0.00484708184376359, -0.0071778446435928345, 0.03729220852255821, 0.026720046997070312, 0.008159933611750603, 0.012119967490434647, 0.03091994673013687, 0.029145851731300354, -0.01621124893426895, -0.003582133911550045, 0.01601211540400982, 0.02597782388329506, -0.02614075131714344, -0.03823356330394745, -0.04384549707174301, 0.02340719662606716, -0.0031635016202926636, -0.0017412835732102394, -0.007874811068177223, -0.028819996863603592, -0.004638897255063057, -0.03209664300084114, -0.05391077324748039, -0.06531567126512527, 0.02069174498319626, -0.032494910061359406, 0.008440529927611351, 0.003982663154602051, -0.007553482428193092, 0.00905603263527155, -0.041636932641267776, 0.036821529269218445, 0.0158582404255867, -0.05756758153438568, 0.016835803166031837, 0.04178175330162048, -0.011694546788930893, -0.01852843351662159, 0.04652474448084831, -0.041854165494441986, -0.009721318259835243, -0.045800622552633286, -0.0030865638982504606, -0.04377308487892151, -0.025525249540805817, 0.01563195139169693, 0.01235530711710453, -0.006829361896961927, 0.05123152956366539, -0.009178227744996548, 0.017931034788489342, 0.017206914722919464, 0.00804226379841566, 0.034051768481731415, -0.004530278965830803, -0.0138669079169631, -0.013541053980588913, -0.016763390973210335, 0.034468136727809906, 0.02089087665081024, 0.0005320588825270534, -0.005105049815028906, -0.012572542764246464, 0.0244571715593338, -0.022936517372727394, -0.018329301849007607, -0.004324357490986586, -0.032494910061359406, 0.00892931129783392, 0.031915612518787384, -0.04431617632508278, -0.042867936193943024, -0.017460357397794724, 0.0237511545419693, 0.02366063930094242, 0.06393984705209732, -0.0396818071603775, 0.002017354592680931, -0.018329301849007607, -0.029507912695407867, 0.051376353949308395, 0.004514439031481743, -0.00816445890814066, 0.0035527164582163095, -0.04359205812215805, 0.013269509188830853, 0.032331980764865875, 0.029471706598997116, -0.011893680319190025, 0.0009272136958315969, 0.000014036906577530317, 0.011069992557168007, -0.06882765889167786, 0.03913871571421623, -0.04308517277240753, -0.0012117704609408975, -0.026032133027911186, 0.03540949523448944, 0.046886805444955826, -0.03939215838909149, 0.01271736714988947, -0.012002297677099705, 0.009875194169580936, 0.033164720982313156, -0.023932183161377907, 0.0020399834029376507, 0.03142683207988739, 0.0018759247614070773, -0.03772668167948723, -0.03187940642237663, -0.020800363272428513, 0.04811780899763107, -0.02635798789560795, 0.07632230222225189, -0.010128635913133621, 0.019460739567875862, 0.023425299674272537, -0.0038966736756265163, 0.0270277988165617, 0.003740535117685795, -0.04963846132159233, -0.006503507494926453, -0.03654998540878296, 0.0161750428378582, -0.016636669635772705, -0.006680011749267578, 0.006530662067234516, 0.0002868196170311421, -0.0012434507953003049, 0.006340580526739359, -0.00969416368752718, -0.03794391453266144, -0.017804313451051712, -0.007023969199508429, -0.03698445484042168, -0.0035662937443703413, -0.045257534831762314, -0.004007554613053799, -0.03452244773507118, -0.00022303478908725083, 0.0011444499250501394, -0.014029835350811481, -0.014283278025686741, -0.002683771774172783, 0.04145590215921402, 0.00262267398647964, 0.04902296140789986, -0.01630176417529583, -0.026050236076116562, -0.015351355075836182, -0.0016813173424452543, -0.03084753453731537, -0.028548453003168106, 0.008340963162481785, -0.0316440686583519, 0.007729986682534218, -0.013767342083156109, 0.005684346426278353, -0.010943271219730377, -0.005593831185251474, 0.08102908730506897, 0.023027032613754272, -0.03776288777589798, 0.023479608818888664, -0.007186896167695522, 0.022103779017925262, 0.03079322539269924, 0.04931261017918587, -0.02929067611694336, -0.017614232376217842, -0.05459868907928467, 0.010191996581852436, 0.017297429963946342, -0.029055336490273476, 0.015966858714818954, -0.010110532864928246, -0.0009266479755751789, -0.01849222742021084 ]
Code pre-trained models (CodePTMs) have recently demonstrated significant success in code intelligence. To interpret these models, some probing methods have been applied. However, these methods fail to consider the inherent characteristics of codes. In this paper, to address the problem, we propose a novel probing method CAT-probing to quantitatively interpret how CodePTMs attend code structure. We first denoise the input code sequences based on the token types pre-defined by the compilers to filter those tokens whose attention scores are too small. After that, we define a new metric CAT-score to measure the commonality between the token-level attention scores generated in CodePTMs and the pair-wise distances between corresponding AST nodes. The higher the CAT-score, the stronger the ability of CodePTMs to capture code structure. We conduct extensive experiments to integrate CAT-probing with representative CodePTMs for different programming languages. Experimental results show the effectiveness of CAT-probing in CodePTM interpretation. Our codes and data are publicly available at https://github.com/nchen909/CodeAttention.
[ -0.006097076926380396, 0.007680392358452082, -0.032663535326719284, -0.011564326472580433, 0.04282824695110321, -0.0076760184019804, -0.00978856347501278, 0.02472071535885334, 0.0197695754468441, 0.0501762293279171, -0.018299978226423264, -0.05486494302749634, 0.027729889377951622, -0.056649453938007355, 0.011887987144291401, -0.018824834376573563, 0.03429058939218521, 0.03243609890341759, -0.008393321186304092, -0.05091102793812752, 0.003549338551238179, -0.06287774443626404, 0.009849797002971172, -0.010637081228196621, 0.05874887853860855, 0.012544057331979275, -0.01966460421681404, -0.004362865351140499, -0.01754768379032612, 0.01561446487903595, -0.007916577160358429, 0.049406442791223526, -0.012762747704982758, -0.07620908319950104, -0.005672818049788475, 0.0014499146491289139, 0.0080128014087677, 0.023303605616092682, -0.053570300340652466, 0.020784296095371246, -0.020434392616152763, -0.07438958436250687, 0.007400468923151493, -0.027659909799695015, -0.02113419957458973, 0.011887987144291401, -0.00025969435228034854, -0.022778749465942383, -0.015588222071528435, -0.036040108650922775, 0.053115423768758774, 0.03308342024683952, 0.011074461042881012, 0.0395391508936882, 0.0560896061360836, 0.05437507852911949, 0.03663494437932968, 0.006945593748241663, 0.05021122097969055, 0.016996584832668304, 0.047027092427015305, 0.06217793747782707, -0.02206144481897354, -0.005283549893647432, 0.05699935927987099, 0.02190398797392845, -0.029374439269304276, -0.029112011194229126, 0.03485043719410896, 0.01712779887020588, -0.05283550173044205, 0.001969303237274289, -0.007820353843271732, 0.0016784456092864275, 0.03659995645284653, 0.05510987713932991, 0.04079880192875862, 0.04286323860287666, 0.026242798194289207, -0.010094729252159595, 0.01644548587501049, 0.040623851120471954, -0.002792671089991927, 0.019839555025100708, 0.030214209109544754, -0.04055387154221535, -0.060393426567316055, -0.05500490590929985, -0.007098677102476358, 0.009552378207445145, -0.04461275786161423, 0.027764881029725075, -0.0140224015340209, -0.019997011870145798, 0.026032855734229088, 0.028902068734169006, -0.02690761536359787, 0.001854491070844233, -0.058468952775001526, 0.02368849888443947, 0.006320140324532986, 0.0184224434196949, 0.00267457845620811, -0.03429058939218521, 0.01873735710978508, -0.04986131563782692, -0.05720929801464081, 0.038279496133327484, 0.010217196308076382, 0.12449583411216736, -0.06812630593776703, -0.004478770773857832, -0.03107147291302681, -0.03747471421957016, 0.0014324194053187966, -0.011091955937445164, -0.04520759359002113, -0.03642500191926956, -0.03352079913020134, -0.02758992835879326, 0.0008239145390689373, 0.05724428966641426, 0.02097674272954464, -0.024580754339694977, -0.015728183090686798, 0.06557200849056244, 0.034010667353868484, -0.017346490174531937, -0.01836995780467987, 0.01619180664420128, -0.006324514281004667, -0.002643961925059557, 0.07026071846485138, -0.04205845668911934, 0.05388521030545235, -0.012858971022069454, 0.03472796827554703, 0.06371751427650452, 0.02940942905843258, -0.08180754631757736, 0.019892040640115738, -0.006648175418376923, 0.020434392616152763, -0.0016882866621017456, 0.005392895080149174, -0.014783442951738834, 0.011678045615553856, 0.12785491347312927, 0.007877212949097157, 0.04944143071770668, -0.0384194552898407, -0.0007347983191721141, 0.029059525579214096, 0.0194721557199955, 0.0015844089211896062, 0.019332194700837135, 0.06165308132767677, 0.03890932351350784, -0.030879026278853416, -0.03490292280912399, 0.023286109790205956, -0.09118497371673584, 0.01449477206915617, -0.02050437219440937, 0.04562747851014137, 0.01423234399408102, 0.003912363667041063, 0.006687539629638195, -0.06312267482280731, 0.03652997314929962, 0.04408790171146393, 0.08397695422172546, -0.017862597480416298, 0.02029442973434925, -0.04688713327050209, 0.007969062775373459, 0.001002693548798561, 0.013462555594742298, -0.04527757316827774, 0.033695753663778305, -0.02493065781891346, -0.0034924789797514677, 0.03799957036972046, -0.03493791073560715, 0.011433112435042858, 0.01868487149477005, 0.06336761265993118, 0.04065884277224541, 0.04121868684887886, -0.030004266649484634, -0.022708768025040627, 0.006132067181169987, 0.013882440514862537, -0.026085341349244118, 0.01181800663471222, -0.03869938105344772, -0.07998804748058319, -0.002064433414489031, 0.018387453630566597, -0.00026748518575914204, -0.0672515407204628, -0.07127544283866882, -0.04716705530881882, 0.0026374012231826782, 0.012990185059607029, 0.013418816961348057, 0.01295519433915615, 0.03845444694161415, 0.0312289297580719, -0.011013227514922619, -0.0411137156188488, 0.01966460421681404, -0.04237337037920952, -0.05507488548755646, 0.013357584364712238, 0.006066460162401199, 0.009403669275343418, 0.006709408480674028, 0.008187753148376942, -0.002692073816433549, 0.04783187434077263, 0.016323020681738853, 0.05367526784539223, 0.03560272976756096, -0.043947938829660416, -0.01884232833981514, 0.003409376833587885, -0.02627778798341751, -0.004470023326575756, 0.004487518686801195, 0.009797311387956142, 0.005812780000269413, -0.01931469887495041, -0.010374653153121471, 0.0566144622862339, -0.03586515784263611, 0.052800510078668594, -0.04226839914917946, 0.016060592606663704, 0.001701408065855503, -0.05647450312972069, -0.03642500191926956, -0.018229996785521507, -0.024580754339694977, 0.07970812171697617, -0.008467676118016243, -0.04027394577860832, -0.02654021605849266, 0.014564752578735352, 0.0507010854780674, -0.00559408962726593, 0.004004213493317366, 0.01857990026473999, 0.009622359648346901, -0.0032256771810352802, 0.03992404416203499, 0.06119820475578308, -0.005677192006260157, 0.019944526255130768, -0.05468999221920967, 0.025105610489845276, 0.02996927499771118, -0.022971196100115776, 0.056859396398067474, -0.041603583842515945, -0.012937699444591999, 0.05318540334701538, -0.05241561681032181, -0.000004736859409604222, 0.02753744274377823, 0.027974823489785194, -0.03283848986029625, -0.05517985671758652, 0.019997011870145798, 0.04002901539206505, 0.004749946296215057, -0.00012294478074181825, 0.003982344642281532, -0.023723488673567772, -0.020836781710386276, -0.02024194411933422, -0.0018490238580852747, 0.0259103886783123, 0.0336257703602314, 0.011643054895102978, -0.031508851796388626, -0.027957327663898468, -0.010059739463031292, -0.05136590451002121, -0.03694985806941986, -0.004039204213768244, 0.001975863939151168, -0.030896520242094994, -0.006560699548572302, -0.005008000414818525, -0.01358502171933651, -0.026365265250205994, 0.012054191902279854, -0.0017856037011370063, -0.0453825443983078, -0.08306720107793808, -0.03761467710137367, -0.009893534705042839, 0.041918497532606125, -0.05094601958990097, 0.06063835695385933, 0.0015778482193127275, 0.026785150170326233, -0.06270278990268707, -0.01550949364900589, 0.013978663831949234, -0.04132365807890892, -0.012439086101949215, -0.00378552358597517, -0.007872839458286762, 0.014258586801588535, 0.02727501466870308, -0.031508851796388626, -0.05731426924467087, -0.01311265118420124, 0.019122252240777016, -0.02398591674864292, -0.14262086153030396, 0.012535310350358486, 0.006070834118872881, 0.04772690311074257, 0.03352079913020134, 0.03320588544011116, 0.01857990026473999, -0.002088489243760705, -0.04783187434077263, 0.013803712092339993, -0.03086153045296669, -0.07180029898881912, -0.04968636482954025, -0.01514209434390068, -0.03488542512059212, 0.05934371426701546, -0.02134414203464985, 0.010077234357595444, 0.0006227197009138763, 0.05262555927038193, -0.05147087574005127, 0.01444228645414114, 0.011476850137114525, -0.06473223865032196, -0.035462766885757446, -0.004889908246695995, -0.028552165254950523, -0.0021191060077399015, 0.0009206848335452378, -0.007754746824502945, -0.014687219634652138, -0.01396991591900587, 0.04541753605008125, 0.009552378207445145, -0.027344996109604836, 0.005200447980314493, 0.027047576382756233, 0.07375975698232651, 0.014451034367084503, -0.047691911458969116, 0.00422946410253644, -0.023128652945160866, -0.018404949456453323, -0.02190398797392845, -0.018404949456453323, -0.011109450832009315, 0.0019222849514335394, 0.0036761786323040724, -0.013410069979727268, 0.09657349437475204, 0.021256666630506516, -0.006914977449923754, -0.007977810688316822, -0.005423511378467083, 0.002416524337604642, -0.009569874033331871, -0.028639640659093857, 0.025490503758192062, -0.03992404416203499, -0.024055898189544678, 0.046607211232185364, 0.035462766885757446, -0.006530082784593105, 0.05892382934689522, 0.025438018143177032, -0.0010201887926086783, 0.008572647348046303, 0.026102837175130844, 0.012404096312820911, -0.02300618588924408, -0.0075535522773861885, -0.031718794256448746, 0.07127544283866882, 0.04968636482954025, -0.0026505226269364357, -0.005064859986305237, 0.00005662020339514129, -0.07956816256046295, -0.034273095428943634, 0.04307318106293678, -0.024808192625641823, 0.0024034029338508844, -0.023793470114469528, -0.020329421386122704, -0.014328567311167717, 0.006910603493452072, 0.003934232983738184, 0.01166054978966713, -0.02195647358894348, -0.06168806925415993, -0.0019900789484381676, 0.027449967339634895, 0.0269601009786129, 0.0024493278469890356, -0.053220394998788834, 0.03248858451843262, 0.047132063657045364, 0.027152547612786293, 0.038174524903297424, -0.005882760509848595, -0.0023487303406000137, -0.041813526302576065, 0.01743396557867527, 0.012159163132309914, 0.042338382452726364, 0.00978856347501278, -0.013121399097144604, -0.0031950606498867273, 0.03719479218125343, 0.038384467363357544, 0.018457435071468353, -0.016279282048344612, -0.031403880566358566, -0.04205845668911934, -0.01428482960909605, -0.05038617178797722, -0.01048837136477232, 0.014066140167415142, -0.0698758214712143, -0.012500319629907608, 0.01805504597723484, -0.024318326264619827, -0.04986131563782692, -0.010505867190659046, -0.03708982095122337, -0.01311265118420124, -0.0009113905252888799, -0.0384194552898407, -0.052695538848638535, 0.010549604892730713, -0.0501762293279171, -0.03091401606798172, 0.019962022081017494, -0.0009228717535734177, -0.054829951375722885, -0.026207808405160904, -0.007076807785779238, -0.06966587901115417, 0.004347556736320257, 0.02727501466870308, 0.018037550151348114, -0.01571943610906601, -0.015063365921378136, 0.06347258388996124, -0.004526882898062468, -0.018195006996393204, 0.0012279442744329572, 0.0158768929541111, 0.037229783833026886, -0.07271004468202591, 0.031403880566358566, -0.032908469438552856, 0.027852356433868408, 0.0037264772690832615, 0.006460102275013924, -0.033065926283597946, 0.04048388823866844, -0.018702367320656776, 0.04079880192875862, -0.04657221958041191, -0.048426710069179535, -0.02737998589873314, 0.028604649007320404, 0.009552378207445145, -0.007391721475869417, 0.011783015914261341, 0.004833048675209284, 0.00020379172929096967, 0.004161670338362455, -0.02253381535410881, 0.005957114975899458, -0.012552805244922638, 0.012491571716964245, -0.012281629256904125, -0.033748239278793335, -0.053360357880592346, 0.02524557150900364, 0.016104331240057945, -0.009893534705042839, -0.04100874438881874, -0.007068060338497162, 0.017915083095431328, 0.0008982691215351224, 0.03275101259350777, -0.037124812602996826, 0.028184765949845314, -0.0030288563575595617, 0.012089182622730732, -0.0065213353373110294, -0.057279281318187714, 0.026977596804499626, -0.028237251564860344, -0.007929698564112186, 0.01514209434390068, 0.038594409823417664, 0.005095476750284433, -0.006390121299773455, 0.018667377531528473, 0.021606570109725, -0.06525709480047226, -0.00524418568238616, 0.018177511170506477, 0.02284872904419899, 0.04818177595734596, 0.05710433050990105, 0.008380199782550335, -0.01316513679921627, -0.0576641745865345, 0.02071431465446949, 0.029321953654289246, 0.003663057228550315, -0.048111796379089355, -0.0014050831086933613, -0.01764390803873539, 0.019297204911708832, 0.017967568710446358, -0.026242798194289207, -0.021729037165641785, -0.001371186226606369, 0.02722252905368805, -0.008327714167535305, 0.04142862930893898, -0.008607638068497181, -0.0006948874215595424, -0.029846809804439545, -0.024650735780596733, -0.025420524179935455, -0.0025892893318086863, 0.01480968575924635, 0.009561126120388508, 0.010724556632339954, 0.03992404416203499, -0.010917004197835922, -0.03357328474521637, -0.03855941817164421, 0.0071642836555838585, -0.0004067633708473295, 0.014932151883840561, -0.03831448405981064, -0.00853328313678503, 0.05329037457704544, -0.02638275921344757, 0.004122306127101183, -0.018247492611408234, 0.01475720014423132, 0.03915425390005112, 0.03887433186173439, 0.023198634386062622, 0.009053765796124935, 0.009596116840839386, -0.0007205834845080972, 0.04877661541104317, 0.0015570727409794927, 0.036564964801073074, -0.016664177179336548, -0.022936206310987473, 0.011091955937445164, -0.044682737439870834, -0.01847492903470993, -0.048531681299209595, -0.0011962342541664839, 0.027624918147921562, 0.01940217614173889, 0.004467836581170559, -0.014792190864682198, -0.02701258659362793, -0.024528268724679947, -0.02029442973434925, 0.009552378207445145, 0.04153360053896904, 0.005126093048602343, -0.009701088070869446, 0.02382845990359783, -0.03189374879002571, 0.023093663156032562, 0.000995586160570383, 0.03378322720527649, -0.017355237156152725, 0.02585790306329727, -0.0014028962468728423, 0.05276551842689514, -0.007146788761019707, -0.032978449016809464, 0.0014958394458517432, 0.03215617686510086, -0.029007039964199066, 0.007059312891215086, 0.04079880192875862, -0.022393854334950447, -0.03315339982509613, 0.014424791559576988, 0.009394921362400055, -0.012220396660268307, -0.03469298034906387, 0.014897162094712257, 0.01659419573843479, 0.0009830114431679249, -0.012220396660268307, 0.052905481308698654, -0.007680392358452082, 0.036250051110982895, -0.047446977347135544, 0.027397481724619865, 0.03238361328840256, -0.013095156289637089, -0.005725303664803505, -0.010243439115583897, -0.010986984707415104, -0.024528268724679947, 0.0061933002434670925, -0.03803456202149391, -0.01774013228714466, 0.023128652945160866, 0.03904928267002106, 0.01697034202516079, 0.0047149560414254665, 0.01059334259480238, -0.00005077708192402497, 0.00015923364844638854, 0.0016117452178150415, -0.04923148825764656, 0.058259010314941406, -0.024913163855671883, -0.02529805712401867, -0.037649668753147125, 0.009132493287324905, 0.07963814586400986, -0.016576699912548065, -0.013908683322370052, 0.012666523456573486, -0.0027642413042485714, 0.04408790171146393, -0.027782374992966652, 0.0057121822610497475, -0.0027401854749768972, -0.007103050593286753, 0.038489438593387604, -0.008318967185914516, 0.030406655743718147, -0.01936718448996544, 0.02232387289404869, 0.007339235860854387, 0.052380625158548355, -0.059728607535362244, -0.09461403638124466, -0.03897930309176445, -0.034675482660532, 0.045977383852005005, -0.0176351610571146, -0.008905055932700634, -0.06749647855758667, 0.0016817259602248669, 0.011791763827204704, -0.0243008304387331, -0.013278855942189693, -0.010707061737775803, -0.007584168575704098, -0.01744271256029606, -0.01571943610906601, 0.005169831216335297, -0.009561126120388508, -0.00030479917768388987, 0.023653509095311165, -0.0060314699076116085, -0.007579794619232416, -0.0280448030680418, -0.03131640702486038, -0.03782461956143379, -0.07250010222196579, -0.013952421024441719, 0.014739705249667168, 0.012963942252099514, 0.004161670338362455, -0.0022164229303598404, -0.018877319991588593, -0.01017345767468214, 0.03472796827554703, -0.0747394859790802, -0.013777469284832478, 0.002921698149293661, -0.04797183349728584, -0.027502452954649925, 0.012753999792039394, 0.020836781710386276, -0.010558352805674076, -0.02155408449470997, 0.017783869057893753, 0.0184224434196949, 0.0007222236599773169, 0.03184126317501068, 0.010365905240178108, 0.021571580320596695, -0.003302218858152628, -0.008537656627595425, 0.024738211184740067, 0.020749306306242943, -0.021868998184800148, 0.024108383804559708, -0.004693087190389633, 0.0028364090248942375, 0.007732877973467112, -0.03918924555182457, -0.01664668135344982, 0.02472071535885334, -0.0030441645067185163, 0.021309152245521545, 0.006543204188346863, -0.003759280778467655, 0.037649668753147125, -0.03918924555182457, -0.0052223168313503265, 0.004763067699968815, 0.006013974547386169, -0.034483037889003754, 0.0336257703602314, 0.03670492768287659, 0.003461862448602915, -0.022096436470746994, 0.019437165930867195, -0.017250265926122665, -0.018020054325461388, 0.006000853143632412, -0.0405888594686985, 0.02221890166401863, -0.04825175926089287, 0.028972048312425613, -0.01068956684321165, 0.0020917695946991444, 0.017294004559516907, 0.00038516774657182395, -0.00457936804741621, -0.04818177595734596, -0.026260294020175934, -0.03334584832191467, -0.01613057404756546, 0.027817366644740105, 0.018492424860596657, -0.04086878523230553, -0.044682737439870834, 0.028692126274108887, -0.031106462702155113, -0.014459781348705292, 0.041498612612485886, 0.011214422062039375, 0.0014127372996881604, 0.006775015499442816, 0.03887433186173439, -0.0007293311064131558, -0.004531256388872862, 0.028342222794890404, 0.08593641966581345, 0.040098994970321655, 0.03285598382353783, 0.004951141308993101, 0.02414337359368801, -0.001562539953738451, -0.013707487843930721, 0.02577042765915394, 0.03028418868780136, -0.01664668135344982, -0.008415190503001213, 0.047481968998909, 0.04335310310125351, 0.0005057206144556403, -0.001921191462315619, -0.01873735710978508, -0.007794111035764217, 0.01821250095963478, 0.009692340157926083, -0.08299722522497177, 0.0378945991396904, 0.0004718236450571567, 0.07375975698232651, 0.001639081398025155, -0.01038340013474226, 0.01997951604425907, -0.026890119537711143, 0.0047849370166659355, 0.06686665117740631, 0.02654021605849266, 0.01706656627357006, -0.017722636461257935, -0.004859291482716799, -0.028797097504138947, -0.020206954330205917, -0.00003235928306821734, -0.03929421678185463, 0.026662683114409447, 0.0210817139595747, -0.01470471452921629, 0.03352079913020134, 0.06056837737560272, 0.02066182903945446, 0.00017618211859371513, 0.0015494185499846935, 0.005847770255059004, 0.017862597480416298, -0.02144911326467991, -0.007417964283376932, -0.020311925560235977, 0.02743247151374817, -0.006831875070929527, -0.03262854740023613, -0.008397695608437061, 0.03771964833140373, 0.0315263494849205, 0.04492767155170441, -0.006210795603692532, 0.018299978226423264, -0.005025495775043964, -0.009429912082850933, 0.01826498657464981, -0.009744825772941113, 0.021921483799815178, -0.030983997508883476, -0.025682952255010605, -0.015255813486874104, 0.0009862917941063643, -0.07851845026016235, -0.05360528826713562, -0.022603796795010567, -0.02680264413356781, -0.014057392254471779, -0.000001392440140079998, 0.029181990772485733, -0.018020054325461388, -0.029654361307621002, 0.021938979625701904, 0.01696159504354, 0.03611009195446968, 0.04937145113945007, 0.03173629194498062, 0.0040282695554196835, 0.039994023740291595, -0.027519946917891502, -0.012027949094772339, 0.021046724170446396, -0.046292297542095184, 0.0008151669171638787, -0.015343288891017437, -0.040308937430381775, -0.018649881705641747, 0.02200895920395851, 0.036040108650922775, -0.02914700098335743, -0.014923404902219772, -0.03981907293200493, -0.0021497225388884544, 0.01784510351717472, -0.000139073163154535, -0.0331009142100811, 0.03521783649921417, -0.007986558601260185, 0.026417750865221024, -0.016935352236032486, 0.016987837851047516, 0.05297546088695526, -0.001552698900923133, 0.053010452538728714, -0.03563772141933441, 0.006600063759833574, 0.02461574412882328, -0.02685512974858284, -0.014564752578735352, 0.0056596966460347176, -0.018020054325461388, -0.040308937430381775, -0.039784081280231476, 0.03283848986029625, 0.0411137156188488, 0.013978663831949234, 0.002724877092987299, 0.03922423720359802, 0.007986558601260185, 0.0029916788917034864, 0.023758480325341225, -0.027502452954649925, -0.00131104642059654, 0.006858117878437042, -0.0050167483277618885, -0.03450053185224533, -0.023356091231107712, 0.04289822652935982, 0.0030091742519289255, -0.0014958394458517432, -0.030319178476929665, 0.05584467574954033, 0.006844996474683285, 0.03530531004071236, -0.00026516159414313734, -0.04856667295098305, -0.04583742097020149, -0.00015622665523551404, 0.005615958943963051, -0.008253360167145729, -0.03038915991783142, 0.030424149706959724, 0.01017345767468214, 0.018142521381378174, 0.05710433050990105, 0.01337507925927639, 0.01332259364426136, -0.04398293048143387, 0.01634926348924637, 0.005471623502671719, 0.003505600383505225, -0.019139748066663742, -0.01236035767942667, -0.05091102793812752, 0.015448260121047497, -0.047551948577165604, -0.009823554195463657, 0.007973437197506428, 0.0145472576841712, 0.014311072416603565, -0.026942605152726173, -0.01654171012341976, -0.034220609813928604, -0.0075535522773861885, 0.009088755585253239, -0.0009272455354221165, 0.024475783109664917, 0.0014400735963135958, -0.0046449750661849976, 0.02835971675813198, 0.008192126639187336, -0.011844249442219734, 0.024318326264619827, 0.0051392144523561, -0.052485596388578415, 0.01529955118894577, -0.022148922085762024, -0.023461060598492622, -0.017827607691287994, -0.01012097205966711, -0.009429912082850933, 0.002921698149293661, 0.022673778235912323, -0.008222742937505245, -0.008419563993811607, 0.013541284017264843, -0.026715168729424477, -0.015439513139426708, -0.026680178940296173, -0.023356091231107712, -0.053220394998788834, -0.022306378930807114, 0.02585790306329727, 0.009981011040508747, -0.04184851422905922, 0.00751856155693531, 0.04359803348779678, 0.042548324912786484, 0.003284723497927189, -0.00318193924613297, -0.01685662381350994, 0.018649881705641747, 0.012264134362339973, 0.01327010802924633, 0.020259439945220947, 0.0021858063992112875, 0.027152547612786293, -0.014267334714531898, -0.050456151366233826, 0.04440281540155411, 0.0280448030680418, -0.012692766264081001, -0.00508672883734107, 0.038279496133327484, 0.01696159504354, 0.029934285208582878, 0.0011688979575410485, -0.024108383804559708, 0.011704287491738796, -0.02066182903945446, -0.025787923485040665, -0.010628333315253258, -0.026995090767741203, 0.009289950132369995, 0.0062370384112000465, 0.006066460162401199, 0.06546703726053238, 0.018037550151348114, 0.011625560000538826, 0.051645826548337936, 0.005852143745869398, -0.04881160333752632, 0.025420524179935455, -0.018824834376573563, -0.010864518582820892, 0.007006827276200056, 0.00575154647231102, 0.018649881705641747, 0.019962022081017494, -0.016323020681738853, 0.043947938829660416, 0.05437507852911949, 0.0016423617489635944, 0.013305098749697208, -0.07410965859889984, 0.03199872002005577, -0.044892679899930954 ]
The high effectiveness of neural models of code, such as OpenAI Codex and AlphaCode, suggests coding capabilities of models that are at least comparable to those of humans. However, previous work has only used these models for their raw completion, ignoring how the model reasoning, in the form of attention weights, can be used for other downstream tasks. Disregarding the attention weights means discarding a considerable portion of what those models compute when queried. To profit more from the knowledge embedded in these large pre-trained models, this work compares multiple approaches to post-process these valuable attention weights for supporting code exploration. Specifically, we compare to which extent the transformed attention signal of CodeGen, a large and publicly available pretrained neural model, agrees with how developers look at and explore code when each answering the same sense-making questions about code. At the core of our experimental evaluation, we collect, manually annotate, and open-source a novel eye-tracking dataset comprising 25 developers answering sense-making questions on code over 92 sessions. We empirically evaluate five attention-agnostic heuristics and ten attention-based post processing approaches of the attention signal against our ground truth of developers exploring code, including the novel concept of follow-up attention which exhibits the highest agreement. Beyond the dataset contribution and the empirical study, we also introduce a novel practical application of the attention signal of pre-trained models with completely analytical solutions, going beyond how neural models' attention mechanisms have traditionally been used.
[ 0.003026155987754464, -0.011716032400727272, -0.020342763513326645, -0.012289205566048622, 0.0229851845651865, 0.012512645684182644, 0.01327039860188961, 0.02943580411374569, -0.021955417469143867, 0.006863496731966734, 0.04087982326745987, -0.05828871950507164, 0.0077864015474915504, -0.024558980017900467, 0.01121086347848177, 0.030834732577204704, 0.046009231358766556, 0.02943580411374569, -0.09100811928510666, -0.04472687840461731, 0.01655399613082409, -0.06532222777605057, -0.01941985823214054, -0.012289205566048622, 0.024753276258707047, 0.01327039860188961, -0.009112469851970673, 0.01240578293800354, -0.060348253697156906, 0.014115585014224052, -0.018623245880007744, 0.0413849912583828, -0.0023521927651017904, -0.03549782931804657, -0.02471441775560379, 0.012910951860249043, 0.008194422349333763, -0.035342395305633545, -0.0154853705316782, 0.02731798030436039, -0.0067712063901126385, -0.02366522140800953, -0.006625484675168991, -0.05945449322462082, -0.002773571526631713, -0.03192279115319252, -0.0035653267987072468, -0.0684698149561882, -0.010074233636260033, -0.06971330940723419, 0.04857393354177475, -0.015553373843431473, -0.007407525088638067, -0.011521737091243267, 0.01024909969419241, 0.053431328386068344, 0.022246861830353737, -0.007519245147705078, 0.05945449322462082, 0.037188202142715454, 0.03157305717468262, 0.013911575078964233, -0.04876822978258133, 0.00842272024601698, 0.029183220118284225, -0.02174169197678566, -0.03048500046133995, 0.010394821874797344, 0.029979832470417023, -0.007397809997200966, -0.07620278745889664, -0.0090444665402174, -0.03742135688662529, 0.05432508885860443, -0.028988923877477646, 0.032661113888025284, 0.03837340697646141, 0.015135637484490871, -0.00812641903758049, 0.013357832096517086, 0.022849177941679955, -0.028697479516267776, -0.03722706437110901, 0.014902482740581036, 0.07387124001979828, -0.08253683149814606, -0.011997761204838753, -0.06664343923330307, 0.00449551735073328, -0.019973602145910263, -0.057472679764032364, 0.029882684350013733, 0.01082227285951376, -0.027726002037525177, -0.01748661696910858, 0.021275382488965988, -0.015563088469207287, -0.018108362331986427, -0.02654079720377922, 0.04087982326745987, 0.00007472037395928055, 0.029008353129029274, 0.005809442605823278, -0.035905852913856506, 0.005527713801711798, -0.021217094734311104, -0.057472679764032364, 0.0017098024254664779, 0.019750161096453667, 0.11681059747934341, -0.04989514499902725, -0.01072512473911047, -0.040530089288949966, -0.026385361328721046, 0.006727489642798901, 0.013386975973844528, -0.035245247185230255, -0.048224203288555145, -0.011298296973109245, -0.05751153826713562, 0.03895629569888115, 0.11121487617492676, 0.04538748413324356, 0.002630278468132019, 0.008923031389713287, 0.08323629200458527, -0.011910328641533852, -0.021217094734311104, 0.011978331953287125, 0.005532571114599705, 0.02047877013683319, 0.0392671674489975, 0.01780720427632332, 0.012561219744384289, 0.06403987109661102, 0.00928247906267643, 0.033030275255441666, 0.04107411950826645, -0.009365054778754711, -0.048807088285684586, 0.010899990797042847, -0.0342349074780941, -0.005780298262834549, -0.015300788916647434, 0.0032520247623324394, 0.007441526744514704, 0.008957033045589924, 0.11230293661355972, -0.05739495903253555, -0.0198084507137537, -0.034001752734184265, 0.04655325785279274, -0.044765736907720566, 0.0058774459175765514, 0.008199280127882957, 0.022829748690128326, 0.03231137990951538, 0.036585886031389236, -0.038043104112148285, 0.009481632150709629, 0.04115183651447296, -0.054674819111824036, 0.01806950382888317, 0.020925650373101234, 0.060076240450143814, 0.005357705056667328, 0.007830117829144001, 0.010171381756663322, -0.11447905004024506, 0.049389977008104324, 0.001188847003504634, 0.03254453465342522, 0.010841702111065388, 0.002154253888875246, 0.0022635452914983034, 0.009739073924720287, 0.04892366752028465, -0.00397091917693615, -0.03518695756793022, 0.006154317408800125, -0.06302953511476517, 0.0058288718573749065, 0.052382130175828934, -0.01577681303024292, 0.04049123078584671, 0.025530459359288216, 0.08331400901079178, 0.013435550034046173, 0.05475253984332085, -0.017836349084973335, -0.035050950944423676, -0.0376739427447319, 0.023723509162664413, -0.004172500688582659, 0.022169142961502075, -0.02646307833492756, -0.07896178960800171, -0.029124930500984192, 0.050439171493053436, 0.016573425382375717, -0.05626804381608963, -0.04713614657521248, -0.01226977538317442, 0.006222320720553398, 0.0039199162274599075, 0.014183588325977325, 0.0037766234017908573, 0.028814056888222694, 0.010715410113334656, -0.07732970267534256, 0.029766106978058815, -0.029843825846910477, -0.04049123078584671, -0.03460406884551048, 0.026715664193034172, -0.006368042901158333, 0.01771005615592003, 0.018730109557509422, 0.002688567154109478, -0.020847931504249573, 0.006431188900023699, 0.0223245806992054, 0.05378105863928795, 0.02788143791258335, 0.02867805026471615, 0.005017687566578388, 0.02317948080599308, -0.01924499310553074, 0.04989514499902725, -0.03483722358942032, -0.005071118474006653, -0.01885640062391758, -0.020711924880743027, -0.0407632440328598, 0.03421548008918762, -0.07080136239528656, 0.05366448312997818, -0.06314611434936523, -0.007198656909167767, -0.011716032400727272, -0.055452004075050354, -0.05599603056907654, -0.03157305717468262, -0.019662728533148766, 0.11533395200967789, -0.006266037467867136, -0.012716655619442463, 0.0022283291909843683, 0.030621007084846497, -0.003203450934961438, -0.009452487342059612, -0.006154317408800125, -0.011026282794773579, -0.00808270275592804, -0.004004920832812786, 0.03470121696591377, 0.04523204639554024, -0.012007476761937141, -0.001544651109725237, -0.021275382488965988, 0.02067306637763977, 0.0006861067959107459, -0.024306396022439003, 0.03384631872177124, -0.03951975330710411, -0.03780994936823845, 0.0632626935839653, -0.029183220118284225, 0.017564333975315094, 0.03672189265489578, 0.026035629212856293, -0.004774817731231451, 0.009641925804316998, 0.008719021454453468, 0.038140252232551575, 0.009209617972373962, 0.011055427603423595, -0.002807573415338993, -0.006630341988056898, -0.0034341770224273205, -0.012697226367890835, 0.011735462583601475, 0.05413079261779785, 0.025647036731243134, -0.010744553990662098, -0.030951309949159622, 0.016194550320506096, -0.027648283168673515, -0.040530089288949966, -0.04538748413324356, -0.008816168643534184, -0.013785282149910927, -0.03456521034240723, 0.019672444090247154, 0.01904098130762577, -0.05273186415433884, -0.06155288964509964, 0.041695863008499146, -0.02500586025416851, -0.03903401270508766, -0.0965261235833168, 0.009967370890080929, -0.005508284084498882, 0.03580870479345322, -0.060736846178770065, 0.04876822978258133, -0.007266660686582327, 0.0788840651512146, -0.06108658015727997, 0.01283323299139738, 0.03720763325691223, -0.014455602504312992, 0.01617511920630932, -0.040724385529756546, 0.014805334620177746, 0.04725272208452225, 0.008379003964364529, 0.01398929301649332, -0.005610289517790079, -0.014523605816066265, 0.024189818650484085, -0.013756138272583485, -0.11137031763792038, 0.009918796829879284, -0.007290947251021862, 0.024656128138303757, 0.027745431289076805, 0.014727616682648659, 0.020070750266313553, -0.020342763513326645, -0.0511774979531765, 0.0029168648179620504, -0.03262225538492203, -0.014183588325977325, -0.0018518812721595168, 0.0062903244979679585, -0.062096916139125824, 0.04690299183130264, 0.024209247902035713, 0.03372973948717117, -0.03643045201897621, 0.012619508430361748, -0.06372900307178497, -0.045814935117959976, -0.014960771426558495, -0.05308159440755844, -0.028406037017703056, 0.016330556944012642, 0.00894731841981411, 0.003609043313190341, 0.0012799231335520744, -0.010550258681178093, -0.030523860827088356, -0.0031160179059952497, -0.0036551884841173887, 0.02040105313062668, -0.019002122804522514, -0.012823518365621567, 0.0008603658061474562, 0.06656572222709656, -0.0005926020094193518, -0.04849621653556824, 0.003511895425617695, 0.00610574334859848, -0.04655325785279274, 0.0016502994112670422, -0.019934741780161858, -0.02230514958500862, 0.015378507785499096, -0.008160420693457127, -0.01587396115064621, 0.06415645033121109, -0.01703002117574215, 0.04577607661485672, 0.04165700450539589, -0.000863401684910059, -0.05071118846535683, 0.012337779626250267, -0.05413079261779785, 0.052187833935022354, 0.013299543410539627, 0.007553246803581715, 0.009199903346598148, 0.02595791034400463, -0.007300662342458963, 0.03942260518670082, 0.013056673109531403, -0.020886791869997978, -0.015796244144439697, 0.018234655261039734, 0.014562465250492096, -0.05926020070910454, -0.003679475514218211, -0.038217972964048386, 0.018050074577331543, 0.044960033148527145, 0.01934214122593403, 0.017059165984392166, 0.034681789577007294, -0.03497323393821716, -0.040646668523550034, 0.04200673848390579, 0.004471230786293745, 0.04084096476435661, -0.025025291368365288, -0.006066884379833937, 0.007091794162988663, 0.027007106691598892, -0.006863496731966734, 0.022829748690128326, -0.035439543426036835, -0.0006460333243012428, -0.0329136960208416, 0.02914435975253582, 0.04709728807210922, 0.011201148852705956, -0.022868607193231583, 0.03413775935769081, 0.009559350088238716, -0.0007941838121041656, 0.026307642459869385, 0.03532296419143677, 0.002754142042249441, -0.024772705510258675, -0.015718525275588036, -0.0267350934445858, 0.00589201832190156, 0.02865862101316452, -0.022538306191563606, -0.039480894804000854, 0.03613900765776634, -0.0017377324402332306, 0.04010263830423355, -0.057472679764032364, 0.014737331308424473, -0.037460219115018845, -0.028736339882016182, 0.002897435100749135, -0.04278391972184181, -0.000042388346628285944, -0.023257199674844742, -0.024850424379110336, 0.001330925733782351, -0.030426712706685066, 0.010054804384708405, -0.019167274236679077, -0.05416965112090111, -0.012600078247487545, 0.013309258036315441, -0.045970369130373, -0.07286090403795242, 0.03116503544151783, -0.06435074657201767, -0.026851670816540718, 0.03644987940788269, -0.03629444167017937, -0.02432582527399063, -0.026501938700675964, 0.02500586025416851, -0.08067158609628677, 0.04523204639554024, 0.019973602145910263, -0.004075353033840656, -0.011230293661355972, 0.01856495812535286, 0.005469425115734339, -0.03876199945807457, -0.03744078800082207, 0.005032259505242109, 0.045931510627269745, -0.008952176198363304, -0.042745061218738556, 0.03347715362906456, -0.008728736080229282, 0.02384008653461933, 0.005134264938533306, 0.020051319152116776, -0.0015519371954724193, -0.004978828132152557, -0.012774944305419922, 0.05615146830677986, -0.012590363621711731, 0.0076698241755366325, -0.025627607479691505, 0.0009198688785545528, 0.0021469679195433855, 0.04604808986186981, 0.01627226732671261, 0.0006812494248151779, -0.03372973948717117, -0.043522246181964874, -0.04628124460577965, 0.03547840192914009, 0.017622623592615128, -0.00046722052502445877, -0.029396945610642433, -0.019196419045329094, -0.031592488288879395, 0.02125595323741436, -0.00548399705439806, 0.020925650373101234, -0.03258339315652847, 0.028736339882016182, 0.027628853917121887, -0.0000666373671265319, 0.03157305717468262, -0.01739918254315853, -0.007859262637794018, -0.009263048879802227, -0.013095532543957233, 0.028114592656493187, -0.04278391972184181, -0.004031636286526918, -0.007383238058537245, -0.009501061402261257, 0.009321337565779686, -0.003922345116734505, 0.011609170585870743, 0.011035997420549393, -0.011949188075959682, -0.008553870022296906, -0.046786412596702576, 0.010637691244482994, 0.02403438277542591, -0.010307388380169868, 0.06221349537372589, 0.03656645864248276, 0.017933497205376625, 0.020847931504249573, -0.01283323299139738, 0.0052799866534769535, 0.025627607479691505, -0.05028373748064041, -0.025064149871468544, -0.01748661696910858, -0.020828502252697945, 0.024481263011693954, 0.007485243026167154, 0.006960644852370024, 0.0034244623966515064, -0.04480459541082382, 0.016592856496572495, -0.038334548473358154, 0.0376739427447319, -0.00817985087633133, -0.013221824541687965, 0.054869115352630615, -0.01971130259335041, 0.0022538304328918457, -0.0035191813949495554, -0.027745431289076805, 0.0024104814510792494, 0.0005977629916742444, 0.013814426958560944, -0.033418867737054825, -0.059299059212207794, -0.04095754027366638, -0.02452012151479721, -0.01318296603858471, -0.027589993551373482, -0.022169142961502075, -0.005853158887475729, 0.036585886031389236, -0.03404061123728752, 0.004539234098047018, -0.001953886589035392, 0.003640616312623024, 0.029086071997880936, 0.011463448405265808, -0.000816649233456701, -0.012415497563779354, 0.003203450934961438, -0.0026351360138505697, 0.045970369130373, 0.012007476761937141, 0.06147516891360283, 0.02654079720377922, -0.0427062027156353, 0.015087063424289227, -0.043988555669784546, -0.01317325048148632, -0.009015321731567383, 0.0133675467222929, 0.057744693011045456, 0.022149713709950447, -0.02143082022666931, -0.031126176938414574, -0.03895629569888115, -0.016039112582802773, -0.0005947271129116416, -0.04787446931004524, 0.050633467733860016, -0.00572200957685709, -0.0272208321839571, -0.019701587036252022, 0.010074233636260033, 0.010210241191089153, 0.03355487436056137, 0.02634650096297264, -0.07227801531553268, -0.03472064808011055, -0.032058797776699066, 0.0482630617916584, 0.005590859800577164, -0.028814056888222694, -0.024597840383648872, 0.03386574611067772, -0.013454979285597801, 0.010744553990662098, 0.012998384423553944, 0.006591483019292355, 0.006144602783024311, 0.01240578293800354, -0.05012829974293709, -0.009802219457924366, -0.05075004696846008, -0.005226555280387402, 0.024286966770887375, -0.004262362606823444, 0.0073200915940105915, 0.06710974872112274, -0.01606825739145279, 0.01951700635254383, -0.007548389490693808, 0.04538748413324356, 0.03701333701610565, 0.00565400579944253, -0.02010960876941681, -0.01739918254315853, 0.025705326348543167, -0.018399806693196297, -0.010501684620976448, -0.03613900765776634, -0.0036551884841173887, 0.004607237409800291, 0.04779675230383873, 0.03287483751773834, 0.0407632440328598, -0.01683572493493557, -0.01838037744164467, -0.0037183347158133984, 0.015601947903633118, -0.04348338395357132, 0.09287336468696594, 0.0033273145090788603, 0.0288529172539711, -0.009097897447645664, -0.009136756882071495, 0.053819917142391205, -0.015067634172737598, 0.03287483751773834, 0.02030390501022339, -0.002715282840654254, 0.043794259428977966, -0.043988555669784546, -0.01961415447294712, 0.02597733959555626, 0.009340767748653889, 0.002145753474906087, 0.001895597786642611, 0.04033579304814339, -0.003980633802711964, 0.014523605816066265, -0.00035398255567997694, 0.04414398968219757, -0.036003001034259796, -0.0298243947327137, 0.040646668523550034, -0.01665114425122738, 0.06567195802927017, -0.014863623306155205, -0.05191582068800926, -0.06722632795572281, 0.05510227009654045, 0.028444895520806313, -0.02712368406355381, 0.013668704777956009, 0.04872937127947807, -0.04604808986186981, 0.013503553345799446, -0.0020401051733642817, -0.028153451159596443, -0.014037867076694965, -0.03306913375854492, -0.009607924148440361, -0.0007577533833682537, -0.015057919546961784, 0.021955417469143867, -0.06695430725812912, -0.03320514038205147, -0.06030939519405365, -0.014397313818335533, -0.00836443156003952, 0.000058782050473382697, 0.030815303325653076, 0.01941985823214054, -0.025141868740320206, -0.008515010587871075, 0.007417239714413881, -0.030174126848578453, 0.002153039677068591, -0.007713540457189083, -0.016573425382375717, -0.005488854367285967, 0.010783413425087929, 0.01914784498512745, 0.010744553990662098, -0.0030698725022375584, 0.005012829788029194, 0.02086736261844635, -0.02354864403605461, 0.02471441775560379, 0.0029071499593555927, 0.033127423375844955, 0.022071994841098785, -0.002353407209739089, 0.040258076041936874, 0.014445887878537178, -0.020634207874536514, 0.037285350263118744, -0.019546151161193848, 0.03751850500702858, -0.006892641074955463, -0.04200673848390579, -0.02191655896604061, -0.011813180521130562, -0.0029605813324451447, 0.012940095737576485, 0.007052935194224119, -0.006742062047123909, 0.045270904898643494, -0.03845112770795822, -0.04192902147769928, -0.004119069781154394, -0.004507660865783691, -0.0386454202234745, 0.008995892480015755, 0.028386607766151428, 0.008242996409535408, -0.04437714442610741, -0.0049181110225617886, 0.0067857783287763596, 0.007354093715548515, -0.01951700635254383, -0.009913939982652664, 0.028872346505522728, -0.025821903720498085, 0.013056673109531403, 0.011434303596615791, 0.004218646325170994, 0.06963559240102768, -0.008092417381703854, 0.040918681770563126, -0.02692938968539238, -0.0220137070864439, -0.0017365181120112538, -0.015582517720758915, -0.0016442276537418365, 0.029552381485700607, -0.028639191761612892, -0.0013564270921051502, 0.012852663174271584, 0.0024590555112808943, 0.022732600569725037, 0.04721386358141899, 0.000896796234883368, -0.013134391978383064, 0.012425212189555168, 0.024306396022439003, 0.016466563567519188, -0.008286712691187859, -0.01778777502477169, 0.09559350460767746, -0.0026861384976655245, 0.006499192211776972, -0.0022902609780430794, -0.0015458654379472136, -0.021042227745056152, -0.06559424102306366, 0.01442645862698555, 0.019565580412745476, -0.019575295969843864, -0.019293567165732384, 0.06302953511476517, 0.012561219744384289, 0.013552127406001091, 0.031320471316576004, -0.021663974970579147, -0.008723878301680088, 0.047952186316251755, 0.00541113642975688, -0.03963632881641388, 0.031592488288879395, 0.02558874897658825, 0.06372900307178497, -0.021042227745056152, -0.01519392617046833, -0.019672444090247154, -0.018584387376904488, -0.04511547088623047, 0.034953802824020386, -0.007694111205637455, 0.03174792230129242, 0.012415497563779354, 0.008043843321502209, -0.050244878977537155, -0.03050442971289158, 0.005318845622241497, 0.0036381876561790705, 0.03827625885605812, 0.009243619628250599, 0.010317103937268257, 0.011852039955556393, 0.026812812313437462, 0.03213651478290558, -0.009748788550496101, -0.05078890547156334, 0.015495085157454014, 0.039480894804000854, -0.03289426863193512, 0.0052799866534769535, -0.01423216238617897, 0.0298243947327137, -0.02790086716413498, -0.011939472518861294, -0.007368665654212236, 0.026482509449124336, -0.015320219099521637, 0.05226555094122887, 0.004840392619371414, -0.04251190647482872, 0.01751575991511345, -0.05300387740135193, 0.020847931504249573, 0.003662474686279893, 0.02395666390657425, -0.008034128695726395, -0.019176989793777466, 0.005532571114599705, 0.028911205008625984, -0.058055564761161804, -0.0042137885466217995, 0.005707437172532082, -0.008437292650341988, -0.009603066369891167, 0.015096778981387615, -0.000781433132942766, 0.006858639419078827, -0.021100517362356186, -0.002758999355137348, 0.008675304241478443, 0.016039112582802773, 0.040530089288949966, 0.004578093066811562, -0.007936980575323105, 0.036119576543569565, -0.011356585659086704, -0.00490353861823678, -0.00018594709399621934, -0.018020929768681526, 0.014941342175006866, -0.04359996318817139, -0.001998817315325141, -0.04946769401431084, 0.03598356992006302, -0.0023874088656157255, -0.021022798493504524, -0.032661113888025284, -0.005804585292935371, 0.00017046414723154157, -0.026229923591017723, 0.02836717665195465, -0.03800424560904503, 0.024986431002616882, 0.0029120072722434998, 0.020925650373101234, -0.016330556944012642, -0.01684544049203396, 0.03038785234093666, -0.0012872092192992568, 0.007227801252156496, -0.011123430915176868, 0.016962017863988876, 0.02096451073884964, 0.060076240450143814, -0.01140515971928835, -0.04223989322781563, -0.045542921870946884, -0.04461029917001724, -0.07185056060552597, 0.032466817647218704, 0.036003001034259796, 0.010783413425087929, -0.02403438277542591, 0.00538199208676815, 0.00822356715798378, 0.004476088099181652, 0.01912841573357582, -0.012872092425823212, 0.022344009950757027, 0.036974478513002396, -0.017476901412010193, -0.015903105959296227, -0.05665663629770279, 0.016291696578264236, -0.01713688299059868, 0.0014390028081834316, -0.011920043267309666, 0.047757890075445175, 0.015310503542423248, 0.011055427603423595, -0.002506414894014597, -0.005911447573453188, -0.021663974970579147, 0.028639191761612892, -0.02261602319777012, -0.011842325329780579, 0.0220137070864439, -0.00021691297297365963, -0.019070126116275787, 0.04204559698700905, 0.07289975881576538, 0.00012242149387020618, 0.002963009988889098, -0.043910834938287735, 0.01913812942802906, 0.014698472805321217, 0.01380471233278513, -0.008879315108060837, -0.0068392097018659115, -0.011172004975378513, 0.04297821596264839, 0.012697226367890835, 0.014679042622447014, -0.006620627362281084, -0.029649529606103897, -0.04336680844426155, 0.016379131004214287, -0.015368792228400707, -0.0211782343685627, -0.008296428248286247, 0.023878945037722588, -0.0067663490772247314, 0.04359996318817139, 0.02481156587600708, -0.00918533094227314, 0.0376739427447319, -0.00651376461610198, 0.01062797661870718, 0.02951352298259735, 0.014465317130088806, -0.02799801528453827, 0.01642770506441593, -0.016719147562980652, -0.05700637027621269, -0.008578157052397728, -0.01952672190964222, -0.027162544429302216, 0.006814923137426376, 0.05549086257815361, 0.030854161828756332, -0.013338401913642883, -0.04103526100516319, -0.005066261161118746, -0.002550131641328335, -0.02827003039419651, -0.025258446112275124, -0.05242098867893219, -0.044182851910591125, 0.016311127692461014, 0.021683404222130775, -0.039675187319517136, 0.0072520882822573185, 0.03402118384838104, 0.06369014084339142, 0.007990412414073944, 0.0048088193871080875, -0.0022720457054674625, 0.01284294854849577, 0.00942820031195879, 0.03163134679198265, -0.016087686643004417, 0.018691249191761017, 0.01058911718428135, 0.020362192764878273, -0.027201402932405472, 0.01787520758807659, 0.024597840383648872, -0.023898376151919365, 0.03817911073565483, 0.0038786286022514105, 0.018827257677912712, 0.022149713709950447, 0.02174169197678566, -0.014533321373164654, 0.03547840192914009, 0.00028491648845374584, -0.020847931504249573, 0.004017064347863197, 0.011259437538683414, 0.001837309100665152, -0.025938481092453003, -0.002060749102383852, 0.05172152444720268, -0.016612285748124123, 0.04845735803246498, 0.05906590446829796, 0.011191434226930141, -0.06722632795572281, 0.004529519472271204, 0.005950307007879019, -0.01178403664380312, -0.026035629212856293, 0.009554493241012096, 0.03491494432091713, 0.020420482382178307, -0.013911575078964233, 0.018914690241217613, 0.012483500875532627, -0.030718155205249786, 0.02261602319777012, -0.043716538697481155, 0.05883274972438812, -0.06493363529443741 ]
This paper proposes a model that generates a drum track in the audio domain to play along to a user-provided drum-free recording. Specifically, using paired data of drumless tracks and the corresponding human-made drum tracks, we train a Transformer model to improvise the drum part of an unseen drumless recording. We combine two approaches to encode the input audio. First, we train a vector-quantized variational autoencoder (VQ-VAE) to represent the input audio with discrete codes, which can then be readily used in a Transformer. Second, using an audio-domain beat tracking model, we compute beat-related features of the input audio and use them as embeddings in the Transformer. Instead of generating the drum track directly as waveforms, we use a separate VQ-VAE to encode the mel-spectrogram of a drum track into another set of discrete codes, and train the Transformer to predict the sequence of drum-related discrete codes. The output codes are then converted to a mel-spectrogram with a decoder, and then to the waveform with a vocoder. We report both objective and subjective evaluations of variants of the proposed model, demonstrating that the model with beat information generates drum accompaniment that is rhythmically and stylistically consistent with the input audio.
[ 0.042783889919519424, 0.0011206670897081494, -0.019574088975787163, -0.05115704610943794, -0.03958887234330177, 0.036816179752349854, -0.007666212040930986, 0.028736818581819534, -0.03655910864472389, 0.034539271146059036, 0.046676672995090485, 0.02085944265127182, 0.011788522824645042, -0.05284636840224266, 0.00807477068156004, 0.019996419548988342, -0.004340361338108778, 0.00031014878186397254, -0.017407352104783058, -0.0692988857626915, 0.025964129716157913, 0.007294377777725458, -0.061807114630937576, -0.01160490047186613, 0.01864679902791977, 0.036797817796468735, 0.015763936564326286, -0.00826298352330923, -0.03778937831521034, 0.042343199253082275, 0.013679827563464642, 0.012256758287549019, -0.05108359828591347, 0.0023285546340048313, -0.054315343499183655, 0.028975527733564377, 0.03674273192882538, 0.05413172021508217, -0.029030613601207733, -0.01252301037311554, -0.048219095915555954, -0.05339723452925682, -0.022346779704093933, -0.07418322563171387, -0.02253040112555027, -0.016718769446015358, -0.0489535853266716, 0.01962917484343052, 0.031656406819820404, 0.0038858973421156406, 0.06430437415838242, -0.015754755586385727, 0.010126745328307152, -0.011586538515985012, -0.03962559625506401, 0.05743691325187683, 0.017719509080052376, -0.012614821083843708, 0.06823387742042542, -0.004546936135739088, 0.008524644188582897, 0.05508655309677124, -0.007510133553296328, -0.023577045649290085, -0.025431625545024872, -0.04072732478380203, 0.02557852305471897, 0.01876615360379219, 0.04891686141490936, 0.04520769789814949, -0.04939427599310875, -0.030003810301423073, -0.034447457641363144, 0.03532884269952774, 0.037367045879364014, -0.04058042913675308, 0.0036793227773159742, 0.06926216185092926, 0.02532145380973816, 0.02601921558380127, 0.02100634016096592, 0.012201671488583088, 0.0024467611219733953, 0.021502118557691574, 0.014515306800603867, -0.011099941097199917, 0.025009294971823692, -0.04961462318897247, -0.006624158006161451, 0.03213382512331009, -0.017903130501508713, 0.056261733174324036, -0.00396164134144783, 0.0033579845912754536, -0.028828630223870277, -0.0010747616179287434, -0.019004860892891884, -0.02517455630004406, -0.04869651421904564, -0.017168642953038216, -0.01043890230357647, -0.050275661051273346, -0.017141100019216537, -0.017407352104783058, 0.04245337098836899, -0.02058400958776474, -0.016994202509522438, 0.015240613371133804, 0.0416821613907814, 0.05618828535079956, 0.020785992965102196, -0.05479275807738304, 0.027378017082810402, -0.020106593146920204, -0.029563117772340775, 0.03655910864472389, -0.03411693871021271, -0.05442551523447037, -0.021520480513572693, -0.028167592361569405, 0.04660322517156601, 0.06838077306747437, -0.028957165777683258, 0.058061227202415466, 0.008611864410340786, 0.09511611610651016, -0.009185682982206345, -0.04447321221232414, -0.0016307915793731809, 0.06738921999931335, -0.05648208037018776, 0.04271044209599495, -0.02153884246945381, 0.007390779443085194, 0.051671188324689865, -0.025211280211806297, -0.022475315257906914, -0.05005531758069992, 0.03520030900835991, -0.0016916162567213178, 0.013257497921586037, 0.013578835874795914, -0.018114294856786728, 0.023981014266610146, -0.0022803538013249636, 0.0358797088265419, 0.017737871035933495, 0.06794008612632751, 0.03279486298561096, -0.02363213151693344, -0.03231744468212128, 0.023044541478157043, -0.041498538106679916, 0.06529592722654343, 0.026643529534339905, -0.003270764136686921, -0.004432172514498234, 0.011540633626282215, -0.05618828535079956, -0.009263722226023674, 0.04759478196501732, -0.019684262573719025, 0.03185839205980301, 0.01767360232770443, 0.020896166563034058, 0.0013978213537484407, 0.019849522039294243, 0.011311105452477932, -0.009323399513959885, 0.03147278353571892, 0.03268468752503395, 0.014552031643688679, -0.0064543080516159534, -0.029654929414391518, -0.02824104018509388, 0.020767631009221077, 0.03397004306316376, -0.015093715861439705, -0.01847235858440399, -0.009842131286859512, -0.0375506691634655, 0.044840455055236816, 0.042233023792505264, 0.013367670588195324, 0.06316591799259186, 0.05607811361551285, 0.04998186603188515, 0.010613342747092247, -0.022493677213788033, -0.04575856402516365, 0.04660322517156601, 0.010200194083154202, 0.006472670007497072, 0.009823769330978394, 0.002531686332076788, -0.025560161098837852, -0.025964129716157913, -0.034429095685482025, -0.007652440574020147, 0.06301902234554291, -0.031215714290738106, -0.017177823930978775, 0.06147659569978714, 0.013744095340371132, 0.004709900356829166, 0.030628124251961708, -0.004120015073567629, 0.0386340357363224, -0.01403789035975933, -0.11773832887411118, -0.005031238775700331, 0.0031697722151875496, -0.05424189567565918, -0.018876325339078903, 0.000867039430886507, -0.030775021761655807, 0.004595136735588312, -0.01586492732167244, 0.03903800621628761, -0.050679631531238556, 0.0016778446733951569, -0.014799920842051506, 0.006569071672856808, -0.011476365849375725, -0.04006628692150116, -0.03439237177371979, -0.02697405032813549, 0.008639408275485039, 0.032188910990953445, -0.006555300205945969, 0.010392996482551098, 0.032758139073848724, 0.028755182400345802, -0.0662507638335228, 0.028461387380957603, -0.054205168038606644, 0.01399198453873396, 0.00020930021128151566, 0.019390467554330826, 0.008235439658164978, -0.03116062842309475, -0.012293483130633831, -0.03222563490271568, -0.08703675866127014, 0.025615248829126358, -0.030921919271349907, -0.014937637373805046, 0.04329803213477135, 0.04215957596898079, -0.02657008171081543, 0.018554987385869026, 0.059016063809394836, -0.002135751536116004, 0.006518575828522444, -0.016608595848083496, 0.025431625545024872, -0.034686166793107986, -0.025523437187075615, 0.027506552636623383, -0.03564099967479706, 0.007349464576691389, -0.01824283041059971, 0.00819871574640274, 0.016581052914261818, -0.04539132118225098, -0.01833464205265045, 0.020382024347782135, -0.034557633101940155, -0.009355532936751842, -0.0106408866122365, -0.054866209626197815, -0.019702624529600143, -0.08733054995536804, -0.02668025530874729, 0.009277493692934513, -0.046125806868076324, 0.003507177345454693, 0.05582104250788689, 0.06680162996053696, 0.04605235904455185, 0.05997089669108391, -0.0010845165234059095, 0.014790739864110947, -0.015534408390522003, -0.09188437461853027, -0.026459908112883568, 0.019170120358467102, -0.01611281745135784, -0.021447032690048218, 0.004459715448319912, 0.0012555144494399428, 0.017131919041275978, -0.030646486207842827, 0.03687126561999321, 0.018013304099440575, -0.006748103071004152, -0.033327367156744, 0.019555727019906044, 0.023007817566394806, -0.0014712701085954905, -0.023338336497545242, -0.05732674151659012, 0.008024274371564388, 0.015828203409910202, -0.041535262018442154, 0.011641625314950943, -0.017306359484791756, 0.053470682352781296, -0.004641042090952396, -0.02697405032813549, 0.0209879782050848, -0.006637929938733578, -0.008290526457130909, -0.028975527733564377, -0.011145845986902714, 0.030132345855236053, 0.01962917484343052, -0.02517455630004406, 0.0053617581725120544, -0.015525227412581444, -0.029526393860578537, -0.016186265274882317, -0.10444410890340805, 0.015580314211547375, 0.03742213174700737, -0.0005112721119076014, 0.020767631009221077, 0.05358085408806801, 0.06797681003808975, 0.010337909683585167, -0.009722776710987091, -0.0035117678344249725, 0.011650806292891502, 0.002169033046811819, 0.0069914017803967, 0.04322458431124687, -0.025339815765619278, -0.02405446209013462, 0.01891305111348629, -0.05842847377061844, -0.0138359060510993, 0.02210807055234909, -0.006339544430375099, -0.01252301037311554, 0.013496206142008305, -0.012706631794571877, -0.020216764882206917, 0.006569071672856808, -0.06547955423593521, -0.04366527497768402, 0.0009393405052833259, -0.042490094900131226, -0.004526278469711542, -0.04781512916088104, -0.020749269053339958, -0.04399579390883446, -0.039001282304525375, -0.027598364278674126, 0.029710015282034874, 0.043040961027145386, 0.02280583418905735, -0.015561951324343681, -0.012669907882809639, 0.0029218827839940786, -0.0698864758014679, -0.005894261412322521, -0.051928259432315826, -0.020528921857476234, -0.04076404869556427, -0.012807624414563179, 0.02199789695441723, 0.044032517820596695, -0.004198054317384958, -0.003316669724881649, -0.015102896839380264, -0.00618805643171072, 0.013174867257475853, -0.045281149446964264, -0.039001282304525375, 0.063496433198452, -0.023117991164326668, 0.034300561994314194, 0.011595719493925571, 0.0035094725899398327, 0.02769017405807972, 0.03132588788866997, 0.008469557389616966, 0.016920752823352814, -0.012688269838690758, 0.02280583418905735, 0.040947671979665756, -0.023393424227833748, -0.06834404915571213, -0.07109837979078293, 0.02445843070745468, 0.029728377237915993, 0.029856912791728973, 0.04351837933063507, -0.0025500485207885504, -0.004528573714196682, -0.047521334141492844, -0.004468896891921759, -0.031656406819820404, -0.017333902418613434, -0.05247912555932999, -0.011871152557432652, 0.010806146077811718, 0.020124955102801323, 0.04641960188746452, -0.002109355991706252, 0.05064290761947632, 0.024660414084792137, 0.018683522939682007, -0.08182189613580704, 0.046786848455667496, -0.016599414870142937, -0.02280583418905735, -0.018307099118828773, 0.026111027225852013, -0.027047498151659966, 0.033749695867300034, 0.03507177159190178, 0.027928883209824562, 0.0281125046312809, -0.0008481034310534596, 0.05993417277932167, 0.029416220262646675, -0.0070373076014220715, -0.079030841588974, 0.012128222733736038, 0.079030841588974, 0.00994312297552824, 0.040543705224990845, -0.01203641202300787, -0.003720637643709779, 0.004237073939293623, -0.0053617581725120544, -0.02769017405807972, -0.050312384963035583, 0.05398482456803322, -0.011503908783197403, -0.02908570133149624, -0.024017738178372383, -0.013147324323654175, -0.024972571060061455, -0.05358085408806801, -0.03988266736268997, -0.004087881185114384, -0.03995611518621445, -0.026239562779664993, -0.006839913781732321, -0.002311340067535639, -0.09812751412391663, -0.02030857652425766, 0.016516786068677902, 0.00840070005506277, 0.01244038064032793, 0.016590233892202377, -0.015516046434640884, -0.036522384732961655, -0.006830732803791761, 0.0623212568461895, 0.046235982328653336, -0.022438589483499527, -0.00241462723352015, -0.013193230144679546, -0.03196856379508972, -0.017884768545627594, -0.04157198593020439, -0.004746624734252691, 0.07091476023197174, -0.02948966808617115, 0.036779455840587616, 0.025486713275313377, -0.03639385104179382, 0.010466445237398148, -0.041498538106679916, -0.06353315711021423, -0.0024238084442913532, 0.001278467127121985, 0.004650223534554243, -0.05078980326652527, 0.023191438987851143, -0.010861231945455074, -0.001020822674036026, 0.00807477068156004, 0.06107262521982193, 0.015396691858768463, 0.001218790072016418, -0.013661465607583523, -0.01751752384006977, -0.0035783308558166027, -0.03116062842309475, 0.009070918895304203, -0.03132588788866997, -0.0483659952878952, -0.027781985700130463, -0.0241829976439476, 0.05163446441292763, -0.03160132095217705, 0.025358177721500397, -0.06592024117708206, 0.02377902902662754, -0.030775021761655807, 0.055123280733823776, 0.03988266736268997, -0.03578789904713631, 0.024109547957777977, 0.017471618950366974, -0.001654891879297793, 0.013275859877467155, -0.03029760532081127, 0.022842558100819588, 0.021777551621198654, -0.007982959970831871, -0.002905815839767456, 0.009575879201292992, 0.011522270739078522, -0.019078310579061508, -0.030958643183112144, -0.0017570315394550562, -0.003220268292352557, -0.007147480268031359, 0.07139217853546143, -0.05857536941766739, 0.03808317333459854, 0.07939808815717697, 0.004253141116350889, 0.04553821682929993, -0.018463177606463432, -0.04891686141490936, 0.010815327055752277, 0.016379069536924362, -0.007110755890607834, 0.023430148139595985, -0.010402177460491657, -0.0009238474303856492, 0.030664848163723946, -0.03756903111934662, -0.010824508033692837, 0.013119781389832497, 0.021373583003878593, -0.00800591241568327, 0.06059521064162254, 0.006610386539250612, -0.040690600872039795, 0.026606805622577667, -0.0006145593943074346, -0.029526393860578537, 0.005921804811805487, 0.022879282012581825, -0.004207235760986805, -0.0048476168885827065, 0.02989363670349121, -0.02739637903869152, -0.01459793746471405, -0.0392216257750988, -0.018821239471435547, 0.0030389416497200727, 0.014441858045756817, -0.00018563021149020642, -0.0056326002813875675, 0.031215714290738106, -0.01584656536579132, 0.017903130501508713, -0.004533164203166962, 0.03439237177371979, 0.024862397462129593, -0.010714334435760975, -0.010604161769151688, -0.015892470255494118, 0.0004989349981769919, -0.008979108184576035, 0.007771794684231281, 0.03272141516208649, 0.029691653326153755, 0.03848714008927345, -0.020492197945713997, -0.011907876469194889, -0.016452517360448837, 0.04465683549642563, 0.008318069390952587, -0.011256019584834576, 0.026772065088152885, -0.005595875903964043, -0.024109547957777977, -0.027855435386300087, -0.07253062725067139, 0.0020932890474796295, 0.004661699756979942, -0.01724209077656269, 0.03940524905920029, 0.03659583628177643, 0.0003775724326260388, -0.040139734745025635, -0.06312919408082962, 0.012936159037053585, -0.015213070437312126, 0.03446581959724426, -0.06456144154071808, -0.01210067979991436, 0.002905815839767456, 0.005729001481086016, -0.010053296573460102, -0.03160132095217705, -0.008501691743731499, 0.05600466579198837, 0.003720637643709779, 0.03578789904713631, 0.011797703802585602, -0.004048861563205719, -0.014698929153382778, 0.03018743172287941, -0.009043375961482525, 0.05185481160879135, -0.03086683340370655, 0.022769108414649963, -0.010833689011633396, -0.010347091592848301, -0.03160132095217705, -0.015268156304955482, 0.013018788769841194, 0.03187675401568413, -0.05207515507936478, -0.01574557274580002, 0.01390935480594635, -0.00692254351451993, -0.038193345069885254, -0.019720986485481262, -0.0014333981089293957, 0.002334292745217681, -0.0017570315394550562, -0.004503326024860144, -0.0024329894222319126, 0.01584656536579132, 0.00022837967844679952, 0.015277338214218616, 0.013073875568807125, 0.0161219984292984, -0.04436304047703743, -0.010530713014304638, 0.006128379143774509, 0.00827216450124979, 0.01824283041059971, -0.006435945630073547, 0.020418750122189522, 0.00027026841416954994, 0.015763936564326286, -0.007900330238044262, 0.06522247940301895, 0.03536556661128998, 0.010236917994916439, 0.002334292745217681, 0.04381217435002327, -0.03156459704041481, -0.02473386377096176, 0.034704528748989105, 0.015497684478759766, -0.026386460289359093, -0.0037022754549980164, 0.023889202624559402, -0.015525227412581444, 0.03393331915140152, -0.051671188324689865, 0.07073113322257996, -0.0486597903072834, 0.01029200479388237, -0.027781985700130463, -0.0623212568461895, 0.04961462318897247, -0.016030186787247658, -0.047080643475055695, -0.019096672534942627, -0.03551246598362923, 0.0194639153778553, -0.01793985441327095, 0.04230647534132004, 0.038744211196899414, -0.013808363117277622, -0.01042054034769535, -0.027653450146317482, -0.01889468915760517, -0.05394810065627098, 0.036632560193538666, 0.07319167256355286, -0.008786305785179138, 0.028002332895994186, 0.006348725408315659, -0.014478582888841629, -0.01217412855476141, 0.0034268428571522236, 0.005476521793752909, 0.022916005924344063, 0.019720986485481262, -0.013441119343042374, 0.012486285530030727, -0.024164635688066483, 0.013643103651702404, 0.0017650650115683675, 0.005545380059629679, -0.017297178506851196, -0.023558683693408966, -0.028571559116244316, -0.0024811902549117804, 0.018279554322361946, 0.011210113763809204, 0.02352195978164673, -0.04399579390883446, -0.018178563565015793, -0.0013392918044701219, -0.008102314546704292, 0.015433416701853275, 0.023044541478157043, 0.002275763312354684, -0.04337147995829582, 0.009268312714993954, 0.037091612815856934, 0.008914840407669544, -0.029673291370272636, 0.03380478173494339, -0.0043472470715641975, 0.03688963130116463, 0.020932890474796295, -0.02881026826798916, 0.03925834968686104, 0.013303402811288834, 0.0328315868973732, 0.00966768991202116, 0.012871891260147095, -0.008093132637441158, -0.018040847033262253, -0.05372775346040726, -0.017049288377165794, 0.022181520238518715, 0.0033924137242138386, 0.008097723126411438, 0.0015917719574645162, 0.021520480513572693, -0.01202723104506731, 0.0027566230855882168, 0.001984263537451625, 0.009520793333649635, 0.04127819091081619, 0.004406924359500408, -0.015396691858768463, 0.0067756460048258305, 0.019941333681344986, -0.017893949523568153, 0.0005921804695390165, -0.055013105273246765, 0.055049829185009, -0.039845939725637436, 0.01232102606445551, -0.004443648736923933, -0.08027946949005127, 0.025248004123568535, 0.023981014266610146, -0.035824622958898544, 0.015571133233606815, -0.03266632556915283, 0.015277338214218616, 0.004383971448987722, -0.010135926306247711, -0.034686166793107986, 0.02587231807410717, -0.006550709251314402, -0.047631505876779556, 0.0027153079863637686, -0.0000989836553344503, -0.0010024604853242636, 0.05115704610943794, -0.002602839609608054, 0.06107262521982193, 0.000281457876553759, 0.007712117861956358, 0.022218244150280952, 0.048219095915555954, -0.034979961812496185, 0.012798442505300045, 0.0016663683345541358, -0.0246236901730299, -0.0029861503280699253, 0.018252011388540268, -0.016737131401896477, -0.03336409106850624, 0.015635401010513306, -0.016204629093408585, -0.03782610222697258, 0.028039056807756424, -0.011191751807928085, 0.014506125822663307, -0.012137404642999172, 0.00178227957803756, -0.04271044209599495, 0.050826527178287506, 0.03171149268746376, -0.012385293841362, -0.022034622728824615, -0.032060373574495316, -0.04711736738681793, 0.0030527133494615555, -0.004581365268677473, -0.009337170980870724, 0.020400388166308403, -0.0009737696382217109, -0.019684262573719025, -0.03268468752503395, -0.024109547957777977, 0.025394901633262634, 0.013633922673761845, -0.021189961582422256, -0.00402820436283946, -0.010475626215338707, -0.023540321737527847, -0.001654891879297793, -0.07528495788574219, -0.023613769561052322, 0.06658127903938293, -0.039295077323913574, -0.012210853397846222, -0.028957165777683258, -0.0011591129004955292, 0.006031977944076061, 0.00855677854269743, -0.027029136195778847, -0.0350901335477829, 0.02434825710952282, -0.0075652203522622585, 0.021043064072728157, 0.0019785254262387753, 0.021612292155623436, 0.008102314546704292, 0.015075353905558586, 0.011659987270832062, -0.0748075395822525, 0.01459793746471405, 0.03250106796622276, -0.03380478173494339, -0.007730479817837477, 0.02502765879034996, -0.01737980730831623, 0.020749269053339958, -0.020363662391901016, -0.05717984214425087, -0.002229857724159956, -0.00016970674914773554, 0.004879750777035952, -0.006876638159155846, -0.044289588928222656, -0.009387667290866375, 0.03031596727669239, 0.04340820387005806, 0.03409857675433159, -0.02502765879034996, -0.03685290366411209, 0.015910834074020386, 0.02519291825592518, 0.030426140874624252, 0.035402294248342514, -0.004682356957346201, -0.003353394102305174, 0.0008779419586062431, 0.016360707581043243, -0.018050028011202812, 0.008809258230030537, -0.016186265274882317, -0.00027528931968845427, -0.04186578094959259, -0.024091186001896858, -0.058208126574754715, -0.08351121842861176, 0.020124955102801323, -0.02559688501060009, -0.009158140048384666, -0.0010862379567697644, -0.000762030656915158, -0.02473386377096176, -0.0007987550343386829, 0.02181427553296089, -0.049027033150196075, -0.019243570044636726, 0.006385449785739183, 0.031123902648687363, 0.013661465607583523, 0.07297132164239883, -0.023117991164326668, 0.014083796180784702, -0.02530308999121189, 0.021171599626541138, -0.031638044863939285, -0.031619682908058167, 0.027892159298062325, -0.05038583651185036, -0.021245047450065613, 0.08262982964515686, 0.046382877975702286, -0.0005178709980100393, -0.012743356637656689, -0.019959695637226105, -0.020492197945713997, 0.0017891654279083014, -0.048035476356744766, -0.011623263359069824, 0.0037367045879364014, 0.005499474238604307, -0.0039570508524775505, -0.008386927656829357, -0.038707487285137177, 0.045281149446964264, -0.04546476900577545, -0.034851428121328354, 0.015506865456700325, 0.014662204310297966, -0.0051873172633349895, 0.0044367630034685135, -0.014019528403878212, 0.02862664684653282, -0.005228632129728794, 0.037642478942871094, -0.021373583003878593, -0.02073090709745884, 0.030848471447825432, 0.01861925609409809, 0.03867075964808464, -0.04293078929185867, 0.027598364278674126, -0.04006628692150116, 0.04120474308729172, 0.002142637502402067, -0.0069822208024561405, -0.02934277057647705, 0.0017214547842741013, -0.0559312142431736, 0.03848714008927345, 0.03621022775769234, 0.051964983344078064, -0.009621785022318363, 0.01230266410857439, -0.03376805782318115, -0.015323243103921413, 0.018839601427316666, 0.006518575828522444, 0.00010959929204545915, 0.004191168583929539, 0.0167095884680748, -0.05101015046238899, 0.03382314369082451, 0.03264796361327171, 0.0018006417667493224, 0.00784983392804861, -0.003130752593278885, -0.009116824716329575, -0.013431938365101814, -0.01920684613287449, 0.004989923909306526, -0.01670040749013424, -0.023870840668678284, -0.038340240716934204, -0.012339388020336628, -0.017187004908919334, -0.011568176560103893, 0.02394428849220276, -0.010264460928738117, -0.00403738534078002, -0.02961820363998413, -0.021759189665317535, -0.016369888558983803, 0.002428398933261633, -0.011265200562775135, 0.021612292155623436, -0.005729001481086016, -0.04282061383128166, -0.03955214470624924, -0.017590973526239395, 0.03382314369082451, 0.00618805643171072, -0.06764628738164902, 0.00295401643961668, -0.038744211196899414, -0.00525158504024148, -0.007776385173201561, -0.018417270854115486, 0.025505075231194496, 0.03516358509659767, -0.003087142249569297, 0.0014483173144981265, 0.03141769766807556, -0.02993036061525345, -0.049173932522535324, -0.009360123425722122, -0.041498538106679916, -0.009612604044377804, 0.012532191351056099, -0.02504602074623108, -0.0018006417667493224, -0.010126745328307152, -0.000562915753107518, -0.05101015046238899, 0.02003314346075058, 0.02587231807410717, -0.05942003056406975, -0.005210270173847675, 0.00241462723352015, 0.038597311824560165, -0.0011585390893742442, 0.040139734745025635, 0.07609289139509201, -0.02489912323653698, -0.02185099944472313, 0.03071993589401245, -0.020363662391901016, -0.007165842689573765, 0.0023388832341879606, -0.004618089646100998, -0.026074303314089775, 0.04785185307264328, -0.03878093510866165, 0.012265939265489578, 0.0073724170215427876, 0.03422711417078972, 0.07748842239379883, -0.053617581725120544, 0.027029136195778847, -0.0099523039534688 ]
Machine learning on electromyography (EMG) has recently achieved remarkable success on a variety of tasks, while such success relies heavily on the assumption that the training and future data must be of the same data distribution. However, this assumption may not hold in many real-world applications. Model calibration is required via data re-collection and label annotation, which is generally very expensive and time-consuming. To address this problem, transfer learning (TL), which aims to improve target learners' performance by transferring the knowledge from related source domains, is emerging as a new paradigm to reduce the amount of calibration effort. In this survey, we assess the eligibility of more than fifty published peer-reviewed representative transfer learning approaches for EMG applications. Unlike previous surveys on purely transfer learning or EMG-based machine learning, this survey aims to provide an insight into the biological foundations of existing transfer learning methods on EMG-related analysis. In specific, we first introduce the physiological structure of the muscles and the EMG generating mechanism, and the recording of EMG to provide biological insights behind existing transfer learning approaches. Further, we categorize existing research endeavors into data based, model based, training scheme based, and adversarial based. This survey systematically summarizes and categorizes existing transfer learning approaches for EMG related machine learning applications. In addition, we discuss possible drawbacks of existing works and point out the future direction of better EMG transfer learning algorithms to enhance practicality for real-world applications.
[ -0.003072702791541815, 0.0285221878439188, -0.02052164636552334, -0.054860860109329224, 0.026696905493736267, 0.031524524092674255, 0.001230360590852797, 0.0031622610986232758, 0.012649044394493103, 0.01407344825565815, -0.003929903730750084, -0.05045970901846886, -0.005927906837314367, -0.00207689986564219, 0.006333051715046167, -0.021067526191473007, -0.005770113784819841, -0.04926559701561928, -0.015992555767297745, 0.013894331641495228, 0.058272603899240494, -0.03398098051548004, -0.01299021951854229, -0.01920812390744686, -0.006017465144395828, 0.027669252827763557, 0.053223222494125366, -0.029033949598670006, 0.009032594971358776, -0.004132476169615984, 0.020231647416949272, 0.0016173804178833961, -0.03503862023353577, -0.016256965696811676, -0.004887324757874012, -0.032172754406929016, 0.0020139957778155804, 0.04008800536394119, -0.028078662231564522, 0.03998565301299095, 0.028283366933465004, 0.012614927254617214, -0.004004535730928183, -0.01612049527466297, -0.019464004784822464, -0.013681097887456417, -0.04244210943579674, 0.0004504569515120238, 0.07151017338037491, 0.024172212928533554, 0.04469386115670204, -0.026969844475388527, -0.01228228211402893, 0.022824574261903763, -0.03447568416595459, 0.06291257590055466, 0.10242058336734772, 0.04165740683674812, 0.03903036192059517, -0.036505673080682755, -0.027345135807991028, 0.023012220859527588, -0.009544356726109982, -0.021357523277401924, 0.05776084214448929, -0.0764913260936737, 0.05076676607131958, -0.030944528058171272, 0.028590423986315727, 0.014849619939923286, -0.03589155897498131, 0.005228499416261911, -0.009271416813135147, -0.01997576653957367, -0.012606398202478886, 0.014866678975522518, -0.008277746848762035, 0.07260193675756454, -0.0453420914709568, 0.010738467797636986, 0.015463734045624733, 0.09218534827232361, -0.004639973398298025, -0.02176693268120289, 0.04977735877037048, 0.07041841745376587, -0.006580403074622154, -0.027805721387267113, -0.0405997671186924, 0.0049598244950175285, 0.023694569244980812, 0.04339739680290222, -0.01055082120001316, -0.004134608432650566, -0.001217566546984017, -0.023404570296406746, 0.023677511140704155, -0.015821967273950577, -0.05069852992892265, -0.042510341852903366, 0.03534567728638649, 0.00565496739000082, -0.0338786281645298, -0.010081706568598747, 0.002917042002081871, -0.02002694271504879, -0.009808766655623913, 0.001695210812613368, 0.014781385660171509, 0.12016166001558304, -0.03140511363744736, -0.006333051715046167, 0.0006418345146812499, 0.0028765276074409485, -0.017195194959640503, -0.024786327034235, 0.01241875160485506, -0.12364163994789124, 0.04261269420385361, -0.011036994867026806, 0.05277969688177109, 0.09320887178182602, -0.025349264964461327, -0.0033477747347205877, -0.03589155897498131, 0.05748790502548218, 0.00473379623144865, -0.0260316152125597, 0.07983483374118805, 0.03534567728638649, 0.01873048022389412, 0.05202911049127579, 0.04049741476774216, 0.0021280760411173105, 0.03360568732023239, 0.03459509462118149, 0.01309257186949253, 0.029528653249144554, 0.023950450122356415, -0.014824031852185726, 0.0033371131867170334, 0.030432766303420067, 0.04087270423769951, -0.017186665907502174, 0.011565815657377243, -0.07185135036706924, -0.017135489732027054, 0.07560426741838455, 0.027686310932040215, -0.004507767967879772, -0.03143922984600067, 0.016052260994911194, 0.0009558217134326696, 0.013706685975193977, 0.04199858009815216, -0.04715031757950783, 0.0013071248540654778, -0.02273928001523018, 0.008060247637331486, 0.004160196520388126, 0.013664038851857185, 0.00472100218757987, -0.01780930906534195, 0.07307957857847214, 0.06837137043476105, 0.0017506516305729747, 0.05670320242643356, -0.030432766303420067, -0.027191607281565666, 0.044250331819057465, -0.06540315598249435, -0.007595397531986237, 0.01317786518484354, -0.01791166141629219, -0.0033029955811798573, 0.047764431685209274, 0.029051009565591812, 0.007151870522648096, -0.04766207933425903, -0.040292710065841675, -0.03321333974599838, -0.012879337184131145, 0.011975225061178207, 0.03372510150074959, 0.07860660552978516, 0.0016653580823913217, 0.053120870143175125, -0.0025033678393810987, 0.028436895459890366, -0.020692232996225357, 0.032070402055978775, 0.045546796172857285, 0.050630297511816025, -0.007339516654610634, 0.042305637151002884, -0.006567609030753374, -0.020095178857445717, 0.03445862606167793, 0.019958708435297012, -0.03804095834493637, -0.044625625014305115, -0.04404562711715698, -0.011403758078813553, -0.031848639249801636, 0.029835710301995277, -0.049606774002313614, 0.013553157448768616, 0.02316574938595295, 0.032820988446474075, -0.041759759187698364, 0.0011184127070009708, 0.028488071635365486, -0.05933024734258652, -0.053666748106479645, -0.036130379885435104, -0.018167542293667793, 0.05632790923118591, 0.0022112373262643814, 0.001689879922196269, 0.0363692007958889, 0.006512168329209089, 0.07110076397657394, 0.04479621350765228, -0.02094811387360096, -0.038893893361091614, 0.011821696534752846, 0.007893925532698631, -0.0025822645984590054, 0.029631005600094795, 0.016598138958215714, 0.03063747100532055, 0.037802133709192276, 0.02645808272063732, -0.05397380515933037, -0.025997497141361237, 0.03333275020122528, 0.029682181775569916, 0.00936524011194706, -0.04837854579091072, 0.023506922647356987, -0.012947572395205498, 0.009766120463609695, 0.012538162991404533, 0.00001559274096507579, 0.050630297511816025, -0.006682755425572395, -0.012376105412840843, 0.09047947824001312, -0.025246912613511086, -0.008158335462212563, -0.06987253576517105, -0.03481685742735863, 0.014551092870533466, 0.00028466747608035803, -0.038723304867744446, 0.052745576947927475, 0.04599032178521156, -0.022039873525500298, 0.0035482149105519056, -0.09621120989322662, 0.05110793933272362, -0.024121036753058434, -0.03285510465502739, -0.017399899661540985, -0.0075826034881174564, 0.016094908118247986, 0.10630997270345688, 0.0265263170003891, 0.02371162734925747, -0.03415156900882721, -0.05243851989507675, 0.022005755454301834, -0.008913183584809303, -0.004089829511940479, -0.05069852992892265, -0.04281739890575409, 0.008085835725069046, -0.022278694435954094, 0.04107740893959999, 0.04677502438426018, -0.004469385836273432, 0.048310309648513794, 0.04012212157249451, 0.028215130791068077, -0.028010426089167595, -0.013740803115069866, 0.008299069479107857, 0.016589609906077385, -0.05660085007548332, -0.035482149571180344, 0.002160061150789261, -0.014320800080895424, -0.015079912729561329, -0.03708566725254059, 0.05008441582322121, -0.03514097258448601, -0.017979895696043968, 0.000542414141818881, 0.010542292147874832, -0.03386157006025314, -0.031848639249801636, 0.004068505950272083, 0.005799966398626566, 0.057351432740688324, -0.0023903539404273033, -0.012563751079142094, 0.01763872243463993, 0.06741607934236526, -0.026065731421113014, -0.05083500221371651, 0.024172212928533554, 0.003277407493442297, 0.010004942305386066, -0.02505926787853241, 0.0202998835593462, 0.020879879593849182, 0.060865532606840134, 0.03896212950348854, -0.004844678100198507, -0.03491920977830887, -0.02483750320971012, 0.047969136387109756, -0.0904112458229065, 0.017391370609402657, 0.022875750437378883, -0.07014548033475876, 0.030944528058171272, 0.021511051803827286, 0.009126418270170689, -0.018269894644618034, -0.040667999535799026, -0.004352107178419828, -0.03691508248448372, -0.043260928243398666, -0.010047589428722858, 0.05776084214448929, -0.07103253155946732, -0.00048004317795857787, -0.05298440158367157, 0.006623050197958946, -0.0363692007958889, 0.02473515085875988, -0.05110793933272362, -0.03186569735407829, 0.023558098822832108, -0.029033949598670006, -0.03058629482984543, 0.02754984050989151, -0.056907907128334045, -0.021203994750976562, 0.0007703080773353577, -0.029204538092017174, 0.03647155314683914, 0.00852083321660757, -0.012521103955805302, -0.049709126353263855, 0.038996245712041855, 0.014440210536122322, 0.004170858301222324, 0.0066955494694411755, -0.010909054428339005, -0.0528138130903244, -0.036778610199689865, 0.01801401376724243, -0.07301134616136551, 0.01022670604288578, -0.011412287130951881, -0.033690981566905975, 0.05646438151597977, 0.0010080640204250813, 0.004563209135085344, -0.0018156880978494883, 0.050357356667518616, -0.03551626577973366, -0.02797630988061428, 0.04595620557665825, 0.022381046786904335, 0.032889220863580704, -0.01147199235856533, 0.049982063472270966, -0.024939855560660362, -0.06403845548629761, -0.00262491125613451, 0.022500459104776382, 0.04442092031240463, -0.002351971808820963, 0.0016120495274662971, -0.029903944581747055, -0.030569234862923622, 0.026918668299913406, 0.02739631198346615, 0.01134405191987753, -0.0016760197468101978, -0.06912195682525635, -0.04653620347380638, -0.00790245458483696, -0.025946320965886116, 0.08283717185258865, 0.029085125774145126, 0.023251041769981384, -0.0019009816460311413, -0.006269081495702267, -0.0052882046438753605, 0.0032070402521640062, -0.005433204118162394, -0.045922089368104935, -0.01920812390744686, 0.045649148523807526, 0.006708343513309956, -0.010627585463225842, 0.009314063936471939, -0.004763648845255375, -0.014320800080895424, -0.08317834138870239, -0.0016642918344587088, -0.040190357714891434, -0.04827619343996048, -0.0028786598704755306, 0.006448198109865189, -0.03793860599398613, -0.03507274016737938, 0.008695685304701328, 0.025144560262560844, -0.017297547310590744, -0.024428093805909157, 0.03732449188828468, -0.0008294805302284658, -0.02608279138803482, -0.0037166697438806295, -0.023336336016654968, 0.006328787188977003, -0.0030748352874070406, 0.02700396254658699, -0.05325733870267868, 0.03236040100455284, 0.015139618888497353, 0.0650278627872467, -0.014116095378994942, -0.026799257844686508, -0.02917042002081871, -0.034441567957401276, 0.054042041301727295, 0.028539247810840607, -0.024376917630434036, -0.027993367984890938, -0.030057473108172417, 0.04929971694946289, -0.022756339982151985, -0.008239364251494408, 0.011864343658089638, 0.008448333479464054, 0.04080447182059288, -0.06652902811765671, -0.03350333496928215, 0.019344594329595566, 0.006431139539927244, 0.029955120757222176, -0.04025859013199806, -0.010909054428339005, -0.037426844239234924, -0.014824031852185726, 0.036608025431632996, 0.04496679827570915, -0.03302569314837456, 0.017144018784165382, -0.0020971570629626513, -0.03416862711310387, -0.02197163738310337, -0.03555038198828697, 0.01710990071296692, -0.02685043402016163, -0.03664214164018631, -0.0157537329941988, -0.0341174490749836, -0.00001704206624708604, 0.014815502800047398, -0.01840636506676674, -0.05022088810801506, -0.01953224092721939, -0.00435637217015028, -0.000616779550909996, -0.013715215027332306, 0.013800508342683315, -0.007207311224192381, 0.013860214501619339, -0.007906719110906124, 0.006081435363739729, 0.02548573538661003, 0.017502252012491226, -0.04551267996430397, -0.025741616263985634, -0.0060857003554701805, 0.00957847386598587, 0.009535827673971653, -0.02077752724289894, -0.04687737673521042, 0.004456591792404652, -0.010166999883949757, 0.06311728060245514, 0.0018498054705560207, 0.011113759130239487, 0.028215130791068077, -0.029204538092017174, 0.031746286898851395, 0.009245828725397587, 0.020811645314097404, -0.014081977307796478, -0.0014276020228862762, -0.024803387001156807, -0.019685769453644753, 0.007646573707461357, -0.0019095110474154353, 0.014721679501235485, -0.04295387119054794, -0.03485097736120224, 0.0562937930226326, 0.015608733519911766, -0.053769100457429886, 0.017451075837016106, 0.017237842082977295, 0.0073608397506177425, -0.0004832416889257729, 0.022056931629776955, 0.03031335398554802, -0.03923506662249565, 0.015736674889922142, 0.012376105412840843, -0.0016600271919742227, 0.04861736670136452, -0.008913183584809303, -0.022534575313329697, -0.016871079802513123, 0.000657827069517225, 0.007898190058767796, 0.01796283759176731, -0.006874666083604097, 0.028812186792492867, -0.03321333974599838, -0.03630096837878227, -0.004431003704667091, -0.05769260972738266, 0.031149232760071754, -0.03978094831109047, -0.006307463627308607, 0.02809572033584118, -0.015574616380035877, 0.023609274998307228, -0.0321386381983757, 0.018866950646042824, 0.009186123497784138, -0.037529196590185165, 0.01418432965874672, -0.0004797766450792551, -0.022636927664279938, -0.035106856375932693, -0.06304904818534851, -0.03507274016737938, -0.031643934547901154, -0.031046880409121513, 0.003413877449929714, 0.01861106976866722, 0.005748790223151445, -0.004324386827647686, 0.02625337801873684, -0.019736945629119873, -0.052574992179870605, -0.005889524705708027, 0.04871971905231476, 0.030176885426044464, 0.018389305099844933, -0.010661703534424305, 0.0006684887921437621, -0.004716737661510706, -0.015003148466348648, 0.0016461670165881515, 0.06311728060245514, 0.01206904835999012, -0.012623456306755543, 0.0028807921335101128, 0.013774920254945755, -0.018048131838440895, 0.025997497141361237, 0.022756339982151985, 0.048139721155166626, 0.033042751252651215, -0.017033137381076813, -0.06567609310150146, -0.021801050752401352, 0.03599391132593155, -0.024973973631858826, 0.026867492124438286, 0.003482112195342779, -0.024103978648781776, -0.024769268929958344, -0.017416957765817642, -0.01888400875031948, 0.01317786518484354, 0.014278152957558632, 0.06564197689294815, -0.01770695671439171, 0.01229081116616726, 0.00004427938620210625, 0.012904925271868706, 0.04854913055896759, 0.03599391132593155, 0.008192452602088451, -0.027942191809415817, -0.0478326641023159, 0.003119614440947771, -0.02338751219213009, -0.0028061603661626577, -0.0006466322811320424, 0.05042559280991554, 0.019668709486722946, 0.007727602496743202, -0.02273928001523018, 0.01310110092163086, -0.009868472814559937, 0.053939688950777054, 0.0036271114367991686, 0.008004806935787201, 0.009962295182049274, 0.0009670165018178523, -0.023796921595931053, -0.02018047124147415, 0.007714808452874422, 0.014303741045296192, -0.06891725212335587, -0.03643743693828583, -0.0028701305855065584, -0.05049382522702217, 0.029375124722719193, 0.00015472796803805977, -0.023029278963804245, 0.044079747051000595, 0.018594009801745415, 0.015617262572050095, -0.008311863988637924, 0.021067526191473007, 0.04926559701561928, -0.00792804267257452, 0.007898190058767796, -0.050800882279872894, 0.04612679407000542, 0.0004424606740940362, -0.005364968907088041, -0.005104823503643274, 0.04179387539625168, 0.02917042002081871, 0.005991877056658268, -0.01309257186949253, 0.006260551977902651, -0.016589609906077385, 0.02099929004907608, -0.08201835304498672, -0.03555038198828697, -0.006503638811409473, 0.0024031479842960835, 0.004558944143354893, 0.025349264964461327, 0.01117346528917551, 0.023831039667129517, 0.0019852090626955032, -0.003002335550263524, 0.042407989501953125, -0.01323757041245699, 0.03481685742735863, -0.01584755629301071, 0.031575702130794525, 0.018048131838440895, -0.026116907596588135, -0.03858683630824089, -0.011463463306427002, 0.04107740893959999, -0.023029278963804245, -0.014354917220771313, 0.04080447182059288, 0.026048673316836357, -0.009808766655623913, -0.04674090817570686, -0.016325199976563454, -0.009220240637660027, 0.011454934254288673, 0.0066486382856965065, 0.03160981833934784, -0.006883195601403713, 0.01036317553371191, -0.002042782260105014, -0.06455021351575851, 0.02580985054373741, 0.019020479172468185, 0.0038147573359310627, 0.024018684402108192, -0.04169152304530144, -0.005910848267376423, 0.023558098822832108, -0.028010426089167595, 0.014730209484696388, 0.03340098261833191, 0.01786048524081707, -0.014824031852185726, -0.04438680410385132, -0.0027528516948223114, 0.003482112195342779, 0.05141499638557434, -0.004254019819200039, 0.0028743951115757227, -0.02620220184326172, -0.015480793081223965, -0.0015576748410239816, -0.005463056731969118, 0.02413809671998024, 0.014423152431845665, 0.054314982146024704, 0.06089964881539345, 0.00024255375319626182, 0.006486580241471529, 0.0453420914709568, -0.00952729769051075, 0.05161970108747482, -0.01496050227433443, 0.04421621561050415, 0.027515724301338196, -0.04523973912000656, -0.05250675603747368, 0.06905371695756912, 0.006350110284984112, -0.060865532606840134, 0.007267016917467117, -0.0025140296202152967, 0.024547506123781204, -0.005863936617970467, -0.021681640297174454, 0.011480522342026234, 0.0421009324491024, -0.04421621561050415, -0.031132172793149948, 0.049060892313718796, -0.01402227208018303, 0.0028466747608035803, -0.016222847625613213, 0.022381046786904335, 0.025895144790410995, -0.059944361448287964, 0.0014734474243596196, -0.030501000583171844, -0.019907532259821892, 0.029682181775569916, -0.04114564508199692, -0.009979354217648506, 0.03647155314683914, -0.02966512367129326, 0.05724908038973808, 0.0017282620538026094, -0.0264069065451622, -0.021357523277401924, 0.029102185741066933, -0.007595397531986237, 0.021988697350025177, -0.012009342201054096, -0.035686854273080826, 0.021613404154777527, 0.03160981833934784, -0.0022730750497430563, 0.016589609906077385, 0.07062312215566635, -0.05407615751028061, 0.041862111538648605, -0.008537892252206802, -0.011906989850103855, 0.006141141057014465, 0.0455809123814106, 0.08051718026399612, 0.012307870201766491, 0.003497038735076785, 0.018696362152695656, 0.02830042503774166, 0.0142610939219594, -0.03183158114552498, 0.05110793933272362, 0.0038211543578654528, 0.012717279605567455, 0.033810392022132874, -0.008341716602444649, -0.010047589428722858, 0.037256255745887756, 0.0075399563647806644, -0.009220240637660027, -0.03694919869303703, -0.016410494223237038, -0.025519853457808495, -0.0043968865647912025, 0.004507767967879772, 0.020794585347175598, 0.005744525697082281, -0.027464548125863075, -0.01044846884906292, 0.015523440204560757, -0.03920095041394234, -0.030006296932697296, 0.0026739551685750484, 0.0018124895868822932, -0.009015535935759544, 0.010951701551675797, -0.04244210943579674, -0.03599391132593155, -0.024649858474731445, -0.015139618888497353, 0.011557286605238914, 0.026014555245637894, -0.0004222034476697445, 0.023609274998307228, -0.012674632482230663, -0.0007319259457290173, 0.02804454416036606, -0.014559621922671795, -0.014491386711597443, -0.013476393185555935, 0.0014265358913689852, -0.021084584295749664, -0.012862279079854488, -0.048139721155166626, -0.014977560378611088, 0.01231639925390482, -0.04929971694946289, 0.001314588007517159, -0.0016674903454259038, -0.00001675886414886918, 0.02906806766986847, 0.004362768959254026, 0.0013753597158938646, -0.027891015633940697, -0.019464004784822464, -0.0059748184867203236, -0.008188188076019287, 0.06594903022050858, -0.006512168329209089, -0.023899273946881294, -0.0020374516025185585, 0.047491490840911865, -0.0036868168972432613, -0.024428093805909157, -0.02857336401939392, -0.02338751219213009, -0.008870537392795086, -0.00922877062112093, 0.04506915062665939, 0.013280217535793781, 0.011710815131664276, 0.024172212928533554, 0.025349264964461327, -0.004605855792760849, 0.0023221189621835947, 0.018150484189391136, -0.0027613812126219273, -0.022500459104776382, 0.03413451090455055, 0.0934135764837265, 0.004418209660798311, 0.017877543345093727, -0.02792513370513916, 0.011318463832139969, 0.029648063704371452, -0.035482149571180344, 0.006384227890521288, -0.025673381984233856, 0.027635134756565094, -0.026099849492311478, -0.013356981799006462, -0.04994794726371765, 0.000606117828283459, 0.05622555688023567, 0.015003148466348648, 0.0001270741777261719, -0.009126418270170689, 0.030552176758646965, -0.03423686325550079, 0.006644373293966055, 0.01301580760627985, -0.0113355228677392, 0.02024870738387108, 0.014371976256370544, 0.013749332167208195, -0.03382745385169983, 0.00798774790018797, 0.020265765488147736, -0.035959791392087936, -0.04790090024471283, -0.010772584937512875, -0.010644644498825073, -0.013646979816257954, 0.03657390549778938, -0.005475850775837898, -0.03739272430539131, 0.05748790502548218, -0.01225669402629137, -0.015404028818011284, -0.017996955662965775, -0.012051989324390888, 0.0453420914709568, -0.020641056820750237, 0.005347910337150097, -0.022483399137854576, -0.022159283980727196, -0.03701743483543396, -0.019498122856020927, -0.00785127840936184, 0.002927703782916069, 0.04718443378806114, -0.01509697176516056, -0.007702014409005642, -0.05748790502548218, -0.003955491818487644, -0.03943977132439613, 0.029733357951045036, 0.01791166141629219, 0.04493268206715584, -0.02354104071855545, -0.0003521027392707765, -0.014644915238022804, -0.012913455255329609, 0.019071655347943306, 0.004942765459418297, 0.01861106976866722, -0.048787955194711685, -0.016572551801800728, -0.007714808452874422, 0.02311457321047783, 0.02894865721464157, 0.0048361485823988914, -0.03500450402498245, 0.040292710065841675, 0.017340194433927536, -0.00602173013612628, 0.02673102170228958, -0.02824924886226654, -0.010235235095024109, 0.03275275230407715, -0.030142767354846, 0.00506217684596777, -0.006883195601403713, -0.008341716602444649, 0.04957265406847, 0.027618076652288437, -0.0056037912145257, -0.01523344125598669, 0.01134405191987753, 0.03507274016737938, 0.025093384087085724, -0.040019769221544266, -0.0005322855431586504, -0.006567609030753374, 0.04165740683674812, -0.05400792509317398, -0.03116629086434841, 0.04295387119054794, -0.029784534126520157, 0.0011866475688293576, -0.01992459036409855, 0.02483750320971012, -0.01564285159111023, 0.06072906032204628, -0.03616449609398842, 0.0039021833799779415, -0.03247981145977974, 0.007834219373762608, -0.044898565858602524, -0.00955288577824831, -0.01499461941421032, -0.012504045851528645, 0.002695278497412801, 0.027089254930615425, -0.020163413137197495, 0.014354917220771313, 0.00603452417999506, -0.008670097216963768, 0.008465392515063286, -0.015293147414922714, 0.004558944143354893, 0.003695346415042877, 0.005842613521963358, 0.0022027078084647655, 0.013664038851857185, 0.000612514850217849, -0.004460856784135103, -0.04220328480005264, -0.004652767442166805, -0.00009588869579602033, -0.023506922647356987, -0.01402227208018303, 0.0224151648581028, -0.025042207911610603, 0.011864343658089638, -0.012904925271868706, -0.03382745385169983, -0.040667999535799026, 0.01828695274889469, 0.010320528410375118, -0.005599526688456535, 0.002923439024016261, -0.03640332072973251, 0.007625250145792961, 0.02099929004907608, 0.024206330999732018, -0.02548573538661003, 0.055509090423583984, 0.051926758140325546, 0.006964224390685558, 0.010729937814176083, -0.005684820003807545, 0.03265039995312691, -0.0222957544028759, 0.01710137166082859, -0.01520785316824913, -0.0010667034657672048, -0.0038296838756650686, -0.04715031757950783, -0.006426874548196793, -0.014585210010409355, -0.038552720099687576, -0.02705513872206211, -0.024820445105433464, -0.003204907989129424, -0.07683249562978745 ]
Electroencephalograms (EEGs) are brain dynamics measured outside the brain, which have been widely utilized in non-invasive brain-computer interface applications. Recently, various neural network approaches have been proposed to improve the accuracy of EEG signal recognition. However, these approaches severely rely on manually designed network structures for different tasks which generally are not sharing the same empirical design cross-task-wise. In this paper, we propose a cross-task neural architecture search (CTNAS-EEG) framework for EEG signal recognition, which can automatically design the network structure across tasks and improve the recognition accuracy of EEG signals. Specifically, a compatible search space for cross-task searching and an efficient constrained searching method is proposed to overcome challenges brought by EEG signals. By unifying structure search on different EEG tasks, this work is the first to explore and analyze the searched structure difference cross-task-wise. Moreover, by introducing architecture search, this work is the first to analyze model performance by customizing model structure for each human subject. Detailed experimental results suggest that the proposed CTNAS-EEG could reach state-of-the-art performance on different EEG tasks, such as Motor Imagery (MI) and Emotion recognition. Extensive experiments and detailed analysis are provided as a good reference for follow-up researchers.
[ 0.029237354174256325, -0.041314393281936646, -0.027685077860951424, -0.07225754112005234, 0.025638122111558914, 0.043668393045663834, 0.020060168579220772, 0.027616847306489944, -0.02998790331184864, -0.003264468163251877, 0.02234593592584133, -0.042269639670848846, -0.001420075655914843, -0.03246130794286728, 0.012426728382706642, 0.000755881133954972, 0.015326582826673985, -0.01156530063599348, 0.004814610816538334, -0.026542194187641144, 0.024802282452583313, -0.03198368474841118, 0.02372763119637966, -0.05847470834851265, 0.023642340674996376, 0.035071179270744324, 0.0404956117272377, 0.002161031123250723, -0.04646589979529381, 0.022755326703190804, 0.022516515105962753, 0.011642062105238438, -0.03155723586678505, -0.0012132477713748813, -0.05298204347491264, -0.051242128014564514, 0.006371150258928537, 0.06461557745933533, -0.018968457356095314, 0.003499015234410763, 0.06348975002765656, 0.039506249129772186, 0.0068274508230388165, -0.012409670278429985, -0.013109046965837479, -0.06154514104127884, -0.03848277032375336, -0.0531185045838356, 0.036640509963035583, 0.004631237592548132, 0.03896039351820946, -0.014251930639147758, 0.024188196286559105, 0.028077412396669388, 0.006140867713838816, 0.0186955314129591, 0.04332723468542099, 0.003283658530563116, 0.09491052478551865, 0.03217132389545441, 0.04530595615506172, 0.05656421557068825, -0.08399342745542526, -0.012844648212194443, 0.04748937860131264, -0.02464876137673855, 0.027480382472276688, -0.008703826926648617, 0.019429022446274757, -0.012699655257165432, -0.03899450972676277, 0.00593617232516408, -0.0662190243601799, -0.00760358851402998, -0.003925464581698179, -0.03636758401989937, 0.038721583783626556, 0.09538814425468445, 0.01514747366309166, 0.02939087525010109, 0.028520919382572174, 0.059702880680561066, 0.010661228559911251, 0.014857488684356213, 0.03991563990712166, -0.0100044971331954, -0.014286046847701073, -0.05902056396007538, -0.007590794935822487, -0.004228243138641119, -0.03449120745062828, 0.057007722556591034, 0.02277238480746746, 0.025024035945534706, -0.027190398424863815, 0.01229026447981596, 0.02193654514849186, 0.008750736713409424, -0.06649195402860641, 0.017637936398386955, 0.016674160957336426, 0.00913454033434391, -0.0390627421438694, -0.007607853040099144, 0.004503303207457066, 0.007727258373051882, -0.022687094286084175, 0.016844742000102997, -0.004140821285545826, 0.09634339064359665, -0.027258628979325294, 0.030909033492207527, -0.014644264243543148, 0.001444596447981894, -0.033621251583099365, -0.010712402872741222, -0.014465155079960823, -0.02272121049463749, -0.0029467635322362185, -0.01051623560488224, 0.03174487501382828, 0.061203982681035995, -0.02944204956293106, 0.03295598924160004, -0.061272215098142624, 0.07607852667570114, -0.004151482600718737, 0.018644357100129128, 0.03923332318663597, 0.07696554064750671, 0.027855658903717995, 0.02770213596522808, 0.05987346172332764, 0.0035907018464058638, 0.05837235972285271, 0.02788977511227131, -0.014678379520773888, 0.008571627549827099, 0.007403157185763121, -0.08249232172966003, -0.04175790026783943, 0.018968457356095314, -0.018064385280013084, -0.0013763646129518747, 0.03510529547929764, -0.013057872653007507, 0.009578048251569271, 0.058747634291648865, 0.01706649549305439, 0.011437365785241127, -0.05775827169418335, 0.0752597451210022, -0.030567875131964684, 0.014021648094058037, -0.010985329747200012, -0.018047327175736427, -0.004895636346191168, -0.017876747995615005, 0.027804484590888023, 0.003283658530563116, 0.08617684245109558, -0.037049900740385056, -0.02427348494529724, -0.011582358740270138, 0.05301615968346596, 0.01243525743484497, -0.016912972554564476, 0.002315618796274066, -0.06792481988668442, 0.052197374403476715, -0.009185714647173882, 0.0535961277782917, 0.02098129875957966, 0.053527895361185074, 0.015002480708062649, 0.005535310134291649, 0.05745122954249382, -0.059771113097667694, -0.0738268792629242, 0.009271004237234592, -0.05090096965432167, 0.015070713125169277, 0.07007412612438202, -0.005300763063132763, 0.026849238201975822, 0.011454423889517784, 0.045715346932411194, -0.013091988861560822, 0.05018453672528267, -0.057485345751047134, 0.026832180097699165, 0.008285907097160816, 0.07000589370727539, -0.03401358425617218, 0.054653722792863846, -0.051412709057331085, -0.00650761416181922, 0.007987392134964466, -0.019974878057837486, -0.012665539979934692, -0.03606054186820984, -0.02162950113415718, 0.026064572855830193, 0.025433426722884178, -0.05499488115310669, 0.022704152390360832, 0.03749340772628784, -0.01568480022251606, -0.0378686860203743, -0.05786062031984329, -0.03469590097665787, -0.004746378865092993, -0.040836770087480545, -0.0688459500670433, 0.0038359099999070168, -0.036333467811346054, 0.038619235157966614, -0.02193654514849186, -0.0010591930476948619, 0.03217132389545441, 0.0373910628259182, 0.02848680317401886, 0.06731073558330536, -0.02998790331184864, -0.01100238785147667, 0.03478119149804115, 0.04489656537771225, -0.019633719697594643, 0.0009675064939074218, -0.018405545502901077, -0.03343361243605614, -0.00895543210208416, 0.02956145443022251, -0.016622988507151604, 0.014234872534871101, -0.04772818833589554, 0.06140867620706558, -0.04957044869661331, 0.026832180097699165, -0.005151505582034588, -0.04424836486577988, -0.008729414083063602, -0.031813107430934906, -0.008742207661271095, 0.0681295171380043, -0.03101138211786747, -0.015190118923783302, 0.06799305230379105, 0.011335018090903759, 0.029953788965940475, -0.013509908691048622, 0.029544396325945854, 0.007138758897781372, 0.06021462008357048, 0.015454516746103764, 0.001731383497826755, 0.030312005430459976, -0.012281735427677631, 0.015838321298360825, -0.02476816624403, 0.04980926215648651, 0.004997984040528536, -0.04892224818468094, 0.006494820583611727, -0.04339546710252762, -0.010405358858406544, 0.06877771764993668, -0.005671773571521044, -0.025092268362641335, -0.07137052714824677, 0.027616847306489944, -0.041314393281936646, -0.035855844616889954, -0.02788977511227131, 0.024614645168185234, -0.016546227037906647, 0.04974102973937988, -0.039335668087005615, 0.011752938851714134, 0.03186428174376488, 0.0030640370678156614, 0.03660639375448227, 0.003840174525976181, -0.008605743758380413, -0.027685077860951424, 0.00005500527549884282, -0.008541776798665524, 0.016546227037906647, -0.03232484683394432, -0.008234732784330845, -0.002458479255437851, -0.019974878057837486, -0.03889216110110283, 0.02277238480746746, 0.047148216515779495, -0.04680705815553665, -0.021373631432652473, -0.06130633130669594, 0.046124741435050964, -0.017441770061850548, -0.022090066224336624, -0.01310051791369915, 0.013364916667342186, 0.07171168923377991, -0.07450919598340988, 0.014695437625050545, 0.015352169051766396, 0.06137455999851227, 0.020264863967895508, -0.04032503068447113, 0.010601526126265526, -0.019139038398861885, -0.01671680621802807, -0.009467171505093575, -0.026371615007519722, 0.05032099783420563, 0.06417206674814224, 0.007351983338594437, 0.0010250771883875132, -0.013160220347344875, -0.012358495965600014, -0.004648295696824789, -0.08508513122797012, 0.0635920986533165, -0.05458549037575722, -0.013168749399483204, 0.07198461890220642, 0.015582451596856117, 0.0039809029549360275, -0.011855286546051502, -0.01699826307594776, -0.003356154775246978, -0.03203485906124115, -0.027002759277820587, -0.03575349599123001, 0.03041435405611992, -0.041621435433626175, 0.02139068953692913, -0.04622708633542061, 0.007838135585188866, 0.0036141565069556236, 0.032000742852687836, -0.04701175540685654, 0.002486198442056775, -0.02098129875957966, 0.006281596142798662, -0.04755760729312897, 0.015659213066101074, -0.03222249820828438, -0.041860248893499374, 0.0009120681206695735, -0.0369134396314621, 0.04141674190759659, -0.02162950113415718, -0.02229476161301136, -0.038312193006277084, 0.012614365667104721, -0.0024627437815070152, 0.05605247616767883, 0.04151909053325653, -0.016495052725076675, -0.04363427683711052, -0.004558741580694914, -0.004614179953932762, -0.08296994864940643, -0.013569612056016922, -0.01814967580139637, -0.02710510790348053, -0.007258164696395397, 0.016136836260557175, -0.016793567687273026, 0.08604037761688232, 0.00005467211303766817, -0.002174890600144863, -0.027258628979325294, 0.030209656804800034, 0.01886611059308052, 0.017876747995615005, -0.01652063988149166, 0.054005518555641174, -0.004528889898210764, 0.00005560497083934024, -0.002980879507958889, 0.04018856957554817, 0.018797878175973892, 0.05356201156973839, 0.04213317483663559, -0.013356387615203857, -0.056939490139484406, 0.079080730676651, 0.006874360144138336, -0.06724250316619873, -0.05373259261250496, -0.0402567982673645, 0.051105666905641556, -0.029493223875761032, 0.024972861632704735, 0.015898024663329124, -0.00910042505711317, -0.012247619219124317, -0.03575349599123001, -0.04902459308505058, -0.015616567805409431, 0.0025629594456404448, -0.02962968684732914, -0.034405916929244995, -0.05983934551477432, 0.01049064937978983, 0.019974878057837486, 0.030004961416125298, -0.012034394778311253, -0.05697360634803772, -0.0025714882649481297, -0.01171882264316082, -0.004221846349537373, 0.01760382018983364, -0.02591104991734028, 0.017220016568899155, 0.06441088020801544, -0.040359146893024445, -0.08556275814771652, 0.014166641049087048, 0.046056509017944336, 0.000546921044588089, 0.01081475056707859, 0.02565518021583557, 0.0011418175417929888, -0.0050235711969435215, -0.024256426841020584, -0.014055764302611351, 0.007224048487842083, 0.020759545266628265, 0.02614986151456833, -0.02229476161301136, 0.006882889196276665, -0.01580420508980751, 0.00606837123632431, -0.002019236795604229, -0.03841453790664673, -0.04622708633542061, -0.03841453790664673, -0.011991750448942184, -0.041075583547353745, -0.05816766247153282, -0.0416896678507328, -0.01310051791369915, 0.005390317179262638, 0.03041435405611992, -0.0028209611773490906, -0.02727568708360195, -0.024256426841020584, 0.00013073331501800567, -0.050457462668418884, 0.0030427146703004837, 0.024546412751078606, 0.012068510986864567, 0.00015112292021512985, -0.03394535183906555, 0.024051731452345848, -0.01024330873042345, 0.050935085862874985, 0.024017615243792534, -0.00380179425701499, -0.06799305230379105, 0.004499038681387901, 0.028810905292630196, -0.0412120446562767, -0.05632540211081505, 0.010021555237472057, 0.03896039351820946, 0.035309989005327225, -0.029169121757149696, 0.055199578404426575, 0.0814688429236412, 0.013305213302373886, 0.028145642951130867, -0.024051731452345848, -0.03670874238014221, 0.021595384925603867, -0.023539993911981583, -0.03449120745062828, -0.029612628743052483, 0.040120337158441544, -0.011616474948823452, -0.015283937565982342, 0.00276339054107666, -0.026422789320349693, 0.015940669924020767, -0.02746332436800003, -0.02836739830672741, 0.04592004418373108, 0.012273206375539303, 0.04544242098927498, -0.023591166362166405, -0.022925905883312225, -0.045647118240594864, -0.03365536779165268, -0.03367242589592934, 0.054721955209970474, 0.014618677087128162, -0.024307601153850555, -0.004375368356704712, 0.0357193797826767, -0.010260366834700108, 0.017220016568899155, 0.017168842256069183, -0.007249635644257069, 0.04957044869661331, 0.0058679403737187386, -0.006315711885690689, 0.036026425659656525, -0.01983841508626938, 0.04080265387892723, -0.03467884659767151, 0.002737803617492318, 0.022550631314516068, -0.006119545083492994, -0.01295552495867014, 0.016674160957336426, -0.003867893712595105, 0.007096113637089729, -0.0016674161888659, 0.021680675446987152, 0.0129214096814394, -0.024137021973729134, -0.005232531111687422, 0.0190537478774786, 0.019309617578983307, 0.012153800576925278, -0.01833731308579445, -0.06754954159259796, -0.021168936043977737, 0.024171138182282448, -0.031881339848041534, 0.01481484342366457, -0.00690847635269165, 0.022090066224336624, -0.02319883368909359, -0.013091988861560822, -0.04213317483663559, -0.012409670278429985, 0.04742114618420601, 0.012094098143279552, -0.024017615243792534, -0.025569891557097435, 0.0059191142208874226, 0.020776603370904922, -0.04735291376709938, 0.03339949622750282, 0.048956360667943954, 0.016358589753508568, -0.007151552010327578, -0.04974102973937988, -0.019309617578983307, 0.0005255985888652503, -0.05373259261250496, -0.0066952514462172985, -0.02012839913368225, -0.008827497251331806, -0.02729274518787861, 0.00017337822646368295, 0.00910042505711317, 0.022994138300418854, -0.015957728028297424, -0.000021955467673251405, -0.001915822853334248, 0.014123995788395405, 0.03803926333785057, 0.03227367252111435, 0.024546412751078606, -0.009654808789491653, -0.00140514993108809, -0.008810439147055149, 0.0547901876270771, -0.0006194174056872725, 0.03575349599123001, 0.04523772746324539, -0.02867444045841694, 0.013083459809422493, 0.02162950113415718, 0.045715346932411194, 0.0006487357895821333, 0.027122166007757187, 0.04789876937866211, -0.017927922308444977, -0.021714789792895317, -0.034047700464725494, -0.029902614653110504, 0.002071476774290204, -0.045408304780721664, 0.017339423298835754, 0.02957851253449917, 0.001406216062605381, 0.006618490908294916, -0.013296684250235558, -0.0262010358273983, -0.01499395165592432, 0.029732035472989082, 0.06427441537380219, -0.04291784390807152, 0.04547653719782829, 0.04008622094988823, 0.015326582826673985, 0.03735694661736488, 0.007833871059119701, -0.014268988743424416, 0.013381973840296268, -0.00032996502704918385, -0.002746332436800003, 0.04803523048758507, 0.0036354789044708014, 0.0022068743128329515, 0.0357193797826767, -0.01043094601482153, 0.05107155069708824, 0.03130136802792549, 0.023898210376501083, -0.004605650901794434, -0.005377523601055145, -0.002957424847409129, 0.0260816290974617, 0.011735880747437477, 0.05533604323863983, -0.010115373879671097, 0.0132796261459589, 0.03588996082544327, -0.0027953742537647486, -0.0378686860203743, -0.007138758897781372, 0.027241570875048637, -0.03351890295743942, 0.013996060937643051, -0.027241570875048637, -0.013689017854630947, 0.019258443266153336, 0.017501473426818848, -0.010831808671355247, 0.0015053654788061976, -0.016205066815018654, 0.01699826307594776, -0.010959743522107601, 0.01924138516187668, -0.02951028198003769, 0.033689484000205994, 0.006567317061126232, 0.0069297985173761845, -0.02024780586361885, -0.01300669927150011, 0.06775423884391785, 0.0014541916316375136, 0.031284309923648834, 0.03606054186820984, 0.010456533171236515, 0.02817975915968418, -0.03484942391514778, -0.04622708633542061, -0.003737826831638813, 0.02710510790348053, -0.0030107309576123953, -0.03065316565334797, -0.02481934055685997, 0.005744270049035549, 0.027958005666732788, -0.010379772633314133, 0.044930681586265564, -0.036265235394239426, -0.012349966913461685, -0.005479871761053801, 0.012204974889755249, 0.06802716851234436, -0.012716713361442089, -0.036981672048568726, -0.04844462499022484, 0.02115187793970108, 0.011727351695299149, -0.02452935464680195, 0.02422231249511242, 0.061442792415618896, 0.018593182787299156, -0.04568123444914818, 0.001550142653286457, -0.013834010809659958, -0.0002667972585186362, -0.042815495282411575, 0.014379865489900112, -0.007684613578021526, -0.002422231249511242, 0.030926091596484184, -0.030022019520401955, -0.03469590097665787, 0.0002923842112068087, -0.006959650199860334, -0.016733864322304726, -0.026525137946009636, 0.02770213596522808, 0.03971094638109207, -0.035787612199783325, 0.023966442793607712, 0.06226157397031784, 0.004490509629249573, 0.000422717712353915, 0.03960859775543213, 0.016094190999865532, -0.023045312613248825, 0.01833731308579445, 0.03660639375448227, 0.02374468930065632, -0.038789816200733185, -0.061988648027181625, -0.0075694723054766655, -0.006963914725929499, -0.011804112233221531, 0.006887153722345829, 0.04247433692216873, 0.02788977511227131, 0.006823186296969652, 0.007381834555417299, 0.0195313710719347, -0.04435070976614952, 0.07416803389787674, -0.014132524840533733, 0.04370250925421715, 0.012384083122015, -0.05584777891635895, 0.00003728098454303108, 0.07457742840051651, 0.0024627437815070152, 0.0032260878942906857, -0.034474149346351624, -0.001994716003537178, -0.00749697582796216, -0.0058508822694420815, -0.03365536779165268, 0.021851254627108574, 0.006870095618069172, -0.02398350089788437, 0.015266879461705685, 0.025382254272699356, -0.020708370953798294, -0.038380421698093414, -0.030022019520401955, -0.022038891911506653, -0.019701950252056122, 0.013501379638910294, 0.021919487044215202, 0.02122011035680771, -0.029646744951605797, 0.009714511223137379, -0.03113078698515892, -0.0195313710719347, 0.03167664259672165, -0.035548802465200424, 0.047318797558546066, -0.04673882573843002, -0.043907202780246735, 0.02212418243288994, 0.007245371118187904, -0.04261079803109169, 0.020947182551026344, -0.003428651252761483, 0.016674160957336426, 0.02169773355126381, -0.005249589215964079, 0.05253853648900986, 0.011795583181083202, 0.031949568539857864, -0.01958254538476467, 0.03636758401989937, 0.009262475185096264, -0.008895729668438435, 0.025740470737218857, -0.007057733368128538, 0.08897434920072556, -0.012520547024905682, 0.0006732565816491842, 0.007514033932238817, 0.03125019371509552, 0.02265297807753086, 0.009450113400816917, 0.03971094638109207, -0.006899947300553322, 0.006754954345524311, 0.02487051486968994, 0.02855503559112549, -0.02103247120976448, -0.06471792608499527, -0.033024221658706665, -0.04424836486577988, -0.005740005522966385, 0.052265606820583344, 0.007829606533050537, -0.020691312849521637, 0.038073379546403885, 0.009211301803588867, 0.004993719514459372, 0.003110946621745825, -0.02055484987795353, 0.027787426486611366, -0.040052104741334915, 0.001120495144277811, 0.003473428310826421, 0.013467264361679554, -0.015258350409567356, -0.010038613341748714, 0.019872529432177544, -0.021663617342710495, -0.03426945209503174, 0.0547901876270771, -0.012580249458551407, -0.010695344768464565, 0.009987439028918743, -0.017893806099891663, 0.0061920415610075, -0.008550305850803852, 0.02782154269516468, 0.0009237954509444535, -0.04472598806023598, 0.0021034604869782925, 0.001379563007503748, -0.03370654210448265, -0.0258428193628788, -0.001562936115078628, -0.013262568973004818, 0.009450113400816917, -0.06147690862417221, -0.04441894218325615, 0.06570728123188019, 0.004194127395749092, 0.019736066460609436, -0.013407560996711254, -0.017220016568899155, 0.008213410153985023, -0.005471342708915472, 0.003605627454817295, -0.023352354764938354, 0.04830816015601158, 0.014627206139266491, -0.010371243581175804, 0.01211115624755621, 0.020588964223861694, 0.018354371190071106, 0.025689296424388885, -0.008767794817686081, -0.04254256561398506, -0.034098874777555466, 0.0003491552488412708, -0.003475560573861003, 0.008870142512023449, 0.002503256546333432, -0.031233135610818863, 0.03370654210448265, 0.0676518902182579, 0.030209656804800034, 0.011369134299457073, 0.014746611937880516, 0.009816859848797321, 0.012000279501080513, 0.021254224702715874, -0.015113357454538345, -0.043429579585790634, 0.014831901527941227, 0.022499457001686096, -0.0007409554091282189, 0.0036141565069556236, 0.004364707041531801, -0.014456626027822495, 0.012332909740507603, -0.024853456765413284, -0.023812919855117798, 0.0001760435407049954, 0.017569705843925476, 0.032120149582624435, -0.025501659139990807, -0.00009035391121869907, 0.00020642804156523198, -0.0020608154591172934, -0.039403900504112244, 0.004989454988390207, 0.002098129829391837, 0.007791225798428059, 0.0242905430495739, -0.009236888960003853, 0.04172378405928612, -0.023454703390598297, 0.0500139556825161, 0.027241570875048637, -0.016145365312695503, -0.01689591445028782, 0.007445801980793476, -0.041314393281936646, 0.008038566447794437, 0.029117947444319725, -0.0026802329812198877, -0.02650807984173298, 0.01850789226591587, 0.001157809398137033, 0.00919424369931221, -0.006942592095583677, 0.030482584610581398, 0.0514468252658844, -0.0015544071793556213, -0.035617031157016754, -0.015411872416734695, -0.023642340674996376, -0.01814967580139637, -0.01995781995356083, 0.021168936043977737, -0.02372763119637966, -0.0005751732969656587, -0.013629314489662647, -0.03745929151773453, -0.01432869117707014, -0.011309431865811348, 0.008213410153985023, 0.00967186689376831, 0.041860248893499374, 0.021066587418317795, -0.028282107785344124, 0.009927736595273018, -0.012477901764214039, 0.04551065340638161, 0.05154917389154434, -0.05919114127755165, 0.035071179270744324, -0.02007722668349743, -0.012691127136349678, -0.03851688653230667, -0.004878578241914511, -0.00904072169214487, -0.013390502892434597, -0.03725459799170494, 0.04325900226831436, 0.02843562886118889, 0.026218093931674957, 0.0185761246830225, -0.003285790793597698, -0.02512638457119465, -0.0064607048407197, -0.016119778156280518, 0.00728801591321826, 0.007667555473744869, 0.0077528455294668674, -0.003059772541746497, 0.061988648027181625, 0.005633393302559853, -0.039574481546878815, 0.023932326585054398, -0.028111528605222702, 0.007189932744950056, 0.004592857323586941, -0.012878764420747757, -0.005966023541986942, 0.011113264597952366, -0.012025865726172924, -0.028862077742815018, 0.005036364309489727, -0.01671680621802807, -0.0025629594456404448, -0.02650807984173298, -0.005522516556084156, -0.00606837123632431, -0.0035139410756528378, -0.020810717716813087, -0.01153971441090107, 0.01219644583761692, 0.0047719660215079784, -0.020333094522356987, -0.026286326348781586, -0.04400955140590668, 0.01598331332206726, 0.0025416368152946234, 0.0020416253246366978, -0.0036568015348166227, -0.018797878175973892, 0.026098687201738358, -0.018900226801633835, 0.0025586949195712805, 0.018252024427056313, 0.024137021973729134, -0.00495533924549818, -0.007688878104090691, -0.0013891580747440457, 0.0185761246830225, -0.06492261588573456, 0.010567409917712212, -0.012418199330568314, 0.006597168277949095, -0.01066975761204958, -0.09839034825563431, 0.0185761246830225, -0.030601991340517998, 0.012324380688369274, 0.03984740749001503, -0.003910538740456104, -0.04339546710252762, 0.002447818173095584, -0.003452105913311243, 0.004209053236991167, 0.04711410030722618, 0.004206920973956585, -0.000969638756942004, -0.01171882264316082, -0.01189793087542057, 0.04042737931013107, -0.006366885732859373, 0.019753124564886093, 0.04175790026783943, 0.013970473781228065, 0.005121654365211725, 0.009543932043015957, 0.020691312849521637, -0.005373259074985981, 0.012008807621896267, -0.011778525076806545, -0.010499178431928158, 0.022448282688856125, -0.022687094286084175, 0.04902459308505058, 0.0021322458051145077, -0.023301182314753532, 0.0033881384879350662, -0.00426875613629818, -0.003571511711925268, -0.051412709057331085 ]
To operate safely, an automated vehicle (AV) must anticipate how the environment around it will evolve. For that purpose, it is important to know which prediction models are most appropriate for every situation. Currently, assessment of prediction models is often performed over a set of trajectories without distinction of the type of movement they capture, resulting in the inability to determine the suitability of each model for different situations. In this work we illustrate how standardized evaluation methods result in wrong conclusions regarding a model's predictive capabilities, preventing a clear assessment of prediction models and potentially leading to dangerous on-road situations. We argue that following evaluation practices in safety assessment for AVs, assessment of prediction models should be performed in a scenario-based fashion. To encourage scenario-based assessment of prediction models and illustrate the dangers of improper assessment, we categorize trajectories of the Waymo Open Motion dataset according to the type of movement they capture. Next, three different models are thoroughly evaluated for different trajectory types and prediction horizons. Results show that common evaluation methods are insufficient and the assessment should be performed depending on the application in which the model will operate.
[ -0.028489504009485245, -0.0246164221316576, -0.035416364669799805, -0.0018527487991377711, -0.011209595948457718, 0.0054791090078651905, -0.03012811578810215, 0.015231643803417683, -0.07947268337011337, 0.008607367984950542, 0.05567556619644165, 0.012969241477549076, 0.0006488112267106771, -0.03992254659533501, -0.05504246801137924, 0.03657083958387375, 0.011107182130217552, -0.019328173249959946, -0.018723003566265106, -0.04647699370980263, -0.021283335983753204, -0.026143310591578484, -0.04893491417169571, 0.048525258898735046, 0.004203598480671644, 0.01417026948183775, 0.04081633687019348, -0.005157903768122196, -0.07492925971746445, 0.05046180263161659, 0.04800388216972351, 0.02759571559727192, -0.006331000942736864, -0.015957847237586975, -0.026217792183160782, 0.0019982222001999617, 0.043460458517074585, 0.04990318417549133, -0.053478337824344635, 0.032139141112565994, 0.009738569147884846, -0.022586775943636894, 0.012792346067726612, -0.029159845784306526, -0.029588118195533752, -0.0010817399015650153, -0.040741853415966034, 0.01957024075090885, -0.023238496854901314, 0.009943395853042603, -0.04435424879193306, -0.05448384955525398, 0.03469016030430794, -0.03703635558485985, -0.01699128933250904, 0.009040297009050846, 0.009757190011441708, -0.006331000942736864, 0.034671541303396225, 0.02441159449517727, 0.007769441697746515, 0.006680137012153864, -0.06982721388339996, -0.00947322603315115, -0.014849921688437462, -0.027092959731817245, 0.04245494678616524, -0.015417849645018578, -0.027930885553359985, -0.0028605882544070482, -0.058431413024663925, 0.014058546163141727, -0.014794059097766876, -0.008993745781481266, 0.009342881850898266, -0.008760987780988216, 0.05429764464497566, 0.07738717645406723, -0.002741882111877203, 0.039624616503715515, 0.004229201935231686, 0.03496947139501572, -0.060032784938812256, -0.002462573116645217, 0.05128110572695732, -0.0218978151679039, 0.007881165482103825, -0.059287961572408676, 0.028768813237547874, -0.029122604057192802, -0.02470952458679676, 0.02338746190071106, 0.003286534221842885, 0.027670199051499367, -0.012494416907429695, 0.020333684980869293, 0.013118206523358822, 0.005730486940592527, -0.023741252720355988, -0.008691160939633846, 0.03899151831865311, 0.02113437093794346, 0.055265914648771286, 0.03528602048754692, 0.03407568112015724, -0.08908090740442276, -0.044019076973199844, 0.07131686061620712, 0.004301356617361307, 0.15983915328979492, 0.024486077949404716, 0.009673397056758404, 0.014337855391204357, -0.050945937633514404, -0.06986445933580399, 0.01061373669654131, -0.033349476754665375, -0.06844929605722427, 0.0703485906124115, -0.015976466238498688, 0.0088913319632411, 0.04185909032821655, 0.04171012341976166, -0.004441010765731335, -0.03707359731197357, 0.015427160076797009, 0.040183234959840775, 0.00004891541902907193, -0.020277824252843857, -0.045434240251779556, 0.08148370683193207, 0.02629227377474308, -0.00422454671934247, 0.011591318063437939, 0.007950992323458195, -0.03632877394556999, -0.0005976046086288989, 0.01994265243411064, -0.00992477498948574, 0.002277530962601304, -0.017633698880672455, -0.05023835599422455, -0.063682422041893, 0.002602227497845888, -0.022326089441776276, -0.008481679484248161, 0.0503128357231617, 0.06632654368877411, -0.05053628236055374, -0.010930286720395088, -0.0025184350088238716, -0.011377180926501751, 0.010464772582054138, 0.052919719368219376, 0.05828244984149933, 0.00040179744246415794, -0.0649113804101944, 0.011470284312963486, -0.026552962139248848, -0.036366015672683716, 0.05671831965446472, -0.05370178446173668, -0.015818191692233086, 0.039736341685056686, 0.0282660573720932, -0.005427902098745108, 0.06774170696735382, -0.03722256049513817, -0.05444660782814026, 0.02854536660015583, -0.014291303232312202, 0.00603307131677866, -0.02517503872513771, 0.009370812214910984, 0.03940116986632347, 0.026981236413121223, 0.010976837947964668, 0.05530315637588501, -0.04744526743888855, 0.046179067343473434, -0.05858037993311882, -0.005618763156235218, 0.0004954822943545878, -0.03154328092932701, 0.07511546462774277, -0.002083178609609604, 0.06774170696735382, 0.03221362084150314, 0.04368390515446663, 0.01268062274903059, 0.05485625937581062, 0.02236332930624485, 0.054781779646873474, -0.010474082082509995, 0.014943024143576622, 0.0017643009778112173, -0.04096530005335808, -0.03208327665925026, -0.019607482478022575, -0.0026930030435323715, -0.0246909037232399, -0.038693588227033615, 0.01729852892458439, 0.04994042590260506, 0.01525026373565197, 0.03398257866501808, 0.02105988748371601, 0.032530173659324646, 0.03031432256102562, -0.08893194049596786, -0.015408539213240147, -0.03413154184818268, -0.03301430866122246, 0.004415407776832581, -0.01099545881152153, -0.013118206523358822, -0.014198200777173042, 0.02919708751142025, 0.009757190011441708, -0.052063170820474625, 0.030388804152607918, 0.018210938200354576, -0.02115299180150032, 0.020631615072488785, -0.04696112871170044, 0.010055119171738625, 0.026161929592490196, 0.046923890709877014, -0.04539700224995613, -0.03182258829474449, 0.027260545641183853, -0.015939226374030113, -0.0030305010732263327, -0.017400942742824554, 0.031226731836795807, 0.032790862023830414, 0.04044392332434654, -0.02619917131960392, -0.030723975971341133, -0.005302213132381439, 0.012540968134999275, -0.044875625520944595, -0.0004218727699480951, -0.054781779646873474, 0.034746021032333374, 0.037762559950351715, -0.022475052624940872, 0.032809481024742126, 0.0038870484568178654, 0.03528602048754692, -0.02413228526711464, -0.03366602957248688, -0.09332640469074249, 0.016823703423142433, 0.026515722274780273, 0.03301430866122246, 0.02161850593984127, 0.02113437093794346, 0.0008902970002964139, -0.011954419314861298, 0.06729481369256973, 0.07258306443691254, -0.04755698889493942, 0.08915539085865021, -0.01694473810493946, 0.0175499077886343, 0.08096233010292053, 0.008267542347311974, 0.02994191087782383, -0.04033220186829567, -0.04696112871170044, -0.037576351314783096, 0.0241509061306715, -0.019626103341579437, 0.006964100990444422, -0.005232386291027069, 0.03312603011727333, -0.028657089918851852, 0.044577695429325104, 0.020538512617349625, -0.022772982716560364, -0.04051840677857399, 0.020910924300551414, 0.0020331358537077904, -0.04435424879193306, -0.06178312003612518, -0.0005484346183948219, -0.005386006087064743, -0.02236332930624485, 0.004813422914594412, 0.0014163287123665214, -0.03405706211924553, -0.06081485003232956, 0.018257489427924156, -0.010958218015730381, 0.028955018147826195, -0.014700956642627716, -0.002404383849352598, 0.010092359967529774, -0.06129898503422737, -0.008598057553172112, 0.018909210339188576, 0.0503128357231617, 0.028135713189840317, 0.027856403961777687, -0.0205757524818182, 0.026403997093439102, 0.006191346328705549, -0.04293908178806305, -0.03651497885584831, 0.00002805817530315835, -0.0018376195803284645, -0.006074967794120312, -0.02001713588833809, 0.024169526994228363, 0.020054375752806664, -0.014645094983279705, -0.006056347396224737, -0.05764934793114662, 0.008895987644791603, 0.007280651014298201, -0.02424400858581066, -0.0565321147441864, -0.025100557133555412, -0.014244752004742622, 0.014328544959425926, -0.015520262531936169, -0.023741252720355988, -0.06859825551509857, 0.028098471462726593, -0.017540596425533295, -0.019328173249959946, -0.07515270262956619, -0.005251006688922644, 0.021786091849207878, 0.03608670458197594, -0.028843294829130173, 0.030146736651659012, -0.019868170842528343, -0.03329361602663994, -0.003132914425805211, 0.013555790297687054, -0.04528527706861496, 0.04077909514307976, -0.013583720661699772, -0.05802176147699356, 0.026832271367311478, 0.034001197665929794, 0.011051320470869541, -0.0009694345062598586, 0.0010380978928878903, -0.019905412569642067, -0.03519291803240776, 0.013835099525749683, 0.012987862341105938, 0.03351706266403198, -0.015026817098259926, -0.027018478140234947, 0.00842581782490015, -0.008360645733773708, 0.00003589555490179919, -0.05791003629565239, -0.05578729137778282, 0.010306497104465961, -0.022493673488497734, 0.026832271367311478, -0.03394533693790436, -0.008020819164812565, 0.03740876913070679, -0.02020334079861641, -0.00874236784875393, 0.05183972418308258, 0.048599742352962494, -0.011898557655513287, -0.033535685390233994, 0.025752278044819832, -0.0196447242051363, -0.027856403961777687, -0.0184809360653162, 0.03534188121557236, -0.043832872062921524, 0.0074528916738927364, -0.007802027743309736, -0.0020517564844340086, -0.05783555656671524, 0.05210041254758835, 0.03733428567647934, 0.024579180404543877, 0.009906154125928879, 0.04204529523849487, 0.017373010516166687, -0.0029676565900444984, -0.032790862023830414, -0.01813645474612713, 0.03910323977470398, 0.01515716128051281, 0.053850747644901276, -0.05548936128616333, 0.006987376604229212, -0.002881536493077874, -0.011842695996165276, 0.011861316859722137, 0.022791603580117226, 0.04025771841406822, -0.019067484885454178, 0.026255033910274506, 0.0026068827137351036, -0.019532999023795128, 0.018965071067214012, 0.01234545186161995, -0.018313352018594742, 0.012959931045770645, -0.03349844366312027, 0.017373010516166687, 0.01927231252193451, 0.005842210259288549, 0.002180936746299267, 0.024765385314822197, -0.04789216071367264, 0.005926003213971853, -0.0341687835752964, 0.016171982511878014, 0.07213617116212845, -0.006303070113062859, -0.013444066978991032, 0.032325346022844315, -0.05321764945983887, 0.005251006688922644, -0.04595561698079109, -0.026813650503754616, 0.05228662118315697, -0.03228810429573059, 0.06576792895793915, -0.06148518994450569, 0.04077909514307976, 0.032623276114463806, 0.007909095846116543, 0.008621333166956902, 0.003949892707169056, -0.048301812261343, -0.04319977015256882, -0.012531657703220844, 0.006144795101135969, 0.01889989897608757, 0.013509239070117474, -0.032232243567705154, 0.01624646596610546, -0.053478337824344635, -0.035714294761419296, -0.021953675895929337, -0.04063012823462486, 0.08133473992347717, -0.023722633719444275, -0.025510210543870926, 0.013155447319149971, -0.01675853133201599, 0.0014268028317019343, -0.05615970119833946, 0.027353648096323013, -0.025789517909288406, 0.0102878762409091, 0.03301430866122246, 0.03217638283967972, -0.009282364509999752, 0.04893491417169571, 0.006689447443932295, -0.04368390515446663, -0.024635041132569313, -0.012699242681264877, 0.008700471371412277, -0.005427902098745108, -0.040555648505687714, -0.03806048631668091, 0.010064429603517056, 0.027465371415019035, -0.006703412625938654, -0.040294960141181946, 0.002199557377025485, -0.010492702946066856, -0.037576351314783096, 0.031561899930238724, 0.05362730100750923, 0.05392523109912872, -0.01192648895084858, 0.021078508347272873, 0.015976466238498688, 0.018648521974682808, -0.011879936791956425, -0.056196942925453186, -0.032604653388261795, -0.03426188603043556, -0.04792940244078636, 0.010380979627370834, -0.009319606237113476, -0.024951592087745667, 0.012997172772884369, 0.012550278566777706, 0.028675710782408714, 0.04044392332434654, 0.027856403961777687, 0.012168556451797485, -0.02040816843509674, 0.0016467585228383541, -0.014645094983279705, 0.0066428957507014275, 0.016004398465156555, 0.011135113425552845, -0.02066885679960251, 0.0019388690125197172, -0.01449612993746996, 0.022139882668852806, -0.011963729746639729, 0.004089547321200371, -0.009738569147884846, 0.045508723706007004, 0.0016095173778012395, 0.022791603580117226, -0.001529216067865491, 0.0047459229826927185, 0.005199800245463848, -0.006363586988300085, 0.03666394203901291, -0.022437812760472298, 0.03442947193980217, 0.0081930598244071, 0.04681216552853584, 0.02854536660015583, -0.03725980222225189, 0.019346794113516808, -0.01687956601381302, -0.006237898021936417, 0.010166842490434647, -0.07932371646165848, -0.06762998551130295, 0.008695815689861774, -0.033461201936006546, -0.04152391850948334, 0.029215706512331963, -0.02478400617837906, -0.017382321879267693, -0.021357817575335503, 0.006782550364732742, 0.026217792183160782, -0.0024788661394268274, 0.005730486940592527, 0.02824743650853634, 0.01449612993746996, -0.04156116023659706, 0.01198235061019659, -0.02582675963640213, 0.006908239331096411, 0.012373383156955242, 0.02685089223086834, 0.03969909995794296, -0.051243867725133896, 0.01829473115503788, -0.025324003770947456, -0.0430135652422905, 0.019998515024781227, -0.014887162484228611, -0.007932371459901333, -0.035621192306280136, -0.017540596425533295, 0.03567705303430557, 0.007964957505464554, -0.010557875037193298, 0.001149821444414556, 0.0484507791697979, -0.016516463831067085, 0.060032784938812256, -0.04375838860869408, -0.02899225987493992, -0.04226874187588692, -0.023722633719444275, 0.03428050875663757, -0.022326089441776276, 0.003740411251783371, -0.05504246801137924, -0.038581863045692444, 0.019719205796718597, -0.015790261328220367, 0.030723975971341133, 0.009235813282430172, 0.044503211975097656, -0.021469540894031525, 0.003901013871654868, -0.03936392813920975, -0.040369439870119095, 0.012838897295296192, -0.011088562197983265, -0.0015350349713116884, 0.07124238461256027, -0.0008053405326791108, -0.009184606373310089, -0.04223150014877319, -0.04442872852087021, -0.018397143110632896, -0.0021658074110746384, -0.022977808490395546, -0.028694329783320427, 0.02515641786158085, 0.02310815267264843, 0.007243409752845764, 0.06416655331850052, 0.012568898499011993, 0.016330258920788765, 0.0024649007245898247, 0.015306125394999981, -0.040369439870119095, -0.004268770571798086, 0.015594745054841042, -0.043088048696517944, 0.00273489928804338, 0.00006397191464202479, 0.022381950169801712, 0.011898557655513287, 0.010883735492825508, 0.02113437093794346, -0.01713094301521778, 0.0024788661394268274, 0.012894758954644203, 0.0055768671445548534, 0.0610382966697216, 0.009030986577272415, -0.009813051670789719, 0.04353494197130203, 0.04200805351138115, 0.008649264462292194, -0.019141968339681625, -0.01348130777478218, -0.03070535510778427, 0.000427982653491199, -0.007918406277894974, -0.020892303436994553, -0.00806737132370472, 0.023722633719444275, 0.0016130086733028293, 0.024001941084861755, -0.00809995736926794, -0.010706840083003044, 0.0019330501090735197, -0.016097500920295715, -0.0034448092337697744, 0.060963813215494156, 0.0012196487514302135, 0.03247430920600891, -0.03117086924612522, -0.009515121579170227, 0.04305080696940422, 0.0018457660917192698, 0.015743710100650787, 0.063682422041893, -0.019886791706085205, 0.044950105249881744, -0.007336512673646212, -0.01034373790025711, 0.027186062186956406, 0.002713951049372554, 0.03256741538643837, 0.01973782666027546, 0.007220134139060974, 0.012987862341105938, 0.0016281378921121359, -0.009654776193201542, 0.018006110563874245, 0.028303299099206924, 0.030723975971341133, -0.03677566722035408, -0.04886043071746826, 0.053664542734622955, 0.016870254650712013, -0.03640325367450714, -0.03482050448656082, 0.022772982716560364, 0.024169526994228363, 0.008630643598735332, -0.017913008108735085, 0.04919560253620148, 0.03707359731197357, 0.008872712031006813, 0.025696415454149246, 0.044130802154541016, -0.02031506411731243, 0.06889618933200836, -0.05437212437391281, -0.016777152195572853, 0.0024020562414079905, -0.0047575607895851135, -0.002658089390024543, -0.02489572949707508, -0.012540968134999275, -0.0028675710782408714, -0.01905817538499832, 0.02105988748371601, 0.04994042590260506, -0.04424252361059189, -0.007057203911244869, -0.045806653797626495, 0.01701921969652176, 0.02377849444746971, -0.010809252969920635, 0.025789517909288406, -0.050499044358730316, 0.0044363560155034065, 0.013993374072015285, -0.02161850593984127, 0.005884106736630201, 0.01515716128051281, -0.02619917131960392, -0.029439155012369156, -0.007792717311531305, 0.0343177504837513, -0.028861915692687035, 0.0088913319632411, 0.06744378060102463, 0.0005181761225685477, -0.0026627446059137583, 0.03629153221845627, -0.06301207840442657, 0.011060630902647972, -0.011861316859722137, -0.0027721405494958162, 0.03344258293509483, -0.04941904917359352, -0.04126323014497757, 0.017633698880672455, -0.0038335141725838184, -0.014207511208951473, -0.04319977015256882, 0.011172354221343994, 0.057872798293828964, -0.05939968675374985, 0.03647773712873459, 0.015110609121620655, 0.013630272820591927, -0.016563015058636665, 0.003284206846728921, 0.005548936314880848, -0.02366677112877369, -0.023927459493279457, 0.01739163137972355, -0.04867422580718994, 0.01720542646944523, -0.007280651014298201, -0.009082193486392498, 0.028098471462726593, 0.003284206846728921, 0.01632094755768776, -0.013863029889762402, 0.015361987985670567, 0.07783406972885132, -0.034671541303396225, 0.04245494678616524, -0.027912266552448273, -0.05306868255138397, 0.01671198010444641, 0.0025207626167684793, -0.01624646596610546, -0.014859231188893318, -0.01908610574901104, -0.0065125515684485435, 0.02936467155814171, 0.011405112221837044, 0.012000970542430878, 0.048227328807115555, -0.012177866883575916, -0.03212051838636398, -0.005102042108774185, 0.01305303443223238, 0.007867199368774891, 0.0011137441033497453, 0.00442239036783576, 0.03361016511917114, -0.008048750460147858, -0.014812679961323738, 0.014933713711798191, 0.03666394203901291, -0.041486676782369614, 0.003102655988186598, 0.001984256785362959, -0.03396395966410637, -0.024206768721342087, 0.01417957991361618, 0.06081485003232956, -0.03219500184059143, 0.04390735179185867, -0.006428759079426527, -0.026143310591578484, 0.00885874591767788, -0.0191047266125679, -0.011805454269051552, -0.009338226169347763, 0.02638537809252739, -0.013108896091580391, 0.027353648096323013, -0.031133627519011497, -0.05359005928039551, -0.02273574098944664, -0.022028159350156784, -0.017466114833950996, -0.004976353142410517, -0.012792346067726612, -0.0006930351373739541, -0.005111352074891329, -0.004515493288636208, -0.010790632106363773, -0.014375096186995506, -0.03614256531000137, -0.012922690249979496, 0.03312603011727333, -0.003535584779456258, -0.009435984306037426, -0.01198235061019659, -0.007601856254041195, 0.010222704149782658, -0.007815993390977383, -0.00674065388739109, 0.014719577506184578, -0.018871968612074852, -0.0027907611802220345, 0.01908610574901104, -0.06033071503043175, -0.01862059161067009, -0.026999857276678085, -0.04014599323272705, -0.06252794712781906, 0.01652577519416809, 0.02085506170988083, 0.043646663427352905, -0.01715887524187565, -0.004699371755123138, 0.027186062186956406, -0.048897672444581985, 0.024448836222290993, -0.029215706512331963, 0.0013942167861387134, -0.004617906641215086, -0.022102640941739082, -0.009617535397410393, 0.02424400858581066, 0.020277824252843857, 0.00025079608894884586, 0.01722404733300209, -0.014645094983279705, 0.009328915737569332, -0.029979150742292404, -0.016581635922193527, -0.004336270038038492, -0.001745680347084999, 0.013211308978497982, 0.05135558918118477, -0.005967899225652218, 0.03750187158584595, 0.007303926628082991, -0.02787502482533455, 0.019681964069604874, -0.00370782520622015, 0.027297785505652428, -0.01385371945798397, -0.02798674814403057, 0.0045131659135222435, -0.010036498308181763, 0.019197829067707062, -0.008588748052716255, 0.04077909514307976, 0.021004026755690575, -0.00585152069106698, -0.06870998442173004, -0.03899151831865311, -0.08140922337770462, 0.000439038616605103, 0.030202599242329597, -0.016395431011915207, 0.040555648505687714, 0.02733502723276615, 0.03992254659533501, 0.006777895148843527, -0.015818191692233086, 0.055265914648771286, -0.0400715135037899, 0.05597349628806114, 0.018173696473240852, 0.014477509073913097, -0.00015812955098226666, 0.029588118195533752, -0.004068599082529545, -0.004915835801512003, -0.04189632833003998, -0.029811566695570946, -0.031785350292921066, -0.002774468157440424, -0.022772982716560364, -0.03273499757051468, -0.009226502850651741, 0.026180550456047058, 0.015883363783359528, -0.023983322083950043, 0.0010718477424234152, -0.009766499511897564, 0.03444809466600418, 0.019495759159326553, 0.016842324286699295, -0.06506034731864929, -0.010744080878794193, -0.004380493890494108, 0.009999257512390614, 0.014263372868299484, 0.012140625156462193, 0.021469540894031525, 0.007401684764772654, -0.009398743510246277, -0.05046180263161659, 0.008220991119742393, -0.004934456665068865, 0.06792791932821274, 0.0055768671445548534, -0.023815736174583435, -0.007704269606620073, 0.01132131926715374, -0.01787576824426651, 0.0055023846216499805, 0.007997543551027775, -0.022214364260435104, 0.024951592087745667, -0.03631015121936798, -0.027651578187942505, -0.017186805605888367, -0.021786091849207878, -0.002037790836766362, -0.0074156504124403, -0.016330258920788765, 0.033349476754665375, 0.02591986209154129, -0.02696261554956436, 0.036254290491342545, 0.0029024847317487, 0.025044694542884827, -0.010073740035295486, -0.012559588998556137, -0.019020933657884598, -0.00040237934445030987, -0.011684420518577099, -0.009412708692252636, 0.0318412110209465, -0.0073877195827662945, -0.022959189489483833, 0.05306868255138397, 0.021786091849207878, -0.0005251588299870491, 0.014468199573457241, -0.02068747580051422, -0.022605396807193756, 0.0116099389269948, -0.015296815894544125, -0.05567556619644165, 0.061447951942682266, -0.015790261328220367, -0.03050052747130394, -0.0081139225512743, 0.06308656185865402, -0.016777152195572853, 0.002946708584204316, -0.05228662118315697, 0.003970840945839882, -0.026981236413121223, 0.005674625281244516, -0.0161533635109663, 0.011190975084900856, -0.06882170587778091, -0.007220134139060974, -0.02452331781387329, -0.05895278975367546, 0.042343225330114365, 0.008579437620937824, -0.007871855050325394, 0.00704323872923851, 0.01034373790025711, -0.06085209175944328, -0.016581635922193527, -0.01905817538499832, 0.025603312999010086, -0.015222333371639252, 0.002599900122731924, -0.03331223875284195, 0.013118206523358822, -0.007867199368774891, -0.015566813759505749, -0.028396401554346085, 0.0033354132901877165, 0.04640251398086548, 0.0378929041326046, 0.0161533635109663, 0.02515641786158085, -0.01197304017841816, -0.044875625520944595, 0.0016839996678754687, 0.004420062992721796, 0.03668256476521492, 0.030947422608733177, 0.004720319993793964, -0.04439149051904678, -0.005451178178191185, -0.041486676782369614, 0.0411515049636364, 0.008337369188666344, -0.003081707749515772, 0.06699688732624054, 0.01170304138213396, 0.004068599082529545, -0.02208402007818222, -0.009235813282430172, -0.02152540348470211, -0.037762559950351715, 0.011312008835375309, -0.0241509061306715, 0.004571354947984219, -0.049456290900707245, 0.03487636521458626, 0.03470878303050995, -0.059287961572408676, 0.021488161757588387, -0.02659020386636257, 0.013546479865908623, -0.019905412569642067 ]
The utilization of broad datasets has proven to be crucial for generalization for a wide range of fields. However, how to effectively make use of diverse multi-task data for novel downstream tasks still remains a grand challenge in robotics. To tackle this challenge, we introduce a framework that acquires goal-conditioned policies for unseen temporally extended tasks via offline reinforcement learning on broad data, in combination with online fine-tuning guided by subgoals in learned lossy representation space. When faced with a novel task goal, the framework uses an affordance model to plan a sequence of lossy representations as subgoals that decomposes the original task into easier problems. Learned from the broad data, the lossy representation emphasizes task-relevant information about states and goals while abstracting away redundant contexts that hinder generalization. It thus enables subgoal planning for unseen tasks, provides a compact input to the policy, and facilitates reward shaping during fine-tuning. We show that our framework can be pre-trained on large-scale datasets of robot experiences from prior work and efficiently fine-tuned for novel tasks, entirely from visual inputs without any manual reward engineering.
[ 0.017194503918290138, -0.016546448692679405, -0.024491436779499054, -0.0486462228000164, 0.04999282956123352, 0.0065647149458527565, -0.02824510633945465, 0.03470882773399353, -0.10321751981973648, 0.00587037019431591, 0.003858874086290598, -0.05211373791098595, 0.02577071450650692, -0.03139280527830124, -0.013171511702239513, 0.010983273386955261, 0.005020323675125837, 0.02984420396387577, 0.03477615863084793, -0.03696439415216446, 0.048747215420007706, -0.016319207847118378, -0.022926004603505135, -0.005609464831650257, 0.015124093741178513, 0.015469161793589592, 0.02263985015451908, -0.007099150214344263, -0.06012605503201485, 0.04103788360953331, 0.02326265722513199, 0.021091250702738762, 0.005213898606598377, 0.038176342844963074, -0.05985673516988754, 0.0056894198060035706, 0.03457416594028473, 0.019105004146695137, -0.030281852930784225, 0.06130433827638626, -0.012750696390867233, 0.011631328612565994, -0.056961528956890106, -0.026309357956051826, -0.004822540562599897, -0.058442797511816025, -0.010141642764210701, 0.005399057175964117, -0.004029304254800081, -0.015166174620389938, -0.022084373980760574, -0.03948928415775299, 0.033362217247486115, -0.009013858623802662, -0.0038357293233275414, 0.03858032450079918, 0.07702598720788956, -0.010554041713476181, 0.04995916411280632, 0.036728739738464355, -0.016293959692120552, -0.010385715402662754, -0.011572414077818394, 0.006181773263961077, 0.028110446408391, -0.07870925217866898, 0.05403265357017517, -0.01925649680197239, 0.0140720559284091, 0.002588012721389532, -0.013087348081171513, -0.024525102227926254, -0.045616354793310165, -0.00029141444247215986, 0.029473887756466866, 0.015031513758003712, 0.057634830474853516, -0.023935960605740547, 0.026848001405596733, -0.03460783138871193, -0.0057230847887694836, 0.017270250245928764, -0.012775945477187634, 0.007902907207608223, 0.06012605503201485, -0.042451824992895126, 0.019054505974054337, -0.03844566270709038, 0.05231573060154915, -0.03726738318800926, -0.026376688852906227, 0.03615643084049225, -0.025198405608534813, -0.0002434152120258659, -0.022134872153401375, 0.0034843487665057182, -0.04103788360953331, 0.017977219074964523, -0.04888187721371651, -0.03134230524301529, 0.021293241530656815, 0.010848612524569035, -0.012616035528481007, -0.025636054575443268, 0.009114854037761688, -0.026915332302451134, -0.015107261016964912, -0.031729456037282944, -0.01293585542589426, 0.09439723193645477, 0.009956484660506248, 0.005226523149758577, -0.031931448727846146, 0.06928299367427826, -0.03528113663196564, -0.0012308841105550528, -0.007587295491248369, -0.08369170129299164, 0.0648728534579277, -0.03800801560282707, 0.03773869574069977, 0.00921585038304329, 0.03405235335230827, -0.06325691938400269, -0.02750447206199169, 0.046154994517564774, -0.025636054575443268, 0.011934314854443073, 0.02657867968082428, 0.060732029378414154, -0.005571591667830944, 0.008904446847736835, -0.004995074588805437, 0.04746793955564499, 0.043865762650966644, 0.02346464805305004, -0.014274046756327152, 0.007149647921323776, -0.05453763157129288, -0.037570368498563766, 0.014408707618713379, -0.022724013775587082, -0.024760758504271507, 0.010074312798678875, 0.05096912011504173, 0.027218317613005638, -0.013920562341809273, 0.06961964070796967, -0.011227346025407314, 0.040835894644260406, -0.03528113663196564, 0.06834036856889725, -0.034271180629730225, 0.003307606326416135, 0.027807459235191345, 0.03366520628333092, -0.03364837169647217, 0.034187015146017075, 0.03713272139430046, -0.02565288543701172, 0.08584627509117126, -0.021461568772792816, 0.019172335043549538, 0.09130003303289413, 0.1129131019115448, 0.03763769939541817, 0.06514216959476471, -0.002970954403281212, -0.01696726307272911, 0.03709905594587326, -0.03443950414657593, -0.021596228703856468, 0.026090534403920174, 0.07015828788280487, 0.04723228141665459, 0.008736120536923409, 0.025181572884321213, 0.024508269503712654, -0.04995916411280632, -0.01052037626504898, -0.04278847575187683, -0.0243062786757946, 0.027588635683059692, 0.05460496246814728, 0.009914402849972248, 0.07978653907775879, 0.04251915588974953, -0.010368883609771729, 0.04140820354223251, -0.06877801567316055, -0.014972600154578686, 0.02742031030356884, 0.034944482147693634, -0.01254028920084238, 0.029608547687530518, -0.064637191593647, -0.08355703949928284, 0.01779206097126007, 0.002421790733933449, 0.027807459235191345, -0.04918486624956131, -0.051238443702459335, 0.017893057316541672, 0.03568511828780174, -0.005777790676802397, 0.004641590174287558, 0.012582370080053806, 0.012961103580892086, 0.02341414988040924, -0.06803738325834274, -0.002928872825577855, -0.03395136073231697, -0.06275194138288498, -0.02981053851544857, -0.027100490406155586, -0.012220469303429127, -0.019929802045226097, 0.0140888886526227, -0.03642575070261955, -0.01683260314166546, -0.00800390262156725, 0.005163400899618864, -0.0005801987717859447, 0.013095764443278313, 0.018414868041872978, 0.03068583458662033, 0.03787335753440857, -0.0002623518812470138, 0.01785939186811447, -0.004814124200493097, -0.011631328612565994, 0.004073489923030138, 0.04376476630568504, -0.0322849303483963, 0.010368883609771729, 0.004965617787092924, 0.020670436322689056, -0.0012172075221315026, -0.0076167527586221695, -0.015671152621507645, 0.039017971605062485, 0.004448015242815018, -0.01638653874397278, -0.027201484888792038, 0.05453763157129288, 0.0483768992125988, 0.008365803398191929, 0.058476462960243225, 0.03726738318800926, 0.038176342844963074, -0.03413651883602142, 0.001991507364436984, -0.02575388178229332, 0.037536703050136566, 0.005420098081231117, -0.004277585074305534, 0.023767635226249695, -0.01254028920084238, -0.006164940539747477, -0.026797503232955933, 0.009502003900706768, 0.05016115680336952, -0.0005023480043746531, 0.04117254540324211, 0.005937700625509024, 0.001333983731456101, 0.03928729519248009, -0.005394848994910717, 0.017893057316541672, 0.03783969208598137, -0.02174772322177887, 0.01525033824145794, -0.01858319342136383, 0.007591503672301769, -0.007094942033290863, -0.058409132063388824, 0.05288803577423096, -0.02097342349588871, 0.021091250702738762, 0.05022848770022392, 0.024693427607417107, -0.03134230524301529, 0.019811972975730896, 0.014610699377954006, -0.01660536229610443, -0.015216672793030739, 0.03142647072672844, -0.0009152727434411645, -0.07796861231327057, 0.007940780371427536, -0.005125527270138264, 0.0005157614359632134, -0.0483432337641716, 0.0121447229757905, 0.024659762158989906, -0.013415584340691566, -0.026124199852347374, -0.00703181978315115, 0.012750696390867233, 0.0006712000467814505, -0.030382847413420677, -0.0045953006483614445, 0.023784467950463295, -0.0400952585041523, -0.0281272791326046, 0.0121531393378973, -0.031123481690883636, 0.010469879023730755, 0.013928978703916073, -0.008521504700183868, -0.01861685886979103, -0.0018999800086021423, -0.0242557805031538, -0.009392592124640942, 0.02247152477502823, 0.07736264169216156, 0.04302413389086723, -0.004401725716888905, -0.06362723559141159, -0.03154429793357849, -0.029170900583267212, -0.008912863209843636, -0.08126780390739441, 0.01445078942924738, 0.010554041713476181, 0.012607619166374207, -0.017926720902323723, 0.03689706325531006, -0.04349544644355774, 0.007742997258901596, -0.0485115610063076, -0.014122553169727325, -0.013087348081171513, 0.011959563940763474, 0.028009450063109398, -0.008904446847736835, -0.048006583005189896, 0.012759112752974033, -0.03864765539765358, -0.06854236125946045, -0.017421742901206017, -0.02895207703113556, 0.051070116460323334, -0.03726738318800926, 0.02568655088543892, -0.025955872610211372, -0.05221473425626755, 0.02642718516290188, -0.06106868386268616, 0.048040248453617096, 0.0009010702488012612, -0.004355435725301504, -0.020687269046902657, 0.02083876170217991, 0.01780889369547367, 0.009872321039438248, -0.014274046756327152, 0.03154429793357849, -0.022050708532333374, 0.01851586252450943, 0.03443950414657593, -0.0638965591788292, -0.0806618332862854, 0.03790701925754547, -0.043125126510858536, -0.0037326295860111713, -0.010596123524010181, -0.06914833188056946, -0.0160078052431345, 0.02351514622569084, 0.002184030134230852, 0.005213898606598377, 0.009670330211520195, 0.003608489176258445, -0.004696296062320471, 0.023834966123104095, 0.015023097395896912, -0.014223549515008926, -0.053494010120630264, 0.0402299202978611, -0.031056152656674385, 0.04575101286172867, -0.03595443814992905, 0.0021735099144279957, 0.008513088338077068, 0.09082872420549393, -0.012733863666653633, 0.030366014689207077, -0.045481692999601364, 0.027891622856259346, 0.05315735936164856, -0.026359856128692627, -0.05379699915647507, 0.011555581353604794, -0.009274763986468315, 0.009300013072788715, 0.05585057660937309, -0.02008129470050335, -0.0018042445881292224, -0.009779741987586021, -0.02166355960071087, -0.012767529115080833, 0.018768351525068283, 0.009863904677331448, -0.010789697989821434, -0.023818133398890495, 0.0121278902515769, 0.013171511702239513, 0.015384999103844166, 0.04120621085166931, -0.0032002986408770084, -0.05561491847038269, -0.010596123524010181, 0.02654501423239708, 0.008896030485630035, -0.005369600374251604, -0.043832097202539444, -0.012363546527922153, -0.03632475808262825, 0.007381096016615629, -0.06834036856889725, 0.014652780257165432, 0.015427079983055592, 0.052686046808958054, 0.01665586046874523, -0.013011601753532887, 0.017489073798060417, 0.008572002872824669, -0.043192457407712936, -0.06817203760147095, 0.09857171773910522, 0.0029499134980142117, 0.048780880868434906, 0.0021671976428478956, 0.02080509625375271, 0.022033877670764923, 0.00044264484313316643, 0.04187951609492302, -0.03972494229674339, -0.0319819450378418, 0.007343222852796316, -0.03713272139430046, -0.018751518800854683, -0.027655966579914093, 0.07002362608909607, -0.03447316959500313, -0.03524747118353844, -0.01256553828716278, -0.008336346596479416, -0.024861754849553108, -0.09399325400590897, 0.03464149683713913, -0.039017971605062485, -0.013895313255488873, -0.001786359935067594, -0.024003291502594948, 0.029591714963316917, -0.03076999820768833, 0.054436635226011276, -0.059351757168769836, 0.06288660317659378, -0.0020662019960582256, -0.017539571970701218, -0.03162845969200134, -0.01286010816693306, 0.02669650688767433, -0.036796070635318756, -0.025568723678588867, -0.016251876950263977, 0.04682829976081848, 0.019138669595122337, -0.04164385795593262, -0.01929016225039959, -0.0070023625157773495, 0.009485171176493168, 0.04164385795593262, -0.02166355960071087, -0.04275481030344963, 0.013912145979702473, -0.015090428292751312, -0.0007206458249129355, -0.010293136350810528, 0.019609982147812843, -0.07379412651062012, -0.01638653874397278, 0.015553324483335018, 0.03410285338759422, -0.000445800949819386, 0.007907114923000336, 0.008168020285665989, -0.03152746334671974, -0.04982450231909752, -0.018246540799736977, 0.011782822199165821, 0.011799653992056847, -0.02100708894431591, -0.01779206097126007, -0.03605543449521065, 0.04514503851532936, -0.02008129470050335, -0.01485477201640606, -0.035011813044548035, 0.011202096939086914, 0.02666284330189228, 0.016394954174757004, 0.010865445248782635, 0.04299046844244003, 0.05716351792216301, 0.029305560514330864, -0.008231142535805702, -0.00018450109928380698, -0.0017569029005244374, 0.0020725142676383257, -0.029322393238544464, 0.011925898492336273, 0.03612276539206505, 0.008403676562011242, -0.05231573060154915, 0.03625742718577385, -0.0024596641305834055, -0.009518836624920368, 0.028463931754231453, 0.034220680594444275, -0.012355130165815353, -0.05309002846479416, 0.05174342170357704, 0.004591092467308044, -0.013087348081171513, 0.056826867163181305, 0.0063543072901666164, -0.007957613095641136, 0.06386289745569229, -0.04161019250750542, -0.025299401953816414, -0.01562907174229622, -0.012169972062110901, 0.049656178802251816, -0.0008006006828509271, 0.015368166379630566, -0.015477578155696392, -0.026965828612446785, 0.023818133398890495, 0.0010983273386955261, -0.007949196733534336, 0.006169148720800877, 0.020316950976848602, 0.052012741565704346, -0.02487858571112156, 0.016352873295545578, 0.015309251844882965, -0.0070023625157773495, -0.0004663156869355589, -0.017270250245928764, 0.009594583883881569, -0.004742585588246584, -0.046323321759700775, -0.008412092924118042, -0.001634866581298411, -0.03706539049744606, -0.0035537832882255316, 0.037469372153282166, 0.0008879197994247079, -0.034254346042871475, 0.02346464805305004, 0.015772148966789246, -0.00684666121378541, 0.026275692507624626, 0.044000424444675446, 0.023228991776704788, 0.005348559468984604, -0.027588635683059692, 0.0014539160765707493, -0.04733327776193619, 0.002493329346179962, 0.034355342388153076, -0.0025543475057929754, -0.0017148214392364025, -0.04484205320477486, -0.06026071682572365, -0.03571878373622894, 0.022875506430864334, -0.003766294801607728, -0.013129429891705513, 0.062347959727048874, -0.004923536442220211, -0.039792273193597794, -0.001284537953324616, -0.02003079652786255, 0.012422461062669754, -0.008142771199345589, -0.0481412447988987, 0.02723515033721924, 0.018078215420246124, -0.015191423706710339, -0.039085302501916885, -0.007524173241108656, -0.005117111373692751, -0.012010062113404274, 0.036829736083745956, -0.03290773928165436, -0.001688520424067974, 0.0324532575905323, -0.013407167978584766, 0.004561635199934244, -0.02332998812198639, -0.03403552249073982, 0.05787048861384392, 0.0007111774757504463, -0.012700198218226433, 0.015839479863643646, 0.03378303349018097, 0.008946528658270836, 0.0014076264342293143, -0.04763626679778099, 0.02407062239944935, 0.03060167096555233, 0.03858032450079918, -0.007351639214903116, 0.01843170076608658, -0.01324725802987814, 0.008870781399309635, 0.00583670474588871, -0.015334500931203365, -0.024525102227926254, 0.005769374314695597, 0.02908673696219921, 0.016647443175315857, -0.05487428605556488, 0.0024407273158431053, 0.022017044946551323, 0.00003144606307614595, 0.04736694321036339, -0.006985530257225037, -0.026157865300774574, -0.002190342405810952, -0.007936571724712849, 0.016563281416893005, 0.03689706325531006, 0.01129467599093914, 0.0159909725189209, -0.05790415406227112, 0.024205282330513, -0.008744536899030209, 0.04171118885278702, -0.007090733852237463, 0.017371246591210365, 0.007873449474573135, -0.008946528658270836, -0.0014044702984392643, 0.012801194563508034, -0.04437074065208435, 0.0015549116069450974, 0.018280206248164177, 0.05938542261719704, -0.04113887995481491, -0.0013581806560978293, 0.00043896271381527185, -0.004029304254800081, -0.03445633873343468, 0.015898393467068672, 0.027773793786764145, -0.05170975625514984, -0.021377405151724815, -0.013154678978025913, 0.02506374567747116, -0.02018229104578495, 0.04262014850974083, 0.04517870396375656, -0.025147907435894012, 0.04285580664873123, 0.030147191137075424, 0.003526430344209075, -0.008067024871706963, 0.040835894644260406, 0.026073701679706573, 0.01686626859009266, 0.014526535756886005, 0.043158791959285736, 0.02260618470609188, -0.019727809354662895, 0.0012771737528964877, -0.031190812587738037, -0.004376476630568504, -0.000641216931398958, -0.0017064050771296024, -0.00744001055136323, 0.0324532575905323, 0.013743819668889046, -0.03689706325531006, 0.027807459235191345, -0.048410564661026, -0.008525713346898556, -0.047097623348236084, -0.011597663164138794, 0.010352050885558128, 0.04262014850974083, -0.03135913982987404, -0.037435706704854965, 0.06595014035701752, 0.00014583872689399868, -0.04733327776193619, 0.014543368481099606, -0.025939039885997772, 0.03371570259332657, 0.055345598608255386, -0.006699375808238983, 0.0015317668439820409, -0.02006446197628975, -0.014922101981937885, 0.017573237419128418, -0.00722539471462369, 0.007385304197669029, -0.020502109080553055, 0.021579395979642868, 0.003526430344209075, 0.035853441804647446, 0.007751413621008396, -0.02166355960071087, -0.00546217942610383, 0.03374936804175377, -0.021175414323806763, 0.018903013318777084, 0.021579395979642868, -0.062347959727048874, -0.03528113663196564, 0.004574259743094444, 0.016891516745090485, -0.014004725031554699, 0.027706464752554893, -0.016445452347397804, 0.0720435380935669, -0.05140676721930504, -0.016714774072170258, -0.0006291185272857547, 0.02893524430692196, -0.024727093055844307, -0.013550245203077793, 0.0028594383038580418, -0.013836399652063847, -0.04251915588974953, 0.05884677916765213, -0.02262301743030548, 0.05090178921818733, -0.021108083426952362, 0.011252595111727715, 0.019542651250958443, 0.0002827351272571832, 0.03625742718577385, 0.0044311825186014175, 0.0121531393378973, 0.07446743547916412, 0.008744536899030209, 0.019643647596240044, 0.008912863209843636, -0.03955661505460739, 0.04352911189198494, -0.006387972738593817, 0.0007874501752667129, 0.01364282425493002, -0.02009812742471695, -0.010419380851089954, 0.02743714302778244, 0.011984813027083874, 0.01858319342136383, 0.05857745558023453, 0.017909890040755272, -0.01695043034851551, 0.014720111154019833, 0.025434061884880066, -0.014551784843206406, 0.021326906979084015, -0.015755316242575645, 0.0324869230389595, -0.028396600857377052, 0.010402548126876354, 0.023666638880968094, -0.010183724574744701, 0.007978653535246849, -0.04531336575746536, 0.02087242715060711, -0.009535669349133968, 0.02504691295325756, -0.016580114141106606, 0.048713553696870804, -0.00723381107673049, 0.04363010451197624, -0.0404992401599884, -0.01330617256462574, 0.011521916836500168, 0.033564209938049316, -0.03146013244986534, -0.00547059578821063, -0.02888474613428116, -0.008374219760298729, 0.04921853169798851, -0.06228062883019447, -0.04413508251309395, -0.023952793329954147, -0.004464847967028618, -0.056961528956890106, 0.0054411389864981174, 0.012270967476069927, -0.004307042341679335, 0.023144828155636787, -0.016748439520597458, 0.014610699377954006, -0.02664601057767868, 0.03071950003504753, 0.0011046394938603044, -0.0035579914692789316, 0.006409013643860817, 0.038277339190244675, -0.029288727790117264, 0.02269034832715988, 0.02656184695661068, -0.04107154905796051, 0.018229708075523376, 0.005007699131965637, 0.007469467353075743, -0.0808638259768486, -0.001837909803725779, -0.03730104863643646, 0.030012531206011772, 0.019862471148371696, -0.025535058230161667, 0.007528381422162056, -0.0399605967104435, -0.013533412478864193, 0.01920599862933159, -0.002869958756491542, 0.01865052431821823, 0.02188238315284252, -0.044034089893102646, -0.023161660879850388, -0.02664601057767868, 0.02183188498020172, 0.01576373167335987, 0.003821000689640641, 0.026309357956051826, 0.04565001651644707, -0.02188238315284252, -0.015788981691002846, -0.02738664485514164, -0.018027717247605324, 0.0323185957968235, -0.011951147578656673, 0.0032991901971399784, 0.023161660879850388, -0.008492047898471355, 0.031712621450424194, -0.0015990972751751542, 0.035112809389829636, 0.04995916411280632, 0.016327625140547752, -0.023851796984672546, 0.03331172093749046, 0.014164634980261326, 0.08221042901277542, -0.03359787538647652, 0.0070107788778841496, 0.03534846380352974, -0.014585450291633606, -0.021444736048579216, 0.0005391692975535989, 0.021192247048020363, 0.019525818526744843, 0.03398502618074417, -0.046289656311273575, -0.0037873354740440845, -0.0402635857462883, 0.03450683504343033, 0.024727093055844307, -0.05746650695800781, 0.05790415406227112, -0.011353590525686741, 0.015090428292751312, -0.021158581599593163, -0.03763769939541817, -0.020367449149489403, -0.039792273193597794, -0.031089816242456436, 0.016336040571331978, 0.07022561877965927, -0.03608909994363785, 0.04366376996040344, -0.007583087310194969, -0.03247009217739105, 0.003515909891575575, -0.016033053398132324, -0.03767136484384537, 0.010251054540276527, 0.025551890954375267, -0.046222325414419174, -0.03541579470038414, 0.015124093741178513, 0.038344670087099075, -0.013179928064346313, -0.03528113663196564, 0.02974320948123932, 0.012801194563508034, -0.013895313255488873, 0.017337581142783165, -0.02750447206199169, -0.02250519022345543, -0.006922408007085323, 0.00506240501999855, 0.00642163772135973, 0.01657169684767723, 0.013179928064346313, -0.001237196265719831, -0.0008631969103589654, -0.0038041681982576847, 0.024777591228485107, -0.011117934249341488, 0.015873143449425697, -0.004826748743653297, -0.014543368481099606, -0.031965114176273346, 0.0065352581441402435, -0.015418663620948792, -0.0024091661907732487, -0.01293585542589426, 0.01253187283873558, 0.05780315771698952, -0.055076275020837784, 0.00606394512578845, 0.023161660879850388, -0.01843170076608658, 0.017152421176433563, -0.001939957495778799, -0.023919127881526947, -0.016277126967906952, 0.009064356796443462, 0.022841840982437134, -0.009291596710681915, 0.005500053055584431, 0.023531978949904442, -0.020552607253193855, -0.048040248453617096, 0.00608077785000205, -0.02329632267355919, -0.0030887825414538383, -0.012237302027642727, 0.04349544644355774, 0.04171118885278702, -0.011479835025966167, 0.036829736083745956, 0.017270250245928764, -0.03794068470597267, 0.006741457153111696, 0.008778202347457409, 0.03454050049185753, 0.006960281170904636, -0.02184871770441532, -0.032503753900527954, 0.027033159509301186, -0.004990866873413324, 0.025215238332748413, -0.03558412194252014, 0.06049637496471405, 0.03213343769311905, 0.048679888248443604, -0.021899215877056122, -0.028632257133722305, -0.04534703120589256, 0.05383066460490227, -0.02011496014893055, -0.028413433581590652, -0.021528897807002068, 0.00566417071968317, -0.00585774565115571, -0.01848219707608223, -0.016184547916054726, -0.008197477087378502, 0.0026195738464593887, -0.019761474803090096, -0.03730104863643646, -0.01760690286755562, -0.020485278218984604, -0.02014862559735775, 0.07776662707328796, -0.04211517050862312, 0.06652244180440903, 0.010133226402103901, -0.03948928415775299, -0.0242726132273674, -0.023885462433099747, -0.010082729160785675, -0.027807459235191345, -0.008458382450044155, -0.010023814626038074, -0.00682562030851841, 0.029204566031694412, -0.0007553630275651813, -0.016394954174757004, 0.0030635336879640818, -0.007158064283430576, -0.008719287812709808, 0.024743925780057907, -0.0021671976428478956, -0.02104075253009796, -0.0046289656311273575, -0.01782572641968727, 0.03309289738535881, 0.039085302501916885, 0.003781023435294628, 0.02888474613428116, 0.030382847413420677, -0.011185264214873314, 0.0323185957968235, 0.0054790121503174305, -0.020350616425275803, -0.039926934987306595, 0.010983273386955261, -0.003210818860679865, 0.007894490845501423, -0.003374936757609248, 0.02334681898355484, -0.051272109150886536, -0.060025062412023544, 0.03480982035398483, -0.02184871770441532, 0.021512066945433617, -0.02747080661356449 ]
In drug discovery, aqueous solubility is an important pharmacokinetic property which affects absorption and assay availability of drug. Thus, in silico prediction of solubility has been studied for its utility in virtual screening and lead optimization. Recently, machine learning (ML) methods using experimental data has been popular because physics-based methods like quantum mechanics and molecular dynamics are not suitable for high-throughput tasks due to its computational costs. However, ML method can exhibit over-fitting problem in a data-deficient condition, and this is the case for most chemical property datasets. In addition, ML methods are regarded as a black box function in that it is difficult to interpret contribution of hidden features to outputs, hindering analysis and modification of structure-activity relationship. To deal with mentioned issues, we developed Bayesian graph neural networks (GNNs) with the self-attention readout layer. Unlike most GNNs using self-attention in node updates, self-attention applied at readout layer enabled a model to improve prediction performance as well as to identify atom-wise importance, which can help lead optimization as exemplified for three FDA-approved drugs. Also, Bayesian inference enables us to separate more or less accurate results according to uncertainty in solubility prediction task We expect that our accurate, reliable and interpretable model can be used for more careful decision-making and various applications in the development of drugs.
[ -0.0267521683126688, -0.002841210225597024, -0.020762352272868156, -0.01796066388487816, 0.038679104298353195, -0.05083438754081726, -0.012418767437338829, 0.003954420331865549, -0.027630440890789032, 0.02424030937254429, 0.011171621270477772, -0.017003348097205162, 0.03924119845032692, -0.02028808556497097, -0.03815213963389397, 0.04728617146611214, 0.013692261651158333, -0.031231356784701347, -0.058809101581573486, -0.009046202525496483, 0.04296507313847542, -0.03477957472205162, 0.03804674744606018, 0.02394169755280018, 0.04405412822961807, 0.00893641822040081, 0.014579316601157188, 0.010758833028376102, -0.06161957234144211, 0.05582297593355179, 0.028280362486839294, -0.002193484688177705, 0.03001934103667736, 0.01486036367714405, -0.029703162610530853, -0.002507466822862625, 0.03544706106185913, 0.02095557190477848, 0.00830406229943037, -0.011320927180349827, 0.003581154393032193, 0.01564202643930912, 0.025610415264964104, 0.05115056782960892, -0.005994207225739956, -0.03372564911842346, -0.006516778841614723, -0.04317585751414299, -0.02049887180328369, 0.003802918130531907, -0.020779918879270554, -0.0069383494555950165, 0.01923415996134281, -0.01667838729918003, -0.020920442417263985, 0.05185318365693092, 0.04243810847401619, 0.028368188068270683, 0.001261418336071074, -0.017170218750834465, -0.008918853476643562, 0.023906566202640533, -0.024644315242767334, 0.010205522179603577, 0.021956803277134895, -0.03888988867402077, 0.014465141110122204, -0.026646776124835014, -0.0014864755794405937, 0.011654671281576157, -0.051607269793748856, 0.0542420856654644, 0.008115233853459358, -0.029755858704447746, -0.017126306891441345, 0.050061509013175964, 0.021658189594745636, -0.012058676220476627, -0.0035460235085338354, 0.015852810814976692, 0.015317065641283989, 0.04152470454573631, -0.01814510114490986, 0.04437030851840973, 0.021570362150669098, -0.010829094797372818, 0.01683647558093071, -0.054874442517757416, -0.00395002868026495, 0.020094865933060646, 0.008145974017679691, 0.03239067643880844, -0.009731254540383816, -0.01129457913339138, 0.029000544920563698, 0.01902337372303009, 0.042473237961530685, 0.008817851543426514, 0.007070090621709824, 0.005730725359171629, 0.03546462580561638, -0.03260146081447601, 0.021605493500828743, -0.0032100845128297806, -0.006683650892227888, -0.05171266198158264, -0.041805751621723175, 0.0032276499550789595, -0.01033726241439581, 0.17354656755924225, 0.005260849837213755, -0.01645003631711006, -0.00672756414860487, -0.02258915826678276, -0.03054630383849144, -0.04823470488190651, -0.04781313240528107, -0.015545416623353958, -0.035851068794727325, 0.007614619098603725, 0.030353084206581116, 0.05522574856877327, -0.045599889010190964, -0.053258419036865234, -0.028807325288653374, 0.04992098733782768, -0.026067115366458893, -0.03846831992268562, -0.02422274462878704, 0.008910070173442364, -0.03625507280230522, 0.03412965312600136, -0.006046903319656849, -0.030669262632727623, -0.014930625446140766, 0.016590559855103493, 0.025961723178625107, 0.055050093680620193, -0.011268231086432934, -0.018303191289305687, -0.021535232663154602, -0.04468648508191109, 0.007807839196175337, -0.06263836473226547, 0.06147904694080353, 0.022027064114809036, -0.018988242372870445, 0.06007381156086922, -0.02474970743060112, 0.039662767201662064, -0.0364307276904583, 0.036149680614471436, 0.04995611682534218, -0.02044617384672165, 0.0047602346166968346, 0.043667688965797424, -0.0031793450471013784, 0.003249606816098094, 0.021342013031244278, -0.031178658828139305, 0.062322188168764114, -0.029404550790786743, 0.00426620664075017, 0.0176444873213768, 0.07475852221250534, 0.06228705868124962, 0.008418237790465355, -0.01962059922516346, -0.11164595186710358, 0.056209415197372437, 0.010732484981417656, 0.01464079599827528, -0.05002637952566147, 0.03699282184243202, -0.013762523420155048, 0.029492376372218132, 0.023801174014806747, 0.0010028769029304385, -0.02399439364671707, -0.0011077206581830978, -0.050728995352983475, 0.008892505429685116, 0.015694722533226013, 0.045143187046051025, 0.00514667434617877, 0.02950994297862053, 0.07412616908550262, 0.009011072106659412, 0.014052353799343109, 0.0758124515414238, -0.025469891726970673, -0.0056999861262738705, 0.04208679869771004, -0.008312845602631569, 0.03374321386218071, -0.028491146862506866, -0.026172509416937828, -0.04496753215789795, -0.01084666047245264, -0.03797648474574089, -0.02489023096859455, -0.03449852764606476, -0.038011617958545685, 0.027243999764323235, 0.01519410777837038, 0.025680676102638245, 0.007149134762585163, -0.04036538675427437, 0.01645003631711006, 0.00828210636973381, 0.01549271959811449, 0.013253126293420792, -0.10384689271450043, -0.02592659182846546, -0.010609527118504047, -0.01628316566348076, 0.002683121245354414, -0.005673637613654137, -0.0363955944776535, -0.023432299494743347, -0.024099785834550858, 0.02012999728322029, 0.08129286766052246, 0.009819081984460354, 0.08333045989274979, -0.003174953628331423, -0.014526620507240295, 0.0252766702324152, 0.023976828902959824, -0.021166358143091202, 0.03562271595001221, 0.03829266503453255, 0.03629020228981972, -0.006973480340093374, -0.034217480570077896, -0.012234330177307129, 0.04338664188981056, -0.04528370872139931, -0.05297737196087837, -0.029158633202314377, -0.02950994297862053, -0.015606895089149475, -0.014201659709215164, -0.034375570714473724, 0.05561218783259392, 0.001169199706055224, -0.004808539990335703, 0.07001585513353348, 0.09246448427438736, 0.05378538370132446, 0.02585633099079132, -0.06337611377239227, 0.0226769857108593, 0.008874939754605293, -0.030669262632727623, -0.011935718357563019, 0.03546462580561638, -0.022343242540955544, 0.02594415843486786, -0.08206574618816376, 0.04057617112994194, -0.02845601551234722, 0.01962059922516346, 0.02622520551085472, -0.02555771730840206, -0.014930625446140766, 0.053012505173683167, -0.02950994297862053, -0.024134917184710503, 0.07707715779542923, -0.014359748922288418, -0.024556487798690796, -0.0028280362021178007, 0.01602846570312977, -0.06330585479736328, -0.08016867935657501, 0.04257863014936447, -0.028596539050340652, 0.012392419390380383, -0.0061654699966311455, 0.0026435989420861006, -0.005243284627795219, 0.014790101908147335, 0.022237850353121758, -0.013235560618340969, -0.02548745647072792, -0.0174600500613451, -0.00025511058629490435, -0.051466744393110275, 0.013130167499184608, -0.021658189594745636, -0.010469003580510616, -0.049675069749355316, -0.03685229644179344, 0.019567903131246567, 0.02429300546646118, -0.038608841598033905, -0.03709821403026581, -0.0004383126797620207, -0.05385564640164375, -0.027735833078622818, -0.03695768862962723, -0.026330597698688507, 0.000024821478291414678, 0.03850344941020012, 0.022606724873185158, -0.0042266845703125, 0.10532239079475403, -0.013674696907401085, -0.016854042187333107, 0.06527318060398102, 0.013138950802385807, 0.00006641932850470766, -0.04430004581809044, 0.01200597919523716, 0.037203606218099594, 0.03198666870594025, -0.07012124359607697, -0.0076629240065813065, -0.006367472931742668, 0.013209212571382523, 0.01422800775617361, -0.07588271051645279, 0.023291775956749916, -0.02111366204917431, 0.05828213691711426, -0.02868436649441719, 0.056139152497053146, -0.04043564945459366, 0.04004920646548271, 0.010793964378535748, -0.02624277025461197, -0.04668894410133362, 0.023010728880763054, 0.0058009871281683445, -0.0765150636434555, -0.014245573431253433, 0.034884966909885406, 0.012041110545396805, 0.014781319536268711, -0.01255929097533226, -0.059476587921381, -0.023221515119075775, -0.03910067304968834, 0.0025118582416325808, -0.019831383600831032, -0.02155279740691185, 0.03339190408587456, 0.03611454740166664, 0.006991046015173197, 0.000931517337448895, 0.021148791536688805, -0.02907080575823784, 0.02875462919473648, 0.04342177137732506, 0.007930797524750233, 0.0014557359972968698, -0.02169332094490528, -0.01427192147821188, 0.04036538675427437, 0.03463905304670334, -0.07510983198881149, -0.02088531106710434, 0.04155983775854111, -0.08972427994012833, 0.06211140379309654, -0.0006515681161545217, 0.01940981298685074, 0.04704025387763977, -0.03822240233421326, -0.012216764502227306, 0.07405590265989304, -0.020551567897200584, 0.00970490649342537, -0.011408754624426365, -0.011197969317436218, -0.0009172454010695219, 0.04890219122171402, -0.06843496114015579, 0.03881962597370148, -0.024398399516940117, 0.03783596307039261, -0.025821199640631676, 0.009634644724428654, -0.0045670149847865105, -0.019444944337010384, 0.032882507890462875, -0.011145273223519325, -0.013657131232321262, 0.059195540845394135, 0.0018246102845296264, -0.025013189762830734, 0.05181805416941643, -0.03896015137434006, 0.0031991060823202133, 0.005901988595724106, 0.06362202763557434, 0.016985783353447914, 0.06643249839544296, -0.014201659709215164, -0.022922901436686516, 0.004935889039188623, 0.01642368920147419, -0.012418767437338829, 0.0003812249924521893, 0.011347275227308273, -0.03906554356217384, -0.07644480466842651, 0.005427721422165632, -0.017117522656917572, -0.01695065200328827, -0.01147901639342308, -0.006415777839720249, 0.004141053184866905, 0.018619367852807045, 0.03200423717498779, -0.00406639976426959, -0.0061171650886535645, 0.026734603568911552, 0.020270520821213722, 7.461882205461734e-7, -0.010416307486593723, 0.006516778841614723, -0.0011082695564255118, -0.013911830261349678, -0.011637105606496334, 0.01612507551908493, -0.02801688015460968, 0.0161689892411232, -0.05438260734081268, 0.04858601093292236, 0.01422800775617361, -0.012611987069249153, -0.04356229677796364, -0.05157213658094406, -0.008497282862663269, -0.029597770422697067, -0.02424030937254429, -0.022624289616942406, -0.02176358364522457, -0.027841225266456604, -0.004004920832812786, -0.0274899173527956, 0.005594593472778797, -0.058528054505586624, -0.058668576180934906, -0.03149483725428581, -0.04503779485821724, -0.011171621270477772, -0.035657849162817, -0.06337611377239227, 0.03574567288160324, -0.05996841937303543, -0.013990874402225018, 0.031178658828139305, -0.023607954382896423, -0.009300901554524899, -0.013999657705426216, 0.07967684417963028, -0.03604428842663765, -0.011452668346464634, 0.02921132929623127, -0.03945198282599449, -0.020938007161021233, -0.009564382955431938, 0.02525910548865795, -0.043667688965797424, 0.033866170793771744, 0.024925362318754196, -0.018320756033062935, -0.012884251773357391, 0.01998947374522686, 0.017117522656917572, -0.016107510775327682, 0.0323028489947319, -0.04303533211350441, 0.04742669314146042, -0.021517666056752205, 0.044335175305604935, 0.023660650476813316, 0.02518884465098381, 0.01047778595238924, -0.01895311288535595, -0.00198709056712687, -0.0334446020424366, -0.02847358211874962, -0.0006905414629727602, -0.0161689892411232, 0.030739523470401764, -0.010653440840542316, -0.049815595149993896, -0.034884966909885406, -0.03031795285642147, -0.02727913111448288, 0.014482706785202026, -0.029527507722377777, 0.024029524996876717, 0.002806079341098666, 0.08424386382102966, 0.07050768285989761, 0.0256455447524786, -0.05009664222598076, 0.016810128465294838, -0.020534001290798187, 0.012076240964233875, 0.019128765910863876, 0.012936947867274284, 0.03084491565823555, -0.03850344941020012, 0.024029524996876717, 0.020340781658887863, -0.022343242540955544, -0.025065885856747627, -0.0042069233022630215, -0.018672065809369087, -0.006125947926193476, -0.03797648474574089, -0.0009759798995219171, 0.025294236838817596, 0.04510805383324623, 0.00722817936912179, -0.009292119182646275, -0.009924475103616714, 0.05269632488489151, -0.04570528119802475, 0.00836115051060915, 0.005370634142309427, -0.029386984184384346, 0.011057445779442787, 0.020094865933060646, -0.02824523113667965, 0.009520469233393669, -0.03695768862962723, -0.011136489920318127, -0.025680676102638245, -0.012594422325491905, 0.012357288040220737, -0.01189180463552475, -0.02624277025461197, 0.01292816549539566, -0.03625507280230522, 0.030950309708714485, -0.02185140922665596, 0.022624289616942406, 0.020165126770734787, 0.03001934103667736, 0.06288428604602814, -0.016476385295391083, -0.010995966382324696, 0.019040938466787338, -0.007979102432727814, 0.03818727284669876, 0.06446517258882523, -0.01602846570312977, 0.0031464097555726767, -0.046794336289167404, 0.0019969712011516094, -0.02840331941843033, -0.01805727370083332, 0.018970677629113197, 0.025961723178625107, 0.008172322064638138, -0.0065694754011929035, -0.05441774055361748, -0.03402426093816757, -0.07229936122894287, 0.033321645110845566, 0.02332690730690956, 0.01587037742137909, 0.04166522994637489, 0.013033557683229446, -0.03839805722236633, -0.023801174014806747, 0.012989643961191177, 0.00024358327209483832, 0.03239067643880844, 0.01679256185889244, -0.018092405050992966, 0.006551909726113081, -0.038081876933574677, 0.062462713569402695, -0.021306881681084633, 0.009169160388410091, 0.023274211212992668, -0.008962767198681831, -0.03762517869472504, -0.005006150808185339, -0.03969790041446686, -0.06861061602830887, -0.029000544920563698, -0.06218166649341583, 0.05255580320954323, 0.023291775956749916, -0.00663534551858902, -0.06857548654079437, -0.034516092389822006, 0.01084666047245264, 0.009037420153617859, 0.04103287309408188, -0.052590932697057724, 0.004720712546259165, 0.009669776074588299, 0.05315302684903145, 0.03558758646249771, -0.012936947867274284, 0.060389988124370575, 0.02659408003091812, 0.03247850388288498, 0.005673637613654137, -0.001798262121155858, -0.004685581661760807, 0.009292119182646275, 0.011812759563326836, -0.0297207273542881, 0.02467944659292698, -0.005036890506744385, -0.021060965955257416, -0.013138950802385807, -0.008585109375417233, -0.016625691205263138, 0.01881258934736252, -0.05037768930196762, 0.03372564911842346, -0.020534001290798187, 0.02139470912516117, -0.04865627363324165, 0.005906379781663418, -0.030142297968268394, 0.012313375249505043, -0.0065036048181355, -0.04992098733782768, 0.011909369379281998, -0.059336062520742416, -0.031547535210847855, 0.0193219855427742, -0.016801346093416214, -0.0030893220100551844, 0.04096261039376259, 0.021219054237008095, 0.019708426669239998, -0.032952770590782166, 0.016362208873033524, -0.016458818688988686, -0.0019486661767587066, -0.0010462416103109717, 0.016827693209052086, -0.019796254113316536, -0.018759891390800476, 0.023291775956749916, -0.0006213774904608727, -0.018549107015132904, 0.009801516309380531, 0.015694722533226013, 0.03128405287861824, -0.00917794369161129, -0.013165298849344254, 0.010785181075334549, -0.005673637613654137, 0.023537691682577133, 0.015448805876076221, -0.0007608032319694757, 0.04444056749343872, 0.0008777231560088694, 0.02571580745279789, -0.0023427908308804035, -0.0234147347509861, 0.03017742931842804, 0.028877586126327515, 0.028578974306583405, 0.04296507313847542, -0.015729853883385658, -0.010591961443424225, -0.016441253945231438, 0.04391360655426979, 0.027525046840310097, -0.023520126938819885, 0.005168631207197905, -0.009151595644652843, -0.03737926110625267, -0.05311789736151695, -0.012813990004360676, -0.052063971757888794, -0.023748477920889854, 0.014219225384294987, 0.014632013626396656, 0.013279474340379238, -0.008549978956580162, 0.018707195296883583, 0.004909540992230177, 0.026558948680758476, 0.0064772567711770535, -0.01723169907927513, 0.045143187046051025, -0.0009518273873254657, 0.03434043750166893, 0.008484108373522758, -0.015571764670312405, -0.018549107015132904, -0.01716143637895584, -0.025996854528784752, 0.006608997471630573, 0.04545936360955238, 0.014482706785202026, -0.0029466028790920973, 0.005357459653168917, -0.0011121120769530535, 0.019427379593253136, 0.000978175550699234, 0.00397857278585434, 0.013253126293420792, 0.006169861648231745, -0.01047778595238924, -0.033409472554922104, -0.012629552744328976, 0.0003296264912933111, -0.022097326815128326, 0.016177771613001823, -0.02840331941843033, 0.025399629026651382, 0.018478844314813614, -0.001326190889813006, -0.007632184773683548, -0.005287197884172201, -0.05371512100100517, 0.019040938466787338, 0.027964184060692787, 0.01192693505436182, 0.023572823032736778, 0.009950823150575161, 0.004121291916817427, 0.035851068794727325, -0.021886540576815605, -0.023168819025158882, 0.01033726241439581, 0.010899356566369534, -0.03395399823784828, 0.002235202584415674, 0.025311801582574844, 0.02237837389111519, -0.059933289885520935, 0.00026403056108392775, -0.008242583833634853, -0.00038067606510594487, -0.051607269793748856, 0.034902531653642654, 0.0408572182059288, -0.008339193649590015, 0.008233800530433655, -0.029316723346710205, 0.03126648813486099, 0.03773057088255882, -0.03216232359409332, 0.02882489003241062, -0.060530513525009155, -0.03107326664030552, 0.0030717565678060055, 0.025399629026651382, -0.0014381705550476909, -0.005511157680302858, -0.02236080728471279, -0.026998084038496017, 0.014061136171221733, 0.005326720420271158, 0.020569132640957832, 0.04777800291776657, 0.0263832937926054, -0.04651328921318054, 0.027770964428782463, -0.01464079599827528, -0.02014756202697754, 0.01619533821940422, -0.0009534741402603686, 0.0690673217177391, -0.04538910090923309, -0.002597489859908819, 0.04212193191051483, -0.004584580194205046, -0.017117522656917572, -0.055260881781578064, 0.061268262565135956, -0.009265771135687828, -0.011619539931416512, -0.0012559291208162904, 0.018268059939146042, -0.007531183306127787, -0.009054985828697681, 0.026418425142765045, -0.046548422425985336, -0.009801516309380531, 0.01404357049614191, -0.028930282220244408, -0.027296697720885277, -0.004558232147246599, -0.013780089095234871, 0.07855265587568283, -0.009160378016531467, 0.009669776074588299, 0.001607237965799868, -0.01773231290280819, -0.00825575739145279, 0.048410359770059586, -0.008541196584701538, 0.025030754506587982, 0.06070616841316223, -0.060530513525009155, -0.058809101581573486, -0.03189884126186371, -0.003925876226276159, 0.024205179885029793, -0.020920442417263985, 0.025610415264964104, -0.0022209305316209793, 0.029088372364640236, 0.00700422003865242, 0.02102583460509777, -0.03618481010198593, -0.0431055948138237, 0.009274553507566452, -0.0001366810902254656, 0.021956803277134895, -0.003642633557319641, 0.00976638589054346, -0.024363268166780472, -0.05171266198158264, -0.03472688049077988, -0.018777457997202873, 0.03130161762237549, 0.007184265647083521, 0.033181119710206985, 0.005757073871791363, 0.05757951736450195, 0.025241540744900703, -0.011619539931416512, 0.025399629026651382, -0.06745129823684692, 0.01940981298685074, 0.020639395341277122, 0.042402978986501694, 0.014807667583227158, 0.014500272460281849, -0.023520126938819885, 0.02757774479687214, -0.04489726945757866, -0.03165292739868164, -0.007215005345642567, -0.01888285018503666, -0.003849027445539832, -0.03114352934062481, 0.02215002290904522, 0.056455329060554504, -0.013007209636271, -0.03210962936282158, 0.013086254708468914, 0.006661694031208754, -0.03590376302599907, 0.024925362318754196, 0.040014076977968216, -0.016985783353447914, -0.009529252536594868, 0.020463740453124046, 0.037484653294086456, -0.0237836092710495, 0.013007209636271, -0.009555600583553314, 0.010302131995558739, -0.01977868750691414, 0.005546288564801216, -0.05118569731712341, 0.018900414928793907, -0.0393817201256752, -0.0058492920361459255, -0.025821199640631676, -0.03483227267861366, 0.023871436715126038, 0.00031782471342012286, 0.026998084038496017, -0.011162838898599148, 0.028262795880436897, -0.020252954214811325, -0.01858423836529255, -0.0027885138988494873, -0.015931855887174606, -0.0016346839256584644, -0.016037248075008392, 0.034358005970716476, 0.005937119480222464, -0.025136146694421768, -0.02520640939474106, -0.0483049638569355, -0.004375990945845842, -0.05375025421380997, 0.043878473341464996, -0.03562271595001221, -0.02392413280904293, -0.003912702202796936, -0.004121291916817427, 0.021342013031244278, -0.010855442844331264, -0.035482194274663925, 0.0068900445476174355, 0.0057965959422290325, -0.02176358364522457, -0.010082563385367393, -0.022835073992609978, 0.032812245190143585, 0.0019179267110303044, -0.011057445779442787, -0.05508522689342499, 0.015290717594325542, 0.021219054237008095, -0.019357116892933846, -0.0174600500613451, -0.04349203407764435, -0.006385038141161203, 0.012734945863485336, 0.019076069816946983, 0.019444944337010384, 0.02422274462878704, 0.01596698723733425, 0.008650979958474636, 0.01527315191924572, 0.008558761328458786, -0.025733372196555138, 0.017670834437012672, -0.02058669738471508, -0.009160378016531467, 0.001182373845949769, 0.06365716457366943, 0.015150194056332111, -0.014491490088403225, 0.01549271959811449, 0.022132456302642822, 0.040751826018095016, 0.03685229644179344, 0.020990703254938126, -0.056666117161512375, 0.006459691096097231, -0.008554370142519474, -0.0025799244176596403, 0.00681978277862072, -0.027226435020565987, 0.03411208838224411, -0.0027160565368831158, 0.0025952940341085196, -0.014579316601157188, -0.03205693140625954, 0.016107510775327682, 0.0698753297328949, -0.017012130469083786, 0.046864598989486694, 0.009081333875656128, 0.03969790041446686, -0.005809769965708256, -0.029668031260371208, -0.033268947154283524, 0.0070305680856108665, -0.022395938634872437, 0.02049887180328369, -0.005585810635238886, -0.0002456417423672974, -0.023818738758563995, -0.0017587399343028665, -0.029843686148524284, -0.0073950509540736675, -0.0013064297381788492, -0.009415077045559883, -0.03256633132696152, -0.018303191289305687, -0.02847358211874962, -0.01953277178108692, 0.03272441774606705, -0.031705621629953384, 0.029755858704447746, 0.0787634402513504, -0.0256455447524786, -0.0008211844251491129, -0.021658189594745636, -0.008668545633554459, -0.0176444873213768, -0.007671706844121218, 0.03137188032269478, 0.009985953569412231, 0.0005442542606033385, -0.0011329710250720382, 0.0014249965315684676, 0.0034779575653374195, 0.010697354562580585, -0.002223126357421279, -0.023678215220570564, 0.016643255949020386, 0.01741613633930683, 0.025680676102638245, -0.004101530648767948, -0.04370281845331192, -0.06344638019800186, -0.0024086611811071634, 0.028596539050340652, 0.009230639785528183, -0.00007177129737101495, 0.01229580957442522, 0.03632533550262451, -0.027823660522699356, 0.004108117893338203, 0.027384523302316666, 0.060389988124370575, 0.006854913663119078, 0.04848061874508858, 0.022501330822706223, -0.03167049214243889, 0.02719130367040634, 0.009520469233393669, 0.0024833143688738346, -0.025838764384388924, 0.007017394062131643, -0.02489023096859455, -0.013551738113164902, -0.036746904253959656, 0.01738978736102581, 0.01925172470510006, -0.0237836092710495, 0.016529081389307976, -0.0172756128013134, 0.00726770143955946, -0.04479187726974487 ]
Reference-model-assisted deep reinforcement learning (DRL) for inverter-based Volt-Var Control (IB-VVC) in active distribution networks is proposed. We investigate that a large action space increases the learning difficulties of DRL and degrades the optimization performance in the process of generating data and training neural networks. To reduce the action space of DRL, we design a reference-model-assisted DRL approach. We introduce definitions of the reference model, reference-model-based optimization, and reference actions. The reference-model-assisted DRL learns the residual actions between the reference actions and optimal actions, rather than learning the optimal actions directly. Since the residual actions are considerably smaller than the optimal actions for a reference model, we can design a smaller action space for the reference-model-assisted DRL. It reduces the learning difficulties of DRL and optimises the performance of the reference-model-assisted DRL approach. It is noteworthy that the reference-model-assisted DRL approach is compatible with any policy gradient DRL algorithms for continuous action problems. This work takes the soft actor-critic algorithm as an example and designs a reference-model-assisted soft actor-critic algorithm. Simulations show that 1) large action space degrades the performance of DRL in the whole training stage, and 2) reference-model-assisted DRL requires fewer iteration times and returns a better optimization performance.
[ -0.009447536431252956, 0.03406616300344467, -0.02683834172785282, -0.0034281716216355562, 0.002006454858928919, 0.04428417980670929, -0.020949682220816612, 0.009841947816312313, -0.06794888526201248, 0.03287375718355179, 0.03914765641093254, -0.0045907688327133656, -0.008360611274838448, -0.028929639607667923, 0.004051892552524805, 0.036726150661706924, 0.00896140094846487, 0.026104550808668137, -0.020087480545043945, -0.04380721598863602, 0.0035680499859154224, 0.011814006604254246, -0.004847595002502203, 0.0641331747174263, -0.037478283047676086, 0.014684956520795822, -0.0111077344045043, 0.003918893169611692, -0.06501372158527374, 0.07015024870634079, 0.05242924019694328, 0.031149351969361305, -0.0217201616615057, 0.003886789781972766, -0.04659561440348625, 0.011208630166947842, 0.005223662126809359, 0.0006925135967321694, -0.024728696793317795, 0.004719181917607784, -0.0010055205784738064, 0.026416411623358727, -0.06163829565048218, -0.007149858865886927, 0.03291044756770134, -0.008314749225974083, -0.002990191103890538, 0.0006070959498174489, -0.00045890489127486944, 0.011419595219194889, 0.048503465950489044, -0.08262466639280319, 0.0538601279258728, 0.019720586016774178, -0.053309787064790726, 0.03197486698627472, 0.04369714856147766, 0.05242924019694328, -0.003551998408511281, 0.04472445324063301, 0.053933508694171906, -0.035698845982551575, -0.0599505789577961, -0.03237845003604889, -0.010915114544332027, -0.017381632700562477, 0.01514357514679432, 0.018473144620656967, -0.0026278826408088207, -0.0030681563075631857, -0.05488743260502815, 0.04072530195116997, -0.045421551913022995, 0.004230753518640995, 0.003749204333871603, 0.02804909273982048, -0.039000898599624634, 0.012501933611929417, 0.007314961403608322, 0.01900514028966427, 0.02349960058927536, 0.028471020981669426, -0.03014039248228073, -0.029241500422358513, 0.04989766702055931, 0.017656803131103516, 0.052649375051259995, -0.05980382114648819, 0.007159030996263027, 0.005604315083473921, -0.028929639607667923, -0.004290373995900154, 0.007351650856435299, -0.020362650975584984, -0.00025224004639312625, -0.0005798654747195542, 0.03812035173177719, -0.025719312950968742, -0.03951454907655716, 0.054520539939403534, -0.023261118680238724, 0.008021233603358269, 0.009213641285896301, -0.013520066626369953, 0.047696299850940704, -0.045201417058706284, -0.10111615806818008, 0.0065490687265992165, 0.0424497053027153, 0.13098137080669403, 0.00821385346353054, -0.058483000844717026, 0.03612077608704567, 0.027260269969701767, -0.0569787323474884, -0.052062343806028366, 0.023866495117545128, -0.03714808076620102, -0.015914054587483406, -0.04637547954916954, 0.00090290472144261, 0.09025607258081436, -0.0019032658310607076, -0.009621811099350452, -0.01798700913786888, 0.013400825671851635, -0.023958217352628708, 0.009667673148214817, 0.04322018474340439, 0.05873982608318329, -0.05884989723563194, -0.027407027781009674, -0.022527329623699188, -0.02960839495062828, -0.008044164627790451, 0.014767508022487164, 0.029938600957393646, -0.03406616300344467, -0.0052282484248280525, 0.005141110625118017, 0.009277847595512867, -0.05154869332909584, 0.02683834172785282, 0.032488517463207245, -0.028929639607667923, 0.06791219115257263, -0.016042467206716537, 0.035515397787094116, -0.018463971093297005, -0.010594082064926624, -0.013428342528641224, 0.07712125033140182, 0.014052063226699829, 0.017583424225449562, 0.006704999133944511, 0.03327734023332596, -0.0330938957631588, -0.008401886560022831, 0.012731242924928665, -0.08108370751142502, 0.054116956889629364, -0.00488428445532918, -0.004077116493135691, 0.05154869332909584, 0.01962886191904545, 0.04696251079440117, 0.01670287735760212, 0.012896345928311348, -0.08379872888326645, 0.039661306887865067, 0.01121780276298523, -0.019115209579467773, -0.003233258845284581, 0.019243622198700905, -0.048503465950489044, 0.009557604789733887, 0.029186466708779335, -0.06244546175003052, -0.015015161596238613, 0.005498833023011684, -0.061124641448259354, -0.05140193551778793, 0.02599448338150978, 0.0011832350865006447, 0.05026456341147423, 0.05694204196333885, 0.04703588783740997, -0.05859306827187538, -0.006507792975753546, 0.00212340266443789, 0.011511318385601044, 0.028966329991817474, 0.052062343806028366, -0.028709502890706062, 0.008832987397909164, -0.04322018474340439, -0.022894224151968956, -0.008062508888542652, 0.05624494329094887, -0.004620579071342945, 0.0020098944660276175, 0.014006202109158039, -0.01547378022223711, 0.015849847346544266, 0.016822118312120438, 0.03911096602678299, 0.07062721252441406, -0.0003568623505998403, -0.003079621586948633, -0.04476114362478256, 0.03656104952096939, 0.004939318634569645, -0.027040133252739906, 0.008443161845207214, 0.0005666802171617746, 0.009456709027290344, -0.016280949115753174, -0.00361161888577044, -0.05169545114040375, -0.043330252170562744, 0.0030498113483190536, 0.028562745079398155, -0.0002198501315433532, -0.011447112075984478, -0.03450643643736839, 0.014712474308907986, -0.021151473745703697, -0.02038099616765976, -0.027186891064047813, 0.005388764664530754, -0.018152110278606415, 0.0011889678426086903, 0.013235722668468952, -0.03107597306370735, 0.03546036407351494, 0.015152747742831707, -0.002191048813983798, 0.024673663079738617, -0.017097288742661476, -0.01997741125524044, 0.009227399714291096, 0.025132281705737114, -0.004893457051366568, 0.02652648091316223, 0.06189512088894844, 0.005310799460858107, 0.012437727302312851, 0.0681690201163292, 0.06996680051088333, -0.019555483013391495, -0.02078457921743393, -0.05712549015879631, 0.006989342160522938, -0.03474491834640503, -0.013868615962564945, 0.0233161523938179, 0.04079867899417877, -0.0034786195028573275, -0.02876453846693039, -0.03509347140789032, 0.041899364441633224, 0.019280312582850456, 0.0629958063364029, 0.06226201727986336, -0.030048668384552002, 0.07026031613349915, 0.026379723101854324, 0.013382481411099434, 0.011896558105945587, -0.005723556037992239, 0.022949257865548134, -0.06901287287473679, -0.03113100863993168, -0.029039708897471428, 0.011832350865006447, -0.059693753719329834, -0.013217378407716751, 0.017023909837007523, 0.056208252906799316, -0.03184645250439644, 0.04553162306547165, -0.02724192477762699, 0.03929441422224045, 0.022490639239549637, -0.040468476712703705, -0.032396793365478516, -0.022105399519205093, -0.00024235108867287636, -0.034176234155893326, 0.0030200013425201178, -0.025132281705737114, 0.0013208206510171294, -0.01427219994366169, -0.018436454236507416, 0.034799955785274506, -0.007035204209387302, -0.0008507368620485067, -0.04883367195725441, 0.02315104939043522, 0.03845055401325226, 0.008970573544502258, 0.003950996324419975, 0.03823041915893555, 0.036817874759435654, -0.04391728341579437, -0.036010704934597015, -0.023921528831124306, 0.03903758525848389, 0.0089292973279953, -0.0027448302134871483, -0.007140686269849539, 0.059070032089948654, -0.02028927206993103, -0.132228821516037, -0.07536015659570694, 0.03019542619585991, 0.019959066063165665, 0.00017169521015603095, -0.03076411411166191, -0.013226551003754139, 0.021701816469430923, 0.03221334517002106, -0.0671784058213234, 0.008076267316937447, 0.011373733170330524, 0.001969765406101942, 0.007062721066176891, 0.0041963569819927216, -0.034854989498853683, -0.0011866748100146651, -0.01174980029463768, 0.027810610830783844, -0.018519004806876183, -0.0017347235698252916, 0.015904881060123444, 0.00864954013377428, -0.001442354405298829, -0.03513015806674957, -0.04589851573109627, -0.01741832122206688, -0.001634974149055779, -0.03911096602678299, -0.005067731719464064, -0.03347913175821304, 0.001370122074149549, -0.023297807201743126, -0.009961188770830631, -0.011612214148044586, -0.0027792267501354218, 0.03138783574104309, 0.0009997878223657608, 0.00393494451418519, 0.016712049022316933, 0.013116482645273209, 0.06450007110834122, -0.008658712729811668, -0.04703588783740997, 0.0165836364030838, -0.05712549015879631, -0.02359132282435894, 0.028379298746585846, -0.03243348374962807, -0.11241650581359863, 0.007415857166051865, -0.03094756044447422, -0.002877829596400261, 0.0050769043155014515, -0.025077246129512787, 0.039881445467472076, 0.013345791958272457, -0.02315104939043522, 0.06130808964371681, 0.036854565143585205, -0.027718888595700264, 0.0165836364030838, -0.0020408511627465487, 0.010337255895137787, -0.04692582041025162, -0.020839614793658257, 0.032396793365478516, -0.027718888595700264, 0.01792280189692974, -0.05565791204571724, -0.021573403850197792, 0.014373096637427807, 0.028782881796360016, 0.017244046553969383, -0.027058478444814682, -0.0300119798630476, 0.02751709520816803, -0.00598496850579977, -0.07756152004003525, -0.04311011731624603, -0.016812944784760475, -0.004051892552524805, 0.0008948788745328784, 0.006782964337617159, 0.01411627046763897, 0.03751497343182564, -0.02439849078655243, -0.00920905452221632, -0.01009877398610115, -0.030654044821858406, -0.006714171264320612, -0.07719462364912033, 0.025407452136278152, -0.04718264564871788, -0.020931337028741837, 0.003118604188784957, 0.0003193129668943584, -0.007594718597829342, -0.06163829565048218, -0.042926669120788574, -0.06813232600688934, -0.001004374003969133, 0.007796510588377714, -0.04413742199540138, -0.032305069267749786, -0.004226167220622301, -0.054924122989177704, 0.0029076398350298405, 0.06174836307764053, 0.0714343786239624, 0.055547844618558884, 0.011914902366697788, 0.02836095355451107, -0.01174980029463768, -0.01556550431996584, -0.018463971093297005, 0.0671784058213234, -0.019610516726970673, 0.009117331355810165, 0.014684956520795822, -0.04780636727809906, -0.04685244336724281, 0.019463758915662766, 0.013501721434295177, 0.03896420821547508, -0.01741832122206688, -0.008686229586601257, -0.021866919472813606, -0.04384390637278557, -0.05716218054294586, -0.02131657674908638, -0.01455654390156269, -0.0653439313173294, -0.03173638507723808, -0.0486869141459465, 0.01369434129446745, 0.024196699261665344, -0.04325687512755394, -0.0018103956244885921, -0.06149153783917427, 0.01766597479581833, 0.03023211658000946, -0.00027029812918044627, 0.04931063577532768, -0.048099882900714874, 0.020325960591435432, 0.00030784751288592815, -0.032928790897130966, 0.018840039148926735, 0.010117119178175926, -0.039808064699172974, -0.0233161523938179, 0.02287587895989418, -0.009832775220274925, -0.012437727302312851, -0.025976138189435005, 0.0340845100581646, -0.0024329698644578457, -0.018785003572702408, 0.01792280189692974, 0.020436029881238937, 0.010401462204754353, 0.018739141523838043, -0.008920125663280487, -0.08541306853294373, -0.0034281716216355562, -0.017968663945794106, 0.061821743845939636, -0.030929215252399445, 0.03125942125916481, 0.008626609109342098, 0.0320299006998539, 0.037753455340862274, 0.003886789781972766, 0.013143999502062798, 0.0032951722387224436, -0.01076835673302412, 0.008736678399145603, 0.006576586049050093, -0.07092072814702988, 0.030874181538820267, -0.034891676157712936, -0.04156915843486786, -0.012547795660793781, 0.027462061494588852, 0.06226201727986336, 0.014501509256660938, 0.0035932741593569517, -0.017528390511870384, 0.009557604789733887, 0.002531572710722685, 0.009277847595512867, 0.02979184314608574, 0.01673039421439171, -0.01558384858071804, -0.02524234913289547, -0.010915114544332027, 0.032451827079057693, 0.04373383894562721, -0.010254704393446445, -0.017968663945794106, -0.0071177552454173565, -0.009085227735340595, -0.012437727302312851, -0.017757698893547058, 0.03241514042019844, 0.030177081003785133, -0.02823254093527794, 0.010181325487792492, -0.006815067492425442, 0.017803560942411423, -0.04949408397078514, 0.021683471277356148, 0.014052063226699829, -0.04098212718963623, 0.023334497585892677, 0.05756576359272003, -0.03307554870843887, 0.034543126821517944, -0.015042679384350777, -0.05587805062532425, -0.014198821038007736, -0.013327446766197681, -0.020949682220816612, 0.0289479847997427, 0.013868615962564945, 0.012171728536486626, -0.024196699261665344, 0.0672517791390419, 0.0126670366153121, 0.014703301712870598, -0.036726150661706924, -0.030030323192477226, 0.016198396682739258, 0.006365621462464333, -0.01866576261818409, 0.003806531662121415, -0.012978896498680115, -0.01196993701159954, 0.024325111880898476, 0.018179627135396004, -0.02988356538116932, -0.00825971458107233, 0.011988281272351742, -0.06842584162950516, -0.03241514042019844, -0.023426221683621407, 0.005636418703943491, 0.0033387409057468176, -0.005017283838242292, -0.03201155364513397, -0.01157552469521761, 0.027883989736437798, 0.007525925524532795, 0.054300401359796524, -0.009305364452302456, 0.023169394582509995, -0.015391228720545769, -0.008704574778676033, -0.026911720633506775, -0.02006913535296917, -0.019959066063165665, 0.011208630166947842, 0.0068517569452524185, -0.010337255895137787, 0.0075029949657619, -0.017189012840390205, -0.017344942316412926, -0.03135114535689354, 0.04300004988908768, 0.02823254093527794, 0.022619053721427917, 0.005567625630646944, -0.002118816366419196, 0.008172577247023582, 0.016097500920295715, -0.04347700998187065, -0.006296828854829073, -0.0017083530547097325, 0.009053124114871025, 0.0011643171310424805, 0.00782402791082859, 0.004870526026934385, 0.02546248584985733, -0.0029420361388474703, 0.05323641002178192, -0.06897618621587753, 0.022233814001083374, 0.06185843050479889, 0.01610667258501053, 0.003208034671843052, -0.03402947634458542, -0.01870245300233364, 0.057859279215335846, -0.0011253345292061567, 0.020270926877856255, -0.007296616677194834, 0.003542826045304537, 0.003276827512308955, 0.06361952424049377, -0.026416411623358727, 0.01199745386838913, 0.020894648507237434, -0.04362376779317856, 0.04743947461247444, 0.010869252495467663, -0.04901712015271187, 0.03191982954740524, -0.06556406617164612, 0.030525632202625275, -0.06046423316001892, 0.009713535197079182, 0.012850483879446983, 0.004255977459251881, -0.007654338609427214, -0.03782683610916138, -0.022013677284121513, 0.014969300478696823, 0.006920549552887678, -0.009667673148214817, -0.0030910870991647243, 0.0057097976095974445, -0.016024122014641762, -0.024581938982009888, 0.02069285698235035, 0.03566215559840202, -0.011667248792946339, -0.05147531256079674, 0.01817045547068119, 0.01605163887143135, 0.04083536937832832, -0.003405240597203374, -0.013795237056910992, 0.0005517750978469849, -0.004957663360983133, 0.030599011108279228, 0.019610516726970673, 0.03023211658000946, 0.009566777385771275, 0.01953713782131672, 0.02559089846909046, -0.011593869887292385, 0.0118873855099082, 0.05114511027932167, -0.0024260906502604485, 0.021298231557011604, 0.040064889937639236, 0.009085227735340595, 0.009851120412349701, 0.024857109412550926, -0.010979320853948593, 0.017904456704854965, -0.010401462204754353, 0.039441172033548355, 0.03023211658000946, 0.04593520611524582, 0.06835246831178665, -0.0316079705953598, -0.0010920847998932004, -0.01561136543750763, 0.017693493515253067, 0.02729695849120617, -0.0466323047876358, 0.04424748942255974, 0.06450007110834122, -0.018840039148926735, -0.06431662291288376, -0.04740278422832489, 0.041532471776008606, 0.009007262997329235, 0.02082126960158348, 0.016812944784760475, -0.012813794426620007, -0.009676845744252205, -0.041532471776008606, -0.007521339692175388, 0.03668946027755737, -0.03138783574104309, -0.025224003940820694, 0.04637547954916954, -0.021518368273973465, 0.04120226576924324, 0.007915751077234745, 0.01633598282933235, -0.027590474113821983, -0.0012829846236854792, 0.013235722668468952, -0.02680165134370327, -0.01052070315927267, -0.019738929346203804, 0.03384602814912796, 0.011465456336736679, -0.024471869692206383, 0.013923650607466698, 0.00449445890262723, -0.02368304692208767, -0.03296548128128052, -0.029846876859664917, 0.017840251326560974, 0.016491912305355072, 0.024068286642432213, 0.02028927206993103, 0.03764338791370392, 0.004150495398789644, -0.010603254660964012, -0.015492125414311886, -0.027058478444814682, 0.028966329991817474, 0.029333224520087242, -0.01882169395685196, -0.08049667626619339, -0.02549917623400688, -0.026379723101854324, 0.04865022376179695, -0.0034396369010210037, 0.026544824242591858, -0.0024765385314822197, -0.0034717402886599302, 0.0029420361388474703, -0.052465930581092834, -0.007654338609427214, 0.009172365069389343, 0.019280312582850456, -0.027168545871973038, 0.05444715917110443, -0.04303673654794693, -0.03546036407351494, 0.04340363293886185, -0.010447324253618717, 0.04054185375571251, 0.027186891064047813, 0.002682916820049286, 0.0026301757898181677, -0.0058015212416648865, 0.007241582497954369, -0.00410463334992528, -0.010557392612099648, 0.053529925644397736, -0.06853591650724411, 0.017537562176585197, -0.043330252170562744, -0.05771252140402794, 0.04156915843486786, -0.002164678182452917, -0.006631620228290558, 0.04241301864385605, -0.013584272935986519, -0.015969088301062584, 0.0007928363047540188, 0.027902334928512573, -0.006076692137867212, 0.0372031144797802, -0.06750860810279846, 0.009612638503313065, 0.00029437561170198023, 0.027131857350468636, -0.010649115778505802, 0.016436878591775894, 0.02626965381205082, 0.0025201074313372374, -0.053896818310022354, 0.016537774354219437, 0.018381420522928238, 0.005154869519174099, -0.017179839313030243, 0.023206084966659546, 0.02586607076227665, -0.022252157330513, 0.008663298562169075, 0.008489023894071579, 0.0347265750169754, -0.01729908026754856, 0.038377176970243454, -0.04472445324063301, -0.027223579585552216, 0.025535864755511284, 0.007521339692175388, 0.000736655609216541, 0.01469412911683321, -0.041275642812252045, 0.004615992773324251, 0.032176658511161804, 0.006269311532378197, -0.01065828837454319, -0.003932651598006487, 0.010805046185851097, -0.0041734264232218266, -0.005920761730521917, -0.02412332035601139, -0.025609243661165237, 0.017161495983600616, 0.015776468440890312, 0.007975371554493904, -0.01667536050081253, -0.026691583916544914, -0.001437768223695457, 0.0007486942922696471, -0.009594294242560863, 0.008122129365801811, -0.038157038390636444, -0.002749416511505842, -0.01611584611237049, -0.0704437643289566, -0.01705142669379711, 0.04259646311402321, 0.02100471593439579, -0.017133979126811028, 0.022820845246315002, -0.019298655912280083, -0.0014698714949190617, -0.021573403850197792, -0.01695053093135357, -0.025792691856622696, -0.0025751416105777025, 0.02439849078655243, -0.008690816350281239, 0.014538198709487915, 0.006480276118963957, 0.03804697096347809, -0.03771676495671272, 0.007236996199935675, -0.04219288006424904, 0.031369488686323166, -0.01922527700662613, 0.03577222302556038, -0.011043528094887733, 0.04134902358055115, 0.0022575485054403543, -0.001227950444445014, -0.039441172033548355, -0.006017071660608053, -0.024765387177467346, -0.0403217189013958, 0.003854686627164483, -0.02680165134370327, -0.011300354264676571, 0.0372031144797802, 0.019995756447315216, 0.013896133750677109, 0.01822548918426037, -0.012602830305695534, -0.03536863997578621, 0.004533441737294197, 0.026544824242591858, 0.056428391486406326, -0.007177375722676516, -0.0009929084917530417, -0.031241076067090034, -0.0142446830868721, 0.04619203135371208, -0.028837917372584343, 0.06090450659394264, 0.006296828854829073, -0.0047696297988295555, -0.01623508706688881, 0.033148929476737976, -0.036230843514204025, -0.02617792971432209, 0.041715916246175766, 0.016684532165527344, 0.015308677218854427, -0.009704362601041794, -0.017335770651698112, -0.010731667280197144, 0.0011436792556196451, 0.026544824242591858, -0.020582787692546844, 0.040028203278779984, 0.008016646839678288, 0.02359132282435894, -0.024141665548086166, -0.004732940346002579, -0.009420019574463367, 0.0015742072137072682, -0.04986097663640976, -0.0044394247233867645, -0.028177505359053612, 0.0007893966976553202, 0.030874181538820267, -0.0015042679151520133, -0.01988568715751171, 0.03256189823150635, 0.004916387610137463, 0.004533441737294197, 0.01586819253861904, -0.029314879328012466, 0.03830379620194435, 0.007622235454618931, -0.014519854448735714, 0.020050790160894394, -0.025187315419316292, 0.08233115077018738, 0.016473568975925446, 0.014437302947044373, 0.009227399714291096, 0.005700625013560057, -0.05250261723995209, -0.04465107247233391, 0.01455654390156269, 0.005292454734444618, -0.029241500422358513, -0.008076267316937447, 0.015969088301062584, -0.013446687720716, -0.028782881796360016, 0.03698297590017319, -0.00016725235036574304, -0.019078519195318222, 0.016913842409849167, -0.001321967109106481, 0.015510469675064087, -0.03357085585594177, -0.04857684671878815, 0.01741832122206688, 0.0335892029106617, 0.04083536937832832, 0.008865091018378735, -0.01698722131550312, 0.029241500422358513, 0.037790145725011826, -0.014042891561985016, 0.03580891340970993, 0.02836095355451107, -0.03338741138577461, 0.01826217956840992, 0.013327446766197681, -0.025480831041932106, -0.0253707617521286, -0.01333661936223507, -0.007608477026224136, -0.04718264564871788, 0.055547844618558884, 0.002992484252899885, 0.016125017777085304, 0.002728778636083007, -0.015492125414311886, 0.04248639568686485, -0.02206871099770069, -0.021921953186392784, -0.014611577615141869, -0.061198022216558456, -0.005819865968078375, -0.05107172951102257, -0.03390106186270714, -0.024636972695589066, -0.005242006853222847, 0.04677906259894371, -0.004613699857145548, -0.0011471189791336656, 0.001610896666534245, -0.014373096637427807, -0.017757698893547058, 0.050374630838632584, -0.011382905766367912, 0.009667673148214817, -0.07778165489435196, -0.0023079963866621256, -0.005287868436425924, -0.018931761384010315, 0.023756425827741623, 0.02144498936831951, 0.010162980295717716, 0.02639806643128395, 0.04329356551170349, -0.016491912305355072, -0.033203963190317154, -0.006585758179426193, 0.025609243661165237, 0.03580891340970993, 0.010704150423407555, 0.02390318363904953, -0.019812308251857758, -0.04909050092101097, 0.038377176970243454, 0.007879061624407768, 0.023609668016433716, 0.01090594194829464, -0.037441596388816833, 0.003279120661318302, 0.046045273542404175, -0.05727224797010422, 0.021078094840049744, -0.012290969491004944, 0.01174980029463768, -0.05921678990125656, 0.02449021488428116, 0.0454949326813221, -0.039661306887865067, 0.01670287735760212, -0.005833624396473169, 0.04347700998187065, -0.0007962759700603783, 0.03705635666847229, 0.04013827070593834, 0.019738929346203804, -0.022637397050857544, 0.06472020596265793, -0.03518519178032875, 0.004664147738367319, -0.006727930158376694, 0.01770266517996788, 0.010814218781888485, 0.05510757118463516, 0.005219075828790665, 0.021298231557011604, 0.0042880806140601635, -0.02867281436920166, 0.021701816469430923, 0.024270078167319298, -0.006296828854829073, 0.0026072447653859854 ]
Affective computing strives to unveil the unknown relationship between affect elicitation, manifestation of affect and affect annotations. The ground truth of affect, however, is predominately attributed to the affect labels which inadvertently include biases inherent to the subjective nature of emotion and its labeling. The response to such limitations is usually augmenting the dataset with more annotations per data point; however, this is not possible when we are interested in self-reports via first-person annotation. Moreover, outlier detection methods based on inter-annotator agreement only consider the annotations themselves and ignore the context and the corresponding affect manifestation. This paper reframes the ways one may obtain a reliable ground truth of affect by transferring aspects of causation theory to affective computing. In particular, we assume that the ground truth of affect can be found in the causal relationships between elicitation, manifestation and annotation that remain \emph{invariant} across tasks and participants. To test our assumption we employ causation inspired methods for detecting outliers in affective corpora and building affect models that are robust across participants and tasks. We validate our methodology within the domain of digital games, with experimental results showing that it can successfully detect outliers and boost the accuracy of affect models. To the best of our knowledge, this study presents the first attempt to integrate causation tools in affective computing, making a crucial and decisive step towards general affect modeling.
[ 0.002140361350029707, -0.05150410532951355, -0.030298808589577675, -0.028905760496854782, 0.02718379721045494, 0.02946685068309307, -0.08358292281627655, 0.011570043861865997, -0.028267279267311096, 0.007308668922632933, 0.010747757740318775, -0.04275885596871376, 0.029582936316728592, -0.024126829579472542, 0.042139723896980286, -0.021998560056090355, 0.02319813147187233, 0.004967573098838329, -0.008900033310055733, -0.03082120232284069, -0.00042142142774537206, -0.012111784890294075, -0.04388103261590004, 0.041094936430454254, 0.027493363246321678, 0.045312777161598206, 0.020605511963367462, -0.0218244306743145, -0.049994971603155136, 0.05289715528488159, 0.062493711709976196, -0.01835148222744465, -0.042371898889541626, -0.016871368512511253, -0.03854101523756981, -0.045661039650440216, -0.004307325929403305, 0.018612679094076157, 0.01851593889296055, 0.04101754352450371, 0.0026458250358700752, 0.014578641392290592, 0.0016953595913946629, -0.0018090285593643785, 0.012740591540932655, -0.06218414753675461, -0.011260476894676685, -0.025771401822566986, -0.031111421063542366, 0.02306269481778145, 0.02685488387942314, -0.054522380232810974, 0.06883982568979263, 0.02093442715704441, -0.0654732882976532, 0.03221425041556358, 0.05835326388478279, -0.05154280364513397, 0.08288639783859253, 0.026564665138721466, 0.002090782392770052, 0.030763158574700356, -0.05200715363025665, 0.00577534781768918, -0.015101035125553608, -0.06462198495864868, 0.03391686826944351, 0.007705300580710173, 0.02321747876703739, -0.0192608330398798, 0.00409691734239459, -0.004810371436178684, -0.02081833966076374, -0.015700818970799446, -0.009180578403174877, 0.019405942410230637, 0.03691579028964043, 0.04368755593895912, -0.010380147956311703, -0.012885700911283493, 0.04504190757870674, 0.02103116549551487, -0.023333566263318062, 0.028750978410243988, 0.013572551310062408, -0.08505336195230484, 0.019057679921388626, -0.07580506801605225, 0.008590467274188995, 0.018738439306616783, -0.020450729876756668, 0.02126334048807621, 0.011105693876743317, 0.016078103333711624, -0.023140087723731995, 0.02352704480290413, 0.03877319023013115, -0.0023253755643963814, -0.07031026482582092, -0.010612322017550468, 0.009228947572410107, 0.005015942733734846, -0.01613614708185196, -0.020044423639774323, -0.0047620018012821674, -0.04039841145277023, -0.02025724947452545, 0.016687562689185143, 0.04643495753407478, 0.21963734924793243, 0.007990682497620583, 0.07038765400648117, -0.04809887707233429, -0.025190964341163635, 0.016619844362139702, -0.022791825234889984, 0.05200715363025665, -0.04148189350962639, 0.015845928341150284, -0.030453592538833618, -0.02602292411029339, 0.09016120433807373, 0.03585165739059448, -0.028035106137394905, 0.021669646725058556, 0.048369746655225754, 0.02195986546576023, -0.02025724947452545, 0.008619489148259163, 0.02989250421524048, 0.03254316747188568, 0.04012754186987877, 0.0550641193985939, 0.04817626625299454, 0.045661039650440216, 0.021979212760925293, -0.009175741113722324, 0.04864061623811722, 0.0013386327773332596, 0.015275166369974613, -0.036451440304517746, -0.023275522515177727, -0.028151191771030426, -0.0013495159801095724, -0.01923181116580963, -0.020663555711507797, -0.03809601441025734, 0.020895730704069138, -0.049646709114313126, -0.008513075299561024, -0.026177706196904182, 0.048485834151506424, -0.0037196334451436996, 0.006162305828183889, 0.05034323409199715, -0.02753205969929695, 0.0031464521307498217, -0.03714796528220177, 0.025771401822566986, -0.021785734221339226, 0.018902897834777832, -0.03205946832895279, 0.014336792752146721, -0.0018706999253481627, 0.05552846938371658, -0.0035745243076235056, -0.028383366763591766, -0.016358647495508194, -0.012527764774858952, 0.06942026317119598, -0.012992113828659058, 0.006670188158750534, -0.00858079269528389, 0.01711321622133255, 0.019618770107626915, 0.056805431842803955, 0.049298446625471115, -0.017006803303956985, -0.03799927234649658, 0.04333929345011711, -0.039063408970832825, -0.03910210356116295, -0.013911139219999313, 0.019405942410230637, 0.028383366763591766, 0.009683622978627682, 0.07882334291934967, -0.04539017006754875, 0.04705408960580826, 0.03788318485021591, -0.018902897834777832, 0.017142238095402718, 0.060675010085105896, 0.011599065735936165, 0.02401074208319187, 0.007328016683459282, -0.0600171834230423, 0.02275312878191471, -0.005944641772657633, -0.02991185151040554, -0.031014680862426758, -0.05251019820570946, -0.033491212874650955, -0.012779287062585354, 0.024745961651206017, -0.024978136643767357, 0.03196272999048233, 0.010612322017550468, -0.012537438422441483, -0.01722930371761322, 0.019580073654651642, 0.024146176874637604, 0.028035106137394905, -0.029621632769703865, 0.009286991320550442, -0.03252381831407547, 0.02909923903644085, 0.01818702556192875, -0.035542089492082596, -0.002370117697864771, -0.008885522373020649, 0.04333929345011711, 0.029021847993135452, -0.015381579287350178, 0.04434538260102272, 0.0071925814263522625, 0.038947321474552155, -0.022888563573360443, 0.007942312397062778, -0.007942312397062778, -0.04562234506011009, 0.004300070460885763, 0.0038574873469769955, -0.05661195144057274, 0.024881398305296898, 0.007695626933127642, 0.002936043543741107, 0.01734539121389389, 0.040901459753513336, -0.035213176161050797, -0.04697669669985771, -0.06791112571954727, -0.02522966079413891, 0.014907555654644966, 0.08869076520204544, -0.02457183226943016, -0.004539500921964645, 0.0400114543735981, 0.03182729333639145, -0.01825474202632904, -0.03505839407444, 0.03250446915626526, 0.05370976775884628, 0.05107845366001129, 0.008692043833434582, 0.06903330236673355, 0.020334642380475998, -0.06017196550965309, 0.020392686128616333, -0.03014402650296688, 0.013446789234876633, 0.06353849917650223, 0.003163381479680538, 0.018128981813788414, 0.0016748025082051754, -0.06856895238161087, 0.04194624349474907, 0.0005441596731543541, 0.005934968125075102, -0.013659616932272911, -0.005591542925685644, 0.007361875381320715, -0.01928018033504486, -0.06288067251443863, 0.004650751128792763, -0.032485123723745346, 0.04376494511961937, 0.02571335807442665, 0.018564308062195778, 0.020276598632335663, -0.00915155652910471, -0.002345932647585869, 0.03749622777104378, -0.023797916248440742, 0.023604435846209526, -0.02909923903644085, 0.01860300451517105, 0.002599873812869191, -0.08814902603626251, -0.04933714121580124, -0.004333929158747196, -0.036780353635549545, -0.06814330071210861, 0.020276598632335663, 0.04539017006754875, 0.019734857603907585, -0.034265127032995224, 0.020334642380475998, 0.0007424756186082959, -0.06473807245492935, 0.01914474554359913, -0.020644208416342735, 0.027435319498181343, 0.04438408091664314, -0.003441507462412119, 0.042565375566482544, 0.07568898051977158, 0.01097025815397501, 0.0017026150599122047, -0.028015756979584694, -0.02025724947452545, 0.02056681551039219, -0.010747757740318775, -0.04709278419613838, 0.01830311305820942, -0.025384442880749702, -0.006012359634041786, -0.054638467729091644, -0.04945322871208191, -0.00653958972543478, -0.008759761229157448, -0.05312933027744293, -0.04767322167754173, 0.018970614299178123, 0.024126829579472542, -0.0050836605951189995, 0.0034971327986568213, 0.03285273164510727, -0.004005014896392822, -0.016677888110280037, -0.05413541942834854, 0.026990318670868874, -0.011734500527381897, 0.0015865276800468564, -0.036335352808237076, -0.029989242553710938, 0.04500321298837662, 0.020102467387914658, -0.037360791116952896, -0.015439623035490513, -0.015604080632328987, -0.009925471618771553, -0.05127193033695221, -0.012421350926160812, -0.04047580435872078, -0.025384442880749702, -0.01734539121389389, -0.006510567851364613, -0.022946607321500778, -0.010486560873687267, 0.001256404211744666, -0.009175741113722324, -0.03799927234649658, 0.003204495646059513, -0.008653347380459309, -0.019434964284300804, 0.022695085033774376, -0.024842701852321625, 0.023585088551044464, 0.04767322167754173, 0.027203146368265152, -0.029757067561149597, -0.01585560292005539, 0.07607594132423401, -0.06562807410955429, -0.036006439477205276, 0.008817804977297783, -0.003361697308719158, 0.05432889983057976, -0.03560013324022293, -0.0532454177737236, 0.029582936316728592, -0.009320850484073162, -0.04217841848731041, -0.03151772543787956, 0.014868860132992268, -0.005586705636233091, 0.015110708773136139, -0.06489285081624985, 0.04287494346499443, -0.04148189350962639, -0.04573843255639076, -0.03115011751651764, -0.000375167845049873, -0.008754923939704895, -0.001974694896489382, 0.022656388580799103, -0.005161052104085684, 0.01932855136692524, 0.030840551480650902, -0.03933427855372429, -0.028634890913963318, -0.025094224140048027, -0.07777855545282364, 0.028518803417682648, -0.05127193033695221, -0.009185414761304855, 0.042797550559043884, 0.07170331478118896, 0.015178426168859005, 0.03070511482656002, -0.011076672002673149, 0.012547112070024014, 0.01319526694715023, 0.020779643207788467, 0.0281898882240057, 0.0527423731982708, 0.05483194440603256, 0.004868415184319019, 0.014510923996567726, -0.03037620149552822, 0.008213182911276817, 0.009533677250146866, -0.007289320696145296, 0.0007025705999694765, 0.013233962468802929, -0.017887132242321968, -0.024146176874637604, 0.028518803417682648, -0.021514862775802612, -0.02728053741157055, -0.01783876307308674, 0.03722535818815231, -0.04171406850218773, -0.015168752521276474, -0.012073088437318802, -0.019928336143493652, 0.01143460813909769, -0.00971264485269785, -0.04163667932152748, 0.02000572718679905, 0.01006090734153986, 0.03289142623543739, -0.009857754223048687, 0.04035971686244011, 0.0005831577582284808, 0.017683979123830795, -0.02161160297691822, 0.002824793104082346, 0.002803026931360364, 0.0014619756257161498, 0.026216402649879456, 0.007627909071743488, 0.029292719438672066, 0.049530621618032455, -0.06303545087575912, -0.02242421545088291, -0.060094572603702545, -0.04477103799581528, -0.007071657106280327, -0.04809887707233429, 0.03844427317380905, -0.007705300580710173, -0.03796057775616646, -0.0025490857660770416, -0.01131852064281702, 0.02762879990041256, -0.04368755593895912, 0.043726250529289246, -0.06527981162071228, 0.007845573127269745, 0.04562234506011009, 0.004404065664857626, 0.004077569581568241, -0.012015044689178467, 0.00416705384850502, -0.03641274571418762, -0.03467143326997757, -0.0013289587805047631, 0.0011965465964749455, 0.024629874154925346, -0.06624720245599747, -0.03730274736881256, -0.019057679921388626, 0.04287494346499443, 0.009973841719329357, 0.011753848753869534, -0.06574416160583496, 0.0836603119969368, -0.012034392915666103, -0.007521495688706636, 0.0017570310737937689, 0.012198850512504578, 0.0015417856629937887, 0.06996200233697891, -0.009727155789732933, 0.013514507561922073, -0.012721243314445019, 0.010089929215610027, -0.033491212874650955, -0.040437109768390656, -0.044306688010692596, 0.07866855710744858, 0.007981007918715477, 0.021456819027662277, 0.004362951032817364, -0.021863125264644623, -0.0006006917683407664, 0.031072724610567093, 0.039411671459674835, 0.0009806966409087181, -0.02341095730662346, -0.008029378019273281, 0.03275599330663681, 0.027706190943717957, -0.010612322017550468, -0.0020883637480437756, 0.0006862457958050072, 0.060558922588825226, -0.034303825348615646, 0.007144211791455746, -0.00995449349284172, 0.005518988240510225, -0.0224048662930727, -0.014772120863199234, 0.004193657077848911, -0.014501250348985195, -0.017771044746041298, 0.029137935489416122, -0.00043230460141785443, -0.00665567722171545, -0.015371905639767647, -0.012934070080518723, 0.024300960823893547, -0.0023483512923121452, 0.03881188482046127, 0.024475092068314552, 0.014336792752146721, 0.03238838165998459, -0.019850943237543106, -0.012663199566304684, 0.05394194275140762, -0.03546469658613205, -0.057347171008586884, -0.014568967744708061, -0.04852452874183655, 0.064157634973526, 0.06346110999584198, -0.015226796269416809, -0.04217841848731041, -0.02956358902156353, 0.012189175933599472, 0.0036011275369673967, 0.017335716634988785, -0.02797706238925457, -0.006999102421104908, 0.025423139333724976, 0.0007521495572291315, 0.033587951213121414, 0.028789673000574112, 0.05363237485289574, 0.011811892502009869, 0.006176816765218973, 0.019599420949816704, 0.022211387753486633, 0.008106769993901253, -0.030105330049991608, 0.035754915326833725, -0.01750984787940979, -0.05243280529975891, 0.0020617605186998844, 0.012256894260644913, -0.005175563041120768, -0.0013966764090582728, -0.03169185668230057, 0.022250084206461906, 0.03707057237625122, 0.06825938820838928, -0.015720168128609657, -0.0003113802522420883, -0.029312066733837128, -0.029021847993135452, -0.013398420065641403, 0.011279825121164322, 0.0338975191116333, 0.04422929510474205, -0.0013204941060394049, -0.00873073935508728, -0.005388389807194471, 0.04515799507498741, 0.016745606437325478, -0.020508771762251854, 0.0030303646344691515, 0.030666420236229897, -0.02242421545088291, -0.016610171645879745, -0.032581862062215805, -0.061797186732292175, -0.040978848934173584, 0.00383572094142437, -0.026661405339837074, 0.05014975368976593, -0.008479217067360878, -0.04047580435872078, -0.016619844362139702, -0.0015018805861473083, 0.01837082952260971, -0.013504832983016968, 0.05955283343791962, -0.039392322301864624, 0.005741489119827747, 0.0019311620853841305, -0.011250803247094154, 0.01386276911944151, -0.014849511906504631, -0.03134359419345856, 0.00046616344479843974, -0.01638766936957836, -0.017355065792798996, 0.04163667932152748, 0.05823717638850212, -0.024494439363479614, 0.021282687783241272, -0.01876746118068695, 0.009364383295178413, -0.030395548790693283, 0.047479745000600815, -0.03608383238315582, 0.01795485056936741, 0.008967750705778599, 0.031904686242341995, -0.016890715807676315, 0.03925688564777374, -0.023952698335051537, 0.04411320760846138, -0.010815475136041641, -0.012160154059529305, -0.03205946832895279, -0.02716444991528988, -0.01704549789428711, -0.033375125378370285, -0.0033399309031665325, -0.0552189014852047, 0.022714432328939438, 0.05262628570199013, 0.013350049965083599, -0.00008343781519215554, 0.06148762255907059, 0.018641700968146324, -0.005035290494561195, 0.00497724674642086, 0.02627444639801979, -0.027686843648552895, 0.017819413915276527, -0.018680395558476448, 0.02025724947452545, -0.011289498768746853, -0.013272658921778202, 0.009906124323606491, 0.03778644651174545, -0.0013204941060394049, 0.021127905696630478, -0.004529826808720827, 0.042023636400699615, -0.018283763900399208, -0.029312066733837128, 0.05216193571686745, -0.014646359719336033, -0.03550339490175247, 0.013137223199009895, -0.007850409485399723, 0.0012467302149161696, 0.059320658445358276, 0.012605155818164349, 0.03770905360579491, -0.014472228474915028, -0.0008047516457736492, 0.02025724947452545, -0.000009985707947635092, 0.041094936430454254, -0.027377277612686157, -0.025055529549717903, -0.06957504153251648, 0.010825149714946747, 0.036006439477205276, -0.014752772636711597, 0.0021149672102183104, 0.054290205240249634, 0.007656930945813656, -0.02137942798435688, -0.003983248490840197, -0.033491212874650955, 0.007826224900782108, -0.022830519825220108, 0.027241840958595276, -0.025442486628890038, 0.015836255624890327, 0.016513431444764137, 0.02194051630795002, -0.02877032570540905, -0.003105337731540203, -0.03596774488687515, -0.01916409283876419, -0.009625579230487347, -0.016745606437325478, -0.003151288954541087, -0.03221425041556358, -0.01690039038658142, 0.009925471618771553, 0.0058914353139698505, -0.06891721487045288, -0.00571246724575758, 0.017248651012778282, 0.06276458501815796, -0.005122356116771698, 0.006201001349836588, 0.025500530377030373, 0.020063770934939384, 0.01790647953748703, -0.009775525890290737, -0.003920367918908596, 0.028460759669542313, -0.01630060374736786, 0.01455929409712553, 0.04469364508986473, 0.003006179817020893, 0.057927608489990234, -0.013949834741652012, -0.03693513944745064, 0.04600930213928223, 0.02501683309674263, -0.009973841719329357, 0.03145968168973923, -0.02557792142033577, 0.008092259056866169, 0.014259401708841324, 0.013262984342873096, 0.020740946754813194, -0.03250446915626526, -0.008324433118104935, 0.07069722563028336, 0.0012164991348981857, -0.0054464335553348064, -0.0008277273154817522, -0.03229164332151413, -0.015052665024995804, 0.02706770971417427, 0.00830024853348732, 0.016377996653318405, -0.012111784890294075, -0.008174487389624119, -0.020624859258532524, 0.004399228375405073, 0.0037196334451436996, -0.007178070489317179, 0.03159511834383011, -0.0042444453574717045, 0.03850231692194939, 0.009320850484073162, 0.06121675297617912, 0.020276598632335663, -0.004745072219520807, -0.004026781301945448, -0.0448097325861454, -0.025094224140048027, -0.011724826879799366, 0.0365481823682785, -0.001454720157198608, -0.026197055354714394, -0.008759761229157448, -0.0034149042330682278, 0.005180399864912033, -0.0048297191970050335, 0.01580723375082016, 0.022927260026335716, 0.028905760496854782, -0.05518020689487457, 0.008130954578518867, 0.025984227657318115, -0.01764528453350067, 0.008682369254529476, 0.027686843648552895, 0.04012754186987877, -0.02352704480290413, 0.05494803190231323, -0.010873518884181976, 0.03298816829919815, -0.02739662490785122, -0.049530621618032455, -0.006752416491508484, -0.015633102506399155, 0.002231054473668337, -0.03948906064033508, 0.030318157747387886, -0.003770421724766493, 0.034400563687086105, -0.03385882452130318, -0.025500530377030373, -0.020431380718946457, 0.009611068293452263, -0.048718009144067764, -0.02126334048807621, 0.0479440912604332, -0.005296487361192703, 0.02557792142033577, -0.042487986385822296, -0.031904686242341995, -0.002611966338008642, -0.034961652010679245, -0.041094936430454254, -0.0001745845511322841, -0.011028301902115345, -0.009678786620497704, 0.00022038465249352157, 0.0019855780992656946, -0.00011276196892140433, -0.03411034494638443, -0.03691579028964043, -0.013756356202065945, 0.027377277612686157, 0.022482259199023247, 0.01664886623620987, 0.0018948848592117429, -0.016223212704062462, -0.010080255568027496, 0.003833302529528737, -0.00934987235814333, 0.009224110282957554, 0.01006090734153986, -0.0031682183034718037, -0.06725329905748367, -0.04852452874183655, 0.0066750249825417995, -0.057269781827926636, -0.009659438394010067, 0.01346613746136427, 0.04186885431408882, -0.009398241527378559, 0.07940377295017242, -0.0007146630086936057, -0.012034392915666103, 0.05262628570199013, -0.030453592538833618, -0.02592618390917778, -0.042565375566482544, 0.020334642380475998, 0.00029792741406708956, -0.014830164611339569, 0.051117148250341415, 0.011811892502009869, -0.02559727057814598, -0.022230735048651695, -0.01855463534593582, 0.001818702439777553, 0.017500175163149834, 0.03134359419345856, 0.005591542925685644, 0.006370295770466328, -0.0030327830463647842, -0.01410461775958538, 0.0049530621618032455, 0.014007878489792347, 0.03981797397136688, 0.020895730704069138, 0.0073908972553908825, -0.022830519825220108, 0.005330346059054136, -0.016126474365592003, 0.027203146368265152, -0.019831595942378044, -0.018941592425107956, -0.0019275344675406814, 0.01860300451517105, 0.009224110282957554, 0.00539806392043829, 0.026912927627563477, -0.008958077058196068, -0.07526332885026932, -0.02275312878191471, -0.02317878231406212, -0.020199205726385117, -0.0029868318233639, -0.02774488739669323, 0.03707057237625122, 0.023120738565921783, 0.03049228899180889, -0.003816372947767377, -0.012382655404508114, -0.011395912617444992, -0.007057146169245243, 0.014452880248427391, 0.022811172530055046, 0.04922105371952057, -0.018477242439985275, 0.003073897445574403, -0.021998560056090355, -0.006950732786208391, -0.00405096635222435, 0.0021185949444770813, -0.0025249007157981396, 0.013166245073080063, -0.017238978296518326, -0.04035971686244011, 0.010351126082241535, -0.00451773451641202, -0.0034971327986568213, 0.01410461775958538, -0.02457183226943016, 0.01221819780766964, -0.011444281786680222, -0.0028925109654664993, -0.03726405277848244, 0.007115189917385578, -0.0019613932818174362, -0.020373336970806122, -0.03534861281514168, 0.005199747625738382, -0.01886420138180256, 0.02343030460178852, 0.019947683438658714, -0.027009665966033936, -0.041675373911857605, -0.005552846938371658, -0.03697383403778076, 0.014849511906504631, -0.03134359419345856, -0.024378351867198944, 0.024939442053437233, 0.048834096640348434, 0.010873518884181976, -0.001228591543622315, -0.001956556225195527, 0.00634127389639616, 0.005741489119827747, -0.0811837837100029, -0.02035398967564106, -0.01825474202632904, 0.044074513018131256, -0.02308204397559166, -0.020276598632335663, -0.027919018641114235, 0.03898601606488228, 0.022327475249767303, 0.045544952154159546, 0.05014975368976593, -0.0009933937108144164, 0.02548118308186531, 0.030453592538833618, -0.008769434876739979, -0.05467716231942177, 0.0034971327986568213, 0.0025829444639384747, -0.0030352016910910606, -0.038599058985710144, 0.009286991320550442, -0.0011378983035683632, -0.001225568470545113, -0.002718379721045494, -0.02613901160657406, -0.0509236678481102, 0.01608777791261673, -0.003625312587246299, 0.04124971851706505, -0.0008404243271797895, -0.050652798265218735, 0.06357719749212265, -0.0005402296083047986, -0.01382407359778881, 0.011782870627939701, 0.025094224140048027, -0.023372260853648186, 0.02592618390917778, -0.04775061458349228, -0.015487993136048317, -0.06574416160583496, 0.02673879638314247, -0.02594553306698799, 0.026874231174588203, 0.007700463756918907, 0.02025724947452545, 0.03743818402290344, 0.0008791201398707926, -0.036664269864559174, 0.022250084206461906, 0.03805731609463692, -0.021553559228777885, 0.017983872443437576, 0.012266567908227444, 0.001917860470712185, 0.0006892688688822091, 0.022675737738609314, 0.012808308936655521, 0.031092073768377304, -0.01804191619157791, -0.03627730906009674, 0.008914544247090816, 0.021089209243655205, 0.029969895258545876, -0.03840557858347893, 0.04028232395648956, 0.0012660780921578407, -0.0062300232239067554, 0.02329486981034279, -0.004718468990176916, -0.06373197585344315, -0.01131852064281702, -0.020663555711507797, -0.014781794510781765, -0.002403976395726204, 0.0038381393533200026, 0.005219095852226019, -0.023275522515177727, -0.010389821603894234, -0.011753848753869534, -0.012121458537876606, 0.02501683309674263, 0.028944456949830055, 0.02401074208319187, -0.02310139127075672, 0.001408768817782402, 0.014027226716279984, -0.017829088494181633, -0.04515799507498741, 0.004242026712745428, -0.06609242409467697, 0.03333643078804016, -0.020160511136054993, -0.02604227140545845, 0.011008954606950283, -0.0491049662232399, 0.027125753462314606, -0.027145102620124817, 0.015633102506399155, -0.042487986385822296 ]
There has been a flurry of research in recent years on notions of fairness in ranking and recommender systems, particularly on how to evaluate if a recommender allocates exposure equally across groups of relevant items (also known as provider fairness). While this research has laid an important foundation, it gave rise to different approaches depending on whether relevant items are compared per-user/per-query or aggregated across users. Despite both being established and intuitive, we discover that these two notions can lead to opposite conclusions, a form of Simpson's Paradox. We reconcile these notions and show that the tension is due to differences in distributions of users where items are relevant, and break down the important factors of the user's recommendations. Based on this new understanding, practitioners might be interested in either notions, but might face challenges with the per-user metric due to partial observability of the relevance and user satisfaction, typical in real-world recommenders. We describe a technique based on distribution matching to estimate it in such a scenario. We demonstrate on simulated and real-world recommender data the effectiveness and usefulness of such an approach.
[ -0.014298688620328903, 0.019155530259013176, -0.04729984328150749, -0.020134147256612778, -0.02339620515704155, 0.007756449282169342, -0.04313165694475174, 0.006519585847854614, -0.04389280453324318, 0.011235978454351425, -0.037912365049123764, -0.017923196777701378, 0.03552018851041794, -0.017234541475772858, -0.02027912810444832, 0.04146438464522362, 0.044762685894966125, 0.02834366075694561, -0.0021463888697326183, -0.022870652377605438, -0.012821700423955917, -0.02881484664976597, 0.0016548149287700653, 0.016337474808096886, -0.005921541713178158, 0.04541509971022606, -0.02482788637280464, -0.026023974642157555, -0.04947454854846001, 0.00516492547467351, 0.04266047105193138, 0.006071052514016628, -0.02156582847237587, -0.030282773077487946, -0.06995302438735962, -0.0015019059646874666, 0.041573118418455124, 0.001894938643090427, 0.005414110608398914, 0.05041692033410072, -0.04983700066804886, 0.036009497940540314, -0.018548425287008286, 0.02520846016705036, -0.012332391925156116, -0.02803557738661766, -0.010810098610818386, -0.005871704779565334, 0.0004309767682570964, -0.0015540082240477204, 0.02087717317044735, -0.03903596103191376, -0.0031487923115491867, -0.0072762020863592625, -0.03696999326348305, 0.009423723444342613, 0.002935852389782667, -0.041174422949552536, 0.03399789333343506, 0.004313165787607431, -0.001456599566154182, 0.012395820580422878, -0.06487870961427689, -0.0002609363291412592, 0.009351233020424843, 0.0064652180299162865, 0.023287471383810043, -0.03262058272957802, 0.044001538306474686, 0.0014146912144497037, -0.07288888096809387, 0.058390840888023376, 0.05654234066605568, 0.025860872119665146, -0.025172214955091476, 0.010112380608916283, 0.07201899588108063, -0.01600220799446106, -0.029829708859324455, 0.012341453693807125, 0.006737056188285351, 0.014353055506944656, 0.01669086515903473, 0.051323048770427704, 0.023885514587163925, -0.008046410046517849, 0.020297251641750336, -0.06187037006020546, -0.008671637624502182, -0.05335277318954468, -0.03124326840043068, -0.022453833371400833, 0.013111661188304424, -0.050018224865198135, 0.03434222191572189, 0.03416099771857262, 0.01783258467912674, 0.007711143232882023, -0.02368616685271263, 0.033707935363054276, 0.018267525359988213, -0.02598772943019867, 0.009668378159403801, 0.006084644701331854, 0.0005360309151001275, -0.061834122985601425, -0.055128782987594604, 0.01926426589488983, -0.010583566501736641, 0.16542258858680725, 0.006139012053608894, 0.056578587740659714, -0.07509982585906982, -0.0249909907579422, -0.055636215955019, 0.014769874513149261, -0.0740487203001976, -0.07071417570114136, 0.0099492771551013, -0.007647714111953974, -0.027618758380413055, 0.05338902026414871, 0.036081988364458084, 0.03213127329945564, -0.03117077797651291, 0.04436399042606354, 0.00997646152973175, -0.005862643476575613, 0.0481334812939167, 0.017560746520757675, -0.00011404461110942066, 0.05973190814256668, -0.06690843403339386, -0.049873244017362595, -0.03816607967019081, 0.009650255553424358, 0.059478193521499634, 0.0512143149971962, -0.0009248161222785711, -0.028832970187067986, -0.021819544956088066, -0.03983335569500923, -0.008526657707989216, 0.0025462175253778696, -0.042769208550453186, 0.007339630741626024, -0.004614453297108412, 0.025317195802927017, -0.022218240424990654, -0.01637372002005577, 0.006737056188285351, 0.02354118600487709, -0.016419027000665665, 0.0030400569085031748, 0.06277649849653244, 0.020895294845104218, -0.0015676001785323024, -0.04005082696676254, 0.0032212825026363134, 0.031660087406635284, 0.027528146281838417, -0.016890212893486023, -0.005926072131842375, 0.08133397996425629, 0.016092820093035698, 0.047807276248931885, 0.03635382652282715, -0.011480632238090038, -0.04878589138388634, 0.057412222027778625, -0.01124503929167986, -0.022961264476180077, -0.052156686782836914, 0.035465821623802185, 0.010656056925654411, 0.054222654551267624, 0.07509982585906982, -0.025353441014885902, -0.04990949109196663, -0.035157736390829086, -0.0638638511300087, 0.002543952316045761, -0.004181777127087116, -0.015413224697113037, 0.006120889913290739, -0.008408861234784126, 0.05770218372344971, 0.0027478309348225594, -0.008291064761579037, 0.036154478788375854, 0.0335267074406147, 0.05150427296757698, 0.05030818656086922, 0.029014194384217262, 0.003420630469918251, -0.04320414736866951, 0.017642298713326454, -0.08872798085212708, 0.02475539781153202, 0.0068865674547851086, -0.016500577330589294, -0.038746003061532974, 0.01439836248755455, -0.04671992361545563, 0.06063803657889366, -0.027147572487592697, 0.046284981071949005, 0.0004876097373198718, -0.046140000224113464, -0.02171080932021141, -0.02857925370335579, -0.08017414063215256, -0.029739096760749817, 0.015186692588031292, -0.04588628560304642, -0.0057176630944013596, 0.0113900201395154, 0.04342161864042282, 0.004956515971571207, -0.01093695592135191, -0.03655317425727844, -0.002312889788299799, 0.05781092122197151, 0.022000769153237343, 0.06650973856449127, -0.0040571847930550575, 0.004816066473722458, 0.05030818656086922, 0.010393279604613781, -0.014026850461959839, -0.031225144863128662, -0.005545498803257942, -0.04465395212173462, -0.010710424743592739, 0.006836730055510998, -0.019753575325012207, -0.03740493208169937, 0.01070136297494173, -0.021076520904898643, 0.03062710165977478, -0.05469384044408798, -0.005328028462827206, 0.059623174369335175, 0.0411381796002388, 0.043095413595438004, -0.018539363518357277, -0.0278181079775095, 0.022055137902498245, 0.007656775414943695, -0.0020342557691037655, -0.040123313665390015, -0.03185943514108658, -0.03164196386933327, 0.019717330113053322, -0.019445491954684258, 0.04733608663082123, 0.0443277470767498, -0.01736139878630638, -0.010683240368962288, -0.050706882029771805, 0.06118171289563179, 0.01904679462313652, 0.009559642523527145, 0.008091716095805168, 0.02413923107087612, 0.04106568917632103, 0.032421234995126724, -0.007860654033720493, -0.017868829891085625, 0.040884461253881454, -0.02986595407128334, -0.015811920166015625, -0.019137408584356308, -0.03758616000413895, 0.03530271723866463, -0.0011824960820376873, 0.033943526446819305, -0.02301563322544098, 0.047807276248931885, -0.0070451395586133, -0.010193931870162487, 0.01524106040596962, -0.007924082688987255, -0.01957234926521778, -0.05164925381541252, -0.03503087908029556, 0.03252996876835823, -0.014371178112924099, -0.03611823171377182, 0.008182329125702381, -0.01052013784646988, -0.05197545886039734, -0.013610031455755234, 0.010529198683798313, 0.037984855473041534, 0.004519309848546982, 0.005699540488421917, -0.03416099771857262, 0.04653869569301605, -0.04871340095996857, 0.012885130010545254, 0.022073259577155113, 0.024719152599573135, 0.005545498803257942, -0.02140272594988346, -0.026911979541182518, -0.018548425287008286, 0.09010529518127441, -0.069518081843853, -0.023668043315410614, 0.054222654551267624, -0.010791976004838943, -0.002224542433395982, -0.04356659948825836, -0.01850311830639839, 0.021076520904898643, 0.014162769541144371, -0.012812639586627483, 0.053896449506282806, -0.04646620526909828, -0.017941320315003395, -0.016718048602342606, -0.08785810321569443, -0.01820409670472145, -0.0392896793782711, -0.03769489377737045, -0.030681468546390533, 0.036154478788375854, -0.0028429743833839893, -0.0027342389803379774, -0.03852853178977966, 0.02104027569293976, 0.024266088381409645, -0.04498015716671944, 0.017932258546352386, 0.012857945635914803, -0.03243935480713844, -0.014044973067939281, -0.007584285456687212, -0.07227271050214767, 0.0030106077902019024, 0.010121441446244717, -0.02422984316945076, 0.01185214426368475, 0.023414328694343567, -0.021747054532170296, -0.025806505233049393, -0.003130669705569744, 0.048640910536050797, 0.0259152390062809, 0.0009865460451692343, -0.04037703201174736, -0.012993864715099335, 0.03450532630085945, 0.059550683945417404, -0.03160572052001953, 0.030427753925323486, 0.002901872619986534, 0.035393331199884415, -0.0010482759680598974, 0.02337808348238468, -0.05980439856648445, -0.08329121768474579, 0.02254444733262062, -0.07973919808864594, -0.03903596103191376, -0.0013999666552990675, 0.0627402514219284, 0.020152270793914795, -0.02292501926422119, -0.07966671139001846, 0.023450573906302452, -0.018031932413578033, -0.01322039682418108, -0.044835176318883896, 0.0070451395586133, 0.0015460796421393752, -0.006601137109100819, -0.047263599932193756, 0.036245089024305344, -0.062450289726257324, -0.02903231792151928, 0.052156686782836914, 0.005640642251819372, 0.002473727334290743, 0.016663679853081703, 0.06234155595302582, 0.005264599341899157, 0.0005578345735557377, -0.03885473683476448, -0.010221115313470364, -0.023124366998672485, -0.0001102926762541756, -0.023450573906302452, -0.02026100642979145, -0.01973545178771019, -0.012287085875868797, -0.022743795067071915, 0.018539363518357277, 0.008730536326766014, 0.009147354401648045, -0.03269307315349579, -0.04661118611693382, 0.07444741576910019, -0.0023083591368049383, -0.00080248893937096, 0.0022958999034017324, -0.030065303668379784, 0.058862026780843735, 0.023722412064671516, -0.0006954526761546731, 0.01743388921022415, 0.012160227634012699, 0.04951079562306404, 0.009278743527829647, 0.019789818674325943, -0.05552747845649719, 0.009813358075916767, 0.04693739116191864, -0.06216033175587654, -0.04389280453324318, 0.040268294513225555, 0.09894909709692001, -0.034324102103710175, -0.03762240335345268, -0.007027016952633858, 0.02223636396229267, -0.05074312537908554, 0.0199529230594635, -0.036390069872140884, 0.02439294569194317, 0.05404143035411835, 0.007040608674287796, -0.06241404637694359, 0.03747742250561714, 0.022127628326416016, -0.01062887255102396, -0.0009888113709166646, 0.01668180339038372, -0.03557455539703369, 0.0005482069682329893, 0.001219873782247305, -0.020913416519761086, 0.038601022213697433, -0.044617705047130585, -0.011535000056028366, -0.0015324876876547933, -0.018249403685331345, -0.029594115912914276, -0.0036471623461693525, -0.05683230236172676, -0.023794902488589287, -0.05965941771864891, -0.0385647751390934, 0.056796059012413025, -0.037513669580221176, 0.0562523789703846, -0.0316782109439373, 0.011834021657705307, -0.04624873399734497, -0.02171080932021141, 0.06382760405540466, 0.035175859928131104, -0.015820981934666634, -0.014498036354780197, 0.034487202763557434, -0.04146438464522362, -0.011226916685700417, -0.02156582847237587, -0.04929332435131073, -0.027310675010085106, 0.01089164987206459, -0.03481340780854225, -0.0010012706043198705, -0.009396540001034737, 0.02856113202869892, 0.01447085291147232, -0.04664743319153786, 0.035157736390829086, -0.05454886332154274, 0.035846393555402756, 0.07386749237775803, -0.006850322242826223, -0.020840927958488464, 0.012876068241894245, 0.0023310123942792416, 0.0038283877074718475, 0.02185579016804695, -0.051395539194345474, -0.05005447193980217, 0.013691582717001438, -0.009659316390752792, -0.02741941064596176, 0.014769874513149261, -0.012586107477545738, 0.004526105709373951, 0.0012470576912164688, -0.07756449282169342, 0.0373324416577816, -0.009228906594216824, 0.0028905458748340607, 0.09249746799468994, 0.011172548867762089, -0.006456156726926565, 0.04501640424132347, -0.01881120167672634, -0.02484600991010666, -0.01682678423821926, -0.04871340095996857, -0.0040753073990345, 0.03468655049800873, 0.008037349209189415, 0.015087018720805645, -0.01843968965113163, -0.037441179156303406, -0.0028271169867366552, 0.006184318568557501, -0.03769489377737045, 0.027546269819140434, 0.007742857560515404, -0.010175809264183044, -0.0028860154561698437, -0.010927895084023476, 0.08909043669700623, -0.04454521834850311, 0.019699206575751305, 0.006166195962578058, -0.0068004853092134, 0.011208794079720974, 0.002786341356113553, 0.019681084901094437, 0.026640141382813454, 0.004220287781208754, -0.029449136927723885, 0.02751002460718155, -0.010175809264183044, 0.03117077797651291, 0.013764073140919209, 0.03131575882434845, -0.021674564108252525, -0.011598428711295128, 0.06437128037214279, 0.02064157836139202, 0.0018745508277788758, -0.02223636396229267, 0.03899971768260002, 0.012939497828483582, -0.056107401847839355, 0.036390069872140884, -0.00039048423059284687, 0.05349775403738022, -0.013537541031837463, -0.011580306105315685, -0.04142813757061958, 0.0007294324459508061, -0.002731973771005869, -0.020931540057063103, 0.055491235107183456, -0.006392728071659803, -0.015603511594235897, -0.011118181981146336, 0.02292501926422119, -0.0006161665660329163, -0.004530636128038168, 0.008422452956438065, -0.0012561188777908683, 0.008603678084909916, 0.0980067253112793, -0.0310076754540205, -0.00921531394124031, -0.02102215215563774, -0.006687219254672527, -0.014452730305492878, -0.03252996876835823, -0.020786559209227562, 0.004335818812251091, 0.01797756552696228, -0.04244299978017807, 0.007326039019972086, 0.019934799522161484, -0.020206637680530548, -0.0046439021825790405, 0.010683240368962288, 0.01661837473511696, 0.016255922615528107, 0.024864131584763527, 0.007262609899044037, -0.031587596982717514, -0.008481351658701897, 0.003189567942172289, 0.0078062862157821655, 0.048568420112133026, -0.008214043453335762, 0.009070334024727345, -0.03109828755259514, 0.026875734329223633, 0.018847446888685226, 0.007403059862554073, 0.03686125576496124, -0.04516138136386871, 0.018195034936070442, -0.021239623427391052, 0.008644454181194305, 0.0010375156998634338, -0.014923916198313236, 0.05045316740870476, 0.025715891271829605, -0.00762053020298481, 0.007362284231930971, 0.04142813757061958, -0.04251549020409584, -0.02301563322544098, 0.05179423466324806, -0.02301563322544098, 0.021692687645554543, -0.038057345896959305, 0.02986595407128334, -0.02185579016804695, -0.013854686170816422, 0.02033349499106407, 0.024701029062271118, -0.00102449010591954, 0.07412120699882507, 0.03305552154779434, -0.014380239881575108, 0.04229802265763283, -0.0016978560015559196, -0.038818493485450745, 0.0006082379259169102, -0.008920823223888874, -0.04092070832848549, 0.03109828755259514, -0.014715506695210934, -0.014026850461959839, 0.0016650088364258409, 0.0033639974426478148, 0.025643400847911835, 0.0550200492143631, 0.01314790640026331, -0.0031940985936671495, 0.009052211418747902, 0.03845604136586189, 0.03138824924826622, 0.07792694866657257, -0.005146802868694067, 0.03276556357741356, 0.015975024551153183, -0.025117848068475723, 0.019916677847504616, -0.0010233575012534857, -0.04472644254565239, 0.026712631806731224, 0.013311009854078293, 0.03709685057401657, 0.01853030174970627, -0.01766948215663433, -0.021130887791514397, 0.00792861357331276, 0.018629977479577065, 0.005436763633042574, -0.005839990451931953, 0.006197910290211439, 0.00860820896923542, -0.010112380608916283, -0.013455989770591259, 0.005300844553858042, -0.000843264686409384, 0.022689426317811012, 0.008349962532520294, 0.031352002173662186, -0.0029562402050942183, -0.001531355082988739, -0.060601793229579926, 0.029449136927723885, 0.014797057956457138, -0.02292501926422119, -0.01531355082988739, 0.057484712451696396, -0.013582848012447357, -0.005871704779565334, -0.027491901069879532, -0.004852311685681343, -0.003891816595569253, -0.0037876120768487453, 0.0038351835682988167, -0.010202992707490921, 0.027383165434002876, 0.0015302224783226848, 0.018756834790110588, -0.01797756552696228, -0.0017182438168674707, -0.04005082696676254, 0.009958338923752308, 0.02613271027803421, 0.012785456143319607, -0.015676001086831093, -0.0069182817824184895, -0.015349796041846275, -0.013021049089729786, -0.011190671473741531, 0.009124701842665672, 0.02337808348238468, 0.010619811713695526, 0.018919937312602997, -0.0009655918693169951, -0.004086634144186974, -0.011498754844069481, 0.02133023552596569, -0.02453792653977871, -0.010338911786675453, 0.00752538675442338, -0.006089175119996071, -0.04983700066804886, 0.0379486083984375, 0.02917729876935482, -0.0053597427904605865, 0.05904325097799301, 0.010801036842167377, -0.03368981182575226, 0.011045691557228565, -0.008562902919948101, -0.014697384089231491, 0.03925343230366707, -0.025625279173254967, 0.0018043259624391794, 0.0010159951634705067, 0.00039274952723644674, 0.022997509688138962, 0.012522678822278976, 0.01223271805793047, 0.031496983021497726, 0.02301563322544098, -0.015984084457159042, -0.00895706843584776, -0.023559309542179108, 0.04382031410932541, -0.030300896614789963, 0.0037740201223641634, 0.036770645529031754, -0.03285617381334305, 0.033726055175065994, -0.018303770571947098, 0.03533896431326866, 0.005631580948829651, 0.026187077164649963, 0.03358107805252075, 0.032493725419044495, 0.024501681327819824, 0.021656442433595657, -0.017995687201619148, -0.010375156998634338, -0.0045442283153533936, 0.026458915323019028, -0.006179788149893284, -0.03976086527109146, -0.000019202110706828535, 0.00009117905574385077, 0.00822310522198677, -0.0009293467737734318, -0.005051659420132637, 0.02850676327943802, 0.033562954515218735, 0.01911928504705429, 0.01988043263554573, 0.026096465066075325, -0.00153815106023103, -0.07151156663894653, 0.031968168914318085, 0.0017374990275129676, -0.049039606004953384, 0.01261329185217619, -0.015830043703317642, -0.010148625820875168, -0.04534260928630829, -0.001315017230808735, 0.03503087908029556, 0.016246862709522247, 0.0049066790379583836, -0.036444440484046936, 0.045378852635622025, 0.019010549411177635, 0.009201722219586372, -0.007307916413992643, 0.004043593071401119, -0.012006185948848724, -0.03932592272758484, 0.014162769541144371, -0.020587211474776268, 0.04878589138388634, 0.0370243601500988, -0.04947454854846001, -0.015032651834189892, -0.038202326744794846, -0.006791424006223679, 0.02934040129184723, 0.003212221199646592, -0.01834907755255699, 0.009369355626404285, -0.05019944906234741, -0.03838355094194412, 0.008558372035622597, -0.0015336204087361693, 0.02888733707368374, 0.0505981482565403, -0.055817440152168274, -0.04440023750066757, 0.009894909337162971, -0.005604397039860487, -0.021892035380005836, 0.027636881917715073, 0.024701029062271118, 0.052084196358919144, 0.002281175460666418, -0.021819544956088066, -0.006872975267469883, -0.02529907412827015, -0.003998286556452513, 0.029974689707159996, -0.012160227634012699, 0.003583733458071947, -0.032276254147291183, -0.04244299978017807, -0.015558205544948578, -0.03209502622485161, 0.004469472914934158, -0.035175859928131104, -0.00913829356431961, 0.0044105746783316135, 0.038347307592630386, -0.005849051289260387, 0.007094976492226124, 0.035792026668787, -0.022109504789114, -0.006882036570459604, -0.00384651031345129, -0.009885848499834538, -0.016564005985856056, 0.0036539582069963217, 0.010973201133310795, 0.04044952243566513, 0.06248653680086136, 0.006283992435783148, -0.004888556431978941, -0.023559309542179108, 0.009197191335260868, 0.007987512275576591, -0.012033370323479176, 0.013247580267488956, -0.0006518453010357916, -0.00011524806177476421, 0.0018405710579827428, 0.021438971161842346, 0.026785122230648994, -0.03450532630085945, 0.023885514587163925, -0.01973545178771019, 0.018086301162838936, -0.01242300495505333, -0.03903596103191376, 0.017841646447777748, 0.0011507816379889846, 0.005128680262714624, -0.026386426761746407, -0.033327359706163406, 0.050779372453689575, 0.001760152168571949, -0.006093706004321575, -0.0874231606721878, -0.005323497578501701, -0.06208784133195877, -0.02475539781153202, 0.03117077797651291, -0.005681417882442474, 0.035248350352048874, 0.020297251641750336, 0.02660389617085457, 0.026096465066075325, -0.005328028462827206, 0.025045357644557953, -0.004884026013314724, 0.028017455711960793, 0.014742691069841385, -0.04454521834850311, -0.025407807901501656, -0.0039280615746974945, -0.05386020615696907, -0.0423705093562603, -0.008626331575214863, -0.015739429742097855, -0.05737597867846489, 0.010003644973039627, 0.021239623427391052, -0.03205878287553787, -0.05313530191779137, 0.008064532652497292, 0.009505274705588818, 0.008449636399745941, 0.046284981071949005, -0.017959441989660263, -0.008562902919948101, 0.004884026013314724, 0.032946787774562836, -0.0015891207149252295, -0.028778601437807083, 0.03841979801654816, 0.03144261613488197, 0.008377146907150745, -0.02118525467813015, 0.04092070832848549, 0.005337089765816927, 0.007774571888148785, -0.055817440152168274, -0.0024714621249586344, -0.02337808348238468, 0.005092435050755739, -0.0379486083984375, -0.03582827374339104, 0.02827117033302784, -0.005414110608398914, -0.027546269819140434, 0.02073219232261181, 0.021167133003473282, 0.0405220128595829, 0.028162434697151184, 0.030590856447815895, -0.03202253580093384, 0.009804297238588333, 0.03238498792052269, -0.003952980041503906, -0.004671086091548204, -0.03247560188174248, -0.010130503214895725, -0.007516325917094946, -0.0316782109439373, -0.007289793808013201, 0.04211679473519325, -0.079811692237854, -0.00014823675155639648, -0.014126524329185486, -0.005491131450980902, 0.014724568463861942, 0.042334266006946564, 0.017098622396588326, 0.012758271768689156, 0.008377146907150745, -0.013365376740694046, 0.010112380608916283, -0.004811535589396954, 0.011308467946946621, 0.05371522530913353, -0.06556736677885056, 0.010257360525429249, -0.037151217460632324, -0.025770260021090508, 0.0140902791172266, -0.0038827552925795317, -0.020206637680530548, 0.035683292895555496, -0.016727108508348465, 0.0006354217184707522, -0.02993844449520111, -0.032584335654973984, -0.011625613085925579, -0.012359576299786568, -0.06734337657690048, 0.00214412366040051, -0.018720589578151703, -0.020822804421186447, -0.03870975598692894, 0.027383165434002876, 0.0024193597491830587, 0.0016502842772752047, 0.020460354164242744, 0.015331673435866833, 0.034016016870737076, -0.00040322664426639676, -0.006805015727877617, -0.011072875000536442, -0.025480298325419426, 0.05117806792259216, 0.03084457293152809, 0.0315694734454155, 0.009931154549121857, 0.017017070204019547, -0.0040232050232589245, -0.0034478141460567713, -0.004766229540109634, 0.002564340131357312, -0.005590805318206549, 0.002571136225014925, -0.006447095423936844, -0.03648068383336067, 0.006773301400244236, -0.03983335569500923, -0.006225094199180603, 0.008748658932745457, 0.00307630212046206, -0.01112724281847477, -0.017198296263813972, 0.0053597427904605865, -0.06226906552910805, -0.005640642251819372, 0.0034704674035310745, 0.022073259577155113, 0.03031901828944683, -0.009777112863957882, 0.05694103613495827, -0.02529907412827015, 0.0019062652718275785, 0.04429150000214577, 0.0035724067129194736, 0.016790539026260376, -0.017542622983455658, 0.024628538638353348, -0.030917061492800713, -0.0034500795882195234, -0.021221499890089035, 0.0026957285590469837, 0.038746003061532974, -0.06741587072610855, 0.031062042340636253, -0.004048123490065336, 0.041174422949552536, -0.0074393050745129585 ]
Airbnb is a two-sided marketplace, bringing together hosts who own listings for rent, with prospective guests from around the globe. Applying neural network-based learning to rank techniques has led to significant improvements in matching guests with hosts. These improvements in ranking were driven by a core strategy: order the listings by their estimated booking probabilities, then iterate on techniques to make these booking probability estimates more and more accurate. Embedded implicitly in this strategy was an assumption that the booking probability of a listing could be determined independently of other listings in search results. In this paper we discuss how this assumption, pervasive throughout the commonly-used learning to rank frameworks, is false. We provide a theoretical foundation correcting this assumption, followed by efficient neural network architectures based on the theory. Explicitly accounting for possible similarities between listings, and reducing them to diversify the search results generated strong positive impact. We discuss these metric wins as part of the online A/B tests of the theory. Our method provides a practical way to diversify search results for large-scale production ranking systems.
[ -0.01983826793730259, 0.003993809223175049, -0.03044147789478302, -0.038489457219839096, 0.0027363128028810024, -0.01716231368482113, -0.012615206651389599, 0.02203134074807167, -0.05162778124213219, 0.01204178761690855, -0.01567343808710575, 0.01730315387248993, -0.04317740350961685, -0.0707014948129654, -0.02517005242407322, -0.000448297563707456, 0.0018434900557622313, -0.007439350243657827, -0.027262527495622635, -0.032212033867836, -0.027101567015051842, -0.041688527911901474, -0.030682917684316635, 0.02168930135667324, 0.018510350957512856, 0.01040201261639595, -0.014717740938067436, -0.007278390694409609, -0.062693752348423, 0.005155736114829779, 0.05504817143082619, 0.004914296790957451, -0.022494100034236908, -0.07585220038890839, -0.041366610676050186, -0.02154846303164959, 0.06076223775744438, 0.03211143612861633, 0.009194815531373024, 0.04201044887304306, 0.035270266234874725, 0.009763203561306, -0.00010460799967404455, -0.008098278194665909, -0.00082303152885288, -0.054565295577049255, 0.00017369171837344766, -0.01658889651298523, -0.028711162507534027, -0.06716038286685944, 0.00010500096686882898, -0.015331398695707321, 0.012605146504938602, -0.014345522038638592, -0.05327761918306351, 0.038147419691085815, -0.017081834375858307, -0.013842523097991943, 0.016407815739512444, 0.02114606276154518, 0.04611491784453392, 0.0393344946205616, -0.06522886455059052, -0.029435481876134872, 0.0049319020472466946, 0.006765332072973251, -0.01661907508969307, -0.01272586639970541, 0.005180886015295982, -0.018118010833859444, -0.021810021251440048, 0.03269491344690323, 0.0510241836309433, -0.005698974709957838, -0.013993422500789165, 0.012232927605509758, 0.05999768152832985, 0.001080189598724246, 0.013319404795765877, 0.026176050305366516, 0.04426388069987297, 0.040058813989162445, 0.016598954796791077, 0.03782549872994423, 0.04575275629758835, 0.012393887154757977, 0.04345908388495445, -0.0823710635304451, 0.05287522077560425, 0.008711936883628368, -0.04639659449458122, -0.011277229525148869, 0.008460437878966331, 0.006896111648529768, -0.02675952948629856, 0.014647320844233036, 0.00836486741900444, 0.02032114565372467, -0.0324937142431736, 0.06015864014625549, -0.033620432019233704, -0.04426388069987297, 0.017051653936505318, 0.019425807520747185, 0.0046829176135361195, -0.022131940349936485, -0.02285625971853733, 0.032453473657369614, 0.0005787628469988704, 0.11661520600318909, 0.04064229130744934, 0.021367382258176804, -0.03132675588130951, 0.037865739315748215, -0.07850802689790726, 0.051144905388355255, -0.07891043275594711, -0.037463340908288956, 0.0172427948564291, -0.061607275158166885, -0.03913329541683197, -0.01508995983749628, -0.001011027256026864, -0.003905784571543336, 0.005844844505190849, 0.027322886511683464, 0.007801508996635675, 0.007464500144124031, 0.019224608317017555, 0.020622944459319115, 0.017544593662023544, 0.02092474326491356, -0.017192494124174118, -0.022071581333875656, -0.018771909177303314, 0.018661249428987503, 0.04869027063250542, 0.0018560650059953332, 0.0064585027284920216, -0.045310117304325104, -0.009541884995996952, -0.02029096521437168, -0.0262162908911705, -0.05746256560087204, -0.04993770644068718, -0.0019868446979671717, -0.0015203134389594197, 0.05412265658378601, -0.0306426789611578, -0.037584058940410614, -0.0581466443836689, 0.008450377732515335, 0.005502805113792419, 0.03406306728720665, 0.022655058652162552, -0.003123621689155698, 0.012222867459058762, 0.0036341652739793062, -0.013259044848382473, 0.0067753917537629604, 0.04102456942200661, -0.058589283376932144, 0.026256529614329338, 0.03607506304979324, 0.018289031460881233, 0.09327606856822968, -0.00012040530418744311, -0.039093054831027985, -0.09222983568906784, 0.04458580166101456, -0.014989360235631466, 0.011900948360562325, -0.03394234925508499, 0.019677307456731796, -0.06289495527744293, 0.030079320073127747, 0.03804681822657585, -0.030662797391414642, -0.01764519326388836, 0.024325015023350716, -0.024184174835681915, 0.01837957091629505, 0.021870382130146027, -0.0014083962887525558, -0.007710969541221857, 0.01837957091629505, 0.03470690920948982, 0.0017768427496775985, 0.054364096373319626, -0.0099744638428092, -0.008691816590726376, -0.017222674563527107, 0.05959527939558029, 0.0003080866881646216, 0.014808280393481255, -0.05919288098812103, 0.007640549447387457, -0.025290772318840027, 0.026940608397126198, -0.0009733024053275585, -0.009315535426139832, -0.023701297119259834, -0.00243702856823802, -0.027886245399713516, 0.03750358149409294, -0.012685625813901424, 0.04062217101454735, -0.03372102975845337, -0.00036435964284464717, -0.01013039331883192, -0.020592765882611275, 0.010884891264140606, -0.05999768152832985, 0.04349932447075844, 0.009295415133237839, -0.002488585887476802, 0.022071581333875656, 0.0618487149477005, 0.009300445206463337, -0.012273167259991169, -0.010412071831524372, 0.05782472714781761, 0.04985722526907921, -0.0060711936093866825, 0.03337899222970009, -0.01138788927346468, -0.011911008507013321, 0.01758483238518238, 0.01693093404173851, -0.029093442484736443, -0.046356357634067535, 0.025693170726299286, -0.00793731864541769, -0.01218262780457735, 0.0225142203271389, -0.014727801084518433, 0.018007351085543633, -0.07484620064496994, -0.046477075666189194, -0.020502224564552307, -0.03764441981911659, -0.004054169170558453, -0.013128264807164669, 0.03583362326025963, 0.0832161009311676, -0.027343006804585457, -0.0070973108522593975, 0.0439017228782177, 0.014305281452834606, 0.01581427827477455, 0.0042981235310435295, -0.03865041583776474, -0.014929000288248062, 0.007067131344228983, -0.060037918388843536, 0.038489457219839096, 0.032212033867836, -0.005915264133363962, 0.004491778090596199, -0.04808667302131653, 0.0008532115025445819, -0.009214935824275017, 0.0017278003506362438, 0.01755465380847454, -0.02641749009490013, -0.00947649497538805, 0.04144708812236786, -0.018973110243678093, -0.002145289210602641, 0.0589916817843914, -0.001015428570099175, -0.06655678153038025, 0.011820468120276928, 0.004074288997799158, -0.01758483238518238, -0.03140723705291748, 0.0766569972038269, -0.041366610676050186, 0.053680017590522766, 0.02935500256717205, -0.00046778874821029603, -0.01087483111768961, -0.022655058652162552, -0.03241323307156563, -0.0707014948129654, -0.04309692606329918, 0.013701683841645718, 0.00631263293325901, -0.04325788468122482, -0.036356743425130844, -0.030904237180948257, -0.0004146595310885459, -0.009240085259079933, 0.03852969780564308, 0.018228670582175255, 0.025532212108373642, 0.04973650723695755, -0.024526214227080345, 0.030763396993279457, -0.014848520047962666, -0.025129813700914383, 0.024184174835681915, -0.006569162476807833, -0.016769975423812866, -0.008334687910974026, -0.0019214549101889133, 0.022393500432372093, 0.08076146245002747, -0.0066295224241912365, -0.01655871607363224, 0.0162468571215868, 0.019526407122612, 0.03207119554281235, -0.05738208815455437, -0.012504546903073788, 0.035390984266996384, 0.022071581333875656, -0.03174927458167076, 0.014265041798353195, -0.04241284728050232, 0.01470768079161644, 0.007710969541221857, -0.06015864014625549, 0.056335851550102234, -0.02627664990723133, -0.00552795547991991, -0.00030352824251167476, 0.07774347066879272, -0.011619268916547298, 0.016206616535782814, -0.022554459050297737, -0.05404217541217804, -0.07738131284713745, -0.042050689458847046, 0.036155544221401215, -0.015260979533195496, 0.007957438938319683, 0.013621203601360321, -0.00022587784042116255, 0.0010619559325277805, 0.025693170726299286, 0.0017278003506362438, 0.004499323200434446, 0.042654287070035934, 0.04836834967136383, -0.06426310539245605, -0.03599458560347557, 0.03571290522813797, 0.01690075546503067, -0.018741730600595474, 0.001309053972363472, -0.003432965837419033, -0.006720061879605055, 0.05021938681602478, 0.025089573115110397, -0.049213387072086334, 0.0041572838090360165, -0.04082337021827698, -0.024546334519982338, 0.016085896641016006, -0.05738208815455437, -0.03579338267445564, -0.05013890564441681, 0.008545947261154652, -0.03645734116435051, 0.024868253618478775, -0.004730702377855778, -0.03044147789478302, 0.003993809223175049, 0.012524666264653206, -0.01616637594997883, 0.036578062921762466, -0.013500483706593513, -0.049495067447423935, -0.07033932954072952, 0.0018032501684501767, 0.009486555121839046, -0.005548075307160616, 0.013882762752473354, 0.033218029886484146, 0.021709421649575233, -0.02688024751842022, 0.03003907948732376, -0.031246276572346687, -0.0029651771765202284, 0.012776166200637817, 0.056818727403879166, -0.03154807537794113, 0.028147805482149124, 0.03351983055472374, -0.04221164807677269, -0.03603482246398926, -0.050259627401828766, -0.035672664642333984, 0.08281370252370834, -0.032875992357730865, -0.023137938231229782, -0.020341265946626663, 0.017604952678084373, -0.018761849030852318, -0.03593422472476959, -0.008047978393733501, -0.01416444219648838, 0.03981737419962883, -0.05774424597620964, -0.013067904859781265, -0.00879241619259119, -0.03032075986266136, 0.01789669133722782, 0.029858000576496124, -0.04800619184970856, -0.0027664925437420607, -0.06365951150655746, 0.01690075546503067, 0.02229290083050728, 0.027041207998991013, -0.012202747166156769, 0.004006384406238794, 0.04038073122501373, -0.017464112490415573, 0.020542465150356293, 0.01581427827477455, 0.07557051628828049, 0.01494911964982748, -0.07585220038890839, 0.04623563587665558, 0.00025935866869986057, -0.006730122026056051, 0.002274811500683427, -0.05734184756875038, 0.04096421226859093, 0.01053279172629118, 0.038549818098545074, 0.003928419668227434, -0.0208040252327919, -0.011991487815976143, -0.02354033663868904, -0.010422131977975368, -0.014999420382082462, -0.013128264807164669, 0.0019893597345799208, 0.014526600949466228, -0.05295569822192192, 0.007705939467996359, -0.036356743425130844, 0.020683305338025093, -0.02770516648888588, -0.04317740350961685, 0.012745985761284828, -0.03414354845881462, -0.050098665058612823, -0.003453085897490382, -0.10212884843349457, -0.0666775032877922, 0.046356357634067535, -0.05150706321001053, -0.012333527207374573, -0.03995821252465248, 0.04808667302131653, -0.04341884329915047, -0.020944863557815552, 0.04603443667292595, 0.037523698061704636, -0.02776552550494671, 0.02873128280043602, 0.04297620430588722, -0.046758756041526794, -0.054484814405441284, 0.01963706687092781, 0.02277577854692936, -0.00901876576244831, -0.06860901415348053, 0.030743278563022614, 0.006780421826988459, 0.02585413120687008, 0.027725286781787872, -0.017313214018940926, -0.06522886455059052, 0.023178178817033768, 0.005739214830100536, 0.039052814245224, 0.08329657465219498, 0.017484232783317566, -0.03838885575532913, -0.006896111648529768, -0.006025923881679773, 0.011045850813388824, 0.003993809223175049, -0.06494718790054321, -0.010995551012456417, -0.019204488024115562, 0.037342619150877, 0.02148810215294361, 0.004003869369626045, -0.019828207790851593, -0.0515875406563282, -0.024244535714387894, -0.04856954887509346, -0.003279551165178418, 0.03442522883415222, 0.02374153584241867, -0.013792223297059536, 0.024063454940915108, 0.00288218236528337, -0.0013794738333672285, -0.03563242405653, -0.009853743948042393, -0.017232734709978104, 0.00034423969918861985, 0.001112255733460188, 0.030562197789549828, 0.05231186002492905, 0.03470690920948982, -0.011327529326081276, -0.0005715322331525385, 0.0439017228782177, 0.06192919611930847, -0.006996711250394583, 0.04985722526907921, 0.01579415798187256, 0.015351518988609314, 0.0020170246716588736, -0.029998840764164925, 0.06148655712604523, -0.045994196087121964, 0.04184948652982712, 0.016458116471767426, -0.010070033371448517, 0.05287522077560425, -0.05971600115299225, -0.03856993839144707, 0.02859044447541237, 0.006232153158634901, -0.03406306728720665, 0.006513832602649927, -0.011076030321419239, 0.007278390694409609, 0.0652691051363945, -0.026980847120285034, -0.02722228690981865, -0.000179822018253617, 0.06567150354385376, 0.00417488906532526, 0.004869027063250542, 0.00429560849443078, 0.006870961748063564, 0.06015864014625549, -0.05685896798968315, -0.046557556837797165, -0.001134261954575777, 0.016468176618218422, -0.029918359592556953, 0.03291623294353485, -0.038207776844501495, -0.02072354406118393, -0.04591371864080429, -0.02915380150079727, -0.029113562777638435, 0.01017566304653883, -0.026578448712825775, -0.002266008872538805, 0.011357709765434265, -0.006544012576341629, -0.03784561902284622, 0.006710002198815346, -0.010502612218260765, 0.009411104954779148, 0.035129427909851074, -0.050863225013017654, -0.02160882204771042, -0.0010883633513003588, 0.018399691209197044, -0.02545173279941082, -0.019375508651137352, -0.038268137723207474, 0.020884504541754723, 0.01969742774963379, -0.02696072869002819, 0.006222093477845192, -0.007736119441688061, 0.0036090153735131025, -0.007399110123515129, -0.006528922356665134, 0.03700058162212372, 0.04261404648423195, 0.05355929583311081, -0.014848520047962666, -0.018289031460881233, -0.008540917187929153, -0.030340878292918205, 0.013943122699856758, 0.06305591017007828, -0.0312060359865427, -0.04422364383935928, -0.007645579520612955, 0.021226543933153152, -0.019113948568701744, 0.017635133117437363, 0.02981775999069214, -0.044706519693136215, 0.03955581411719322, -0.020904624834656715, 0.0007356355199590325, 0.005522925406694412, -0.027081448584794998, 0.010301412083208561, 0.04623563587665558, 0.03460630774497986, 0.003707100171595812, 0.04309692606329918, -0.05227161943912506, 0.022836139425635338, 0.03981737419962883, -0.06192919611930847, 0.026779647916555405, 0.00045552814844995737, -0.019999226555228233, 0.005190946161746979, -0.019657187163829803, 0.03195047378540039, 0.017916811630129814, 0.013339524157345295, 0.025572452694177628, 0.03072315827012062, -0.028087444603443146, 0.05718088895082474, 0.023218417540192604, -0.025532212108373642, 0.02428477443754673, 0.018651191145181656, -0.014275101944804192, -0.0000980847398750484, 0.02183014154434204, -0.034928224980831146, 0.0615670345723629, -0.013148385100066662, -0.007821628823876381, 0.0487305112183094, 0.029234282672405243, -0.03281563147902489, -0.012947185896337032, 0.006106403656303883, -0.011045850813388824, 0.08196865767240524, 0.010472431778907776, -0.017705552279949188, -0.007595279719680548, -0.019023409113287926, 0.059555042535066605, 0.022554459050297737, -0.0027011027559638023, 0.02291661873459816, 0.026457728818058968, 0.02605533041059971, 0.004308183677494526, -0.04184948652982712, 0.022152060642838478, 0.015271039679646492, 0.01786651276051998, 0.011900948360562325, 0.020331205800175667, 0.009154575876891613, 0.030703037977218628, 0.0026080480311065912, 0.02291661873459816, 0.004381118342280388, 0.027182048186659813, -0.032735154032707214, 0.011629329062998295, 0.060440320521593094, -0.004549623001366854, -0.0370609425008297, -0.0692528560757637, 0.02106558345258236, 0.017967112362384796, -0.05762352794408798, 0.018661249428987503, 0.08482569456100464, -0.002831882331520319, -0.015462178736925125, -0.009959373623132706, -0.0223733801394701, -0.02380189672112465, -0.010593151673674583, -0.02619617059826851, -0.023017218336462975, 0.030904237180948257, 0.02525053173303604, 0.0015039659338071942, 0.003002902027219534, -0.0584283247590065, -0.064424067735672, -0.007555040065199137, 0.03380151093006134, 0.01912400871515274, -0.00766066974028945, 0.02168930135667324, 0.04253356531262398, 0.01385258324444294, 0.009255175478756428, -0.023640936240553856, -0.014405881986021996, -0.001183933112770319, 0.00008896788494894281, -0.014858580194413662, 0.002289901487529278, 0.007881988771259785, -0.014305281452834606, -0.004200038965791464, -0.009899013675749302, 0.005517895333468914, 0.016890695318579674, 0.014194621704518795, 0.05492745339870453, 0.02907332219183445, 0.009471464902162552, 0.009446314536035061, -0.020109886303544044, -0.019365448504686356, 0.019476108253002167, 0.010884891264140606, -0.003863029647618532, 0.025351133197546005, -0.044988200068473816, -0.002449603518471122, -0.02126678265631199, 0.006010834127664566, -0.023218417540192604, 0.0016712130745872855, -0.0015743857948109508, 0.005905204452574253, -0.0012713291216641665, -0.052714258432388306, 0.0020685819908976555, 0.022655058652162552, 0.016176436096429825, -0.00017023360123857856, 0.026457728818058968, 0.019315147772431374, -0.015884697437286377, 0.015190559439361095, -0.057221125811338425, 0.03730238229036331, -0.010432192124426365, 0.013490423560142517, 0.020472045987844467, -0.019989166408777237, -0.015804218128323555, 0.011739988811314106, -0.006041014101356268, 0.0039460244588553905, -0.010412071831524372, 0.036899980157613754, -0.05943432077765465, -0.05669800937175751, 0.011558908969163895, 0.037805378437042236, 0.014033662155270576, -0.007283420767635107, 0.006061133928596973, 0.03098471648991108, 0.027061328291893005, 0.002394273644313216, 0.03372102975845337, 0.0257937703281641, -0.028147805482149124, -0.04257380589842796, 0.012947185896337032, -0.012574966065585613, -0.026980847120285034, 0.011951248161494732, -0.03671890124678612, 0.0009626136743463576, -0.04064229130744934, -0.0487305112183094, 0.0022043916396796703, 0.0172427948564291, -0.009295415133237839, -0.03158831596374512, 0.00974811427295208, 0.01450648158788681, 0.001685045543126762, 0.023037338629364967, -0.021850261837244034, -0.004964596591889858, 0.03009944036602974, -0.007721029222011566, -0.047644034028053284, 0.006785451900213957, 0.008596247062087059, -0.01060321182012558, -0.035753145813941956, -0.039857614785432816, 0.01351054385304451, 0.021105824038386345, -0.01932520791888237, 0.014224802143871784, 0.0028218224178999662, -0.025552332401275635, -0.024948732927441597, 0.045471079647541046, -0.005392145831137896, -0.01382240280508995, 0.004270458593964577, -0.0555712915956974, -0.019566647708415985, 0.007006771396845579, 0.002869607415050268, -0.013570903800427914, 0.024988973513245583, 0.028610562905669212, 0.033922228962183, -0.016709614545106888, 0.02140762284398079, 0.00879241619259119, 0.009753144346177578, -0.03824801743030548, 0.046356357634067535, -0.030220160260796547, -0.018138131126761436, -0.04329812526702881, -0.01330934464931488, -0.016629135236144066, -0.00444650836288929, -0.021669182926416397, 0.005824724677950144, 0.020250726491212845, -0.02352021634578705, 0.06172799691557884, 0.008601277135312557, 0.0031764365267008543, 0.0015391758643090725, -0.0068106018006801605, -0.0009556974400766194, -0.027121687307953835, -0.006176823750138283, 0.00499477656558156, 0.07102341204881668, 0.013621203601360321, 0.02531089261174202, 0.012514607049524784, -0.015683498233556747, -0.02893248200416565, 0.009929193183779716, 0.03160843625664711, 0.01938556879758835, -0.017293093726038933, 0.006830721627920866, 0.016920875757932663, 0.01351054385304451, 0.029576320201158524, 0.07347804307937622, 0.04007893428206444, 0.013792223297059536, -0.008701876737177372, -0.03687985986471176, 0.012705746106803417, 0.023479977622628212, -0.020190365612506866, -0.01180034875869751, 0.04297620430588722, 0.014003482647240162, 0.005452505312860012, -0.043056685477495193, 0.02846972458064556, -0.05138634145259857, 0.001964209834113717, -0.052231378853321075, 0.006327723152935505, -0.046155158430337906, 0.006357903126627207, 0.00974811427295208, -0.0035888953134417534, 0.047724511474370956, 0.011669568717479706, -0.0042654285207390785, 0.0470404326915741, -0.001140549429692328, 0.010125363245606422, -0.055168893188238144, 0.017765913158655167, -0.004114529117941856, 0.02770516648888588, -0.05001818761229515, 0.057704005390405655, -0.02476765401661396, -0.03329851105809212, -0.009154575876891613, -0.0015228284755721688, -0.04086361080408096, 0.006528922356665134, 0.03460630774497986, -0.023218417540192604, -0.052995938807725906, 0.011428129859268665, 0.0031487715896219015, 0.026357129216194153, 0.0005363223026506603, 0.0478854738175869, 0.011579029262065887, 0.012524666264653206, 0.002196846529841423, -0.01801741123199463, -0.03913329541683197, 0.04522963985800743, -0.006262333132326603, 0.010653511621057987, -0.01941574737429619, -0.0019189398735761642, 0.00855097733438015, -0.03032075986266136, -0.040260013192892075, -0.009345714934170246, 0.0027815825305879116, 0.031286515295505524, -0.022876378148794174, 0.017604952678084373, -0.027000967413187027, 0.009164635092020035, -0.03203095495700836, 0.0618487149477005, 0.009868833236396313, 0.007494680117815733, 0.013520603999495506, -0.03275527432560921, 0.03203095495700836, -0.02203134074807167, 0.028831882402300835, -0.0020786419045180082, -0.0698162168264389, -0.04591371864080429, 0.03142735734581947, 0.00456722779199481, -0.002741342643275857, 0.023842137306928635, 0.05126562342047691, -0.020200425758957863, -0.010693751275539398, -0.0014448636211454868, 0.0010418359888717532, -0.013671503402292728, 0.04683923348784447, -0.004491778090596199, 0.07054053246974945, -0.01265544630587101, -0.07408164441585541, 0.041688527911901474, -0.0036140454467386007, -0.019305087625980377, 0.04414316266775131, -0.02106558345258236, 0.0062120333313941956, -0.036779262125492096, -0.02339949831366539, -0.011236989870667458, 0.024807894602417946, -0.02291661873459816, 0.00956200435757637, -0.024385374039411545, 0.01593499816954136, 0.024264656007289886, 0.00708222109824419, -0.015784097835421562, -0.016377637162804604, -0.024727413430809975, -0.013661443255841732, -0.03030063956975937, 0.015784097835421562, -0.032795511186122894, 0.01091507077217102, -0.027886245399713516, 0.0010839621536433697, 0.034384988248348236, -0.003236796474084258, 0.01285664550960064, -0.007273360621184111, 0.022212421521544456, -0.02128690294921398, -0.023419616743922234, 0.016427936032414436, 0.032473593950271606, 0.04551132023334503, -0.006569162476807833, -0.022152060642838478, 0.01416444219648838, -0.03442522883415222, -0.006056103855371475, -0.021528342738747597, -0.04434436187148094, -0.010492552071809769, 0.006870961748063564, 0.007630489766597748, -0.0031663766130805016, -0.030280519276857376, 0.0004335219564381987, 0.0353507474064827, -0.014566841535270214, 0.013148385100066662, 0.041084930300712585, 0.045953959226608276, -0.03490810841321945, -0.04571251943707466, -0.012222867459058762, 0.05050106346607208, 0.016297155991196632, 0.020451925694942474, 0.043539565056562424, -0.012202747166156769, 0.0049394466914236546, 0.04563203826546669, 0.05118514224886894, 0.028751403093338013, -0.004655252676457167, -0.0208040252327919, -0.020029406994581223, 0.004099438898265362, -0.05537009239196777, 0.02126678265631199, 0.0006677306955680251, -0.0324937142431736, 0.017192494124174118, -0.010004643350839615, -0.004461598116904497, -0.025471851229667664 ]
In this talk, we introduce Merlin HugeCTR. Merlin HugeCTR is an open source, GPU-accelerated integration framework for click-through rate estimation. It optimizes both training and inference, whilst enabling model training at scale with model-parallel embeddings and data-parallel neural networks. In particular, Merlin HugeCTR combines a high-performance GPU embedding cache with an hierarchical storage architecture, to realize low-latency retrieval of embeddings for online model inference tasks. In the MLPerf v1.0 DLRM model training benchmark, Merlin HugeCTR achieves a speedup of up to 24.6x on a single DGX A100 (8x A100) over PyTorch on 4x4-socket CPU nodes (4x4x28 cores). Merlin HugeCTR can also take advantage of multi-node environments to accelerate training even further. Since late 2021, Merlin HugeCTR additionally features a hierarchical parameter server (HPS) and supports deployment via the NVIDIA Triton server framework, to leverage the computational capabilities of GPUs for high-speed recommendation model inference. Using this HPS, Merlin HugeCTR users can achieve a 5~62x speedup (batch size dependent) for popular recommendation models over CPU baseline implementations, and dramatically reduce their end-to-end inference latency.
[ -0.0012127729132771492, -0.02223779261112213, -0.03297821804881096, -0.007022191770374775, 0.027515944093465805, -0.04959007352590561, -0.033551041036844254, 0.070661760866642, -0.022094586864113808, 0.07057993113994598, 0.026124803349375725, -0.002337320940569043, 0.024304045364260674, -0.02857975848019123, -0.012949883006513119, 0.05163586884737015, -0.013768200762569904, -0.021480849012732506, -0.016172010451555252, -0.002623732201755047, 0.006766467355191708, -0.027740981429815292, -0.013359041884541512, -0.008397988975048065, 0.033387377858161926, 0.016499336808919907, -0.0072523439303040504, 0.02935715951025486, -0.05351800099015236, 0.0018002997385337949, 0.017276739701628685, 0.02882525324821472, -0.006567002274096012, -0.013850033283233643, -0.05049022287130356, -0.044680166989564896, 0.09402474761009216, 0.028804795816540718, -0.02555198036134243, 0.0005923216231167316, 0.03158707544207573, 0.011395079083740711, -0.04064995050430298, 0.049917399883270264, 0.02137855812907219, 0.01884177327156067, -0.018575819209218025, 0.0013029157416895032, 0.01636636070907116, -0.012336144223809242, 0.003746362403035164, -0.01059721875935793, 0.03987254574894905, -0.005723111797124147, 0.03545362874865532, 0.012377060949802399, 0.05830515921115875, 0.056504860520362854, 0.06313323974609375, 0.026738543063402176, 0.04097727686166763, 0.028743421658873558, -0.0296026561409235, -0.03526950627565384, -0.033264629542827606, -0.02246282994747162, -0.03934064134955406, 0.02096940018236637, 0.020273828878998756, -0.010244319215416908, -0.04136597737669945, -0.016468651592731476, 0.029316244646906853, -0.02242191508412361, 0.009845389053225517, -0.007288144901394844, 0.048239849507808685, -0.015578730031847954, 0.00012338701344560832, 0.014964991249144077, 0.03833819925785065, -0.004945709835737944, -0.02211504615843296, 0.025347402319312096, 0.10826347768306732, -0.03469668701291084, -0.06436071544885635, -0.07344404608011246, -0.05961446836590767, 0.02379259653389454, -0.0501219816505909, 0.0019933716394007206, -0.01688803918659687, -0.025449691340327263, -0.06444254517555237, 0.027229532599449158, -0.04142735153436661, 0.010617677122354507, -0.02737273834645748, 0.07929501682519913, 0.017747271806001663, 0.024140382185578346, 0.021951381117105484, -0.02174680307507515, -0.0029536166694015265, 0.027700066566467285, -0.011650803498923779, 0.02753640152513981, 0.029459450393915176, 0.07225748151540756, 0.04959007352590561, -0.05527738481760025, -0.016570940613746643, 0.0034829662181437016, -0.03592416271567345, -0.016325445845723152, -0.06202850863337517, -0.050776634365320206, 0.010402868501842022, -0.03758125752210617, -0.014330795034766197, -0.011170041747391224, -0.022912904620170593, 0.029520824551582336, -0.014719495549798012, 0.025899766013026237, -0.00017133534129243344, -0.014422855339944363, 0.054704561829566956, -0.023219775408506393, -0.02639075741171837, -0.005375326611101627, -0.023669850081205368, -0.05478639155626297, 0.03160753473639488, -0.025470148772001266, 0.006219217088073492, 0.06256041675806046, 0.00257514463737607, 0.0029766319785267115, 0.0007262572762556374, -0.029766319319605827, -0.0018923605093732476, -0.032344020903110504, -0.017593838274478912, -0.018238263204693794, -0.028068309649825096, 0.049876485019922256, 0.01590605638921261, 0.006142499856650829, -0.04193880036473274, 0.03285546973347664, 0.0042578112334012985, 0.06125110760331154, -0.014555832371115685, -0.008311042562127113, -0.02258557826280594, 0.03569912537932396, -0.028375178575515747, 0.0085360798984766, 0.009686839766800404, -0.003513653064146638, -0.00033212205744348466, 0.04398459568619728, 0.05544104799628258, 0.051144879311323166, 0.09206078201532364, -0.015558271668851376, -0.09156978875398636, 0.04754427820444107, 0.03553546220064163, 0.022135503590106964, 0.012520265765488148, -0.027290906757116318, 0.0005983950686641037, 0.05605478584766388, 0.061169274151325226, -0.014422855339944363, -0.03604691103100777, -0.041836511343717575, -0.0021608711685985327, 0.041713763028383255, 0.03238493576645851, 0.031157460063695908, 0.047994352877140045, 0.01096546184271574, 0.07774021476507187, 0.021542223170399666, 0.05388624221086502, 0.017532464116811752, 0.004861320834606886, 0.038051787763834, 0.03287592902779579, 0.014821785502135754, 0.01056653168052435, 0.031157460063695908, -0.027740981429815292, -0.03375561907887459, -0.009431115351617336, -0.007359747774899006, -0.0023910230956971645, -0.0027183503843843937, 0.012704387307167053, -0.05822332948446274, -0.017491547390818596, -0.057609591633081436, 0.019557802006602287, 0.018238263204693794, -0.006945474538952112, -0.008756003342568874, 0.002206901554018259, 0.01627429947257042, -0.05429540202021599, -0.07045718282461166, 0.013921636156737804, -0.008684400469064713, -0.026902206242084503, 0.022749241441488266, -0.04553939774632454, -0.033735159784555435, -0.02567472867667675, -0.004718115087598562, 0.05302701145410538, -0.02765914984047413, -0.05728226527571678, -0.022728784009814262, -0.007308603264391422, 0.012530495412647724, 0.022074129432439804, -0.035780955106019974, -0.012786219827830791, -0.007247229106724262, -0.03455347940325737, 0.008111577481031418, 0.0707026794552803, -0.029254870489239693, -0.00196012738160789, -0.027515944093465805, 0.003291172906756401, 0.043166276067495346, 0.0063879950903356075, -0.0016123423120006919, 0.014126215130090714, -0.01763475313782692, 0.01540483720600605, -0.038992855697870255, -0.01543552428483963, 0.04337085783481598, 0.007646159268915653, -0.042920783162117004, -0.043166276067495346, -0.0014806442195549607, 0.009461802430450916, 0.01268392987549305, -0.04337085783481598, 0.07225748151540756, 0.006689750123769045, -0.046603213995695114, 0.030584637075662613, -0.054950058460235596, -0.0005859285010956228, -0.040445368736982346, 0.010085769928991795, 0.05118579417467117, -0.008254783228039742, -0.0018744597909972072, 0.03402157127857208, -0.005866317544132471, -0.0471351183950901, 0.03514676168560982, 0.012550952844321728, -0.0616193488240242, 0.022217335179448128, -0.0003794310614466667, -0.009538520127534866, -0.03792904317378998, 0.014862701296806335, 0.0011341376230120659, 0.0010369623778387904, 0.015190028585493565, 0.0024383319541811943, 0.019158871844410896, 0.05527738481760025, 0.010310807265341282, -0.03451256453990936, -0.024304045364260674, 0.015732165426015854, -0.04791252315044403, -0.03756079822778702, -0.015026365406811237, -0.035494543612003326, -0.002204344142228365, -0.03997483849525452, 0.050285644829273224, 0.05122670903801918, -0.013553393073379993, -0.02307656966149807, -0.0064493692480027676, -0.0030865934677422047, -0.0049482667818665504, -0.06546544283628464, -0.003690103068947792, 0.04079315438866615, 0.012878280133008957, -0.025817934423685074, 0.05220869183540344, 0.026124803349375725, 0.0350240133702755, -0.026902206242084503, -0.02289244718849659, 0.04435283690690994, -0.006735780276358128, -0.0023539429530501366, -0.011118896305561066, -0.03164844959974289, 0.036947060376405716, 0.018504217267036438, -0.010295463725924492, -0.06517903506755829, -0.019128184765577316, 0.046848706901073456, -0.009830045513808727, -0.1280667781829834, 0.002163428347557783, 0.002066252985969186, -0.004759030882269144, 0.004017430357635021, 0.02007947862148285, 0.01120072789490223, 0.02186954952776432, -0.006091354880481958, -0.06292866170406342, -0.06939337402582169, 0.0015394608490169048, -0.03099379688501358, -0.02833426184952259, -0.01726651005446911, 0.0011251872638240457, -0.03514676168560982, 0.02440633624792099, -0.04155009984970093, -0.054827310144901276, -0.006111812777817249, 0.04447558522224426, -0.01464789267629385, -0.0049124653451144695, -0.012796448543667793, 0.051267627626657486, 0.0012325915740802884, -0.02997089922428131, 0.0012588032986968756, 0.01890314742922783, 0.02610434591770172, 0.022074129432439804, 0.0428798645734787, 0.0018463301239535213, -0.05265876650810242, 0.012162252329289913, -0.04680779203772545, 0.028354721143841743, -0.00358781311661005, -0.05400899052619934, -0.03285546973347664, 0.048485346138477325, -0.032159898430109024, 0.02972540259361267, -0.013624995946884155, -0.006009523291140795, 0.007262572646141052, 0.03545362874865532, -0.011886069551110268, 0.0037361334543675184, -0.0005168829229660332, 0.0017900707898661494, -0.04126368835568428, -0.020243143662810326, 0.009165162220597267, -0.020989857614040375, -0.031321123242378235, 0.04598947614431381, -0.01331812608987093, -0.022258250042796135, 0.020989857614040375, 0.005712883081287146, 0.08052249252796173, 0.060923777520656586, 0.0172255951911211, -0.07389412075281143, -0.03299867361783981, 0.00884806364774704, 0.02107168920338154, -0.0579778328537941, 0.002601995598524809, -0.019414596259593964, 0.02131718583405018, 0.047748859971761703, 0.015026365406811237, -0.005462273024022579, 0.018391698598861694, -0.010648363269865513, -0.062314920127391815, 0.0401589572429657, -0.002066252985969186, 0.02125581167638302, -0.007927455939352512, 0.0038358657620847225, 0.02706586942076683, -0.028620673343539238, 0.028682047501206398, -0.019199786707758904, -0.0071705118753015995, -0.08854201436042786, -0.018207576125860214, 0.01682666502892971, 0.04095681756734848, 0.004764145240187645, -0.04693054035305977, -0.026083888486027718, -0.0036287291441112757, -0.0477079413831234, -0.03637423738837242, -0.005625936668366194, 0.07806754112243652, 0.024754121899604797, -0.01311354711651802, 0.07769929617643356, 0.012898738496005535, -0.0029485023114830256, -0.008515622466802597, -0.02471320517361164, 0.05188136547803879, -0.015016135759651661, 0.01624361239373684, -0.04275711625814438, 0.0027157929725944996, 0.007993943989276886, 0.026595337316393852, 0.007784250658005476, -0.07053901255130768, 0.02610434591770172, -0.01034660916775465, -0.030114104971289635, -0.018023455515503883, -0.015701478347182274, -0.04999923333525658, -0.0014333352446556091, -0.053845327347517014, -0.025695186108350754, -0.008341729640960693, -0.04206154868006706, -0.08780552446842194, 0.03074830025434494, -0.05695493519306183, -0.01549689844250679, 0.0287025049328804, -0.029029833152890205, 0.03420569375157356, 0.013215836137533188, 0.005850974004715681, -0.03238493576645851, 0.022380998358130455, 0.026472589001059532, 0.00720631331205368, -0.04803526774048805, 0.0017402045195922256, 0.012162252329289913, -0.07180740684270859, 0.017706356942653656, 0.0039100260473787785, 0.006551658734679222, -0.009021956473588943, 0.010055082850158215, 0.04126368835568428, 0.03238493576645851, 0.02020222693681717, -0.02452908270061016, 0.011333704926073551, -0.05830515921115875, 0.025817934423685074, 0.006781810894608498, 0.009937449358403683, 0.03999529406428337, 0.03817453607916832, 0.04762611165642738, 0.039893005043268204, 0.045334819704294205, 0.02864113263785839, 0.00889409426599741, -0.03201669454574585, -0.03158707544207573, -0.0731167197227478, 0.015548042953014374, 0.008034860715270042, -0.025020074099302292, -0.02276969887316227, -0.010275006294250488, -0.039893005043268204, -0.0232606902718544, 0.02542923390865326, -0.041713763028383255, -0.04971282184123993, 0.0037335760425776243, -0.01596743054687977, 0.01105752307921648, -0.04553939774632454, 0.03248722478747368, -0.004237353336066008, 0.006224331445991993, -0.0639924705028534, 0.019915815442800522, 0.01574239321053028, 0.05184044688940048, 0.01716422103345394, -0.018882688134908676, 0.0338374525308609, -0.013359041884541512, 0.019527114927768707, 0.002935715951025486, 0.0185860488563776, 0.0287025049328804, 0.012724845670163631, -0.043575435876846313, -0.021951381117105484, 0.02585885114967823, -0.004505863878875971, 0.03680385276675224, -0.015640104189515114, 0.009114017710089684, 0.045580316334962845, -0.05286334455013275, -0.02592022344470024, 0.05118579417467117, -0.008096233941614628, -0.022606035694479942, -0.00518097635358572, -0.007334175519645214, 0.007835395634174347, 0.011507597751915455, -0.03839957341551781, -0.02682037465274334, -0.050162896513938904, 0.05818241462111473, 0.014218276366591454, 0.028436552733182907, -0.03201669454574585, -0.0022964049130678177, 0.035780955106019974, -0.04157055541872978, -0.036333322525024414, 0.02882525324821472, -0.029766319319605827, -0.0211330633610487, 0.0011226300848647952, -0.03189394623041153, -0.010474471375346184, -0.010719966143369675, -0.011517826467752457, -0.026083888486027718, 0.011947443708777428, 0.025695186108350754, -0.0031147231347858906, -0.026861289516091347, -0.0172255951911211, -0.023588018491864204, -0.015384379774332047, -0.014954762533307076, 0.04885358735918999, 0.027209075167775154, -0.012448662891983986, 0.01784956268966198, 0.0014857586938887835, -0.04193880036473274, -0.009298139251768589, -0.015200258232653141, -0.011804237961769104, 0.024754121899604797, -0.014392168261110783, -0.011998588219285011, -0.00032764687784947455, 0.0004622218257281929, 0.029132122173905373, -0.034226153045892715, 0.03631286323070526, 0.024242673069238663, 0.009778901003301144, -0.014791098423302174, -0.019312305375933647, -0.04118185490369797, -0.003485523397102952, -0.04578489437699318, 0.003938155714422464, 0.03878827393054962, -0.008786690421402454, -0.027925103902816772, -0.03504446893930435, -0.015640104189515114, -0.01371705625206232, 0.03303959220647812, 0.04754427820444107, -0.052945178002119064, -0.0022964049130678177, 0.014085299335420132, 0.00028992752777412534, 0.00432941410690546, -0.00021273072343319654, -0.0005325460224412382, 0.009027071297168732, -0.009830045513808727, 0.002595602534711361, 0.007993943989276886, -0.025633813813328743, 0.005912347696721554, 0.03508538752794266, 0.0008144821622408926, 0.03592416271567345, 0.006602803710848093, 0.028191056102514267, -0.017655212432146072, -0.029316244646906853, -0.03741759434342384, 0.06755215674638748, 0.0008317435858771205, 0.029766319319605827, 0.007124481722712517, 0.017808645963668823, 0.010126685723662376, 0.017061932012438774, -0.003505981294438243, 0.004830633755773306, -0.038215454667806625, 0.0003516210417728871, 0.00003759947503567673, -0.01365568209439516, -0.04598947614431381, 0.027147701010107994, -0.007543869316577911, 0.0023015195038169622, -0.01331812608987093, 0.012878280133008957, 0.00997836608439684, -0.04562123119831085, 0.004339642822742462, 0.026002056896686554, 0.05634119734168053, 0.0053497543558478355, -0.018729254603385925, -0.019905585795640945, 0.03690614551305771, 0.04163192957639694, -0.012970341369509697, 0.027413655072450638, -0.0005056950030848384, 0.01778818853199482, 0.03492172434926033, 0.01642773486673832, -0.023097027093172073, 0.009405543096363544, 0.019690778106451035, 0.017522234469652176, 0.03175073862075806, 0.00548273092135787, 0.020427264273166656, 0.022135503590106964, -0.004178536590188742, 0.05969630181789398, -0.016008347272872925, -0.015701478347182274, 0.01738925836980343, -0.00958966463804245, 0.03733576089143753, 0.015670791268348694, -0.02972540259361267, -0.03782675042748451, -0.012888508848845959, 0.023342521861195564, -0.03786766901612282, 0.023588018491864204, 0.00829058513045311, -0.004656740929931402, 0.039054229855537415, -0.0015087738865986466, -0.03729484602808952, 0.005168189760297537, -0.05756867304444313, -0.0413864366710186, -0.021051231771707535, -0.03526950627565384, 0.06395155191421509, -0.03604691103100777, -0.049876485019922256, 0.010832484811544418, -0.05265876650810242, 0.022749241441488266, -0.018176889047026634, -0.03136203810572624, -0.012561182491481304, -0.014034154824912548, 0.013399957679212093, 0.015793537721037865, -0.0694752037525177, -0.013134004548192024, 0.03179165720939636, -0.014167130924761295, 0.010556302964687347, -0.03402157127857208, 0.037478968501091, 0.0017325327498838305, -0.020734133198857307, -0.04122277349233627, 0.0008547587785869837, -0.009789129719138145, -0.005508303176611662, -0.019046353176236153, 0.008239439688622952, -0.025695186108350754, -0.007820052094757557, 0.018422385677695274, -0.004303841385990381, -0.004349872004240751, 0.03179165720939636, 0.03553546220064163, 0.05531829968094826, 0.032098524272441864, -0.07475335150957108, -0.030461888760328293, 0.03508538752794266, 0.044680166989564896, 0.030400516465306282, -0.001113679725676775, -0.0026365185622125864, -0.00409159017726779, -0.06305140256881714, -0.00257514463737607, 0.005436700768768787, -0.010975690558552742, -0.044434670358896255, 0.002728579333052039, 0.015159341506659985, 0.020028334110975266, -0.0023565003648400307, 0.007267687004059553, 0.016386818140745163, 0.009569206275045872, -0.01948619820177555, 0.027945561334490776, -0.010152257978916168, 0.020713675767183304, 0.04447558522224426, -0.014729725196957588, 0.013594308868050575, -0.012070191092789173, -0.017890477553009987, -0.00007076373731251806, -0.023608475923538208, -0.09132429212331772, -0.009594779461622238, 0.022606035694479942, 0.000020048391888849437, -0.0028692276682704687, -0.028845710679888725, -0.0034676226787269115, 0.032159898430109024, 0.008408217690885067, 0.01480132807046175, 0.05085846781730652, 0.016376590356230736, -0.06665200740098953, 0.022871989756822586, 0.007727990858256817, -0.0015279531944543123, 0.013860261999070644, 0.029152579605579376, 0.025633813813328743, -0.04124322906136513, -0.03737667575478554, 0.03369424492120743, 0.04378001391887665, 0.04402551054954529, -0.03580141440033913, 0.03535133972764015, -0.052576933056116104, 0.009789129719138145, -0.023772139102220535, 0.030727842822670937, -0.008919666521251202, 0.023833513259887695, 0.02614526078104973, 0.001562476041726768, 0.002388465916737914, 0.05769142135977745, 0.02669762633740902, -0.009860732592642307, 0.04283894971013069, 0.017798418179154396, 0.049630988389253616, -0.009702183306217194, -0.008305927738547325, 0.002887128386646509, -0.03913605958223343, -0.04332993924617767, 0.04783068969845772, -0.00224270299077034, -0.005088915582746267, 0.07287122309207916, 0.029889067634940147, -0.007835395634174347, -0.009876076132059097, -0.010740424506366253, 0.02087733894586563, 0.012141793966293335, 0.005416242405772209, 0.033612415194511414, 0.02258557826280594, 0.039606593549251556, 0.040199875831604004, -0.028375178575515747, -0.015312776900827885, -0.008725316263735294, -0.0011852825991809368, -0.04909908398985863, 0.017767731100320816, -0.019844213500618935, -0.0172255951911211, -0.032528143376111984, -0.027045411989092827, 0.010213632136583328, 0.04447558522224426, -0.0018910819198936224, 0.02978677675127983, -0.006746009457856417, 0.034410275518894196, 0.03371470421552658, -0.022544661536812782, 0.03117791749536991, -0.003398577217012644, 0.07041627168655396, -0.02017153985798359, -0.007298374082893133, -0.031157460063695908, 0.05805966630578041, 0.049917399883270264, 0.036026451736688614, -0.027352280914783478, -0.02471320517361164, -0.0004587056173477322, -0.0035929277073591948, -0.029070748016238213, -0.0042347959242761135, 0.002540621906518936, 0.006643719505518675, 0.06391064077615738, 0.04040445387363434, 0.0064391400665044785, -0.017409715801477432, -0.0005677081644535065, -0.03128020837903023, 0.026063429191708565, -0.02107168920338154, 0.001772170071490109, -0.016049262136220932, 0.0033014018554240465, 0.02796601876616478, -0.010546074248850346, -0.02313794195652008, 0.013594308868050575, 0.053804412484169006, -0.005477616563439369, -0.01503659412264824, 0.033428292721509933, -0.06476987153291702, 0.025470148772001266, -0.016253842040896416, -0.024979159235954285, -0.025756560266017914, 0.003746362403035164, 0.008807147853076458, -0.007144939620047808, -0.024856410920619965, -0.0032118982635438442, -0.02663625217974186, 0.024979159235954285, 0.006444254424422979, 0.0265748780220747, -0.012274770997464657, -0.009078215807676315, -0.042429789900779724, -0.03486035019159317, -0.03569912537932396, -0.00926233734935522, -0.040752239525318146, -0.03377607837319374, 0.02827288769185543, 0.020468180999159813, -0.004513535648584366, 0.02307656966149807, -0.02911166474223137, -0.017440402880311012, 0.013236294500529766, 0.01800299622118473, -0.054581813514232635, -0.0046183825470507145, -0.030236851423978806, -0.05061297118663788, -0.03377607837319374, 0.0507357195019722, 0.036333322525024414, 0.0060044084675610065, 0.014248963445425034, 0.07536709308624268, -0.03483989089727402, -0.007272801827639341, -0.006960818078368902, -0.010203403420746326, -0.009114017710089684, 0.03226218745112419, 0.027945561334490776, -0.01772681437432766, -0.01126210205256939, 0.0338374525308609, 0.016969870775938034, 0.005431585945188999, 0.03842003270983696, 0.004022544715553522, 0.016039034351706505, -0.054336316883563995, -0.017215365543961525, -0.011384849436581135, 0.01135416328907013, -0.03099379688501358, 0.040936361998319626, -0.06456529349088669, 0.030482348054647446, 0.02283107303082943, -0.00867417175322771, 0.023403896018862724, -0.02626800909638405, -0.023669850081205368, 0.008761117234826088, -0.017593838274478912, -0.02761823497712612, -0.04447558522224426, -0.03201669454574585, 0.006618147250264883, 0.019588489085435867, -0.018176889047026634, -0.04373909905552864, 0.010106228291988373, 0.0004510339058469981, -0.009952792897820473, 0.011640573851764202, -0.007022191770374775, 0.0075489841401577, 0.02276969887316227, -0.05429540202021599, -0.03287592902779579, 0.00859745405614376, -0.012581639923155308, 0.033203255385160446, 0.014023925177752972, 0.027413655072450638, -0.00954363401979208, 0.004183650948107243, -0.03357149660587311, -0.012775990180671215, -0.005058228503912687, 0.024324504658579826, -0.06771581619977951, -0.026186177507042885, -0.036456070840358734, 0.009206078015267849, -0.050531137734651566, -0.02778189815580845, 0.03940201550722122, -0.007937684655189514, 0.009809588082134724, 0.04206154868006706, 0.024508625268936157, -0.01830986700952053, 0.027945561334490776, -0.0024050879292190075, 0.04476199671626091, -0.015609417110681534, 0.04105910658836365, 0.07086634635925293, 0.04873083904385567, -0.012039504013955593, 0.04011804237961769, -0.02518373727798462, -0.06837047636508942, 0.023608475923538208, -0.023240232840180397, 0.008321271277964115, 0.016079949215054512, -0.06976161152124405, -0.01741994544863701, 0.004012315534055233, 0.0028078537434339523, -0.0029485023114830256, 0.02409946732223034, -0.000995407230220735, -0.022155961021780968, -0.02645213156938553, -0.017143763601779938, 0.07164374738931656, 0.01126210205256939, 0.004897122271358967, -0.0009762278641574085, 0.009047528728842735, -0.02004879154264927, 0.012949883006513119, -0.014791098423302174, -0.038031332194805145, -0.0075234114192426205, -0.02632938325405121, 0.013532934710383415, 0.01135416328907013, -0.016744833439588547, -0.017430175095796585, 0.001635357504710555, 0.016509566456079483, 0.01685735210776329, -0.039483845233917236, 0.021051231771707535, -0.017931394279003143 ]
Recommendation systems are of crucial importance for a variety of modern apps and web services, such as news feeds, social networks, e-commerce, search, etc. To achieve peak prediction accuracy, modern recommendation models combine deep learning with terabyte-scale embedding tables to obtain a fine-grained representation of the underlying data. Traditional inference serving architectures require deploying the whole model to standalone servers, which is infeasible at such massive scale. In this paper, we provide insights into the intriguing and challenging inference domain of online recommendation systems. We propose the HugeCTR Hierarchical Parameter Server (HPS), an industry-leading distributed recommendation inference framework, that combines a high-performance GPU embedding cache with an hierarchical storage architecture, to realize low-latency retrieval of embeddings for online model inference tasks. Among other things, HPS features (1) a redundant hierarchical storage system, (2) a novel high-bandwidth cache to accelerate parallel embedding lookup on NVIDIA GPUs, (3) online training support and (4) light-weight APIs for easy integration into existing large-scale recommendation workflows. To demonstrate its capabilities, we conduct extensive studies using both synthetically engineered and public datasets. We show that our HPS can dramatically reduce end-to-end inference latency, achieving 5~62x speedup (depending on the batch size) over CPU baseline implementations for popular recommendation models. Through multi-GPU concurrent deployment, the HPS can also greatly increase the inference QPS.
[ -0.004972033202648163, 0.010503803379833698, -0.030505632981657982, 0.004329211078584194, 0.04260993376374245, -0.034266360104084015, -0.03239474445581436, 0.04887198284268379, -0.021934669464826584, 0.027234673500061035, 0.025433022528886795, 0.0006286101997829974, 0.020482853055000305, -0.04198022931814194, 0.020028067752718925, 0.034878574311733246, 0.0009713394101709127, -0.010731196030974388, -0.004989525303244591, 0.03428385406732559, 0.03925151377916336, -0.02522312104701996, -0.0006827253382652998, -0.01772790029644966, 0.0749347060918808, 0.02403368055820465, -0.027619492262601852, 0.01971321552991867, -0.03412642702460289, 0.022109586745500565, 0.037152502685785294, 0.04348452016711235, 0.014369482174515724, -0.031222794204950333, -0.04086075723171234, -0.03900662809610367, 0.07528454065322876, 0.013827238231897354, -0.01381849218159914, -0.023543911054730415, 0.009489281103014946, 0.0018202364444732666, -0.03283203765749931, 0.03080299310386181, 0.036872632801532745, -0.016433510929346085, 0.028861407190561295, 0.008072447963058949, 0.017622949555516243, -0.007578305900096893, 0.01655595190823078, -0.018313875421881676, 0.038481876254081726, 0.014124597422778606, -0.025363054126501083, 0.0048802015371620655, 0.024645892903208733, 0.045513562858104706, 0.034966032952070236, 0.03115282766520977, -0.039216529577970505, 0.014605620875954628, -0.03592807799577713, -0.03526339307427406, -0.0163023229688406, -0.019748199731111526, 0.017045721411705017, 0.057128094136714935, -0.03321685642004013, -0.04887198284268379, -0.04901191592216492, -0.0045347390696406364, 0.05188056454062462, -0.008444148115813732, 0.00394001929089427, 0.014605620875954628, 0.0755644142627716, 0.021567342802882195, 0.04226009547710419, -0.0030960419680923223, 0.041000690311193466, 0.00931436289101839, 0.015427733771502972, 0.025817841291427612, 0.07941260188817978, -0.00690924609079957, -0.03606801480054855, -0.05030630901455879, -0.02286173216998577, 0.004499755799770355, -0.04295976832509041, -0.0018694320460781455, -0.0011172862723469734, -0.03585811331868172, -0.02520562894642353, 0.04369442164897919, -0.06024162843823433, -0.006493816617876291, -0.006948602385818958, 0.03337428346276283, -0.02594028227031231, 0.011238456703722477, 0.024278566241264343, -0.05247528478503227, 0.012480372563004494, -0.051740631461143494, 0.01757047511637211, 0.039916202425956726, 0.006633750628679991, 0.08661920577287674, 0.02457592636346817, -0.052370335906744, 0.007604543585330248, 0.02342147007584572, -0.06185087189078331, -0.023718828335404396, -0.03743236884474754, -0.03757230564951897, 0.01854126714169979, -0.038936663419008255, 0.022301996126770973, 0.010530040599405766, 0.01773664727807045, 0.023159092292189598, -0.0360330305993557, 0.017535490915179253, -0.006830533035099506, -0.02744457498192787, 0.016503477469086647, -0.042469996958971024, -0.009375584311783314, 0.009358092211186886, -0.025520481169223785, -0.04932677000761032, 0.00005565250103245489, 0.00024420139379799366, 0.08850831538438797, 0.08109180629253387, 0.0014627486234530807, -0.013564861379563808, -0.03897164389491081, -0.028966357931494713, -0.015366513282060623, -0.0721360296010971, 0.01565512642264366, 0.031642597168684006, -0.04404425621032715, 0.022546881809830666, -0.011588292196393013, 0.008208009414374828, -0.0823512151837349, 0.04621323570609093, -0.026989787817001343, 0.06485944986343384, -0.0006799922557547688, 0.005177561659365892, -0.02728714793920517, 0.0035748789086937904, -0.021672293543815613, 0.039846234023571014, 0.01910100318491459, -0.005934080109000206, -0.03097791038453579, 0.04540861397981644, 0.03251718729734421, 0.05195053294301033, 0.06367001682519913, -0.020675262436270714, -0.09186673164367676, 0.03026074729859829, 0.028144244104623795, 0.0032119248062372208, -0.012156774289906025, 0.025083186104893684, 0.008859577588737011, 0.024540942162275314, 0.08060204237699509, -0.021269982680678368, -0.059541959315538406, 0.010407598689198494, -0.026430051773786545, 0.02420859783887863, 0.03386405110359192, -0.027689458802342415, 0.007643899880349636, 0.021182524040341377, 0.05327990651130676, 0.03528088331222534, 0.04824227839708328, 0.01918846368789673, -0.020202985033392906, 0.05286010354757309, 0.0649644061923027, -0.006209575571119785, -0.0267449039965868, -0.057757798582315445, -0.0034327583853155375, -0.00416303938254714, -0.004473518114537001, 0.0055186511017382145, -0.05104096233844757, -0.02872147224843502, 0.002218174049630761, -0.051355812698602676, 0.0053349873051047325, -0.03535085171461105, 0.0432046502828598, 0.004001240711659193, 0.03526339307427406, -0.03274457901716232, 0.02529308758676052, 0.0048845745623111725, -0.06020664423704147, -0.04621323570609093, -0.005859740078449249, -0.00504637323319912, 0.006555037572979927, 0.06052149459719658, -0.021654801443219185, -0.05188056454062462, 0.002977972384542227, 0.0034240123350173235, 0.060626447200775146, -0.023701338097453117, 0.009909083135426044, -0.002835851861163974, -0.012349183671176434, 0.035963062196969986, 0.018436316400766373, -0.024278566241264343, 0.03267461061477661, -0.007521457504481077, -0.001202558632940054, 0.004053715616464615, 0.0369076170027256, -0.026132691651582718, -0.03242972493171692, -0.04890696704387665, -0.028511572629213333, -0.008431029506027699, 0.005837875418365002, 0.008973273448646069, 0.025502989068627357, 0.038132041692733765, -0.0025210001040250063, 0.0014113665092736483, -0.015410242602229118, 0.04267989844083786, 0.03577065467834473, -0.03970630094408989, -0.03599804639816284, -0.05097099393606186, 0.019468331709504128, -0.02889639139175415, 0.02412113919854164, 0.06080136448144913, 0.05828255042433739, -0.06328519433736801, 0.02711223065853119, -0.036522798240184784, 0.0025494243018329144, -0.004801488481462002, -0.019590772688388824, 0.020832687616348267, -0.030225764960050583, 0.03743236884474754, 0.08221127837896347, 0.005947199184447527, 0.01927592232823372, 0.06223569065332413, 0.004031850956380367, -0.025100678205490112, -0.009996541775763035, -0.03697758540511131, -0.004156480077654123, -0.046423137187957764, -0.004740267526358366, -0.030942926183342934, 0.03207989037036896, 0.01404588483273983, -0.02819672040641308, -0.008146787993609905, 0.028021803125739098, 0.01255908515304327, -0.04754260927438736, -0.049466703087091446, -0.00661625899374485, -0.03351421654224396, 0.0016606241697445512, 0.011579546146094799, -0.028773948550224304, -0.013302484527230263, -0.05303502082824707, 0.03258715197443962, 0.01756172813475132, 0.03613797947764397, -0.032272301614284515, 0.028109261766076088, 0.013643573969602585, -0.0009352626511827111, -0.02800431102514267, 0.012357929721474648, 0.01746552437543869, 0.0004321011947467923, -0.06422974914312363, -0.012226741760969162, -0.045058779418468475, 0.05985680967569351, -0.01220050361007452, -0.014701825566589832, 0.042190130800008774, 0.007915021851658821, 0.0010090559953823686, -0.02168978564441204, 0.006310153286904097, 0.062270671129226685, 0.026167675852775574, 0.00713663874194026, -0.0301732886582613, -0.061081234365701675, 0.03405646234750748, 0.0011282186023890972, -0.11411625146865845, 0.03311190381646156, -0.0133724519982934, -0.01062624529004097, -0.006900500040501356, 0.0363478809595108, 0.003537708893418312, 0.005186307244002819, -0.01719440147280693, -0.06545417010784149, -0.042190130800008774, 0.008850831538438797, 0.017605459317564964, -0.022267013788223267, -0.03837692737579346, -0.00024338146613445133, -0.033006954938173294, 0.020220477133989334, -0.01836634986102581, -0.028161736205220222, 0.009576739743351936, 0.06237562373280525, 0.030365698039531708, 0.018418826162815094, -0.0574779286980629, 0.03666273131966591, 0.012296708300709724, -0.004814607556909323, 0.0009789920877665281, -0.0005662958137691021, 0.004307346418499947, 0.027392098680138588, 0.04495382681488991, -0.0013840356841683388, -0.03225480765104294, 0.015908757224678993, -0.03932148218154907, 0.022127078846096992, 0.027217181399464607, -0.03610299527645111, -0.05044624209403992, 0.0612211674451828, -0.023176584392786026, 0.01539275050163269, -0.01631106808781624, -0.00454348511993885, 0.0035879977513104677, 0.004117123316973448, -0.0446389764547348, -0.011509579606354237, -0.023089125752449036, 0.0035705058835446835, -0.0457584485411644, -0.021724767982959747, -0.007005450781434774, -0.016249846667051315, -0.016074929386377335, 0.02711223065853119, 0.018068989738821983, -0.006362628191709518, -0.0008324985392391682, 0.03514095023274422, 0.07808322459459305, 0.011360899545252323, 0.017710408195853233, -0.03837692737579346, -0.04670300334692001, 0.029333684593439102, 0.026604969054460526, -0.062340639531612396, 0.013197534717619419, -0.043519504368305206, -0.029823454096913338, 0.002170071704313159, 0.0428897999227047, -0.0369076170027256, -0.023456452414393425, -0.030645566061139107, -0.02366635389626026, 0.04194524511694908, 0.0045959604904055595, 0.052720170468091965, -0.03367164358496666, -0.03508847579360008, 0.05212545022368431, -0.022931700572371483, 0.027147214859724045, 0.011754464358091354, -0.018226416781544685, -0.04309970140457153, -0.03701256960630417, 0.0298934206366539, 0.01711568981409073, 0.014754300937056541, -0.037222471088171005, -0.0090869702398777, 0.008855204097926617, -0.03774722293019295, -0.0657690241932869, -0.0013949680142104626, 0.04166537523269653, 0.012821461074054241, 0.002101197838783264, 0.06426473706960678, 0.04330960288643837, -0.02205711230635643, 0.00010406231740489602, -0.05863238498568535, 0.024785825982689857, -0.012427897192537785, 0.013573607429862022, -0.05408452823758125, -0.04908188432455063, 0.021829718723893166, 0.02459341660141945, 0.03953138366341591, -0.05520400032401085, -0.01583879068493843, -0.0383419431746006, -0.03549078479409218, -0.025415530428290367, 0.03528088331222534, -0.008124923333525658, -0.021042589098215103, -0.019293412566184998, -0.013582353480160236, -0.023106617853045464, -0.05933205783367157, -0.1024317592382431, 0.010241426527500153, -0.04124557599425316, -0.02952609397470951, 0.020920148119330406, -0.006559410598129034, -0.01018020510673523, -0.0018792711198329926, -0.015873774886131287, -0.05104096233844757, -0.007320302538573742, 0.04369442164897919, 0.013827238231897354, -0.0557987205684185, -0.006397611927241087, 0.06150103360414505, -0.029228733852505684, -0.0369076170027256, 0.019835658371448517, -0.005256274249404669, -0.020465360954403877, 0.024890776723623276, 0.032552167773246765, 0.028126753866672516, 0.046318184584379196, -0.011282186023890972, 0.03354920074343681, -0.03995118290185928, 0.017343081533908844, -0.022284504026174545, 0.008597200736403465, 0.03451124578714371, 0.06825285404920578, 0.008492249995470047, 0.00542244641110301, 0.03270959481596947, -0.018961070105433464, 0.011955618858337402, -0.01855875924229622, -0.020920148119330406, -0.03725745156407356, 0.005488040391355753, 0.0048933206126093864, -0.0356307178735733, -0.019415855407714844, 0.0015775383217260242, -0.01602245308458805, -0.02088516391813755, 0.025905299931764603, -0.005151323974132538, -0.029403651133179665, 0.004357635043561459, -0.0071628764271736145, -0.0009358092793263495, -0.028791440650820732, 0.02312410995364189, 0.01093235146254301, -0.011964364908635616, -0.07850302755832672, -0.0034568095579743385, -0.0019393990514799953, 0.0635300800204277, 0.02971850335597992, -0.024523450061678886, 0.015235324390232563, -0.014255786314606667, -0.019503314048051834, -0.004464772064238787, 0.030820485204458237, 0.04142049327492714, -0.009856607764959335, 0.006852397695183754, -0.0583525188267231, 0.021007606759667397, -0.06629377603530884, 0.0451987124979496, 0.0019230005564168096, -0.03764227032661438, 0.023159092292189598, -0.03932148218154907, 0.00033917618566192687, 0.028074277564883232, -0.03297197073698044, -0.027864376083016396, -0.000571761978790164, -0.02268681488931179, 0.01328499335795641, 0.042190130800008774, 0.00720223318785429, -0.012086807750165462, -0.03620794788002968, 0.051740631461143494, 0.028756456449627876, 0.029753487557172775, -0.035963062196969986, 0.033724118024110794, 0.010390106588602066, -0.05383964255452156, -0.04876703396439552, -0.01367855817079544, 0.003994680941104889, -0.03391652554273605, 0.02223202958703041, -0.02826668694615364, -0.01619737222790718, -0.037852171808481216, -0.017859088256955147, -0.03816702589392662, 0.024820810183882713, -0.01454440038651228, -0.0270247720181942, 0.00735965883359313, -0.012681527063250542, -0.05887727066874504, -0.016634665429592133, -0.03234226629137993, 0.014701825566589832, 0.030837975442409515, 0.01763169653713703, 0.007893157191574574, -0.020780213177204132, -0.02385876327753067, -0.01241915114223957, -0.011509579606354237, -0.025730382651090622, 0.012148028239607811, -0.016354797407984734, -0.05223040282726288, -0.008872696198523045, -0.010285155847668648, 0.03743236884474754, -0.03377659246325493, 0.04393930733203888, 0.02782939374446869, 0.008763372898101807, 0.015340275131165981, -0.011457104235887527, -0.04243501275777817, 0.00047337080468423665, -0.044079240411520004, 0.009375584311783314, 0.05034128949046135, -0.022896716371178627, 0.022459423169493675, -0.062270671129226685, -0.029316192492842674, 0.006900500040501356, 0.009611723013222218, 0.008815848268568516, -0.01012772973626852, 0.00416085310280323, 0.04554854705929756, -0.009891591034829617, 0.026167675852775574, -0.007193487137556076, 0.019923117011785507, 0.04201521351933479, -0.018978562206029892, -0.03115282766520977, 0.0353158675134182, -0.030295731499791145, -0.0032097382936626673, 0.05258023738861084, -0.03585811331868172, 0.045688483864068985, -0.026937313377857208, 0.050026439130306244, -0.004252684768289328, -0.022494405508041382, -0.023648861795663834, 0.07969246804714203, 0.0022542509250342846, 0.06650368124246597, 0.009559247642755508, -0.03648781403899193, 0.012987633235752583, 0.010897367261350155, 0.017360573634505272, 0.014159581623971462, -0.032009925693273544, -0.030383190140128136, 0.019205953925848007, -0.028686489909887314, -0.039216529577970505, 0.00542244641110301, -0.009410567581653595, -0.008343570865690708, 0.008710897527635098, 0.02151486650109291, 0.02648252807557583, -0.020377902314066887, 0.005068237893283367, 0.013162550516426563, 0.0408957377076149, -0.00017655747069511563, 0.024995727464556694, -0.020762721076607704, 0.021759752184152603, 0.06150103360414505, 0.015523938462138176, 0.02216206304728985, 0.01656469888985157, 0.045863401144742966, 0.037677254527807236, 0.022914208471775055, -0.012576577253639698, 0.013258755207061768, 0.009655452333390713, 0.0228792242705822, 0.0111597441136837, 0.011369645595550537, 0.025590447708964348, 0.026062725111842155, 0.019958101212978363, 0.03284952789545059, 0.027322132140398026, -0.025537973269820213, 0.039566364139318466, 0.00409307237714529, 0.06003172695636749, -0.027759425342082977, -0.018156448379158974, -0.03725745156407356, 0.016503477469086647, 0.034441281110048294, -0.03592807799577713, 0.032202333211898804, 0.031485170125961304, 0.0065331729128956795, 0.02466338500380516, 0.004622198175638914, -0.011063539423048496, 0.011220965534448624, -0.042994752526283264, -0.03711751848459244, -0.018961070105433464, 0.010783671401441097, 0.044988811016082764, -0.013940934091806412, -0.016774600371718407, -0.017343081533908844, -0.029875928536057472, 0.02216206304728985, -0.010206443257629871, -0.007915021851658821, -0.0026740531902760267, 0.0023635742254555225, 0.017719155177474022, 0.018961070105433464, -0.014614366926252842, -0.012069315649569035, 0.028599031269550323, 0.005614855792373419, 0.0064238496124744415, 0.004766505211591721, 0.029386160895228386, 0.003336553694680333, -0.002588780829682946, -0.07171622663736343, -0.00899951159954071, 0.013888458721339703, 0.01981816627085209, -0.040475938469171524, 0.041105639189481735, 0.026342593133449554, 0.0007701841532252729, -0.006318898871541023, -0.045163728296756744, -0.008474758826196194, 0.0163810346275568, 0.01988813281059265, 0.0008920798427425325, 0.02980596199631691, -0.038132041692733765, -0.02214457094669342, 0.010188951157033443, 0.0036426594015210867, 0.020482853055000305, -0.0326046459376812, -0.0012003721203655005, 0.037957124412059784, -0.028301671147346497, -0.004412297159433365, 0.00014034405467100441, -0.002564729657024145, 0.009979050606489182, 0.028406621888279915, 0.010197697207331657, -0.000502068258356303, -0.03423137962818146, -0.02648252807557583, -0.0363478809595108, 0.013311230577528477, 0.0013031362323090434, -0.00986535381525755, 0.008291095495223999, 0.028581539168953896, 0.026692429557442665, -0.04778749495744705, -0.02466338500380516, 0.004471331834793091, 0.008365435525774956, 0.017124434933066368, -0.03764227032661438, -0.10865882784128189, 0.026989787817001343, 0.0032294164411723614, -0.015558922663331032, -0.021724767982959747, -0.005689195357263088, 0.020482853055000305, 0.0766838863492012, 0.004565349780023098, 0.014902980998158455, 0.04086075723171234, -0.009358092211186886, -0.03333929926156998, 0.003601116593927145, -0.00720660574734211, -0.006581275258213282, 0.025328071787953377, 0.042714882642030716, 0.029246225953102112, -0.043344587087631226, 0.0036054893862456083, 0.035805635154247284, 0.025502989068627357, 0.05611357092857361, -0.06360004842281342, 0.01871618442237377, -0.011964364908635616, -0.003592370543628931, 0.007092909421771765, 0.05195053294301033, -0.011920635588467121, 0.009602976962924004, 0.01727311499416828, 0.016608428210020065, 0.013940934091806412, 0.025188136845827103, 0.05513403192162514, 0.025363054126501083, -0.008763372898101807, 0.010101492516696453, 0.04554854705929756, 0.00020170188508927822, -0.01799902319908142, -0.03501850739121437, -0.0012451948132365942, -0.023736320436000824, 0.03827197477221489, -0.048941951245069504, 0.03386405110359192, 0.07084163278341293, 0.015891265124082565, -0.005457429680973291, -0.00044603992137126625, -0.01862872578203678, 0.04026603698730469, 0.01595248654484749, 0.004431975074112415, 0.02789936028420925, -0.0009850048227235675, 0.0572330467402935, 0.036767683923244476, -0.0318874828517437, -0.025642922148108482, 0.03396899998188019, -0.027689458802342415, -0.038586825132369995, -0.001397154526785016, -0.012296708300709724, -0.012506609782576561, -0.01836634986102581, -0.0033103160094469786, -0.02800431102514267, 0.015716347843408585, 0.023176584392786026, 0.047857459634542465, -0.010433835908770561, 0.04267989844083786, 0.04274986684322357, -0.0038241364527493715, 0.032377250492572784, -0.041735343635082245, 0.04491884633898735, -0.011868160218000412, 0.05576373636722565, 0.030837975442409515, 0.0423300638794899, 0.045688483864068985, -0.009375584311783314, -0.04302973300218582, 0.0003602209617383778, -0.01736931875348091, -0.016792090609669685, -0.023648861795663834, 0.014238294214010239, -0.01631106808781624, 0.02735711634159088, 0.024890776723623276, 0.03872676193714142, -0.01477179303765297, -0.01936338096857071, -0.02971850335597992, 0.0006947509245947003, -0.0013009498361498117, 0.012322946451604366, -0.015401496551930904, -0.016538461670279503, 0.016276083886623383, -0.0003741597174666822, -0.01631106808781624, 0.03311190381646156, 0.005597363691776991, 0.03423137962818146, 0.0053349873051047325, -0.034808605909347534, 0.0037519829347729683, -0.04292478412389755, 0.02475084364414215, 0.04901191592216492, -0.01908351294696331, -0.010031525045633316, -0.015961233526468277, -0.008973273448646069, -0.0010123357642441988, -0.010425089858472347, -0.01197311095893383, -0.02079770527780056, 0.0338815413415432, 0.01147459540516138, 0.042190130800008774, 0.021899685263633728, 0.05013138800859451, -0.02611520141363144, -0.0197307076305151, -0.03242972493171692, -0.01567261852324009, -0.034878574311733246, 0.0023854391183704138, 0.024698367342352867, 0.020640278235077858, -0.01048631127923727, 0.012279217131435871, -0.0016158014768734574, -0.004451653454452753, 0.04016108438372612, 0.0011610157089307904, -0.0018016514368355274, 0.011081031523644924, -0.03645283356308937, -0.04701785743236542, -0.04869706556200981, 0.04337957128882408, 0.011046047322452068, -0.009620469063520432, -0.010565023869276047, 0.044708944857120514, -0.03521091863512993, 0.003601116593927145, 0.009856607764959335, 0.0026172047946602106, -0.04887198284268379, 0.03333929926156998, 0.012130537070333958, 0.006786803714931011, -0.03577065467834473, 0.04904690012335777, -0.03764227032661438, -0.0004796569119207561, 0.01864621788263321, 0.0010987012647092342, 0.03655778244137764, -0.016354797407984734, -0.013809746131300926, 0.002188656711950898, 0.007853801362216473, -0.016179880127310753, 0.015996215865015984, -0.0806720033288002, 0.010678720660507679, 0.043904323130846024, 0.010267664678394794, 0.04509376361966133, -0.01718565635383129, -0.054154496639966965, -0.049571651965379715, -0.03545580059289932, -0.012165520340204239, -0.0417703278362751, -0.03753732144832611, 0.031100353226065636, 0.04484887793660164, -0.023613879457116127, -0.0318874828517437, -0.0032053652685135603, 0.01792905665934086, -0.00334311299957335, 0.002184283686801791, -0.031922467052936554, 0.02233698032796383, 0.018926085904240608, -0.03655778244137764, -0.00949802715331316, 0.010722449980676174, -0.011684496887028217, 0.032814543694257736, -0.009699181653559208, 0.011614530347287655, -0.016949517652392387, -0.013241264037787914, -0.003415266517549753, -0.009375584311783314, -0.001106900512240827, -0.005125086288899183, -0.0437643900513649, -0.01584753580391407, -0.03792214021086693, 0.025677906349301338, -0.031555138528347015, -0.03648781403899193, 0.03438880294561386, 0.024261074140667915, 0.02025545947253704, 0.015733839944005013, 0.0296135526150465, -0.01646849326789379, 0.0053481063805520535, 0.022127078846096992, 0.044359106570482254, 0.017413049936294556, 0.03683765232563019, 0.04715779051184654, 0.044079240411520004, -0.06709840148687363, 0.0383419431746006, -0.004814607556909323, -0.07276573032140732, 0.017168164253234863, -0.0500614233314991, -0.0015873773954808712, 0.0817914754152298, -0.062165722250938416, -0.03346174210309982, 0.010836146771907806, 0.007250335533171892, 0.0002916204684879631, 0.0005679356399923563, -0.02133994922041893, -0.017264369875192642, -0.02286173216998577, 0.0008860670495778322, 0.06786803901195526, 0.013984663411974907, 0.01503416895866394, 0.026587478816509247, 0.0014354176819324493, -0.04240003228187561, 0.037397388368844986, -0.003537708893418312, -0.04869706556200981, -0.017421795055270195, -0.02655249461531639, -0.009323108941316605, 0.02817922830581665, -0.023701338097453117, -0.015497701242566109, 0.0012517542345449328, 0.0020837062038481236, -0.010704957880079746, 0.003043566597625613, 0.05177561566233635, -0.016249846667051315 ]
Knowledge tracing and dropout prediction are crucial for online education to estimate students' knowledge states or to prevent dropout rates. While traditional systems interacting with students suffered from data sparsity and overfitting, recent sample-level contrastive learning helps to alleviate this issue. One major limitation of sample-level approaches is that they regard students' behavior interaction sequences as a bundle, so they often fail to encode temporal contexts and track their dynamic changes, making it hard to find optimal representations for knowledge tracing and dropout prediction. To apply temporal context within the sequence, this study introduces a novel student modeling framework, SAICL: \textbf{s}tudent modeling with \textbf{a}uxiliary \textbf{i}nteraction-level \textbf{c}ontrastive \textbf{l}earning. In detail, SAICL can utilize both proposed self-supervised/supervised interaction-level contrastive objectives: MilCPC (\textbf{M}ulti-\textbf{I}nteraction-\textbf{L}evel \textbf{C}ontrastive \textbf{P}redictive \textbf{C}oding) and SupCPC (\textbf{Sup}ervised \textbf{C}ontrastive \textbf{P}redictive \textbf{C}oding). While previous sample-level contrastive methods for student modeling are highly dependent on data augmentation methods, the SAICL is free of data augmentation while showing better performance in both self-supervised and supervised settings. By combining cross-entropy with contrastive objectives, the proposed SAICL achieved comparable knowledge tracing and dropout prediction performance with other state-of-art models without compromising inference costs.
[ 0.03470171242952347, 0.0009236885816790164, -0.03656719997525215, -0.04064229875802994, 0.011093318462371826, -0.017215019091963768, -0.05665289983153343, 0.003187631256878376, -0.03700187802314758, -0.008136609569191933, -0.009725897572934628, -0.08526913076639175, 0.0161373820155859, -0.03345201537013054, -0.012424517422914505, -0.004462230950593948, 0.05614577606320381, 0.05121943727135658, 0.03437570482492447, -0.01824737712740898, -0.012315847910940647, -0.041294313967227936, -0.010124350897967815, 0.04701755940914154, 0.040098950266838074, 0.055421315133571625, 0.007240088656544685, 0.015059745870530605, -0.06121700629591942, 0.012161899358034134, 0.011817780323326588, 0.02392534539103508, 0.0014093042118474841, -0.054660629481077194, -0.03620497137308121, -0.030246272683143616, 0.03247399255633354, 0.03410403057932854, -0.012940695509314537, 0.03756333515048027, -0.02057470940053463, 0.01188117079436779, 0.002234511310234666, -0.020140033215284348, 0.029721038416028023, -0.0894710123538971, -0.053247928619384766, -0.05002407729625702, -0.021462175995111465, 0.02711297571659088, 0.00841281097382307, -0.07693782448768616, 0.06646935641765594, 0.003531750524416566, -0.006687686312943697, 0.05393616855144501, 0.03323467820882797, -0.01463412493467331, 0.07737249881029129, 0.008616565726697445, -0.04466306045651436, 0.04995162785053253, -0.028109110891819, -0.025301821529865265, 0.041547875851392746, -0.042127445340156555, 0.02075582556426525, -0.017468580976128578, 0.01116576511412859, -0.005682495888322592, -0.07505422830581665, -0.0006537134177051485, 0.010160574689507484, -0.021226726472377777, 0.003853230271488428, 0.042381007224321365, 0.03372368961572647, 0.08012545853853226, -0.0023816677276045084, -0.04517018422484398, 0.0171606857329607, 0.016925234347581863, 0.028815461322665215, 0.017296520993113518, 0.06165168434381485, -0.05255969241261482, 0.0029453893657773733, -0.06056499108672142, 0.06284704804420471, 0.044300828129053116, -0.03321656584739685, -0.0003568539395928383, 0.011998895555734634, -0.004118111450225115, -0.03825157508254051, -0.021933075040578842, 0.0019300110870972276, -0.001004058518446982, -0.030409276485443115, -0.008978796191513538, 0.006977471057325602, 0.014416786842048168, -0.011446493677794933, 0.015385753475129604, -0.002347708446905017, 0.0038396466989070177, -0.06723003834486008, -0.006040198728442192, -0.014036444015800953, 0.1585122048854828, -0.040026504546403885, 0.013710436411201954, -0.019886471331119537, 0.0010419795289635658, 0.0030517945997416973, 0.005922473967075348, -0.04390237480401993, -0.017531972378492355, 0.054262176156044006, -0.05397239327430725, -0.010396024212241173, 0.051002100110054016, 0.015086913481354713, 0.016952402889728546, -0.0855589210987091, 0.03908470645546913, 0.016834676265716553, -0.015231805853545666, 0.028109110891819, -0.01162760891020298, 0.02542860247194767, -0.016427166759967804, -0.0498429611325264, 0.00009289239824283868, 0.015711762011051178, 0.0351363904774189, 0.04524262994527817, -0.015286140143871307, -0.0037128657568246126, 0.021933075040578842, -0.023889122530817986, 0.008476201444864273, -0.05277702957391739, 0.007471010554581881, 0.03372368961572647, -0.016445279121398926, -0.0019368028733879328, 0.06368017941713333, -0.037345997989177704, 0.07052633911371231, -0.016934290528297424, 0.042707014828920364, -0.02834456041455269, 0.019053341820836067, 0.028561899438500404, 0.017450468614697456, -0.022711873054504395, -0.009137271903455257, 0.006769188214093447, -0.023653673008084297, 0.06107211485505104, 0.04582219943404198, 0.009327443316578865, 0.058681391179561615, 0.040461182594299316, -0.057341139763593674, -0.007471010554581881, 0.0007267255568876863, -0.08570381253957748, 0.05987675487995148, -0.008095858618617058, 0.04701755940914154, -0.01657206006348133, 0.006207730621099472, 0.035860851407051086, -0.006280176807194948, 0.03499149531126022, -0.06248481571674347, -0.05806560069322586, 0.05437084659934044, -0.03461115434765816, 0.022313417866826057, 0.0010900883935391903, -0.023798564448952675, 0.08729762583971024, -0.02124483697116375, 0.08396510034799576, 0.021136168390512466, -0.011265378445386887, -0.027420872822403908, -0.013882496394217014, -0.007529872935265303, 0.05984053015708923, 0.023400111123919487, -0.020864494144916534, -0.027149200439453125, -0.06172413006424904, 0.046727776527404785, -0.0011132938088849187, 0.013529321178793907, -0.04017139598727226, -0.05502286180853844, -0.013619878329336643, -0.0021315019112080336, 0.021281059831380844, 0.036422308534383774, -0.010776367038488388, 0.04075096547603607, -0.029413141310214996, -0.05984053015708923, -0.03778067231178284, -0.019886471331119537, -0.04382992908358574, -0.002079431200399995, -0.04096830636262894, -0.012560353614389896, 0.029992710798978806, 0.0089878523722291, 0.014706570655107498, -0.003857758129015565, 0.027384649962186813, 0.0006899365107528865, 0.043467696756124496, -0.03814290463924408, -0.013991164974868298, -0.04259834438562393, 0.045967090874910355, -0.011663832701742649, 0.027547653764486313, -0.04267079010605812, 0.03363313153386116, -0.002377139637246728, -0.010712976567447186, -0.005198012106120586, 0.02658774144947529, 0.015829486772418022, 0.010866924189031124, -0.026714522391557693, 0.021353507414460182, 0.025700276717543602, -0.01598343439400196, -0.0057639977894723415, -0.04687266796827316, -0.05437084659934044, -0.00895162858068943, -0.0450252890586853, 0.026334179565310478, 0.020121922716498375, 0.024305688217282295, 0.04448194429278374, 0.007221976760774851, -0.04082341119647026, 0.016879955306649208, 0.04317791387438774, -0.011690999381244183, 0.03265510872006416, 0.05306681618094444, -0.04158409684896469, 0.06139812245965004, -0.060854777693748474, 0.055602431297302246, 0.01908956468105316, 0.012035118415951729, 0.08295086026191711, 0.02066526748239994, -0.004523357376456261, 0.07454710453748703, -0.007566096261143684, 0.01916201040148735, -0.0027461624704301357, 0.0027144672349095345, 0.01890844851732254, -0.07240994274616241, -0.008363003842532635, -0.013982109725475311, -0.0241064615547657, 0.0036358917132019997, -0.017459524795413017, -0.02734842710196972, 0.009436112828552723, 0.025066372007131577, -0.010205852799117565, 0.01543103251606226, 0.005628161132335663, -0.023055991157889366, -0.04991540685296059, -0.061361901462078094, -0.014597902074456215, -0.0488649383187294, -0.008702595718204975, -0.04299679771065712, -0.038686249405145645, -0.06277459859848022, -0.011663832701742649, 0.060347653925418854, 0.05208878964185715, -0.04560485854744911, 0.03144163638353348, -0.013167089782655239, -0.06444086134433746, -0.019198233261704445, -0.014498288743197918, 0.019759690389037132, -0.016517724841833115, -0.021353507414460182, 0.014199447818100452, 0.02896035462617874, 0.016544893383979797, -0.04317791387438774, -0.05418973043560982, 0.02383478730916977, -0.05118321254849434, -0.00978023186326027, -0.011446493677794933, -0.007090668193995953, -0.007181225810199976, 0.006692214403301477, -0.02894224226474762, -0.07577868551015854, -0.008113970048725605, 0.017459524795413017, 0.020429817959666252, -0.048466481268405914, -0.01614643819630146, -0.005881723016500473, -0.02359933778643608, 0.0058319163508713245, -0.02829022705554962, 0.008598454296588898, -0.015177471563220024, -0.036422308534383774, 0.013529321178793907, -0.03470171242952347, -0.004921811167150736, -0.004840309266000986, 0.00849431287497282, -0.008938045240938663, 0.010676753707230091, -0.06846162676811218, -0.024523025378584862, -0.024197017773985863, -0.055928438901901245, 0.0021190503612160683, 0.0023658201098442078, 0.004917283542454243, 0.04397482052445412, 0.011989840306341648, -0.004387520719319582, 0.014217559248209, 0.017857979983091354, 0.0010912202997133136, 0.007883047685027122, 0.008046052418649197, 0.004650138318538666, 0.04198255017399788, -0.031677085906267166, 0.02785554900765419, 0.005279514007270336, -0.016418112441897392, -0.005021424498409033, 0.03548050671815872, -0.059188514947891235, -0.02075582556426525, 0.03587896376848221, -0.03656719997525215, -0.01783081144094467, 0.013357261195778847, 0.03002893552184105, 0.07672048360109329, -0.0036494755186140537, -0.040280066430568695, 0.01559403631836176, 0.015014467760920525, -0.013402540236711502, 0.0017760629998520017, 0.005786637309938669, 0.008449033834040165, -0.0030155715066939592, -0.027420872822403908, 0.04100452736020088, -0.008503368124365807, 0.017423301935195923, 0.007058972958475351, 0.03705621138215065, -0.013701380230486393, 0.028000442311167717, 0.046474214643239975, -0.00045052458881400526, -0.05998542159795761, 0.0247584767639637, 0.03113373927772045, -0.027420872822403908, -0.00667410297319293, -0.027819326147437096, 0.056109555065631866, 0.049806736409664154, -0.0019164273981004953, 0.010731087997555733, 0.04049740359187126, -0.0034276091028004885, -0.0297029260545969, -0.0030291550792753696, 0.028109110891819, -0.0017624793108552694, -0.005003313068300486, -0.015539702028036118, 0.01925256848335266, 0.01814776472747326, 0.016418112441897392, 0.02501203864812851, 0.03069906122982502, -0.01858244091272354, 0.006040198728442192, 0.007697404827922583, 0.058174267411231995, 0.03446626290678978, -0.015566869638860226, 0.011057095602154732, -0.005786637309938669, 0.034683600068092346, 0.015059745870530605, 0.03519072383642197, 0.03658531233668327, -0.02251264452934265, 0.046655330806970596, 0.010649586096405983, 0.026316069066524506, 0.003823799081146717, -0.01806626282632351, -0.011455549858510494, 0.04426460713148117, 0.009734952822327614, 0.022222859784960747, -0.024613583460450172, -0.0349733866751194, -0.01714257337152958, -0.051002100110054016, 0.01630944199860096, -0.007267255801707506, 0.012533186003565788, -0.07168547809123993, -0.00537912780418992, -0.013284815475344658, -0.010486582294106483, -0.016916178166866302, -0.024631695821881294, -0.029630480334162712, -0.00589530635625124, 0.008915405720472336, -0.014434898272156715, -0.08860165625810623, 0.049154721200466156, -0.03937448933720589, -0.0295399222522974, -0.008200000040233135, -0.04531507566571236, 0.06505665183067322, -0.02952181175351143, 0.016445279121398926, 0.032166097313165665, 0.020900718867778778, 0.048901159316301346, -0.032347213476896286, -0.030173826962709427, -0.04958939924836159, 0.0383240208029747, -0.042127445340156555, -0.012026063166558743, -0.018356045708060265, 0.023490669205784798, 0.05313926190137863, -0.045387521386146545, -0.010685808956623077, 0.02066526748239994, 0.02267564833164215, 0.028398895636200905, -0.013864384032785892, -0.085631363093853, 0.006280176807194948, 0.016436222940683365, 0.03707432374358177, -0.019705357030034065, -0.0054923249408602715, 0.010260188020765781, 0.040461182594299316, 0.02584516815841198, -0.013474985957145691, 0.024305688217282295, 0.017332743853330612, -0.05741358548402786, 0.035607289522886276, 0.006253009662032127, 0.011455549858510494, 0.007575151976197958, -0.0027144672349095345, -0.05437084659934044, 0.026497183367609978, -0.07164925336837769, 0.03439381718635559, 0.0029997238889336586, -0.03439381718635559, -0.011772501282393932, -0.031749531626701355, 0.04147543013095856, -0.02157084457576275, -0.009300276637077332, -0.013293870724737644, -0.03749088943004608, 0.0007233296637423337, 0.021299172192811966, -0.0075253453105688095, 0.0060673663392663, 0.007602319121360779, -0.02935880795121193, 0.011944561265408993, 0.02401590347290039, 0.03421270102262497, -0.013121811673045158, 0.03078961931169033, 0.0038147433660924435, 0.0028503036592155695, 0.043540142476558685, -0.022784318774938583, -0.025392379611730576, -0.04158409684896469, 0.021770071238279343, 0.07212015241384506, -0.012306791730225086, 0.09280353784561157, -0.01036885753273964, -0.015929101034998894, -0.012406405061483383, -0.03287244588136673, -0.041294313967227936, -0.015231805853545666, -0.025971949100494385, 0.03357879817485809, 0.04542374610900879, -0.014371507801115513, 0.0004261871799826622, -0.05404483899474144, 0.022458311170339584, 0.013710436411201954, 0.041801437735557556, -0.03959182649850845, -0.006465820129960775, 0.017550082877278328, -0.020466040819883347, -0.01824737712740898, 0.028435118496418, -0.005795693024992943, 0.0031310326885432005, 0.005564771126955748, 0.025048261508345604, -0.023798564448952675, -0.02151651121675968, -0.02935880795121193, 0.005845499690622091, -0.01622794009745121, -0.0062122587114572525, 0.0038147433660924435, 0.006266593001782894, 0.027475208044052124, 0.035498619079589844, -0.002128106076270342, -0.026316069066524506, 0.03716488182544708, 0.05744980648159981, 0.02182440645992756, 0.012071342207491398, -0.04056985303759575, -0.0036607952788472176, -0.015068802051246166, -0.043793704360723495, 0.028000442311167717, 0.04658288136124611, 0.01841038092970848, -0.01544008869677782, -0.004654665943235159, 0.01782175526022911, -0.0049987854436039925, -0.006565433461219072, 0.009001435711979866, 0.003008779603987932, 0.002050000010058284, 0.026406627148389816, 0.03155030310153961, -0.0029770846012979746, -0.0032623412553220987, -0.028924129903316498, 0.059188514947891235, 0.056218221783638, 0.016418112441897392, -0.014543566852807999, -0.05770336836576462, -0.013764770701527596, 0.015286140143871307, -0.0386500284075737, 0.015920044854283333, -0.058427829295396805, 0.0383240208029747, -0.001319878501817584, -0.0009684014366939664, 0.00389850907959044, -0.050060298293828964, -0.03368746489286423, 0.05802937597036362, -0.001396852545440197, 0.04393859952688217, 0.04509773477911949, 0.04024384543299675, -0.007199337240308523, 0.012732413597404957, -0.061941470950841904, 0.04759712889790535, -0.04332280531525612, 0.045061513781547546, 0.011446493677794933, -0.027565764263272285, -0.015367642045021057, 0.024903368204832077, 0.016925234347581863, 0.046981338411569595, -0.023146549239754677, 0.01688901148736477, 0.033832356333732605, 0.012832026928663254, -0.005741358269006014, -0.01308558788150549, -0.04172898828983307, 0.009753064252436161, 0.005524019710719585, -0.02885168418288231, -0.051654115319252014, -0.021226726472377777, -0.021697625517845154, 0.028797348961234093, 0.06813561916351318, 0.009264052845537663, -0.062448590993881226, -0.031097516417503357, 0.0006039066938683391, -0.020303037017583847, 0.036440420895814896, -0.005569298751652241, 0.025917615741491318, -0.016092104837298393, -0.0424896739423275, 0.04607576131820679, 0.0004123205435462296, -0.011301601305603981, 0.027221646159887314, 0.03991783410310745, 0.04900982975959778, -0.0298659298568964, -0.004867476411163807, 0.04252589866518974, -0.016427166759967804, 0.007203865330666304, 0.00961722806096077, 0.0249214805662632, -0.04727112129330635, 0.004754279274493456, -0.019795913249254227, 0.006746549159288406, -0.010350745171308517, -0.015376698225736618, -0.00865731667727232, -0.028761126101017, 0.03287244588136673, -0.038939811289310455, -0.07657559216022491, -0.03955560550093651, 0.01899900659918785, 0.04075096547603607, -0.03160464018583298, -0.0027506903279572725, 0.0463293194770813, 0.00978023186326027, -0.0048765321262180805, -0.04176521301269531, -0.02785554900765419, -0.0007595527567900717, 0.023979680612683296, 0.022277195006608963, -0.0020318885799497366, 0.03037305362522602, 0.056508008390665054, -0.060456324368715286, -0.016083048656582832, -0.007575151976197958, -0.0026374931912869215, 0.015965323895215988, 0.002836720086634159, 0.004362617153674364, -0.0060990615747869015, -0.03323467820882797, -0.005804748740047216, 0.02368989586830139, 0.0260262843221426, -0.012560353614389896, 0.022385863587260246, 0.0012146051740273833, 0.018193041905760765, 0.031332965940237045, 0.0008982192375697196, 0.004385256674140692, -0.021281059831380844, -0.009499503299593925, -0.010070016607642174, 0.0061307563446462154, 0.002045472152531147, 0.0010702788131311536, 0.006959359627217054, 0.025464827194809914, 0.015095969662070274, 0.02175196073949337, -0.009988514706492424, -0.019451795145869255, 0.036512866616249084, 0.011156708933413029, 0.012795803137123585, 0.03062661550939083, -0.016291331499814987, -0.040461182594299316, 0.044300828129053116, 0.012605632655322552, 0.044300828129053116, -0.01948801800608635, 0.0037377693224698305, 0.034937161952257156, -0.021878741681575775, -0.016789399087429047, -0.00518442876636982, 0.06313683092594147, 0.0015496687265112996, 0.007611374836415052, 0.03671209141612053, 0.027040529996156693, -0.01932501420378685, 0.0415116511285305, -0.042707014828920364, -0.011763446033000946, 0.01146460510790348, 0.016771286725997925, 0.011201987974345684, 0.06317305564880371, 0.020900718867778778, 0.0014353395672515035, 0.010205852799117565, 0.043866150081157684, -0.01588382199406624, 0.03365124389529228, -0.018220210447907448, -0.05777581408619881, -0.00545610161498189, -0.03988161310553551, -0.005664384458214045, -0.013855328783392906, -0.07628580927848816, -0.006058310158550739, 0.01563931629061699, -0.013791938312351704, -0.010685808956623077, 0.005152733530849218, 0.018962783738970757, -0.011138597503304482, 0.04350392147898674, -0.01429906114935875, -0.05418973043560982, 0.0625934824347496, -0.007416675798594952, 0.08157438039779663, -0.031332965940237045, -0.02066526748239994, 0.04719867557287216, -0.0005345734534785151, 0.021226726472377777, -0.014262838289141655, -0.00848525669425726, 0.010948426090180874, 0.031495969742536545, -0.02399779111146927, 0.019886471331119537, -0.011609497480094433, 0.03803423419594765, 0.002972556743770838, -0.012587521225214005, -0.003579293144866824, -0.02008569799363613, 0.015150303952395916, -0.004622970707714558, 0.050313860177993774, -0.00865731667727232, 0.04401104524731636, -0.018446603789925575, -0.015322363935410976, -0.013167089782655239, -0.024559250101447105, -0.026370404288172722, 0.0485389307141304, -0.028489453718066216, 0.010613363236188889, 0.013936830684542656, 0.010260188020765781, 0.0062303701415658, 0.01805720664560795, -0.01874544471502304, -0.006262065377086401, 0.02006758749485016, -0.004795030225068331, 0.012506019324064255, -0.005216123536229134, -0.0064250691793859005, 0.01647244580090046, -0.024704141542315483, -0.0036200443282723427, 0.000921424652915448, -0.03298111632466316, -0.012669023126363754, 0.011681944131851196, -0.03153219074010849, -0.004659194033592939, -0.05897117778658867, -0.01999514177441597, -0.021299172192811966, 0.009571949020028114, 0.024142684414982796, 0.024722253903746605, -0.020647156983613968, 0.038939811289310455, -0.00794191099703312, 0.003783048130571842, 0.016834676265716553, -0.05455195903778076, 0.04448194429278374, 0.00537459971383214, 0.023526892066001892, 0.006488459650427103, 0.01664450578391552, -0.003939260262995958, -0.006828051060438156, 0.01656300388276577, -0.02676885761320591, 0.00791021529585123, -0.0058319163508713245, -0.01956046372652054, -0.029721038416028023, 0.025917615741491318, -0.027420872822403908, -0.006533738225698471, 0.017215019091963768, 0.05831916257739067, 0.011736278422176838, -0.0034570402931421995, 0.04393859952688217, -0.01990458369255066, 0.018618663772940636, 0.017187852412462234, -0.004627498798072338, 0.004613914992660284, 0.010115295648574829, -0.021099945530295372, -0.010522805154323578, -0.001052733277902007, 0.043214134871959686, -0.006180563475936651, -0.015331419184803963, -0.01104803942143917, -0.009336499497294426, 0.010070016607642174, 0.01162760891020298, -0.05078475922346115, 0.05879006162285805, -0.016789399087429047, -0.02300165593624115, 0.0072446162812411785, 0.00961722806096077, -0.003198950784280896, -0.04861137643456459, -0.012985974550247192, -0.0005707965465262532, 0.0421636663377285, 0.0029635007958859205, 0.05212501436471939, 0.024794699624180794, -0.005062175448983908, -0.017785532400012016, 0.003663059091195464, -0.044445719569921494, 0.006981999147683382, 0.03339768201112747, -0.0003528920642565936, 0.0029929322190582752, 0.05111076682806015, 0.03680264949798584, -0.03544428572058678, 0.01543103251606226, -0.020556598901748657, -0.022892987355589867, -0.009553837589919567, -0.018011927604675293, 0.0009123688796535134, -0.0036766426637768745, 0.009979458525776863, 0.02224097214639187, 0.04426460713148117, 0.0021484815515577793, 0.001707012765109539, -0.010685808956623077, -0.004632026422768831, 0.027982329949736595, 0.03807045891880989, -0.017676863819360733, 0.001290447311475873, 0.020973164588212967, -0.017595361918210983, -0.012687134556472301, 0.024215130135416985, 0.04879249259829521, 0.03345201537013054, 0.006461292039602995, 0.015874765813350677, 0.039193373173475266, -0.013927774503827095, 0.003543070051819086, 0.034756045788526535, -0.0035521259997040033, 0.005890778731554747, 0.00961722806096077, -0.06056499108672142, 0.05288570001721382, 0.0009967007208615541, 0.045894645154476166, 0.01205323077738285, -0.011854003183543682, -0.02818155661225319, -0.00013123791723046452, -0.016952402889728546, -0.004143015015870333, 0.0023975151125341654, -0.004749751649796963, -0.021281059831380844, -0.003794367890805006, 0.03548050671815872, 0.0015440088463947177, 0.02350877970457077, 0.01765875145792961, 0.012071342207491398, -0.017876090481877327, -0.05792070925235748, -0.028109110891819, 0.017441414296627045, -0.009241413325071335, 0.038360241800546646, -0.05879006162285805, -0.039446935057640076, 0.015693649649620056, -0.058608945459127426, 0.03506394475698471, 0.014679403975605965, 0.0052568744868040085, -0.03135107830166817, 0.01981402561068535, 0.017948536202311516, 0.02886979654431343, -0.044445719569921494, -0.02660585381090641, 0.004894644021987915, 0.00277106580324471, 0.018202098086476326, -0.04042495787143707, -0.020973164588212967, 0.03452059626579285, 0.030047046020627022, 0.003520430764183402, -0.01831076852977276, -0.021552734076976776, -0.022403975948691368, 0.021697625517845154, 0.012877305038273335, -0.017097294330596924, 0.04332280531525612, 0.018636776134371758, -0.02577272243797779, -0.029395030811429024, 0.03287244588136673, -0.00014390185242518783, -0.02198741026222706, 0.024559250101447105, -0.012650910764932632, -0.00024139287415891886, -0.0013504417147487402, -0.01898089423775673, -0.03846891224384308, -0.005080287344753742, 0.0009151988197118044, -0.023454444482922554, 0.023291440680623055, 0.012777691707015038, -0.040352512151002884, 0.013103699311614037, 0.01639094389975071, 0.048720043152570724, -0.029902154579758644, -0.031061291694641113, 0.04690888896584511, -0.022114191204309464, -0.06375262141227722, 0.04542374610900879, 0.012895417399704456, 0.012234346009790897, -0.045967090874910355, 0.01413605734705925, 0.007126891519874334, -0.011038984172046185, -0.030246272683143616, -0.0014817503979429603, -0.005822860170155764, -0.033669352531433105, 0.04067851975560188, -0.02995648793876171, 0.06556377559900284, -0.014579790644347668 ]
Knowledge Tracing (KT), which aims to model student knowledge level and predict their performance, is one of the most important applications of user modeling. Modern KT approaches model and maintain an up-to-date state of student knowledge over a set of course concepts according to students' historical performance in attempting the problems. However, KT approaches were designed to model knowledge by observing relatively small problem-solving steps in Intelligent Tutoring Systems. While these approaches were applied successfully to model student knowledge by observing student solutions for simple problems, they do not perform well for modeling complex problem solving in students.M ost importantly, current models assume that all problem attempts are equally valuable in quantifying current student knowledge.However, for complex problems that involve many concepts at the same time, this assumption is deficient. In this paper, we argue that not all attempts are equivalently important in discovering students' knowledge state, and some attempts can be summarized together to better represent student performance. We propose a novel student knowledge tracing approach, Granular RAnk based TEnsor factorization (GRATE), that dynamically selects student attempts that can be aggregated while predicting students' performance in problems and discovering the concepts presented in them. Our experiments on three real-world datasets demonstrate the improved performance of GRATE, compared to the state-of-the-art baselines, in the task of student performance prediction. Our further analysis shows that attempt aggregation eliminates the unnecessary fluctuations from students' discovered knowledge states and helps in discovering complex latent concepts in the problems.
[ 0.0013322500744834542, -0.011870197020471096, -0.03453826531767845, -0.05564912408590317, 0.02560531161725521, 0.0017611810471862555, -0.0244677122682333, 0.005025951657444239, -0.016905473545193672, -0.01654181443154812, 0.008014481514692307, -0.04453422129154205, 0.038603782653808594, -0.0244490634649992, -0.04807756096124649, 0.02648182213306427, 0.04583965986967087, -0.0012401698622852564, -0.0391259603202343, -0.04009571671485901, -0.01679357886314392, -0.07224688678979874, 0.03362445533275604, -0.007464330643415451, 0.04699591174721718, 0.030118411406874657, 0.003268267260864377, 0.026686962693929672, -0.08504021912813187, 0.02567990869283676, 0.02657506801187992, 0.029185952618718147, -0.030118411406874657, -0.032057926058769226, -0.04028220847249031, -0.008485372178256512, 0.03172224014997482, 0.046511031687259674, -0.028719723224639893, 0.005478193983435631, 0.008028468117117882, -0.012578865513205528, -0.01675627939403057, -0.0028952837456017733, 0.015441513620316982, -0.06620455533266068, -0.020103806629776955, -0.0587075874209404, -0.021987373009324074, -0.021278703585267067, -0.011236125603318214, -0.024132026359438896, 0.04971868917346001, 0.03532152995467186, -0.00141500576864928, 0.0488608255982399, 0.058371905237436295, -0.01653249002993107, 0.04494450241327286, 0.007128645665943623, 0.005874488968402147, 0.08056441694498062, -0.061131980270147324, -0.03028625249862671, 0.06974789500236511, -0.136586531996727, -0.007482979912310839, 0.019805418327450752, -0.009921358898282051, -0.002771733095869422, -0.037913765758275986, 0.00927329994738102, 0.017474273219704628, -0.006727688480168581, 0.010947063565254211, -0.01171167939901352, 0.059080570936203, 0.0390140637755394, -0.020980317145586014, -0.0067789736203849316, -0.019824068993330002, 0.09123174101114273, 0.028141599148511887, -0.01086314208805561, 0.004482794553041458, -0.04677211865782738, 0.005664685741066933, -0.06482451409101486, 0.023069024085998535, -0.005226430017501116, -0.042632002383470535, 0.0035246931947767735, -0.04330337420105934, 0.029130004346370697, -0.0010088036069646478, 0.014425133354961872, -0.0017215515254065394, 0.007151957135647535, -0.05188199132680893, 0.029614882543683052, 0.0008030799217522144, -0.019376488402485847, -0.00395129295065999, -0.016047611832618713, 0.04688401520252228, -0.05083763971924782, -0.041624948382377625, 0.011767626740038395, 0.04225901886820793, 0.11957848072052002, -0.012737383134663105, 0.037857815623283386, -0.00981878861784935, -0.04035680368542671, -0.016094233840703964, -0.010536781512200832, -0.03149845078587532, -0.04125196486711502, 0.07232148200273514, -0.026295330375432968, 0.0015000926796346903, 0.044683411717414856, -0.020905720070004463, 0.00443150894716382, -0.09011279046535492, 0.054380983114242554, 0.012103311717510223, 0.02733968384563923, 0.010835167951881886, -0.02157709002494812, 0.038939468562603, 0.05975194275379181, 0.004652968142181635, -0.05024086683988571, -0.0033988114446401596, 0.03364310413599014, 0.0584837980568409, -0.010984361171722412, -0.006536534521728754, -0.032803889364004135, -0.035787757486104965, 0.01172100380063057, -0.030230306088924408, -0.06482451409101486, 0.010098526254296303, -0.004342925734817982, 0.017399676144123077, 0.046511031687259674, 0.0017332072602584958, 0.08250392973423004, -0.006690389942377806, 0.056320495903491974, -0.0028323428705334663, 0.03308362886309624, -0.01585179567337036, 0.010900440625846386, -0.024225272238254547, 0.03752212971448898, -0.014136071316897869, -0.012112636119127274, 0.010919089429080486, -0.015991663560271263, 0.0024337167851626873, 0.06083359569311142, 0.006699714343994856, -0.016401944682002068, 0.011991417035460472, 0.013315508142113686, -0.0493457056581974, 0.03653372451663017, -0.0391632579267025, 0.02144654653966427, 0.033904191106557846, 0.042855795472860336, -0.044646114110946655, -0.02045813947916031, -0.01371646486222744, 0.004300964996218681, -0.053336627781391144, -0.014910011552274227, -0.0389767661690712, 0.02760077267885208, -0.019283242523670197, 0.01087246648967266, 0.07377611845731735, -0.02924189902842045, 0.06646564602851868, 0.03472475707530975, 0.01172100380063057, -0.02855188027024269, 0.0003595793095882982, 0.02265874296426773, 0.03258009999990463, 0.0295029878616333, 0.04818945750594139, -0.009068159386515617, -0.03560126572847366, -0.026239383965730667, -0.004151771776378155, -0.04785377159714699, -0.04472070932388306, -0.06262391805648804, 0.004478131886571646, -0.025250976905226707, 0.014359861612319946, 0.04099087789654732, 0.014704870991408825, 0.029782725498080254, -0.018490653485059738, -0.046511031687259674, -0.043825551867485046, -0.003969942219555378, -0.03798836097121239, 0.008182323537766933, 0.008690513670444489, -0.01761414110660553, 0.025735855102539062, 0.021987373009324074, 0.046660225838422775, -0.0018392744241282344, 0.022285759449005127, 0.019208645448088646, 0.08190716058015823, 0.031852781772613525, 0.039760030806064606, -0.00589780043810606, 0.03541477397084236, -0.010751246474683285, 0.005995708517730236, -0.04233361780643463, 0.02857052907347679, 0.029857322573661804, -0.010033253580331802, -0.04445962235331535, -0.027302386239171028, -0.015917066484689713, -0.03660832345485687, -0.008117051795125008, 0.039760030806064606, -0.029204601421952248, -0.001758849946781993, -0.04580236226320267, -0.0590432733297348, -0.05165820196270943, 0.034818001091480255, 0.0032705983612686396, -0.010117175057530403, 0.013007796369493008, 0.03610479459166527, 0.009650945663452148, -0.016513841226696968, -0.0880240872502327, 0.05184469372034073, 0.027731316164135933, -0.001071161706931889, 0.06180335208773613, 0.047629982233047485, -0.03498584404587746, 0.026761559769511223, -0.05374690890312195, 0.033027682453393936, 0.038678381592035294, 0.010564754717051983, 0.009343234822154045, -0.002909270580857992, 0.009632296860218048, 0.04804026335477829, -0.030789781361818314, 0.01579584740102291, 0.01851862668991089, 0.016905473545193672, -0.04121466726064682, -0.012364400550723076, -0.000776271743234247, -0.05512695014476776, -0.06930031627416611, 0.00024331339227501303, -0.04703320935368538, -0.022117916494607925, 0.03427717462182045, -0.022379005327820778, -0.04453422129154205, -0.050427358597517014, -0.014984608627855778, -0.001758849946781993, -0.021819530054926872, -0.015460162423551083, 0.00985608622431755, -0.014005526900291443, 0.0006352373748086393, -0.020252998918294907, -0.00006090119859436527, -0.025903698056936264, -0.005175144877284765, 0.04252010956406593, 0.04024491086602211, -0.02045813947916031, 0.0007920069620013237, 0.00591644924134016, -0.07146362215280533, -0.019022153690457344, -0.018192265182733536, -0.004820810630917549, -0.004454820416867733, -0.001370714046061039, -0.0017763335490599275, -0.022192513570189476, 0.04035680368542671, -0.02862647734582424, -0.04453422129154205, 0.051620904356241226, -0.009422493167221546, -0.030677884817123413, -0.031759537756443024, -0.0294656902551651, 0.002004785928875208, 0.04330337420105934, 0.04184873774647713, -0.046622928231954575, -0.029167301952838898, -0.005389610305428505, -0.02060733363032341, -0.046585626900196075, -0.022826584056019783, 0.008541320450603962, -0.008023805916309357, 0.025008538737893105, 0.06639105081558228, 0.007907248102128506, -0.009119444526731968, 0.012401698157191277, 0.0014627943746745586, -0.06952410936355591, -0.015217723324894905, -0.028775669634342194, -0.025232328101992607, -0.010741922073066235, -0.017875229939818382, -0.006834920961409807, -0.023404709994792938, -0.03334471583366394, -0.022975778207182884, 0.00381375546567142, -0.01560935564339161, 0.04307958483695984, 0.044608816504478455, -0.008005156181752682, 0.02636992745101452, 0.002387093845754862, -0.003729834221303463, 0.0011743149952962995, 0.04777917638421059, -0.03724239394068718, -0.006359367165714502, 0.03209522366523743, -0.060311418026685715, 0.06560777872800827, 0.02347930520772934, 0.016243427991867065, 0.006354704964905977, 0.011431941762566566, -0.026798857375979424, -0.005837190430611372, 0.024747449904680252, -0.06586886942386627, -0.03039814904332161, -0.00659248186275363, 0.008676527068018913, 0.014369186013936996, 0.01782860793173313, -0.019087426364421844, 0.03787646442651749, 0.06370556354522705, -0.02159573882818222, -0.013604570180177689, 0.026966700330376625, -0.012858603149652481, -0.014900687150657177, -0.04647373408079147, 0.059378959238529205, 0.062101736664772034, -0.043564461171627045, 0.03244955837726593, 0.02733968384563923, -0.014555677771568298, 0.05699186399579048, 0.0390886627137661, 0.0035316867288202047, -0.004932705778628588, 0.02944703958928585, 0.014415808953344822, -0.02661236561834812, -0.013921605423092842, -0.014136071316897869, 0.05031546205282211, -0.0008240602328442037, -0.011515863239765167, 0.009082145988941193, 0.060311418026685715, -0.023124972358345985, -0.0487489327788353, 0.0392751544713974, -0.0244863610714674, -0.035694513469934464, -0.013362131081521511, -0.024262571707367897, 0.03604884818196297, 0.03164764121174812, 0.09361883997917175, 0.006946816109120846, 0.015460162423551083, 0.02077517658472061, -0.032897137105464935, -0.020141104236245155, 0.023870937526226044, 0.04151305556297302, -0.017903203144669533, 0.04322877898812294, 0.0007045889506116509, 0.013968228362500668, -0.027843210846185684, 0.030565990135073662, 0.019917314872145653, -0.0075482516549527645, -0.006294094957411289, 0.04009571671485901, 0.006676402874290943, -0.03645912930369377, -0.00031383056193590164, -0.04121466726064682, 0.053336627781391144, 0.027041297405958176, 0.036701567471027374, 0.007226553745567799, -0.006988776847720146, -0.036832112818956375, -0.005077236797660589, 0.06299690157175064, 0.002988529624417424, -0.025139082223176956, -0.005431571044027805, -0.03754078224301338, 0.0028183558024466038, -0.0029255887493491173, 0.006606468465179205, 0.030025165528059006, -0.03755943104624748, -0.0021295021288096905, 0.010508807376027107, -0.02761942148208618, -0.05993843451142311, 0.04147575423121452, -0.03308362886309624, -0.016476541757583618, 0.033027682453393936, -0.004858109168708324, 0.0683678612112999, -0.03614209219813347, 0.01464892365038395, -0.04013301432132721, -0.029969217255711555, 0.03565721586346626, -0.0070027634501457214, -0.025269625708460808, -0.03653372451663017, 0.01326888520270586, -0.023926885798573494, 0.006191524676978588, -0.017949827015399933, 0.005687997210770845, 0.06967329978942871, -0.0889192447066307, -0.03416528180241585, 0.00028979062335565686, 0.009772165678441525, 0.011944794096052647, 0.007939884439110756, -0.10488293319940567, 0.008308205753564835, 0.017353054136037827, 0.03737293928861618, 0.023031726479530334, 0.0008211462991312146, 0.02174493297934532, -0.000034675802453421056, -0.03345661237835884, 0.02540017105638981, -0.0009289617883041501, 0.028999460861086845, -0.02454230934381485, -0.019245944917201996, -0.014052149839699268, -0.005762593820691109, -0.02260279469192028, 0.024710150435566902, -0.058371905237436295, -0.01275603286921978, -0.03703725337982178, -0.01369781605899334, -0.049271110445261, -0.02047679014503956, 0.0032892473973333836, 0.007422369904816151, 0.046548329293727875, 0.006555183324962854, 0.018136318773031235, -0.02150249294936657, 0.045615870505571365, -0.0390140637755394, 0.0010898108594119549, -0.02457960695028305, 0.002967549255117774, 0.0005417001084424555, -0.002471015090122819, 0.000913809344638139, 0.02370309643447399, 0.019973261281847954, -0.02241630293428898, 0.029950568452477455, 0.007431694306433201, -0.03599289804697037, 0.05206848308444023, -0.03806295618414879, -0.01328753400593996, -0.08563698828220367, 0.03433312475681305, 0.03522828221321106, -0.03334471583366394, 0.07399991154670715, -0.047443490475416183, 0.01078854501247406, 0.022304408252239227, -0.011040309444069862, 0.0008415438351221383, -0.023964183405041695, -0.015898417681455612, 0.05121062323451042, 0.042706601321697235, -0.00004338117651059292, -0.04252010956406593, -0.010191772133111954, 0.02355390228331089, -0.01319428812712431, -0.0022239135578274727, -0.018910259008407593, -0.013054419308900833, -0.008816394954919815, -0.027805913239717484, 0.02260279469192028, 0.007823326624929905, 0.016429919749498367, -0.007058711256831884, -0.0037508143577724695, -0.003046808298677206, 0.014537028968334198, -0.012923874892294407, -0.05516424775123596, -0.007310474757105112, 0.019432436674833298, 0.02756347507238388, 0.033997438848018646, -0.006503898184746504, 0.011413292028009892, 0.0008636896964162588, 0.0019348514033481479, -0.0044688074849545956, 0.057290252298116684, 0.04401204362511635, 0.002678487217053771, 0.0061402395367622375, 0.007175268605351448, -0.041886039078235626, -0.021353300660848618, -0.003331208135932684, 0.014798116870224476, 0.002811362501233816, -0.0007203242275863886, -0.027880510315299034, -0.01666303351521492, -0.018900934606790543, 0.022173864766955376, -0.035936951637268066, -0.0031027558725327253, 0.017213184386491776, 0.030715184286236763, -0.037745922803878784, 0.0026015592738986015, -0.023124972358345985, 0.021110860630869865, -0.03203927353024483, -0.022155214101076126, 0.04621264338493347, -0.017949827015399933, -0.015208398923277855, -0.06456343084573746, -0.008098402060568333, 0.03051004372537136, -0.022173864766955376, 0.05426908656954765, -0.06792028248310089, 0.04244551062583923, 0.012345750816166401, 0.05326203256845474, 0.04121466726064682, -0.04229632019996643, -0.011646406725049019, 0.046809419989585876, -0.03433312475681305, -0.0005315013695508242, 0.009497090242803097, 0.043825551867485046, -0.03136790543794632, 0.023106321692466736, -0.06594346463680267, 0.024877993389964104, -0.03701860457658768, 0.012849278748035431, 0.030193006619811058, -0.02155844122171402, -0.004890745040029287, 0.051434412598609924, -0.0014954303624108434, 0.041662245988845825, -0.026090189814567566, -0.000618919322732836, -0.007520277984440327, -0.009781490080058575, -0.0007721922011114657, -0.010825843550264835, -0.04707050696015358, 0.000325486296787858, -0.0022915168665349483, -0.03256145119667053, 0.004331269767135382, 0.014723519794642925, -0.03246820718050003, -0.008196310140192509, 0.07355232536792755, 0.038603782653808594, -0.005674010142683983, -0.06023682281374931, 0.004184407647699118, -0.017166562378406525, 0.05326203256845474, -0.021334651857614517, -0.009650945663452148, 0.0036272637080401182, 0.010807194747030735, 0.0196748748421669, 0.02148384414613247, -0.01171167939901352, 0.034836649894714355, 0.03644048050045967, 0.049494899809360504, -0.0017483597621321678, -0.04315418004989624, -0.021316001191735268, -0.03834269568324089, 0.02043949067592621, 0.0028370050713419914, 0.019954612478613853, 0.02066328190267086, 0.030752481892704964, 0.008746461011469364, 0.036906708031892776, 0.029801374301314354, -0.025773154571652412, 0.008308205753564835, 0.008797746151685715, 0.021763581782579422, -0.008079753257334232, -0.059490855783224106, -0.05221767723560333, 0.03694400563836098, 0.03202062472701073, -0.032803889364004135, -0.028738372027873993, 0.04781647399067879, -0.0392005555331707, -0.04528018459677696, -0.021819530054926872, -0.020943019539117813, 0.028757020831108093, 0.0039116633124649525, 0.03041679784655571, -0.019171347841620445, -0.053336627781391144, 0.049010019749403, -0.056357793509960175, 0.0013835353311151266, -0.0034897259902209044, 0.000727317645214498, 0.009706893004477024, 0.033960141241550446, -0.008984237909317017, -0.011963442899286747, -0.006182200275361538, -0.0036808799486607313, -0.010462184436619282, -0.03429582342505455, -0.04624994471669197, 0.029223250225186348, -0.04125196486711502, -0.0027833888307213783, 0.02860782854259014, 0.02256549708545208, 0.01276535727083683, 0.0061728754080832005, -0.026966700330376625, 0.007776704151183367, 0.01861187256872654, -0.000055546846851939335, 0.001266977982595563, 0.011180177330970764, -0.034948546439409256, -0.009912034496665001, 0.0037554767914116383, -0.019115399569272995, -0.02942839078605175, 0.007385071367025375, -0.031162764877080917, 0.011487889103591442, 0.03761537745594978, -0.03412798047065735, -0.024766098707914352, 0.03998382017016411, 0.02653777040541172, 0.037634026259183884, 0.01670033298432827, -0.008518008515238762, 0.02349795587360859, -0.08093740046024323, 0.017381027340888977, 0.013007796369493008, 0.00589780043810606, 0.015534759499132633, 0.00463664997369051, 0.03595560044050217, -0.031964678317308426, -0.02851458266377449, 0.01575854979455471, 0.03313957527279854, -0.028141599148511887, 0.008718486875295639, -0.012019390240311623, 0.03299038112163544, 0.018975531682372093, 0.029764076694846153, -0.022043319419026375, 0.025866400450468063, 0.021129509434103966, -0.055425334721803665, 0.0017530220793560147, -0.026034241542220116, -0.07974385470151901, 0.0005612234817817807, -0.031050868332386017, -0.01415472012013197, -0.0030538015998899937, -0.02851458266377449, 0.011674380861222744, 0.05389610305428505, -0.04774187505245209, 0.021353300660848618, 0.024094728752970695, 0.024766098707914352, -0.06154226139187813, 0.04035680368542671, -0.02545611746609211, -0.04412393644452095, 0.0072545274160802364, 0.009343234822154045, 0.08265312761068344, -0.018033748492598534, 0.007972520776093006, 0.020215701311826706, 0.017119938507676125, 0.0020595677196979523, -0.05814811587333679, 0.014583650976419449, -0.001754187629558146, 0.015572057105600834, 0.017865905538201332, 0.034799352288246155, 0.02659371681511402, 0.03511638939380646, 0.016056936234235764, -0.014462431892752647, -0.011236125603318214, 0.013362131081521511, -0.03200197592377663, -0.012420347891747952, 0.008154349401593208, 0.0066810655407607555, 0.06348177790641785, -0.01653249002993107, -0.00783265195786953, 0.010415561497211456, -0.027768615633249283, -0.014052149839699268, 0.017017368227243423, -0.005161157809197903, -0.00638734083622694, 0.04636183753609657, -0.01431323867291212, 0.0015303975669667125, 0.027209140360355377, -0.013986878097057343, -0.015413539484143257, 0.04050599783658981, 0.0034710769541561604, -0.011096256785094738, -0.00835482869297266, -0.0196375772356987, 0.015478811226785183, -0.0006602971698157489, -0.03319552540779114, -0.0587448887526989, -0.01778198406100273, -0.029185952618718147, -0.032747942954301834, -0.015115153044462204, -0.012028714641928673, -0.037913765758275986, -0.04770457744598389, -0.002533955965191126, 0.007618186064064503, 0.02249090000987053, 0.03811890631914139, -0.04218442365527153, 0.006760324351489544, 0.039648137986660004, -0.0195070318877697, -0.019115399569272995, -0.03852918744087219, 0.037671323865652084, -0.02636992745101452, 0.007142632268369198, 0.008200972341001034, 0.03407203406095505, -0.009594998322427273, -0.040729787200689316, 0.0011206986382603645, 0.02942839078605175, -0.02152114361524582, 0.010984361171722412, -0.02068193070590496, -0.010695299133658409, -0.0013275878736749291, 0.025866400450468063, 0.02955893613398075, 0.054343681782484055, 0.020812474191188812, 0.05717835575342178, 0.027694018557667732, 0.03412798047065735, 0.0030281590297818184, 0.04501909762620926, 0.021912775933742523, -0.03244955837726593, 0.02838403731584549, -0.012019390240311623, -0.025661258026957512, -0.014070799574255943, 0.0098094642162323, 0.006564508192241192, 0.011329371482133865, -0.001405681250616908, -0.005361636634916067, 0.005902462638914585, -0.00928262434899807, -0.036832112818956375, -0.05303823947906494, 0.05229227617383003, 0.008508684113621712, 0.024877993389964104, 0.009650945663452148, 0.011413292028009892, 0.01321293693035841, -0.043713655322790146, 0.024691501632332802, -0.021894127130508423, 0.003478070255368948, -0.015460162423551083, 0.02236035466194153, 0.004970003850758076, -0.010014604777097702, 0.015889093279838562, 0.01867714524269104, -0.05378420650959015, -0.018192265182733536, -0.01128274854272604, 0.0017751678824424744, -0.040543295443058014, 0.018266862258315086, 0.02258414588868618, 0.008070428855717182, 0.03147979825735092, -0.006312744226306677, 0.029708128422498703, -0.0010734929237514734, -0.026798857375979424, -0.005972397048026323, 0.0244677122682333, 0.030659236013889313, -0.031200062483549118, 0.03252415359020233, -0.011450590565800667, 0.01866781897842884, 0.004014234058558941, 0.0007331455126404762, 0.03711184859275818, 0.04300498589873314, -0.033717699348926544, 0.006051655858755112, -0.007142632268369198, -0.01567462831735611, -0.04035680368542671, -0.017893878743052483, 0.032803889364004135, -0.013427402824163437, 0.03327012062072754, 0.032766591757535934, 0.03174088895320892, -0.005809216760098934, -0.033046331256628036, 0.02642587386071682, -0.004060856997966766, 0.025064485147595406, -0.006802285090088844, -0.04110277071595192, 0.019954612478613853, -0.02073787711560726, 0.050464656203985214, 0.03164764121174812, 0.01122680027037859, 0.013958903960883617, 0.04983058571815491, 0.006088954396545887, -0.027973756194114685, 0.01566530391573906, 0.008117051795125008, 0.01670965738594532, 0.012355075217783451, 0.01320361252874136, -0.017194535583257675, 0.057476744055747986, 0.01776333525776863, 0.017381027340888977, -0.008601929992437363, 0.00021752508473582566, -0.04013301432132721, 0.006392003037035465, -0.02269604057073593, -0.0001656570821069181, 0.02650047093629837, -0.018910259008407593, -0.011944794096052647, -0.002736765891313553, 0.04531748592853546, -0.01776333525776863, 0.06254931539297104, -0.034873947501182556, -0.0038300734013319016, -0.023964183405041695, -0.011254774406552315, -0.051471710205078125, -0.02739563211798668, -0.026183435693383217, -0.007534265052527189, -0.0033964801114052534, -0.019861366599798203, 0.005324338097125292, 0.017343727871775627, -0.004004909191280603, 0.012205881997942924, -0.01683087646961212, 0.005921111907809973, 0.008704500272870064, -0.0017856580670922995, 0.012634812854230404, -0.009422493167221546, 0.010611377656459808, -0.007515615783631802, -0.004217043519020081, -0.023162269964814186, 0.024952590465545654, 0.003370837541297078, -0.008960926905274391, 0.022789286449551582, -0.017269132658839226, 0.007730081211775541, 0.02351660467684269, 0.03263605013489723, -0.030715184286236763, 0.045690469443798065, -0.01655113883316517, 0.028757020831108093, -0.008089077658951283, -0.0057859052903950214, -0.05307554081082344, -0.0392005555331707, -0.017474273219704628, 0.029670830816030502, -0.006881543900817633, -0.024859344586730003, 0.05702916532754898, 0.015012582764029503, 0.0037857815623283386, 0.06795758008956909, -0.03463150933384895, 0.03739158809185028, 0.0011982092401012778, 0.009977306239306927, 0.005259065888822079, 0.010527457110583782, -0.032915785908699036, 0.01326888520270586, 0.001963990740478039, -0.03841729089617729, 0.035787757486104965, -0.015889093279838562, -0.0011137051042169333, -0.06400395184755325 ]
Machine learning (ML) enabled classification models are becoming increasingly popular for tackling the sheer volume and speed of online misinformation and other content that could be identified as harmful. In building these models, data scientists need to take a stance on the legitimacy, authoritativeness and objectivity of the sources of ``truth" used for model training and testing. This has political, ethical and epistemic implications which are rarely addressed in technical papers. Despite (and due to) their reported high accuracy and performance, ML-driven moderation systems have the potential to shape online public debate and create downstream negative impacts such as undue censorship and the reinforcing of false beliefs. Using collaborative ethnography and theoretical insights from social studies of science and expertise, we offer a critical analysis of the process of building ML models for (mis)information classification: we identify a series of algorithmic contingencies--key moments during model development that could lead to different future outcomes, uncertainty and harmful effects as these tools are deployed by social media platforms. We conclude by offering a tentative path toward reflexive and responsible development of ML tools for moderating misinformation and other harmful content online.
[ 0.010464911349117756, -0.02532043494284153, -0.033078424632549286, -0.04029688611626625, 0.03220402076840401, 0.007967285811901093, -0.0802961066365242, -0.0004898160113953054, 0.010743975639343262, 0.0474037230014801, 0.026287857443094254, -0.012697426602244377, 0.016827577725052834, -0.011395125649869442, -0.014836919493973255, -0.008571925573050976, 0.0016511305002495646, -0.000006040942935214844, 0.016195032745599747, -0.03523651883006096, -0.0322970412671566, -0.034250494092702866, -0.06533825397491455, 0.024483243003487587, -0.014455531723797321, 0.007520783226937056, -0.006004533730447292, -0.038324832916259766, -0.06742193549871445, 0.056222155690193176, 0.03940388187766075, 0.0040510836988687515, -0.002565066097304225, -0.04100384935736656, -0.04442703723907471, -0.013376482762396336, 0.026269253343343735, 0.03067846968770027, 0.009850970469415188, 0.04070618003606796, -0.013729964382946491, 0.018967071548104286, -0.014455531723797321, -0.018808934837579727, -0.021487951278686523, -0.05443614348769188, -0.039366673678159714, -0.0274785328656435, -0.006311504635959864, -0.0425294004380703, 0.03568302467465401, -0.027850618585944176, 0.0034371421206742525, -0.06805448234081268, -0.059273261576890945, 0.03633417189121246, 0.0017267104703933, -0.06522662937641144, 0.03551558405160904, -0.0102602643892169, 0.0027487834449857473, 0.05164550244808197, 0.0016732231015339494, 0.016492700204253197, -0.0122230164706707, -0.03854808211326599, -0.027125051245093346, 0.012771843001246452, 0.03620394319295883, 0.009999804198741913, -0.010818392969667912, -0.007381251081824303, 0.030492426827549934, 0.009195169433951378, 0.002425533952191472, 0.023906508460640907, 0.03026917576789856, 0.00545105617493391, 0.012474174611270428, -0.019385667517781258, 0.019274041056632996, 0.01831592060625553, 0.0007168464362621307, 0.016362471505999565, 0.08141236007213593, -0.005818490870296955, 0.013283461332321167, -0.0802961066365242, -0.0008034726488403976, -0.0006325457943603396, -0.03332027792930603, 0.018892653286457062, -0.001155791338533163, -0.020129838958382607, -0.023311171680688858, -0.017962438985705376, -0.0023173964582383633, -0.025841355323791504, -0.0479990616440773, -0.023515818640589714, -0.004692931659519672, 0.01673455722630024, 0.03825041651725769, 0.02256700024008751, -0.046064216643571854, -0.024632075801491737, -0.03612952679395676, 0.03038080222904682, 0.040520139038562775, 0.23486052453517914, 0.04033409431576729, 0.008269606158137321, -0.000997073482722044, 0.00014272976841311902, -0.01860428787767887, 0.007511481177061796, -0.03970155119895935, -0.07077071070671082, 0.029506400227546692, 0.021004240959882736, -0.04509679228067398, 0.04479912295937538, 0.04100384935736656, 0.023366985842585564, -0.045915380120277405, 0.04159918799996376, -0.03168310225009918, -0.028018057346343994, 0.031199390068650246, 0.03155286982655525, 0.02587856352329254, 0.018250806257128716, 0.006171972490847111, -0.02252979204058647, -0.012595102190971375, 0.004855718929320574, 0.06678938865661621, 0.045766547322273254, 0.03884575143456459, -0.03185053914785385, 0.015022962354123592, 0.05410126969218254, -0.052166420966386795, 0.003518535755574703, -0.030883116647601128, -0.024706494063138962, -0.003718531923368573, 0.05875233933329582, -0.04059455543756485, -0.02225072868168354, -0.02621344104409218, 0.07084512710571289, -0.03402724117040634, 0.0383620411157608, 0.10031431913375854, -0.04234335944056511, -0.005385941360145807, -0.017078736796975136, -0.013348576612770557, -0.013255555182695389, -0.00813937559723854, -0.052761759608983994, 0.038771335035562515, 0.044724706560373306, 0.04494795948266983, -0.002115075010806322, -0.0007546364213339984, -0.005330128129571676, -0.04744093120098114, 0.053617555648088455, -0.0015127611113712192, -0.027906430885195732, -0.04290148615837097, -0.02357163280248642, 0.020483320578932762, 0.026808777824044228, 0.026529714465141296, 0.013776474632322788, -0.0425294004380703, 0.013320669531822205, -0.06749635189771652, 0.019850775599479675, 0.0012616032036021352, -0.012762540951371193, 0.015106681734323502, 0.0715520903468132, 0.09078892320394516, 0.012567196041345596, 0.057970959693193436, 0.00893470924347639, -0.020632155239582062, -0.05138504132628441, 0.032948192209005356, -0.03663184121251106, 0.006334759760648012, -0.03750624507665634, -0.05945930257439613, -0.015674112364649773, 0.015153191983699799, -0.02587856352329254, -0.0012104414636269212, -0.05949651077389717, 0.02079959399998188, 0.02299490012228489, -0.03248308598995209, -0.053915224969387054, 0.03263191878795624, 0.02329256758093834, -0.027720388025045395, -0.025711124762892723, 0.010706767439842224, -0.008716108277440071, 0.027850618585944176, -0.01657642051577568, 0.003004592377692461, -0.012753238901495934, 0.034864433109760284, -0.0016069452976807952, -0.008599831722676754, 0.0007674268563278019, 0.02152516134083271, -0.02009263075888157, -0.008009145967662334, -0.0345853716135025, -0.02009263075888157, -0.023478610441088676, 0.03010173700749874, 0.0205205287784338, -0.008553321473300457, 0.01949729397892952, -0.006060346495360136, 0.03248308598995209, 0.007809149567037821, 0.007432412821799517, 0.0479990616440773, 0.03127380833029747, -0.0041185240261256695, -0.018715912476181984, -0.00545105617493391, -0.03754345327615738, -0.03166449815034866, -0.003730159718543291, -0.0392550453543663, -0.05004553496837616, 0.04963623732328415, -0.0497850738465786, 0.007669617421925068, -0.025115787982940674, -0.016808973625302315, 0.02956221252679825, -0.014790408313274384, 0.007795196492224932, 0.010864904150366783, -0.007483574561774731, -0.0006505686906166375, 0.020111234858632088, 0.03313423693180084, -0.0009866086766123772, -0.008995172567665577, -0.04744093120098114, 0.06500338017940521, -0.007544038351625204, 0.0000037517434066103306, 0.04178522899746895, -0.02502276748418808, -0.03333888202905655, 0.06373828649520874, -0.017395008355379105, 0.0070045143365859985, 0.02022286131978035, -0.024687889963388443, 0.000011954708497796673, -0.014697386883199215, 0.015320630744099617, -0.013999726623296738, -0.00625569187104702, 0.004467354621738195, 0.006120810750871897, -0.028036661446094513, 0.018892653286457062, 0.019571710377931595, 0.0552547350525856, 0.04003642499446869, 0.02954360842704773, 0.011320709250867367, -0.03082730434834957, -0.00658126687631011, -0.043720073997974396, -0.05588727816939354, -0.006818471476435661, -0.023032108321785927, 0.0022080964408814907, -0.07843567430973053, 0.02195305936038494, 0.025934375822544098, -0.013795078732073307, 0.0082975123077631, 0.032501690089702606, 0.01643688790500164, -0.0028720367699861526, -0.025432061403989792, -0.00829286128282547, 0.0143346032127738, 0.04364565759897232, -0.008576576597988605, 0.07017537206411362, 0.05313384532928467, 0.031069159507751465, -0.03521791473031044, -0.049412988126277924, 0.024911141023039818, 0.024985557422041893, -0.03813878819346428, 0.013376482762396336, 0.0016255496302619576, 0.05864071473479271, 0.009581208229064941, 0.0058789546601474285, 0.01317183580249548, -0.021785620599985123, 0.011823024600744247, -0.03214820846915245, -0.08557972311973572, 0.028911063447594643, -0.05931046977639198, 0.0007121953531168401, -0.023925114423036575, 0.010204452089965343, -0.042268939316272736, -0.020687967538833618, -0.0835704579949379, 0.0030371500179171562, -0.013525317423045635, 0.012148600071668625, -0.0035278380382806063, -0.07490085810422897, 0.01992519199848175, 0.056817494332790375, 0.012799750082194805, -0.024780910462141037, -0.04305032268166542, -0.03372957184910774, -0.06038951873779297, 0.0012116042198613286, 0.012157902121543884, -0.02284606546163559, 0.005474311765283346, 0.035441167652606964, 0.009264934808015823, -0.00487432349473238, 0.0010552118765190244, 0.0028069219551980495, -0.009227726608514786, 0.019720545038580894, 0.03114357776939869, -0.0073998551815748215, -0.046659551560878754, -0.0012336968211457133, 0.024241385981440544, 0.029283149167895317, 0.03668765351176262, -0.08461230248212814, -0.002288327319547534, -0.027143655344843864, -0.053022220730781555, -0.03263191878795624, -0.042678236961364746, 0.0286692064255476, 0.04189685359597206, -0.01616712659597397, 0.004699908196926117, -0.00586035056039691, 0.0033859803806990385, 0.01820429600775242, -0.0008139375713653862, 0.009850970469415188, 0.0027720388025045395, -0.010771882720291615, -0.031069159507751465, 0.05257571488618851, -0.041971273720264435, 0.00014142165309749544, 0.03410165756940842, 0.009711437858641148, -0.04535725340247154, 0.007999843917787075, 0.007967285811901093, 0.005678958725184202, -0.01802755519747734, 0.01688339002430439, -0.007292880676686764, 0.03505047783255577, 0.03205518797039986, -0.05413847789168358, 0.0038231811486184597, 0.022511187940835953, 0.0038301576860249043, -0.007325438316911459, 0.017125247046351433, -0.02007402665913105, 0.015655508264899254, -0.0285203717648983, 0.032817963510751724, -0.0020022864919155836, -0.002899943385273218, -0.008688202127814293, 0.037617869675159454, -0.017060130834579468, 0.011878837831318378, -0.02124609611928463, 0.007302182726562023, 0.03054823912680149, 0.05324546992778778, 0.030511030927300453, -0.0031022648327052593, 0.02792503498494625, -0.016641534864902496, 0.007781243417412043, -0.008241699077188969, -0.025655312463641167, 0.04654792696237564, -0.007790545467287302, 0.07073350250720978, -0.011190478689968586, 0.014799710363149643, 0.04930136352777481, -0.014502041973173618, -0.02617623284459114, -0.005590588320046663, -0.015274119563400745, 0.021915851160883904, 0.00757194496691227, -0.0245948676019907, -0.031162181869149208, 0.0053115240298211575, -0.017553145065903664, 0.02865060232579708, 0.028445955365896225, -0.032948192209005356, 0.027608763426542282, 0.03172031044960022, 0.019739149138331413, -0.00345807196572423, 0.03624115139245987, -0.05633378401398659, -0.013488108292222023, -0.032948192209005356, -0.0285203717648983, -0.06020347401499748, -0.01786941848695278, -0.04174802079796791, 0.07798917591571808, -0.0841657966375351, -0.03973875939846039, 0.03858529403805733, -0.02035309001803398, 0.035590000450611115, -0.055664028972387314, 0.04985949024558067, -0.05060366168618202, -0.013041605241596699, 0.07992401719093323, 0.015357838943600655, 0.001515086623840034, -0.004609212279319763, -0.013116022571921349, -0.08818431943655014, -0.007269625551998615, 0.011925348080694675, -0.01519040111452341, -0.0007732406957075, -0.01921822875738144, -0.051459457725286484, -0.05298501253128052, 0.022790251299738884, 0.009306794963777065, 0.008697504177689552, -0.010539328679442406, 0.03780391067266464, -0.03767368197441101, 0.03406444936990738, 0.05443614348769188, -0.022306540980935097, 0.03596208617091179, -0.02850176766514778, 0.021729808300733566, 0.007748685777187347, 0.00015799110406078398, -0.00959981232881546, -0.09056567400693893, -0.04275265336036682, -0.003734810743480921, 0.030194759368896484, -0.00974864698946476, 0.010632350109517574, 0.014148560352623463, 0.00440456485375762, -0.007325438316911459, 0.04587817192077637, -0.0203716941177845, 0.021320512518286705, 0.007511481177061796, -0.004818510264158249, 0.039366673678159714, 0.01772988587617874, -0.024092553183436394, 0.03817599639296532, -0.026083210483193398, -0.014529948122799397, 0.03720857575535774, -0.018808934837579727, 0.036445800215005875, 0.025227414444088936, -0.02254839614033699, 0.014148560352623463, 0.04394332692027092, 0.03142264112830162, -0.01762756146490574, 0.06987770646810532, 0.016083406284451485, 0.023050712421536446, -0.027292490005493164, -0.005734771490097046, 0.03549697995185852, -0.060017433017492294, 0.03333888202905655, 0.029804067686200142, -0.012650915421545506, 0.00008829768921714276, -0.061170898377895355, -0.025376247242093086, 0.03320865333080292, -0.033487718552351, -0.0032208673655986786, 0.026659943163394928, -0.033673759549856186, 0.02954360842704773, 0.01497645117342472, -0.027311094105243683, -0.030808700248599052, -0.010130034759640694, 0.041115473955869675, 0.02199026755988598, 0.0017220593290403485, 0.0002562449953984469, 0.039664339274168015, 0.013767172582447529, -0.007432412821799517, -0.0006488244980573654, -0.019739149138331413, -0.035273730754852295, -0.029506400227546692, 0.022287936881184578, -0.029338961467146873, -0.04874323308467865, 0.01759965531527996, 0.018957769498229027, 0.01846475526690483, -0.02606460638344288, 0.00807426031678915, 0.014753200113773346, -0.02020425535738468, -0.018390338867902756, 0.00009730914462124929, -0.01847405731678009, -0.021785620599985123, -0.010464911349117756, 0.08141236007213593, -0.032948192209005356, -0.0019162415992468596, 0.0037743449211120605, -0.04535725340247154, -0.0331900492310524, -0.01990658789873123, -0.010864904150366783, 0.011023039929568768, 0.028427351266145706, -0.037878330796957016, -0.011897441931068897, -0.011153270490467548, -0.006325457710772753, 0.01891125738620758, 0.028297120705246925, 0.03495745733380318, -0.012502080760896206, 0.007827754132449627, 0.0034534209407866, -0.024948349222540855, 0.006651032716035843, 0.007981238886713982, 0.01244626846164465, 0.03880854323506355, -0.07039862126111984, -0.009646323509514332, -0.05209200456738472, -0.0011749770492315292, 0.014743898063898087, -0.006413828115910292, 0.022473979741334915, -0.028297120705246925, 0.04100384935736656, 0.028725020587444305, 0.05235246568918228, 0.012604405172169209, -0.015236911363899708, -0.008846338838338852, -0.02182282879948616, -0.007720779161900282, 0.0068975393660366535, 0.018139179795980453, -0.012743936851620674, -0.02267862670123577, 0.0401480533182621, -0.0011778839398175478, -0.018529869616031647, -0.024669285863637924, 0.02965523488819599, -0.003958062268793583, 0.0032417969778180122, 0.008576576597988605, 0.018836840987205505, 0.02329256758093834, 0.02487393282353878, 0.04375728592276573, -0.01934845931828022, 0.03988759219646454, -0.0055208224803209305, -0.020706571638584137, 0.011041644960641861, 0.02022286131978035, -0.06690102070569992, -0.0054650092497467995, -0.012027671560645103, -0.017971741035580635, -0.004278986249119043, -0.02649250626564026, 0.01806476339697838, 0.060910437256097794, -0.012688123621046543, -0.049412988126277924, -0.008450997993350029, 0.027534345164895058, -0.017413612455129623, 0.051719918847084045, 0.001783686107955873, 0.03929225355386734, -0.004995251074433327, -0.02020425535738468, 0.041673604398965836, 0.012976490892469883, -0.0020197280682623386, 0.03157147765159607, 0.003706904361024499, 0.047924645245075226, -0.024501847103238106, -0.032222624868154526, -0.02329256758093834, 0.010474213398993015, 0.02184143289923668, 0.0037371362559497356, 0.010297473520040512, 0.011441636830568314, 0.025246018543839455, -0.00909284595400095, 0.02210189402103424, -0.001198813784867525, -0.015106681734323502, 0.03999921679496765, 0.01010212767869234, 0.07739383727312088, 0.04278986155986786, 0.00945562869310379, -0.0363713838160038, 0.020036818459630013, 0.0015127611113712192, -0.046064216643571854, -0.01834382675588131, 0.02796224318444729, -0.009325399063527584, -0.003983642905950546, -0.009427722543478012, -0.02621344104409218, 0.009390514343976974, 0.002792968647554517, -0.04930136352777481, -0.005102226044982672, -0.011674189940094948, 0.04189685359597206, -0.004581305664032698, -0.0291157104074955, -0.03142264112830162, -0.041413143277168274, -0.020762383937835693, -0.0019011256517842412, 0.03480862081050873, -0.030920324847102165, -0.026436692103743553, -0.023739071562886238, 0.0037371362559497356, 0.0034255143254995346, 0.012929979711771011, -0.01586945727467537, -0.0193298552185297, 0.030045924708247185, -0.036017902195453644, 0.049971114844083786, 0.022083289921283722, -0.01921822875738144, -0.01905078999698162, -0.009646323509514332, -0.01714385114610195, 0.024501847103238106, 0.029859881848096848, 0.058715131133794785, 0.04974786564707756, 0.0319993756711483, 0.027683179825544357, 0.018883351236581802, 0.05849187821149826, 0.037152763456106186, 0.00952539499849081, 0.005818490870296955, -0.001575550646521151, -0.04844556376338005, -0.05596169829368591, 0.02111586555838585, 0.01846475526690483, 0.016846181824803352, 0.010660256259143353, -0.0010604443959891796, 0.041971273720264435, -0.000985445803962648, -0.0012883469462394714, 0.00305342860519886, -0.0028859900776296854, -0.02226933278143406, 0.014111352153122425, 0.015488069504499435, 0.010316077619791031, 0.0003520280006341636, 0.019106602296233177, -0.02952500432729721, 0.021487951278686523, -0.0392550453543663, -0.008655644953250885, 0.01631595939397812, -0.012120692990720272, 0.02634367160499096, -0.016911298036575317, 0.047068845480680466, 0.015915967524051666, -0.04572933912277222, 0.07702174782752991, -0.042678236961364746, -0.025711124762892723, -0.021171679720282555, 0.0065394071862101555, 0.0073114847764372826, 0.012697426602244377, 0.007939379662275314, -0.0337853878736496, 0.05339430645108223, 0.04178522899746895, -0.007576595991849899, 0.03825041651725769, 0.002955756150186062, -0.051012955605983734, 0.015162494033575058, 0.014715990982949734, -0.01106024906039238, 0.002427859464660287, 0.015078774653375149, 0.03627835959196091, -0.04398053511977196, -0.01010212767869234, -0.03724578395485878, 0.050864122807979584, -0.0292645450681448, -0.012390455231070518, 0.003079009475186467, -0.027032028883695602, 0.021432138979434967, -0.06481733918190002, 0.027125051245093346, -0.04011084511876106, 0.029190126806497574, 0.009804459288716316, -0.02602739818394184, -0.007585898041725159, 0.04305032268166542, -0.04494795948266983, -0.026957612484693527, -0.01615782454609871, -0.0004825486976187676, 0.01302300114184618, -0.004346426576375961, -0.01628805324435234, 0.02634367160499096, 0.009655625559389591, -0.02558089606463909, 0.04959902912378311, -0.03240866959095001, 0.034566767513751984, -0.014139258302748203, -0.0416363961994648, -0.044575873762369156, -0.042715445160865784, -0.008544019423425198, 0.028334328904747963, 0.012985792942345142, 0.05975697189569473, 0.07932867854833603, 0.011116061359643936, -0.006474291905760765, -0.014771804213523865, -0.018855445086956024, -0.024799514561891556, 0.022585604339838028, 0.00341853778809309, 0.036296963691711426, 0.021599577739834785, -0.06414758414030075, 0.009381212294101715, -0.021860036998987198, -0.03583185747265816, 0.007655664347112179, 0.02241816557943821, -0.0019127533305436373, 0.03722717985510826, -0.02679017372429371, 0.008585878647863865, 0.04349682480096817, 0.01099513377994299, 0.020855406299233437, -0.03155286982655525, 0.04364565759897232, 0.011116061359643936, -0.01368345320224762, 0.002020890824496746, 0.013004397042095661, -0.048929277807474136, -0.011832326650619507, 0.03609231859445572, -0.04115268215537071, 0.02517160028219223, 0.009981200098991394, 0.016529910266399384, -0.003795274533331394, 0.05030599236488342, -0.015506673604249954, 0.01732059195637703, 0.05131062492728233, 0.01730198785662651, 0.05428731068968773, -0.015441558323800564, -0.03981317579746246, 0.034994665533304214, 0.05004553496837616, 0.019106602296233177, 0.04785022884607315, -0.011450938880443573, -0.029208730906248093, -0.012585800141096115, -0.01819499395787716, 0.021450743079185486, -0.03393422067165375, 0.024836724624037743, -0.06704985350370407, -0.0013150905724614859, -0.035850461572408676, 0.006864982191473246, 0.010288170538842678, -0.003167379880324006, 0.06924515962600708, 0.010678861290216446, 0.004285962786525488, 0.016083406284451485, -0.008827734738588333, 0.046027008444070816, 0.01850196346640587, 0.03449234738945961, 0.05878954753279686, 0.023460006341338158, -0.022883273661136627, 0.006813820451498032, -0.04029688611626625, -0.027013424783945084, 0.012334642931818962, 0.0061254617758095264, -0.025971585884690285, -0.007018467411398888, 0.023366985842585564, 0.00243716174736619, -0.03880854323506355, 0.01646479405462742, 0.03769228607416153, -0.02995290234684944, 0.002205770928412676, -0.0416363961994648, -0.012929979711771011, -0.004762697499245405, -0.021618181839585304, -0.0191810205578804, 0.02719946764409542, 0.022473979741334915, -0.009627718478441238, -0.0013162533286958933, -0.009344003163278103, 0.04878044128417969, -0.018669402226805687, -0.006999863311648369, -0.0654870942234993, -0.01994379609823227, -0.019106602296233177, 0.035143498331308365, -0.009111450053751469, 0.004418518394231796, -0.018408942967653275, 0.04334798827767372, 0.018427547067403793, -0.03350632265210152, -0.010678861290216446, -0.005395243410021067, 0.023627445101737976, -0.029022688046097755, 0.0193298552185297, 0.028166892006993294, 0.02693900838494301, -0.03010173700749874, -0.025934375822544098, -0.028334328904747963, -0.001244161743670702, 0.029320357367396355, 0.031645894050598145, 0.05443614348769188, -0.005902210250496864, 0.00374876381829381, 0.04803626984357834, -0.00033051680657081306, -0.04025967791676521, -0.0017650817753747106, 0.05052924528717995, 0.03041801042854786, -0.007292880676686764, -0.020018212497234344, -0.023106524720788002, 0.01587875932455063, 0.017850814387202263, -0.037301596254110336, 0.01163698174059391, -0.034994665533304214, -0.0004247009928803891, 0.05108737200498581, 0.04904090240597725, -0.024557659402489662, 0.02954360842704773, -0.00684172660112381, 0.011116061359643936, -0.02606460638344288, 0.03739461675286293, -0.018985675647854805, -0.019683336839079857, 0.007911473512649536, -0.016613628715276718, -0.02009263075888157, 0.007767289876937866, -0.02254839614033699, -0.03988759219646454, -0.05015715956687927, 0.022660022601485252, 0.012790448032319546, 0.047924645245075226, -0.00893936026841402, 0.007627757731825113, 0.006609173025935888, 0.005441754125058651, -0.006944050081074238, -0.03248308598995209, 0.02022286131978035, 0.025841355323791504, 0.010492818430066109, -0.05075249448418617, -0.022808857262134552, -0.01919962465763092, 0.00643708324059844, -0.020315881818532944, 0.011143968440592289, 0.0038487620186060667, -0.0005648145452141762, 0.034976061433553696, 0.009888178668916225, 0.00717195263132453, 0.01113466639071703, -0.015627602115273476, -0.053617555648088455, -0.01287416648119688, 0.003862715093418956, 0.01010212767869234, -0.013432295992970467, 0.04539446160197258, -0.021301908418536186, 0.022641418501734734, -0.010595141910016537, 0.027906430885195732, -0.014185769483447075, 0.022027475759387016, 0.013441598042845726, -0.017488030716776848, -0.018390338867902756, 0.01786941848695278, 0.014957847073674202, 0.011534658260643482, 0.014855523593723774, 0.040668971836566925, 0.004390611778944731, -0.0165950246155262, -0.031776122748851776, -0.028278516605496407, 0.0012778820237144828, -0.06623126566410065, 0.00024272780865430832, -0.021580973640084267, -0.004744093399494886, -0.055626820772886276 ]
In complex environments, where the human sensory system reaches its limits, our behaviour is strongly driven by our beliefs about the state of the world around us. Accessing others' beliefs, intentions, or mental states in general, could thus allow for more effective social interactions in natural contexts. Yet these variables are not directly observable. Theory of Mind (TOM), the ability to attribute to other agents' beliefs, intentions, or mental states in general, is a crucial feature of human social interaction and has become of interest to the robotics community. Recently, new models that are able to learn TOM have been introduced. In this paper, we show the synergy between learning to predict low-level mental states, such as intentions and goals, and attributing high-level ones, such as beliefs. Assuming that learning of beliefs can take place by observing own decision and beliefs estimation processes in partially observable environments and using a simple feed-forward deep learning model, we show that when learning to predict others' intentions and actions, faster and more accurate predictions can be acquired if beliefs attribution is learnt simultaneously with action and intentions prediction. We show that the learning performance improves even when observing agents with a different decision process and is higher when observing beliefs-driven chunks of behaviour. We propose that our architectural approach can be relevant for the design of future adaptive social robots that should be able to autonomously understand and assist human partners in novel natural environments and tasks.
[ -0.0015212211292237043, 0.0021595906000584364, -0.02165929041802883, -0.044151630252599716, 0.04791846498847008, 0.05099712684750557, -0.016307853162288666, -0.014044131152331829, -0.037016380578279495, 0.06617312133312225, 0.009942266158759594, 0.008022630587220192, 0.005242779850959778, -0.014641753397881985, -0.018870385363698006, 0.0395517498254776, 0.029555153101682663, -0.004953023511916399, -0.02884887158870697, -0.06102994084358215, 0.02178606018424034, 0.0049439687281847, -0.059617381542921066, -0.003017541253939271, 0.04324614256620407, 0.01802828162908554, 0.019431788474321365, -0.029011860489845276, -0.09467790275812149, 0.027997711673378944, 0.011563091538846493, 0.014976783655583858, 0.014351996593177319, -0.033883389085531235, -0.030370093882083893, -0.0408194325864315, 0.019558556377887726, -0.006777583155781031, -0.006080356892198324, 0.04907749220728874, 0.013274465687572956, 0.03730613738298416, -0.04860663786530495, -0.09967619925737381, -0.0010707405162975192, -0.036328207701444626, -0.02727332152426243, -0.019504228606820107, -0.08178374171257019, -0.024756062775850296, 0.05581432580947876, -0.083377406001091, 0.06305823475122452, 0.04969322308897972, -0.067875437438488, 0.04324614256620407, 0.02490094117820263, -0.053351398557424545, 0.0412902869284153, 0.022383682429790497, 0.020319167524576187, 0.043137483298778534, -0.05183017626404762, -0.028251249343156815, 0.00797282811254263, -0.05827725678682327, 0.02464740350842476, -0.010213913396000862, -0.006505936849862337, -0.03922577202320099, -0.016172029078006744, 0.024248989298939705, 0.001886812155134976, -0.07240287959575653, 0.002596488920971751, 0.021170327439904213, 0.08011764287948608, 0.042775288224220276, 0.016253523528575897, -0.032959792762994766, 0.020101850852370262, 0.040457237511873245, 0.01807355508208275, -0.021369535475969315, 0.06505031138658524, -0.014931509271264076, 0.057733964174985886, -0.05443798378109932, 0.026204844936728477, -0.03317710757255554, -0.034209366887807846, 0.024629294872283936, 0.023488378152251244, 0.04465870559215546, 0.024013562127947807, -0.011608365923166275, 0.005496316589415073, 0.003816635115072131, -0.04085565358400345, 0.023307280614972115, -0.002168645616620779, 0.010494614951312542, -0.016316907480359077, 0.02790716290473938, -0.002535368548706174, -0.008230892941355705, -0.045201998203992844, -0.004826255142688751, 0.013935471884906292, 0.14328454434871674, -0.02446630597114563, 0.00046208224375732243, -0.02453874610364437, -0.010250132530927658, 0.008516121655702591, 0.04773736745119095, -0.04378943517804146, -0.03397393971681595, 0.040710773319005966, -0.06936044245958328, 0.004486696794629097, 0.06653531640768051, 0.03879113867878914, -0.06037798896431923, -0.03352119401097298, 0.014976783655583858, -0.03352119401097298, 0.00469495914876461, 0.015212210826575756, -0.011608365923166275, 0.010050925426185131, 0.03279680386185646, -0.04378943517804146, 0.017575537785887718, -0.011843793094158173, -0.016932640224695206, 0.06729592382907867, 0.033140890300273895, 0.02721899189054966, 0.008529704064130783, -0.038827359676361084, -0.020953010767698288, -0.03605656325817108, 0.05624896287918091, 0.031438570469617844, 0.011680805124342442, 0.003024332458153367, 0.05298920348286629, -0.04882395267486572, -0.007325403857976198, -0.02051837556064129, 0.035893574357032776, -0.0361471101641655, 0.02921106666326523, 0.049403466284275055, -0.01708657294511795, -0.004129028879106045, -0.0007617424125783145, -0.020826241001486778, 0.004744761157780886, 0.049222368746995926, -0.007225800305604935, 0.00588114932179451, 0.02202148735523224, 0.0365455262362957, 0.016153918579220772, -0.016162974759936333, -0.005890204571187496, -0.034571561962366104, 0.0391533337533474, -0.08127667009830475, 0.0021256348118185997, -0.030388202518224716, 0.06711483001708984, -0.029808690771460533, 0.05726310983300209, 0.03904467448592186, -0.0032846604008227587, -0.0541844479739666, -0.025190697982907295, -0.006922461558133364, -0.02347026951611042, -0.0050435722805559635, -0.0294646043330431, 0.04994675889611244, 0.030985824763774872, 0.07370678335428238, -0.004149402026087046, 0.05657493695616722, -0.04016748070716858, -0.015067333355545998, 0.025389904156327248, 0.06363774836063385, 0.02026483789086342, 0.0003429538628552109, -0.0717509314417839, -0.021623071283102036, 0.02140575461089611, -0.03723369911313057, 0.023144293576478958, 0.026259174570441246, -0.0648692175745964, -0.008375771343708038, 0.007701181806623936, 0.015529132448136806, -0.02854100614786148, 0.028486676514148712, -0.009471412748098373, 0.030315764248371124, -0.0524459108710289, 0.059979576617479324, -0.026241064071655273, -0.01577361486852169, -0.005451042205095291, -0.03900845721364021, 0.0026734555140137672, -0.00696320878341794, -0.022039595991373062, 0.009924156591296196, 0.006293146871030331, 0.003157892031595111, 0.058856770396232605, -0.0039298213087022305, 0.0010509329149499536, 0.07895862311124802, 0.014641753397881985, -0.0062524001114070415, -0.016153918579220772, 0.02015618048608303, -0.05342383682727814, 0.0028432346880435944, 0.05795127898454666, 0.06562982499599457, -0.058675672858953476, 0.015583461150527, 0.006605540402233601, 0.06168189272284508, -0.0268567968159914, 0.0031692106276750565, 0.0011793990852311254, -0.014668918214738369, -0.037197478115558624, -0.0070220655761659145, 0.00741595309227705, 0.07968301326036453, 0.04799090325832367, -0.03009844571352005, 0.014016966335475445, 0.03609278053045273, 0.05476396158337593, -0.003764569526538253, 0.004939441103488207, 0.002711938926950097, -0.004584036767482758, 0.0087017472833395, 0.038211625069379807, 0.025045819580554962, 0.02247423119843006, 0.014370107091963291, -0.03886357694864273, 0.017557427287101746, 0.044332731515169144, 0.038827359676361084, 0.049149930477142334, -0.004332763608545065, -0.00810412410646677, 0.07290995866060257, 0.009462357498705387, 0.0434272401034832, 0.01714995689690113, 0.006904351990669966, -0.005781545769423246, -0.06392750889062881, -0.0019649106543511152, -0.006569320801645517, -0.013582331128418446, 0.016660993918776512, -0.02202148735523224, 0.03621955215930939, 0.037704553455114365, 0.07678544521331787, 0.00960723590105772, 0.02971814200282097, 0.012676842510700226, 0.0023225785698741674, 0.017602700740098953, -0.02146008424460888, -0.011119402013719082, -0.06526762992143631, -0.030750397592782974, -0.010974523611366749, 0.05201127380132675, -0.0529167614877224, 0.0027028839103877544, 0.05443798378109932, 0.014433491043746471, -0.036835283041000366, -0.017946787178516388, 0.051793958991765976, -0.02039160765707493, 0.02647649124264717, -0.0294646043330431, 0.03991394490003586, 0.0037215587217360735, 0.015022058971226215, 0.03065984882414341, 0.043209925293922424, 0.05820481851696968, -0.009186183102428913, -0.06171811372041702, 0.01495867408812046, 0.009752114303410053, 0.00879682321101427, -0.013518947176635265, -0.05106956511735916, 0.03659985587000847, 0.015501967631280422, -0.04281150922179222, -0.039261993020772934, -0.018308982253074646, -0.06483299285173416, -0.016036206856369972, -0.07044702768325806, 0.007837004959583282, -0.021749839186668396, 0.038827359676361084, 0.07519178837537766, 0.0018788891611620784, -0.0350424163043499, -0.015719285234808922, -0.050960905849933624, 0.030370093882083893, 0.01901526376605034, -0.004162984434515238, -0.009249567985534668, -0.030243324115872383, 0.03065984882414341, 0.02372380532324314, -0.02921106666326523, -0.04636102542281151, -0.01288510486483574, -0.030370093882083893, 0.007406897842884064, -0.02127898670732975, -0.01288510486483574, -0.04998297989368439, 0.00932653434574604, 0.05574188753962517, 0.00327107822522521, 0.021351424977183342, 0.0011029985034838319, -0.035151075571775436, -0.02097111940383911, 0.00247198436409235, 0.020826241001486778, -0.0240860003978014, 0.002761740703135729, 0.032253511250019073, -0.027925273403525352, 0.018942825496196747, 0.020572705194354057, -0.06055909022688866, -0.0003259759396314621, 0.03937065228819847, -0.07167848944664001, -0.03493375703692436, -0.013654770329594612, 0.006872659549117088, -0.021876608952879906, -0.010992633178830147, -0.003490659175440669, 0.013872087933123112, 0.027544967830181122, -0.03596601262688637, -0.02835990861058235, 0.0025149949360638857, 0.0004875491140410304, 0.02721899189054966, -0.003599317744374275, 0.04617992788553238, -0.015800779685378075, -0.04263041168451309, -0.016996024176478386, 0.07088165730237961, -0.04541931673884392, 0.03861004114151001, 0.012839830480515957, -0.027056004852056503, 0.022872645407915115, 0.0666801929473877, 0.02864966355264187, -0.03498808667063713, -0.022311242297291756, -0.0034476483706384897, 0.045709073543548584, 0.01852630078792572, 0.03600223362445831, -0.0031760018318891525, -0.0003655910841189325, -0.0020679100416600704, -0.017992062494158745, 0.0008155058021657169, 0.048715297132730484, -0.04266662895679474, 0.025082038715481758, -0.025389904156327248, 0.005405767820775509, -0.0245206356048584, -0.012930379249155521, 0.028993749991059303, 0.01445160061120987, 0.0012586293742060661, -0.008683636784553528, -0.03674473240971565, -0.005446515046060085, -0.030333872884511948, -0.027816614136099815, 0.03268814459443092, 0.0044029392302036285, -0.004416521638631821, -0.01288510486483574, 0.02120654657483101, 0.013654770329594612, -0.02935594506561756, -0.02071758359670639, 0.029863018542528152, -0.025389904156327248, -0.012966599315404892, -0.04809956252574921, -0.022202584892511368, 0.03152911737561226, -0.027671735733747482, 0.02064514346420765, -0.020427826792001724, 0.03734235838055611, -0.010195803828537464, 0.009281259961426258, 0.04791846498847008, -0.05385847017168999, -0.019540447741746902, 0.004830782767385244, -0.020246729254722595, -0.020554594695568085, 0.026512710377573967, 0.01061232853680849, -0.06081262603402138, 0.018001116812229156, -0.06907068192958832, -0.012522909790277481, 0.014089405536651611, -0.09982108324766159, 0.04531065747141838, -0.011019797995686531, -0.014822850935161114, 0.01596376672387123, 0.0011329927947372198, 0.03674473240971565, -0.03174643591046333, -0.005405767820775509, -0.050164077430963516, -0.012314647436141968, 0.045709073543548584, 0.0034159563947468996, 0.016434621065855026, 0.0378132089972496, -0.013138641603291035, -0.07113520056009293, -0.015130717307329178, -0.014641753397881985, 0.020065631717443466, 0.008597616106271744, -0.013174861669540405, -0.015284650027751923, -0.011988671496510506, 0.02953704260289669, 0.04147138446569443, 0.015547242015600204, -0.01682398095726967, -0.0018019226845353842, 0.012903214432299137, 0.03766833245754242, 0.020355386659502983, 0.0524459108710289, -0.06371019035577774, -0.01870739832520485, 0.03806674852967262, 0.003624218748882413, 0.02522691711783409, -0.0004739667638204992, -0.051975056529045105, -0.013020928017795086, -0.07185959070920944, 0.0264583807438612, 0.019793983548879623, -0.020445935428142548, 0.0094533022493124, -0.004461796022951603, -0.04034857824444771, 0.05624896287918091, 0.025860758498311043, -0.0004360494203865528, -0.021315205842256546, -0.011318609118461609, 0.016679102554917336, -0.0019309547496959567, 0.004389356821775436, 0.005437459796667099, -0.01959477737545967, -0.0024380285758525133, 0.01689642108976841, 0.005496316589415073, 0.0219128280878067, 0.05230103060603142, 0.00003063098847633228, 0.01888849586248398, -0.0023678531870245934, 0.0014159580459818244, 0.022256914526224136, 0.05226480960845947, -0.006659870035946369, 0.022419901564717293, -0.002535368548706174, -0.016751542687416077, 0.033394426107406616, -0.057407986372709274, 0.07584373652935028, 0.010385955683887005, -0.006709671579301357, 0.002979058073833585, -0.032905463129282, -0.025607222691178322, 0.017041297629475594, -0.07066434621810913, -0.03484320640563965, 0.00008453586633550003, -0.007855115458369255, 0.06863604485988617, 0.0094533022493124, 0.027146553620696068, -0.05364115536212921, 0.0018132412806153297, -0.01163553074002266, -0.004708541557192802, 0.0007945664110593498, -0.029681921005249023, -0.0061301589012146, 0.08801350742578506, -0.005383130628615618, 0.002381435362622142, 0.006039610132575035, 0.0012959807645529509, 0.005342383868992329, -0.019540447741746902, 0.008439155295491219, -0.015266540460288525, -0.0136457160115242, -0.0264583807438612, 0.00950763188302517, -0.022945085540413857, 0.0022727767936885357, 0.02803393267095089, -0.04679565876722336, -0.06570226699113846, -0.016298796981573105, -0.0019275591475889087, -0.0036423285491764545, -0.01013241894543171, 0.0013740791473537683, 0.05273566395044327, 0.03991394490003586, -0.020554594695568085, -0.010648547671735287, -0.007044702768325806, -0.0005514992517419159, 0.043644558638334274, 0.02915673889219761, 0.031239362433552742, -0.02051837556064129, -0.00810412410646677, -0.01620824821293354, -0.00407017208635807, -0.01207922026515007, 0.01665193773806095, 0.014279557392001152, -0.0046994867734611034, -0.04339102283120155, -0.03944309055805206, -0.03748723492026329, 0.02039160765707493, -0.01614486426115036, -0.005192977841943502, 0.04411541298031807, -0.000028579488571267575, 0.011807573027908802, 0.01145443320274353, -0.0382840633392334, 0.005011880304664373, 0.014877180568873882, 0.04049345850944519, -0.023289170116186142, -0.0460350476205349, -0.0029337836895138025, 0.03824784606695175, 0.05737176910042763, -0.0008868130389600992, 0.021858498454093933, 0.03498808667063713, 0.015085442923009396, 0.007153361104428768, 0.006157323718070984, -0.0018336147768422961, 0.008674582466483116, 0.010123364627361298, -0.007841533049941063, 0.01870739832520485, -0.024810392409563065, 0.02341593988239765, 0.00044595322106033564, -0.005138648673892021, -0.023361610248684883, 0.004520652815699577, -0.005292581859976053, 0.049729444086551666, 0.020862460136413574, -0.03350308537483215, 0.003350308397784829, 0.02615051530301571, 0.0007724951137788594, -0.0146145885810256, 0.018743617460131645, -0.03565814718604088, 0.029899239540100098, 0.015465748496353626, -0.002870399272069335, 0.02303563430905342, -0.0006757209775969386, 0.024267097935080528, 0.04154382273554802, 0.06671641021966934, -0.029247287660837173, 0.008728912100195885, 0.0073525686748325825, -0.048027124255895615, 0.03629199042916298, -0.009462357498705387, 0.06725970655679703, -0.03109448403120041, -0.05483639985322952, 0.053967129439115524, 0.00016737393161747605, -0.02046404592692852, 0.007148833945393562, -0.025860758498311043, 0.031185032799839973, 0.027128443121910095, -0.014026020653545856, 0.01555629726499319, 0.006926989182829857, 0.010766261257231236, 0.040891870856285095, 0.008117706514894962, -0.003950194921344519, -0.004158457275480032, 0.020953010767698288, 0.030677959322929382, -0.023560818284749985, 0.012024890631437302, 0.06269603967666626, -0.000029286902645253576, 0.045527976006269455, 0.0012099593877792358, -0.021478192880749702, 0.015375198796391487, 0.0404210165143013, 0.01405318547040224, -0.006859077140688896, 0.04013126343488693, 0.027128443121910095, -0.01577361486852169, -0.04150760546326637, 0.00588114932179451, 0.0007515556644648314, -0.014487819746136665, -0.01789245754480362, -0.0070492299273610115, -0.024248989298939705, 0.006723253987729549, 0.0009247303823940456, -0.05907408520579338, 0.02270965836942196, -0.0219128280878067, -0.003241649828851223, 0.022926975041627884, -0.005863039754331112, -0.01535708922892809, -0.014424435794353485, -0.025245025753974915, 0.00449122441932559, 0.04661456122994423, -0.029953567311167717, -0.03529595211148262, -0.010385955683887005, -0.02146008424460888, 0.004704013932496309, 0.0438256561756134, -0.017973951995372772, 0.02466551400721073, -0.028015822172164917, 0.000803055358119309, -0.015719285234808922, -0.0021969422232359648, 0.026422161608934402, 0.008194672875106335, 0.02540801465511322, 0.016226358711719513, 0.015266540460288525, 0.04357212036848068, -0.017131848260760307, -0.02165929041802883, 0.04860663786530495, 0.023923013359308243, -0.03937065228819847, -0.006560266017913818, -0.024502525106072426, -0.006134686525911093, 0.061355918645858765, -0.0013039037585258484, -0.0191420316696167, 0.017792854458093643, -0.01073004212230444, 0.033756621181964874, -0.034209366887807846, -0.025299355387687683, 0.021369535475969315, 0.013310684822499752, -0.050598710775375366, 0.00982455350458622, -0.001657044398598373, 0.0378132089972496, -0.03455344960093498, 0.0059354789555072784, -0.012242208234965801, -0.014351996593177319, 0.011463487520813942, -0.015257485210895538, 0.029374055564403534, -0.00782342255115509, 0.02247423119843006, -0.005029989872127771, -0.02441197633743286, 0.04607126861810684, -0.003017541253939271, 0.018761727958917618, -0.008235420100390911, -0.015628736466169357, 0.00602150009945035, 0.0404210165143013, 0.0008307859534397721, 0.018308982253074646, -0.02433953806757927, 0.03292357176542282, -0.004989243112504482, 0.0030514970421791077, 0.027255211025476456, 0.04078321531414986, -0.04085565358400345, -0.015846053138375282, -0.03471643850207329, 0.03629199042916298, -0.04349967837333679, 0.027889054268598557, 0.00907752476632595, 0.04549175500869751, -0.06298580020666122, -0.018299927935004234, -0.014469710178673267, -0.007859642617404461, 0.01235992182046175, -0.032633814960718155, -0.01001470535993576, -0.011400103569030762, 0.02464740350842476, 0.005125066265463829, 0.04661456122994423, 0.04031236097216606, 0.027436308562755585, -0.010114309377968311, -0.04704919457435608, -0.0014193536480888724, 0.008162980899214745, -0.035458941012620926, -0.007492919452488422, 0.02828746847808361, -0.014261447824537754, 0.05306164175271988, -0.007737401407212019, -0.03277869150042534, 0.03399204835295677, 0.012006781063973904, -0.018816055729985237, 0.013437453657388687, 0.0015336716314777732, -0.00755630386993289, 0.02897563949227333, -0.04197845980525017, 0.0005568756023421884, -0.06077640503644943, -0.013111477717757225, -0.004178830422461033, 0.02864966355264187, 0.016923584043979645, 0.033448755741119385, -0.03861004114151001, -0.009059415198862553, 0.02184038981795311, -0.030750397592782974, -0.017720414325594902, 0.00782342255115509, 0.009498577564954758, -0.03937065228819847, -0.022075815126299858, -0.029192958027124405, 0.02866777405142784, 0.02202148735523224, -0.006569320801645517, 0.0017215604893863201, -0.009580071084201336, 0.006872659549117088, 0.010820590890944004, -0.03842894360423088, 0.06896202266216278, 0.0683462917804718, 0.003832481103017926, -0.015031113289296627, -0.025824539363384247, 0.04505712166428566, -0.025063928216695786, -0.0015019795391708612, 0.004262588452547789, 0.04632480442523956, -0.06077640503644943, -0.0018324828706681728, -0.008810405619442463, -0.0016242205165326595, 0.012296536937355995, -0.015031113289296627, 0.02634972333908081, 0.027454419061541557, 0.03824784606695175, 0.04266662895679474, -0.00954385194927454, 0.054293107241392136, 0.03355741500854492, 0.042956385761499405, -0.029518933966755867, -0.007959246635437012, -0.00087832409190014, 0.05827725678682327, 0.006306729279458523, 0.01796489767730236, 0.0034499121829867363, -0.0009060546872206032, -0.027617407962679863, -0.043644558638334274, -0.016552334651350975, -0.03647308796644211, 0.010539889335632324, -0.007927553728222847, -0.07490202784538269, -0.01776568964123726, 0.011037907563149929, -0.021061668172478676, -0.04780980572104454, 0.034136924892663956, -0.0007181657711043954, 0.023542707785964012, -0.017566481605172157, -0.01451498456299305, -0.014225228689610958, -0.01555629726499319, 0.017738524824380875, 0.024430086836218834, 0.015148826874792576, -0.03929821401834488, 0.054474204778671265, 0.005636667367070913, -0.020790021866559982, 0.0022331615909934044, 0.01626257784664631, -0.01467797253280878, -0.01511260773986578, 0.003350308397784829, -0.0322716198861599, -0.04074699431657791, 0.035006195306777954, 0.02015618048608303, -0.002458401955664158, -0.014478765428066254, 0.007216745521873236, 0.006424442864954472, 0.007456699851900339, -0.0446949265897274, -0.015800779685378075, -0.05056249350309372, 0.005994335748255253, -0.0035857355687767267, 0.005777018144726753, 0.011001688428223133, -0.006786638405174017, 0.013011873699724674, -0.038573820143938065, 0.0061301589012146, 0.0034499121829867363, -0.038320284336805344, 0.018924714997410774, -0.04907749220728874, -0.04795468598604202, -0.04150760546326637, 0.0015212211292237043, 0.059472501277923584, 0.036255769431591034, -0.004830782767385244, 0.006112049333751202, 0.002689301734790206, 0.010159583762288094, 0.01946800760924816, 0.017005078494548798, 0.019051482900977135, 0.02327106148004532, -0.012124494649469852, -0.024393867701292038, 0.011780409142374992, -0.004529707599431276, 0.027617407962679863, 0.02979058027267456, -0.02553478255867958, -0.051649078726768494, 0.008891900070011616, -0.02240179106593132, -0.01701413467526436, -0.01870739832520485, -0.034951865673065186, 0.033014118671417236, 0.005899259354919195, 0.007900389842689037, 0.00985171739012003, 0.03145667910575867, 0.03178265690803528, 0.038646262139081955, 0.031511008739471436, 0.019359350204467773, -0.011807573027908802, -0.02671191841363907, -0.015003948472440243, -0.025878868997097015, 0.019848313182592392, -0.03312277793884277, 0.02533557638525963, -0.002800223883241415, 0.06657153367996216, 0.026295393705368042, 0.020554594695568085, -0.045709073543548584, -0.011255225166678429, -0.021949047222733498, 0.04835309833288193, -0.037885650992393494, -0.01638934575021267, -0.033267658203840256, -0.015574406832456589, 0.0010735701071098447, 0.0162173043936491, 0.008325968869030476, 0.004916803911328316, -0.0030198050662875175, -0.026947345584630966, -0.02627728320658207, -0.025806428864598274, -0.002451610751450062, -0.004984715487807989, 0.052083712071180344, -0.043028827756643295, 0.03468022122979164, -0.009235985577106476, -0.015375198796391487, 0.012106385082006454, 0.04994675889611244, 0.01594565622508526, -0.016986969858407974, -0.002945102285593748, -0.03147478774189949, -0.00671419920399785, 0.02383246459066868, 0.016914529725909233, -0.022854536771774292, -0.01964910700917244, -0.013464617542922497, 0.003110353834927082, 0.04581773281097412, -0.019123923033475876, -0.047338951379060745, 0.007162415888160467, -0.026621369644999504, 0.03516918420791626, 0.008199200965464115, 0.055234815925359726, 0.02383246459066868, -0.015121662057936192, -0.04512955993413925, 0.03274247422814369, -0.013410288840532303, 0.03384716808795929, -0.0012099593877792358, 0.017729470506310463, -0.01628068834543228, 0.01820937916636467, 0.003739668522030115, -0.009960376657545567, 0.0008704010979272425, -0.0408194325864315, 0.028522895649075508, -0.03096771612763405, 0.06867226958274841, -0.05432932451367378 ]
We demonstrate the first large-scale application of model-based generative adversarial imitation learning (MGAIL) to the task of dense urban self-driving. We augment standard MGAIL using a hierarchical model to enable generalization to arbitrary goal routes, and measure performance using a closed-loop evaluation framework with simulated interactive agents. We train policies from expert trajectories collected from real vehicles driving over 100,000 miles in San Francisco, and demonstrate a steerable policy that can navigate robustly even in a zero-shot setting, generalizing to synthetic scenarios with novel goals that never occurred in real-world driving. We also demonstrate the importance of mixing closed-loop MGAIL losses with open-loop behavior cloning losses, and show our best policy approaches the performance of the expert. We evaluate our imitative model in both average and challenging scenarios, and show how it can serve as a useful prior to plan successful trajectories.
[ 0.015152846463024616, -0.02908068336546421, -0.031495194882154465, -0.06114399805665016, -0.028086470440030098, 0.003925803583115339, -0.04275108873844147, 0.05553380772471428, -0.07097958773374557, 0.00173210259526968, -0.050420720130205154, 0.005929760634899139, 0.06849405914545059, -0.023736797273159027, -0.04527212306857109, 0.03699886426329613, 0.005627946462482214, 0.025334635749459267, -0.03838365897536278, -0.01675068587064743, 0.05422002822160721, -0.037495970726013184, -0.07208032160997391, 0.07470788061618805, 0.03937787190079689, -0.00032289678347297013, 0.031051350757479668, 0.012374380603432655, -0.03621770069003105, 0.0220146793872118, 0.007070440798997879, 0.03053649142384529, 0.018286388367414474, -0.0009759027743712068, -0.023754550144076347, 0.03920033574104309, 0.02639986202120781, 0.04101121798157692, -0.04047860577702522, 0.08067315071821213, -0.003710538847371936, -0.006333658937364817, 0.0033576826099306345, -0.002829507691785693, 0.006511196959763765, -0.051983051002025604, -0.028192993253469467, 0.0110073396936059, -0.015623321756720543, 0.0202748104929924, -0.023026645183563232, -0.007691822946071625, 0.041401803493499756, -0.02061213180422783, -0.038738735020160675, 0.035933639854192734, 0.017443083226680756, 0.018179865553975105, 0.02774914912879467, 0.016599779948592186, -0.018392911180853844, 0.022511785849928856, -0.032418392598629, 0.006857395172119141, 0.0033576826099306345, -0.025476666167378426, 0.062173716723918915, 0.0026253394316881895, 0.03367891162633896, 0.014265158213675022, -0.023861072957515717, -0.010900817811489105, -0.07513397186994553, -0.040088023990392685, 0.02941800467669964, -0.02771364152431488, -0.003852569032460451, 0.03767351061105728, 0.026790445670485497, 0.016306841745972633, 0.0007917073671706021, -0.03785104677081108, -0.059120070189237595, 0.0018053369130939245, 0.061925165355205536, -0.005814360920339823, 0.0639490932226181, -0.07335859537124634, 0.019972996786236763, -0.04800620675086975, 0.01177962962538004, 0.016830578446388245, -0.010936325415968895, -0.0006025187321938574, -0.022884614765644073, 0.0438518226146698, 0.008242189884185791, 0.0028494808357208967, -0.0501011498272419, -0.01667967066168785, 0.004163260105997324, 0.012019305489957333, 0.04104672744870186, 0.030003879219293594, 0.004913357086479664, -0.03234737738966942, 0.0004086142289452255, 0.010678895749151707, 0.027127766981720924, 0.08997613191604614, -0.025618696585297585, -0.027181029319763184, -0.009516023099422455, 0.015587814152240753, -0.057699766010046005, -0.027500595897436142, -0.05869397893548012, -0.04647938162088394, 0.10069940984249115, -0.04246702790260315, 0.047402579337358475, 0.028068717569112778, 0.028672344982624054, -0.061818644404411316, -0.04782866686582565, 0.014140881597995758, 0.016377856954932213, -0.04509458690881729, 0.021340036764740944, 0.002089397283270955, 0.006675419397652149, 0.00732343178242445, -0.016022780910134315, 0.044455450028181076, 0.02943575754761696, -0.034229278564453125, 0.0016455529257655144, 0.003936899360269308, 0.0003292770416010171, -0.0034531091805547476, -0.017895804718136787, -0.050207674503326416, -0.023026645183563232, 0.019458137452602386, -0.015783105045557022, 0.019830966368317604, 0.0011240357998758554, 0.08266157656908035, -0.009915483184158802, 0.02505057491362095, -0.06014978885650635, 0.06423315405845642, 0.026666169986128807, 0.008876887150108814, 0.03248940780758858, 0.025885002687573433, -0.059013545513153076, 0.031033597886562347, 0.017709389328956604, -0.08905293047428131, 0.048858385533094406, -0.025707464665174484, -0.0008072419441305101, 0.053119294345378876, 0.04935549199581146, 0.06306140869855881, 0.04410037398338318, -0.013608268462121487, -0.000719582661986351, 0.04640836641192436, -0.009933236986398697, -0.02054111659526825, 0.007785030175000429, -0.03706987947225571, 0.04406486824154854, 0.004125533159822226, 0.0585874542593956, 0.012631810270249844, -0.024020856246352196, 0.01448708027601242, -0.06881362944841385, -0.02323969081044197, 0.03193904086947441, 0.05425553396344185, 0.03524124249815941, 0.06884913891553879, 0.05844542384147644, 0.011380169540643692, 0.06114399805665016, -0.02336396649479866, 0.034193769097328186, 0.051841020584106445, 0.006613281089812517, -0.010270558297634125, 0.02203243412077427, -0.012569672428071499, -0.03346586599946022, 0.007882676087319851, -0.00811347458511591, 0.003137979656457901, 0.0025121590588241816, -0.035720594227313995, -0.01613818109035492, 0.022866861894726753, 0.049142446368932724, -0.010670018382370472, -0.006311466917395592, 0.053296830505132675, -0.020754162222146988, -0.027340812608599663, -0.024091871455311775, -0.03643074631690979, -0.07140567898750305, -0.044632989913225174, -0.009666929952800274, -0.016306841745972633, -0.015463537536561489, 0.006475689355283976, 0.022209972143173218, -0.046195320785045624, -0.015791982412338257, 0.02176612801849842, 0.003577385563403368, -0.008650526404380798, -0.050385210663080215, 0.006684296298772097, 0.02611580304801464, 0.01588962785899639, -0.03792206197977066, -0.04630184546113014, -0.02893865294754505, -0.015552306547760963, 0.03538327291607857, 0.0263466015458107, 0.06352300196886063, -0.028086470440030098, 0.017514098435640335, -0.001269394881092012, 0.019813211634755135, -0.01885450817644596, -0.014105373993515968, -0.03689234331250191, -0.04942650720477104, -0.03067852184176445, 0.09168048948049545, 0.010199543088674545, -0.0020239301957190037, 0.051805514842271805, 0.040159039199352264, 0.01524161547422409, -0.03809959813952446, -0.010022005997598171, -0.02508608251810074, 0.019617920741438866, -0.029986124485731125, 0.032684698700904846, 0.02927597425878048, -0.0028361654840409756, 0.03266694396734238, -0.050349704921245575, 0.03827713802456856, 0.02771364152431488, 0.018517186865210533, 0.07016291469335556, -0.04640836641192436, 0.0012804910074919462, 0.0007034933078102767, 0.051947545260190964, -0.002343498170375824, -0.006409112364053726, -0.020754162222146988, -0.04651488736271858, -0.017966819927096367, 0.041401803493499756, -0.03955540806055069, -0.054504089057445526, -0.010430342517793179, 0.017150146886706352, 0.035844869911670685, 0.015046323649585247, 0.040194544941186905, -0.03650176152586937, 0.016404487192630768, -0.023843318223953247, -0.06103747710585594, -0.03941337764263153, -0.02624007873237133, 0.06267082691192627, -0.042786598205566406, 0.03057199902832508, -0.017167899757623672, -0.009853344410657883, -0.00871710292994976, -0.005809922702610493, 0.019529152661561966, 0.0231331679970026, -0.005348324775695801, -0.025689711794257164, 0.025565434247255325, 0.008082405664026737, -0.00814010575413704, 0.029719818383455276, 0.025920510292053223, -0.021269021555781364, 0.03461986035108566, 0.016342349350452423, -0.03387420251965523, 0.014167511835694313, -0.002927153604105115, -0.032791219651699066, 0.009143194183707237, 0.024482455104589462, -0.03467312082648277, -0.022813599556684494, 0.021411051973700523, 0.03817061334848404, 0.04868084937334061, -0.005601315759122372, -0.04196992143988609, 0.024180641397833824, 0.01901429332792759, 0.0019595727790147066, -0.04243152216076851, 0.005157471634447575, -0.002487747697159648, 0.03944888710975647, 0.02485528402030468, 0.022423017770051956, -0.03809959813952446, -0.0189787857234478, -0.03934236243367195, -0.031335413455963135, -0.03678582236170769, -0.0003353798820171505, 0.00023287958174478263, -0.010741033591330051, -0.0201860424131155, 0.041330788284540176, -0.02020379528403282, -0.049106940627098083, -0.014185265637934208, -0.031424179673194885, -0.009258593432605267, -0.01400772761553526, 0.006466812454164028, -0.03817061334848404, 0.010022005997598171, 0.012480903416872025, -0.006910656578838825, -0.022565048187971115, 0.0009115453576669097, -0.010625634342432022, -0.02473100833594799, -0.05453959479928017, 0.0016211415641009808, 0.01539252232760191, -0.022902369499206543, 0.0021626316010951996, -0.02797994762659073, 0.025263620540499687, 0.04722503945231438, -0.03927134722471237, -0.056208450347185135, 0.02638210915029049, -0.04640836641192436, 0.01662641018629074, -0.009107686579227448, 0.008774803020060062, 0.011903905309736729, 0.030980335548520088, 0.006169436499476433, 0.01691047102212906, 0.00016713514924049377, 0.0234882440418005, 0.000845523492898792, -0.0006641021464020014, 0.017105761915445328, -0.03252491354942322, 0.008805871941149235, 0.030376708135008812, 0.024287164211273193, 0.03834815323352814, -0.019955242052674294, 0.009684683755040169, -0.019316107034683228, 0.11497344076633453, -0.002009505406022072, -0.013155546970665455, 0.03508145734667778, 0.002667504595592618, 0.075560063123703, -0.02927597425878048, -0.022689323872327805, 0.007429954595863819, 0.02902742102742195, 0.027127766981720924, 0.05848093330860138, -0.057451214641332626, 0.004456197377294302, -0.0010480275377631187, -0.011522199958562851, 0.02210344932973385, 0.0008954560034908354, 0.04782866686582565, -0.05539177730679512, -0.005192979238927364, 0.019440382719039917, -0.0037793347146362066, -0.00585430720821023, -0.0013814655831083655, -0.0067908186465501785, -0.08280360698699951, 0.0014524806756526232, -0.016795070841908455, 0.027500595897436142, -0.0067064883187413216, -0.015330384485423565, 0.011850644834339619, -0.010723279789090157, 0.001382575137540698, 0.004691435024142265, 0.035880379378795624, 0.022831354290246964, -0.0008699349709786475, -0.010048636235296726, 0.07222235202789307, 0.014975308440625668, 0.017895804718136787, -0.053509876132011414, -0.027145521715283394, 0.009986498393118382, -0.02476651594042778, 0.03204556182026863, -0.038490183651447296, 0.0013526156544685364, 0.018304141238331795, 0.0024833092465996742, 0.019493645057082176, -0.0292049590498209, 0.0017365410458296537, -0.004236494190990925, -0.038703229278326035, -0.019245091825723648, -0.010945201851427555, 0.011300276964902878, -0.010501357726752758, -0.008868010714650154, -0.051663484424352646, 0.01890777051448822, -0.028654592111706734, -0.11433430761098862, 0.06657665222883224, -0.06860058754682541, -0.075560063123703, 0.03809959813952446, -0.035844869911670685, -0.009294101037085056, -0.02215670980513096, -0.00013648213644046336, -0.012764964252710342, 0.06792593747377396, -0.004331920761615038, -0.02332845889031887, -0.02505057491362095, -0.0026297778822481632, 0.014948678202927113, -0.02165960520505905, 0.005392708815634251, 0.0028516999445855618, 0.013581637293100357, 0.045982275158166885, -0.0034242591354995966, 0.0022502909414470196, -0.00953377690166235, -0.004220959730446339, 0.04236050695180893, -0.047296054661273956, -0.03973294794559479, 0.028512561693787575, -0.005756661295890808, -0.007421077694743872, 0.038596704602241516, 0.03513471782207489, -0.07889777421951294, 0.010909694246947765, 0.006773064844310284, 0.06682520359754562, -0.021233513951301575, -0.06480127573013306, 0.011397923342883587, -0.043212685734033585, -0.053403355181217194, -0.03190353140234947, -0.037247419357299805, -0.023701289668679237, -0.031246643513441086, 0.01885450817644596, 0.00272964290343225, -0.012019305489957333, 0.02318642847239971, -0.0033066405449062586, -0.012702825479209423, 0.010456972755491734, -0.03055424615740776, 0.022334247827529907, 0.03231186792254448, 0.040336575359106064, 0.04356776177883148, -0.014274034649133682, -0.013430730439722538, -0.00902335625141859, 0.011273646727204323, 0.017096884548664093, -0.060753416270017624, 0.025334635749459267, -0.011176001280546188, 0.005801045801490545, -0.016688548028469086, 0.032702453434467316, 0.02213895693421364, 0.0006291493773460388, -0.02023930288851261, -0.005654577165842056, -0.0035418779589235783, -0.03316405043005943, 0.05734468996524811, 0.015152846463024616, -0.04935549199581146, 0.08436593413352966, 0.030234677717089653, -0.04399385303258896, 0.025192605331540108, -0.027358565479516983, -0.05077579617500305, -0.018091095611453056, -0.02338172122836113, 0.007088194601237774, 0.026950228959321976, -0.004771326668560505, -0.011939412914216518, -0.010829802602529526, 0.006404674146324396, 0.009817836806178093, 0.017549606040120125, 0.03556080907583237, -0.007434392813593149, 0.026985736563801765, -0.03799307718873024, -0.02908068336546421, 0.011486692354083061, 0.02316867560148239, 0.005951952654868364, 0.0016666356241330504, 0.008592827245593071, -0.04829026758670807, 0.0016466625966131687, -0.008317643776535988, -0.022689323872327805, -0.011300276964902878, -0.028228500857949257, 0.020061764866113663, -0.03628871589899063, -0.041898906230926514, 0.02176612801849842, -0.017620621249079704, -0.022795846685767174, 0.009018917568027973, 0.05517873167991638, -0.02627558633685112, -0.01878349296748638, -0.062173716723918915, 0.002407855587080121, -0.016777316108345985, -0.024198394268751144, 0.06753535568714142, -0.03399847820401192, -0.025157097727060318, -0.027127766981720924, -0.022423017770051956, -0.014513710513710976, 0.0032134330831468105, -0.006102859973907471, 0.0042342753149569035, 0.0727904736995697, -0.0016599779482930899, -0.001341519528068602, -0.04655039682984352, -0.0377800315618515, 0.02908068336546421, 0.0008205572376027703, 0.03660828247666359, 0.044597480446100235, -0.005277309566736221, 0.011859521269798279, -0.04534313827753067, -0.040088023990392685, 0.013288700021803379, 0.02039908617734909, 0.0015590033726766706, -0.04399385303258896, -0.01470900233834982, 0.0033643401693552732, 0.01527712307870388, -0.0009836701210588217, -0.0072923628613352776, -0.027252044528722763, 0.06416214257478714, 0.019529152661561966, -0.00199951883405447, -0.031051350757479668, 0.013333084993064404, 0.03616444021463394, -0.003639523871243, -0.08429492264986038, 0.038738735020160675, -0.014664617367088795, 0.03838365897536278, 0.008251066319644451, -0.027252044528722763, -0.028477054089307785, 0.033075280487537384, 0.0123477503657341, 0.044419944286346436, 0.012401011772453785, -0.057806290686130524, 0.026879213750362396, -0.02206794172525406, 0.006196067202836275, -0.00255432422272861, 0.011957166716456413, -0.0004987700958736241, -0.013466238044202328, -0.014629109762609005, -0.01878349296748638, -0.0016899374313652515, 0.014114250428974628, -0.012818224728107452, 0.02338172122836113, -0.025405650958418846, 0.014105373993515968, -0.03756698593497276, -0.004123314283788204, -0.0434967465698719, 0.034477829933166504, -0.012214596383273602, 0.019440382719039917, -0.01892552338540554, -0.05102434754371643, 0.003934680484235287, 0.03696335852146149, -0.006302590016275644, 0.010226174257695675, -0.0049710567109286785, 0.028956405818462372, 0.028441546484827995, 0.011193755082786083, -0.013288700021803379, -0.02347048930823803, -0.014842155389487743, 0.016395609825849533, 0.008029144257307053, -0.026843706145882607, 0.035702839493751526, -0.04094020277261734, 0.03525899723172188, 0.0162091962993145, 0.024393685162067413, 0.0005831005400978029, -0.028654592111706734, 0.03689234331250191, 0.009338485077023506, -0.012960255146026611, -0.06142805889248848, 0.004524993244558573, 0.041614849120378494, 0.0003911378444172442, -0.019546905532479286, 0.01896103098988533, -0.0013248753966763616, 0.005348324775695801, -0.004169917665421963, 0.007066002115607262, -0.05801933631300926, -0.006511196959763765, 0.006777503527700901, -0.027500595897436142, -0.014788893982768059, 0.0587649941444397, -0.014265158213675022, -0.02496180683374405, -0.02474876120686531, -0.021411051973700523, -0.043070655316114426, 0.017372068017721176, -0.0026075856294482946, 0.008388658054172993, -0.03920033574104309, 0.014984185807406902, 0.021553082391619682, -0.03548979386687279, -0.025636449456214905, 0.008668280206620693, -0.02050560899078846, 0.014424941502511501, 0.040336575359106064, -0.01659090258181095, 0.007789468392729759, 0.019937489181756973, 0.0070837559178471565, 0.003965749405324459, 0.015410276129841805, 0.022973384708166122, 0.011460061185061932, 0.03057199902832508, 0.004513897001743317, 0.01306677795946598, 0.02068314701318741, -0.04207644611597061, 0.005694522988051176, 0.048964910209178925, 0.05074028670787811, -0.005516985431313515, 0.041614849120378494, -0.06998538225889206, -0.032933250069618225, -0.0070793177001178265, -0.012596302665770054, -0.012596302665770054, -0.019706688821315765, 0.0021615219302475452, 0.021233513951301575, -0.05425553396344185, 0.010971833020448685, 0.005712276790291071, 0.03248940780758858, -0.02055887132883072, -0.00577885378152132, 0.00834871269762516, -0.005006564315408468, -0.029542280361056328, 0.031069105491042137, -0.05695410817861557, 0.06991436332464218, 0.004518335685133934, 0.0022325371392071247, 0.03699886426329613, 0.008947902359068394, 0.03983946889638901, 0.017878049984574318, 0.0012782717822119594, 0.06718028336763382, 0.03248940780758858, 0.028068717569112778, -0.01528599951416254, -0.0030159223824739456, -0.0013071215944364667, 0.021446559578180313, 0.0022170026786625385, 0.014957554638385773, -0.042893119156360626, 0.02654189243912697, 0.029116190969944, -0.012631810270249844, 0.03316405043005943, 0.029648803174495697, 0.00045188903459347785, -0.011575461365282536, -0.008375342935323715, -0.01303127035498619, 0.017238914966583252, 0.021570835262537003, 0.012170212343335152, 0.02615131065249443, -0.013306453824043274, 0.028459301218390465, 0.007993636652827263, -0.008761487901210785, 0.002973757218569517, -0.05425553396344185, -0.03247165307402611, 0.0020549993496388197, 0.0002248349046567455, -0.00381928076967597, 0.06178313493728638, -0.019440382719039917, 0.028335023671388626, -0.0578773058950901, -0.0028161925729364157, -0.012187966145575047, -0.0027030122000724077, 0.002651970135048032, -0.02797994762659073, -0.011655353009700775, 0.023790057748556137, 0.024393685162067413, -0.015499045141041279, -0.03327057510614395, 0.016812823712825775, -0.00942725408822298, -0.021464312449097633, 0.0023168674670159817, 0.02785567194223404, 0.008206682279706001, 0.029986124485731125, -0.03254266828298569, -0.060859937220811844, 0.012969132512807846, 0.031086858361959457, -0.018623709678649902, -0.00838422030210495, 0.003355463268235326, 0.028565822169184685, -0.03167273476719856, 0.016386734321713448, -0.03048323094844818, -0.04378080740571022, 0.001966230571269989, -0.008868010714650154, -0.04339022561907768, -0.05848093330860138, -0.02783791907131672, -0.041792385280132294, -0.021215761080384254, 0.01168198324739933, -0.028139732778072357, 0.0015279342187568545, -0.0017609525239095092, -0.006502320058643818, 0.021624097600579262, -0.002911618910729885, 0.02052336372435093, 0.05439756438136101, -0.04353225603699684, 0.038738735020160675, -0.03930685669183731, 0.021304529160261154, 0.031353164464235306, 0.015170600265264511, 0.007527600508183241, 0.030128154903650284, 0.003475301433354616, 0.02038133330643177, 0.016466625034809113, -0.042964134365320206, -0.009720191359519958, -0.022671569138765335, -0.01880124770104885, -0.0117885060608387, -0.014460449106991291, -0.03476189076900482, -0.007913745008409023, 0.06391359120607376, 0.013510622084140778, -0.014700124971568584, -0.020718654617667198, 0.03841916844248772, 0.01009302120655775, 0.054752640426158905, -0.05812585726380348, -0.0034020671155303717, 0.01164647564291954, 0.009436131455004215, 0.010909694246947765, -0.012711702845990658, 0.027305305004119873, 0.01400772761553526, -0.015676582232117653, -0.05418451875448227, -0.03515247255563736, -0.03991048410534859, 0.00657333480194211, -0.0036040162667632103, -0.03895178064703941, 0.06245777755975723, -0.019333859905600548, 0.05507220700383186, 0.03934236243367195, -0.013590514659881592, -0.027323059737682343, -0.05095333233475685, -0.003610673826187849, -0.018037835136055946, 0.0014791113790124655, -0.014771140180528164, 0.012294488959014416, -0.004948864690959454, -0.005836553405970335, -0.0012527507496997714, -0.03607567027211189, -0.017869174480438232, -0.03323506563901901, 0.004021229688078165, -0.04236050695180893, -0.0023457175120711327, 0.059297606348991394, 0.018215373158454895, -0.028885390609502792, -0.03165498003363609, -0.009773452766239643, 0.005974145140498877, 0.00011352706496836618, 0.02203243412077427, -0.040017008781433105, 0.03930685669183731, 0.0007123702089302242, 0.00941837765276432, 0.019795458763837814, -0.01400772761553526, -0.0016089357668533921, -0.008819187059998512, -0.06749985367059708, 0.014504834078252316, 0.05855194851756096, 0.0053261322900652885, 0.05539177730679512, -0.011824013665318489, -0.024375932291150093, -0.026808198541402817, 0.05830339342355728, 0.013421853072941303, -0.000057144960010191426, 0.028068717569112778, -0.00954265333712101, 0.011957166716456413, -0.023008892312645912, 0.0010119650978595018, 0.05308378487825394, -0.021357791498303413, 0.035880379378795624, 0.02940024994313717, -0.02213895693421364, 0.0363064669072628, 0.019564660266041756, 0.026967983692884445, 0.061925165355205536, -0.004620419815182686, -0.041579339653253555, -0.04832577332854271, -0.027198782190680504, 0.02916945144534111, -0.0814543142914772, -0.05521423742175102, -0.0020394648890942335, 0.007629684638231993, 0.024429192766547203, -0.005774415098130703, 0.01878349296748638, 0.02331070601940155, -0.000706822145730257, -0.03852568939328194, -0.02485528402030468, -0.013412976637482643, -0.01302239391952753, -0.0013881232589483261, -0.050278689712285995, -0.005636823363602161, -0.0007706247852183878, -0.02508608251810074, 0.0042964136227965355, 0.09302977472543716, -0.004944426007568836, 0.007842729799449444, -0.04257355257868767, -0.011380169540643692, 0.004877849481999874, 0.01746971346437931, -0.016342349350452423, -0.00438962085172534, -0.011025093495845795, 0.020931700244545937, 0.000047678593546152115, -0.05066927149891853, -0.003774896264076233, 0.009808960370719433, 0.02604478783905506, 0.014922047033905983, -0.028494808822870255, -0.03399847820401192, -0.044597480446100235, -0.008579511195421219, 0.009942113421857357, 0.014842155389487743, 0.030376708135008812, 0.01603165827691555, -0.0035174665972590446, -0.015570060350000858, -0.0008100159466266632, -0.034300293773412704, -0.014797771349549294, -0.001642224146053195, 0.0017465275013819337, -0.004083367995917797, -0.0292049590498209, -0.031353164464235306, -0.034158263355493546, -0.008330958895385265, 0.007736206986010075, 0.01691047102212906, 0.04853881895542145, 0.03392746299505234, 0.005712276790291071, -0.0201860424131155, -0.02650638483464718, 0.004855657462030649, 0.04999462887644768, 0.009258593432605267, 0.05386495217680931, 0.02611580304801464, -0.0433192104101181, 0.0033576826099306345, 0.0062049441039562225, -0.0433192104101181, 0.007771714590489864, -0.016457749530673027, -0.019475890323519707, -0.004145506303757429, -0.07619919627904892, -0.002356813522055745, -0.02924046665430069, -0.03509921208024025, 0.00946276169270277, -0.05120188370347023, 0.018428418785333633, -0.03396296873688698 ]
Unsupervised representation learning for dynamic graphs has attracted a lot of research attention in recent years. Compared with static graph, the dynamic graph is a comprehensive embodiment of both the intrinsic stable characteristics of nodes and the time-related dynamic preference. However, existing methods generally mix these two types of information into a single representation space, which may lead to poor explanation, less robustness, and a limited ability when applied to different downstream tasks. To solve the above problems, in this paper, we propose a novel disenTangled representation learning framework for discrete-time Dynamic graphs, namely DyTed. We specially design a temporal-clips contrastive learning task together with a structure contrastive learning to effectively identify the time-invariant and time-varying representations respectively. To further enhance the disentanglement of these two types of representation, we propose a disentanglement-aware discriminator under an adversarial learning framework from the perspective of information theory. Extensive experiments on Tencent and five commonly used public datasets demonstrate that DyTed, as a general framework that can be applied to existing methods, achieves state-of-the-art performance on various downstream tasks, as well as be more robust against noise.
[ 0.019855190068483353, -0.03277962654829025, -0.03624500334262848, -0.03765944391489029, 0.05961861088871956, 0.022542623803019524, -0.03659861534833908, 0.007973900996148586, -0.04582782834768295, -0.020491687580943108, 0.022825513035058975, -0.013834983110427856, -0.010740897618234158, -0.039887186139822006, -0.025159336626529694, 0.040912654250860214, 0.026927385479211807, -0.0009094401611946523, 0.017379920929670334, -0.04805557057261467, 0.05084908753633499, -0.03762408345937729, 0.005096401087939739, 0.009909914806485176, 0.048833511769771576, 0.023073038086295128, 0.027687646448612213, -0.019749106839299202, -0.08705873042345047, 0.05696653947234154, 0.012190697714686394, 0.03150663152337074, 0.023055357858538628, -0.008221427910029888, -0.09243360161781311, -0.0130835622549057, 0.08232036232948303, 0.02323216386139393, 0.017362240701913834, 0.043317198753356934, -0.018405389040708542, 0.015284783206880093, -0.007682172581553459, -0.048762790858745575, 0.017892654985189438, -0.013994107954204082, -0.0261317640542984, -0.025548307225108147, 0.01548810862004757, -0.0060378871858119965, -0.026290887966752052, -0.02211829274892807, -0.018493792042136192, 0.023974744603037834, -0.013879184611141682, 0.04947001114487648, 0.08232036232948303, -0.03628036379814148, 0.03762408345937729, 0.040983375161886215, 0.002032151212915778, 0.029561778530478477, -0.06333151459693909, 0.0016045044176280499, 0.030781732872128487, -0.03159503638744354, 0.026838982477784157, -0.02461124211549759, 0.024381395429372787, 0.015302463434636593, -0.03262050449848175, 0.009936435148119926, 0.05031867325305939, -0.023019997403025627, 0.049965064972639084, -0.043600086122751236, 0.010829299688339233, 0.027599243447184563, 0.009352979250252247, -0.02733403630554676, -0.017866134643554688, 0.03398190066218376, -0.02623784728348255, -0.014002948068082333, 0.04130162298679352, -0.021092824637889862, 0.008804883807897568, -0.04377689212560654, 0.019006526097655296, 0.04268070310354233, -0.03550242260098457, -0.022966956719756126, 0.01810482144355774, -0.06191707402467728, -0.026785941794514656, 0.00579478032886982, -0.006356135942041874, 0.0013613976771011949, -0.06156346574425697, -0.027917493134737015, -0.020350243896245956, 0.0010442539351060987, -0.007081035990267992, -0.029526418074965477, 0.0026366030797362328, -0.02871311455965042, -0.013702379539608955, 0.03375205397605896, 0.009432541206479073, 0.11499390751123428, -0.002091822912916541, 0.03620964288711548, -0.037235110998153687, 0.04554494097828865, -0.07241928577423096, 0.05343043804168701, -0.029526418074965477, -0.06930752098560333, -0.00394716951996088, -0.06156346574425697, 0.03523721545934677, 0.013888024725019932, -0.018582195043563843, -0.03596211597323418, 0.00020152995421085507, 0.0902412161231041, -0.03005683235824108, -0.02358577400445938, -0.027634605765342712, 0.010767417959868908, -0.04264534264802933, 0.021075144410133362, 0.010961903259158134, -0.02622016705572605, 0.005038939416408539, 0.02581351436674595, 0.014630605466663837, 0.028306463733315468, -0.006661124527454376, 0.0392153263092041, 0.04512060806155205, 0.018953485414385796, -0.0522281676530838, -0.0391446053981781, -0.0007359503651969135, 0.013773101381957531, -0.007138497661799192, 0.07906714826822281, 0.0010790623491629958, 0.06011366471648216, -0.014179753139615059, 0.015532310120761395, -0.0004928436246700585, -0.021287309005856514, 0.015364345163106918, -0.008734161965548992, -0.026414651423692703, -0.06990865617990494, -0.051344141364097595, -0.016036204993724823, 0.0919385477900505, -0.009971796534955502, 0.03597979620099068, 0.030657969415187836, -0.010387287475168705, 0.014612924307584763, 0.04324647784233093, -0.0021349191665649414, -0.03419406712055206, 0.05976005643606186, 0.022312777116894722, 0.004073143005371094, 0.009202694520354271, 0.028889920562505722, -0.04169059544801712, 0.03014523535966873, -0.0032443697564303875, -0.03758871927857399, -0.02477036602795124, 0.031930964440107346, -0.055233851075172424, 0.02316144108772278, 0.012349821627140045, 0.06913071125745773, 0.017680490389466286, 0.046039994806051254, 0.06927216053009033, 0.008044622838497162, -0.025000212714076042, 0.00046577039756812155, 0.021870765835046768, 0.016434015706181526, 0.09236288070678711, -0.0130835622549057, -0.007646811660379171, -0.044873081147670746, -0.04844454303383827, -0.015505789779126644, 0.009609346278011799, 0.020049674436450005, -0.0521928071975708, -0.0011260261526331306, 0.025141656398773193, -0.007642391603440046, 0.015956642106175423, 0.00718269869685173, 0.018670596182346344, -0.03205472603440285, -0.005777100101113319, -0.06828205287456512, 0.0062986742705106735, -0.04802021011710167, -0.05473879724740982, -0.01098842453211546, -0.0007370554376393557, -0.0018000948475673795, 0.00516270287334919, 0.00492843659594655, 0.012915597297251225, -0.015293623320758343, 0.019147969782352448, -0.00037018524017184973, 0.03205472603440285, 0.023037677630782127, -0.01936013624072075, -0.03615660220384598, 0.03523721545934677, -0.001471900730393827, -0.04236245155334473, 0.002320564351975918, 0.006577142048627138, -0.009706588461995125, 0.020474007353186607, -0.03741191700100899, -0.031736478209495544, 0.010051358491182327, 0.021128185093402863, -0.039604295045137405, 0.006285414099693298, -0.02333824709057808, -0.0004743343743029982, -0.01574447564780712, -0.015382026322185993, -0.03511345386505127, 0.051485586911439896, -0.021658599376678467, 0.014727847650647163, 0.02082761749625206, 0.03134750947356224, 0.027882132679224014, 0.0007790465606376529, -0.02484108880162239, -0.0012774154311046004, -0.04667649418115616, -0.0015172070125117898, 0.009954115375876427, -0.0017083772690966725, -0.02222437597811222, -0.0259195975959301, -0.08246180415153503, 0.08352263271808624, 0.022790150716900826, -0.04575710743665695, 0.07277289777994156, -0.008208167739212513, 0.02342664822936058, 0.0258665569126606, 0.02197684906423092, 0.03509577363729477, 0.016000842675566673, -0.021729322150349617, -0.009653547778725624, -0.04961145296692848, -0.02876615710556507, -0.0031493371352553368, -0.011819407343864441, 0.02351505123078823, -0.017715850844979286, 0.02347969077527523, 0.009096612222492695, -0.008093244396150112, -0.014860451221466064, -0.001586823957040906, 0.015947801992297173, -0.006267733406275511, -0.02082761749625206, 0.04420122504234314, -0.04978825896978378, -0.020456327125430107, -0.04515597224235535, 0.0022763630840927362, 0.00556051405146718, -0.013375290669500828, 0.001912807929329574, -0.0035250475630164146, -0.0013138813665136695, -0.03102925978600979, -0.04908103868365288, 0.030375082045793533, -0.08359335362911224, -0.010484530590474606, 0.01225257944315672, 0.04777268320322037, 0.021729322150349617, 0.011200590059161186, -0.031877923756837845, 0.056648287922143936, 0.06633719801902771, -0.00900378916412592, -0.03414102643728256, -0.04423658549785614, -0.007169438526034355, -0.007991581223905087, 0.030640289187431335, 0.008539676666259766, -0.01699979044497013, -0.007372764404863119, 0.009423701092600822, 0.008314250037074089, -0.035573143512010574, 0.01958998292684555, 0.025636710226535797, -0.07100484520196915, 0.01297747902572155, 0.0044886344112455845, 0.005617975722998381, 0.017866134643554688, -0.012332141399383545, 0.0038432965520769358, 0.061598826199769974, -0.06810524314641953, -0.015443908050656319, -0.025106295943260193, 0.03645716980099678, -0.006400337442755699, -0.023904021829366684, 0.0023603453300893307, 0.01706167310476303, -0.043564725667238235, -0.03537866100668907, -0.003036624053493142, 0.024381395429372787, 0.0029482217505574226, -0.0391446053981781, 0.026503054425120354, -0.0261317640542984, -0.03751799836754799, 0.000889549613930285, 0.04964681342244148, -0.01577099598944187, 0.0009099927265197039, -0.03497200831770897, -0.0017172176158055663, 0.01684066653251648, 0.05597643181681633, -0.029650181531906128, -0.010944223031401634, 0.015258262865245342, -0.00452178530395031, 0.0261671245098114, -0.00453946553170681, -0.011616081930696964, -0.024292992427945137, 0.025583667680621147, -0.08076447993516922, -0.06753946840763092, -0.08154241740703583, -0.01571795530617237, -0.044766999781131744, 0.044802360236644745, -0.039675019681453705, 0.013136603869497776, -0.06152810528874397, -0.009892233647406101, -0.017397601157426834, 0.04547422006726265, -0.006811408791691065, -0.015523470006883144, -0.0259019173681736, 0.03992254659533501, -0.053854770958423615, -0.035749949514865875, 0.051273420453071594, -0.00041355768917128444, -0.003531677881255746, 0.051131974905729294, 0.02866007387638092, 0.02086297795176506, 0.006068828050047159, 0.02579583413898945, 0.06322543323040009, -0.05558745935559273, -0.03520185500383377, -0.022949276491999626, 0.057992007583379745, 0.008292149752378464, 0.006603662855923176, 0.03129446506500244, 0.04306967183947563, -0.05724942684173584, -0.053890131413936615, -0.018635235726833344, -0.031718797981739044, -0.031789518892765045, 0.02093369886279106, -0.021693961694836617, 0.008018102496862411, -0.05307682976126671, 0.053890131413936615, -0.024947170168161392, 0.027935173362493515, -0.01812250167131424, -0.034441594034433365, 0.006988213397562504, 0.010015997104346752, 0.008057883009314537, -0.04314039647579193, -0.01710587367415428, 0.026573775336146355, -0.04430730640888214, 0.001448695082217455, 0.024257631972432137, 0.04147842898964882, 0.05480951815843582, -0.0041085039265453815, 0.06966112554073334, 0.012022732757031918, -0.022542623803019524, 0.003920648712664843, -0.03502504900097847, 0.03212545067071915, -0.022295096889138222, 0.051308780908584595, -0.06927216053009033, -0.05756767466664314, 0.042433176189661026, 0.013339929282665253, 0.0260964035987854, -0.055198486894369125, 0.012862556613981724, -0.07666260004043579, -0.04169059544801712, -0.039604295045137405, 0.020155757665634155, -0.0388970784842968, 0.012332141399383545, -0.012243739329278469, -0.03350452706217766, -0.06191707402467728, -0.048550624400377274, -0.04572174698114395, -0.021234268322587013, -0.04837381839752197, -0.044590193778276443, -0.00031686751754023135, -0.02328520454466343, -0.011191749945282936, -0.03790697082877159, 0.051379501819610596, -0.04002862796187401, 0.029331931844353676, 0.03659861534833908, -0.02876615710556507, -0.03498968854546547, 0.002160334726795554, 0.030852453783154488, 0.0024708483833819628, -0.012986320070922375, -0.00779709592461586, 0.040983375161886215, 0.026343930512666702, -0.033257000148296356, 0.0028819197323173285, 0.04179667681455612, 0.013896864838898182, 0.05862850323319435, -0.023055357858538628, -0.10976047813892365, 0.01297747902572155, -0.00613512983545661, 0.023143760859966278, -0.02210061252117157, 0.0646752342581749, -0.013419491238892078, 0.0024067566264420748, 0.01692906953394413, 0.02982698567211628, -0.0012542097829282284, -0.03136518970131874, 0.008305409923195839, 0.042185649275779724, 0.01487813238054514, -0.009971796534955502, -0.0032642604783177376, 0.008888865821063519, -0.0022166913840919733, -0.016575459390878677, -0.037164390087127686, 0.07645043730735779, 0.011174069717526436, 0.005688697565346956, 0.011395075358450413, -0.005264365579932928, -0.026308568194508553, 0.03532561659812927, -0.008451273664832115, 0.01693790964782238, 0.038437385112047195, -0.017415281385183334, -0.001812250236980617, -0.017733531072735786, -0.002963692182675004, -0.016018522903323174, -0.01297747902572155, 0.004470953717827797, 0.025601349771022797, -0.012102294713258743, -0.04964681342244148, -0.022383499890565872, 0.03790697082877159, 0.017371080815792084, 0.01680530607700348, -0.025106295943260193, 0.012102294713258743, -0.08331046998500824, 0.041124820709228516, 0.043564725667238235, -0.00683350907638669, -0.021287309005856514, 0.01236750278621912, -0.0008956273086369038, 0.01936013624072075, -0.017415281385183334, 0.0035935596097260714, 0.024169228971004486, 0.012181857600808144, -0.01167796365916729, 0.01844075135886669, 0.0017868344439193606, 0.002036571502685547, 0.04296359047293663, 0.03242601826786995, -0.039604295045137405, 0.05809808894991875, 0.014294675551354885, -0.038083773106336594, 0.013693539425730705, -0.04441339150071144, -0.004698589909821749, 0.02349737100303173, 0.013720059767365456, -0.00014724532957188785, -0.01687602698802948, 0.03642180934548378, -0.03543170168995857, 0.016363292932510376, -0.046181440353393555, -0.021039782091975212, -0.008756262250244617, 0.007576089818030596, 0.02982698567211628, 0.04009934887290001, 0.02455819956958294, -0.02482340671122074, -0.020438646897673607, -0.003998000640422106, 0.01829930767416954, 0.07348011434078217, 0.026750581339001656, 0.005759419407695532, -0.007991581223905087, -0.03495432808995247, -0.0646398738026619, 0.017848454415798187, 0.022560304030776024, 0.0019923702348023653, 0.04052368178963661, 0.0008840244845487177, -0.01235866267234087, 0.022772470489144325, 0.012146496213972569, 0.011412756517529488, 0.04720690846443176, 0.014241634868085384, 0.0007917543989606202, -0.010873501189053059, -0.013136603869497776, -0.039356768131256104, 0.03102925978600979, 0.0029703222680836916, -0.004592507146298885, 0.04289286956191063, 0.07871353626251221, 0.01167796365916729, 0.001715007470920682, -0.019996633753180504, -0.03392885997891426, -0.004672069568186998, 0.06608966737985611, -0.027723006904125214, 0.009529784321784973, 0.014975374564528465, -0.0012597348541021347, 0.042221009731292725, -0.025318460538983345, -0.02970322221517563, 0.0387909933924675, -0.014126711525022984, -0.0019603243563324213, 0.02210061252117157, -0.044908445328474045, 0.007699853274971247, 0.05579962581396103, -0.016071565449237823, 0.05558745935559273, 0.012164176441729069, 0.05587034672498703, 0.02980930544435978, -0.054066937416791916, -0.04423658549785614, 0.026202484965324402, 0.003925068769603968, 0.09314081817865372, 0.017503684386610985, -0.0015348874730989337, 0.010210482403635979, 0.018546832725405693, -0.0387556329369545, -0.0007116397027857602, -0.04381225258111954, 0.01236750278621912, 0.041018735617399216, -0.03470680117607117, 0.050106506794691086, -0.03352220728993416, -0.004795833025127649, 0.012597348541021347, 0.039887186139822006, 0.030675649642944336, 0.04190276190638542, -0.0012453694362193346, 0.005631235893815756, -0.026467692106962204, 0.013216165825724602, 0.002307303948327899, 0.017751211300492287, -0.006647863890975714, 0.03129446506500244, 0.03140055015683174, 0.04321111738681793, -0.0049372767098248005, 0.030357399955391884, 0.012473585084080696, 0.04130162298679352, -0.02722795493900776, -0.008491055108606815, 0.036952223628759384, -0.031842563301324844, 0.039568934589624405, 0.019925910979509354, 0.023939382284879684, -0.011342033743858337, 0.015850558876991272, -0.005233424715697765, 0.021817725151777267, -0.003925068769603968, 0.05505704507231712, 0.02977394498884678, -0.0011702274205163121, 0.08946327865123749, -0.0129509586840868, -0.005374868866056204, -0.01102378498762846, -0.013684699311852455, 0.016398653388023376, -0.019784467294812202, 0.008557356894016266, 0.006104188971221447, 0.017211956903338432, -0.00041190016781911254, 0.00291728088632226, -0.05074300616979599, -0.06294254213571548, 0.018476111814379692, -0.012181857600808144, 0.0038322461768984795, -0.008097664453089237, -0.013463692739605904, -0.0020144707523286343, 0.04954073205590248, 0.025565987452864647, -0.03617428243160248, -0.00838939193636179, -0.0523342490196228, -0.00008874777267919853, 0.020332563668489456, 0.010228163562715054, -0.0024929491337388754, -0.03408798575401306, 0.0646752342581749, -0.009688908234238625, -0.006979373283684254, -0.0038786574732512236, 0.018776679411530495, 0.012173017486929893, 0.02736939862370491, 0.0029327513184398413, 0.0194485392421484, -0.061669547110795975, -0.009591666050255299, 0.025230059400200844, -0.03468912094831467, 0.021181225776672363, 0.013605136424303055, 0.0028266683220863342, 0.053996216505765915, -0.021623238921165466, 0.004959377460181713, -0.02706882916390896, 0.030215956270694733, -0.008133024908602238, 0.008712061680853367, 0.039639659225940704, -0.0005389786674641073, -0.03387581929564476, 0.020562410354614258, 0.014648285694420338, 0.01578867807984352, -0.01363165769726038, -0.0010420439066365361, 0.0516977533698082, -0.029208168387413025, 0.018529152497649193, 0.02095138095319271, 0.01583287864923477, 0.002848768839612603, -0.017680490389466286, 0.02862471342086792, 0.009220375679433346, -0.048550624400377274, 0.039533574134111404, -0.006090928800404072, 0.0001200339465867728, 0.033133238554000854, 0.013472532853484154, 0.02339128777384758, 0.0391799658536911, 0.04936392605304718, 0.0006099768797867, -0.011509998701512814, 0.018776679411530495, -0.03002147190272808, 0.01960766315460205, -0.028872240334749222, -0.037093665450811386, -0.010829299688339233, -0.003536097938194871, -0.013278047554194927, -0.00007548740541096777, 0.03203704580664635, 0.023656494915485382, 0.0013359820004552603, -0.025583667680621147, 0.011403915472328663, 0.03346916660666466, 0.016045045107603073, -0.025583667680621147, -0.01158956065773964, 0.0024708483833819628, 0.014444960281252861, 0.04275142401456833, -0.00453062541782856, 0.0784306526184082, -0.005233424715697765, 0.006740686483681202, 0.055304571986198425, 0.035732269287109375, -0.025477586314082146, -0.013295727781951427, 0.006652284413576126, -0.011509998701512814, -0.00016837903240229934, -0.035838354378938675, 0.020049674436450005, -0.0034874766133725643, 0.002316144062206149, 0.007801515981554985, -0.03131214901804924, -0.02197684906423092, 0.009105452336370945, -0.03398190066218376, 0.011996212415397167, 0.044590193778276443, 0.057638395577669144, 0.04992970451712608, 0.00021589535754173994, -0.033186279237270355, -0.0032907810527831316, -0.005467691458761692, -0.025336140766739845, 0.020085036754608154, -0.03638644888997078, 0.002517259679734707, 0.038225218653678894, -0.00838055182248354, 0.030675649642944336, -0.032072409987449646, -0.0022034309804439545, 0.03783624619245529, -0.021022101864218712, -0.014710167422890663, 0.019236372783780098, -0.00004599689782480709, -0.026838982477784157, 0.02208293229341507, 0.031842563301324844, -0.01181056722998619, -0.0259019173681736, -0.026343930512666702, -0.039356768131256104, 0.006219112314283848, -0.04186739772558212, -0.035661548376083374, 0.0032355296425521374, -0.04388297349214554, -0.04073584824800491, 0.0038322461768984795, 0.006784887984395027, 0.011280152015388012, -0.010873501189053059, 0.004115134011954069, 0.03985182195901871, -0.004565986339002848, 0.004773732274770737, -0.041018735617399216, 0.006868870463222265, -0.011271311901509762, 0.017707010731101036, 0.03677541762590408, 0.03804841265082359, 0.011739845387637615, 0.00984803307801485, -0.0518391951918602, -0.02729867585003376, -0.03737655654549599, 0.006409177556633949, -0.024133868515491486, -0.020332563668489456, 0.0023426648695021868, -0.020031994208693504, 0.013180805370211601, 0.015143339522182941, 0.03748263791203499, 0.013322249054908752, 0.01941317692399025, 0.002036571502685547, 0.03113534301519394, 0.044979166239500046, 0.029650181531906128, -0.019006526097655296, 0.042079564183950424, 0.013180805370211601, -0.04589855298399925, -0.021269628778100014, 0.035926755517721176, -0.023780258372426033, 0.022931594401597977, -0.023850981146097183, 0.0023647653870284557, -0.04466091841459274, 0.017132394015789032, 0.00195921934209764, -0.01802525855600834, 0.0390031598508358, -0.0012663650559261441, 0.008893285878002644, 0.016354452818632126, -0.04009934887290001, 0.022737110033631325, -0.05597643181681633, 0.034282468259334564, -0.03516649454832077, 0.05710798129439354, -0.01098842453211546, 0.05947716534137726, -0.02855399064719677, -0.004508524667471647, -0.027723006904125214, -0.025035573169589043, -0.03373437374830246, 0.0130658820271492, 0.024469798430800438, -0.03230225294828415, -0.0034565357491374016, 0.027033468708395958, -0.020491687580943108, -0.01817554421722889, -0.008345191366970539, -0.005410229787230492, 0.011633762158453465, -0.009512103162705898, -0.03999326750636101, 0.02466428279876709, -0.023055357858538628, 0.056648287922143936, -0.014506842009723186, 0.006338455714285374, -0.007023574318736792, 0.035679228603839874, -0.01179288700222969, -0.011660282500088215, -0.07722838222980499, 0.03378741443157196, -0.04455483332276344, 0.016681542620062828, 0.011085666716098785, -0.01955462247133255, -0.019784467294812202, 0.01237634290009737, 0.002716165268793702, -0.03375205397605896, 0.06191707402467728, -0.0043604508973658085, 0.04823237657546997, -0.0070191542617976665, 0.00778825581073761, 0.0032731005921959877, -0.00047378186718560755, 0.009397179819643497, 0.026255527511239052, -0.02195916883647442, 0.03392885997891426, 0.010528731159865856, -0.013180805370211601, 0.014736687764525414, 0.014135551638901234, -0.024381395429372787, 0.039745740592479706, -0.00839381292462349, -0.007956220768392086, -0.006267733406275511, -0.006188171450048685, -0.034529995173215866, 0.03741191700100899, 0.00549421226605773, -0.031718797981739044, 0.029597138985991478, 0.013225005939602852, -0.021287309005856514, 0.00036825143615715206, -0.06941360235214233, 0.021623238921165466, -0.026343930512666702, -0.022878553718328476, -0.01664618030190468, 0.0009779520332813263, -0.03378741443157196, 0.029066724702715874, 0.0005265470826998353, 0.03224921226501465, 0.028889920562505722, 0.011748685501515865, -0.02061545103788376, -0.009503263048827648, -0.025000212714076042, 0.06937824189662933, 0.013348769396543503, -0.010935382917523384, 0.00013819789455737919, 0.02623784728348255, 0.008088824339210987, 0.004515155218541622, 0.015912441536784172, -0.038437385112047195, -0.008265628479421139, 0.02340896800160408, -0.013781941495835781, 0.0034189647994935513, -0.00963586661964655, -0.025442223995923996, -0.004751631524413824, 0.03417638689279556, 0.01309240236878395, 0.006784887984395027, 0.0009453537059016526, -0.00003902139360434376, 0.014727847650647163, -0.022737110033631325, -0.017203116789460182, -0.005087560974061489, 0.0013956537004560232, -0.022984636947512627, 0.0073506636545062065, -0.011943170800805092, -0.029243530705571175, 0.007187119219452143, -0.012111135758459568, -0.019307095557451248, 0.016080405563116074, 0.050247952342033386, 0.022966956719756126, 0.007310882676392794, -0.007518628146499395, 0.0521574430167675, -0.009680068120360374, -0.011483478359878063, 0.07411660999059677, 0.033009473234415054, -0.03118838369846344, 0.004466533660888672, -0.005635655950754881, 0.026379290968179703, -0.023090720176696777, -0.0013879184843972325, -0.034459274262189865, -0.018458431586623192, -0.024469798430800438, 0.015152179636061192, -0.025636710226535797, -0.02218901365995407, -0.006413597613573074, -0.03003915213048458, -0.04183203727006912, -0.025725113227963448 ]
Digital human recommendation system has been developed to help customers find their favorite products and is playing an active role in various recommendation contexts. How to timely catch and learn the dynamics of the preferences of the customers, while meeting their exact requirements, becomes crucial in the digital human recommendation domain. We design a novel practical digital human interactive recommendation agent framework based on Reinforcement Learning(RL) to improve the efficiency of the interactive recommendation decision-making by leveraging both the digital human features and the superior flexibility of RL. Our proposed framework learns through real-time interactions between the digital human and customers dynamically through the state-of-art RL algorithms, combined with multimodal embedding and graph embedding, to improve the accuracy of personalization and thus enable the digital human agent to timely catch the attention of the customer. Experiments on real business data demonstrate that our framework can provide better personalized customer engagement and better customer experiences.
[ -0.03278025984764099, -0.024502601474523544, -0.033697959035634995, -0.030247405171394348, 0.0073874881491065025, 0.015279712155461311, -0.013692090287804604, 0.020831799134612083, -0.028099985793232918, 0.011471254751086235, 0.016830625012516975, -0.021364064887166023, 0.005171241704374552, -0.02962336875498295, -0.018363185226917267, 0.03832316771149635, -0.0021015340462327003, 0.02340136095881462, -0.0046733892522752285, -0.015931278467178345, -0.015068640932440758, -0.009089822880923748, -0.03448718041181564, 0.05715438351035118, 0.03606562688946724, 0.034689076244831085, -0.009727624244987965, -0.0392775759100914, -0.08831948786973953, 0.0729755386710167, 0.021309003233909607, 0.035129573196172714, -0.0007221155101433396, -0.044416699558496475, -0.056199971586465836, -0.022960864007472992, 0.0439394973218441, 0.038800373673439026, 0.04041552543640137, 0.029660077765583992, -0.0035124982241541147, 0.02536523900926113, -0.06563393026590347, -0.0017172469524666667, 0.004790395963937044, -0.05010644346475601, 0.026301294565200806, 0.036909911781549454, -0.027567720040678978, 0.006726744119077921, 0.016454368829727173, -0.03452388942241669, -0.023951981216669083, 0.003055942477658391, -0.0369466170668602, 0.021015338599681854, 0.033881500363349915, -0.017004989087581635, 0.053593702614307404, 0.021309003233909607, 0.019436893984675407, 0.031293585896492004, -0.027090515941381454, 0.014343657530844212, -0.03340429440140724, -0.040488943457603455, 0.004076884128153324, 0.0073737227357923985, 0.03650612384080887, -0.014875923283398151, -0.0530063770711422, 0.011847511865198612, 0.026301294565200806, -0.038066212087869644, -0.03828646242618561, 0.010984874330461025, 0.02569561079144478, 0.04783054441213608, 0.026833560317754745, -0.012168707326054573, 0.04408632963895798, 0.03791937977075577, 0.003436787985265255, -0.0012710150331258774, 0.05704425647854805, -0.0316239558160305, 0.04349900037050247, -0.07224137336015701, -0.008507083170115948, -0.023603254929184914, -0.061008721590042114, 0.00671756686642766, -0.029329705983400345, -0.03472578525543213, -0.06952498108148575, 0.012700974009931087, -0.0666617602109909, 0.008484140038490295, -0.04114968702197075, 0.016123997047543526, -0.010883927345275879, -0.04526098445057869, -0.020391304045915604, -0.014306949451565742, 0.020409656688570976, -0.019969161599874496, -0.06559722870588303, 0.04445340856909752, -0.06813007593154907, 0.044049620628356934, -0.07455398142337799, -0.02330959029495716, 0.0029159931000322104, 0.034065037965774536, -0.0682402029633522, 0.022263411432504654, -0.033000506460666656, -0.07308565825223923, 0.048711538314819336, -0.06203654780983925, 0.008892516605556011, 0.018234707415103912, 0.003991996869444847, -0.01129689160734415, -0.0018858743133023381, 0.03595550358295441, -0.033349234610795975, 0.013049700297415257, 0.04294838011264801, 0.0005810190923511982, -0.06790982931852341, 0.03791937977075577, -0.042361050844192505, 0.008227184414863586, 0.0074333734810352325, 0.036542829126119614, 0.02615446224808693, -0.03643270581960678, 0.0040218220092356205, 0.0004416433221194893, -0.01626165211200714, -0.040048446506261826, -0.042287636548280716, 0.009507376700639725, 0.039424408227205276, 0.028191756457090378, -0.037185221910476685, 0.014077524654567242, -0.045407816767692566, 0.007905988954007626, -0.05990748107433319, 0.015784448012709618, -0.045224275439977646, -0.006423902697861195, 0.03123852238059044, -0.014215179719030857, -0.01908816769719124, -0.050216566771268845, -0.03144041448831558, -0.01724359020590782, 0.07525143027305603, 0.006130238529294729, -0.0060843536630272865, 0.05542910471558571, 0.03375302255153656, 0.011370307765901089, -0.01258167251944542, -0.04239775985479355, -0.07591217756271362, 0.04544452577829361, -0.07561851292848587, 0.028705669566988945, -0.008727330714464188, 0.039240870624780655, -0.014306949451565742, 0.027255702763795853, 0.05186842754483223, -0.09485351294279099, -0.07161734253168106, 0.009562438353896141, -0.03481755405664444, 0.05605314299464226, 0.049152035266160965, 0.038249753415584564, 0.05216209217905998, 0.028173401951789856, 0.05594301596283913, -0.007717860396951437, -0.0005982259754091501, 0.0020418833009898663, 0.0015658263582736254, 0.016564492136240005, 0.04346229135990143, 0.010269067250192165, 0.013233239762485027, -0.04232434183359146, -0.016977457329630852, -0.004634386859834194, -0.021676084026694298, 0.00556126469746232, -0.04452682286500931, -0.07649950683116913, 0.01253578718751669, -0.03386314585804939, -0.0067450981587171555, -0.029605016112327576, 0.01411423273384571, -0.024943096563220024, -0.008195064961910248, -0.042287636548280716, 0.020060930401086807, -0.024337414652109146, -0.058879658579826355, 0.015958810225129128, -0.04390278831124306, -0.0046963319182395935, 0.018087875097990036, -0.0053960783407092094, 0.009489022195339203, -0.02204316481947899, -0.0046252100728452206, -0.006088942289352417, 0.028099985793232918, -0.007337014656513929, -0.013095584698021412, -0.001502734376117587, -0.0002211084502050653, 0.044343285262584686, -0.007974816486239433, -0.029880326241254807, 0.0024204347282648087, 0.031385354697704315, 0.014518020674586296, 0.008185887709259987, 0.007254421710968018, 0.009571615606546402, 0.0047674537636339664, -0.0767197534441948, -0.02402539737522602, -0.012554141692817211, 0.008814512751996517, -0.04445340856909752, 0.04118639603257179, -0.004471495281904936, 0.05777841806411743, -0.02580573596060276, -0.004753688350319862, 0.05341016501188278, 0.03909403830766678, 0.03375302255153656, -0.02310769632458687, -0.025053221732378006, -0.02492474392056465, 0.03133029118180275, -0.010828864760696888, 0.06838703155517578, 0.08545625954866409, -0.03909403830766678, 0.020207762718200684, -0.021822916343808174, 0.0004092370218131691, 0.024447539821267128, 0.045738186687231064, 0.01910652220249176, -0.029439829289913177, 0.00403788173571229, 0.06629467755556107, 0.008410723879933357, 0.01838153973221779, 0.0013031346024945378, 0.02910945750772953, -0.007355368696153164, -0.0057356273755431175, -0.014444604516029358, -0.030027156695723534, -0.041920553892850876, 0.00719018280506134, -0.051207683980464935, 0.07811465859413147, 0.024080459028482437, 0.004579325206577778, 0.010021288879215717, 0.03193597495555878, -0.008213418535888195, -0.05473165214061737, 0.006988288834691048, -0.06277070939540863, -0.039864905178546906, -0.007304895203560591, 0.04437999054789543, -0.008374015800654888, -0.03305556997656822, -0.026631666347384453, -0.005529144778847694, 0.06831362098455429, 0.02927464246749878, -0.016748031601309776, 0.01938183233141899, 0.005753981415182352, -0.042801547795534134, 0.006740509532392025, -0.040488943457603455, 0.025585487484931946, 0.0015256769256666303, -0.007392076775431633, 0.020960276946425438, 0.001207923167385161, 0.03971807286143303, 0.00267968513071537, -0.012600027024745941, 0.027457596734166145, 0.004785807803273201, -0.007667386904358864, 0.013921515084803104, 0.01253578718751669, 0.05062035471200943, 0.023327944800257683, -0.004613738972693682, 0.020574843510985374, -0.053960785269737244, -0.03608398139476776, 0.022887447848916054, -0.08097788691520691, 0.033349234610795975, 0.012398132123053074, 0.039864905178546906, 0.02009763941168785, -0.030779670923948288, 0.004827104043215513, 0.004987701773643494, -0.06163275986909866, -0.02499816007912159, 0.009736801497638226, 0.0006108443485572934, -0.004095238167792559, -0.014527197927236557, -0.00000918596560950391, -0.009883633814752102, -0.027659490704536438, 0.002298839623108506, 0.021033693104982376, 0.004831692669540644, -0.013728798367083073, -0.007621502038091421, -0.03876366466283798, -0.043425582349300385, -0.02009763941168785, 0.05194184184074402, -0.008612618781626225, 0.022960864007472992, 0.0009561291080899537, -0.013471841812133789, 0.01232471689581871, -0.004111297894269228, 0.07033255696296692, -0.050767187029123306, 0.024869680404663086, -0.02169443853199482, -0.03909403830766678, -0.032706841826438904, 0.03230305388569832, -0.054584819823503494, -0.0872916653752327, 0.016821447759866714, -0.022795679047703743, -0.001577297574840486, -0.038873787969350815, 0.024337414652109146, 0.010076350532472134, 0.0057585700415074825, -0.021676084026694298, 0.026264585554599762, -0.008851220831274986, 0.0505102314054966, -0.020281178876757622, 0.01352690439671278, 0.014160117134451866, -0.03613904118537903, -0.012691796757280827, 0.06060493364930153, 0.03131193667650223, -0.019308416172862053, -0.047169800847768784, 0.01504111010581255, 0.020226117223501205, 0.05256588011980057, -0.011829158291220665, -0.046655889600515366, 0.001296251779422164, 0.05421774089336395, 0.04283825680613518, -0.01293957605957985, -0.03865354135632515, -0.003308309940621257, 0.007548085879534483, -0.02499816007912159, 0.04731663316488266, 0.02705380879342556, 0.02846706658601761, -0.04430657625198364, -0.0263380017131567, -0.00015701280790381134, 0.010314952582120895, 0.0005517673562280834, -0.0009555555297993124, -0.034230224788188934, -0.0036088568158447742, -0.03439541161060333, 0.004076884128153324, 0.011618087068200111, -0.004425610415637493, -0.009085234254598618, -0.05810879170894623, -0.0028953447472304106, 0.0031981859356164932, 0.004689448978751898, -0.049041908234357834, -0.00598340667784214, 0.037460532039403915, -0.07253503799438477, -0.0038382820785045624, 0.028191756457090378, 0.08457527309656143, 0.02909110300242901, -0.06768958270549774, 0.028632253408432007, -0.03500109538435936, -0.012820274569094181, -0.04239775985479355, -0.020281178876757622, 0.021198879927396774, 0.027879739180207253, 0.006832279730588198, -0.1010204628109932, -0.044600240886211395, 0.03590044006705284, -0.006125650368630886, 0.03193597495555878, -0.03698332607746124, -0.0002515072701498866, -0.0455179400742054, -0.08464868366718292, -0.023089341819286346, 0.03971807286143303, 0.006868987809866667, 0.004443964455276728, 0.052015259861946106, 0.006322955712676048, -0.014132586307823658, 0.0006859810673631728, -0.06464281678199768, 0.0034689076710492373, -0.01348101906478405, -0.0275860745459795, -0.004668800625950098, -0.015784448012709618, 0.01468320656567812, -0.010314952582120895, 0.015243004076182842, -0.023070989176630974, -0.012031052261590958, 0.04654576629400253, 0.01379303727298975, -0.019033106043934822, -0.019859036430716515, 0.025053221732378006, -0.03175243362784386, 0.009571615606546402, 0.005318074021488428, 0.04247117415070534, 0.000026814059310709126, 0.0005236627766862512, 0.04188384860754013, -0.006052234210073948, 0.012930398806929588, -0.03144041448831558, 0.020501427352428436, -0.0321195125579834, -0.007924343459308147, 0.0011465519201010466, -0.007460904307663441, 0.029036041349172592, 0.05898978188633919, -0.025328531861305237, 0.008254715241491795, 0.014738268218934536, 0.05818220600485802, 0.024172229692339897, 0.00730030657723546, 0.008442843332886696, -0.05777841806411743, -0.007942697033286095, -0.013921515084803104, 0.015408189967274666, -0.05043681338429451, -0.01704169623553753, -0.017518900334835052, -0.02562219463288784, 0.06622125953435898, -0.016830625012516975, -0.007979405112564564, 0.01371044386178255, -0.011801627464592457, -0.015830332413315773, -0.03839658573269844, 0.04100285470485687, 0.028687315061688423, -0.0299170333892107, -0.0280449241399765, 0.022098226472735405, -0.0061072963289916515, 0.049225449562072754, -0.023639962077140808, -0.014187647961080074, 0.01733536086976528, 0.015086994506418705, -0.030210698023438454, 0.015151233412325382, 0.0342852883040905, 0.023511484265327454, 0.04151676595211029, 0.024319060146808624, -0.021639375016093254, 0.01838153973221779, -0.08457527309656143, -0.009424783289432526, 0.031991034746170044, 0.006125650368630886, 0.03133029118180275, 0.008057409897446632, -0.019235000014305115, 0.027274055406451225, 0.0025420300662517548, -0.029770201072096825, -0.0238418560475111, -0.021088754758238792, 0.0389472059905529, 0.004900520201772451, 0.03902062028646469, -0.015775270760059357, -0.035478297621011734, 0.10168120265007019, 0.023052634671330452, 0.02553042583167553, 0.00645143399015069, -0.0299170333892107, 0.03373466804623604, -0.049041908234357834, -0.0319543294608593, 0.03177078813314438, 0.009383486583828926, -0.0055658528581261635, 0.02793480083346367, -0.02241024374961853, 0.002431906061246991, -0.012957929633557796, -0.02631964720785618, -0.01873944327235222, -0.012104468420147896, -0.04114968702197075, 0.0227589700371027, 0.0054557290859520435, -0.005864105653017759, -0.003943817690014839, -0.005024409852921963, -0.011269360780715942, 0.00567138846963644, 0.02973349392414093, 0.036909911781549454, 0.013196531683206558, -0.05124438926577568, -0.0000072277871367987245, -0.025842443108558655, -0.029513245448470116, -0.02231847494840622, 0.023768439888954163, -0.002014352474361658, -0.028503775596618652, -0.029164519160985947, 0.02749430388212204, 0.005510791204869747, -0.012471548281610012, 0.014866746962070465, -0.015545845031738281, 0.00991116464138031, 0.023181112483143806, -0.025420300662517548, -0.05605314299464226, 0.017885981127619743, -0.0215108972042799, 0.018592610955238342, 0.02464943379163742, 0.021198879927396774, -0.0032440710347145796, -0.040745899081230164, 0.002211658051237464, 0.01936347782611847, 0.001747072208672762, 0.021767854690551758, -0.06335803866386414, 0.006570735014975071, 0.045040737837553024, 0.04243446886539459, 0.035753607749938965, -0.017023341730237007, 0.026448125019669533, 0.03347771242260933, -0.012719327583909035, 0.03338593989610672, 0.03446882590651512, -0.020850153639912605, 0.03256000950932503, 0.08384110778570175, -0.023584900423884392, 0.018629318103194237, -0.01936347782611847, 0.04338887706398964, 0.024576017633080482, -0.014288595877587795, -0.03169737383723259, -0.005731039214879274, -0.03610233590006828, 0.1034431904554367, 0.0044783782213926315, -0.030687902122735977, 0.01081051118671894, 0.02721899375319481, -0.02285074070096016, -0.0009429371566511691, -0.007116766646504402, -0.004159477073699236, 0.03180749714374542, -0.019693851470947266, -0.018996398895978928, 0.019235000014305115, -0.005373136140406132, -0.00224263034760952, 0.03997502848505974, 0.048527996987104416, 0.027035454288125038, -0.053520288318395615, 0.04412303492426872, -0.02687026746571064, 0.08061080425977707, -0.006148592568933964, 0.01204940676689148, 0.03322075307369232, 0.015142057090997696, 0.059063199907541275, 0.0072635989636182785, -0.0232178196310997, -0.002130212029442191, 0.017362892627716064, 0.022648846730589867, -0.00033094570972025394, -0.019877390936017036, 0.018005281686782837, 0.0014407896669581532, 0.016215765848755836, -0.0075664399191737175, 0.019657142460346222, 0.007676564157009125, 0.03485426306724548, -0.015160410664975643, 0.009782686829566956, 0.0161423496901989, 0.05410761758685112, -0.017629025503993034, 0.023621609434485435, 0.06530356407165527, -0.01022318284958601, -0.025383593514561653, -0.05649363622069359, 0.029072748497128487, 0.026209523901343346, -0.008915459737181664, 0.03044929914176464, 0.047463465481996536, -0.007529731839895248, -0.028430359438061714, -0.03982819616794586, -0.03410174697637558, -0.01348101906478405, -0.016913218423724174, -0.025750674307346344, -0.018730266019701958, -0.014472135342657566, 0.0024846738670021296, -0.020428011193871498, 0.01929006353020668, -0.015610083937644958, 0.010342483408749104, 0.03180749714374542, -0.015160410664975643, -0.0017757503082975745, 0.012866159901022911, -0.0288341473788023, -0.05190513655543327, -0.007515966426581144, -0.009856102056801319, 0.00734160328283906, -0.014930985867977142, 0.002592503558844328, 0.00745631568133831, 0.015187941491603851, -0.0067450981587171555, -0.0013983460376039147, 0.04511415213346481, -0.057888541370630264, -0.04849128797650337, 0.027714552357792854, 0.005625503603368998, 0.020281178876757622, 0.034046683460474014, 0.02518169954419136, 0.0161423496901989, 0.007057116366922855, -0.02954995259642601, -0.0039988793432712555, 0.030302466824650764, 0.0501798577606678, -0.02865060605108738, 0.07326920330524445, -0.03525805100798607, -0.023089341819286346, 0.004677977878600359, 0.03935099393129349, -0.0032853675074875355, -0.008424489758908749, -0.00811706017702818, 0.03000880405306816, 0.012746858410537243, -0.04823433235287666, 0.009755155071616173, -0.027384180575609207, -0.017436306923627853, -0.009534907527267933, 0.04739004746079445, -0.007451727520674467, -0.0025902094785124063, -0.011819981038570404, -0.04214080423116684, -0.021492544561624527, -0.00597881805151701, 0.00008746831736061722, -0.029935387894511223, -0.004203068092465401, 0.010425076819956303, -0.033716313540935516, -0.006194477900862694, 0.012746858410537243, 0.01169150322675705, 0.048527996987104416, -0.04437999054789543, -0.0501798577606678, 0.026099400594830513, 0.020207762718200684, -0.017206883057951927, 0.04992290213704109, 0.009337601251900196, -0.0060476455837488174, 0.0564202219247818, -0.032174576073884964, 0.027163932099938393, 0.03463401272892952, -0.015105349011719227, -0.010113058611750603, -0.00571268517524004, 0.0009280245285481215, -0.03026575967669487, 0.02009763941168785, 0.017078405246138573, 0.019602080807089806, -0.04918874055147171, -0.003113298676908016, -0.04162688925862312, 0.019400186836719513, 0.015096171759068966, -0.020391304045915604, 0.006277070846408606, -0.0252551157027483, 0.006391783244907856, 0.0196387879550457, 0.060127731412649155, -0.022979218512773514, 0.009782686829566956, -0.010856395587325096, -0.0028586366679519415, 0.043682537972927094, 0.009938695468008518, 0.014573082327842712, 0.033697959035634995, -0.023584900423884392, 0.017179351300001144, 0.02954995259642601, -0.003267013467848301, 0.011939282529056072, 0.012086114846169949, 0.035221341997385025, -0.01437118835747242, 0.02534688450396061, -0.025677258148789406, -0.019143231213092804, 0.06835032999515533, -0.03278025984764099, 0.04463694989681244, 0.004581619519740343, 0.00008653628174215555, 0.010333307087421417, 0.046288806945085526, 0.00022282912686932832, 0.021143818274140358, 0.013260770589113235, -0.034615658223629, 0.03525805100798607, -0.03975478187203407, -0.002904521767050028, 0.044049620628356934, -0.033514417707920074, -0.041773721575737, 0.012921221554279327, -0.04188384860754013, -0.03448718041181564, 0.01795939728617668, -0.030596131458878517, -0.01769326440989971, 0.016445191577076912, -0.006231185980141163, 0.00567138846963644, -0.018005281686782837, 0.020317887887358665, 0.022189995273947716, 0.004118180368095636, -0.03993832319974899, -0.010186474770307541, 0.04327875003218651, -0.002043030457571149, 0.048931784927845, 0.00871356576681137, 0.031991034746170044, -0.000012241979675309267, 0.0033840201795101166, -0.01766573265194893, -0.03810292109847069, -0.038249753415584564, -0.020923569798469543, -0.019877390936017036, 0.002147418912500143, -0.004836281295865774, 0.018445778638124466, 0.009791863150894642, 0.0074333734810352325, 0.07154392451047897, 0.010883927345275879, 0.021822916343808174, 0.0005626650527119637, 0.0007416166481561959, 0.05014314875006676, 0.01688568666577339, -0.015646792948246002, 0.026301294565200806, -0.011407015845179558, -0.02224505878984928, -0.007593970745801926, 0.024043750017881393, -0.04045223444700241, -0.00033008537138812244, -0.0244658924639225, -0.016280004754662514, -0.00033266638638451695, 0.007093823980540037, 0.012462371960282326, -0.02330959029495716, 0.02169443853199482, -0.009709270671010017, 0.0070479391142725945, 0.01134277693927288, 0.0027531012892723083, 0.011535494588315487, -0.0505102314054966, 0.013985753990709782, 0.0036547419149428606, -0.007892224006354809, 0.002571855438873172, 0.07279199361801147, -0.0396079495549202, -0.05223550647497177, -0.010085527785122395, 0.023511484265327454, -0.03551500663161278, 0.010048819705843925, 0.03828646242618561, 0.03632258251309395, -0.056089848279953, 0.04841787368059158, 0.0017011871095746756, -0.03505615517497063, 0.021676084026694298, 0.006497318856418133, 0.03511121869087219, -0.002317193429917097, -0.02608104608952999, 0.01596798747777939, -0.03345935791730881, 0.023896919563412666, 0.030963212251663208, 0.034615658223629, -0.01677556335926056, 0.04918874055147171, -0.0589163675904274, -0.01632589101791382, 0.002059090184047818, 0.022703908383846283, -0.04313191771507263, -0.011526317335665226, -0.03527640551328659, -0.03839658573269844, -0.03158724680542946, 0.022079871967434883, -0.04346229135990143, 0.034432120621204376, 0.04750017449259758, -0.0294581837952137, 0.03373466804623604, -0.046472348272800446, 0.03869025036692619, -0.033000506460666656, 0.04948240518569946, -0.03624916449189186, -0.012251300737261772, -0.017555609345436096, 0.03221128508448601, 0.02437412366271019, 0.008805335499346256, 0.025603841990232468, 0.009144884534180164, -0.04456353187561035, 0.006469788029789925, -0.02160266786813736, -0.005919167771935463, 0.03391820564866066, 0.006166946608573198, -0.032725196331739426, -0.012600027024745941, 0.0028448712546378374, -0.019253354519605637, -0.010856395587325096, 0.02061155065894127, 0.02865060605108738, -0.009255008772015572, -0.05528227239847183, 0.011150060221552849, -0.03314733877778053, 0.006676270626485348, -0.016536962240934372, -0.02901768684387207, -0.019033106043934822, 0.007901400327682495, -0.00007821962208254263, 0.021822916343808174, -0.02999044954776764, 0.0006882753223180771, -0.016390129923820496, -0.01321488618850708, -0.04981277883052826, 0.010012111626565456, -0.012682619504630566, 0.004049352835863829, -0.035680193454027176, 0.029146164655685425, 0.02196974866092205, -0.006841456517577171, -0.006318367552012205, 0.002431906061246991, 0.014279418624937534, 0.023768439888954163, -0.03292709216475487, -0.0021738028153777122, -0.07374640554189682, 0.01822553016245365, 0.02072167582809925, 0.002798986155539751, -0.00019730559142772108, 0.0028448712546378374, 0.0025190876331180334, -0.04338887706398964, 0.03367960453033447, 0.005281365942209959, 0.02134571224451065, -0.028320234268903732, -0.0601644404232502, -0.021143818274140358, -0.019767267629504204, -0.040305402129888535, -0.03714851289987564, -0.012994637712836266, -0.01044343039393425, -0.029164519160985947, 0.005593384150415659, 0.039314284920692444, -0.025475364178419113, -0.0033564893528819084, -0.0215108972042799, 0.04305850341916084, -0.012251300737261772, 0.001499293022789061, 0.042728129774332047, 0.025034867227077484, -0.01587621681392193, 0.06295424699783325, 0.015922103077173233, 0.027384180575609207, 0.011049113236367702, -0.014765799976885319, -0.03891049697995186, 0.005061117932200432, -0.027696197852492332, -0.004207656253129244, 0.02999044954776764, -0.0610821396112442, 0.037809256464242935, 0.04041552543640137, 0.05572276934981346, -0.028063278645277023 ]
Understanding which student support strategies mitigate dropout and improve student retention is an important part of modern higher educational research. One of the largest challenges institutions of higher learning currently face is the scalability of student support. Part of this is due to the shortage of staff addressing the needs of students, and the subsequent referral pathways associated to provide timeous student support strategies. This is further complicated by the difficulty of these referrals, especially as students are often faced with a combination of administrative, academic, social, and socio-economic challenges. A possible solution to this problem can be a combination of student outcome predictions and applying algorithmic recommender systems within the context of higher education. While much effort and detail has gone into the expansion of explaining algorithmic decision making in this context, there is still a need to develop data collection strategies Therefore, the purpose of this paper is to outline a data collection framework specific to recommender systems within this context in order to reduce collection biases, understand student characteristics, and find an ideal way to infer optimal influences on the student journey. If confirmation biases, challenges in data sparsity and the type of information to collect from students are not addressed, it will have detrimental effects on attempts to assess and evaluate the effects of these systems within higher education.
[ 0.00026229891227558255, 0.03038574941456318, -0.036136455833911896, -0.039287008345127106, 0.01876096986234188, -0.0014744490617886186, -0.005072199739515781, 0.008142090402543545, -0.037977442145347595, -0.009119520895183086, 0.024635042995214462, -0.049953337758779526, -0.007677099201828241, -0.012393438257277012, 0.012032832950353622, 0.01383585948497057, 0.046954620629549026, 0.0151738952845335, 0.054318562150001526, -0.011387539096176624, -0.007140935864299536, -0.0797886922955513, -0.014462174847722054, 0.03970455378293991, 0.016654275357723236, 0.05234472081065178, 0.00009059617877937853, -0.021996930241584778, -0.06950194388628006, 0.03592768684029579, 0.05720340460538864, 0.054166726768016815, 0.003297641407698393, -0.06923623383045197, -0.04129880666732788, -0.003919211216270924, -0.01584765873849392, 0.010988974943757057, -0.001989260781556368, 0.036629918962717056, -0.002728264546021819, 0.04183022677898407, 0.0029156843665987253, 0.016312649473547935, 0.043652232736349106, -0.08396412432193756, -0.006633241660892963, -0.017726602032780647, -0.0636942982673645, 0.019131066277623177, 0.010837141424417496, -0.04019801318645477, 0.04737216234207153, -0.018580667674541473, -0.030082082375884056, 0.06244167312979698, 0.04668891057372093, -0.0049251108430325985, 0.0492321252822876, 0.050332922488451004, 0.0144906435161829, 0.06555426865816116, 0.051205966621637344, -0.047675829380750656, 0.01105540245771408, -0.030063103884458542, 0.0073212385177612305, 0.013797901570796967, -0.0021470256615430117, 0.0029228017665445805, -0.020421653985977173, 0.012345990166068077, 0.054166726768016815, -0.023192621767520905, -0.021977949887514114, 0.011359070427715778, 0.05898745357990265, 0.028753535822033882, -0.02355322614312172, -0.05158555135130882, 0.05371122434735298, 0.02884843200445175, -0.01041959784924984, -0.01808720827102661, 0.0351874940097332, -0.0402359701693058, 0.015430115163326263, -0.06449142843484879, 0.03993230313062668, 0.03175225481390953, -0.06502284854650497, 0.018969742581248283, 0.012659147381782532, -0.021294698119163513, -0.03997026011347771, -0.008735191076993942, -0.025584004819393158, 0.0005978458211757243, -0.03636420890688896, 0.028525784611701965, -0.0053806123323738575, 0.017584258690476418, -0.017081309109926224, 0.003957169596105814, 0.03078431449830532, -0.06646526604890823, -0.061151083558797836, -0.014699415303766727, 0.024635042995214462, 0.13877613842487335, -0.016654275357723236, -0.019795339554548264, -0.0609612911939621, -0.03924905136227608, -0.007250066380947828, 0.030803292989730835, -0.024198520928621292, -0.02753886580467224, 0.01681559905409813, -0.017612727358937263, 0.006139781326055527, 0.0499153807759285, -0.013294951990246773, 0.022528348490595818, -0.06384613364934921, 0.037540920078754425, -0.002692678477615118, -0.015743272379040718, 0.01313362829387188, -0.011026933789253235, 0.022869974374771118, 0.05910132825374603, -0.059746623039245605, 0.014993593096733093, -0.027349073439836502, 0.030575541779398918, 0.07864993810653687, 0.05477406084537506, -0.05481202155351639, -0.01502206176519394, -0.03294794633984566, -0.02526135742664337, -0.019225962460041046, 0.04327264800667763, 0.0068657370284199715, -0.01051449403166771, 0.007031805347651243, 0.03524443507194519, -0.048890501260757446, 0.06836318969726562, 0.0022300598211586475, 0.05705156922340393, 0.013095669448375702, 0.011624779552221298, 0.004109003581106663, -0.016635296866297722, -0.014528601430356503, 0.0020153571385890245, 0.0030034633819013834, 0.03160041943192482, 0.006685434374958277, 0.0057601965963840485, -0.0012621189234778285, 0.05614056810736656, 0.0010954575845971704, -0.022167742252349854, -0.01691998541355133, 0.0053948466666042805, -0.035206474363803864, 0.04114697501063347, -0.053103890269994736, -0.03503566235303879, -0.06657914817333221, 0.020004110410809517, 0.026931529864668846, -0.008711467497050762, 0.05253451317548752, 0.006158760748803616, -0.082369863986969, -0.01661631651222706, -0.06984357535839081, 0.018580667674541473, 0.008246475830674171, 0.013456275686621666, 0.02689357101917267, 0.05739319697022438, 0.08965788781642914, 0.015496542677283287, -0.03059452213346958, -0.009366250596940517, -0.015069509856402874, -0.011121829971671104, 0.022869974374771118, 0.04406977444887161, 0.031486544758081436, -0.041564516723155975, -0.04809337481856346, 0.011615289375185966, -0.006713903043419123, 0.004929855465888977, -0.05986049771308899, -0.07758709788322449, 0.015790721401572227, 0.03188510984182358, 0.002238363027572632, 0.07728343456983566, 0.0683252364397049, 0.03416261821985245, -0.022015908733010292, -0.02554604597389698, -0.005883561912924051, -0.03190409019589424, 0.009973586536943913, 0.04095718264579773, -0.00901513546705246, 0.006296359933912754, -0.004168313927948475, 0.05545731633901596, -0.0009537063888274133, -0.04289306327700615, 0.017603237181901932, -0.024103624746203423, 0.0004549084696918726, -0.04501873627305031, 0.021921012550592422, 0.004948834888637066, 0.021788157522678375, 0.01861862652003765, -0.005902540870010853, -0.06312492489814758, -0.008099387399852276, 0.04915621131658554, -0.02729213424026966, 0.004258465021848679, 0.04748603701591492, 0.03759785741567612, -0.009764814749360085, -0.01784047856926918, -0.00507694436237216, 0.023534247651696205, -0.03611747920513153, 0.004438767675310373, -0.03670583292841911, -0.013883307576179504, 0.05374918505549431, 0.02753886580467224, -0.019206982105970383, 0.04942191764712334, 0.038357026875019073, 0.03397282585501671, -0.005015261936932802, 0.010210826992988586, 0.007928574457764626, 0.024350354447960854, 0.04008413851261139, 0.015771741047501564, 0.059253159910440445, -0.029930248856544495, 0.020687362179160118, -0.020535528659820557, 0.026001546531915665, -0.005167095921933651, 0.00833662785589695, 0.014452684670686722, 0.014101569540798664, -0.011235705576837063, 0.07022316008806229, 0.01958656683564186, 0.02317364141345024, -0.011795592494308949, 0.03917313367128372, 0.010837141424417496, 0.01080867275595665, -0.016454994678497314, 0.02292691171169281, -0.03602258116006851, 0.06399796903133392, -0.06521263718605042, -0.0011731537524610758, 0.01924494095146656, -0.006054374855011702, -0.03543422371149063, -0.0024435759987682104, -0.02753886580467224, -0.054849978536367416, -0.033915888518095016, -0.026115423068404198, -0.034200575202703476, -0.046840742230415344, -0.03234061226248741, -0.025413190945982933, -0.02753886580467224, -0.030556563287973404, -0.006557324435561895, 0.05788665637373924, 0.008815852925181389, -0.03309978172183037, 0.052079010754823685, -0.0072927698493003845, -0.05705156922340393, 0.011985384859144688, -0.039135176688432693, 0.009821752086281776, -0.01710977777838707, -0.020915113389492035, 0.006030650809407234, -0.004248975310474634, 0.023932810872793198, -0.04976354539394379, -0.033858947455883026, 0.05025700479745865, -0.011264174245297909, -0.0011025747517123818, -0.0358707495033741, 0.018333937972784042, 0.040349844843149185, 0.05420468747615814, -0.013067200779914856, -0.04300693795084953, -0.06923623383045197, -0.017290079966187477, -0.013703005388379097, -0.08274944871664047, -0.0047305733896791935, -0.04790358245372772, -0.031106960028409958, -0.05989845469594002, -0.03873661160469055, 0.011254684068262577, -0.021389594301581383, -0.01185252983123064, 0.006661710329353809, 0.04782766476273537, -0.01286791916936636, 0.026931529864668846, -0.030708396807312965, 0.02951270528137684, -0.0064244698733091354, -0.04778970405459404, 0.014557071030139923, -0.04126084968447685, -0.0439179427921772, -0.05595077574253082, -0.029531683772802353, 0.022794056683778763, 0.03590870648622513, 0.012393438257277012, 0.042095936834812164, 0.019406264647841454, -0.025944609194993973, 0.001117402222007513, 0.01466145645827055, -0.063428595662117, 0.06972970068454742, 0.06111312657594681, -0.012877408415079117, 0.0007769623189233243, 0.008374585770070553, 0.00503898598253727, -0.01710977777838707, 0.05052271485328674, -0.025944609194993973, -0.04722032696008682, 0.014727883972227573, -0.03461811691522598, -0.012611699290573597, -0.00785265676677227, 0.004239486064761877, 0.051395758986473083, -0.04308285564184189, -0.011719675734639168, 0.022718140855431557, 0.02452116645872593, -0.009389975108206272, -0.023287517949938774, 0.009745835326611996, 0.008203772827982903, 0.031182877719402313, -0.03854681923985481, 0.02583073452115059, 0.03568095713853836, -0.0009620098280720413, 0.0042537203989923, 0.05078842490911484, -0.015031551942229271, -0.00024791620671749115, 0.04968762770295143, 0.04520852863788605, -0.027899470180273056, 0.04809337481856346, 0.03044268675148487, 0.010761224664747715, -0.026001546531915665, -0.043310604989528656, -0.004182548262178898, 0.017612727358937263, -0.003402027301490307, -0.03068941831588745, 0.0328720286488533, 0.010030523873865604, -0.03163838014006615, -0.01115029864013195, -0.040691472589969635, 0.0059404997155070305, 0.0005269702523946762, -0.0013083807425573468, 0.027121322229504585, -0.004350988660007715, 0.01744191348552704, -0.008028214797377586, 0.03590870648622513, 0.0368197076022625, 0.016350608319044113, 0.058342158794403076, 0.0402359701693058, 0.033669158816337585, -0.03731317073106766, 0.04513261467218399, -0.001044450793415308, -0.01576225273311138, 0.008730446919798851, 0.07250066846609116, -0.015430115163326263, -0.008483716286718845, 0.0068372683599591255, 0.015477563254535198, -0.03784458711743355, -0.032492443919181824, -0.009019879624247551, -0.0033308551646769047, 0.011529883369803429, 0.03917313367128372, -0.013200055807828903, -0.023325474932789803, 0.017214162275195122, -0.008312903344631195, -0.017925884574651718, -0.008464736863970757, -0.010040013119578362, 0.016568869352340698, -0.04251347854733467, -0.021351635456085205, 0.0014139527920633554, 0.045777905732393265, -0.015230833552777767, -0.025242378935217857, -0.013759942725300789, -0.020687362179160118, -0.02345832996070385, -0.008132601156830788, -0.05868378281593323, -0.013721984811127186, -0.06213800609111786, -0.033802010118961334, 0.05386305972933769, -0.0317142978310585, 0.04843499884009361, -0.055912815034389496, 0.029930248856544495, 0.009461146779358387, -0.04387998208403587, 0.05283818021416664, -0.018049249425530434, 0.015686335042119026, -0.019472692161798477, 0.06103720888495445, -0.07925727218389511, -0.06726239621639252, 0.00830815825611353, 0.02956964261829853, 0.01729957014322281, -0.01267812680453062, -0.048245206475257874, 0.03408670052886009, 0.024122603237628937, 0.02850680612027645, -0.008516930043697357, -0.013332909904420376, 0.010865610092878342, 0.001674917177297175, -0.03190409019589424, 0.0356619767844677, -0.016749171540141106, 0.06293512880802155, -0.004061555489897728, 0.00126923609059304, 0.006728137843310833, 0.04482894390821457, 0.0072927698493003845, -0.022566307336091995, -0.003959542140364647, 0.009200182743370533, -0.021010009571909904, -0.016796620562672615, -0.006215698551386595, -0.007178894244134426, 0.016255712136626244, -0.042095936834812164, 0.05040884017944336, -0.0016322139417752624, 0.005390101578086615, -0.02398974820971489, -0.027216218411922455, 0.049611710011959076, -0.032017964869737625, 0.08214211463928223, 0.03401078283786774, 0.005565659608691931, -0.05560914799571037, 0.019425243139266968, 0.010799182578921318, 0.05515364557504654, -0.03476995229721069, -0.018723012879490852, 0.04046372324228287, 0.020269818603992462, -0.002521865302696824, 0.016654275357723236, 0.01221313513815403, 0.012839450500905514, 0.018438324332237244, 0.02326853759586811, -0.04308285564184189, 0.03649706393480301, -0.08123110979795456, -0.019093107432127, 0.045094653964042664, 0.00024836102966219187, 0.05424264445900917, -0.007876381278038025, -0.0043794577941298485, 0.0246160626411438, 0.009314058348536491, -0.038603756576776505, 0.01749885082244873, -0.031182877719402313, 0.013456275686621666, 0.03203694149851799, -0.012640167959034443, -0.03135368973016739, -0.042968980967998505, 0.01224160473793745, 0.010571432299911976, -0.029190057888627052, -0.024786876514554024, 0.008592846803367138, 0.032928965985774994, -0.023287517949938774, -0.021693261340260506, -0.01233650092035532, 0.013437296263873577, -0.02772865816950798, -0.016644787043333054, -0.014965124428272247, 0.005774431396275759, -0.05124392732977867, -0.04581586644053459, 0.005693769548088312, 0.018846377730369568, -0.015278281643986702, 0.007876381278038025, 0.022471411153674126, -0.019548607990145683, -0.008236986584961414, 0.003112593898549676, 0.03924905136227608, 0.0024234105367213488, 0.042437560856342316, 0.00930456817150116, -0.011472945101559162, -0.048207249492406845, -0.0264570489525795, -0.004782766569405794, -0.020383695140480995, 0.0004750739026349038, -0.0028397676069289446, -0.0012063673930242658, -0.019852276891469955, -0.0113211115822196, 0.019852276891469955, -0.01564837619662285, -0.034200575202703476, 0.010391129180788994, -0.001096643740311265, 0.01124519482254982, 0.03122083656489849, 0.00022789905779063702, -0.026058485731482506, 0.002948898123577237, -0.022699160501360893, -0.021503468975424767, 0.03803437948226929, -0.03078431449830532, -0.028241096064448357, -0.05511568859219551, 0.021161843091249466, 0.0007123142713680863, -0.003027187427505851, 0.01807771809399128, 0.029114142060279846, -0.02491973154246807, 0.035415247082710266, 0.01633162796497345, 0.06411184370517731, -0.051395758986473083, -0.0008955824887380004, 0.024654021486639977, 0.004310658201575279, -0.003746025962755084, 0.020136965438723564, 0.02167428284883499, -0.03786356747150421, 0.03718031570315361, -0.02539421245455742, -0.004346244037151337, -0.03668685629963875, 0.011378049850463867, -0.036516040563583374, 0.005176585633307695, 0.02841190993785858, 0.01466145645827055, 0.018115676939487457, 0.06251759082078934, 0.0032810347620397806, -0.0005251909024082124, 0.07223495841026306, 0.011283153668045998, 0.02913312055170536, -0.01359861996024847, -0.014092079363763332, -0.02879149466753006, 0.01585714891552925, 0.003883625380694866, -0.031144918873906136, -0.030328812077641487, 0.027937429025769234, 0.010400619357824326, 0.07956093549728394, 0.012459865771234035, -0.08107927441596985, 0.009579767473042011, 0.011738655157387257, 0.003741281107068062, 0.10058993101119995, -0.008910749107599258, -0.009878690354526043, 0.004225251264870167, -0.02501462772488594, 0.04866274818778038, 0.021977949887514114, -0.003010580549016595, 0.008236986584961414, 0.02064940333366394, 0.03869865462183952, -0.005238268058747053, -0.0020046813879162073, -0.0023463075049221516, -0.013238013722002506, 0.00007739967986708507, 0.016464482992887497, -0.014889207668602467, -0.006087588611990213, -0.0025479618925601244, -0.03909721598029137, 0.02083919569849968, 0.017223652452230453, -0.0009175272425636649, 0.005978458095341921, 0.022433452308177948, 0.04790358245372772, -0.012232114560902119, -0.03243550658226013, -0.04179226979613304, 0.02326853759586811, 0.029057202860713005, -0.005005772225558758, -0.0009305754792876542, 0.05606465041637421, 0.0016737310215830803, -0.012051812373101711, -0.005874072201550007, -0.006400745827704668, 0.017849966883659363, 0.03625033423304558, -0.04076739028096199, -0.004284561611711979, 0.0031624145340174437, 0.045967698097229004, -0.040881264954805374, -0.0031102215871214867, -0.040501680225133896, 0.024786876514554024, 0.0034304962027817965, 0.01585714891552925, -0.0088490666821599, -0.004381830338388681, -0.0016535655595362186, -0.04107105731964111, -0.027064384892582893, -0.05230676382780075, 0.005010517314076424, 0.027254177257418633, -0.037540920078754425, 0.03156246244907379, 0.037199292331933975, 0.02860170230269432, -0.006889461074024439, -0.003065145807340741, -0.02211080491542816, -0.04061555489897728, -0.019890233874320984, 0.0017401583027094603, -0.0016974550671875477, 0.05530548095703125, 0.006694924086332321, 0.04072942957282066, 0.03340344876050949, -0.008165813982486725, -0.009926138445734978, 0.03122083656489849, -0.018258020281791687, 0.017176205292344093, 0.04653707519173622, -0.005945244338363409, -0.02632419392466545, 0.03733214735984802, 0.00465228408575058, 0.00967466365545988, -0.022414471954107285, 0.005105413496494293, 0.037294190376996994, -0.0077340370044112206, 0.001983329653739929, -0.0067328824661672115, 0.007027060724794865, 0.053483474999666214, -0.009973586536943913, 0.02975943498313427, 0.002844512462615967, -0.0014554698718711734, 0.02408464439213276, -0.02975943498313427, 0.0012727946741506457, -0.015506031922996044, 0.0170148815959692, -0.023477310314774513, 0.07849810272455215, 0.03668685629963875, -0.006025906186550856, -0.0241415835916996, -0.0008516930392943323, 0.004080534912645817, 0.047334205359220505, -0.02835497260093689, -0.0756891742348671, -0.004868173040449619, -0.01672070287168026, -0.022699160501360893, -0.002640485530719161, 0.0025455893483012915, -0.02786151133477688, 0.021826116368174553, 0.013342400081455708, 0.005423315335065126, 0.03258734196424484, -0.003456592559814453, -0.042437560856342316, 0.010144399479031563, 0.00498204817995429, -0.04513261467218399, 0.02539421245455742, -0.011491924524307251, 0.038660693913698196, -0.059746623039245605, 0.026248278096318245, 0.008403054438531399, 0.03556707873940468, -0.03625033423304558, -0.04406977444887161, -0.010495515540242195, -0.0063817668706178665, 0.025052586570382118, -0.0029773670248687267, 0.009057838469743729, -0.0020817844197154045, 0.009437423199415207, 0.006932164542376995, -0.022167742252349854, 0.0007562037790194154, 0.0328720286488533, -0.017603237181901932, 0.028298035264015198, 0.003926328383386135, -0.04668891057372093, 0.05579894036054611, -0.04748603701591492, 0.01768864318728447, -0.03619339317083359, -0.052610430866479874, -0.010523984208703041, 0.019064638763666153, -0.06635139137506485, -0.009147989563643932, 0.040008220821619034, -0.04813133180141449, 0.0023652866948395967, -0.024976668879389763, -0.03209388256072998, 0.007553734350949526, 0.03131573274731636, 0.014813289977610111, 0.0030437943059951067, -0.012222625315189362, -0.035016681998968124, -0.0012039949651807547, 0.009669918566942215, 0.0025313550140708685, 0.026551945134997368, -0.02233855612576008, 0.03970455378293991, -0.011738655157387257, -0.04213389381766319, 0.004649911541491747, -0.06802156567573547, -0.0353962667286396, -0.048397041857242584, -0.01134009100496769, -0.012886898592114449, 0.031429607421159744, -0.0012253466993570328, 0.03672481328248978, -0.008716212585568428, 0.014262892305850983, 0.005684279836714268, -0.005399591289460659, 0.018258020281791687, -0.05063658952713013, 0.0053806123323738575, 0.00364164006896317, 0.028525784611701965, 0.019330346956849098, -0.007197873666882515, -0.0098881796002388, 0.0007840794860385358, -0.005162350833415985, -0.0074256244115531445, -0.007919084280729294, 0.0020272191613912582, 0.052041053771972656, 0.004517056979238987, 0.007458838168531656, 0.013551171869039536, -0.003976149018853903, 0.020269818603992462, 0.01051449403166771, 0.002894332865253091, -0.0020853430032730103, 0.03917313367128372, -0.03048064559698105, -0.00027089889044873416, 0.02937985025346279, 0.02146551012992859, -0.043652232736349106, -0.005418570712208748, 0.003976149018853903, -0.027083363384008408, -0.010068482719361782, -0.05705156922340393, -0.0003991569683421403, 0.003269172739237547, 0.0060591199435293674, 0.007055529393255711, -0.04479098692536354, 0.016995901241898537, -0.01788792572915554, 0.02404668740928173, 0.013143117539584637, -0.0011500228429213166, 0.020972050726413727, -0.05166146904230118, 0.052610430866479874, 0.012345990166068077, 0.023591184988617897, 0.013750453479588032, 0.025337275117635727, -0.018685054033994675, -0.04919416829943657, 0.015050530433654785, -0.0062014637514948845, -0.043310604989528656, 0.01224160473793745, 0.021921012550592422, 0.020231861621141434, -0.005522956606000662, 0.014727883972227573, 0.035168517380952835, -0.026134401559829712, -0.005508721806108952, -0.05367326736450195, -0.01876096986234188, -0.0001596924412297085, -0.01905514858663082, 0.0025621962267905474, 0.007539500016719103, -0.008948707953095436, 0.002008239971473813, 0.03503566235303879, -0.0023818935733288527, 0.03890742361545563, -0.003036677138879895, -0.0549638532102108, -0.013238013722002506, 0.01357015036046505, -0.031182877719402313, 0.06092333421111107, -0.008478972129523754, 0.009522829204797745, 0.011453966610133648, 0.019083617255091667, -0.026627862825989723, 0.016502441838383675, -0.011026933789253235, -0.009029369801282883, 0.02841190993785858, -0.02622929774224758, 0.027064384892582893, 0.004237113520503044, 0.013826370239257812, -0.00455738790333271, -0.009394719265401363, -0.011577331461012363, 0.03435241058468819, 0.03488382697105408, 0.04061555489897728, -0.0020628052297979593, -0.0012034019455313683, -0.04581586644053459, 0.06225188076496124, -0.04782766476273537, -0.02059246599674225, -0.00016666138253640383, 0.024597084149718285, -0.003878880525007844, -0.011719675734639168, 0.013010263442993164, -0.015525011345744133, 0.022566307336091995, -0.0054992325603961945, -0.003743653418496251, -0.013703005388379097, -0.05621648579835892, 0.011102850548923016, 0.008327137678861618, 0.03309978172183037, -0.00971736665815115, -0.011786103248596191, -0.038357026875019073, 0.027595803141593933, -0.028317013755440712, 0.03609849885106087, 0.010144399479031563, 0.007563223596662283, -0.00441267155110836, -0.00477327685803175, -0.01007797196507454, 0.02510952390730381, -0.03258734196424484, -0.010723265819251537, -0.03480790928006172, -0.03767377510666847, -0.004476726055145264, -0.016255712136626244, -0.012488334439694881, 0.02854476496577263, 0.010590411722660065, -0.005693769548088312, 0.036231353878974915, -0.00012143742787884548, -0.0017532064812257886, 0.04300693795084953, 0.02273711934685707, -0.030898189172148705, -0.022813037037849426, 0.014974613673985004, -0.022224679589271545, -0.033479366451501846, 0.0029228017665445805, 0.0012217879993841052, -0.014993593096733093, 0.010628369636833668, -0.01661631651222706, -0.03951476141810417, 0.001787606393918395, 0.0170148815959692, -0.045056696981191635, -0.0007953484309837222, 0.009204926900565624, 0.012061301618814468, -0.030670437961816788, 0.04520852863788605, -0.03552912175655365, 0.020535528659820557, 0.013778922148048878, 0.039628636091947556, -0.023534247651696205, -0.0016796620329841971, 0.04338652268052101, -0.029398830607533455, 0.0009922579629346728, 0.09322598576545715, 0.021541427820920944, -0.016398055478930473, -0.0001740751467877999, -0.0018718267092481256, -0.03137267008423805, -0.023913832381367683, -0.041716352105140686, 0.018685054033994675, 0.04741011932492256, -0.10704286396503448, 0.03755990043282509, 0.016597338020801544, 0.058531951159238815, -0.04494282230734825 ]
When robots enter everyday human environments, they need to understand their tasks and how they should perform those tasks. To encode these, reward functions, which specify the objective of a robot, are employed. However, designing reward functions can be extremely challenging for complex tasks and environments. A promising approach is to learn reward functions from humans. Recently, several robot learning works embrace this approach and leverage human demonstrations to learn the reward functions. Known as inverse reinforcement learning, this approach relies on a fundamental assumption: humans can provide near-optimal demonstrations to the robot. Unfortunately, this is rarely the case: human demonstrations to the robot are often suboptimal due to various reasons, e.g., difficulty of teleoperation, robot having high degrees of freedom, or humans' cognitive limitations. This thesis is an attempt towards learning reward functions from human users by using other, more reliable data modalities. Specifically, we study how reward functions can be learned using comparative feedback, in which the human user compares multiple robot trajectories instead of (or in addition to) providing demonstrations. To this end, we first propose various forms of comparative feedback, e.g., pairwise comparisons, best-of-many choices, rankings, scaled comparisons; and describe how a robot can use these various forms of human feedback to infer a reward function, which may be parametric or non-parametric. Next, we propose active learning techniques to enable the robot to ask for comparison feedback that optimizes for the expected information that will be gained from that user feedback. Finally, we demonstrate the applicability of our methods in a wide variety of domains, ranging from autonomous driving simulations to home robotics, from standard reinforcement learning benchmarks to lower-body exoskeletons.
[ 0.005039244890213013, 0.01765257492661476, -0.03434860706329346, -0.04761847108602524, 0.02213963307440281, 0.01680907793343067, -0.015452524647116661, 0.002747888443991542, -0.07895831018686295, 0.004830544348806143, -0.0041892253793776035, -0.057044774293899536, 0.021183088421821594, -0.05036636069417, 0.006678412202745676, -0.023896194994449615, 0.03979220613837242, -0.013748138211667538, -0.045183632522821426, -0.0055696917697787285, -0.01107851229608059, 0.0234787929803133, 0.01965261995792389, 0.055444736033678055, 0.020522205159068108, -0.004974025767296553, 0.0154873076826334, -0.03175724297761917, -0.09934138506650925, 0.04062701016664505, 0.02707887440919876, 0.0278788935393095, -0.051618561148643494, -0.012139406055212021, -0.006447972264140844, -0.036348652094602585, 0.044661883264780045, 0.0160699300467968, -0.010417628102004528, 0.07443647086620331, -0.014052492566406727, 0.008221925236284733, -0.020296113565564156, -0.035009488463401794, 0.003150071483105421, -0.025339705869555473, -0.03575733304023743, 0.03455730527639389, 0.013791617006063461, -0.0016076451865956187, 0.017339523881673813, -0.0013532915618270636, -0.007408863864839077, 0.0033587717916816473, 0.018365634605288506, 0.012556806206703186, 0.02104395627975464, -0.023444009944796562, 0.025287529453635216, -0.008491497486829758, 0.039896558970212936, 0.010574152693152428, -0.08848896622657776, -0.028400644659996033, 0.014739464968442917, -0.10678502917289734, 0.03711388632655144, 0.015426437370479107, -0.024783171713352203, -0.005156638566404581, -0.006452320143580437, -0.01796562410891056, -0.040766142308712006, 0.00042392266914248466, -0.02069612219929695, -0.004478362388908863, 0.06612323969602585, 0.007347992621362209, -0.025844065472483635, 0.0008309971308335662, 0.039444372057914734, 0.0559317022562027, 0.005547951906919479, -0.009808918461203575, 0.010539369657635689, -0.027704976499080658, 0.05495776981115341, -0.06608845293521881, -0.026678865775465965, -0.029183270409703255, -0.011826355010271072, -0.002202223986387253, 0.00685232924297452, 0.019026517868041992, 0.005895785987377167, 0.021652664989233017, 0.03617473319172859, 0.0024348378647118807, -0.011226342059671879, 0.005965352524071932, -0.008187142200767994, -0.001254376256838441, -0.022296158596873283, -0.018313458189368248, 0.04340967908501625, -0.0342094711959362, -0.008039312437176704, -0.01709604077041149, -0.009513258934020996, 0.1084546372294426, -0.03659213334321976, 0.011956793256103992, -0.05203596502542496, 0.023565752431750298, -0.06219271570444107, -0.0320529006421566, -0.030522432178258896, -0.0846627876162529, 0.031165923923254013, -0.0480358712375164, 0.014600330963730812, 0.06671455502510071, 0.019565660506486893, 0.0045479293912649155, -0.05972309410572052, 0.018400417640805244, -0.010739373974502087, 0.03593124821782112, 0.046296700835227966, -0.014730769209563732, -0.004460970871150494, 0.025113612413406372, 0.010617632418870926, 0.017478657886385918, 0.006187096703797579, 0.016817772760987282, 0.028957178816199303, -0.029931113123893738, -0.043235763907432556, -0.0051827263087034225, -0.01772214099764824, -0.021165696904063225, -0.02127004787325859, -0.030209381133317947, -0.012408977374434471, 0.01829606667160988, -0.012235060334205627, 0.05634910613298416, -0.04560103639960289, 0.008621934801340103, -0.0027718020137399435, 0.037148669362068176, 0.0160264503210783, 0.0063610137440264225, 0.0602448470890522, -0.017574312165379524, -0.04400099813938141, -0.002115265466272831, 0.005408818367868662, -0.032226819545030594, 0.05725347250699997, -0.009730655699968338, -0.041044410318136215, 0.09502824395895004, 0.07791481167078018, 0.03233116865158081, 0.03361815586686134, -0.0045566251501441, -0.07071464508771896, 0.038331303745508194, -0.0452532023191452, -0.03641821816563606, 0.04730542004108429, 0.051618561148643494, 0.04114875942468643, 0.03481817990541458, 0.08918463438749313, 0.01230462733656168, -0.02485273778438568, -0.010817636735737324, -0.039096537977457047, -0.004804457072168589, -0.011026336811482906, 0.056279536336660385, 0.05447079986333847, 0.01939174346625805, 0.06330578774213791, -0.046853236854076385, 0.014078580774366856, -0.02379184402525425, -0.00706102978438139, 0.05335773155093193, 0.041322678327560425, 0.02125265635550022, 0.057949140667915344, -0.053218599408864975, -0.05867959186434746, 0.04146181046962738, -0.006287099327892065, 0.042435746639966965, -0.049392424523830414, -0.0430966317653656, -0.02073090523481369, 0.020939605310559273, 0.01311334129422903, -0.03073113225400448, 0.052662063390016556, 0.006039267405867577, -0.040522657334804535, -0.09308037161827087, -0.02076568827033043, -0.03874870389699936, -0.009034987539052963, -0.03687040135264397, -0.01987871155142784, -0.030087638646364212, 0.03431382030248642, -0.026452774181962013, -0.013287258334457874, -0.031705066561698914, -0.008165402337908745, 0.0420183464884758, 0.04612278565764427, -0.0176873579621315, -0.04723585397005081, 0.0325920432806015, 0.03596603497862816, -0.04994896054267883, 0.009217600338160992, -0.019009126350283623, -0.011000249534845352, -0.015322086401283741, -0.005174030549824238, -0.020313505083322525, -0.014687289483845234, -0.0001255463284906, 0.006495799403637648, -0.029461538419127464, 0.016782989725470543, 0.018609117716550827, -0.011895922012627125, -0.016791684553027153, -0.0015032950323075056, 0.0016185150016099215, 0.0756886750459671, -0.001093503087759018, -0.01935696043074131, 0.06963635981082916, 0.03513123095035553, -0.020348288118839264, -0.06480146944522858, 0.008778460323810577, -0.032226819545030594, 0.04285314679145813, -0.03161810711026192, 0.07443647086620331, 0.045496683567762375, -0.0415661595761776, 0.034157298505306244, -0.057079557329416275, 0.045183632522821426, 0.09829787909984589, 0.03280074521899223, -0.0029478929936885834, 0.021774407476186752, 0.01118286233395338, 0.06062746420502663, -0.01273072324693203, 0.020870039239525795, -0.04636627063155174, -0.03641821816563606, -0.04445318132638931, -0.015000340528786182, -0.023617926985025406, -0.04073135927319527, -0.09913268685340881, 0.02434837818145752, -0.062331847846508026, 0.026939742267131805, 0.0068045021034777164, -0.04619235172867775, -0.024504903703927994, 0.01880042627453804, 0.022783124819397926, -0.017826491966843605, -0.05892307683825493, -0.010200231336057186, -0.00953065138310194, -0.021096130833029747, -0.0010478498879820108, 0.018052583560347557, -0.04236617684364319, -0.004565320909023285, 0.01967001147568226, 0.06055789440870285, 0.011652437970042229, -0.03572255000472069, -0.046018436551094055, -0.004865327849984169, 0.027183225378394127, 0.031635500490665436, 0.010835028253495693, -0.0007706696633249521, 0.002989198314025998, 0.024765780195593834, -0.008004529401659966, 0.022748341783881187, 0.02737453393638134, -0.014009013772010803, -0.014965556561946869, -0.002602232852950692, 0.05137507990002632, -0.049601126462221146, -0.031374625861644745, 0.016643855720758438, 0.04469666630029678, 0.04180964455008507, -0.00005268461973173544, -0.003478339873254299, 0.007156684063374996, -0.035009488463401794, -0.007343644741922617, -0.08814112842082977, 0.013843792490661144, -0.035826899111270905, -0.001419597421772778, 0.035009488463401794, 0.003743563313037157, -0.01933956891298294, -0.03892262279987335, -0.034400779753923416, -0.0008967595058493316, 0.005695781204849482, 0.00033777940552681684, 0.024800563231110573, 0.02732235938310623, -0.059583961963653564, -0.0023717929143458605, -0.029948506504297256, -0.027304967865347862, -0.03514862433075905, 0.015609050169587135, -0.027165833860635757, -0.03353119641542435, -0.02320052683353424, -0.04393143206834793, -0.027026699855923653, 0.007343644741922617, -0.03836608678102493, -0.04681845381855965, 0.0010886116651818156, -0.0004334337427280843, 0.018104758113622665, -0.0038370436523109674, 0.07443647086620331, -0.06716673821210861, 0.007487126626074314, -0.0006733848713338375, -0.036905184388160706, 0.004006612580269575, 0.01741778664290905, -0.057114340364933014, -0.05534038692712784, 0.06267968565225601, -0.06974071264266968, -0.0010875246953219175, -0.043270546942949295, -0.028905004262924194, 0.019722186028957367, 0.008113227784633636, -0.043548814952373505, 0.01534817460924387, 0.055409952998161316, -0.007117552682757378, -0.015878621488809586, 0.028626736253499985, -0.012374193407595158, -0.012408977374434471, -0.06654064357280731, 0.04010525718331337, -0.03673126921057701, -0.008878462016582489, -0.005121855530887842, 0.007343644741922617, 0.010652415454387665, 0.04427926614880562, -0.010513282380998135, 0.0010690459748730063, 0.009078467264771461, 0.03123549185693264, 0.04205312952399254, -0.03589646518230438, -0.007748001720756292, -0.009556738659739494, -0.022748341783881187, 0.01963522844016552, 0.03476600721478462, -0.023165743798017502, 0.022991826757788658, 0.00372834550216794, 0.007943658158183098, 0.03121810033917427, -0.009643697179853916, 0.046331487596035004, 0.003519645193591714, -0.021652664989233017, -0.01967001147568226, -0.011035032570362091, 0.004913154989480972, 0.031374625861644745, -0.004028352443128824, -0.026331031695008278, -0.014878598041832447, -0.004821848589926958, 0.02488752081990242, 0.04285314679145813, -0.00871324073523283, -0.0007717566331848502, 0.01827867515385151, -0.06267968565225601, -0.0006440363358706236, 0.01683516427874565, 0.051270727068185806, -0.004952286370098591, 0.030331123620271683, 0.0497402586042881, 0.014522068202495575, 0.03850522264838219, -0.002943545114248991, -0.041044410318136215, 0.01659168116748333, 0.04403578117489815, 0.015496003441512585, -0.001998958410695195, 0.047444555908441544, -0.003239203942939639, 0.003530514892190695, 0.04984460771083832, -0.04914893954992294, -0.03396598994731903, -0.02429620362818241, -0.03756606951355934, -2.632532698498835e-7, -0.045531466603279114, 0.0160699300467968, -0.034383390098810196, 0.01163504645228386, -0.059549178928136826, 0.02655712515115738, 0.011843747459352016, -0.05527082085609436, 0.00581752322614193, -0.04431404918432236, -0.0021337440703064203, 0.03725301846861839, 0.0006712108734063804, 0.020870039239525795, -0.036313869059085846, -0.010435019619762897, -0.06146226450800896, 0.010165448300540447, 0.04431404918432236, -0.019826536998152733, -0.06111443042755127, 0.03596603497862816, 0.0735321044921875, 0.009730655699968338, -0.007113204803317785, -0.01742648147046566, -0.0004375099379103631, -0.004582712892442942, -0.04396621510386467, -0.043827082961797714, 0.011356779374182224, 0.002382662845775485, 0.037461720407009125, 0.014800336211919785, -0.032226819545030594, 0.0036457348614931107, -0.005995788145810366, 0.03372250497341156, -0.006339274346828461, 0.05116637796163559, -0.05280119925737381, 0.0171482153236866, -0.03264421969652176, 0.0868193581700325, -0.016722118481993675, -0.018939560279250145, -0.005204465705901384, -0.04208791255950928, -0.033896420150995255, 0.0102350153028965, 0.0229396503418684, -0.018574334681034088, 0.003256595693528652, -0.010252406820654869, -0.06723631173372269, 0.07311470061540604, -0.027704976499080658, 0.013452479615807533, 0.006239272188395262, 0.01576557569205761, 0.009104554541409016, -0.011895922012627125, -0.02431359514594078, -0.053253382444381714, -0.03069634921848774, -0.044870585203170776, 0.004752281587570906, 0.03739215433597565, 0.015243824571371078, 0.00799583364278078, -0.032522477209568024, 0.012669852934777737, 0.00588274234905839, 0.024000544100999832, 0.00954804290086031, 0.04041830822825432, 0.0047827172093093395, 0.007321905344724655, 0.035235583782196045, 0.010921986773610115, -0.013035078532993793, -0.03725301846861839, 0.03476600721478462, 0.05474906787276268, 0.0069262441247701645, 0.020122196525335312, -0.004608800169080496, -0.03888783976435661, 0.028574561700224876, -0.03234855830669403, -0.05864480882883072, -0.008587151765823364, -0.036070384085178375, 0.06741022318601608, 0.006047963164746761, -0.004074005410075188, 0.03283552825450897, -0.027791934087872505, 0.05558386817574501, 0.016165584325790405, 0.024713603779673576, -0.024991871789097786, 0.009600217454135418, 0.05300989747047424, -0.022487467154860497, -0.0046174959279596806, 0.058749157935380936, 0.008761068806052208, 0.006874069105833769, 0.025304922834038734, -0.019409136846661568, -0.0315137580037117, 0.0009739351226016879, -0.009913268499076366, -0.007639303803443909, -0.005621866788715124, -0.020035237073898315, -0.016487330198287964, -0.001922869705595076, 0.01269594021141529, -0.0016956906765699387, 0.0076610432006418705, -0.0182265006005764, -0.010895899496972561, 0.052731629461050034, 0.04034874215722084, 0.0027522363234311342, -0.04459231719374657, -0.005761000327765942, -0.0381573885679245, -0.032487694174051285, 0.011035032570362091, 0.026713648810982704, -0.003974003251641989, -0.005030549131333828, -0.04045309126377106, 0.00011841301602544263, 0.0016946037067100406, -0.020887430757284164, -0.013339432887732983, 0.03780955448746681, 0.01909608580172062, -0.011148079298436642, -0.01120025385171175, -0.026052765548229218, 0.02880065329372883, -0.0309746153652668, -0.057357821613550186, 0.023339660838246346, 0.0016217759111896157, 0.03280074521899223, -0.006530582904815674, -0.00441314373165369, 0.04194877669215202, 0.011382866650819778, 0.027026699855923653, -0.06532321870326996, 0.004708802327513695, 0.01575687900185585, 0.0070479861460626125, 0.04925329238176346, 0.02048742212355137, -0.0587143748998642, 0.020035237073898315, -0.03648778423666954, -0.023374443873763084, 0.02794845961034298, 0.017826491966843605, 0.026157114654779434, 0.015165561810135841, -0.02687017433345318, 0.030748523771762848, -0.0014532938366755843, -0.01713082380592823, 0.04654018580913544, 0.018087366595864296, -0.026087548583745956, 0.023409226909279823, 0.0037457372527569532, 0.04365316405892372, 0.00871758908033371, -0.04226182773709297, -0.003971829079091549, 0.014409022405743599, -0.03511384129524231, -0.007026246283203363, 0.03377467766404152, 0.00621318444609642, 0.015974275767803192, 0.012895944528281689, -0.02765280194580555, 0.0034196428023278713, -0.015452524647116661, -0.029461538419127464, 0.04320098087191582, 0.051548995077610016, -0.03572255000472069, -0.04375751316547394, 0.0024044024758040905, -0.0037174755707383156, 0.0784713476896286, -0.01848737522959709, 0.01827867515385151, -0.03240073472261429, 0.001301116426475346, 0.03215724974870682, -0.006165357306599617, -0.00869584921747446, 0.022209199145436287, -0.011556783691048622, 0.03888783976435661, 0.004352272488176823, -0.04452275112271309, -0.014330759644508362, 0.02297443524003029, -0.008400190621614456, -0.0023304875940084457, 0.045983653515577316, -0.03520079702138901, 0.007652347441762686, 0.03641821816563606, 0.013174211606383324, 0.0325920432806015, 0.033357277512550354, 0.029113704338669777, 0.0131307328119874, 0.05092289298772812, 0.0020500465761870146, -0.05196639522910118, -0.010321972891688347, 0.039966125041246414, 0.009565434418618679, -0.01993088610470295, 0.011530696414411068, 0.07234946638345718, 0.023704886436462402, -0.02180919051170349, -0.009791526943445206, -0.013635092414915562, 0.01770474947988987, -0.011861138977110386, -0.02128743939101696, -0.021061347797513008, 0.01020892709493637, 0.0036979098804295063, -0.044870585203170776, 0.0413922443985939, -0.06577540189027786, -0.0153307830914855, 0.007678435184061527, 0.01958305388689041, 0.002587015274912119, 0.027809327468276024, -0.0032435518223792315, -0.04897502437233925, -0.006100138183683157, 0.005100115668028593, -0.049601126462221146, -0.017583006992936134, -0.01717430353164673, 0.020122196525335312, 0.04702715575695038, -0.011939401738345623, 0.004521841648966074, 0.027774542570114136, -0.007152336183935404, 0.008221925236284733, 0.014478589408099651, 0.028296293690800667, -0.012069839052855968, 0.018974343314766884, 0.015913404524326324, 0.029791980981826782, 0.02655712515115738, -0.009626305662095547, -0.020956996828317642, 0.010287189856171608, 0.05092289298772812, -0.021443964913487434, 0.03412251174449921, -0.006756674963980913, -0.02520057186484337, -0.00028940875199623406, 0.026209291070699692, 0.005417514126747847, 0.02627885714173317, -0.020122196525335312, 0.06671455502510071, 0.0017228651558980346, -0.013774225488305092, 0.022557033225893974, 0.025061437860131264, 0.015139473602175713, -0.012243756093084812, -0.0029848504345864058, -0.00012167395470896736, -0.0018293893663212657, 0.02184397354722023, 0.0005097941611893475, 0.048522841185331345, 0.0077132186852395535, -0.0010310016805306077, 0.041913993656635284, 0.018609117716550827, 0.032731179147958755, -0.003623995231464505, 0.012956815771758556, 0.07085378468036652, -0.001329377992078662, 0.0348355732858181, -0.016522113233804703, -0.03226160258054733, 0.009365430101752281, 0.014017709530889988, -0.034383390098810196, 0.03307901322841644, -0.02516578882932663, 0.01580035872757435, 0.05614040419459343, -0.014313368126749992, 0.014435109682381153, 0.03179202601313591, -0.05774043872952461, -0.00251744850538671, 0.01855694316327572, 0.03426164761185646, 0.013104645535349846, -0.0036261691711843014, 0.01716560684144497, 0.06810589134693146, -0.05721868947148323, -0.004252270329743624, -0.0021826582960784435, -0.02980937249958515, 0.020296113565564156, -0.016765598207712173, 0.03377467766404152, 0.008752372115850449, 0.054366450756788254, 0.015130777843296528, 0.014669897966086864, 0.003843565471470356, 0.0017826491966843605, -0.009678480215370655, -0.010461106896400452, -0.005147942807525396, 0.0010424149222671986, 0.015835141763091087, 0.002776149893179536, -0.009600217454135418, 0.014504676684737206, 0.052905548363924026, -0.014878598041832447, 0.016478635370731354, -0.01937435194849968, -0.014165538363158703, -0.03502688184380531, 0.031913768500089645, 0.0375312864780426, -0.00953065138310194, 0.025026654824614525, -0.011069816537201405, 0.03787912055850029, -0.0021826582960784435, -0.0009005639003589749, -0.03144419193267822, 0.05812305957078934, 0.004215313121676445, 0.016504721716046333, 0.003550080582499504, 0.03777477145195007, 0.006847981363534927, -0.017322132363915443, 0.017000386491417885, 0.02575710602104664, 0.019461311399936676, 0.0030631129629909992, 0.007656695321202278, -0.03669648617506027, -0.045983653515577316, 0.010904595255851746, -0.022748341783881187, 0.004371838178485632, -0.02238311618566513, 0.015861229971051216, 0.04361838102340698, 0.017356915399432182, 0.02323530986905098, 0.06713195890188217, -0.04459231719374657, -0.00033587717916816473, -0.020504813641309738, 0.02933979593217373, -0.011800267733633518, 0.013017687015235424, 0.0009407821926288307, 0.050192441791296005, 0.0273397509008646, -0.05245336517691612, 0.008039312437176704, -0.03669648617506027, -0.02961806394159794, -0.04608800262212753, -0.015209040604531765, 0.022835301235318184, 0.003950089681893587, 0.0038848707918077707, 0.01796562410891056, 0.02742670848965645, 0.01575687900185585, -0.0023283136542886496, -0.02325270138680935, 0.002854412654414773, -0.021235264837741852, 0.03516601398587227, -0.002171788364648819, -0.004391403868794441, -0.0022848343942314386, -0.0091132503002882, -0.02848760224878788, -0.009843701496720314, 0.031392015516757965, -0.019965671002864838, -0.022191807627677917, -0.03481817990541458, -0.038853056728839874, -0.07179293036460876, -0.002169614424929023, 0.02570493146777153, -0.03902697190642357, -0.010756765492260456, -0.004539233632385731, 0.01989610306918621, -0.01577427051961422, -0.0000303335691569373, 0.02045263722538948, -0.03916610777378082, -0.01629602164030075, 0.031374625861644745, 0.04720107093453407, -0.012774202972650528, 0.020348288118839264, -0.02624407410621643, -0.030887657776474953, -0.021774407476186752, 0.02986154705286026, 0.030870266258716583, 0.016487330198287964, 0.017322132363915443, -0.05941004306077957, -0.034922532737255096, 0.020504813641309738, 0.003826173720881343, -0.018156934529542923, -0.021183088421821594, 0.01632210984826088, 0.023548360913991928, 0.014304672367870808, -0.03071374073624611, 0.024661429226398468, -0.013261170126497746, -0.005243597086519003, 0.010669806972146034, 0.018678683787584305, -0.02433098666369915, 0.07979311794042587, -0.01718299835920334, -0.01716560684144497, -0.001063067582435906, 0.05033157765865326, -0.02184397354722023, -0.000782626448199153, 0.010861116461455822, -0.030487649142742157, -0.025374488905072212, -0.018626509234309196, -0.05374034866690636, 0.01311334129422903, 0.029531104490160942, -0.0480358712375164, 0.01993088610470295, 0.010652415454387665, -0.026609299704432487, -0.0010456759482622147, 0.02097438834607601, 0.02321791835129261, -0.02657451666891575, -0.020330896601080894, 0.0005519146798178554, 0.006952331867069006, 0.03617473319172859, 0.04751412197947502, 0.03241812810301781, 0.001934826490469277, 0.003089200472459197, -0.014148146845400333, 0.02739192545413971, 0.012974207289516926, -0.009591521695256233, 0.03271378576755524, 0.00886107049882412, 0.008213229477405548, 0.03850522264838219, -0.0103915398940444, 0.03676605224609375, 0.0107741579413414, -0.01599166728556156, -0.0021217872854322195, -0.003921828232705593, -0.01718299835920334, -0.00940021313726902, -0.015435133129358292, -0.018974343314766884, -0.0375312864780426, -0.02069612219929695, 0.01654820144176483, 0.04340967908501625, -0.026365814730525017, 0.026122331619262695, -0.04511406645178795, -0.009895876981317997, -0.06368840485811234, 0.026626691222190857, -0.03408772870898247, 0.006800154224038124, -0.0068697212263941765, 0.005778391845524311, -0.009913268499076366, -0.017913449555635452, 0.0670623928308487, 0.011704613454639912, -0.0220874585211277, -0.012808986008167267, -0.014148146845400333, -0.011174166575074196, -0.004795760847628117, 0.030331123620271683, 0.004469666630029678, 0.004310967400670052, 0.043270546942949295, -0.005908829625695944, -0.020939605310559273, -0.00443053524941206, 0.003337032161653042, 0.01493077352643013, 0.008561063557863235, 0.009539347141981125, -0.004878371488302946, -0.03871392086148262, 0.032192036509513855, -0.02687017433345318, -0.02048742212355137, 0.026678865775465965, 0.04125310853123665, 0.02880065329372883, 0.027826718986034393, 0.014713377691805363, -0.03864435479044914, 0.04118354246020317, -0.035792116075754166, 0.01340030413120985, 0.0008326275856234133, 0.01853955164551735, 0.04507928341627121, -0.026939742267131805, -0.025078829377889633, 0.0702972486615181, 0.01300029456615448, -0.009695871733129025, -0.007230598945170641, -0.0309746153652668, -0.010478498414158821, -0.010556761175394058, 0.02182658202946186, -0.01160026341676712, -0.0013815531274303794, -0.04984460771083832, 0.02761801704764366, -0.034435562789440155, 0.04267922788858414, -0.0011608959175646305 ]
There has been a recent surge in the field of Explainable AI (XAI) which tackles the problem of providing insights into the behavior of black-box machine learning models. Within this field, \textit{feature attribution} encompasses methods which assign relevance scores to input features and visualize them as a heatmap. Designing flexible accelerators for multiple such algorithms is challenging since the hardware mapping of these algorithms has not been studied yet. In this work, we first analyze the dataflow of gradient backpropagation based feature attribution algorithms to determine the resource overhead required over inference. The gradient computation is optimized to minimize the memory overhead. Second, we develop a High-Level Synthesis (HLS) based configurable FPGA design that is targeted for edge devices and supports three feature attribution algorithms. Tile based computation is employed to maximally use on-chip resources while adhering to the resource constraints. Representative CNNs are trained on CIFAR-10 dataset and implemented on multiple Xilinx FPGAs using 16-bit fixed-point precision demonstrating flexibility of our library. Finally, through efficient reuse of allocated hardware resources, our design methodology demonstrates a pathway to repurpose inference accelerators to support feature attribution with minimal overhead, thereby enabling real-time XAI on the edge.
[ -0.009055400267243385, 0.037917930632829666, -0.029403027147054672, -0.03542333096265793, 0.05547992140054703, 0.02158661186695099, -0.013903241604566574, 0.03151512145996094, -0.03259611502289772, 0.03901555389165878, -0.00803261436522007, -0.023615553975105286, 0.0825546532869339, -0.019075380638241768, 0.009213391691446304, 0.028704538941383362, 0.02181944064795971, -0.04200907424092293, -0.00592051912099123, -0.03539006784558296, 0.05079007148742676, -0.052353352308273315, -0.03795119374990463, -0.06998186558485031, 0.02860475517809391, 0.005870627239346504, -0.019441254436969757, 0.006577430758625269, -0.0582406111061573, 0.006764525547623634, 0.028355294838547707, 0.045102380216121674, -0.06299698352813721, -0.0403127484023571, -0.058673009276390076, -0.036986611783504486, 0.0007379860617220402, 0.019807130098342896, -0.012722463347017765, 0.08435076475143433, -0.007558640092611313, -0.06628985702991486, -0.0038167391903698444, -0.0032741634640842676, 0.003444627858698368, -0.04866134375333786, -0.024580132216215134, -0.06758704781532288, -0.028405187651515007, -0.03321145102381706, 0.006635637953877449, -0.02196911722421646, 0.046831969171762466, 0.03379352390766144, -0.0014863662654533982, 0.007221869193017483, 0.011175811290740967, 0.06206566467881203, 0.010518900118768215, 0.026060262694954872, 0.006099298596382141, -0.0001158949889941141, -0.030517281964421272, 0.014726459980010986, 0.016023652628064156, -0.027457239106297493, 0.018360260874032974, 0.02749050036072731, -0.035223763436079025, 0.003856237046420574, -0.022268468514084816, -0.03725270554423332, -0.017728295177221298, -0.0011589499190449715, 0.012048921547830105, -0.021669764071702957, 0.056810375303030014, -0.0034903620835393667, 0.002184854354709387, 0.01151673961430788, 0.028305402025580406, 0.051521819084882736, -0.034990932792425156, 0.0088890939950943, 0.051189206540584564, -0.01535010989755392, -0.00030247034737840295, -0.06422765552997589, -0.04616674408316612, -0.05617840960621834, -0.06329633295536041, 0.0002816820051521063, -0.030766742303967476, -0.008764363825321198, 0.01663898676633835, 0.003026782302185893, 0.009570951573550701, -0.027241040021181107, -0.036288123577833176, -0.060103245079517365, -0.05541339889168739, 0.05431577190756798, -0.011441902257502079, 0.009928510524332523, 0.044503677636384964, -0.04959266260266304, -0.01704643853008747, -0.011192441917955875, 0.036620739847421646, 0.09040433168411255, 0.005799946840852499, -0.025128943845629692, -0.030400866642594337, -0.013487474992871284, -0.00004258361514075659, -0.01987365260720253, -0.037685099989175797, -0.04170972481369972, -0.0044320737943053246, -0.016772031784057617, 0.03871620446443558, 0.03615507856011391, 0.036986611783504486, 0.03934817016124725, -0.051288992166519165, 0.060668688267469406, 0.0013761880109086633, -0.02326630987226963, 0.03755205497145653, -0.002725351369008422, -0.010078187100589275, 0.02381512150168419, 0.03218035027384758, -0.01634795032441616, -0.012040605768561363, -0.01806090958416462, 0.036653999239206314, 0.052819013595581055, -0.03602203354239464, -0.00254241400398314, -0.0041535100899636745, 0.0018065066542476416, 0.0020091929472982883, -0.00494346721097827, 0.027706699445843697, 0.0072343419305980206, 0.021154213696718216, 0.024829592555761337, -0.0023158208932727575, 0.02285054326057434, -0.010485637933015823, 0.09798791259527206, 0.018776027485728264, -0.0024883642327040434, 0.024447087198495865, 0.029885316267609596, 0.0035755943972617388, 0.008440066128969193, 0.05641123652458191, 0.01081825140863657, 0.0009484679903835058, -0.020555509254336357, -0.012547841295599937, 0.07024795562028885, 0.033411018550395966, 0.03068358823657036, -0.008323650807142258, 0.01982375979423523, -0.035223763436079025, 0.05288553610444069, 0.07217711210250854, -0.010469007305800915, 0.02827214077115059, -0.0007847598171792924, 0.00005320515629136935, 0.015441578812897205, 0.04550151526927948, -0.022966956719756126, -0.07936156541109085, -0.05428251251578331, -0.05910540744662285, -0.014576783403754234, 0.014518575742840767, -0.003743979847058654, 0.0403127484023571, 0.03562289848923683, 0.07417279481887817, 0.003132802667096257, 0.007729104720056057, -0.02256782166659832, 0.024496978148818016, 0.04280734807252884, 0.05933823436498642, -0.024480348452925682, 0.039913609623909, -0.08727776259183884, 0.024131104350090027, -0.04985875263810158, 0.01632300391793251, -0.013221384026110172, -0.04071188345551491, -0.03931490704417229, -0.032529592514038086, 0.014618360437452793, 0.022867172956466675, -0.031282294541597366, 0.030334344133734703, -0.03194751963019371, 0.008074191398918629, -0.023515770211815834, 0.0128388786688447, 0.0537835918366909, -0.04057883843779564, -0.09526048600673676, -0.02155335061252117, 0.015424948185682297, 0.0167387705296278, -0.05361728370189667, 0.004234584514051676, 0.01369535829871893, 0.009363068267703056, 0.033593956381082535, -0.03269590064883232, -0.008988877758383751, 0.02466328628361225, 0.017794817686080933, -0.004118170123547316, -0.02720777876675129, -0.006581588182598352, 0.05893909931182861, -0.05684363469481468, 0.005234503652900457, -0.0020663610193878412, -0.006190767511725426, 0.03455853462219238, -0.041576679795980453, -0.012722463347017765, -0.016821924597024918, -0.01632300391793251, -0.02326630987226963, -0.04606695845723152, 0.018842549994587898, -0.03319482132792473, 0.03648769482970238, 0.0233993548899889, -0.0038978136144578457, 0.03246307000517845, 0.06801944971084595, 0.018726136535406113, -0.002388580236583948, 0.008514903485774994, -0.02168639563024044, 0.04663240164518356, 0.0024738123174756765, -0.008302862755954266, 0.046599142253398895, 0.000902213912922889, -0.02303347922861576, 0.014734774827957153, -0.03189762681722641, 0.056910157203674316, -0.037917930632829666, -0.029735639691352844, 0.025794170796871185, -0.03994687274098396, -0.04550151526927948, 0.06293045729398727, 0.006165821570903063, 0.015375055372714996, -0.004053726326674223, 0.060901518911123276, -0.03821728378534317, -0.03785140812397003, -0.02042246423661709, -0.007587743923068047, -0.024812960997223854, -0.013437582179903984, 0.045667823404073715, 0.01736242137849331, 0.038050975650548935, -0.025411665439605713, 0.019424624741077423, 0.044270846992731094, 0.03331123664975166, 0.028438448905944824, -0.026392875239253044, -0.04899395629763603, -0.03302851319313049, -0.07324147969484329, -0.020788339897990227, -0.020721817389130592, 0.008664580062031746, 0.008764363825321198, 0.019557669758796692, 0.0156245157122612, -0.04177624732255936, -0.03184773400425911, -0.05069028586149216, 0.09585919231176376, -0.05764190852642059, -0.03191426023840904, -0.01865961402654648, 0.023050110787153244, 0.04540173336863518, -0.012739093974232674, 0.025328513234853745, -0.020089851692318916, 0.0939965546131134, -0.013337798416614532, -0.015641147270798683, 0.03894903138279915, 0.07882938534021378, 0.045102380216121674, -0.028288772329688072, -0.060302816331386566, 0.048960696905851364, 0.0200565904378891, -0.024530241265892982, 0.012007344514131546, -0.05062376335263252, 0.022118793800473213, -0.02549481950700283, -0.09373046457767487, 0.07350756973028183, -0.005629482213407755, 0.006099298596382141, 0.02386501431465149, 0.016081858426332474, -0.067354217171669, 0.0006200122297741473, -0.048029378056526184, -0.015424948185682297, -0.020256157964468002, 0.02358229272067547, -0.04197581484913826, -0.01434395369142294, -0.03106609359383583, 0.04194255173206329, -0.025145575404167175, -0.030101515352725983, -0.01532516349107027, -0.006232344079762697, -0.03412613645195961, -0.018692875280976295, -0.06778661906719208, -0.025295251980423927, -0.04852829873561859, 0.0026796169113367796, 0.021004537120461464, -0.07823067903518677, 0.0009209234267473221, 0.029885316267609596, 0.009670735336840153, -0.011525055393576622, 0.04077840596437454, 0.016614040359854698, 0.011508424766361713, 0.0039955186657607555, 0.031265661120414734, -0.017112961038947105, 0.06479309499263763, -0.022534560412168503, -0.023432616144418716, 0.027241040021181107, -0.045102380216121674, 0.03831706568598747, -0.06768683344125748, -0.05072354897856712, -0.04114428162574768, 0.045202165842056274, -0.04583413153886795, 0.06283067911863327, -0.049892015755176544, 0.028172357007861137, -0.007047247141599655, -0.013919872231781483, 0.008664580062031746, -0.033178187906742096, -0.08368553966283798, 0.05228682979941368, -0.014435422606766224, -0.011508424766361713, 0.016572464257478714, 0.032063934952020645, -0.010460692457854748, 0.03319482132792473, 0.025478187948465347, -0.06555810570716858, -0.029269982129335403, 0.04979223012924194, 0.04586739093065262, -0.0401131808757782, -0.007001512683928013, -0.08075854182243347, 0.014560152776539326, 0.02354903146624565, -0.006369546987116337, -0.04686523228883743, 0.06569115072488785, -0.026908425614237785, -0.036055296659469604, 0.01959093101322651, -0.0012493792455643415, 0.04323974624276161, -0.0038853406440466642, 0.02108769118785858, -0.04141037166118622, -0.012739093974232674, 0.053417716175317764, -0.008169817738234997, 0.025511449202895164, -0.03598877415060997, -0.05291879549622536, -0.014876135624945164, 0.021786179393529892, 0.007941145449876785, -0.06865141540765762, -0.0019021329935640097, -0.020372573286294937, -0.012639310210943222, 0.0011319250334054232, 0.01722937636077404, -0.011999029666185379, -0.023798489943146706, 0.029053783044219017, -0.0167387705296278, -0.030999571084976196, -0.020671924576163292, -0.0010934666497632861, -0.005251134280115366, -0.0200565904378891, -0.007525378838181496, -0.0011194520629942417, -0.053284671157598495, -0.019857021048665047, 0.03741900995373726, 0.00012018258712487295, 0.05162160471081734, -0.04516890272498131, -0.003766847075894475, -0.037585318088531494, -0.04556804150342941, -0.024713177233934402, 0.008028456941246986, -0.02316652610898018, 0.00340720871463418, -0.02404795028269291, -0.02326630987226963, -0.020788339897990227, -0.06143369898200035, -0.05215378478169441, 0.03825054317712784, -0.07264277338981628, -0.07137884199619293, -0.007463013753294945, -0.01322969887405634, 0.01717948354780674, -0.005167981144040823, 0.02961922623217106, -0.08780994266271591, -0.00012882273586001247, 0.08142376691102982, -0.0023095845244824886, -0.0199568048119545, -0.01378682628273964, 0.006569115445017815, -0.049193527549505234, -0.02070518583059311, 0.012630995362997055, 0.02938639558851719, 0.027241040021181107, 0.029170198366045952, 0.006789471488445997, -0.012323327362537384, 0.0267421193420887, 0.012364904396235943, 0.012913716025650501, -0.07270929217338562, 0.016314689069986343, -0.058440178632736206, 0.04350583627820015, -0.027839744463562965, 0.017977755516767502, -0.005039093550294638, 0.023981427773833275, 0.012739093974232674, -0.01239816565066576, 0.018825920298695564, 0.003737743478268385, -0.04317322373390198, 0.001535218907520175, 0.00019177242938894778, -0.017162853851914406, -0.0021453567314893007, -0.005679374095052481, -0.025062421336770058, -0.018360260874032974, -0.03485788777470589, 0.032662637531757355, 0.024946007877588272, -0.033494170755147934, 0.011732938699424267, 0.01158326305449009, -0.051288992166519165, 0.025993740186095238, 0.0072967070154845715, -0.011134234257042408, 0.04160993918776512, -0.004465335514396429, -0.01842678338289261, -0.0006376823293976486, 0.015233694575726986, 0.02404795028269291, -0.06628985702991486, 0.022368252277374268, -0.002619330771267414, -0.01865961402654648, -0.010410800576210022, 0.029735639691352844, 0.004197165835648775, 0.02655918151140213, -0.03143196925520897, 0.013279590755701065, 0.02215205505490303, -0.023931536823511124, 0.04703154042363167, -0.030849896371364594, -0.031648166477680206, 0.04197581484913826, -0.02586069330573082, -0.004186771344393492, 0.013396006077528, -0.025278620421886444, -0.011940822005271912, 0.020821601152420044, 0.012057236395776272, 0.024064581841230392, 0.033643849194049835, 0.012489634566009045, -0.03472484275698662, -0.05957106500864029, 0.04170972481369972, 0.01746220514178276, 0.0468984916806221, -0.031315553933382034, 0.02492937631905079, 0.016007021069526672, -0.015000865794718266, -0.008198920637369156, 0.003371868748217821, -0.003463337430730462, -0.03645443171262741, -0.014518575742840767, -0.01578250713646412, 0.04387171193957329, -0.0003799069090746343, -0.029452919960021973, 0.013287906534969807, -0.02363218367099762, 0.023532399907708168, -0.003991361241787672, -0.04593391343951225, 0.0625978484749794, 0.02103780023753643, -0.00807003304362297, -0.039447952061891556, 0.020954646170139313, 0.046831969171762466, -0.010618683882057667, 0.024480348452925682, -0.03479136526584625, -0.009770519100129604, -0.004698164761066437, 0.011691361665725708, 0.005454860161989927, -0.003521544625982642, 0.009121923707425594, -0.019058749079704285, -0.02316652610898018, 0.02108769118785858, -0.009778834879398346, -0.01239816565066576, 0.0075503247790038586, 0.011574947275221348, 0.008261285722255707, -0.04007991775870323, -0.051056161522865295, -0.006103456486016512, -0.027706699445843697, -0.017379051074385643, -0.019491147249937057, 0.041676461696624756, 0.0011017819633707404, 0.011974083259701729, -0.03425918146967888, 0.01184103824198246, -0.0005410165176726878, -0.009837042540311813, -0.0008725905208848417, -0.028621384873986244, 0.026342984288930893, 0.026060262694954872, 0.022185316309332848, -0.009304860606789589, 0.00814902875572443, 0.017004862427711487, 0.002000877633690834, -0.026342984288930893, -0.0076958429999649525, -0.010618683882057667, 0.03715291991829872, -0.013961448334157467, 0.04400475695729256, 0.008045087568461895, 0.04383844882249832, 0.011367063969373703, 0.04786307364702225, -0.00783720426261425, 0.01792786456644535, -0.022484667599201202, 0.06742074340581894, -0.031648166477680206, 0.05534687638282776, 0.018676243722438812, 0.01847667619585991, 0.022035639733076096, -0.021187474951148033, -0.012888770550489426, -0.0047730025835335255, 0.007043089251965284, -0.01281393226236105, -0.0010446140076965094, -0.06818575412034988, 0.02961922623217106, 0.0026733805425465107, -0.00006775699148420244, -0.011990713886916637, 0.06708812713623047, -0.004222111776471138, -0.044038016349077225, 0.01253952644765377, -0.024264149367809296, -0.011275595054030418, 0.04886091127991676, -0.005504752043634653, 0.032196979969739914, -0.01154168602079153, -0.019441254436969757, 0.0211209524422884, 0.04816242307424545, 0.02363218367099762, 0.05567948892712593, 0.011691361665725708, 0.047763288021087646, 0.012630995362997055, -0.02684190310537815, 0.034658320248126984, 0.006635637953877449, 0.0167886633425951, 0.016023652628064156, 0.03096630983054638, 0.010460692457854748, 0.016805293038487434, 0.027557022869586945, 0.0003216995391994715, -0.02098790742456913, -0.003353159176185727, 0.0356561578810215, 0.0005498515674844384, 0.057142987847328186, -0.01801101677119732, -0.016821924597024918, -0.00533844530582428, 0.05830713361501694, 0.033078406006097794, -0.01086814422160387, 0.025877324864268303, 0.033510804176330566, -0.0017961125122383237, 0.011292225681245327, -0.04779655113816261, -0.03216371685266495, -0.037119656801223755, -0.02298358827829361, -0.05910540744662285, -0.021054429933428764, -0.012473003938794136, 0.04034600779414177, -0.019291579723358154, -0.0035735154524445534, 0.012273435480892658, -0.02127062901854515, 0.016846871003508568, 0.018593091517686844, -0.005903888493776321, 0.03036760538816452, -0.020871492102742195, 0.009537690319120884, 0.027523761615157127, -0.016331318765878677, 0.011591577902436256, 0.02163650281727314, 0.014036286622285843, -0.007450541015714407, -0.005147192627191544, 0.028870845213532448, 0.002134962473064661, -0.019008858129382133, -0.07723283767700195, 0.004706480074673891, -0.008764363825321198, 0.026675596833229065, 0.03055054321885109, 0.0446699820458889, 0.018726136535406113, 0.0020164689049124718, 0.010177970863878727, -0.011034450493752956, -0.015433263033628464, 0.03036760538816452, 0.015108965337276459, 0.006269763223826885, 0.0010368183720856905, -0.09692355245351791, -0.010352592915296555, 0.044137801975011826, -0.003400972345843911, 0.00010680009290808812, -0.021569980308413506, -0.011774515733122826, 0.03445875272154808, -0.004544330760836601, -0.020139742642641068, 0.0025694386567920446, -0.017329160124063492, -0.0029186827596277, 0.03934817016124725, 0.0537835918366909, -0.013687042519450188, -0.012913716025650501, 0.0156245157122612, -0.018027648329734802, 0.02526199072599411, -0.016863500699400902, 0.010552161373198032, -0.015923867002129555, -0.012705832719802856, 0.015533046796917915, -0.015707669779658318, 0.02715788595378399, 0.04077840596437454, -0.03658747673034668, 0.010186286643147469, 0.02521209791302681, -0.029236720874905586, 0.0078496765345335, -0.027290930971503258, -0.0006044209585525095, -0.014934343285858631, 0.016007021069526672, -0.010809936560690403, 0.04995853826403618, -0.025178836658596992, 0.015258640982210636, 0.07217711210250854, -0.0001972293684957549, 0.011325486935675144, 0.00013207091251388192, 0.023665444925427437, -0.017728295177221298, 0.020372573286294937, 0.035689420998096466, 0.00958758220076561, -0.031032832339406013, 0.029569333419203758, -0.016381211578845978, 0.012639310210943222, 0.018227215856313705, 0.024081211537122726, -0.00002955841955554206, 0.0027939528226852417, 0.011076027527451515, -0.02419762685894966, 0.04094471409916878, -0.00851074606180191, 0.004016307182610035, -0.029452919960021973, -0.02140367403626442, -0.028621384873986244, 0.07250972837209702, 0.0034300759434700012, 0.007479644380509853, 0.02777322195470333, -0.014227539300918579, 0.05448208004236221, -0.037452273070812225, -0.0023823436349630356, 0.029319873079657555, 0.006298866588622332, 0.014917712658643723, 0.07437236607074738, 0.00717197684571147, 0.01585734449326992, 0.04047905281186104, -0.0007993116741999984, -0.011508424766361713, 0.008489958010613918, -0.011990713886916637, -0.0334276482462883, -0.00958758220076561, 0.06466004997491837, 0.016905076801776886, -0.03525702282786369, 0.04626652970910072, 0.029968470335006714, -0.057043202221393585, 0.005213715601712465, -0.025228729471564293, -0.01211544405668974, -0.045667823404073715, -0.0031889311503618956, -0.015266956761479378, -0.0063612316735088825, 0.00015643225924577564, -0.03861641883850098, -0.03998013585805893, -0.012273435480892658, -0.001435434794984758, 0.0070763505063951015, -0.022118793800473213, 0.010186286643147469, 0.013745250180363655, -0.03858315944671631, -0.01465162169188261, -0.025611234828829765, 0.06313002854585648, -0.031082725152373314, 0.03133218362927437, 0.014518575742840767, 0.006382020190358162, 0.02549481950700283, 0.0211209524422884, -0.01702149212360382, -0.018875811249017715, -0.020721817389130592, -0.05052398145198822, -0.0002931155904661864, 0.0049309940077364445, 0.0044944388791918755, -0.014601729810237885, 0.015541362576186657, 0.04081166908144951, 0.006303024478256702, -0.02127062901854515, -0.03539006784558296, 0.0016464365180581808, 0.02308337204158306, 0.003415524261072278, -0.004026701208204031, -0.03361058607697487, -0.009878618642687798, 0.029502810910344124, -0.006011987570673227, 0.011067711748182774, 0.0006132560083642602, -0.029635855928063393, 0.007571113295853138, 0.006910043768584728, -0.005313499365001917, -0.02502916008234024, -0.005579590331763029, 0.020023329183459282, -0.008539849892258644, 0.027507130056619644, 0.014543522149324417, 0.007641793694347143, -0.02270086668431759, -0.020771708339452744, 0.032113827764987946, 0.0356561578810215, -0.0014697356382384896, 0.021320519968867302, 0.037352487444877625, 0.012805617414414883, -0.0023615553509444, 0.02042246423661709, -0.03374363109469414, -0.00022464399808086455, -0.018875811249017715, -0.032429810613393784, -0.023415984585881233, 0.02868790738284588, 0.03542333096265793, -0.019707346335053444, 0.03572268411517143, -0.01479298248887062, -0.002438472118228674, 0.022484667599201202, 0.015291902236640453, -0.003631722880527377, 0.024347303435206413, -0.034392230212688446, -0.00017981913697440177, -0.013587258756160736, 0.010485637933015823, 0.037219442427158356, -0.014476999640464783, -0.0025548869743943214, -0.005080670118331909, -0.03904881700873375, 0.009745573624968529, -0.01406954787671566, -0.0013512420700863004, -0.01917516440153122, 0.02358229272067547, -0.004155588801950216, -0.039813827723264694, -0.0043863398022949696, 0.044137801975011826, -0.039215121418237686, 0.012481318786740303, 0.03459179773926735, -0.0400133952498436, 0.01044406183063984, 0.0033240553457289934, 0.009878618642687798, -0.013163176365196705, 0.016547517850995064, -0.05800778046250343, 0.010128078982234001, -0.01448531448841095, 0.03390993922948837, 0.03259611502289772, -0.010660259984433651, 0.0005394574254751205, -0.027690067887306213, -0.05920518934726715, 0.009903565049171448, -0.04573434591293335, -0.0021619873587042093, 0.023748598992824554, 0.007729104720056057, 0.007645951118320227, 0.011666416190564632, -0.004731426015496254, -0.06911706924438477, 0.046732187271118164, 0.04393823444843292, -0.0048478408716619015, 0.04643283411860466, -0.02707473374903202, 0.03632138669490814, -0.03151512145996094, 0.0009167657699435949, -0.022784020751714706, -0.015865661203861237, -0.008144871331751347, -0.007833045907318592, 0.0301846694201231, 0.015898922458291054, 0.0026525920256972313, 0.010768359526991844, 0.02093801461160183, 0.0083693852648139, 0.015790821984410286, -0.007870465517044067, -0.027606913819909096, -0.008319493383169174, -0.03765184059739113, -0.027008211240172386, 0.0045318580232560635, -0.023000217974185944, 0.03854989632964134, 0.030467389151453972, 0.006864309776574373, -0.01811080053448677, 0.016156697645783424, -0.04057883843779564, -0.0009172854479402304, 0.019008858129382133, 0.0513555146753788, 0.02010648138821125, 0.04310670122504234, -0.005799946840852499, 0.0015029968926683068, 0.008207236416637897, -0.014901082031428814, -0.017063068225979805, -0.041443634778261185, 0.010078187100589275, -0.02010648138821125, 0.012705832719802856, 0.015275271609425545, -0.04017970338463783, -0.024297410622239113, -0.044270846992731094, -0.03251296281814575, -0.019141903147101402, -0.0007634517387486994, -0.02122073620557785, 0.0037107185926288366, -0.02516220510005951, -0.02127062901854515, 0.05138877406716347, -0.039913609623909, 0.040146440267562866, -0.014676567167043686, 0.030350975692272186, -0.01839352212846279, 0.019108641892671585, 0.016381211578845978, -0.010294385254383087, -0.004251215606927872, 0.06179957464337349, 0.027107995003461838, 0.011633154936134815, -0.00500167440623045, -0.005234503652900457, -0.029053783044219017, -0.02265097387135029, -0.006806102115660906, -0.04500259831547737, 0.00822802446782589, -0.044137801975011826 ]
As a booming research area in the past decade, deep learning technologies have been driven by big data collected and processed on an unprecedented scale. However, privacy concerns arise due to the potential leakage of sensitive information from the training data. Recent research has revealed that deep learning models are vulnerable to various privacy attacks, including membership inference attacks, attribute inference attacks, and gradient inversion attacks. Notably, the efficacy of these attacks varies from model to model. In this paper, we answer a fundamental question: Does model architecture affect model privacy? By investigating representative model architectures from CNNs to Transformers, we demonstrate that Transformers generally exhibit higher vulnerability to privacy attacks compared to CNNs. Additionally, We identify the micro design of activation layers, stem layers, and LN layers, as major factors contributing to the resilience of CNNs against privacy attacks, while the presence of attention modules is another main factor that exacerbates the privacy vulnerability of Transformers. Our discovery reveals valuable insights for deep learning models to defend against privacy attacks and inspires the research community to develop privacy-friendly model architectures.
[ -0.034176211804151535, -0.0007567066932097077, -0.033728115260601044, -0.03472771868109703, 0.1091984286904335, 0.025679554790258408, 0.031125688925385475, -0.0030246723908931017, -0.024404194205999374, 0.07452241331338882, -0.012788074091076851, -0.03733014315366745, 0.0022146461997181177, -0.011099082417786121, -0.00787621270865202, 0.013046592473983765, 0.03746802359819412, -0.05353067070245743, 0.031539320945739746, -0.02719620056450367, 0.02385268732905388, -0.03529646247625351, 0.009091251529753208, -0.041052818298339844, 0.02878178283572197, 0.03984639793634415, 0.03819187358021736, -0.004743823781609535, -0.016467660665512085, 0.05435793101787567, 0.04811900481581688, 0.0145115340128541, -0.01461494155228138, 0.00010455209121573716, -0.02235327661037445, -0.04649895429611206, 0.03150485083460808, 0.023628637194633484, -0.016054030507802963, 0.04487890005111694, 0.002895412966609001, -0.06018322706222534, 0.006437123287469149, -0.015700720250606537, 0.010487254709005356, -0.03066035360097885, -0.03729567676782608, -0.002337442710995674, 0.023094365373253822, -0.004588712472468615, -0.016640007495880127, -0.04232817888259888, 0.06135517731308937, 0.014683879911899567, -0.07762464135885239, 0.01909593679010868, 0.02964351326227188, -0.0472228042781353, 0.057425688952207565, 0.00936700589954853, 0.00938424002379179, 0.025386566296219826, -0.015071658417582512, 0.012150393798947334, -0.014278866350650787, -0.00024061118892859668, 0.009048165753483772, 0.009246363304555416, -0.018389318138360977, 0.010392463766038418, -0.07790039479732513, 0.03236658126115799, -0.0017191513907164335, -0.023766513913869858, -0.013494692742824554, -0.021681128069758415, 0.008841349743306637, 0.04760196805000305, 0.021267497912049294, 0.02711002714931965, 0.035072412341833115, 0.06114836409687996, -0.03619266301393509, 0.0025356407277286053, 0.08238139003515244, 0.013425753451883793, -0.04873945191502571, -0.056529488414525986, 0.03733014315366745, -0.005006651394069195, -0.024369725957512856, 0.02154325135052204, 0.0050712814554572105, -0.05435793101787567, 0.007415187079459429, 0.02621382661163807, -0.009866808541119099, -0.04381035640835762, -0.02731684222817421, 0.0025507209356874228, -0.011047379113733768, 0.001965821720659733, -0.012081455439329147, 0.004709354601800442, 0.0329008512198925, -0.07679738104343414, -0.03936382755637169, 0.06473316252231598, 0.021956881508231163, 0.12464062869548798, -0.011641972698271275, -0.022404979914426804, -0.03850209712982178, 0.017191514372825623, -0.016924377530813217, 0.06487103551626205, -0.07176487892866135, -0.030522476881742477, 0.009315301664173603, -0.05570222809910774, 0.021922411397099495, 0.03822634369134903, -0.00854836218059063, 0.049566712230443954, -0.05932149663567543, 0.09589331597089767, -0.01217624545097351, 0.018871888518333435, -0.021560484543442726, 0.020078308880329132, 0.0036580439191311598, 0.03888125717639923, 0.031005047261714935, -0.043258845806121826, 0.051117826253175735, -0.014563237316906452, 0.06718046963214874, -0.01083194650709629, -0.005644331686198711, 0.003496469696983695, 0.050014812499284744, -0.030436305329203606, 0.01555422693490982, 0.022939253598451614, -0.0490841418504715, 0.03455537557601929, -0.0037399083375930786, 0.08127837628126144, -0.009211894124746323, -0.02280137687921524, -0.017734404653310776, 0.026937680318951607, 0.04232817888259888, 0.06845583021640778, 0.051117826253175735, -0.028799017891287804, 0.02295648865401745, 0.012331356294453144, -0.0245937742292881, -0.023869922384619713, 0.03102228045463562, -0.026937680318951607, 0.003117308486253023, 0.00725576700642705, 0.03553774580359459, 0.04991140216588974, 0.10926736891269684, 0.021060682833194733, -0.07190275192260742, 0.05284128710627556, 0.017803343012928963, 0.021405374631285667, -0.018372084945440292, 0.009125720709562302, -0.01966467872262001, -0.0023956093937158585, -0.03390045836567879, -0.04294862598180771, -0.04512018337845802, -0.007143741939216852, 0.011753997765481472, 0.03319384157657623, 0.01564040035009384, -0.0014477064833045006, 0.03688204661011696, 0.05477156117558479, 0.07086867839097977, 0.015166448429226875, 0.01156441681087017, -0.0073850261978805065, -0.02752365730702877, 0.04615426063537598, -0.0047352067194879055, -0.043741416186094284, 0.006368184927850962, -0.06094154715538025, 0.040570251643657684, -0.02337011881172657, 0.006807667203247547, 0.02564508654177189, -0.008358781225979328, -0.019716383889317513, 0.022646265104413033, 0.013012123294174671, -0.013718741945922375, -0.041259635239839554, 0.01987149380147457, 0.015226769261062145, -0.000808410462923348, -0.024335255846381187, -0.05377195402979851, 0.012383060529828072, -0.01467526238411665, -0.04994587227702141, -0.023542463779449463, 0.0014703269116580486, 0.002216800581663847, 0.003433994250372052, 0.0073548657819628716, -0.01852719485759735, 0.03045353852212429, -0.004778292961418629, 0.028230275958776474, -0.03795059025287628, -0.04767090454697609, -0.04587850719690323, -0.030884403735399246, 0.017484502866864204, -0.01615743897855282, -0.003056987188756466, -0.037881653755903244, -0.02226710319519043, 0.01876848004758358, -0.01141792256385088, 0.04963564872741699, -0.0709376186132431, 0.03364194184541702, -0.0038971740286797285, -0.024990171194076538, -0.012107307091355324, -0.009272214956581593, -0.023663107305765152, 0.014856225810945034, -0.030384600162506104, 0.04294862598180771, 0.026524050161242485, -0.05708099901676178, 0.026455111801624298, 0.012900098226964474, 0.04991140216588974, 0.02243945002555847, 0.0069498526863753796, -0.01056481059640646, 0.0006705336854793131, -0.05521966144442558, 0.002850172109901905, -0.024817824363708496, -0.01265881396830082, -0.02076769433915615, -0.03729567676782608, 0.04229370877146721, -0.03510688245296478, -0.04501677677035332, 0.08293289691209793, 0.0006915383273735642, 0.02755812555551529, 0.05146251618862152, 0.05501284450292587, 0.04808453470468521, 0.023749278858304024, -0.012426147237420082, -0.02666192688047886, -0.07472922652959824, -0.03546880930662155, -0.025627851486206055, -0.0025291775818914175, 0.02259456180036068, 0.02797175757586956, 0.03252169117331505, -0.02495570108294487, 0.05845976620912552, -0.04970458894968033, -0.001818250399082899, -0.005075589753687382, 0.017820576205849648, 0.01333096344023943, -0.021560484543442726, -0.001472481177188456, -0.037605900317430496, -0.028281979262828827, -0.050669725984334946, -0.004140612669289112, -0.09065400063991547, -0.0210434477776289, 0.02307713031768799, -0.054254524409770966, 0.008212286978960037, -0.041052818298339844, -0.012374443002045155, 0.01134036760777235, -0.06607745587825775, -0.04356906935572624, -0.01599370874464512, 0.01119387336075306, -0.023956093937158585, -0.0062389252707362175, 0.010926736518740654, 0.07948597520589828, -0.009720314294099808, -0.002102621365338564, -0.0023331339471042156, -0.003961803857237101, -0.018596133217215538, 0.0029492711182683706, -0.02373204566538334, 0.05129017308354378, -0.006911074742674828, 0.011202489957213402, -0.03329724818468094, -0.016683094203472137, 0.020285125821828842, 0.04915308207273483, -0.049325425177812576, 0.02312883362174034, -0.039880864322185516, -0.008832733146846294, -0.0017837812192738056, 0.006816284731030464, -0.04408610984683037, 0.009358388371765614, -0.0331249013543129, -0.014985485002398491, -0.050704196095466614, -0.05418558418750763, 0.033934928476810455, 0.05463368445634842, -0.004058748483657837, -0.003617111826315522, -0.021353669464588165, -0.0325733944773674, -0.03367640823125839, 0.010426932945847511, -0.09740996360778809, 0.006195839028805494, -0.030591415241360664, -0.07121337205171585, -0.034021101891994476, -0.0100563894957304, -0.034296855330467224, -0.00917742494493723, 0.0009252825984731317, -0.013830767013132572, -0.0021694053430110216, -0.006402654107660055, 0.004401286132633686, 0.019837025552988052, 0.030177785083651543, -0.05456474423408508, 0.02773047238588333, -0.014795904979109764, 0.028488794341683388, -0.02919541299343109, -0.026920445263385773, 0.022301573306322098, -0.057012058794498444, -0.05939043313264847, -0.037847183644771576, -0.006471592467278242, 0.011185255832970142, 0.04232817888259888, 0.0005388505524024367, 0.045947443693876266, 0.027006618678569794, 0.020578112453222275, 0.047360680997371674, -0.046602360904216766, 0.015019954182207584, -0.00767370592802763, 0.000925821193959564, 0.05797719582915306, -0.057012058794498444, 0.013141383416950703, 0.054943908005952835, 0.04363800957798958, -0.004170773550868034, 0.02695491537451744, 0.058563172817230225, -0.036744169890880585, -0.048670511692762375, 0.07155805826187134, -0.0011267120717093349, -0.021146854385733604, 0.03186677768826485, -0.05194508656859398, 0.03233211115002632, 0.052255310118198395, -0.0012010362697765231, -0.024869529530405998, 0.027937287464737892, -0.06204456090927124, -0.002667054533958435, 0.041707731783390045, -0.00830276869237423, -0.004338810686022043, -0.014985485002398491, -0.0031582405790686607, 0.03057418204843998, -0.009410091675817966, 0.02886795625090599, -0.021887943148612976, 0.003076376160606742, -0.018716776743531227, -0.014468447305262089, -0.022180931642651558, 0.015528375282883644, -0.014123755507171154, -0.02548997476696968, -0.015855832025408745, -0.01146100927144289, -0.017579292878508568, 0.042810749262571335, 0.01347745768725872, 0.032349344342947006, -0.025231454521417618, -0.027385780587792397, 0.033004261553287506, 0.021405374631285667, 0.022853080183267593, 0.03912254422903061, 0.016398722305893898, 0.059459373354911804, -0.03281467780470848, 0.03110845386981964, -0.039225950837135315, -0.04894626513123512, -0.0684213638305664, 0.013692890293896198, -0.000006648112503171433, -0.005605553742498159, 0.018303146585822105, 0.0017708551604300737, 0.01981979049742222, -0.009272214956581593, 0.06369908154010773, -0.009763401001691818, -0.02504187449812889, -0.004946330562233925, -0.0210434477776289, -0.005976097658276558, 0.014856225810945034, -0.012615727260708809, 0.02866114117205143, -0.09217064082622528, -0.08713813871145248, 0.03701992332935333, -0.014692497439682484, 0.017941219732165337, -0.026799803599715233, 0.015424967743456364, -0.05077313259243965, 0.007143741939216852, 0.06007981672883034, -0.017941219732165337, -0.01209007203578949, -0.028730079531669617, 0.019354457035660744, -0.049566712230443954, -0.014632175676524639, -0.005058355163782835, -0.006859370972961187, 0.019078703597187996, -0.0030225180089473724, -0.0021597109735012054, 0.01072853896766901, -0.014795904979109764, -0.00039100999129004776, -0.0009102023323066533, -0.06111389398574829, -0.018596133217215538, -0.020940039306879044, 0.03684757649898529, 0.06287182122468948, 0.011004292406141758, -0.03839869052171707, -0.01539049856364727, -0.013555013574659824, 0.02711002714931965, 0.0033219691831618547, -0.030522476881742477, -0.03188401088118553, 0.0005229624221101403, -0.007298853248357773, 0.0312635637819767, -0.011202489957213402, 0.0007222374551929533, -0.032176997512578964, 0.015045806765556335, -0.018372084945440292, 0.07996854931116104, 0.04294862598180771, -0.009186042472720146, -0.02907477132976055, 0.021991349756717682, -0.009125720709562302, 0.027799410745501518, -0.035279229283332825, -0.052668940275907516, -0.029902031645178795, 0.03670969977974892, 0.03436579182744026, 0.03843316063284874, 0.004498230759054422, 0.026248296722769737, -0.03636500611901283, -0.01009947620332241, -0.016726179048419, 0.020526409149169922, 0.029247118160128593, -0.03252169117331505, 0.008893053978681564, -0.009642759338021278, -0.024990171194076538, -0.021439842879772186, 0.041914548724889755, -0.035847969353199005, 0.06638768315315247, 0.04360353946685791, -0.007148050703108311, 0.00007964270480442792, -0.02397332899272442, 0.012839777395129204, -0.007247149478644133, -0.012495085597038269, -0.002578727202489972, 0.06621533632278442, 0.006527605000883341, 0.008802572265267372, 0.012589875608682632, -0.02402503415942192, 0.008216596208512783, -0.06542254239320755, 0.02328394539654255, -0.008987843990325928, 0.007273001596331596, 0.014373657293617725, -0.007458273321390152, 0.042810749262571335, -0.05566776171326637, -0.0006339101819321513, -0.009832339361310005, 0.038088466972112656, 0.014502916485071182, -0.008057176135480404, -0.010271822102367878, -0.03021225519478321, -0.0197853222489357, -0.00248824548907578, 0.04432739317417145, -0.0003705439157783985, -0.03550327569246292, -0.0631820484995842, 0.023094365373253822, -0.02385268732905388, 0.016467660665512085, -0.04205242544412613, -0.04856710508465767, 0.015588696114718914, 0.030591415241360664, 0.025472739711403847, -0.008733633905649185, -0.0025140973739326, -0.0007146973512135446, -0.02211199328303337, 0.026403408497571945, 0.027833880856633186, 0.023439057171344757, 0.030470773577690125, -0.01816526986658573, 0.019854260608553886, 0.04649895429611206, 0.0031970185227692127, 0.0033025804441422224, -0.028161337599158287, 0.0239388607442379, 0.01567486859858036, -0.006019184365868568, -0.033452358096838, -0.01545081939548254, 0.007113581523299217, -0.012632962316274643, -0.0027467645704746246, 0.018716776743531227, 0.015804128721356392, -0.004549934528768063, 0.018871888518333435, 0.0006091354298405349, 0.060148756951093674, 0.01697608083486557, 0.04498230665922165, -0.052462123334407806, 0.014253014698624611, 0.02014724723994732, 0.04611979052424431, 0.013632569462060928, -0.014339188113808632, -0.013580865226686, 0.009074017405509949, 0.0019345838809385896, -0.0447065532207489, -0.004106143489480019, 0.03066035360097885, -0.011038761585950851, 0.023869922384619713, -0.04432739317417145, 0.0420868955552578, 0.028971362859010696, 0.030384600162506104, 0.009074017405509949, -0.02991926670074463, -0.04453420639038086, -0.014278866350650787, 0.006101048551499844, 0.06342332810163498, 0.010366612114012241, 0.00020466088608372957, 0.05322044715285301, 0.008789646439254284, 0.022766906768083572, 0.006816284731030464, -0.038536567240953445, -0.037157800048589706, 0.0067602721974253654, -0.010401081293821335, -0.02223263494670391, -0.016217758879065514, -0.01733800768852234, 0.03134973719716072, 0.022456685081124306, 0.012469233945012093, 0.00605796230956912, -0.028919659554958344, -0.001020611496642232, -0.021422607824206352, 0.026799803599715233, -0.0018796486547216773, 0.002983740298077464, -0.04039790481328964, 0.006338024511933327, 0.05546094477176666, 0.022318808361887932, 0.010401081293821335, 0.051565926522016525, -0.004349582362920046, 0.022611796855926514, -0.008488040417432785, -0.014218545518815517, 0.027575360611081123, -0.0017945527797564864, 0.020388532429933548, 0.007858977653086185, -0.03269403800368309, 0.0188546534627676, -0.02288755029439926, 0.039432767778635025, 0.015149214304983616, -0.05932149663567543, -0.0010243816068395972, 0.0028523264918476343, -0.004554243292659521, 0.06345780193805695, 0.018820183351635933, -0.012857012450695038, -0.03622712939977646, 0.018372084945440292, 0.040328964591026306, -0.03102228045463562, 0.02149154618382454, 0.012994889169931412, -0.015149214304983616, -0.02121579274535179, -0.013925557024776936, 0.009840956889092922, -0.023232242092490196, 0.016217758879065514, -0.017191514372825623, -0.01461494155228138, 0.02895412966609001, -0.018337614834308624, 0.02454207092523575, -0.03977745771408081, -0.006786123849451542, -0.03321107476949692, -0.00626908615231514, -0.01868230663239956, 0.022939253598451614, -0.025869134813547134, -0.0033327408600598574, 0.018061861395835876, -0.008625918067991734, -0.02250838838517666, 0.014468447305262089, 0.026041481643915176, -0.015769660472869873, 0.00071362016024068, 0.02423184923827648, 0.017648231238126755, 0.014235779643058777, -0.00039020212716422975, -0.011469626799225807, 0.05056631937623024, -0.0018214818555861712, 0.04050131142139435, 0.0033025804441422224, 0.03457260876893997, 0.017605144530534744, 0.0028630979359149933, 0.021405374631285667, 0.02068152092397213, -0.00445945281535387, -0.0002975661482196301, 0.02397332899272442, 0.037192266434431076, -0.00001639306719880551, -0.02166389301419258, -0.01394279208034277, 0.02674810029566288, -0.004164310172200203, 0.017372477799654007, -0.026403408497571945, 0.004679194185882807, 0.047360680997371674, -0.0452580600976944, -0.0069800131022930145, 0.002626122208312154, 0.017191514372825623, -0.03383152186870575, 0.03152208402752876, 0.006126900669187307, 0.009186042472720146, -0.024783356115221977, 0.016278080642223358, 0.00529102236032486, -0.020543644204735756, -0.042603932321071625, 0.016088498756289482, 0.043982699513435364, -0.052668940275907516, -0.01022011786699295, -0.037605900317430496, 0.029160944744944572, 0.03650288283824921, -0.021629422903060913, 0.017855046316981316, 0.003164703492075205, -0.0113145150244236, 0.008311386220157146, 0.0071049639955163, 0.0070877294056117535, 0.00642419746145606, -0.049118611961603165, -0.007148050703108311, 0.0293505247682333, -0.027902819216251373, 0.05139357969164848, 0.020991744473576546, -0.01787228137254715, -0.002132781781256199, 0.009513499215245247, 0.006342332810163498, -0.01913040690124035, 0.016028178855776787, 0.026075949892401695, 0.07286789268255234, -0.02474888600409031, -0.06256160140037537, 0.0347621887922287, 0.013046592473983765, 0.0010184572311118245, -0.01852719485759735, 0.01957850717008114, -0.0322459377348423, 0.0008552670478820801, 0.021956881508231163, 0.041466448456048965, -0.015097510069608688, -0.013675655238330364, 0.03009161353111267, -0.06307864189147949, -0.0023266710340976715, 0.05932149663567543, 0.026696396991610527, -0.032176997512578964, 0.0145115340128541, -0.06276841461658478, 0.00938424002379179, 0.003462000284343958, -0.016433192417025566, 0.05394430086016655, -0.044155046343803406, -0.04512018337845802, 0.050704196095466614, -0.017320774495601654, 0.018578900024294853, -0.024524835869669914, -0.03536539897322655, -0.007699558045715094, -0.023714810609817505, -0.029092006385326385, -0.005527998320758343, -0.02674810029566288, 0.0077598788775503635, -0.026110420003533363, -0.0051703802309930325, -0.009504882618784904, -0.028850721195340157, -0.01198666449636221, -0.007712483871728182, 0.030022675171494484, 0.0029600425623357296, -0.04739515110850334, 0.01954403705894947, -0.0075315204448997974, -0.03110845386981964, -0.023887155577540398, -0.0015317251672968268, -0.0765216276049614, 0.050704196095466614, -0.015657635405659676, 0.047981128096580505, 0.025869134813547134, -0.0027747706044465303, 0.01331372931599617, -0.01530432514846325, 0.052496593445539474, -0.00932391919195652, 0.056805241852998734, 0.010039154440164566, 0.04522359371185303, -0.013623951934278011, -0.014864843338727951, -0.038777850568294525, 0.04239711910486221, -0.013994495384395123, 0.0038713221438229084, 0.0063164811581373215, -0.0011536410311236978, 0.02064705081284046, -0.0046878112480044365, 0.009470413438975811, -0.014873459935188293, 0.030315661802887917, 0.05087653920054436, -0.007092038169503212, 0.03503794223070145, 0.02833368256688118, 0.01321032177656889, -0.03131527081131935, -0.0025140973739326, -0.013649803586304188, -0.04201795533299446, -0.03048800863325596, 0.029609043151140213, 0.018303146585822105, 0.0011644127080217004, -0.012822543270885944, 0.011409305967390537, 0.012219332158565521, 0.0007357019931077957, 0.002919110469520092, -0.059218086302280426, -0.0159592404961586, -0.00014864842523820698, -0.010943971574306488, 0.01539049856364727, -0.001059389323927462, 0.006144135259091854, 0.033555768430233, -0.032108061015605927, 0.010108092799782753, -0.01942339539527893, 0.014856225810945034, 0.0020282971672713757, 0.034296855330467224, 0.020664285868406296, 0.0024839367251843214, 0.004039359744638205, 0.04063918814063072, -0.044637616723775864, -0.00575204798951745, -0.010263204574584961, -0.02650681510567665, -0.008996461518108845, -0.020612582564353943, -0.0025916530285030603, 0.04256946220993996, -0.020509174093604088, 0.0312635637819767, 0.01616605557501316, -0.013201704248785973, 0.02621382661163807, 0.017562057822942734, -0.013244790956377983, 0.005851146765053272, -0.03317660465836525, 0.01823420822620392, 0.0574946291744709, -0.01835484988987446, -0.0027316841296851635, 0.007846051827073097, -0.0073850261978805065, -0.019285518676042557, -0.008195052854716778, -0.04815347492694855, 0.010969823226332664, -0.0007351634558290243, 0.06294076144695282, 0.02931605651974678, -0.02991926670074463, 0.010461402125656605, -0.006191530264914036, 0.02600701153278351, 0.05322044715285301, -0.020181717351078987, 0.04422398656606674, 0.0011601040605455637, -0.0074238041415810585, -0.018665071576833725, 0.027661534026265144, -0.03477942571043968, 0.0315910242497921, -0.045499347150325775, 0.006570691708475351, -0.009720314294099808, 0.015088892541825771, 0.06793879717588425, 0.022853080183267593, -0.025093577802181244, 0.04318990930914879, -0.05187614634633064, 0.014864843338727951, -0.04108728840947151, -0.03162549063563347, 0.03250445798039436, 0.032625097781419754, -0.005420282017439604, 0.0042526377364993095, 0.04232817888259888, 0.01398587878793478, 0.00632078992202878, 0.02206028811633587, -0.026351705193519592, 0.004280644003301859, -0.01762237958610058, 0.003742062719538808, -0.008035632781684399, 0.011107699945569038, -0.01771716959774494, 0.03317660465836525, -0.02361140213906765, 0.03469325229525566, 0.015933388844132423, 0.04343119263648987, 0.03908807411789894, -0.023663107305765152, 0.011685059405863285, 0.00037377540138550103, -0.02988479658961296, -0.030350131914019585, -0.005739122163504362, 0.011486860923469067, -0.015459436923265457, -0.053185977041721344, -0.011064613237977028, -0.021422607824206352, 0.04518912360072136, -0.02133643627166748, 0.033728115260601044, -0.0255244430154562, 0.027092792093753815, 0.020991744473576546, -0.003007437800988555, -0.029402228072285652, 0.022163696587085724, 0.031694430857896805, -0.03147038072347641, -0.04253499582409859, -0.00861299131065607, 0.001602817908860743, -0.061906684190034866, 0.010530341416597366, -0.02280137687921524, 0.01913040690124035, 0.026851506903767586, -0.02540380135178566, -0.008031323552131653, -0.015269855968654156, -0.009763401001691818, -0.05839082598686218, 0.021853473037481308, 0.009608290158212185, -0.031935714185237885, 0.032021887600421906, 0.015097510069608688, 0.05256553366780281, 0.0020304513163864613, 0.04456867650151253, 0.05873551964759827, -0.021870708093047142, -0.017415564507246017, 0.008255373686552048, -0.0017880898667499423, 0.006027801427990198, -0.003914408851414919, 0.04070812836289406, -0.0004079753125552088, 0.017208749428391457, -0.0053987386636435986, 0.032625097781419754, -0.04115622490644455, -0.028919659554958344, 0.06973119080066681, -0.022163696587085724, 0.003925180062651634, -0.002667054533958435 ]
Since the 2004 DARPA Grand Challenge, the autonomous driving technology has witnessed nearly two decades of rapid development. Particularly, in recent years, with the application of new sensors and deep learning technologies extending to the autonomous field, the development of autonomous driving technology has continued to make breakthroughs. Thus, many carmakers and high-tech giants dedicated to research and system development of autonomous driving. However, as the foundation of autonomous driving, the deep learning technology faces many new security risks. The academic community has proposed deep learning countermeasures against the adversarial examples and AI backdoor, and has introduced them into the autonomous driving field for verification. Deep learning security matters to autonomous driving system security, and then matters to personal safety, which is an issue that deserves attention and research.This paper provides an summary of the concepts, developments and recent research in deep learning security technologies in autonomous driving. Firstly, we briefly introduce the deep learning framework and pipeline in the autonomous driving system, which mainly include the deep learning technologies and algorithms commonly used in this field. Moreover, we focus on the potential security threats of the deep learning based autonomous driving system in each functional layer in turn. We reviews the development of deep learning attack technologies to autonomous driving, investigates the State-of-the-Art algorithms, and reveals the potential risks. At last, we provides an outlook on deep learning security in the autonomous driving field and proposes recommendations for building a safe and trustworthy autonomous driving system.
[ -0.019494500011205673, -0.007501436863094568, -0.009495383128523827, -0.04637709632515907, 0.023574745282530785, 0.013432903215289116, 0.010318148881196976, 0.007753303740173578, -0.04026512801647186, 0.016127878800034523, 0.04248155653476715, -0.031752023845911026, 0.04184349253773689, 0.0028859751764684916, -0.04731740057468414, 0.060145821422338486, 0.024011313915252686, -0.03932482376694679, 0.001432493212632835, -0.06451151520013809, 0.016153065487742424, 0.0016906567616388202, -0.05665326863527298, 0.04395917430520058, 0.0032050067093223333, 0.036100927740335464, 0.054671913385391235, 0.012291106395423412, -0.0663585439324379, 0.031886354088783264, -0.0031525343656539917, -0.015556980855762959, -0.008848925121128559, 0.003139941021800041, -0.01850382424890995, -0.013936636969447136, -0.012887191027402878, 0.040500201284885406, -0.01607750542461872, 0.04342185705900192, 0.050642043352127075, -0.03878750652074814, -0.00991516187787056, 0.01731165312230587, -0.00984799675643444, -0.04311961680650711, -0.027403121814131737, -0.03791436925530434, -0.03838451951742172, -0.006111970636993647, -0.00009536836296319962, -0.04943308234214783, 0.041003935039043427, -0.023003846406936646, -0.033515091985464096, 0.021694138646125793, 0.018050463870167732, -0.03825019299983978, 0.03141620010137558, -0.00517586525529623, 0.011157705448567867, -0.0006632495787926018, -0.02555609866976738, 0.006049003917723894, -0.0537651926279068, -0.02926693670451641, 0.06182493641972542, 0.0019572158344089985, 0.01646370254456997, 0.00622950866818428, -0.06111970916390419, 0.0038724541664123535, -0.008097521960735321, -0.05339578911662102, 0.007476250175386667, -0.032625164836645126, -0.04479873180389404, 0.062227923423051834, -0.0429181233048439, -0.006976713892072439, 0.00011819380597444251, 0.05823163315653801, -0.04993681609630585, -0.04738456383347511, 0.05457116663455963, 0.0009544707136228681, -0.0023129780311137438, -0.06850780546665192, 0.04298529028892517, -0.06300031393766403, 0.0026278116274625063, 0.01123326551169157, 0.006833989173173904, -0.005310194566845894, 0.004088639747351408, 0.04076886177062988, -0.02919977344572544, -0.014927313663065434, -0.03794795274734497, -0.008299015462398529, -0.00004935673496220261, 0.03600018098950386, 0.031500156968832016, 0.031248290091753006, 0.027906855568289757, -0.04003005102276802, -0.06135478615760803, 0.05067562684416771, 0.010704344138503075, 0.09470196813344955, -0.033901289105415344, -0.029737088829278946, -0.033380765467882156, 0.033699795603752136, -0.07213468849658966, 0.0412725955247879, -0.027671780437231064, -0.0320206843316555, 0.017848970368504524, 0.005860103759914637, 0.015380674041807652, 0.03952631726861, 0.042145732790231705, -0.02990500070154667, -0.047183070331811905, 0.06891079246997833, 0.024061687290668488, -0.04123901203274727, -0.05497415363788605, -0.008764969184994698, 0.019057931378483772, 0.04372410103678703, -0.033263225108385086, 0.03222217783331871, 0.032692328095436096, 0.0009864787571132183, 0.021946005523204803, -0.004793867468833923, -0.016942249611020088, 0.03482479974627495, 0.024212807416915894, 0.005562061443924904, -0.05557863786816597, 0.056048788130283356, 0.0030706776306033134, 0.020250100642442703, 0.005658610258251429, 0.06847422569990158, -0.03215501084923744, 0.0244143009185791, -0.007211789954453707, 0.06175777316093445, 0.00019572160090319812, 0.007337723392993212, 0.09980647265911102, 0.02315496653318405, 0.003969002980738878, 0.016153065487742424, -0.0004767106438521296, -0.04009721428155899, 0.060649555176496506, -0.07656754553318024, 0.014314437285065651, 0.053026385605335236, 0.011695020832121372, 0.035597193986177444, 0.06340330094099045, 0.0030937655828893185, -0.03636958450078964, 0.040500201284885406, -0.010939420200884342, -0.06494808942079544, -0.00234446139074862, 0.023339668288826942, 0.008697804994881153, -0.00594825716689229, 0.019041139632463455, 0.01639653742313385, -0.014977687038481236, -0.007367107551544905, -0.06642570346593857, -0.0020894461777061224, 0.03203747421503067, 0.01293756440281868, 0.0239777322858572, 0.005847510416060686, 0.03161769360303879, -0.0022877913434058428, 0.054235346615314484, -0.012056030333042145, -0.0012719279620796442, 0.03047589771449566, 0.01868852600455284, -0.031231500208377838, 0.011888119392096996, -0.03858601301908493, 0.00100484408903867, -0.01582563854753971, 0.011241660453379154, 0.0026089216116815805, -0.008483718149363995, -0.0015405860031023622, 0.00780367711558938, 0.03872034326195717, 0.017832178622484207, -0.015976758673787117, -0.012761257588863373, 0.005834917072206736, 0.04587336257100105, -0.01145154982805252, -0.025959085673093796, 0.020552340894937515, -0.0799257755279541, -0.01577526517212391, -0.02669789455831051, -0.006149750668555498, -0.01510362047702074, -0.01498608198016882, -0.003142039990052581, -0.037477798759937286, 0.029350893571972847, 0.0032553800847381353, -0.000004775797151523875, -0.009839601814746857, -0.0538659393787384, -0.06582122296094894, -0.000686337414663285, 0.007249569986015558, -0.04798904433846474, -0.037544962018728256, -0.05232115834951401, -0.014557908289134502, -0.021375106647610664, -0.0144823482260108, 0.025841547176241875, -0.035899434238672256, 0.04577261582016945, -0.00020214944379404187, -0.00912597868591547, -0.015246344730257988, -0.009428218938410282, -0.05846671015024185, -0.01193009689450264, -0.07119438797235489, 0.03479121997952461, 0.024531839415431023, -0.048694271594285965, 0.03694048151373863, 0.017630685120821, 0.033901289105415344, -0.0005184261244721711, 0.018117627128958702, -0.07206752151250839, -0.0038934429176151752, -0.04392559453845024, -0.0065527381375432014, 0.04009721428155899, -0.04986965283751488, -0.007236976642161608, -0.032960984855890274, 0.04486589506268501, -0.04123901203274727, -0.05886969715356827, 0.04547037556767464, -0.03808227926492691, 0.028779994696378708, 0.042145732790231705, 0.09994079917669296, 0.047552477568387985, 0.0027852284256368876, 0.032574791461229324, -0.0412725955247879, -0.028544919565320015, -0.008974858559668064, -0.010704344138503075, 0.014641864225268364, 0.04295170679688454, 0.019477710127830505, 0.0003882948658429086, -0.014373206533491611, 0.01944412663578987, -0.06420927494764328, 0.047552477568387985, -0.0411718487739563, -0.04929875209927559, -0.03455614298582077, -0.02088816463947296, -0.02486766129732132, -0.05195175111293793, 0.037746455520391464, -0.04526888206601143, 0.02612699568271637, -0.05991074815392494, -0.017042996361851692, 0.059843581169843674, 0.015179180540144444, 0.005226238630712032, -0.039694227278232574, -0.0637391209602356, -0.05010472983121872, -0.02493482641875744, -0.019746366888284683, 0.026865806430578232, 0.026076622307300568, 0.016656799241900444, -0.0011690823594108224, -0.006943131797015667, 0.0562838651239872, -0.030106494203209877, 0.017916133627295494, -0.049634575843811035, -0.02713446319103241, -0.030391942709684372, 0.012786444276571274, -0.011258452199399471, 0.027335956692695618, -0.012702489271759987, 0.025321021676063538, -0.05027263984084129, 0.008857320062816143, 0.0336158387362957, 0.017966507002711296, -0.0555114708840847, 0.018705317750573158, -0.006943131797015667, -0.005801334977149963, 0.0034883569460362196, -0.017848970368504524, -0.08637356758117676, 0.014557908289134502, -0.016690382733941078, 0.01774822361767292, -0.07744068652391434, -0.007971588522195816, -0.002304582390934229, -0.002554350532591343, -0.030072910711169243, 0.052018918097019196, 0.04449649155139923, -0.05228757485747337, 0.009100791998207569, -0.0025921305641531944, -0.08778402209281921, -0.025824755430221558, -0.027856482192873955, -0.059272684156894684, -0.008605453185737133, 0.0281923059374094, -0.02720162831246853, -0.015363883227109909, 0.0007907572435215116, -0.0012205052189528942, -0.03838451951742172, -0.02072025276720524, 0.014809775166213512, -0.032574791461229324, -0.031567320227622986, -0.04832486808300018, -0.027335956692695618, -0.0022982857190072536, 0.06494808942079544, -0.03677257150411606, -0.034522559493780136, 0.00547810597345233, -0.05033980309963226, -0.041071102023124695, -0.01397861447185278, -0.01277804933488369, 0.0026739872992038727, 0.03203747421503067, -0.01962883025407791, 0.04355618730187416, -0.010796695947647095, -0.015456234104931355, 0.01384428609162569, -0.03133224695920944, -0.021744512021541595, -0.03166806697845459, -0.022869518026709557, 0.04772038757801056, -0.015153993852436543, 0.0012792741181328893, 0.008441739715635777, 0.012929169461131096, -0.026043040677905083, 0.031432993710041046, 0.0260598324239254, 0.011653043329715729, 0.03020724095404148, 0.05329504236578941, -0.007341920863837004, -0.03418673947453499, 0.0065779248252511024, -0.02807476744055748, 0.035026293247938156, 0.02940126694738865, -0.00000392312267649686, -0.0033792145550251007, -0.0033456324599683285, -0.08798551559448242, -0.0003534007992129773, 0.06931377947330475, 0.02869603969156742, -0.016564449295401573, -0.03133224695920944, 0.03825019299983978, -0.005662808194756508, -0.045671869069337845, 0.022013170644640923, 0.021744512021541595, 0.028998279944062233, -0.03687331825494766, -0.025640053674578667, 0.0327930748462677, 0.03841810300946236, 0.0064016180112957954, -0.0068549783900380135, -0.02342362515628338, 0.004254452418535948, 0.0109226293861866, 0.009621316567063332, 0.02322213165462017, 0.013097080402076244, -0.03858601301908493, 0.005990235134959221, 0.018671734258532524, 0.006221113260835409, -0.029804253950715065, 0.010007512755692005, -0.009587734937667847, 0.07952278852462769, -0.06276524066925049, 0.04016438126564026, -0.02058592438697815, -0.045033808797597885, -0.06011224165558815, 0.034085992723703384, 0.005704786162823439, -0.03835093975067139, 0.040063634514808655, -0.01920905150473118, -0.005986037198454142, -0.028242679312825203, 0.04217931628227234, -0.05947417765855789, -0.059709254652261734, 0.03670540824532509, 0.003696147119626403, -0.003393906867131591, -0.05594804137945175, -0.06333613395690918, 0.035261370241642, -0.07864964753389359, -0.0386531800031662, 0.03935840725898743, -0.02102249301970005, -0.006909549236297607, -0.041205428540706635, -0.021173613145947456, -0.0377800390124321, 0.034455396234989166, 0.10437365621328354, -0.0024011314380913973, -0.02372586540877819, 0.04429499804973602, 0.009512174874544144, -0.09268703311681747, -0.05161593109369278, -0.006922143045812845, -0.006078388541936874, 0.031819187104701996, 0.002017034450545907, 0.057257749140262604, 0.034724052995443344, 0.002896469784900546, 0.01946091838181019, 0.010914233513176441, -0.03255799785256386, -0.0035135436337441206, 0.01564093679189682, 0.0049281963147223, 0.09651540964841843, 0.022802352905273438, -0.04285096004605293, -0.044026341289281845, 0.015053247101604939, 0.06232867017388344, -0.00755181023851037, -0.05866820365190506, -0.04422783479094505, 0.004781274124979973, -0.02063629776239395, -0.02851133607327938, -0.019309798255562782, -0.013021520338952541, -0.01274446677416563, -0.023826612159609795, -0.014683841727674007, 0.05168309435248375, 0.06437718868255615, -0.015909593552350998, -0.0007897077593952417, 0.047183070331811905, 0.013071893714368343, 0.013508463278412819, 0.010200610384345055, 0.0030601832550019026, -0.0361345075070858, -0.015145597979426384, 0.021425480023026466, -0.007799479179084301, 0.0201493538916111, -0.04899651184678078, -0.017899343743920326, 0.013525254093110561, -0.013709956780076027, 0.02216429077088833, -0.010502850636839867, -0.019981443881988525, 0.04859352484345436, 0.006393222138285637, 0.0002959436387754977, 0.014339623972773552, 0.048190537840127945, 0.008294817991554737, 0.06494808942079544, 0.031752023845911026, -0.024716541171073914, -0.007824665866792202, 0.0046007693745195866, -0.02454862929880619, 0.02241615764796734, -0.03683973476290703, -0.03230613097548485, 0.012660510838031769, 0.023138174787163734, 0.0015846628230065107, 0.0513472706079483, -0.006418408825993538, 0.0023969337344169617, -0.06743317097425461, 0.03311210498213768, -0.00649816682562232, 0.02335646003484726, 0.02365870028734207, 0.0025921305641531944, 0.023574745282530785, -0.029619550332427025, -0.008445938117802143, -0.007900225929915905, 0.02241615764796734, -0.00542773213237524, -0.04123901203274727, 0.01907472312450409, -0.05188458785414696, 0.028158722445368767, 0.010746322572231293, 0.00286498642526567, -0.010116655379533768, -0.021324733272194862, -0.03821660950779915, -0.04641067981719971, -0.012803236022591591, 0.02789006568491459, -0.01145154982805252, -0.013642791658639908, -0.009755645878612995, 0.04422783479094505, 0.03989572077989578, 0.001306559657678008, -0.04469798505306244, -0.021072866395115852, -0.0239273589104414, -0.030056120827794075, -0.015515003353357315, -0.004588176030665636, 0.017068183049559593, -0.045168135315179825, -0.029350893571972847, 0.030643809586763382, -0.022063544020056725, 0.013558836653828621, 0.0005163272144272923, 0.015439443290233612, 0.011636252515017986, 0.0064268046990036964, -0.04674650356173515, 0.0044790334068238735, 0.023457206785678864, -0.020804207772016525, 0.008630639873445034, -0.01774822361767292, -0.007644161581993103, -0.03593301400542259, -0.026966553181409836, 0.0007146724383346736, 0.058130886405706406, 0.011300429701805115, -0.010905837640166283, -0.031113961711525917, 0.0009523718035779893, 0.02248332090675831, 0.018487032502889633, 0.03563077375292778, 0.04486589506268501, -0.0012184062507003546, -0.026043040677905083, -0.0070564718917012215, -0.00135693303309381, 0.014205294661223888, 0.033078525215387344, 0.018369494006037712, 0.05185100436210632, -0.03791436925530434, 0.03353188559412956, 0.011753790080547333, 0.0109226293861866, 0.0021314239129424095, 0.0009749348973855376, 0.004903009627014399, -0.026865806430578232, 0.026832222938537598, 0.017462773248553276, 0.008605453185737133, -0.01756351999938488, 0.023121384903788567, -0.0010431489208713174, 0.027906855568289757, -0.005159074440598488, -0.025757592171430588, -0.013399320654571056, -0.011308825574815273, 0.01324820052832365, -0.031516946852207184, -0.04506738856434822, -0.0029447441920638084, -0.007090053986757994, 0.023003846406936646, -0.0018973975675180554, -0.008454333059489727, -0.0004391929542180151, -0.03583226725459099, -0.05010472983121872, 0.07200036197900772, -0.016791129484772682, 0.02631169930100441, -0.03205426409840584, -0.0318695604801178, 0.009772436693310738, 0.030627019703388214, -0.004999558441340923, 0.03386770561337471, 0.005096107721328735, 0.011031772010028362, 0.021626973524689674, -0.017278071492910385, 0.035026293247938156, 0.009428218938410282, 0.030643809586763382, 0.010183819569647312, -0.028293052688241005, -0.0008154191891662776, -0.02612699568271637, 0.015531794168055058, 0.019158678129315376, 0.020569132640957832, 0.07918696105480194, 0.0028691841289401054, 0.011098936200141907, 0.05588087812066078, -0.02033405750989914, -0.02108965814113617, -0.03403561934828758, 0.02340683341026306, 0.02631169930100441, -0.01504485122859478, 0.026865806430578232, 0.024145642295479774, 0.03680615499615669, 0.010125050321221352, 0.010116655379533768, -0.012139986269176006, -0.016295790672302246, 0.019863905385136604, -0.04540321230888367, -0.0044496492482721806, 0.002604723908007145, 0.02209712564945221, -0.007346118800342083, -0.016598030924797058, -0.016942249611020088, 0.001314955297857523, 0.006007026415318251, 0.0029006674885749817, 0.004890416283160448, 0.007438470143824816, -0.017513146623969078, -0.006556935608386993, -0.007576996926218271, -0.017076577991247177, 0.03683973476290703, -0.015531794168055058, -0.035530027002096176, 0.005070921033620834, 0.03198710083961487, 0.0046511427499353886, 0.006355442106723785, -0.00042869849130511284, 0.009545756503939629, 0.005960850510746241, 0.01193009689450264, 0.0746869370341301, 0.01214838121086359, 0.014423579908907413, 0.05520923063158989, 0.016245417296886444, 0.02894790656864643, 0.001341191353276372, 0.002764239674434066, 0.020988911390304565, 0.019343379884958267, -0.006590518169105053, 0.021442271769046783, -0.04899651184678078, -0.05497415363788605, -0.008219257928431034, -0.038183026015758514, -0.017445983365178108, -0.03730988875031471, -0.004894614219665527, 0.050507716834545135, -0.0130299162119627, 0.00494078965857625, -0.0035114448983222246, -0.00468892278149724, -0.04338827729225159, 0.017714640125632286, 0.00982281006872654, 0.012056030333042145, -0.008294817991554737, 0.029099026694893837, -0.009436613880097866, 0.026865806430578232, -0.017697850242257118, -0.0007634716457687318, -0.013550440780818462, -0.01712695136666298, 0.0222818274050951, 0.012878796085715294, 0.04476514831185341, 0.021543018519878387, 0.008681013248860836, 0.03935840725898743, -0.030358361080288887, 0.006993505172431469, 0.0014702732441946864, 0.022584067657589912, -0.004090738948434591, -0.001784057472832501, -0.014012197032570839, 0.01667359098792076, 0.06525032967329025, -0.0264964010566473, 0.011258452199399471, 0.0646122619509697, -0.061421949416399, 0.031752023845911026, 0.01067076250910759, -0.020686671137809753, 0.055813711136579514, 0.04641067981719971, -0.0074846455827355385, 0.03267553821206093, 0.0037549161352217197, -0.0003662564849946648, -0.03882109001278877, 0.044160667806863785, -0.031046796590089798, 0.0033141491003334522, 0.025102738291025162, -0.04382484778761864, 0.02197958715260029, -0.015859220176935196, 0.032440461218357086, -0.0239777322858572, -0.018722107633948326, 0.012005656957626343, -0.003047589911147952, 0.008126906119287014, 0.024145642295479774, 0.028494546189904213, -0.009411427192389965, -0.0077365124598145485, 0.023339668288826942, 0.05094428360462189, -0.01057841069996357, -0.06199284642934799, 0.021862050518393517, -0.0036163893528282642, -0.036974065005779266, 0.04261588305234909, -0.00833679549396038, -0.02108965814113617, 0.0020737044978886843, 0.012601742520928383, -0.033716585487127304, -0.021559808403253555, 0.015447838231921196, -0.011846140958368778, 0.017194116488099098, 0.03183598071336746, 0.005952455103397369, -0.04530246555805206, 0.06770183145999908, -0.005990235134959221, -0.010502850636839867, 0.007883435115218163, 0.023054219782352448, 0.0016948545817285776, -0.050071146339178085, 0.023692281916737556, -0.022550486028194427, -0.05091070383787155, -0.007304140832275152, -0.02291989140212536, -0.01749635674059391, 0.03895542025566101, 0.000167517748195678, 0.004445451311767101, 0.025337813422083855, 0.02051875926554203, 0.020535551011562347, 0.005138085223734379, 0.05329504236578941, -0.005335381254553795, 0.0281419325619936, 0.03643674775958061, -0.0024997792206704617, 0.005188458599150181, 0.03040873445570469, -0.006305068731307983, 0.02115682139992714, 0.023121384903788567, 0.0180672537535429, -0.0260598324239254, -0.010964606888592243, -0.00572997285053134, -0.04130617529153824, 0.030677393078804016, -0.02145906165242195, 0.014667050912976265, -0.004882020875811577, 0.026597147807478905, 0.009268702939152718, -0.02743670344352722, 0.035026293247938156, 0.03620167449116707, -0.006846582517027855, 0.0038325751665979624, -0.031819187104701996, 0.009671689942479134, 0.028847159817814827, -0.012156777083873749, -0.0009570943657308817, 0.026227742433547974, -0.020350847393274307, -0.017697850242257118, -0.018537405878305435, -0.012265919707715511, -0.03982855752110481, 0.025975875556468964, 0.017697850242257118, -0.001257235766388476, 0.007119438610970974, -0.009537361562252045, 0.0016906567616388202, 0.016001945361495018, 0.004462242592126131, 0.021559808403253555, -0.02468295954167843, -0.02033405750989914, -0.035261370241642, 0.030744556337594986, 0.017899343743920326, 0.015473024919629097, -0.041574835777282715, -0.013348947279155254, -0.05940701439976692, 0.00045519700506702065, 0.016035528853535652, 0.011073749512434006, -0.013567231595516205, 0.003108457662165165, -0.0012446424225345254, 0.057123418897390366, 0.020753834396600723, -0.02001502551138401, 0.014339623972773552, -0.027168046683073044, -0.0003977398737333715, -0.008966462686657906, 0.004038266371935606, 0.003834674134850502, 0.013080289587378502, -0.014608281664550304, 0.029636342078447342, 0.012425435706973076, -0.031265079975128174, -0.0037843005266040564, -0.01369316503405571, -0.05363086611032486, -0.031752023845911026, -0.03734346851706505, -0.017143743112683296, 0.04154125228524208, 0.007917016744613647, -0.018537405878305435, -0.024145642295479774, 0.029300520196557045, -0.021878840401768684, 0.026110205799341202, 0.0024326147977262735, -0.07858248054981232, 0.005108701065182686, -0.03626883774995804, -0.0004864180227741599, -0.026916179805994034, -0.02152622677385807, -0.009931952692568302, 0.00043971769628115, -0.03302815183997154, 0.02448146604001522, 0.0144823482260108, 0.06978393346071243, 0.06498166918754578, 0.0028293051291257143, -0.04184349253773689, 0.028293052688241005, -0.039996467530727386, 0.014331228099763393, -0.04254871979355812, -0.057257749140262604, 0.025287440046668053, 0.02461579442024231, 0.01220715045928955, -0.038989000022411346, 0.03680615499615669, 0.0032784678041934967, 0.02063629776239395, 0.02663072943687439, -0.014499139972031116, -0.019427336752414703, -0.017899343743920326, -0.05420176312327385, -0.006145553197711706, 0.04201140254735947, -0.030190449208021164, -0.025975875556468964, -0.03482479974627495, 0.051582347601652145, -0.0010583658004179597, 0.026647521182894707, -0.006535946857184172, -0.02844417281448841, -0.031181126832962036, 0.050709210336208344, -0.017983298748731613, 0.003419093554839492, -0.06682869046926498, -0.00937784556299448, -0.0021398195531219244, -0.040701694786548615, 0.00028833516989834607, -0.00030381447868421674, -0.00887411180883646, 0.004806460812687874, 0.028410589322447777, -0.043656934052705765, -0.0034715658985078335, -0.05413459986448288, 0.010158632881939411, 0.011997261084616184, -0.043086037039756775, -0.010880650952458382, -0.05839954689145088, -0.018084045499563217, 0.03317927196621895, -0.008328399620950222, -0.0289646964520216, 0.013701560907065868, -0.018235165625810623, -0.01605231873691082, 0.00862224493175745, 0.007350316736847162, -0.00675003370270133, -0.00852989312261343, 0.00852989312261343, -0.01925942488014698, 0.006435200106352568, 0.03892183676362038, -0.03657107800245285, 0.031500156968832016, 0.02594229392707348, 0.029686715453863144, -0.01868852600455284, 0.011795767582952976, 0.0503733865916729, -0.030895676463842392, 0.004961778409779072, -0.006582122296094894, -0.020619506016373634, -0.029031861573457718, 0.01708497293293476, 0.016917062923312187, 0.021425480023026466, 0.0013936636969447136, -0.03230613097548485, -0.006078388541936874, -0.03606734424829483, -0.0496009960770607, 0.05255623161792755, -0.01249259989708662, 0.030072910711169243, -0.01535548735409975 ]
Modeling interaction dynamics to generate robot trajectories that enable a robot to adapt and react to a human's actions and intentions is critical for efficient and effective collaborative Human-Robot Interactions (HRI). Learning from Demonstration (LfD) methods from Human-Human Interactions (HHI) have shown promising results, especially when coupled with representation learning techniques. However, such methods for learning HRI either do not scale well to high dimensional data or cannot accurately adapt to changing via-poses of the interacting partner. We propose Multimodal Interactive Latent Dynamics (MILD), a method that couples deep representation learning and probabilistic machine learning to address the problem of two-party physical HRIs. We learn the interaction dynamics from demonstrations, using Hidden Semi-Markov Models (HSMMs) to model the joint distribution of the interacting agents in the latent space of a Variational Autoencoder (VAE). Our experimental evaluations for learning HRI from HHI demonstrations show that MILD effectively captures the multimodality in the latent representations of HRI tasks, allowing us to decode the varying dynamics occurring in such tasks. Compared to related work, MILD generates more accurate trajectories for the controlled agent (robot) when conditioned on the observed agent's (human) trajectory. Notably, MILD can learn directly from camera-based pose estimations to generate trajectories, which we then map to a humanoid robot without the need for any additional training.
[ 0.002380182035267353, -0.013128122314810753, -0.04000452533364296, -0.02325153909623623, 0.022902153432369232, 0.03065849095582962, -0.03623117133975029, 0.009800235740840435, -0.05125470831990242, 0.053141381591558456, -0.022570239380002022, 0.01947818696498871, 0.03616129606962204, 0.008642898872494698, -0.049647536128759384, 0.019757693633437157, -0.00705319968983531, -0.012551638297736645, -0.025976737961173058, 0.0011911827605217695, 0.02171424776315689, 0.009704154916107655, -0.06397230178117752, 0.08042830973863602, 0.06785047054290771, 0.006088024936616421, 0.03392523527145386, -0.027321867644786835, -0.03734920173883438, 0.06145673245191574, -0.025120746344327927, 0.009118935093283653, -0.02410753071308136, -0.028509775176644325, -0.039969585835933685, -0.022238323464989662, 0.039235878735780716, 0.0763055756688118, -0.05205829069018364, 0.04398750886321068, -0.0071012401022017, 0.022954562678933144, -0.07351049780845642, -0.06582403928041458, -0.013494976796209812, 0.004847710020840168, -0.05810264125466347, 0.03485110402107239, 0.004330184310674667, 0.026203837245702744, 0.03647574037313461, -0.04126230999827385, 0.020054670050740242, -0.009162608534097672, -0.028492305427789688, 0.016193971037864685, 0.10181064158678055, 0.016001809388399124, 0.07176357507705688, 0.00823237281292677, -0.02356598526239395, 0.013870565220713615, -0.007092505227774382, -0.03380294889211655, 0.03602154180407524, -0.025784576311707497, 0.05080050602555275, 0.0036052113864570856, -0.019827570766210556, -0.012700126506388187, -0.003199051832780242, -0.03357585147023201, -0.01639486849308014, -0.050765566527843475, -0.010481535457074642, 0.022238323464989662, 0.0142374187707901, 0.09775778651237488, 0.023286476731300354, -0.022675054147839546, 0.022360607981681824, -0.030763305723667145, 0.007677724584937096, 0.008961712941527367, 0.09691926091909409, -0.030309105291962624, 0.025644822046160698, -0.05922067165374756, 0.020229361951351166, -0.0237057376652956, -0.04971741512417793, 0.05621596798300743, 0.0005587422638200223, -0.0008035843493416905, -0.05929055064916611, -0.004061595071107149, -0.004777832888066769, -0.003181582549586892, -0.048704199492931366, -0.02012454718351364, 0.011398669332265854, 0.010324312373995781, 0.009223750792443752, 0.02742668427526951, 0.0011431424645707011, -0.026465876027941704, -0.03734920173883438, -0.001920522889122367, -0.019583001732826233, 0.12808436155319214, -0.02429969236254692, -0.029488051310181618, -0.004179512150585651, 0.016106626018881798, -0.028597122058272362, 0.020875724032521248, -0.03296442702412605, -0.0539100281894207, 0.03170664235949516, -0.08727625012397766, 0.035270366817712784, 0.025662291795015335, 0.008219270035624504, -0.01788848638534546, -0.011040550656616688, 0.03982983157038689, -0.020770909264683723, 0.01009721215814352, 0.03588178753852844, 0.02980249747633934, 0.0012228457489982247, 0.0009029405773617327, -0.012866084463894367, -0.010464065708220005, 0.014123868197202682, 0.0076995608396828175, 0.021941347047686577, -0.05436423048377037, 0.03979489579796791, 0.028160391375422478, -0.04339355602860451, 0.01307571493089199, -0.02304190769791603, 0.008817591704428196, 0.026675507426261902, 0.00799653772264719, -0.03794315829873085, 0.052687183022499084, -0.03212590515613556, -0.011564627289772034, -0.04629344493150711, 0.039969585835933685, 0.009913785383105278, 0.06781553477048874, 0.030763305723667145, -0.03120003640651703, 0.011049284599721432, -0.013355222530663013, 0.0044677541591227055, -0.06051339581608772, 0.06229525804519653, 0.02742668427526951, 0.03140966594219208, 0.04510553926229477, 0.057648442685604095, 0.006895976606756449, -0.02033417858183384, 0.013425099663436413, -0.027234522625803947, 0.05820745974779129, -0.08098732680082321, 0.044860970228910446, 0.0005743007641285658, -0.03415233641862869, -0.04887889325618744, 0.036720313131809235, 0.013337753713130951, -0.019967325031757355, -0.04762110859155655, -0.005843455903232098, -0.03146207332611084, 0.010848389007151127, -0.022482892498373985, 0.026378529146313667, 0.07651520520448685, 0.02304190769791603, 0.0815463438630104, 0.022814808413386345, 0.02788088284432888, -0.04304417222738266, 0.06449637562036514, 0.004214450716972351, 0.0476909838616848, 0.0382925420999527, -0.007813110947608948, -0.027461621910333633, 0.0008478033123537898, -0.012630249373614788, 0.03927081823348999, 0.05827733501791954, 0.0006119688041508198, -0.08909305185079575, -0.0604085810482502, 0.010979408398270607, 0.022203385829925537, -0.059115856885910034, 0.00894424319267273, -0.011346261948347092, 0.016604498028755188, -0.07784286886453629, 0.04765604808926582, 0.02775859832763672, -0.02396777644753456, -0.04028403386473656, -0.021976284682750702, -0.03720945119857788, -0.007489930372685194, 0.01324167288839817, 0.014918718487024307, -0.03369813412427902, 0.009083997458219528, 0.002843116410076618, 0.01774873211979866, -0.012700126506388187, -0.031898804008960724, 0.0472717247903347, -0.010726104490458965, 0.007275932468473911, 0.027059828862547874, 0.0007511766743846238, 0.055062998086214066, 0.03058861382305622, 0.04272972419857979, -0.018063178285956383, 0.058382149785757065, 0.02775859832763672, 0.02548759989440441, -0.024526791647076607, 0.014342233538627625, -0.036650434136390686, -0.014717821963131428, -0.03706969693303108, 0.019303493201732635, 0.03210843726992607, 0.04604887589812279, 0.01739061437547207, 0.011721850372850895, 0.04510553926229477, -0.006909078452736139, -0.025347845628857613, 0.040703292936086655, 0.016814129427075386, -0.01705869846045971, -0.018115585669875145, -0.04038884863257408, 0.09489282965660095, 0.03602154180407524, -0.04035390913486481, -0.011748054064810276, -0.02396777644753456, 0.03551493585109711, 0.05286187678575516, 0.04992704465985298, 0.01853484846651554, -0.00012378583778627217, -0.01224592700600624, 0.06383255124092102, 0.008289147168397903, 0.0540497824549675, -0.024125000461935997, -0.04087798669934273, -0.03762871026992798, -0.041751448065042496, 0.01278747245669365, -0.005135952029377222, -0.02484123781323433, 0.016543356701731682, 0.015241898596286774, 0.04444170743227005, 0.01684906706213951, 0.06585898250341415, -0.015049737878143787, 0.04695727676153183, 0.026378529146313667, 0.016953883692622185, -0.03867686539888382, -0.007171116769313812, 0.0027317500207573175, -0.04356824606657028, -0.005690600257366896, -0.01132005825638771, 0.0053805215284228325, -0.020369116216897964, -0.01404525712132454, 0.05293175205588341, 0.00040943495696410537, -0.031427137553691864, -0.00022259613615460694, 0.033540911972522736, 0.025120746344327927, -0.0035222324077039957, -0.0063413288444280624, 0.06823479384183884, -0.022902153432369232, 0.016901474446058273, 0.016438540071249008, 0.026972483843564987, 0.045210354030132294, -0.010743573307991028, -0.03640586510300636, -0.013853095471858978, 0.03099040500819683, -0.04272972419857979, 0.008101353421807289, -0.02529543824493885, 0.027514029294252396, 0.052617307752370834, -0.029907314106822014, -0.03278973698616028, -0.0328945517539978, -0.027391744777560234, 0.02264011651277542, -0.06788540631532669, -0.011494750156998634, 0.05422447621822357, 0.002703362610191107, -0.024159938097000122, -0.00716674979776144, -0.013704607263207436, -0.0009417004184797406, -0.05495818331837654, 0.007280299440026283, -0.03794315829873085, 0.0057080695405602455, 0.006930915173143148, 0.0038497804198414087, -0.01397537998855114, -0.00917134340852499, -0.010883327573537827, -0.011651973240077496, -0.0476909838616848, 0.01225466188043356, 0.05555213615298271, 0.006053086370229721, 0.024788830429315567, -0.004755996633321047, -0.059115856885910034, 0.06802516430616379, 0.006756222806870937, 0.009538196958601475, 0.0010246792808175087, -0.048774078488349915, 0.02251783199608326, 0.0007004067301750183, 0.010603819973766804, -0.04286947846412659, -0.03892143443226814, 0.022867215797305107, -0.06806010007858276, 0.00900538545101881, 0.02947058342397213, -0.03724438697099686, -0.024352099746465683, -0.020910661667585373, -0.06736133247613907, -0.024317162111401558, -0.048913829028606415, -0.03177652135491371, 0.016124093905091286, 0.021871469914913177, 0.0008838336216285825, -0.047586169093847275, 0.017163513228297234, -0.007559807039797306, -0.03881661966443062, 0.023129254579544067, 0.03986477106809616, -0.02085825428366661, -0.0004225368902552873, 0.07043591886758804, -0.012342007830739021, 0.054538920521736145, -0.10879833251237869, -0.002751403022557497, -0.02901638299226761, 0.06327353417873383, 0.029907314106822014, -0.04293935373425484, 0.020963070914149284, 0.01291849184781313, 0.11047537624835968, -0.029173605144023895, -0.018692070618271828, 0.007664622738957405, 0.05674004182219505, 0.016595764085650444, 0.04807530716061592, -0.004524529445916414, 0.03986477106809616, 0.016333725303411484, -0.009765297174453735, -0.012176049873232841, 0.011782992631196976, -0.010350516065955162, 0.03846723213791847, -0.045070599764585495, 0.029889844357967377, 0.004017921630293131, 0.04328874126076698, -0.004961260128766298, -0.05104507505893707, -0.0016093524172902107, -0.007524868939071894, -0.060303766280412674, 0.0038148420862853527, -0.002591996220871806, 0.021871469914913177, 0.008843795396387577, 0.021888939663767815, -0.0474114753305912, 0.04203095659613609, 0.01774873211979866, 0.07483816146850586, 0.0018724825931712985, -0.024736423045396805, 0.08650760352611542, -0.017643917351961136, -0.0334535650908947, -0.0050573404878377914, -0.03530530259013176, 0.039585262537002563, 0.024876177310943604, 0.014027787372469902, -0.07637545466423035, 0.03067595884203911, 0.03203855827450752, 0.03217831254005432, 0.04786567762494087, -0.012691391631960869, 0.007249728310853243, -0.03581191226840019, -0.023531045764684677, -0.026186369359493256, 0.008455105125904083, 0.002952299080789089, -0.003677272005006671, 0.014909983612596989, -0.045000724494457245, 0.005197094287723303, -0.004330184310674667, -0.08434142172336578, 0.04346343129873276, -0.008594858460128307, -0.05041618272662163, 0.027583906427025795, -0.05523768812417984, 0.027182115241885185, -0.0012108356459066272, -0.019879978150129318, -0.03713957220315933, -0.0014412110904231668, 0.04587418586015701, 0.026902606710791588, -0.01523316465318203, -0.008241106756031513, -0.005812884774059057, -0.027339337393641472, 0.010472800582647324, -0.004142390098422766, 0.013232938013970852, 0.024352099746465683, -0.022203385829925537, -0.007153647486120462, -0.011276384815573692, 0.010184558108448982, 0.06145673245191574, -0.016927680000662804, -0.020875724032521248, 0.006236513610929251, -0.022203385829925537, 0.027182115241885185, -0.008835060521960258, 0.04545492306351662, -0.00809261854737997, 0.018255339935421944, 0.01853484846651554, 0.046782586723566055, 0.014447049237787724, -0.012665187940001488, -0.00881322380155325, -0.016386132687330246, -0.019705286249518394, 0.011529688723385334, -0.010516473092138767, -0.010315577499568462, -0.011774257756769657, -0.007079403381794691, 0.02643093839287758, 0.04548986256122589, 0.015110880136489868, 0.008446370251476765, 0.018587255850434303, -0.007376380264759064, 0.008721510879695415, 0.004878281150013208, -0.010647492483258247, 0.004288694821298122, -0.024544261395931244, -0.00910146627575159, 0.009057792834937572, 0.02164437063038349, 0.05331607535481453, 0.017119839787483215, -0.029383236542344093, 0.05754362791776657, 0.004812771454453468, 0.03167170658707619, -0.013407629914581776, 0.03832748159766197, -0.007267197594046593, 0.016805395483970642, 0.04035390913486481, -0.000060698734159814194, -0.02078837715089321, -0.05153421312570572, 0.046468138694763184, 0.016779189929366112, -0.0024456914979964495, 0.025470130145549774, 0.0026225673500448465, -0.03822266310453415, 0.0006550959660671651, -0.036720313131809235, -0.04838975518941879, 0.007411318831145763, -0.048634324222803116, 0.028859160840511322, 0.033156588673591614, -0.0005213471595197916, -0.018779417499899864, 0.011005612090229988, -0.0009029405773617327, 0.0006048718933016062, 0.019949855282902718, -0.013643465004861355, -0.006638305727392435, 0.014875045046210289, -0.026448406279087067, -0.014062725938856602, 0.02702489122748375, 0.013302815146744251, 0.006721284240484238, 0.01820293255150318, -0.005358684808015823, -0.011381200514733791, -0.015547610819339752, 0.010516473092138767, -0.023356353864073753, -0.02112029306590557, -0.0536305196583271, 0.016429806128144264, -0.027461621910333633, 0.002591996220871806, -0.016578294336795807, 0.005563948303461075, -0.006402471102774143, 0.004808404017239809, 0.04842469096183777, 0.04709703102707863, 0.04276466369628906, -0.03602154180407524, -0.05894116684794426, -0.006926547735929489, -0.02899891324341297, 0.023618392646312714, 0.020369116216897964, 0.005262603983283043, -0.0300645362585783, -0.04730666056275368, 0.015678629279136658, -0.030850650742650032, 0.013259141705930233, 0.034728821367025375, 0.04489590972661972, -0.03584685176610947, -0.006786793936043978, -0.0101932929828763, -0.03403005003929138, 0.004563834983855486, 0.013835626654326916, 0.023950308561325073, 0.04730666056275368, 0.016482213512063026, 0.03364572674036026, 0.024142468348145485, -0.012857349589467049, 0.01867460086941719, -0.061491671949625015, 0.03507820516824722, -0.018307747319340706, -0.0017796773463487625, 0.02152208611369133, 0.012333272956311703, -0.0015842403518036008, -0.0033693767618387938, -0.004111818969249725, 0.024474384263157845, 0.02073596976697445, 0.006332593970000744, 0.0010809083469212055, -0.013835626654326916, -0.012874819338321686, -0.011555892415344715, 0.0047909351997077465, 0.05279199779033661, 0.006577163469046354, 0.031077751889824867, 0.005411092657595873, 0.006843568757176399, -0.07693446427583694, 0.04475615546107292, 0.004847710020840168, 0.04346343129873276, 0.01765265129506588, -0.017215920612215996, -0.01625511422753334, 0.008206168189644814, 0.019390840083360672, -0.0018386360025033355, 0.012638984248042107, 0.026989953592419624, 0.026535753160715103, 0.0014150072820484638, -0.018761947751045227, 0.024421976879239082, -0.011721850372850895, 0.005170890595763922, 0.019914915785193443, 0.04217071086168289, 0.0019401757745072246, -0.03741908073425293, -0.0006267084390856326, -0.007398216985166073, 0.02835255302488804, -0.01290975697338581, -0.006795528810471296, 0.004690486937761307, -0.0005216201534494758, 0.006603367161005735, 0.024858707562088966, -0.009957457892596722, -0.040423788130283356, 0.030885590240359306, 0.026081552729010582, -0.00029643092420883477, 0.0037820872385054827, 0.009450851008296013, -0.038432296365499496, -0.015434060245752335, 0.014307294972240925, 0.06571922451257706, -0.03591672703623772, 0.028055574744939804, -0.009485789574682713, 0.06421687453985214, 0.026046615093946457, 0.013949176296591759, 0.021626900881528854, -0.02548759989440441, 0.0572291798889637, 0.025871923193335533, 0.010420393198728561, -0.05198841542005539, 0.005135952029377222, 0.02828267589211464, 0.006498551927506924, 0.02735680714249611, 0.03340115770697594, 0.013503710739314556, -0.008651633746922016, -0.04084304720163345, -0.01860472559928894, -0.021242577582597733, 0.021888939663767815, 0.0036488843616098166, -0.030903059989213943, 0.030344044789671898, -0.0034545392263680696, -0.07260210067033768, -0.01933843269944191, -0.03247528895735741, -0.023688269779086113, 0.014438314363360405, 0.026273714378476143, 0.0071754842065274715, 0.015888260677456856, -0.029365766793489456, -0.013329018838703632, 0.020089609548449516, 0.03422221168875694, -0.05038124695420265, -0.025260498747229576, 0.002214224310591817, 0.013966645114123821, 0.04720184579491615, -0.010909531265497208, 0.01794089376926422, 0.002989421132951975, -0.018307747319340706, -0.03231806680560112, 0.01182666514068842, 0.044336892664432526, 0.03675524890422821, 0.04126230999827385, 0.06320365518331528, 0.021504616364836693, 0.0009269607835449278, -0.032405413687229156, -0.02861458994448185, 0.03633598983287811, 0.05537744238972664, 0.0052320328541100025, 0.027968229725956917, -0.033156588673591614, -0.015696099027991295, 0.008075149729847908, 0.029697682708501816, 0.006926547735929489, 0.006978955585509539, -0.009197547100484371, 0.07151900976896286, -0.04224058613181114, 0.006236513610929251, 0.018167994916439056, 0.04912346228957176, -0.011389934457838535, 0.0059264344163239, 0.03065849095582962, -0.016761722043156624, 0.013757014647126198, 0.0066295708529651165, -0.0315144807100296, 0.037454020231962204, -0.018447501584887505, -0.024212345480918884, 0.03217831254005432, 0.031077751889824867, 0.025470130145549774, 0.027269460260868073, 0.02616889961063862, 0.061421796679496765, 0.030151883140206337, 0.026867669075727463, -0.03892143443226814, -0.030448859557509422, -0.0003605757374316454, 0.033348750323057175, -0.03415233641862869, 0.04363812506198883, -0.03920094296336174, 0.006197207607328892, 0.021032946184277534, 0.01374827977269888, 0.03378548100590706, 0.025732168927788734, 0.030378982424736023, -0.0071099745109677315, -0.015241898596286774, 0.022884685546159744, -0.012071234174072742, 0.01919867843389511, 0.029121197760105133, 0.025679761543869972, -0.02669297531247139, -0.033156588673591614, -0.02662310004234314, -0.032737329602241516, -0.0042493888176977634, -0.024998461827635765, -0.01841256394982338, -0.02655322290956974, -0.005555213429033756, 0.017172249034047127, 0.04363812506198883, -0.03299936652183533, 0.03132231906056404, -0.02875434421002865, -0.0008177781128324568, -0.0015187307726591825, -0.02251783199608326, 0.024212345480918884, 0.011119161732494831, 0.02550506964325905, 0.00513158505782485, 0.06557947397232056, -0.0022404282353818417, -0.007123076356947422, -0.004646813962608576, -0.02073596976697445, -0.017285797744989395, 0.005332481116056442, -0.029645275324583054, -0.019827570766210556, 0.04933309182524681, -0.01718098297715187, 0.02795075997710228, 0.008262943476438522, -0.008987916633486748, 0.020299239084124565, 0.015407856553792953, -0.0021989387460052967, 0.02887662872672081, 0.004371673800051212, -0.000007084077878971584, 0.04597900062799454, -0.048250000923871994, -0.023880431428551674, 0.002180377719923854, 0.017242124304175377, 0.005406725220382214, -0.014516926370561123, -0.015250633470714092, 0.014726556837558746, -0.006725651677697897, 0.0060836574994027615, -0.0021268781274557114, 0.023548515513539314, -0.004369489848613739, 0.03818772733211517, -0.0005759384948760271, 0.03444931283593178, 0.05977968871593475, -0.011678176932036877, -0.042415279895067215, -0.04203095659613609, 0.016211440786719322, -0.008267310447990894, 0.013093184679746628, 0.007415686268359423, 0.03514808043837547, -0.013171795755624771, -0.022360607981681824, -0.03906118869781494, -0.02985490672290325, -0.027898352593183517, 0.01020202785730362, -0.015180756337940693, -0.0017491062171757221, 0.005004933103919029, 0.016805395483970642, 0.007979068905115128, 0.012542903423309326, 0.0569496750831604, 0.002762321149930358, 0.011599565856158733, 0.00977403111755848, 0.036790188401937485, 0.039759956300258636, 0.02641346864402294, -0.02272746153175831, -0.019687816500663757, -0.04035390913486481, -0.02735680714249611, -0.011119161732494831, 0.025208091363310814, 0.006380634382367134, -0.002096306998282671, -0.014813902787864208, -0.03263251110911369, -0.014813902787864208, 0.009677950292825699, 0.023408761247992516, -0.023269008845090866, -0.0057561094872653484, -0.021364862099289894, -0.004847710020840168, -0.03423967957496643, -0.016211440786719322, -0.012735065072774887, -0.017853548750281334, 0.019251085817813873, 0.013564852997660637, 0.040633417665958405, -0.02994225174188614, 0.04283453896641731, -0.011084223166108131, 0.006808630656450987, -0.00171853497158736, 0.023897899314761162, 0.011241446249186993, -0.0239852461963892, 0.0022447954397648573, -0.019390840083360672, -0.01380942203104496, 0.009948723949491978, 0.0059264344163239, -0.01613282971084118, 0.001919431146234274, -0.01656082458794117, 0.00307895103469491, -0.011477281339466572, -0.030029598623514175, -0.005529009737074375, 0.007236626464873552, 0.014053991995751858, 0.024334629997611046, -0.003288581734523177, 0.013722076080739498, 0.024090060964226723, 0.0025548741687089205, -0.02456173114478588, -0.01753910258412361, 0.0316542349755764, -0.007800009101629257, 0.02728693000972271, -0.018447501584887505, -0.03326140344142914, -0.013853095471858978, 0.021015478298068047, 0.018709540367126465, -0.030833182856440544, 0.0381527878344059, -0.008555552922189236, 0.010953203774988651, -0.04894876852631569, 0.030413921922445297, 0.00014753306459169835, 0.028929036110639572, 0.026395998895168304, 0.05219804495573044, -0.047725923359394073, 0.022797338664531708, -0.005660029128193855, 0.030483797192573547, 0.05167396739125252, -0.013337753713130951, -0.02866699919104576, 0.0057561094872653484, -0.0221160389482975, 0.005590151995420456, -0.002181469462811947, 0.0049481578171253204, 0.0007020444609224796, 0.027251990512013435, 0.029767559841275215, 0.006537857465445995, -0.02576710656285286, 0.02648334577679634, 0.006861038040369749, -0.03808291256427765, -0.03352344408631325, -0.05331607535481453, -0.006214676890522242, -0.0013625995488837361, -0.013634730130434036, 0.011879073455929756, -0.02602914534509182, -0.02166183851659298, -0.045070599764585495, 0.05006679892539978, 0.013669668696820736, 0.049577660858631134, 0.003022175980731845, 0.013163060881197453, -0.06561440974473953, 0.04038884863257408, -0.030553674325346947, -0.02047393098473549, -0.0575086884200573, 0.010699900798499584, -0.01278747245669365, -0.0010203119600191712, 0.020019732415676117, -0.002054817508906126, 0.004013554658740759, 0.04080811142921448, -0.03703475743532181, -0.019216148182749748, -0.04702715575695038, 0.02714717574417591, 0.03609142079949379, -0.014857576228678226, 0.056320782750844955, 0.04947284609079361, 0.010315577499568462, 0.026326121762394905, 0.00011511946649989113, -0.01570483297109604, -0.021312454715371132, -0.014962390996515751, -0.056390658020973206, -0.006048719398677349, -0.01801077090203762, -0.04150687903165817, -0.05443410575389862, 0.007232259027659893, -0.007944130338728428, -0.021871469914913177, 0.006882874760776758, 0.02761884406208992, -0.06645293533802032, 0.004590039141476154, 0.0006338053499348462, 0.06470601260662079, 0.0005841272068209946, -0.0035309670493006706, 0.02171424776315689, -0.0011824482353404164, -0.04653801769018173, 0.0220461618155241, -0.004699221346527338, -0.020176954567432404, -0.052617307752370834, -0.01947818696498871, -0.03948044776916504, 0.016569560393691063, -0.018709540367126465, -0.008952978067100048, 0.028177859261631966, -0.029348298907279968, 0.05597139894962311, -0.03177652135491371, 0.03637092560529709, -0.03490351140499115 ]
Federated Learning (FL) is a distributed learning paradigm that enables different parties to train a model together for high quality and strong privacy protection. In this scenario, individual participants may get compromised and perform backdoor attacks by poisoning the data (or gradients). Existing work on robust aggregation and certified FL robustness does not study how hardening benign clients can affect the global model (and the malicious clients). In this work, we theoretically analyze the connection among cross-entropy loss, attack success rate, and clean accuracy in this setting. Moreover, we propose a trigger reverse engineering based defense and show that our method can achieve robustness improvement with guarantee (i.e., reducing the attack success rate) without affecting benign accuracy. We conduct comprehensive experiments across different datasets and attack settings. Our results on eight competing SOTA defense methods show the empirical superiority of our method on both single-shot and continuous FL backdoor attacks. Code is available at https://github.com/KaiyuanZh/FLIP.
[ -0.08050066232681274, -0.04383159801363945, -0.02921457774937153, -0.06325607746839523, 0.01752679981291294, -0.004700413439422846, -0.006476449314504862, 0.022149359807372093, -0.026956820860505104, -0.0013685208978131413, -0.005493547301739454, 0.0037272428162395954, 0.011522337794303894, -0.039004672318696976, -0.047296084463596344, 0.040172476321458817, 0.016874775290489197, -0.0637621283531189, -0.005488681141287088, -0.0415349155664444, 0.028163552284240723, -0.0593244694173336, -0.03450862318277359, 0.012456581927835941, 0.02401784621179104, 0.03777847811579704, 0.012505240738391876, 0.01089950930327177, -0.056327104568481445, 0.05757276341319084, 0.038848962634801865, 0.0158724095672369, -0.025652773678302765, -0.015882141888141632, -0.022090969607234, -0.02514672465622425, 0.057923104614019394, 0.029292430728673935, -0.010140435770154, 0.04363696277141571, -0.06333393603563309, -0.039627499878406525, 0.004225992597639561, 0.033321354538202286, 0.018509702757000923, -0.028124626725912094, -0.03592945262789726, -0.04032818228006363, -0.04823032766580582, 0.009035887196660042, 0.00010674463555915281, -0.015025751665234566, 0.02514672465622425, -0.03863486647605896, -0.0026007979176938534, -0.0013855514116585255, 0.09373577684164047, 0.0032771513797342777, 0.03149179741740227, -0.01296263001859188, -0.018840579316020012, -0.025029944255948067, -0.003736974438652396, -0.007469083182513714, -0.005182132590562105, 0.029331358149647713, 0.04476584121584892, 0.020183555781841278, -0.02829979732632637, 0.00481719383969903, -0.03295155242085457, -0.0031774016097187996, 0.014471044763922691, -0.04499940201640129, -0.026587016880512238, -0.006247754208743572, 0.03203677013516426, 0.012281411327421665, 0.04387052357196808, 0.018840579316020012, -0.006130973808467388, 0.028027309104800224, 0.005717376247048378, 0.00045069956104271114, 0.051578033715486526, -0.012320337817072868, -0.03740867227315903, -0.08011139184236526, 0.028085699304938316, 0.002861121203750372, 0.010276679880917072, 0.025224577635526657, 0.00749827828258276, -0.0422355979681015, -0.011425021104514599, 0.020494969561696053, -0.047646425664424896, -0.009838753379881382, -0.07773685455322266, 0.014568361453711987, -0.06991256773471832, 0.05052701011300087, -0.02843604050576687, 0.050449155271053314, -0.010344801470637321, -0.0375838428735733, -0.05484788492321968, 0.07290992885828018, 0.048619594424963, 0.1572643518447876, -0.016855312511324883, -0.017536532133817673, -0.06119295954704285, 0.08563899993896484, -0.0037710354663431644, 0.036279793828725815, -0.05585998296737671, -0.03592945262789726, 0.02154599316418171, -0.04134028032422066, 0.013653581030666828, 0.02829979732632637, 0.03914091736078262, 0.007722107693552971, -0.037019405514001846, 0.027015211060643196, 0.023317163810133934, -0.005386498291045427, -0.00836926605552435, 0.014675410464406013, -0.002323444467037916, -0.006242888513952494, 0.03927715867757797, -0.07388310134410858, 0.04095101356506348, -0.009848484769463539, 0.04048389196395874, -0.003518011188134551, -0.008846119046211243, 0.02131243236362934, 0.08454904705286026, 0.030888430774211884, 0.03908252716064453, 0.06547490507364273, 0.01786740869283676, -0.006675949320197105, 0.004398730583488941, 0.040989939123392105, 0.05461432412266731, 0.03779793903231621, -0.0595969595015049, 0.0493202768266201, 0.03483950346708298, 0.018324799835681915, 0.059830520302057266, -0.02063121274113655, 0.0634896382689476, -0.01111360639333725, 0.040600672364234924, -0.05305725336074829, 0.04881422966718674, 0.010870314203202724, 0.040172476321458817, 0.03408043086528778, -0.0016981824301183224, 0.06858905404806137, 0.03557911142706871, -0.013926069252192974, -0.07119715213775635, 0.06407354027032852, 0.004556870553642511, 0.0015570727409794927, 0.004736907314509153, 0.007109010126441717, -0.01956072635948658, -0.007877814583480358, 0.04379266873002052, -0.007055485621094704, -0.021954724565148354, -0.05037130415439606, -0.01892816461622715, 0.009332704357802868, 0.00009488411888014525, -0.012291142717003822, 0.02888369932770729, 0.00342799280770123, 0.018139896914362907, -0.000718321418389678, 0.07649119943380356, -0.012466313317418098, 0.05185052007436752, 0.030499162152409554, -0.0017237281426787376, -0.02508833445608616, 0.030907893553376198, -0.020786920562386513, 0.006218559108674526, -0.021487602964043617, 0.05617139860987663, -0.0014974660007283092, 0.023433944210410118, -0.0466732531785965, -0.030148820951581, -0.042157743126153946, 0.01825667731463909, -0.020981555804610252, 0.042585939168930054, -0.014373727142810822, -0.02144867740571499, -0.013595190830528736, -0.03073272295296192, -0.0103837288916111, -0.05994730070233345, 0.0005233832052908838, -0.010150168091058731, -0.025419212877750397, 0.0014402922242879868, -0.019745629280805588, -0.03382740542292595, 0.017847945913672447, 0.035754282027482986, 0.025107797235250473, -0.014772727154195309, -0.01446131244301796, -0.052239790558815, -0.002178685273975134, 0.007254985626786947, 0.03454755246639252, 0.02140974998474121, 0.0058730836026370525, -0.056716375052928925, -0.02339501678943634, 0.0006356019293889403, 0.004449822008609772, 0.03548179566860199, 0.017205653712153435, -0.01237872801721096, -0.00631101056933403, -0.0011793609010055661, 0.007624790538102388, 0.021001018583774567, 0.02664540708065033, -0.04387052357196808, -0.033807940781116486, 0.013945532962679863, 0.016320068389177322, -0.05628817901015282, 0.08229129016399384, -0.040172476321458817, 0.01155153289437294, -0.04811354726552963, -0.005809827707707882, 0.004756370559334755, 0.02140974998474121, -0.04402622953057289, -0.006286681164056063, 0.02189633436501026, -0.04219667240977287, -0.007225790526717901, -0.008242753334343433, 0.07944963872432709, 0.045077256858348846, -0.0019244445720687509, 0.037350282073020935, 0.024874236434698105, -0.026664869859814644, 0.045155107975006104, 0.01957045868039131, 0.045700084418058395, 0.0505659356713295, -0.01791606843471527, 0.006087181158363819, -0.0583513006567955, -0.05274583771824837, 0.019443945959210396, 0.0002826756099238992, -0.00919646117836237, -0.003184700384736061, -0.020300336182117462, 0.002361154882237315, 0.058701641857624054, -0.01111360639333725, 0.030752185732126236, -0.002254106104373932, 0.027287699282169342, -0.040989939123392105, -0.019774824380874634, -0.019356360659003258, -0.06999041885137558, -0.0068219248205423355, -0.04387052357196808, -0.009230521507561207, -0.01994999498128891, -0.017108336091041565, 0.0302850641310215, 0.035365015268325806, 0.0050020962953567505, 0.05566535145044327, -0.017448946833610535, -0.000032483363611390814, -0.02592526003718376, -0.03727242723107338, 0.013721703551709652, 0.022246677428483963, -0.005274584051221609, 0.0059509375132620335, 0.01140555739402771, 0.030421309173107147, -0.017215386033058167, -0.02946760132908821, 0.028358187526464462, -0.05741705745458603, -0.030693795531988144, -0.03269852697849274, -0.028221942484378815, -0.020183555781841278, -0.036474429070949554, 0.027929991483688354, -0.02911726012825966, -0.037350282073020935, 0.02538028545677662, 0.03285423293709755, -0.0825248509645462, 0.03844023123383522, -0.019113067537546158, -0.0732213482260704, 0.020494969561696053, 0.05247335135936737, -0.0769583210349083, -0.0037175111938267946, -0.024037310853600502, -0.0009123472846113145, -0.07937178015708923, -0.03954964876174927, -0.023122530430555344, -0.025302432477474213, -0.072248175740242, 0.045739009976387024, -0.007435022387653589, -0.015327434986829758, -0.017147263512015343, -0.023180920630693436, -0.038031499832868576, 0.03425560146570206, 0.011240119114518166, -0.0014025819255039096, -0.06551383435726166, 0.019696969538927078, 0.04928135126829147, 0.022869504988193512, 0.000978036317974329, 0.009522472508251667, 0.027307162061333656, -0.009687911719083786, 0.021331897005438805, -0.020747993141412735, 0.023667505010962486, 0.007293912582099438, -0.05426398292183876, 0.011463947594165802, 0.030693795531988144, -0.020942628383636475, -0.01845131255686283, -0.002198148751631379, -0.0380704291164875, -0.011629386804997921, -0.015590190887451172, -0.010734070092439651, -0.028552820906043053, 0.07625763863325119, -0.02135135978460312, 0.06018086150288582, -0.004598230589181185, 0.0035058464854955673, 0.015794556587934494, -0.021468140184879303, -0.027015211060643196, -0.05325188860297203, -0.03964696452021599, 0.04655647277832031, -0.021078871563076973, 0.002133676316589117, 0.062399689108133316, -0.014286141842603683, 0.01395526435226202, -0.029681699350476265, 0.0026348589453846216, -0.05087735131382942, -0.014140166342258453, -0.005474083591252565, 0.03844023123383522, -0.015522068366408348, -0.02508833445608616, -0.014714336954057217, 0.057339202612638474, -0.002227343851700425, -0.028455503284931183, 0.003126310184597969, 0.021468140184879303, -0.04896993562579155, -0.017877141013741493, 0.03047969937324524, 0.025419212877750397, -0.02140974998474121, -0.020280871540308, 0.015045215375721455, 0.03501467406749725, 0.011366630904376507, 0.013390825130045414, -0.001582618453539908, 0.0035155783407390118, -0.019599653780460358, 0.008962899446487427, 0.011989460326731205, 0.01478245947510004, 0.0015582891646772623, -0.05550964176654816, -0.0046882485039532185, -0.03760330751538277, 0.009284046478569508, 0.018519433215260506, 0.019891604781150818, 0.06329500675201416, -0.012894508428871632, -0.0067489370703697205, 0.01478245947510004, 0.023998383432626724, 0.02664540708065033, 0.05901305750012398, -0.031666968017816544, 0.06687626987695694, -0.0150744104757905, 0.018042579293251038, -0.07170319557189941, -0.06594202667474747, 0.005566535051912069, 0.02251916378736496, -0.037447597831487656, -0.0037296756636351347, 0.02615882083773613, -0.010665948502719402, 0.022986285388469696, -0.004393864423036575, 0.026781650260090828, -0.015590190887451172, -0.030557552352547646, 0.03238711133599281, -0.043169841170310974, 0.026372918859124184, 0.03555964678525925, -0.06317822635173798, 0.04546652361750603, -0.06812193244695663, -0.022597018629312515, 0.013507605530321598, -0.013021020218729973, 0.035987842828035355, -0.03779793903231621, 0.053563300520181656, -0.04803569242358208, 0.020747993141412735, 0.08050066232681274, 0.04278057441115379, -0.007989729754626751, -0.01752679981291294, 0.002072853036224842, -0.0398026704788208, -0.058896277099847794, 0.004255187697708607, -0.026217211037874222, -0.008252485655248165, -0.0432087667286396, 0.015123068355023861, 0.01766304299235344, 0.01094816718250513, 0.04480476677417755, -0.008091912604868412, -0.08649539202451706, 0.01965804398059845, -0.03898520767688751, 0.03386633098125458, 0.010734070092439651, 0.029720624908804893, -0.03441130742430687, 0.047879986464977264, 0.0014232618268579245, 0.02504940703511238, -0.023141993209719658, -0.014363995753228664, -0.037155646830797195, 0.0026324260979890823, -0.04534974321722984, 0.004208962433040142, 0.0036542550660669804, 0.0021008315961807966, -0.06387890875339508, -0.026295065879821777, 0.0167385321110487, 0.11436699330806732, -0.020806383341550827, 0.03555964678525925, -0.03626032918691635, 0.005532473791390657, 0.03246496617794037, -0.002081368351355195, -0.04340340197086334, -0.011366630904376507, -0.003170102834701538, 0.025263505056500435, 0.00044248843914829195, -0.01776036061346531, 0.019113067537546158, -0.012806923128664494, -0.03310725837945938, -0.02450443245470524, -0.018509702757000923, 0.006997095420956612, 0.013069679029285908, -0.010880045592784882, 0.016047580167651176, 0.008559034205973148, 0.01654389686882496, 0.01067567989230156, 0.021584920585155487, 0.0019147128332406282, 0.043364476412534714, 0.02199365198612213, 0.006432656664401293, -0.011532070115208626, -0.04044496268033981, 0.00868554599583149, 0.07104144245386124, -0.04558330401778221, 0.022266140207648277, 0.04955383762717247, 0.010208558291196823, -0.01694289781153202, 0.011726703494787216, -0.03810935467481613, -0.004715010989457369, -0.03106360137462616, 0.01380928885191679, 0.018237214535474777, 0.022947359830141068, 0.0008874097838997841, 0.03295155242085457, 0.027949456125497818, -0.04745179042220116, 0.009147802367806435, 0.013926069252192974, 0.05920768901705742, -0.01785767823457718, 0.008602826856076717, 0.048347108066082, -0.009790094569325447, -0.010120972990989685, 0.010695143602788448, 0.008656350895762444, -0.03750598803162575, 0.0028416577260941267, -0.015210654586553574, -0.010052850469946861, -0.0022577554918825626, 0.011171996593475342, 0.0370972566306591, -0.05274583771824837, -0.008354668505489826, 0.07045754045248032, -0.026820577681064606, 0.006345071364194155, 0.013595190830528736, -0.017351629212498665, -0.0069727664813399315, -0.04130135476589203, -0.0027492064982652664, 0.003573968540877104, -0.021954724565148354, 0.007454485632479191, 0.04601150006055832, -0.020786920562386513, -0.031433407217264175, -0.05426398292183876, -0.03641603887081146, 0.030596479773521423, 0.006826790515333414, 0.02736555226147175, -0.036435503512620926, -0.020845310762524605, -0.007970266044139862, -0.023122530430555344, -0.024251407012343407, 0.019395286217331886, -0.014753264375030994, 0.009775497019290924, 0.01133743580430746, 0.0038002305664122105, 0.044337645173072815, -0.04815247282385826, 0.03908252716064453, -0.043169841170310974, -0.028747454285621643, -0.00932297296822071, 0.015054946765303612, -0.0027248773258179426, 0.022305067628622055, -0.01125958189368248, 0.02004731073975563, 0.026042040437459946, 0.03316564857959747, 0.009318106807768345, 0.0693286657333374, 0.027949456125497818, 0.046906813979148865, -0.009575997479259968, 0.03454755246639252, 0.0017711701802909374, 0.012563630938529968, -0.01470460556447506, -0.004031358752399683, -0.008505510166287422, 0.05874056741595268, -0.023317163810133934, 0.052356570959091187, 0.01713753119111061, 0.0077123758383095264, 0.03431399166584015, -0.014208288863301277, -0.016232483088970184, -0.011298509314656258, -0.016135165467858315, -0.00041238099220208824, 0.014665679074823856, -0.06356749683618546, -0.028416577726602554, -0.03275691717863083, -0.028241407126188278, 0.013527069240808487, 0.029389748349785805, 0.0034182611852884293, -0.004656620789319277, 0.009838753379881382, -0.018120434135198593, 0.032834772020578384, 0.03193945437669754, -0.026528626680374146, 0.0024317095521837473, 0.01468514185398817, -0.04636184126138687, 0.04083423316478729, 0.02654808945953846, -0.009556533768773079, 0.008330338634550571, 0.007289046887308359, 0.02329770103096962, -0.005303779151290655, -0.040367111563682556, 0.017439214512705803, -0.014548898674547672, -0.007576132193207741, 0.035793207585811615, 0.038226135075092316, 0.03908252716064453, -0.007955668494105339, 0.007692912593483925, 0.017448946833610535, -0.061815787106752396, -0.0082476194947958, 0.01994999498128891, 0.03742813691496849, 0.0973948985338211, 0.002110563451424241, 0.027248771861195564, -0.008549302816390991, 0.019259043037891388, 0.024095701053738594, -0.016144897788763046, 0.03711672127246857, 0.029000479727983475, 0.02573062665760517, -0.02586686983704567, -0.03388579562306404, 0.02645077370107174, 0.010130704380571842, -0.009104009717702866, -0.04305306077003479, -0.008680680766701698, -0.013507605530321598, 0.02105940878391266, -0.06158222630620003, -0.024134626612067223, 0.001351490500383079, -0.05465325340628624, -0.011152533814311028, -0.021273506805300713, -0.02150706760585308, -0.007308510132133961, -0.020786920562386513, -0.03336028382182121, 0.003739407518878579, 0.04850281402468681, 0.014879776164889336, 0.0007688046316616237, -0.035111989825963974, 0.02853335812687874, 0.02680111490190029, -0.03398311138153076, -0.008651485666632652, -0.001363655086606741, 0.03567642718553543, 0.017546262592077255, 0.015794556587934494, 0.02495209127664566, 0.0014415087644010782, -0.003955937922000885, 0.012291142717003822, 0.018032848834991455, 0.005513010546565056, -0.0038464562967419624, 0.005464352201670408, 0.02901994250714779, 0.018577823415398598, 0.027891065925359726, 0.030304528772830963, -0.034781113266944885, -0.01742948219180107, -0.004719876684248447, -0.007181997876614332, 0.0015059813158586621, -0.017439214512705803, 0.008330338634550571, 0.07785363495349884, -0.008802326396107674, -0.014568361453711987, -0.014276410453021526, -0.012125703506171703, 0.005892547313123941, 0.009619790129363537, 0.024737993255257607, 0.010033387690782547, 0.009619790129363537, 0.04087315872311592, 0.01431533694267273, -0.0035204440355300903, 0.004238157533109188, 0.0030995479319244623, 0.017108336091041565, -0.013828752562403679, 0.03411935642361641, -0.015113336965441704, 0.01771170273423195, 0.026178285479545593, -0.04398730397224426, 0.019395286217331886, -0.017448946833610535, -0.027696430683135986, 0.02248023822903633, 0.012417654506862164, 0.020456042140722275, 0.02228560298681259, 0.00697763217613101, -0.012797191739082336, 0.03581267222762108, -0.004140840377658606, 0.0007201461121439934, 0.04441550001502037, -0.011220655404031277, 0.01634926348924637, -0.04130135476589203, 0.024037310853600502, -0.022869504988193512, 0.011279045604169369, -0.016076775267720222, -0.009425155818462372, -0.034528087824583054, -0.01723484881222248, -0.016757994890213013, 0.02329770103096962, -0.035462331026792526, -0.001591133652254939, 0.015658313408493996, -0.03548179566860199, 0.021760091185569763, -0.01043238677084446, -0.003483950160443783, 0.01655362918972969, 0.012553898617625237, 0.007026290521025658, -0.01751706749200821, 0.017390556633472443, 0.04519403725862503, 0.01121092401444912, 0.006529973819851875, -0.005673583596944809, -0.020222481340169907, 0.04387052357196808, 0.028513893485069275, -0.029934722930192947, 0.05313510820269585, -0.02557491883635521, -0.049047790467739105, 0.06586417555809021, 0.0031482065096497536, -0.005697913002222776, 0.015405287966132164, -0.026139358058571815, -0.0021300269290804863, -0.00426978524774313, -0.02684004046022892, -0.02212989516556263, -0.017108336091041565, 0.019969457760453224, -0.011901875026524067, 0.007590729743242264, -0.0025083469226956367, -0.029525991529226303, -0.02179901860654354, 0.023433944210410118, 0.03252335637807846, 0.02277218922972679, -0.05332973971962929, -0.012096508406102657, -0.018509702757000923, 0.02212989516556263, 0.023862140253186226, 0.015541532076895237, -0.01356599573045969, 0.01853889785706997, 0.003345273435115814, -0.003724809968844056, 0.0077707660384476185, -0.005946071352809668, -0.004476584028452635, -0.00907481461763382, 0.01902548223733902, -0.04387052357196808, 0.02950652875006199, -0.028183016926050186, 0.012213288806378841, -0.004624992609024048, -0.007615058682858944, 0.011989460326731205, -0.018266409635543823, -0.011843484826385975, -0.032601211220026016, -0.021721163764595985, 0.015843214467167854, -0.005313510540872812, -0.006641888525336981, -0.0008302360656671226, 0.009794960729777813, 0.02670379728078842, 0.022888969630002975, 0.05940232425928116, -0.017779823392629623, -0.02189633436501026, -0.034878429025411606, -0.010617289692163467, 0.013176728039979935, -0.028844771906733513, -0.024523895233869553, -0.05138339847326279, 0.03160857781767845, 0.016222750768065453, -0.01052970439195633, 0.032153550535440445, 0.005303779151290655, -0.0013916337629780173, -0.04130135476589203, -0.02440711483359337, -0.03912145271897316, 0.03256228193640709, -0.05761168897151947, -0.012884777039289474, 0.06372319906949997, 0.03840130567550659, 0.007877814583480358, 0.013984459452331066, 0.008145436644554138, 0.013692508451640606, -0.05247335135936737, 0.034528087824583054, 0.008748802356421947, 0.0243097972124815, -0.019093604758381844, -0.003401230787858367, -0.01485058106482029, 0.013186459429562092, -0.038751646876335144, -0.043559107929468155, -0.04558330401778221, -0.03386633098125458, 0.02397892065346241, -0.01970670185983181, -0.010101509280502796, 0.030499162152409554, -0.024251407012343407, 0.008544436655938625, -0.007201461121439934, -0.009619790129363537, 0.004800163209438324, 0.008792595006525517, -0.014227751642465591, -0.01849997043609619, 0.003851321991533041, 0.03287369757890701, 0.036571744829416275, 0.0007943504024296999, -0.015064678154885769, -0.016368726268410683, 0.007420424837619066, -0.01707914099097252, -0.02553599327802658, -0.01858755573630333, -0.014918702654540539, 0.014568361453711987, -0.006169900763779879, -0.018032848834991455, 0.007984863594174385, 0.00035459897480905056, 0.016485506668686867, -0.010043119080364704, 0.04141813516616821, -0.02878638170659542, 0.03555964678525925, -0.014743532054126263, -0.020125165581703186, -0.006092046853154898, 0.006121241953223944, -0.04340340197086334, -0.002525377320125699, -0.004569035489112139, 0.01829560473561287, -0.001993783051148057, 0.054575398564338684, -0.01036426518112421, 0.04480476677417755, -0.049437057226896286, 0.013984459452331066, -0.04285842552781105, -0.0021361091639846563, -0.0013746032491326332, -0.009692777879536152, 0.0027638040482997894, -0.006948437076061964, 0.031569648534059525, -0.06893939524888992, 0.011755898594856262, -0.0216043833643198, -0.006447254214435816, 0.00712360767647624, -0.036279793828725815, -0.01335189864039421, 0.013556264340877533, -0.005488681141287088, -0.0634896382689476, 0.05636603385210037, -0.01708887331187725, 0.01902548223733902, -0.01528850756585598, 0.042157743126153946, 0.02063121274113655, 0.027501797303557396, 0.006111510563641787, -0.019064409658312798, 0.04772428050637245, 0.022090969607234, -0.018967092037200928, -0.054770033806562424, -0.0216043833643198, 0.015560995787382126, -0.022966822609305382, -0.012067313306033611, -0.0016020818147808313, 0.008014058694243431, 0.05329081416130066, 0.03740867227315903, 0.0025229444727301598, -0.03034345433115959, -0.011765630915760994, 0.03534555062651634, 0.02397892065346241, -0.008028656244277954, -0.02650916390120983, 0.06734339892864227, -0.057105641812086105, -0.048853155225515366, -0.02878638170659542, 0.06208827346563339, -0.052200861275196075, -0.004547139164060354, -0.010354533791542053, 0.00429654773324728, 0.021137261763215065, -0.047296084463596344, -0.010928704403340816, -0.00131378008518368, -0.0077853635884821415, -0.05037130415439606, 0.008622290566563606, 0.014986825175583363, -0.020300336182117462, 0.022558091208338737, -0.0048512546345591545, 0.0201446283608675, -0.014062313362956047, -0.007834021933376789, 0.06282788515090942, 0.003527742810547352, -0.0005264243809506297, -0.0024511730298399925, -0.01335189864039421, -0.030596479773521423, -0.008729338645935059, 0.05196730047464371, -0.0625164732336998, -0.02791052870452404, -0.0627889558672905, 0.00044035963946953416, 0.01665094681084156, 0.022168822586536407, 0.021429212763905525, -0.002612962620332837, -0.007347437087446451, -0.006301278714090586 ]
Behaviour biometrics are being explored as a viable alternative to overcome the limitations of traditional authentication methods such as passwords and static biometrics. Also, they are being considered as a viable authentication method for IoT devices such as smart headsets with AR/VR capabilities, wearables, and erables, that do not have a large form factor or the ability to seamlessly interact with the user. Recent behavioural biometric solutions use deep learning models that require large amounts of annotated training data. Collecting such volumes of behaviour biometrics data raises privacy and usability concerns. To this end, we propose using SimSiam-based non-contrastive self-supervised learning to improve the label efficiency of behavioural biometric systems. The key idea is to use large volumes of unlabelled (and anonymised) data to build good feature extractors that can be subsequently used in supervised settings. Using two EEG datasets, we show that at lower amounts of labelled data, non-contrastive learning performs 4%-11% more than conventional methods such as supervised learning and data augmentation. We also show that, in general, self-supervised learning methods perform better than other baselines. Finally, through careful experimentation, we show various modifications that can be incorporated into the non-contrastive learning process to archive high performance.
[ 0.010844213888049126, 0.021079201251268387, -0.029648972675204277, -0.07331012934446335, 0.05755149945616722, 0.010133450850844383, 0.002903974847868085, 0.010925443843007088, -0.023962868377566338, -0.018124457448720932, 0.01573832519352436, -0.07331012934446335, -0.020896434783935547, -0.05828257277607918, 0.014966639690101147, -0.005135263316333294, 0.030237890779972076, -0.044717151671648026, -0.001413910766132176, -0.012712504714727402, -0.012600813992321491, -0.02755729854106903, -0.039132583886384964, -0.0690455511212349, 0.016814623028039932, 0.06571511924266815, 0.04096025973558426, 0.011890050955116749, -0.03557876870036125, -0.00740716652944684, 0.031639110296964645, -0.014448797330260277, -0.038360897451639175, -0.005752103868871927, -0.04500145465135574, -0.025018859654664993, 0.025831161066889763, -0.001538294367492199, -0.007493473589420319, 0.041833482682704926, 0.011666667647659779, 0.0005724180955439806, -0.03602553531527519, -0.03295909985899925, -0.018916450440883636, -0.08902814984321594, -0.04313316568732262, -0.03535538539290428, -0.048372503370046616, -0.03336524963378906, 0.03399478271603584, -0.053611841052770615, 0.007229475770145655, 0.002995358547195792, -0.016337396577000618, 0.04418915510177612, 0.03320278972387314, -0.010549754835665226, 0.09065274894237518, -0.025628086179494858, -0.004729112610220909, 0.033263713121414185, -0.0156570952385664, 0.007838700897991657, -0.0056861042976379395, -0.014570643194019794, 0.01844937913119793, -0.023069338873028755, -0.015139252878725529, 0.004350885283201933, -0.0752190425992012, 0.01853060908615589, 0.022399190813302994, 0.0341978557407856, 0.023617642000317574, 0.018073689192533493, 0.029933279380202293, 0.04906295984983444, 0.02881636470556259, -0.03397447615861893, 0.011879896745085716, 0.010854367166757584, 0.009123151190578938, 0.03521323204040527, 0.08797215670347214, -0.061775464564561844, 0.021810272708535194, -0.07294459640979767, 0.03102988377213478, -0.04053380340337753, -0.042280249297618866, 0.04069626331329346, 0.029669281095266342, 0.012407892383635044, -0.041203949600458145, -0.004437192343175411, -0.0026196695398539305, -0.0321061834692955, -0.0373455211520195, 0.0069908625446259975, 0.00111056724563241, -0.011575284413993359, -0.022033654153347015, -0.001967290649190545, 0.0044067311100661755, 0.03293878957629204, -0.04398607835173607, 0.04004641994833946, 0.0008211851818487048, 0.1290745735168457, -0.03338555619120598, -0.03464462235569954, -0.03411662578582764, 0.0226022657006979, -0.0309892687946558, 0.011778359301388264, -0.005422106944024563, -0.048819269984960556, -0.0027770528104156256, -0.02512039802968502, 0.0141847999766469, 0.07144184410572052, -0.012072818353772163, 0.045448221266269684, -0.027212072163820267, 0.05292138829827309, -0.01800261251628399, 0.023353643715381622, 0.008950538001954556, 0.011879896745085716, -0.010600523091852665, 0.04132579639554024, -0.02183057926595211, -0.013311577029526234, -0.013047578744590282, 0.032045260071754456, 0.026643460616469383, 0.013961417600512505, -0.010209604166448116, -0.022338267415761948, 0.010356833226978779, -0.01994198001921177, -0.03959965705871582, 0.032004646956920624, 0.01979982852935791, -0.015322021208703518, -0.004010734613984823, 0.05296200141310692, -0.048738040030002594, 0.009646070189774036, -0.005523644387722015, 0.0613286979496479, 0.04800696671009064, 0.005620105192065239, 0.03188280016183853, -0.0157890934497118, 0.032674793154001236, -0.06210038438439369, -0.016408473253250122, -0.037325214594602585, 0.06534958630800247, -0.01677400805056095, 0.006681172642856836, 0.028613289818167686, 0.03155788034200668, 0.04045257344841957, 0.01872353069484234, 0.028938209637999535, -0.056942276656627655, 0.06498405337333679, -0.06453728675842285, -0.0208355113863945, 0.01601247675716877, 0.03545692190527916, 0.0626283809542656, 0.05210908502340317, 0.06701480597257614, -0.04613867774605751, -0.03521323204040527, 0.009620686061680317, -0.031232960522174835, 0.011849435977637768, 0.0327560231089592, 0.027029303833842278, 0.04788512364029884, 0.04439223185181618, 0.07339136302471161, -0.013006963767111301, 0.010519293136894703, -0.037548597902059555, 0.008021469227969646, 0.029161592945456505, 0.07578764855861664, -0.02729330211877823, 0.0385233573615551, -0.025810852646827698, -0.020693358033895493, -0.02747606858611107, 0.03580215200781822, 0.026359155774116516, -0.051621705293655396, -0.04739774391055107, 0.008219467476010323, -0.020084133371710777, -0.028166525065898895, 0.02430809661746025, 0.0318421870470047, 0.022216422483325005, -0.003272048430517316, -0.030237890779972076, -0.02304903045296669, -0.03102988377213478, -0.06210038438439369, -0.025425009429454803, -0.013697419315576553, -0.03356832265853882, 0.045123301446437836, -0.005965332966297865, 0.031639110296964645, 0.022724110633134842, -0.011016827076673508, 0.05186539515852928, 0.055358290672302246, -0.03892950713634491, -0.016296781599521637, -0.014134030789136887, -0.005234262440353632, 0.05799826607108116, 0.017342619597911835, -0.005726719740778208, 0.014560488983988762, -0.00942776445299387, 0.03641137480735779, -0.002426748163998127, 0.027536991983652115, -0.015677401795983315, 0.044311001896858215, -0.010219757445156574, 0.02625761739909649, -0.018165072426199913, -0.03671598806977272, -0.03527415543794632, -0.04154917970299721, -0.05231216177344322, 0.035883381962776184, -0.013809110969305038, -0.029831741005182266, 0.07359443604946136, 0.012174355797469616, 0.008656078949570656, -0.031009577214717865, 0.030339429154992104, -0.011219902895390987, 0.015586018562316895, -0.04658544063568115, 0.02021613158285618, 0.03346678614616394, -0.04280824214220047, 0.04398607835173607, -0.012072818353772163, 0.0648622065782547, -0.005594720598310232, -0.01863214559853077, 0.07765594124794006, -0.011057442054152489, 0.027577606961131096, 0.060150861740112305, 0.009290688671171665, 0.024572094902396202, -0.06928924471139908, 0.027415147051215172, 0.018368149176239967, -0.021932117640972137, -0.03224833682179451, 0.04398607835173607, -0.0006434944225475192, 0.04845373332500458, -0.024734554812312126, 0.039762116968631744, 0.03102988377213478, -0.017393387854099274, 0.005879025906324387, 0.031232960522174835, 0.02810560166835785, 0.019231216982007027, -0.021140124648809433, -0.018571224063634872, 0.0022833263501524925, -0.06746156513690948, -0.016002323478460312, -0.028166525065898895, -0.0344618558883667, -0.0630345270037651, -0.007412243168801069, 0.02629823423922062, -0.02371917851269245, -0.029344361275434494, 0.011128518730401993, 0.01867276057600975, -0.03458369895815849, -0.015261098742485046, 0.008742385543882847, -0.017159851267933846, 0.029120977967977524, 0.0011289709946140647, -0.008859153836965561, 0.05462721735239029, 0.020855819806456566, -0.035335078835487366, -0.022521035745739937, 0.009300841949880123, 0.0005076879169791937, 0.005488106049597263, -0.03360893949866295, -0.02382071688771248, 0.006249638274312019, 0.022967800498008728, 0.04317377880215645, 0.02300841547548771, -0.024653324857354164, -0.018977373838424683, 0.01985059678554535, -0.09438933432102203, 0.061044394969940186, 0.005604874342679977, -0.00001128415715356823, 0.04443284496665001, -0.02097766473889351, -0.013210039585828781, -0.02003336511552334, -0.024917323142290115, -0.003995503764599562, -0.05885118246078491, -0.0017997536342591047, 0.0387873575091362, 0.0013669496402144432, -0.0009576263255439699, 0.0028024371713399887, -0.018053382635116577, -0.01850014738738537, -0.008554541505873203, -0.019281987100839615, -0.05950102210044861, -0.04739774391055107, 0.0021995578426867723, 0.021180739626288414, -0.03856397420167923, -0.004010734613984823, 0.021038586273789406, -0.0402291901409626, 0.0013060271739959717, -0.05629243329167366, -0.0002630458038765937, -0.02814621664583683, 0.005620105192065239, -0.03364955261349678, -0.008381927385926247, -0.017941690981388092, -0.03775167092680931, 0.019068757072091103, 0.028308676555752754, -0.05422106757760048, 0.01041775569319725, -0.0002850984747055918, -0.031964030116796494, -0.03602553531527519, -0.04093995317816734, 0.00856977142393589, 0.04398607835173607, 0.018875835463404655, -0.02711053378880024, -0.020287208259105682, -0.049956489354372025, -0.025059474632143974, -0.015718016773462296, 0.009828837588429451, 0.003939657937735319, 0.024328405037522316, -0.035923995077610016, 0.06417175382375717, -0.04735712707042694, -0.010884828865528107, -0.01073252223432064, 0.038767047226428986, 0.0011086635058745742, 0.03025819920003414, 0.04853496327996254, 0.03823905438184738, 0.04325500875711441, 0.07241660356521606, 0.012935888022184372, -0.0701015442609787, -0.029384976252913475, -0.07209168374538422, 0.01889614388346672, 0.00626994576305151, 0.02995358593761921, 0.020358284935355186, 0.04006673023104668, 0.006594866048544645, -0.04252393916249275, 0.02530316449701786, -0.027760375291109085, -0.03084711730480194, -0.03062373399734497, 0.011169133707880974, -0.04085872322320938, 0.02747606858611107, 0.010255295783281326, -0.0440266951918602, 0.016256166622042656, -0.02426748163998127, -0.01294604130089283, 0.022257037460803986, -0.005569336470216513, -0.0006764941499568522, -0.04329562559723854, 0.05223093181848526, 0.0428488589823246, -0.011839281767606735, -0.04154917970299721, 0.027090227231383324, 0.07440673559904099, 0.005696258042007685, -0.011605745181441307, 0.024978244677186012, -0.01573832519352436, 0.012732812203466892, 0.02205396257340908, -0.01943429373204708, -0.010854367166757584, -0.011544822715222836, 0.005564259365200996, -0.08232667297124863, -0.03549753874540329, -0.015728171914815903, 0.05223093181848526, 0.04207717254757881, -0.025607777759432793, -0.025953005999326706, -0.03923412039875984, -0.0008440311648882926, -0.009823760949075222, -0.026582539081573486, -0.007630549371242523, -0.030928347259759903, 0.008909923024475574, 0.01881491392850876, 0.020175516605377197, 0.0029572821222245693, -0.0805802270770073, 0.04800696671009064, -0.08236728608608246, -0.04443284496665001, 0.052027855068445206, -0.053246308118104935, 0.046260520815849304, -0.045082684606313705, -0.018916450440883636, -0.038685817271471024, 0.017383234575390816, 0.03283725306391716, 0.012590659782290459, -0.021282276138663292, 0.02138381451368332, -0.008046853356063366, -0.08082391321659088, -0.04410792514681816, -0.0056810276582837105, 0.0550333671271801, 0.002870975062251091, -0.04459530487656593, -0.030725272372364998, 0.00944807194173336, 0.009666377678513527, -0.010915289632976055, -0.0361676849424839, -0.01728169620037079, -0.012742966413497925, 0.013666958548128605, -0.010976212099194527, 0.010976212099194527, 0.041874099522829056, -0.03172034025192261, -0.010478678159415722, 0.02914128638803959, 0.014266029931604862, 0.019200757145881653, -0.004553960636258125, -0.07623441517353058, -0.01587032340466976, -0.035111695528030396, -0.001173393684439361, 0.0012603352079167962, 0.006716710980981588, -0.0076863947324454784, 0.017870614305138588, -0.019190602004528046, 0.1070612221956253, 0.055764440447092056, -0.015210329554975033, -0.022521035745739937, 0.012072818353772163, -0.016885699704289436, -0.008031622506678104, -0.02678561396896839, -0.04418915510177612, 0.020896434783935547, -0.021525967866182327, 0.017809690907597542, 0.027618221938610077, 0.007529011461883783, -0.008554541505873203, -0.04500145465135574, 0.006803018040955067, 0.016631856560707092, -0.03697998821735382, -0.022622572258114815, 0.03959965705871582, 0.024429941549897194, -0.013930955901741982, 0.02164781279861927, 0.00908761378377676, 0.02363794855773449, -0.05304323136806488, 0.032370179891586304, 0.05145924538373947, 0.015332174487411976, 0.005155570805072784, 0.018327532336115837, -0.03959965705871582, -0.05129678547382355, -0.049509722739458084, -0.02755729854106903, 0.004358500707894564, 0.000006435340765165165, -0.010316218249499798, 0.025384394451975822, 0.019901365041732788, -0.0031375112012028694, -0.043458085507154465, 0.018246302381157875, 0.009818684309720993, -0.0014101031702011824, -0.011362055316567421, -0.001679177745245397, 0.01324050035327673, -0.01003191340714693, 0.02922251634299755, 0.02922251634299755, 0.029303746297955513, 0.0074173202738165855, -0.02412532828748226, 0.006711633875966072, 0.0006152542773634195, -0.017647230997681618, -0.03884827718138695, -0.0033862784039229155, -0.00822962075471878, -0.037954747676849365, -0.004919495899230242, 0.02828836999833584, -0.022439805790781975, -0.013098347932100296, 0.015860170125961304, -0.00021703657694160938, 0.02048012986779213, 0.07684364169836044, 0.03170003369450569, 0.007742240559309721, -0.0378735177218914, -0.0008992421790026128, -0.0011568937916308641, -0.036655064672231674, -0.0009208189439959824, 0.033040329813957214, 0.0271917637437582, -0.012702351436018944, -0.008336235769093037, 0.04788512364029884, 0.0023074415512382984, 0.017423849552869797, 0.04727589711546898, 0.04370177537202835, -0.011534669436514378, 0.02363794855773449, -0.007666087243705988, -0.04906295984983444, 0.02353641204535961, 0.011250363662838936, 0.020094286650419235, 0.06299391388893127, 0.003995503764599562, 0.009016537107527256, -0.0017210619989782572, -0.03553815186023712, -0.024754861369729042, 0.04240209236741066, 0.010742676444351673, -0.029689587652683258, -0.03888889402151108, 0.02138381451368332, 0.03679721802473068, 0.08431680500507355, 0.04154917970299721, -0.008701770566403866, 0.03679721802473068, -0.02914128638803959, 0.00008019882079679519, 0.010163911618292332, -0.029527127742767334, -0.015758631750941277, 0.01902814209461212, -0.02043951489031315, 0.009691761806607246, -0.0018276764312759042, 0.04071656987071037, -0.021485352888703346, -0.05552075058221817, -0.02422686666250229, 0.02678561396896839, -0.015535249374806881, 0.0037111984565854073, -0.023800408467650414, 0.02282564714550972, 0.028897594660520554, 0.02007398009300232, -0.02530316449701786, 0.04077749326825142, -0.0068740942515432835, -0.0220133475959301, -0.01193066593259573, 0.011676821857690811, 0.024247175082564354, 0.027354223653674126, 0.020683204755187035, -0.010681753046810627, 0.007402089424431324, -0.011230056174099445, -0.01723092794418335, 0.03933565691113472, 0.028024371713399887, -0.03149695694446564, 0.05137801542878151, -0.0008484733989462256, -0.00078945467248559, -0.023475488647818565, 0.00626994576305151, 0.032370179891586304, 0.028532059863209724, 0.03135480359196663, -0.01141282357275486, 0.03716275468468666, 0.022744417190551758, -0.01763707771897316, -0.021180739626288414, 0.029344361275434494, 0.03992457687854767, -0.0128749655559659, 0.016337396577000618, 0.020185671746730804, -0.02666376903653145, -0.017464464530348778, 0.01890629716217518, 0.010478678159415722, 0.020449668169021606, 0.027232378721237183, -0.006005947943776846, 0.016114013269543648, 0.014367567375302315, -0.013524806126952171, -0.08159559965133667, -0.045407604426145554, 0.00597548671066761, 0.019241372123360634, -0.05868872255086899, 0.05348999798297882, -0.004942341707646847, 0.0147737180814147, -0.028613289818167686, -0.024754861369729042, -0.04134610295295715, 0.005427183583378792, -0.03539600223302841, -0.00915361288934946, -0.02696838043630123, -0.016845084726810455, 0.022988108918070793, -0.020723819732666016, 0.0010934327729046345, -0.008630693890154362, -0.03080650232732296, 0.010427909903228283, -0.005868872161954641, 0.061369314789772034, 0.0004775439447257668, -0.0385233573615551, 0.0037111984565854073, 0.0023315567523241043, 0.02007398009300232, -0.04276762902736664, -0.0169669296592474, -0.015941400080919266, 0.04333623871207237, 0.036248914897441864, 0.012793734669685364, 0.018246302381157875, -0.007026400417089462, -0.0025803237222135067, 0.016946621239185333, -0.005170801188796759, -0.0023569411132484674, 0.004018349573016167, 0.03531477227807045, 0.038360897451639175, -0.021932117640972137, 0.010722368955612183, -0.0030664349906146526, -0.04118364304304123, 0.03216710686683655, -0.00585364131256938, 0.01318973209708929, 0.028308676555752754, -0.06189730763435364, 0.002797360299155116, 0.06108500808477402, 0.033080942928791046, 0.007087322883307934, -0.026643460616469383, 0.006970555055886507, 0.05133740231394768, -0.027597913518548012, -0.022967800498008728, 0.018733683973550797, 0.020409053191542625, -0.028085295110940933, 0.016611548140645027, 0.01759646274149418, 0.005782565101981163, -0.0195256769657135, 0.001637293491512537, -0.0003829870547633618, -0.008635771460831165, -0.030786193907260895, 0.015819555148482323, 0.001760407816618681, 0.004041195847094059, 0.05917610228061676, -0.03789382427930832, -0.006564404349774122, 0.03568030521273613, -0.005833333823829889, 0.027780681848526, -0.06624311953783035, -0.016185089945793152, -0.013900495134294033, 0.021891502663493156, -0.024612709879875183, 0.018388455733656883, -0.025973312556743622, 0.019322602078318596, 0.03243110328912735, 0.009798376820981503, 0.02164781279861927, 0.021769657731056213, -0.004005657508969307, -0.027658836916089058, 0.03220771998167038, 0.022439805790781975, -0.06449667364358902, 0.07729040831327438, -0.006071947515010834, 0.058932412415742874, -0.05085001885890961, -0.012387584894895554, 0.021911809220910072, 0.0032466640695929527, -0.005356107372790575, -0.010742676444351673, 0.02629823423922062, -0.01772846095263958, 0.011098057962954044, -0.004223963245749474, 0.05686104670166969, -0.02241949737071991, -0.03827966749668121, -0.01568755693733692, -0.04621990770101547, 0.006635481026023626, 0.03911227732896805, 0.0049093421548604965, 0.023211490362882614, 0.046747900545597076, 0.0024483248125761747, 0.017616769298911095, -0.026826228946447372, -0.03886858746409416, 0.03797505423426628, -0.04051349312067032, -0.031862493604421616, 0.028389908373355865, -0.01041775569319725, -0.0220133475959301, 0.04532637447118759, -0.023170875385403633, -0.03356832265853882, -0.05755149945616722, -0.016347549855709076, 0.006513635627925396, 0.008854077197611332, -0.010438063181936741, 0.022033654153347015, 0.019698290154337883, -0.007742240559309721, 0.009310996159911156, -0.0018289457075297832, -0.034258779138326645, 0.009209458716213703, 0.016134321689605713, -0.06587757915258408, -0.0077676246874034405, -0.05921671539545059, 0.0007716856198385358, -0.016946621239185333, -0.018825067207217216, -0.0335480161011219, 0.011524515226483345, -0.008813462220132351, -0.0031400497537106276, 0.007635626010596752, 0.03342617303133011, 0.022967800498008728, -0.004680882673710585, 0.024998553097248077, -0.04297070577740669, 0.02570931613445282, -0.027821296826004982, 0.03194372355937958, -0.04479838162660599, 0.004198579117655754, 0.01619524322450161, -0.00106868299189955, -0.01256019901484251, -0.019738905131816864, 0.00491695711389184, -0.0033608938101679087, -0.00969683937728405, 0.036919064819812775, 0.02386133186519146, -0.024653324857354164, 0.03559907525777817, -0.022175807505846024, 0.009189151227474213, 0.01848999410867691, -0.029080362990498543, 0.011575284413993359, -0.0019571369048208, 0.0014748333487659693, 0.007544242311269045, -0.02105889469385147, 0.014651873148977757, -0.0012038549175485969, -0.00259936205111444, 0.04865681007504463, 0.014540181495249271, -0.04536699131131172, 0.001997751882299781, -0.015850016847252846, -0.05401799455285072, -0.04821004346013069, -0.017606616020202637, -0.029445897787809372, -0.05178416520357132, -0.008904845453798771, 0.00025209877640008926, 0.05990717187523842, -0.001580178621225059, 0.015992168337106705, 0.0012451045913621783, -0.023292720317840576, 0.018774298951029778, 0.056901659816503525, 0.030786193907260895, 0.0007824740023352206, 0.05105309560894966, 0.023130260407924652, -0.03084711730480194, -0.046910360455513, 0.03153757378458977, -0.020916741341352463, -0.004640267230570316, 0.019830290228128433, -0.017342619597911835, 0.03781259432435036, 0.04366115853190422, 0.015809401869773865, 0.0002909686299972236, -0.01669277809560299, 0.04207717254757881, 0.02985204942524433, -0.02386133186519146, -0.02593269757926464, -0.05210908502340317, -0.005132724530994892, -0.02426748163998127, 0.04812881350517273, 0.007442704867571592, -0.02489701472222805, 0.0082550048828125, -0.0074223969131708145, -0.03172034025192261, -0.03848274424672127, 0.0084834648296237, -0.02648100070655346, 0.023109953850507736, 0.020307516679167747, -0.013677111826837063, -0.003117203712463379, 0.03911227732896805, -0.050809405744075775, 0.04581375792622566, 0.028227446600794792, -0.03549753874540329, 0.01610385999083519, -0.00946837943047285, -0.028389908373355865, -0.02648100070655346, -0.01912968046963215, -0.04085872322320938, -0.005503336898982525, 0.015545403584837914, 0.041792869567871094, 0.029648972675204277, 0.026541924104094505, 0.030481582507491112, -0.015900785103440285, -0.03320278972387314, 0.010783291421830654, -0.06352190673351288, -0.01161589939147234, 0.0009176458697766066, -0.011057442054152489, -0.056454893201589584, -0.022074269130825996, 0.0036553528625518084, -0.03874674066901207, 0.015271252021193504, -0.02700899727642536, 0.018236149102449417, 0.008513926528394222, -0.03336524963378906, -0.027313608676195145, 0.026460694149136543, -0.020307516679167747, -0.04695097729563713, -0.047154054045677185, -0.04374238848686218, -0.03035973571240902, -0.01224543247371912, 0.02800406515598297, -0.03661445155739784, 0.016936467960476875, -0.046747900545597076, 0.005076879169791937, -0.03216710686683655, 0.026440385729074478, -0.017982305958867073, -0.0014329490950331092, 0.007249783258885145, 0.008361619897186756, -0.032146796584129333, -0.02164781279861927, 0.05271831154823303, 0.022561650723218918, -0.024369020015001297, -0.0433768555521965, -0.021810272708535194, -0.013159270398318768, -0.004970264621078968, -0.005655643064528704, -0.0026932843029499054, -0.026237310841679573, 0.014986947178840637, -0.015910938382148743, -0.010427909903228283, -0.025506239384412766, 0.005767334718257189, -0.009778069332242012, -0.059338562190532684, 0.01010806579142809, -0.020733973011374474, -0.023028723895549774, 0.028389908373355865, -0.006117639131844044, -0.025689007714390755, -0.0035588922910392284, -0.0003725159913301468, -0.04272701218724251, -0.018510300666093826, 0.012032203376293182, -0.003355816937983036, -0.0018365610158070922, -0.010498985648155212, 0.01736292615532875, -0.04288947582244873, 0.022358575835824013, 0.019495215266942978, -0.023394258692860603, -0.02485639974474907, 0.013311577029526234, 0.03450246900320053, 0.001554794143885374, 0.0037822749000042677, -0.008620540611445904, -0.00646286690607667, -0.008783000521361828, -0.0021602120250463486, -0.02359733358025551, 0.007153322454541922, -0.018388455733656883, 0.007950392551720142, 0.009864375926554203, 0.06035393849015236, -0.03076588734984398 ]
Traffic signal control has the potential to reduce congestion in dynamic networks. Recent studies show that traffic signal control with reinforcement learning (RL) methods can significantly reduce the average waiting time. However, a shortcoming of existing methods is that they require model retraining for new intersections with different structures. In this paper, we propose a novel reinforcement learning approach with augmented data (ADLight) to train a universal model for intersections with different structures. We propose a new agent design incorporating features on movements and actions with set current phase duration to allow the generalized model to have the same structure for different intersections. A new data augmentation method named \textit{movement shuffle} is developed to improve the generalization performance. We also test the universal model with new intersections in Simulation of Urban MObility (SUMO). The results show that the performance of our approach is close to the models trained in a single environment directly (only a 5% loss of average waiting time), and we can reduce more than 80% of training time, which saves a lot of computational resources in scalable operations of traffic lights.
[ -0.024720970541238785, -0.02114216797053814, -0.030322574079036713, -0.03182022646069527, -0.010211258195340633, 0.024818221107125282, -0.01865256577730179, 0.03508782759308815, -0.09172627329826355, -0.009754182770848274, -0.02654927223920822, 0.0029758524615317583, 0.02829977311193943, -0.035204529762268066, 0.005596742033958435, -0.01610461249947548, -0.026121370494365692, 0.02201741747558117, 0.0024737988132983446, -0.025887971743941307, 0.006442817859351635, -0.010687783360481262, -0.030108625069260597, 0.05908914655447006, -0.029427874833345413, 0.0270744226872921, 0.0021419329568743706, 0.01708683930337429, -0.1132768914103508, 0.05021994188427925, 0.011358809657394886, 0.021006017923355103, 0.021375566720962524, -0.015939287841320038, -0.017154913395643234, -0.011067058891057968, 0.04135073348879814, 0.014461087062954903, -0.042906735092401505, 0.05492684617638588, -0.03217032551765442, 0.006233729887753725, -0.06177325174212456, -0.05659954622387886, 0.021686768159270287, -0.05586044490337372, -0.009759045206010342, -0.006471992935985327, -0.03333732858300209, 0.043334636837244034, -0.024176370352506638, -0.03292887657880783, 0.003092552535235882, -0.018720639869570732, 0.0033770089503377676, 0.056405045092105865, 0.01692151464521885, 0.030672674998641014, 0.0031606275588274, 0.03080882504582405, 0.013799786567687988, -0.02497382089495659, -0.08736947178840637, 0.03981418162584305, 0.023495618253946304, -0.020189115777611732, 0.05037553980946541, -0.006214280147105455, 0.02365121990442276, -0.014587512239813805, -0.04983093962073326, 0.03555462881922722, -0.10417428612709045, -0.011057334020733833, 0.008611494675278664, 0.0016678388928994536, -0.0015863919397816062, 0.01690206304192543, -0.0349905788898468, 0.04018373414874077, 0.04932523891329765, 0.03831653296947479, -0.005450867116451263, 0.03209252655506134, 0.004040740896016359, -0.026957722380757332, -0.0046047912910580635, -0.07169275730848312, 0.05372094362974167, -0.03125617653131485, -0.042089834809303284, 0.006749155465513468, -0.050025440752506256, 0.0019936265889555216, -0.05232054367661476, 0.010794758796691895, 0.0303614754229784, -0.005504354368895292, -0.06815285235643387, 0.012525809928774834, -0.02370956912636757, 0.0030585150234401226, 0.004269278608262539, 0.015064037404954433, 0.05702744796872139, -0.024370869621634483, -0.06885305792093277, 0.012564710341393948, -0.007532018702477217, 0.11389929056167603, 0.032364826649427414, -0.01945001631975174, 0.0159003883600235, 0.024682069197297096, -0.059789348393678665, 0.012700860388576984, -0.012097910046577454, -0.0735599622130394, 0.057610947638750076, 0.04181753471493721, 0.057766545563936234, 0.08246807008981705, 0.017874564975500107, -0.0532541424036026, -0.010882283560931683, -0.014023461379110813, 0.0055870171636343, 0.05107574164867401, 0.05481014400720596, 0.007809181232005358, -0.028941623866558075, 0.04477393627166748, -0.00085762410890311, -0.020033515989780426, -0.001940139103680849, 0.0008497225935570896, -0.00664704293012619, -0.04983093962073326, 0.0005816770135425031, -0.0034329278860241175, -0.0002618154394440353, -0.050025440752506256, -0.06601335108280182, 0.06224004924297333, -0.003112002508714795, 0.015190462581813335, 0.007108980789780617, 0.05197044089436531, -0.02582962065935135, 0.0024798770900815725, -0.023845719173550606, 0.04683563858270645, -0.021647866815328598, 0.07320985943078995, 0.014247136190533638, 0.023573419079184532, -0.02621862106025219, -0.012827285565435886, -0.01182560995221138, -0.08021186292171478, 0.04516293853521347, -0.015375237911939621, -0.03211197629570961, 0.06523535400629044, 0.021881267428398132, 0.0008588397759012878, 0.053915444761514664, -0.03629373013973236, -0.01818576455116272, 0.05107574164867401, -0.052670642733573914, -0.009627757593989372, -0.018954040482640266, -0.0038292219396680593, 0.010104283690452576, 0.008519106544554234, 0.028533173725008965, -0.00269625848159194, -0.022134117782115936, -0.016989588737487793, -0.05998384952545166, -0.013109310530126095, 0.005125079303979874, 0.04442383721470833, 0.08402407169342041, -0.014655587263405323, 0.05784434825181961, 0.0029880087822675705, -0.0031241588294506073, -0.0017103857826441526, -0.02324276976287365, 0.029019422829151154, 0.0539543442428112, -0.0025868520606309175, -0.04442383721470833, -0.031975824385881424, -0.047963738441467285, -0.032267577946186066, 0.006379605270922184, -0.01227295957505703, -0.01632828824222088, -0.0174952894449234, -0.01521963719278574, 0.0004172636254224926, -0.00995840784162283, -0.015521112829446793, 0.0279691219329834, -0.01544331293553114, 0.0203058160841465, -0.1065082848072052, -0.03874443098902702, -0.0455908365547657, -0.044540535658597946, 0.039911434054374695, -0.02542117051780224, -0.00375628424808383, 0.01565726287662983, -0.025965770706534386, -0.0005880590761080384, -0.06336814910173416, 0.024740420281887054, -0.009598582983016968, 0.0008612709934823215, 0.005110491532832384, -0.011271283961832523, -0.00007707828626735136, -0.009292244911193848, 0.023981869220733643, -0.021356116980314255, -0.006749155465513468, -0.028377573937177658, -0.0046850224025547504, 0.008937282487750053, -0.01945001631975174, 0.013741436414420605, 0.04555193707346916, 0.03670217841863632, -0.035729680210351944, 0.04644663631916046, -0.039561331272125244, -0.012321584858000278, 0.0018757109064608812, -0.036079779267311096, -0.016950689256191254, 0.028863823041319847, -0.011942309327423573, 0.06138424947857857, 0.052126042544841766, 0.05438224598765373, 0.026918821036815643, -0.03287052735686302, -0.013848410919308662, 0.04446273669600487, -0.021395018324255943, -0.053448643535375595, 0.026471471413969994, 0.021822918206453323, -0.05115354061126709, -0.010211258195340633, -0.03769413009285927, 0.05667734518647194, 0.053487543016672134, -0.015871213749051094, 0.03452377766370773, -0.04193423315882683, 0.03302612528204918, 0.05656064674258232, 0.015326612628996372, 0.03847213089466095, -0.031800776720047, -0.08169006556272507, -0.006170517299324274, -0.027735723182559013, 0.024837670847773552, 0.0036371529567986727, -0.03664382919669151, -0.000677103700581938, 0.001870848354883492, 0.034737728536129, 0.00506672915071249, -0.009136645123362541, -0.019177716225385666, 0.05290404334664345, -0.04780814051628113, -0.02032526582479477, -0.012613335624337196, -0.05749424546957016, -0.005548117216676474, -0.06274574995040894, 0.0018246546387672424, -0.0031436088029295206, -0.02791077271103859, -0.024215269833803177, -0.004225515760481358, 0.05920584872364998, -0.008076619356870651, -0.006515755318105221, -0.03689667955040932, -0.05119244009256363, -0.02911667339503765, -0.017806489020586014, -0.01822466403245926, 0.02236751839518547, 0.0015341199468821287, 0.0025941459462046623, 0.005839867051690817, -0.02318441867828369, 0.008460757322609425, -0.04193423315882683, -0.042867835611104965, 0.028513723984360695, 0.004376253578811884, -0.00004759935472975485, -0.05718304589390755, -0.0007859022007323802, 0.0151807377114892, 0.03242317587137222, -0.012603609822690487, -0.029777973890304565, -0.0480804406106472, -0.020422516390681267, -0.04018373414874077, -0.06142314895987511, 0.04477393627166748, 0.08200126886367798, 0.02160896733403206, 0.024331970140337944, 0.02024746686220169, -0.03376522660255432, -0.006603280548006296, -0.04656333848834038, -0.0055383918806910515, -0.0657021552324295, 0.03913343325257301, 0.03705228120088577, 0.024156920611858368, -0.020869867876172066, 0.048780638724565506, -0.02584907039999962, -0.0507645420730114, 0.024273619055747986, -0.0031436088029295206, -0.029466774314641953, 0.00034766903263516724, 0.01665893942117691, -0.019362490624189377, 0.0010034992592409253, 0.012409110553562641, 0.009097744710743427, 0.017378589138388634, 0.0011007493594661355, -0.020052965730428696, 0.059361446648836136, -0.009263070300221443, 0.05080344155430794, -0.022523118183016777, -0.0005868434673175216, 0.002929658629000187, -0.00811551883816719, -0.002985577331855893, 0.02192016877233982, -0.011640834622085094, -0.06216225028038025, 0.03561297804117203, -0.0648074522614479, 0.0672970563173294, 0.03602143004536629, -0.015239087864756584, -0.03849158063530922, 0.03304557874798775, -0.055588144809007645, 0.03462102636694908, 0.023340018466114998, -0.028066372498869896, -0.02623807080090046, 0.03749962896108627, 0.006160792429000139, -0.027307821437716484, -0.01875954121351242, 0.029408423230051994, 0.03676053136587143, 0.07289865612983704, -0.027249472215771675, 0.0027205708902329206, 0.045435238629579544, 0.09289327263832092, -0.0042012035846710205, -0.029758524149656296, 0.034854426980018616, 0.05990605056285858, 0.03158682584762573, -0.025187769904732704, 0.029019422829151154, 0.012165985070168972, 0.017018763348460197, 0.007045768201351166, 0.034834977239370346, -0.0381220318377018, 0.04384033754467964, -0.0015401981072500348, 0.011961759999394417, 0.005698854569345713, 0.001376088592223823, 0.0021686768159270287, -0.0016277232207357883, 0.04107843339443207, -0.05123134329915047, -0.0005956567474640906, 0.02151171676814556, -0.023164968937635422, 0.00022489081311505288, -0.05422664433717728, -0.0279691219329834, -0.044112637639045715, 0.03143122419714928, 0.010259883478283882, -0.06262905150651932, -0.012545260600745678, -0.016795089468359947, -0.017018763348460197, 0.003112002508714795, 0.0279691219329834, 0.03537957742810249, 0.01732996478676796, -0.013595561496913433, 0.020052965730428696, 0.010172358714044094, 0.002866446040570736, -0.03755798190832138, -0.01588093861937523, 0.08169006556272507, 0.04193423315882683, 0.022153567522764206, -0.025518421083688736, -0.039502982050180435, 0.017913464456796646, 0.03040037490427494, -0.00492814788594842, -0.0329483263194561, -0.008669844828546047, -0.028124723583459854, -0.023767920210957527, 0.003138746367767453, -0.02658817172050476, -0.02532391995191574, -0.024234719574451447, 0.0002280818298459053, -0.061500951647758484, 0.00048047618474811316, -0.019527815282344818, -0.0584278479218483, 0.03078937530517578, -0.03252042829990387, -0.016299113631248474, 0.054771244525909424, -0.02658817172050476, -0.011310184374451637, -0.01738831400871277, -0.0031654899939894676, 0.004704472608864307, 0.05613274499773979, 0.04364583641290665, 0.029719624668359756, -0.05951704829931259, 0.0019705297891050577, 0.028961073607206345, -0.02197851799428463, -0.04940304160118103, -0.010950358584523201, 0.020072415471076965, -0.020072415471076965, -0.07149825990200043, 0.00687558064237237, 0.021433917805552483, 0.019294416531920433, 0.0559382438659668, -0.04026153311133385, -0.07877256721258163, -0.0296612735837698, -0.04321793466806412, -0.00306337745860219, 0.022464768961071968, 0.03777192905545235, -0.042012035846710205, 0.01623103767633438, 0.03166462481021881, 0.042945634573698044, 0.0036517404951155186, 0.015618362464010715, -0.03164517506957054, 0.019313866272568703, 0.006014917511492968, -0.028144173324108124, 0.009340870194137096, -0.012224335223436356, 0.0016957982443273067, -0.014208236709237099, -0.010016757994890213, 0.019031841307878494, 0.04259553551673889, -0.036546580493450165, 0.008888657204806805, 0.012603609822690487, 0.007347243372350931, -0.018662290647625923, -0.00427657226100564, 0.04870283976197243, 0.004172028508037329, -0.020461415871977806, -0.011942309327423573, 0.006729705259203911, 0.03553517907857895, 0.005810692440718412, -0.03502947837114334, 0.030322574079036713, 0.03176187723875046, -0.031489577144384384, 0.02022801712155342, 0.014859812334179878, 0.05142584070563316, 0.02116161771118641, -0.009583995677530766, -0.006695667747408152, 0.004884385038167238, -0.02625752054154873, 0.020986566320061684, 0.05422664433717728, -0.05360424518585205, 0.053526442497968674, -0.01311903540045023, -0.07114815711975098, 0.018895691260695457, -0.014869537204504013, -0.06562435626983643, -0.04780814051628113, 0.022134117782115936, 0.0048187412321567535, 0.011456059291958809, 0.01610461249947548, -0.016571413725614548, -0.017135463654994965, 0.02203686721622944, -0.005504354368895292, 0.03080882504582405, 0.04197313264012337, -0.0223480686545372, 0.04026153311133385, -0.03969748318195343, 0.0017091701738536358, 0.025615671649575233, 0.008971319533884525, -0.04430713504552841, 0.02452646940946579, 0.02913612313568592, -0.04477393627166748, -0.0012010384816676378, -0.03843323141336441, -0.07009785622358322, -0.04819713905453682, -0.019274964928627014, 0.035301778465509415, -0.055510345846414566, -0.018691465258598328, 0.00857259426265955, 0.020383616909384727, -0.018244115635752678, 0.0338430292904377, 0.0446961373090744, -0.012516085058450699, 0.02582962065935135, -0.014801462180912495, -0.02374846860766411, -0.006228867452591658, -0.024195820093154907, -0.00223553623072803, 0.004283865913748741, 0.003634721739217639, -0.03590472787618637, -0.023592868819832802, -0.03123672492802143, 0.0584278479218483, -0.03679943084716797, 0.02242586761713028, 0.019420841708779335, 0.0029466773848980665, -0.0018428890034556389, -0.04321793466806412, -0.019975166767835617, 0.00025695294607430696, -0.015073762275278568, 0.017407763749361038, 0.02411801926791668, 0.0037489905953407288, -0.008630944415926933, -0.02285376936197281, -0.004162303172051907, -0.027657922357320786, 0.007488256320357323, 0.039580781012773514, -0.017845390364527702, 0.035340677946805954, 0.016989588737487793, 0.028416473418474197, 0.028377573937177658, -0.05158144235610962, -0.03998923301696777, 0.04360693693161011, 0.01822466403245926, 0.023340018466114998, -0.023787369951605797, 0.020597565919160843, -0.002483523916453123, 0.021764567121863365, -0.017436938360333443, 0.03576857969164848, -0.015365512110292912, 0.06896975636482239, 0.026043571531772614, -0.006048955023288727, -0.007595231290906668, -0.0001329590886598453, -0.03720787912607193, 0.029330624267458916, -0.010512733832001686, -0.007867531850934029, 0.03127562627196312, -0.020091867074370384, -0.030614325776696205, 0.00031332758953794837, -0.020422516390681267, 0.019012389704585075, -0.03368742763996124, 0.01796208880841732, -0.012341034598648548, -0.009088019840419292, -0.017524464055895805, -0.015550287440419197, 0.022717619314789772, 0.03849158063530922, 0.01311903540045023, -0.04026153311133385, 0.040806133300065994, -0.022289717569947243, 0.025537870824337006, 0.00375628424808383, -0.016036538407206535, 0.0056648170575499535, -0.031139476224780083, 0.041234035044908524, 0.03253987804055214, -0.019158266484737396, 0.034834977239370346, 0.012068734504282475, 0.040339332073926926, 0.005139666609466076, -0.024818221107125282, 0.011067058891057968, -0.019683416932821274, 0.007026317995041609, 0.0207531675696373, -0.01565726287662983, -0.014957061968743801, -0.009666658006608486, -0.0320536270737648, 0.02532391995191574, -0.013255185447633266, 0.07892816513776779, 0.017242439091205597, 0.009861158207058907, 0.0270744226872921, -0.02582962065935135, -0.01675618812441826, -0.013148210942745209, -0.002752177184447646, 0.03666327893733978, -0.0014854950131848454, -0.01604626327753067, 0.06142314895987511, -0.014412461780011654, -0.03876388072967529, -0.03497112914919853, -0.0042449659667909145, -0.03331787884235382, -0.0017067388398572803, -0.014130436815321445, -0.017787039279937744, 0.0046850224025547504, -0.01327463611960411, -0.04601873829960823, -0.01350803580135107, -0.006933930795639753, -0.03808313235640526, -0.005139666609466076, -0.008742782287299633, -0.0011360024800524116, 0.0026524958666414022, -0.040728334337472916, 0.031859125941991806, 0.01788428984582424, -0.024370869621634483, 0.03220922499895096, -0.010629433207213879, 0.0036760529037564993, 0.026782670989632607, 0.01121293380856514, 0.006418505217880011, 0.0020787203684449196, 0.047574739903211594, -0.0584278479218483, -0.029777973890304565, -0.00013007197412662208, 0.003029339946806431, 0.017193814739584923, 0.007848081178963184, 0.06204555183649063, 0.010269608348608017, 0.010162632912397385, -0.03121727518737316, -0.03874443098902702, -0.012195159681141376, -0.014509711414575577, 0.03854992985725403, 0.03040037490427494, -0.05947814881801605, -0.0340958796441555, -0.03497112914919853, 0.009122057817876339, 0.008334332145750523, 0.0126425102353096, -0.01604626327753067, 0.021278318017721176, 0.004441897384822369, -0.004539147485047579, 0.03222867473959923, 0.029836324974894524, 0.003201958956196904, -0.03038092516362667, 0.03998923301696777, 0.003846240695565939, -0.02954457327723503, 0.043801434338092804, 0.000144279605592601, 0.042012035846710205, -0.0027400210965424776, -0.031606275588274, 0.01628938876092434, -0.01820521429181099, 0.027230022475123405, 0.013430235907435417, -0.015978187322616577, 0.018292739987373352, -0.0269771721214056, 0.02452646940946579, -0.03121727518737316, -0.03123672492802143, -0.014616686850786209, 0.0060051921755075455, 0.017407763749361038, 0.0054751792922616005, 0.011533859185874462, 0.006267767399549484, 0.006048955023288727, -0.017135463654994965, -0.03880278021097183, 0.038666632026433945, -0.008718469180166721, -0.02024746686220169, 0.01459723711013794, 0.00708953058347106, 0.004714197479188442, 0.040845032781362534, 0.007638993673026562, -0.012623060494661331, -0.02872767299413681, -0.001180980703793466, -0.0008533694199286401, -0.0044783661141991615, -0.027366172522306442, -0.02864987403154373, 0.034815527498722076, 0.006758880335837603, -0.008708744309842587, -0.013410786166787148, 0.008149556815624237, -0.01985846646130085, 0.024020768702030182, -0.027560671791434288, -0.014344386756420135, -0.004291159566491842, 0.012127084657549858, 0.026432571932673454, 0.012827285565435886, 0.01712573878467083, 0.0027716271579265594, 0.03084772452712059, -0.013012060895562172, 0.011728359386324883, 0.006661630235612392, 0.0009870883077383041, -0.03504892811179161, 0.00048776992480270565, 0.034387629479169846, -0.038180381059646606, 0.02874712273478508, -0.0027254335582256317, -0.02864987403154373, -0.007799456361681223, -0.035690780729055405, 0.009759045206010342, 0.015521112829446793, 0.025032170116901398, 0.010425208136439323, 0.03222867473959923, 0.0045221284963190556, 0.03248152509331703, -0.04640773683786392, 0.014937612228095531, 0.017485564574599266, -0.06239565089344978, -0.03555462881922722, 0.0040747784078121185, -0.022931568324565887, -0.03816093131899834, 0.04232323542237282, -0.04971424117684364, -0.039522431790828705, 0.020072415471076965, -0.014713937416672707, 0.01056135818362236, 0.005202879197895527, -0.004680159967392683, 0.046291038393974304, -0.0207531675696373, 0.019148539751768112, -0.01777731440961361, 0.041584134101867676, -0.010629433207213879, -0.0015705887926742435, -0.021006017923355103, 0.00822735670953989, -0.013284360989928246, 0.03366797789931297, 0.0206559170037508, -0.029252823442220688, -0.038199830800294876, 0.004269278608262539, 0.007444493472576141, -0.043684735894203186, -0.028455372899770737, 0.010318233631551266, 0.036079779267311096, 0.014422186650335789, 0.03376522660255432, -0.0025674020871520042, 0.002859152387827635, 0.029388973489403725, 0.0151807377114892, 0.06865855306386948, 0.005081316456198692, -0.047107938677072525, 0.0548490434885025, -0.019197165966033936, -0.0020422516390681267, -0.027657922357320786, 0.02275651879608631, 0.018526140600442886, 0.014499986544251442, -0.03333732858300209, -0.011806159280240536, 0.015919838100671768, 0.009297107346355915, 0.023515069857239723, -0.006442817859351635, 0.05379874259233475, -0.005193154327571392, -0.012311859987676144, 0.0464855395257473, -0.017077114433050156, -0.00113661028444767, -0.020014066249132156, 0.004830897785723209, -0.008086344227194786, -0.01543358713388443, -0.010687783360481262, 0.025868522003293037, -0.002611164702102542, -0.015453037805855274, 0.00506672915071249, -0.01586148701608181, -0.04127293452620506, 0.006919343024492264, 0.05714414641261101, -0.02116161771118641, -0.003238427685573697, 0.03711063042283058, 0.042828936129808426, -0.04765253886580467, -0.027774622663855553, 0.03921123221516609, -0.013342711143195629, -0.01571561209857464, -0.030517075210809708, 0.004723922815173864, -0.021297767758369446, 0.03965858370065689, -0.006048955023288727, 0.001355423009954393, 0.004395703785121441, 0.07289865612983704, -0.006919343024492264, -0.009749320335686207, 0.02448756992816925, 0.02020856738090515, -0.006024642381817102, 0.03975583240389824, 0.004563460126519203, -0.03430982679128647, -0.02785242348909378, -0.016075437888503075, -0.01731051318347454, 0.05446004495024681, 0.015346062369644642, -0.006092717405408621, 0.02658817172050476, -0.0507645420730114, 0.03392082825303078, 0.020792067050933838, -0.003449946641921997, 0.00004034358789795078, 0.009068570099771023, -0.0020495455246418715, 0.04228433594107628, 0.04617433622479439, 0.0004509972350206226, 0.01731051318347454, 0.044112637639045715, 0.00953050795942545, -0.002250123769044876, -0.06208445131778717, 0.013342711143195629, -0.06718035787343979, -0.01076558418571949, -0.0016532513545826077, -0.011271283961832523, 0.004432172514498234, -0.037402380257844925, 0.02242586761713028, -0.0186136644333601, -0.011524134315550327, 0.021025467664003372, -0.0325009748339653, -0.021006017923355103, -0.00741531839594245, -0.02073371782898903, -0.019109640270471573, -0.016376912593841553, -0.019274964928627014, -0.04446273669600487, -0.005144529044628143, 0.0879918709397316, -0.009146369993686676, 0.023476168513298035, -0.04773033782839775, -0.014208236709237099, -0.042517732828855515, 0.06301805377006531, -0.028669323772192, -0.005339029245078564, -0.06511865556240082, 0.034834977239370346, -0.0019814702682197094, -0.0044297412969172, 0.010250158607959747, 0.003926471807062626, 0.006802643183618784, 0.025576770305633545, -0.017621714621782303, -0.020169666036963463, -0.0240402203053236, 0.019907090812921524, 0.03394027799367905, -0.021278318017721176, 0.034076426178216934, -0.02024746686220169, 0.017009038478136063, -0.061500951647758484, 0.006710255518555641, -0.014888986945152283, 0.005839867051690817, 0.03331787884235382, 0.019663965329527855, 0.029466774314641953, 0.01950836554169655, 0.0014623980969190598, -0.015666987746953964, 0.008237081579864025, 0.0045221284963190556, -0.03578802943229675, 0.02110326662659645, 0.04660223796963692, -0.020189115777611732, 0.008159281685948372, -0.02911667339503765, 0.07519376277923584, 0.0372273288667202, -0.031042225658893585, 0.04675783962011337, 0.019586166366934776, -0.046718936413526535, 0.028863823041319847, 0.009739595465362072, -0.002944246167317033, -0.00171524821780622, -0.0027837834786623716, -0.029933573678135872, 0.01731051318347454, -0.02654927223920822, 0.004908697679638863, 0.018526140600442886, -0.04228433594107628, 0.033084478229284286, -0.015666987746953964, 0.014898711815476418, 0.008023131638765335 ]
Sequential Recommendation (SR) models user dynamics and predicts the next preferred items based on the user history. Existing SR methods model the 'was interacted before' item-item transitions observed in sequences, which can be viewed as an item relationship. However, there are multiple auxiliary item relationships, e.g., items from similar brands and with similar contents in real-world scenarios. Auxiliary item relationships describe item-item affinities in multiple different semantics and alleviate the long-lasting cold start problem in the recommendation. However, it remains a significant challenge to model auxiliary item relationships in SR. To simultaneously model high-order item-item transitions in sequences and auxiliary item relationships, we propose a Multi-relational Transformer capable of modeling auxiliary item relationships for SR (MT4SR). Specifically, we propose a novel self-attention module, which incorporates arbitrary item relationships and weights item relationships accordingly. Second, we regularize intra-sequence item relationships with a novel regularization module to supervise attentions computations. Third, for inter-sequence item relationship pairs, we introduce a novel inter-sequence related items modeling module. Finally, we conduct experiments on four benchmark datasets and demonstrate the effectiveness of MT4SR over state-of-the-art methods and the improvements on the cold start problem. The code is available at https://github.com/zfan20/MT4SR.
[ 0.0077466582879424095, -0.014900228008627892, -0.034928396344184875, 0.018796367570757866, -0.002354108262807131, -0.04850557819008827, -0.05084143951535225, 0.003928076010197401, 0.00026204282767139375, 0.05533066764473915, 0.026552151888608932, 0.00599932624027133, 0.05215536057949066, -0.005415361374616623, -0.01099496241658926, 0.02688063122332096, 0.03363272547721863, 0.03996509313583374, -0.030329672619700432, -0.026862382888793945, -0.045038286596536636, 0.0015796704683452845, 0.004863332025706768, 0.04171698912978172, 0.038505181670188904, 0.027829574421048164, 0.007336058188229799, -0.03180783614516258, -0.05843298137187958, 0.024252789095044136, 0.0008149275090545416, -0.021515455096960068, -0.0015032532392069697, -0.02195342816412449, -0.027720080688595772, 0.012655613012611866, 0.0721561536192894, 0.05332328751683235, -0.030840642750263214, 0.07018527388572693, 0.007422740571200848, 0.013951284810900688, -0.02724560908973217, -0.016287144273519516, 0.022920619696378708, -0.005310430191457272, -0.019471578299999237, 0.01659737527370453, -0.005994764156639576, -0.016761615872383118, 0.014580871909856796, -0.020475266501307487, -0.054673708975315094, 0.023322096094489098, -0.025931688025593758, 0.03839568793773651, -0.031844332814216614, 0.014608245342969894, 0.051498398184776306, 0.0028924508951604366, -0.018723372370004654, 0.04489229619503021, 0.009662793017923832, -0.005488357041031122, 0.014051653444766998, -0.014079026877880096, 0.01771055907011032, -0.02242789976298809, 0.015310827642679214, -0.019161345437169075, -0.09007657319307327, 0.02242789976298809, 0.05660809203982353, -0.04153449833393097, -0.010347126983106136, 0.03314000368118286, 0.03684453293681145, 0.049053046852350235, 0.04036656767129898, 0.023851314559578896, 0.05040346458554268, 0.07160868495702744, -0.002170478692278266, 0.03209981694817543, 0.05784901604056358, -0.014580871909856796, -0.04069504886865616, -0.05478320270776749, 0.0410965234041214, 0.009334312751889229, -0.01750981993973255, 0.004167592618614435, -0.03085889108479023, -0.032921016216278076, -0.032957516610622406, -0.02014678716659546, 0.046571195125579834, 0.03262903541326523, -0.06007538363337517, 0.02062125876545906, 0.002232068683952093, 0.0009882920421659946, 0.0032893645111471415, 0.012710359878838062, 0.016259770840406418, -0.022135917097330093, -0.02812155708670616, 0.031643595546483994, -0.0431039035320282, 0.05686357617378235, 0.019124848768115044, -0.021478956565260887, -0.026898879557847977, 0.033358991146087646, -0.028468284755945206, -0.0070577627047896385, -0.08686476945877075, -0.03985559940338135, -0.017628438770771027, -0.04321339726448059, 0.026588648557662964, 0.0019218373345211148, 0.02058476023375988, -0.022519143298268318, -0.02219066396355629, 0.029964694753289223, 0.040914036333560944, -0.00045992934610694647, 0.04595073312520981, 0.00666084885597229, 0.003597314702346921, 0.041826482862234116, -0.030347922816872597, -0.0520823635160923, 0.013568057678639889, 0.041388507932424545, -0.006154441740363836, -0.0009301236714236438, -0.011560678482055664, -0.040622055530548096, -0.07449201494455338, -0.031114377081394196, -0.01333994697779417, 0.019435079768300056, 0.0004642064159270376, 0.017062721773982048, -0.03230055421590805, 0.11073432862758636, -0.04565874859690666, 0.03045741654932499, -0.01690760627388954, -0.006866149138659239, -0.0745285153388977, 0.009407308883965015, -0.02872377075254917, 0.06624351441860199, -0.062301747500896454, -0.016351016238331795, 0.017546318471431732, -0.007290435954928398, 0.06171778216958046, -0.0078835254535079, -0.010958464816212654, 0.010547865182161331, 0.02399730496108532, -0.026825884357094765, 0.0610608235001564, 0.009434681385755539, -0.06525807082653046, 0.03949062153697014, -0.014818107709288597, 0.04770262911915779, 0.02021978236734867, 0.017226962372660637, 0.02115047723054886, -0.00870472565293312, 0.03658904507756233, -0.05412624031305313, -0.02094973810017109, 0.02396080642938614, -0.03494664654135704, 0.006113382056355476, -0.01679811254143715, 0.041570995002985, 0.09993097931146622, 0.03178958594799042, 0.022683383896946907, 0.058286990970373154, 0.01610465534031391, 0.01213551964610815, 0.03744674474000931, 0.01007339358329773, 0.06923633068799973, 0.035932086408138275, 0.038067206740379333, 0.01667037047445774, -0.030804144218564034, -0.02071250230073929, 0.020438769832253456, 0.013376444578170776, -0.03357797861099243, -0.03930813446640968, 0.021095730364322662, 0.0039577302522957325, 0.024891501292586327, 0.019124848768115044, -0.0345451682806015, 0.04043956473469734, -0.015566312707960606, -0.07471100240945816, 0.015082716941833496, -0.04934502765536308, -0.036570798605680466, -0.016825485974550247, 0.0305304117500782, 0.015456818975508213, -0.004304459318518639, -0.000054247710068011656, 0.0020678285509347916, -0.013057088479399681, -0.02363232709467411, -0.04602373018860817, 0.09569723904132843, 0.03481890261173248, 0.031004883348941803, -0.005524854641407728, -0.03326774761080742, -0.01430713851004839, 0.030238429084420204, -0.021880432963371277, 0.05233784765005112, 0.01512833870947361, -0.028742019087076187, 0.01566668227314949, -0.009051455184817314, 0.024909749627113342, 0.010237633250653744, -0.052702825516462326, -0.03447217494249344, 0.004936327692121267, -0.0335962250828743, 0.005077756941318512, -0.01067560724914074, 0.003430793294683099, 0.03821319714188576, 0.025548461824655533, -0.03366922214627266, 0.08452890813350677, 0.011104456149041653, 0.011359941214323044, -0.031278617680072784, 0.005483794957399368, -0.011223074048757553, 0.06810490041971207, -0.041789982467889786, 0.02737335115671158, 0.04040306806564331, -0.04186297953128815, -0.005825961474329233, -0.05011148378252983, -0.012646488845348358, 0.003348673228174448, 0.022135917097330093, 0.07226564735174179, 0.0217891875654459, 0.043870359659194946, 0.07343357801437378, -0.024380531162023544, 0.012409253045916557, 0.04474630579352379, 0.04879756271839142, -0.10920142382383347, 0.020092040300369263, -0.07332408428192139, -0.027866071090102196, -0.06182727590203285, -0.006414488889276981, -0.006647162139415741, 0.0800761803984642, -0.03857817500829697, -0.005602412391453981, 0.02932598441839218, 0.02848653495311737, -0.02058476023375988, -0.012564368546009064, -0.0014815826434642076, -0.03883366286754608, 0.03357797861099243, -0.05405324324965477, -0.003549411194398999, -0.03397945314645767, -0.0077284094877541065, -0.05197286978363991, -0.013485938310623169, 0.08993058651685715, 0.017920421436429024, 0.01221763901412487, 0.0516078919172287, 0.07036776095628738, -0.033450234681367874, -0.03045741654932499, 0.030804144218564034, 0.03390645980834961, -0.026953626424074173, -0.050293970853090286, 0.04007458686828613, -0.00014941288100089878, 0.04033007100224495, -0.048980049788951874, -0.047447141259908676, 0.041388507932424545, -0.00957154855132103, 0.026990124955773354, 0.03022018074989319, 0.006843337789177895, -0.004781212192028761, 0.036862779408693314, -0.033687472343444824, -0.028705520555377007, -0.04919903725385666, -0.011314318515360355, 0.004972825758159161, -0.04036656767129898, -0.032045070081949234, -0.021259969100356102, 0.016825485974550247, -0.009580672718584538, 0.00016267184400931, 0.028541281819343567, 0.00146675540599972, 0.019033603370189667, -0.03699052333831787, -0.007025826722383499, -0.014954973943531513, -0.027464596554636955, -0.006501170806586742, 0.001954913605004549, 0.020457018166780472, -0.061498794704675674, -0.04708216339349747, -0.03241004794836044, -0.0013401536270976067, 0.04116952046751976, 0.028103306889533997, 0.031680092215538025, 0.00947117991745472, 0.006419050972908735, 0.06040386110544205, 0.031150873750448227, -0.009854406118392944, 0.000954645627643913, -0.027939068153500557, 0.004288491792976856, 0.020402271300554276, 0.06960131227970123, -0.04803110659122467, 0.0028673585038632154, 0.02640615962445736, 0.05288531631231308, 0.01905185356736183, -0.010201135650277138, -0.05934542790055275, -0.07927322387695312, 0.00020601297728717327, -0.05091443285346031, -0.028194552287459373, -0.05438172444701195, 0.005547665990889072, 0.028358792886137962, 0.0033076133113354445, -0.0627032220363617, 0.015402072109282017, 0.025420719757676125, -0.016259770840406418, -0.0012888286728411913, -0.00945293065160513, 0.024891501292586327, 0.004238307476043701, 0.03355972841382027, 0.0641266405582428, 0.01811203360557556, 0.019070101901888847, -0.021716192364692688, -0.02175269089639187, 0.03414369374513626, 0.04361487179994583, 0.0516078919172287, -0.019197843968868256, -0.09642719477415085, 0.03122386895120144, 0.04938152804970741, -0.002168197650462389, 0.004010195843875408, -0.05930892750620842, 0.01669774390757084, -0.004664875101298094, 0.027501093223690987, 0.013513310812413692, 0.005036696791648865, -0.024508273229002953, -0.013431191444396973, 0.003095469903200865, -0.008312374353408813, 0.007915460504591465, -0.03177133575081825, -0.0011188857024535537, 0.029836952686309814, -0.008389932103455067, 0.04887055605649948, 0.012728608213365078, -0.001277423114515841, 0.018194153904914856, -0.004224620759487152, -0.022975366562604904, 0.029599716886878014, 0.05682707950472832, -0.024909749627113342, -0.007518547121435404, 0.01777442917227745, 0.0033692033030092716, 0.04803110659122467, 0.035968583077192307, 0.06171778216958046, -0.011925657279789448, 0.001247768639586866, 0.05854247510433197, -0.006104257423430681, -0.01831277273595333, -0.013276075944304466, -0.048177096992731094, 0.04529377073049545, 0.02436228282749653, 0.04551275819540024, -0.06806840002536774, 0.02636966109275818, -0.013038840144872665, -0.0001495554461143911, 0.0028468286618590355, -0.00107725546695292, 0.003918951377272606, -0.036899276077747345, 0.004334114026278257, -0.02363232709467411, 0.04365137219429016, 0.00630955770611763, -0.0061772530898451805, -0.01978180930018425, 0.0010652795899659395, 0.00006565327203134075, 0.00008825054828776047, -0.043030910193920135, 0.014234142377972603, -0.05288531631231308, -0.054272230714559555, 0.047447141259908676, -0.06248423829674721, 0.03567660227417946, -0.021734440699219704, -0.006665410939604044, -0.009927402250468731, -0.012354506179690361, 0.011533305048942566, 0.0350196398794651, -0.027829574421048164, 0.020876742899417877, -0.014462254010140896, -0.06328719109296799, 0.010356251150369644, -0.008093387819826603, -0.04533027112483978, 0.01763756200671196, -0.005447296891361475, 0.03668029233813286, 0.021935179829597473, 0.025968186557292938, 0.017993416637182236, -0.011323442682623863, -0.0760614201426506, 0.0052465591579675674, -0.0055431039072573185, 0.049089543521404266, 0.03500139340758324, 0.00920200813561678, 0.042118463665246964, 0.01213551964610815, -0.003216368844732642, 0.0035950334277004004, 0.029563220217823982, -0.008590670302510262, -0.015383823774755001, -0.009900028817355633, -0.03624231740832329, 0.029782205820083618, 0.027391601353883743, -0.034362681210041046, -0.02567620389163494, -0.010940216481685638, 0.008056890219449997, 0.04514778032898903, -0.026515653356909752, -0.02507399022579193, -0.008399056270718575, 0.02376006916165352, 0.006533106788992882, 0.007545920554548502, 0.042118463665246964, -0.009229381568729877, -0.05332328751683235, -0.04321339726448059, 0.024252789095044136, -0.002671182854101062, 0.027501093223690987, -0.0008873527985997498, 0.028504783287644386, -0.020292777568101883, 0.0018659501802176237, 0.01332169771194458, -0.021241720765829086, -0.018449638038873672, 0.0004619253159034997, 0.006551355589181185, 0.016186775639653206, -0.03202681988477707, 0.03615107387304306, -0.03887015953660011, 0.0018260306678712368, 0.02295711822807789, 0.016688620671629906, 0.0921204537153244, 0.036534298211336136, -0.041023530066013336, 0.02808505855500698, 0.006806840188801289, -0.04470980912446976, 0.002703118370845914, -0.029198242351412773, 0.028358792886137962, 0.024727260693907738, -0.020073791965842247, -0.02162494696676731, -0.0471186637878418, -0.008180069737136364, 0.006263935472816229, 0.05299481004476547, -0.011870910413563251, -0.01941683143377304, 0.043432384729385376, -0.03136986121535301, -0.027738329023122787, 0.009014956653118134, -0.0068159643560647964, 0.0015397510724142194, -0.014726863242685795, -0.015392947942018509, -0.0350743867456913, -0.01660650037229061, -0.024216292425990105, 0.02359582856297493, 0.011651922948658466, -0.033650971949100494, 0.008914588019251823, 0.01770143397152424, -0.009945651516318321, -0.006254810839891434, 0.031844332814216614, 0.011542430147528648, -0.001749613438732922, 0.0511334203183651, 0.02865077555179596, 0.0009723242837935686, -0.018686873838305473, 0.022975366562604904, 0.029198242351412773, -0.00905601680278778, -0.0032483043614774942, 0.04635220766067505, 0.014845481142401695, -0.021971676498651505, 0.004826834425330162, 0.0022366310004144907, 0.019124848768115044, -0.035968583077192307, -0.01394216064363718, 0.008166383020579815, -0.03178958594799042, -0.0059172059409320354, -0.041826482862234116, -0.02921649068593979, -0.006013012956827879, -0.019252590835094452, 0.015228708274662495, 0.06182727590203285, -0.022610388696193695, -0.027701832354068756, -0.0686158686876297, -0.004306740593165159, 0.01129607018083334, 0.008403618820011616, 0.07259412854909897, -0.07576943933963776, -0.002016503596678376, 0.01767406053841114, 0.012901972979307175, -0.02989169955253601, -0.06000238656997681, -0.02708136849105358, 0.05883445590734482, 0.02443527802824974, 0.011505932547152042, 0.019909551367163658, 0.019234342500567436, -0.02343158982694149, 0.03759273514151573, -0.026552151888608932, 0.026862382888793945, 0.016542628407478333, 0.06507558375597, 0.028760267421603203, -0.01994604803621769, -0.025730950757861137, 0.027190862223505974, 0.014726863242685795, 0.07540445774793625, 0.011971279047429562, -0.04529377073049545, 0.02764708548784256, 0.043760865926742554, -0.0014656148850917816, -0.012035150080919266, -0.00200053583830595, -0.025822194293141365, -0.008722974918782711, -0.01260086614638567, -0.07237514108419418, 0.01149680744856596, -0.004767525475472212, 0.054345227777957916, 0.003937200177460909, 0.0017587378388270736, 0.009890904650092125, -0.03463641554117203, -0.004142500460147858, 0.0037820846773684025, 0.041826482862234116, 0.005305868107825518, 0.03334074094891548, -0.013020590879023075, -0.017318207770586014, 0.05777601897716522, 0.0022913776338100433, -0.02195342816412449, 0.023176103830337524, -0.0037775225937366486, 0.030037691816687584, 0.0077284094877541065, -0.01420676987618208, 0.009115326218307018, 0.0039075459353625774, 0.03640655800700188, -0.027464596554636955, -0.023285597562789917, 0.010109891183674335, 0.03470940887928009, -0.012591741979122162, 0.035092636942863464, -0.0065148575231432915, -0.013412942178547382, 0.010420122183859348, 0.0008388791466131806, -0.018796367570757866, 0.008180069737136364, -0.012682986445724964, -0.045768242329359055, 0.042665932327508926, 0.05365176871418953, -0.029946446418762207, 0.017683185636997223, 0.0726306289434433, -0.0014177114935591817, -0.00008504273137077689, -0.025749199092388153, -0.012089896947145462, -0.035895589739084244, -0.01737295463681221, 0.05076844245195389, -0.023486334830522537, 0.017026225104928017, -0.03366922214627266, -0.028869761154055595, 0.00798389408737421, -0.025347722694277763, -0.008079701103270054, 0.0210227333009243, -0.0036817158106714487, 0.03377871587872505, -0.021259969100356102, -0.01867775060236454, 0.0015112371183931828, 0.013358195312321186, -0.02195342816412449, 0.004863332025706768, -0.00008782283839536831, -0.02812155708670616, -0.009110763669013977, 0.020037293434143066, 0.012354506179690361, 0.02503749169409275, -0.018467888236045837, -0.00435236282646656, -0.04675368592143059, 0.0059172059409320354, 0.005223747808486223, -0.007372555788606405, 0.021880432963371277, 0.024982744827866554, 0.022117668762803078, -0.01841314136981964, -0.0031684653367847204, -0.02085849456489086, 0.004445888567715883, -0.0013504186645150185, 0.0676669254899025, 0.019836556166410446, 0.0017290833638980985, -0.019635817036032677, 0.02503749169409275, 0.02135121449828148, 0.006455548573285341, -0.009024081751704216, -0.012035150080919266, 0.05241084471344948, -0.03377871587872505, -0.028231050819158554, 0.003013349836692214, -0.0064920466393232346, 0.0005334952147677541, -0.05076844245195389, 0.015082716941833496, -0.008107074536383152, 0.012609990313649178, 0.025931688025593758, 0.01354068424552679, -0.021898681297898293, -0.004297616425901651, -0.003953168168663979, 0.029435478150844574, 0.011661048047244549, 0.0220264233648777, 0.01223588827997446, 0.012454874813556671, 0.0431039035320282, -0.03213631361722946, 0.03126036748290062, 0.0003609860723372549, -0.04244694486260414, -0.0021910087671130896, 0.009872655384242535, 0.005378863774240017, 0.009197446517646313, -0.07000278681516647, 0.020165035501122475, 0.03916214033961296, -0.045038286596536636, 0.020292777568101883, 0.02543896809220314, 0.011551554314792156, -0.07270362228155136, 0.01599516160786152, -0.0044162338599562645, -0.04927203431725502, -0.00019346686895005405, 0.006770342122763395, 0.022172415629029274, -0.017126593738794327, -0.016360139474272728, -0.0002956892130896449, 0.009389059618115425, -0.006879835855215788, -0.018467888236045837, 0.011560678482055664, 0.01067560724914074, 0.03314000368118286, 0.039746105670928955, 0.04000158980488777, -0.017391202971339226, 0.022300157696008682, -0.03505614027380943, -0.020438769832253456, 0.057484038174152374, -0.01791129633784294, 0.01730908267199993, -0.031917326152324677, -0.001528345514088869, 0.006081446073949337, 0.058761462569236755, 0.010639109648764133, -0.03843218460679054, -0.035165634006261826, -0.0070942603051662445, -0.011505932547152042, 0.0151465879753232, -0.021059231832623482, 0.0671924501657486, 0.002186446450650692, -0.019873052835464478, -0.0005480372929014266, -0.004767525475472212, -0.01750069670379162, -0.0062137506902217865, 0.02684413269162178, -0.01149680744856596, 0.018029913306236267, 0.011971279047429562, -0.010109891183674335, 0.022719882428646088, -0.027993815019726753, -0.012609990313649178, 0.03122386895120144, -0.028468284755945206, -0.06569604575634003, 0.0405125617980957, -0.017080971971154213, -0.03146110475063324, -0.0005018447991460562, -0.028231050819158554, -0.034526921808719635, 0.00007435001316480339, 0.03916214033961296, 0.04533027112483978, -0.008212005719542503, -0.006683660205453634, -0.005004761274904013, -0.044636812061071396, -0.02861427702009678, -0.028541281819343567, 0.010128140449523926, 0.012911097146570683, 0.00019603311375249177, -0.025949936360120773, 0.04642520472407341, 0.0008656822610646486, 0.026114176958799362, -0.014079026877880096, -0.013403818011283875, -0.027720080688595772, 0.012363630346953869, 0.00012774231436196715, 0.027026621624827385, 0.009416433051228523, 0.04591423645615578, 0.059089940041303635, 0.02295711822807789, 0.06865236908197403, -0.018851114436984062, -0.008900901302695274, 0.014453129842877388, 0.0036862778943032026, 0.016186775639653206, 0.03901614993810654, -0.01380529347807169, 0.017482446506619453, 0.016259770840406418, -0.025292977690696716, 0.013741422444581985, -0.008631730452179909, -0.01693497970700264, 0.019453328102827072, -0.04197247326374054, -0.018650377169251442, -0.021442458033561707, 0.015119214542210102, -0.010219384916126728, -0.057520534843206406, 0.02239140123128891, 0.0022332093212753534, 0.01680723764002323, 0.009092515334486961, 0.03476415574550629, 0.002981414319947362, -0.008312374353408813, 0.0741635337471962, -0.015228708274662495, 0.032318804413080215, 0.010556989349424839, 0.03952711820602417, -0.015602810308337212, -0.004762963391840458, -0.025749199092388153, -0.0365525484085083, -0.046972669661045074, 0.005935455206781626, 0.05131591111421585, -0.016122903674840927, -0.048177096992731094, 0.016852859407663345, -0.013431191444396973, -0.013266950845718384, 0.02343158982694149, -0.02315785549581051, -0.005004761274904013, 0.0145261250436306, -0.027628835290670395, -0.01697147823870182, -0.04474630579352379, 0.031077878549695015, 0.021916929632425308, 0.02801206335425377, -0.03905264660716057, 0.01689848303794861, -0.0007921163341961801, -0.008280439302325249, 0.006086008623242378, 0.0075732939876616, -0.028942756354808807, 0.022683383896946907, -0.00545642152428627, -0.027318604290485382, -0.001989130163565278, 0.018705124035477638, 0.01791129633784294, 0.0017690028762444854, 0.00221381988376379, 0.014088151976466179, 0.04208196699619293, -0.029745709151029587, 0.032446544617414474, -0.001522642676718533, 0.02728210762143135, 0.034855399280786514, 0.02219066396355629, -0.04073154553771019, 0.0010977854253724217, -0.04412584379315376, -0.011542430147528648, 0.028705520555377007, 0.0038892971351742744, -0.023285597562789917, 0.021296467632055283, 0.002985976403579116, 0.013193955644965172, -0.010474869050085545, 0.006847900338470936, -0.010702980682253838, 0.06569604575634003, -0.023303845897316933, 0.01844051480293274, 0.025986434891819954, -0.0014610526850447059, 0.023705322295427322, -0.008481176570057869, -0.00967191718518734, 0.0282857958227396, -0.03949062153697014, -0.06339668482542038, 0.015493316575884819, 0.030074188485741615, -0.02242789976298809, -0.009247630834579468, -0.046206217259168625, -0.011551554314792156, -0.02463601715862751, 0.03009243868291378, -0.01111358031630516, -0.01065735798329115, -0.06773991882801056, 0.02872377075254917, 0.02640615962445736, 0.016186775639653206, -0.02885151281952858, 0.017163092270493507, -0.0405125617980957, -0.04160749539732933, 0.027701832354068756, -0.018294522538781166, 0.029471974819898605, 0.03916214033961296, -0.011323442682623863, -0.02536597289144993, -0.030840642750263214, 0.043797362595796585, 0.018431389704346657, -0.013631928712129593, 0.024125047028064728, 0.02122347243130207, 0.025949936360120773, 0.024417029693722725, 0.02737335115671158, 0.00004747565617435612, -0.015173961408436298, 0.003918951377272606, 0.005137065425515175, 0.007276749238371849, 0.03397945314645767, -0.023084860295057297, -0.02660689689218998, -0.0017769867554306984, -0.03140635788440704, -0.0081481346860528, -0.005196374375373125, -0.0009860108839347959, -0.08182807266712189, -0.027172613888978958, -0.033358991146087646, 0.0001993122132262215, -0.011925657279789448, 0.021843934431672096, 0.042118463665246964, -0.04565874859690666, -0.017847424373030663, 0.023942558094859123, 0.029946446418762207, 0.01209902111440897, -0.06551355123519897, -0.012126394547522068, 0.014069902710616589, 0.019070101901888847, 0.003832269227132201, 0.0056160991080105305, 0.04554925858974457, 0.00514619005843997, 0.02085849456489086, -0.008316936902701855, 0.04485579952597618, -0.02784782275557518 ]
Proportional-integral-derivative (PID) control underlies more than $97\%$ of automated industrial processes. Controlling these processes effectively with respect to some specified set of performance goals requires finding an optimal set of PID parameters to moderate the PID loop. Tuning these parameters is a long and exhaustive process. A method (patent pending) based on deep reinforcement learning is presented that learns a relationship between generic system properties (e.g. resonance frequency), a multi-objective performance goal and optimal PID parameter values. Performance is demonstrated in the context of a real optical switching product of the foremost manufacturer of such devices globally. Switching is handled by piezoelectric actuators where switching time and optical loss are derived from the speed and stability of actuator-control processes respectively. The method achieves a $5\times$ improvement in the number of actuators that fall within the most challenging target switching speed, $\geq 20\%$ improvement in mean switching speed at the same optical loss and $\geq 75\%$ reduction in performance inconsistency when temperature varies between 5 and 73 degrees celcius. Furthermore, once trained (which takes $\mathcal{O}(hours)$), the model generates actuator-unique PID parameters in a one-shot inference process that takes $\mathcal{O}(ms)$ in comparison to up to $\mathcal{O}(week)$ required for conventional tuning methods, therefore accomplishing these performance improvements whilst achieving up to a $10^6\times$ speed-up. After training, the method can be applied entirely offline, incurring effectively zero optimisation-overhead in production.
[ 0.010827499441802502, 0.0009817591635510325, -0.012895570136606693, -0.03634289652109146, -0.017040902748703957, 0.06000162288546562, -0.057905979454517365, 0.04121435061097145, -0.047832176089286804, 0.03384282812476158, 0.01368603203445673, -0.046582143753767014, 0.03963342681527138, -0.06073693931102753, -0.0023415156174451113, 0.019504204392433167, -0.008377984166145325, 0.014577600173652172, -0.017307454720139503, -0.03485388308763504, 0.024136682972311974, -0.030460383743047714, -0.026820579543709755, 0.029008138924837112, 0.004085588734596968, 0.03636127710342407, -0.004512989893555641, 0.031783949583768845, -0.05860452726483345, 0.03762969374656677, 0.05261171981692314, 0.04194966331124306, -0.012151064351201057, 0.07139898836612701, -0.010735584422945976, -0.04334676265716553, 0.0030998082365840673, 0.015533508732914925, 0.03571787849068642, 0.05831040069460869, 0.04330999776721001, 0.019669650122523308, -0.025184504687786102, 0.010790733620524406, 0.031839098781347275, 0.00743586290627718, -0.029044903814792633, -0.02108513005077839, -0.024559488520026207, -0.019467439502477646, 0.013869861140847206, -0.047979239374399185, 0.04878808557987213, 0.0013695224188268185, -0.06000162288546562, 0.02106674760580063, 0.016535373404622078, 0.05606769397854805, 0.08353167027235031, -0.011057284660637379, 0.015910357236862183, -0.01688464917242527, -0.08000216633081436, -0.0009513125405646861, 0.0025368332862854004, -0.06864156574010849, 0.026452921330928802, -0.003828228684142232, 0.02867724746465683, -0.03941283002495766, -0.03744586557149887, -0.07882566004991531, -0.01981671340763569, 0.0006859101122245193, 0.060516342520713806, -0.017711875960230827, 0.02966991998255253, 0.01729826256632805, 0.035534050315618515, -0.02845665253698826, 0.021489553153514862, 0.04327322915196419, 0.014853343367576599, -0.02593820169568062, 0.04838366433978081, 0.019412290304899216, 0.0519867017865181, -0.05849422886967659, 0.05577356740832329, -0.05136168375611305, -0.08757589757442474, 0.013327566906809807, -0.020643942058086395, 0.028879458084702492, 0.02108513005077839, 0.014209943823516369, -0.01623205654323101, -0.015891974791884422, -0.028419887647032738, 0.01302425004541874, -0.03610391914844513, -0.036728937178850174, 0.02981698326766491, -0.00008494887879351154, -0.0020071775652468204, -0.025717608630657196, -0.10823822766542435, 0.028254441916942596, -0.009356871247291565, 0.13213592767715454, 0.002814874053001404, -0.036728937178850174, 0.022923415526747704, 0.03487226739525795, -0.044155608862638474, -0.01312535535544157, -0.008561812341213226, -0.06713417172431946, 0.025846287608146667, -0.03321781009435654, 0.032905302941799164, 0.0699283629655838, 0.06209727004170418, -0.05103079229593277, -0.025313185527920723, 0.026416156440973282, 0.024633020162582397, 0.01432024035602808, 0.05356762558221817, -0.009687762707471848, -0.04720716178417206, -0.016314780339598656, -0.04834689572453499, -0.021618232131004333, -0.03211484104394913, 0.03490903228521347, 0.03501933068037033, -0.05628828704357147, 0.007968965917825699, 0.023382985964417458, 0.0016383716138079762, -0.025166122242808342, -0.001911816420033574, 0.008001135662198067, 0.035423751920461655, 0.026655133813619614, -0.0690092220902443, 0.06088400259613991, -0.019026249647140503, 0.02981698326766491, -0.07588440924882889, 0.03900840878486633, -0.028107378631830215, 0.0056251524947583675, 0.0704798474907875, -0.008727258071303368, -0.030754508450627327, 0.03117731399834156, -0.023438135161995888, -0.009099511429667473, 0.034192103892564774, -0.04375118389725685, -0.030589062720537186, 0.07066367566585541, 0.07073720544576645, 0.04095699265599251, -0.0022760266438126564, -0.0224638432264328, -0.07610499858856201, 0.029449326917529106, 0.0027275553438812494, -0.06253845989704132, 0.008290665224194527, -0.023254305124282837, 0.02136087231338024, 0.0003587528190109879, 0.06239139661192894, -0.00813441164791584, -0.01727988012135029, -0.034780353307724, -0.0376848429441452, 0.011737450025975704, -0.0047427755780518055, 0.04603065922856331, 0.04356735572218895, 0.047905709594488144, 0.02349328249692917, 0.002238112036138773, 0.0179324708878994, -0.027022790163755417, -0.017868131399154663, 0.028879458084702492, 0.017528047785162926, 0.02007407322525978, -0.046765971928834915, -0.05889865383505821, -0.05338379740715027, -0.023217540234327316, -0.011277878656983376, 0.02614041417837143, -0.01880565658211708, -0.04603065922856331, -0.0137687548995018, 0.0023943663109093904, -0.029596390202641487, -0.0015878187259659171, 0.05331026762723923, 0.00624557351693511, 0.03992754966020584, -0.014347814954817295, 0.019191695377230644, -0.03630613163113594, -0.03215160593390465, -0.002107134321704507, -0.04364088550209999, -0.022849883884191513, 0.009333892725408077, -0.013244844041764736, 0.0019313482334837317, -0.04213349521160126, -0.02755589224398136, 0.03963342681527138, -0.013152929954230785, -0.02097483165562153, -0.04099375754594803, 0.0012638210318982601, 0.02507420815527439, -0.01983509585261345, 0.03614068403840065, 0.00421656621620059, -0.008708875626325607, -0.02742721326649189, -0.012629018165171146, 0.01059771329164505, -0.018364468589425087, -0.012371658347547054, -0.03704144433140755, 0.01970641501247883, -0.000015339986930484883, -0.033089131116867065, -0.010018653236329556, -0.018272552639245987, 0.004542862065136433, 0.0002167165803257376, 0.004278608597815037, -0.017380984500050545, 0.0077391802333295345, 0.0523543581366539, 0.05610445886850357, 0.0041131628677248955, -0.05386175215244293, -0.03535022214055061, 0.024026386439800262, -0.014283474534749985, -0.04312616586685181, 0.03761131316423416, 0.02731691673398018, -0.00995431374758482, 0.040442273020744324, 0.02509259060025215, 0.03959666192531586, 0.05364115908741951, 0.015138277783989906, 0.028346356004476547, -0.025901436805725098, 0.04393501207232475, 0.012206212617456913, 0.03494579717516899, -0.00871347077190876, 0.04246438667178154, -0.008635343983769417, -0.05106755718588829, -0.005956043489277363, -0.01124111283570528, 0.02132410742342472, -0.03501933068037033, 0.007670244202017784, 0.025184504687786102, 0.02507420815527439, 0.015386446379125118, -0.03354870155453682, -0.011572004295885563, 0.05345733091235161, 0.060700174421072006, 0.006663783453404903, -0.040405504405498505, -0.02614041417837143, -0.029559623450040817, -0.056803006678819656, -0.01179259829223156, -0.026802195236086845, 0.043015871196985245, 0.002819469664245844, 0.020552026107907295, 0.02016598731279373, 0.02612202987074852, -0.027022790163755417, -0.06867832690477371, -0.0016762862214818597, -0.014660323038697243, -0.00925576500594616, -0.003449082374572754, 0.04970722645521164, 0.04139817878603935, -0.009926739148795605, 0.0010415033902972937, -0.03101186826825142, 0.03580979257822037, -0.001783136511221528, -0.006388040725141764, 0.002500067697837949, 0.04283204302191734, 0.020496878772974014, -0.07757563143968582, -0.01124111283570528, 0.030864806845784187, 0.009485551156103611, 0.008529642596840858, -0.036912765353918076, -0.03941283002495766, -0.014789002947509289, 0.02628747560083866, -0.07809034734964371, 0.03827309608459473, 0.015294531360268593, 0.0112319216132164, 0.04867778718471527, -0.001087460550479591, -0.02978021837770939, -0.0003306040889583528, -0.021507935598492622, 0.019210079684853554, -0.03959666192531586, 0.0036237193271517754, 0.007275013253092766, 0.00934767909348011, -0.054155878722667694, -0.0288059264421463, -0.03268470987677574, 0.011351410299539566, 0.011351410299539566, -0.025441864505410194, -0.028088996186852455, -0.005827363580465317, 0.03733557090163231, -0.04614095389842987, -0.04875132068991661, 0.015202617272734642, -0.06970776617527008, -0.013805520720779896, 0.0010242694988846779, -0.00449230894446373, 0.05007488653063774, 0.008938660845160484, 0.04463355988264084, -0.037942204624414444, 0.014513260684907436, 0.01753723993897438, -0.03215160593390465, -0.03336487337946892, 0.045368876308202744, -0.104341059923172, -0.04860425740480423, 0.0398540198802948, -0.014127220958471298, 0.07257549464702606, 0.008175772614777088, -0.02123219333589077, 0.015000405721366405, 0.03003757819533348, 0.00399367418140173, 0.031839098781347275, 0.01789570413529873, 0.021673381328582764, -0.01374118123203516, 0.010763159021735191, -0.013299992308020592, 0.007380714640021324, -0.06433998048305511, 0.04908221215009689, -0.014595983549952507, -0.005831959191709757, -0.01058852206915617, 0.02498229406774044, 0.048236601054668427, 0.06614149361848831, 0.022776352241635323, -0.06426644325256348, 0.025864670053124428, 0.010799924843013287, 0.012242978438735008, -0.05206023156642914, -0.05974426493048668, -0.0237322598695755, -0.012463572435081005, -0.020294666290283203, 0.04875132068991661, -0.0013430970720946789, 0.011654727160930634, -0.03610391914844513, 0.004538266453891993, -0.008502067998051643, -0.0599648579955101, -0.02016598731279373, -0.0420231968164444, 0.02369549497961998, -0.02726176753640175, -0.04235408827662468, 0.01981671340763569, -0.016011463478207588, 0.019136548042297363, -0.04989105463027954, -0.00868589710444212, -0.010781541466712952, -0.012105107307434082, 0.023217540234327316, -0.06445027142763138, 0.002991809044033289, 0.004545159637928009, -0.03329134359955788, 0.025570545345544815, 0.0445600301027298, -0.0011592685477808118, -0.025570545345544815, 0.009761293418705463, 0.03955989331007004, 0.04978075996041298, -0.01727988012135029, 0.028199292719364166, 0.030221406370401382, -0.021581467241048813, 0.03443107753992081, -0.02617717906832695, 0.005988213699311018, -0.008465303108096123, 0.01817144826054573, -0.00013464002404361963, 0.029265498742461205, -0.021838827058672905, -0.008396366611123085, 0.0058549377135932446, -0.03636127710342407, -0.0376848429441452, 0.013722797855734825, 0.02005569078028202, -0.015469168312847614, 0.0018095618579536676, -0.05106755718588829, 0.0007249736809171736, 0.0049955397844314575, -0.06342083215713501, -0.007762158755213022, -0.01673758588731289, -0.01989024505019188, 0.02978021837770939, 0.01851153001189232, 0.04393501207232475, -0.053016141057014465, 0.039229001849889755, -0.045332107692956924, 0.0248168483376503, 0.026857344433665276, 0.011480090208351612, -0.06588413566350937, 0.04739098995923996, -0.018336893990635872, -0.02380579151213169, -0.027151471003890038, 0.025460248813033104, 0.026912493631243706, 0.050479307770729065, -0.04117758572101593, 0.024485956877470016, 0.03608553484082222, 0.04878808557987213, -0.015368063002824783, -0.05345733091235161, -0.04338352754712105, -0.002998702460899949, -0.045442406088113785, 0.02722500078380108, -0.052979376167058945, 0.025883054360747337, -0.054045580327510834, -0.02474331669509411, 0.04143494367599487, 0.05003811791539192, 0.0008467600564472377, 0.042942337691783905, 0.05206023156642914, -0.016783542931079865, 0.009641804732382298, -0.020349815487861633, 0.017380984500050545, 0.013447055593132973, -0.003511124523356557, 0.0021507935598492622, -0.004793328233063221, 0.04073639586567879, -0.04459679499268532, -0.031728800386190414, -0.04625125229358673, 0.04698656499385834, 0.03531345725059509, -0.020735856145620346, 0.007941391319036484, 0.07588440924882889, -0.006746506318449974, -0.023916088044643402, -0.005422940943390131, 0.019173312932252884, 0.017656728625297546, 0.006613230332732201, 0.00751858577132225, 0.016241248697042465, 0.04621448740363121, -0.04261144623160362, -0.009844016283750534, 0.04864102229475975, 0.02514773979783058, 0.007559947203844786, -0.00343759311363101, 0.0006594847654923797, -0.0017509665340185165, -0.036839231848716736, 0.0550750195980072, 0.028144143521785736, -0.048126302659511566, 0.03900840878486633, 0.0235484316945076, -0.011103241704404354, 0.024008002132177353, -0.012803655117750168, -0.05323673412203789, -0.04283204302191734, -0.003148063085973263, 0.008065476082265377, 0.028989754617214203, 0.031692035496234894, -0.013152929954230785, -0.03220675513148308, -0.003074531676247716, -0.002185261342674494, -0.012169446796178818, -0.005951447878032923, -0.002239261055365205, 0.02376902662217617, 0.013557352125644684, 0.02472493425011635, 0.004154524300247431, 0.008428537286818027, -0.04503798484802246, 0.00281027820892632, 0.03744586557149887, -0.018989484757184982, -0.03599362075328827, 0.0027091726660728455, -0.03897164389491081, -0.0018693060846999288, -0.04625125229358673, -0.020460112020373344, 0.006061744876205921, -0.040442273020744324, -0.02625071071088314, -0.03273985534906387, -0.06441351026296616, 0.0026241519954055548, 0.038162797689437866, 0.0010087589034810662, 0.007821902632713318, -0.017960045486688614, 0.012776081450283527, 0.012114298529922962, -0.026912493631243706, -0.012776081450283527, 0.041802603751420975, -0.00912248995155096, -0.050552837550640106, -0.0445600301027298, -0.01369522325694561, 0.011176773346960545, -0.03621421381831169, 0.011994809843599796, 0.02891622483730316, 0.001983050024136901, -0.014062880538403988, -0.005533237941563129, -0.00016846158541738987, 0.043015871196985245, -0.016801925376057625, -0.0004521032387856394, 0.024504339322447777, -0.029486091807484627, 0.02255575731396675, -0.07911978662014008, -0.04595712572336197, -0.009595847688615322, 0.018033577129244804, 0.015717336907982826, -0.037004679441452026, 0.022114569321274757, 0.07529615610837936, 0.027923550456762314, 0.010652861557900906, 0.015827633440494537, 0.03509286046028137, 0.006631613243371248, -0.025221271440386772, 0.060626640915870667, 0.003400827292352915, -0.0029803195502609015, 0.02259252406656742, 0.01186612993478775, -0.012123489752411842, 0.040258441120386124, 0.024412425234913826, 0.02364034578204155, 0.0043061827309429646, -0.006778676062822342, -0.04382471740245819, 0.020754238590598106, -0.00457043619826436, 0.017785407602787018, -0.018033577129244804, -0.0022070910781621933, 0.009113297797739506, 0.02498229406774044, -0.03218837082386017, 0.00034324228181503713, -0.012279744260013103, 0.020478496327996254, 0.010358735918998718, 0.024559488520026207, -0.00940282829105854, 0.029486091807484627, 0.022114569321274757, -0.0006543145864270627, 0.0009426955366507173, 0.006571868900209665, 0.020625557750463486, -0.019136548042297363, -0.012546295300126076, 0.0320596918463707, 0.046876270323991776, 0.004917412530630827, 0.014540834352374077, 0.0005207516951486468, -0.029375795274972916, 0.05389851704239845, 0.045626234263181686, 0.012270553037524223, -0.017224730923771858, 0.020184369757771492, 0.07092104107141495, 0.03123246319591999, -0.05878835543990135, 0.024008002132177353, 0.015248574316501617, 0.012950718402862549, 0.01851153001189232, 0.01817144826054573, -0.0009214403689838946, 0.023401368409395218, 0.06860479712486267, -0.010772350244224072, 0.03397150710225105, 0.0500013530254364, 0.03871428221464157, -0.005634343717247248, 0.057905979454517365, -0.02095644921064377, -0.00995431374758482, 0.004228055477142334, -0.014733854681253433, 0.04007461294531822, -0.05382498726248741, 0.022059420123696327, 0.040368739515542984, 0.01574491150677204, -0.02628747560083866, -0.03959666192531586, -0.03849368914961815, 0.004120056517422199, -0.01563461497426033, -0.020791003480553627, -0.03617744892835617, -0.016039036214351654, 0.025405099615454674, -0.04397177696228027, 0.04246438667178154, -0.019485821947455406, -0.012151064351201057, 0.0376848429441452, -0.026471305638551712, 0.02261090651154518, 0.03704144433140755, -0.01557027455419302, 0.028934607282280922, 0.007316374685615301, -0.032850153744220734, -0.04886161535978317, 0.007582925725728273, -0.03448622673749924, -0.0024724933318793774, 0.034302398562431335, -0.042868807911872864, 0.014467303641140461, 0.002240409841760993, 0.0037615906912833452, -0.03126922994852066, 0.020331433042883873, 0.05691330507397652, -0.015947122126817703, 0.03239058330655098, 0.017086859792470932, 0.04371441900730133, 0.018033577129244804, -0.02126895822584629, -0.03266632556915283, 0.004820902366191149, 0.025570545345544815, 0.006002000533044338, 0.0032330837566405535, -0.08470817655324936, -0.017840556800365448, 0.03955989331007004, -0.0012523316545411944, -0.025588927790522575, 0.0015763294650241733, -0.005234516691416502, 0.024614637717604637, 0.010717201977968216, -0.034118570387363434, -0.0015085426857694983, 0.01990862749516964, -0.02000054158270359, 0.03529507294297218, 0.02610364742577076, 0.026765430346131325, -0.008842150680720806, 0.013152929954230785, -0.025644076988101006, 0.06838420778512955, 0.014880917966365814, -0.032886918634176254, -0.020791003480553627, 0.018934335559606552, 0.03535022214055061, 0.025570545345544815, -0.0112319216132164, 0.06496499478816986, -0.06547971069812775, 0.029339030385017395, 0.003890270832926035, -0.012730124406516552, 0.011167582124471664, -0.006286934949457645, -0.02242707833647728, 0.023052094504237175, 0.0021978996228426695, 0.0068843774497509, 0.03216999024152756, -0.016691628843545914, 0.014550026506185532, 0.022151334211230278, -0.04246438667178154, -0.03154497221112251, 0.025386717170476913, 0.030386852100491524, 0.019320376217365265, 0.04349382594227791, 0.016149334609508514, 0.03244573250412941, -0.03237219899892807, -0.030699361115694046, 0.0050966450944542885, 0.003706442192196846, 0.03959666192531586, -0.030864806845784187, -0.008129815571010113, -0.008616961538791656, -0.03711497411131859, -0.04485415667295456, 0.029247114434838295, -0.003832824295386672, 0.01979833096265793, -0.030203023925423622, 0.03614068403840065, -0.004313076380640268, -0.0037960587069392204, -0.018051959574222565, 0.009862399660050869, 0.02503744326531887, 0.013879052363336086, 0.01737179420888424, 0.03286853805184364, -0.010560947470366955, -0.007054418791085482, 0.012261360883712769, -0.017978427931666374, -0.005574599374085665, 0.025239653885364532, -0.014853343367576599, 0.06691357493400574, 0.01625043898820877, -0.02733529917895794, 0.0042372471652925014, -0.013575735501945019, -0.02251899242401123, -0.00462328689172864, 0.013263226486742496, 0.015377254225313663, 0.01983509585261345, -0.029100053012371063, -0.0009248871938325465, -0.04095699265599251, 0.007945987395942211, -0.006116893608123064, 0.005303452257066965, -0.004538266453891993, -0.036637019366025925, -0.025239653885364532, 0.021857209503650665, 0.008120624348521233, -0.03992754966020584, -0.02375064231455326, -0.02737206406891346, -0.008313643746078014, 0.022096186876296997, 0.06283258646726608, -0.004600308369845152, 0.05735449492931366, 0.011002136394381523, 0.023180775344371796, -0.02858533337712288, 0.030736126005649567, 0.030772892758250237, 0.07867860049009323, -0.0494498685002327, 0.03158173710107803, -0.0014890108723193407, 0.00030992337269708514, -0.034118570387363434, -0.03893487900495529, -0.0056159608066082, 0.01115838997066021, -0.01976156421005726, -0.014154794625937939, 0.003768484340980649, -0.03391635790467262, 0.008823768235743046, 0.0022725798189640045, 0.047942474484443665, 0.006282339338213205, -0.03104863502085209, -0.009448785334825516, 0.009752102196216583, 0.0574280247092247, -0.02625071071088314, -0.01671920344233513, 0.0150371715426445, -0.006286934949457645, 0.031875863671302795, -0.02261090651154518, 0.022831499576568604, 0.031728800386190414, -0.003005596110597253, -0.01580006070435047, -0.020570410415530205, -0.06264875829219818, -0.012215403839945793, -0.000642250815872103, 0.01851153001189232, 0.03239058330655098, 0.009825633838772774, -0.002092198235914111, 0.012325701303780079, -0.022721203044056892, -0.03154497221112251, 0.010818307287991047, -0.02623232826590538, 0.02490876242518425, 0.03893487900495529, -0.01549674291163683, 0.01423751749098301, 0.025239653885364532, -0.014191560447216034, -0.01876888982951641, 0.004880646709352732, -0.02856694906949997, 0.0003630612918641418, 0.06945040822029114, -0.007541564293205738, 0.0002045092114713043, 0.019375525414943695, 0.003527209395542741, -0.007918412797152996, -0.03490903228521347, 0.008093049749732018, -0.009274148382246494, -0.015919549390673637, -0.04154524207115173, -0.006769484840333462, -0.002359898528084159, 0.05577356740832329, -0.017757833003997803, 0.012224595993757248, -0.006452380679547787, 0.01432024035602808, -0.0018003704026341438, 0.014347814954817295, -0.017059285193681717, 0.028107378631830215, 0.0067281234078109264, 0.02865886315703392, 0.014577600173652172, -0.05845746397972107, -0.02615879662334919, 0.02996404655277729, -0.05125138908624649, 0.006636208854615688, -0.008198751136660576, -0.0056251524947583675, 0.008718066848814487, 0.015551891177892685, 0.01989024505019188, 0.015202617272734642, 0.018162256106734276, 0.0021530913654714823, 0.030754508450627327, -0.0012799060204997659, 0.0197431817650795, 0.018934335559606552, 0.01597469672560692, 0.01681111752986908, 0.025349950417876244, 0.0033548702485859394, -0.017206348478794098, -0.029651537537574768, -0.005193155258893967, -0.049118977040052414, -0.030883189290761948, 0.003426103852689266, -0.013980157673358917, 0.06570030748844147, -0.03601200506091118, 0.026986025273799896, 0.01692141406238079, -0.01753723993897438, 0.013529778458178043, -0.006576464977115393, -0.02728014998137951, 0.0011925874277949333, -0.019393907859921455, -0.024706551805138588, -0.02489037998020649, 0.0017417750786989927, -0.015790868550539017, 0.023180775344371796, 0.03448622673749924, -0.015515126287937164, 0.00154301046859473, -0.041802603751420975, -0.01122273039072752, -0.02248222567141056, 0.030662594363093376, -0.03579140827059746, -0.039229001849889755, -0.01670081913471222, -0.006411019247025251, -0.030368469655513763, -0.009660188108682632, -0.008750236593186855, 0.0017992214998230338, 0.012748506851494312, 0.006121489219367504, 0.00939363706856966, -0.03000081144273281, -0.005588386673480272, -0.010257630608975887, 0.06217079982161522, 0.008125219494104385, 0.011378984898328781, -0.0026563219726085663, -0.03450461104512215, -0.02625071071088314, -0.02248222567141056, -0.02503744326531887, -0.04228055477142334, 0.010147333145141602, -0.056655947118997574, -0.03650834038853645, 0.025515396147966385, -0.038162797689437866, -0.005730853881686926, 0.00022461546177510172, -0.012941527180373669, -0.0451115146279335, 0.03365899994969368, -0.016535373404622078, -0.006493742112070322, 0.03830986097455025, -0.00722905620932579, 0.02134248986840248, 0.04485415667295456, -0.01565299741923809, 0.026894111186265945, -0.0058549377135932446, -0.0058779167011380196, -0.03216999024152756, -0.015138277783989906, 0.01432024035602808, 0.03775837644934654, 0.010064610280096531, 0.013419480994343758, 0.04577329754829407, 0.01113081630319357, -0.019614500924944878, -0.0525381863117218, -0.024430807679891586, 0.014494877308607101, -0.022169718518853188, 0.020643942058086395, -0.003816739423200488 ]
The behavior of malware threats is gradually increasing, heightened the need for malware detection. However, existing malware detection methods only target at the existing malicious samples, the detection of fresh malicious code and variants of malicious code is limited. In this paper, we propose a novel scheme that detects malware and its variants efficiently. Based on the idea of the generative adversarial networks (GANs), we obtain the `true' sample distribution that satisfies the characteristics of the real malware, use them to deceive the discriminator, thus achieve the defense against malicious code attacks and improve malware detection. Firstly, a new Android malware APK to image texture feature extraction segmentation method is proposed, which is called segment self-growing texture segmentation algorithm. Secondly, tensor singular value decomposition (tSVD) based on the low-tubal rank transforms malicious features with different sizes into a fixed third-order tensor uniformly, which is entered into the neural network for training and learning. Finally, a flexible Android malware detection model based on GANs with code tensor (MTFD-GANs) is proposed. Experiments show that the proposed model can generally surpass the traditional malware detection model, with a maximum improvement efficiency of 41.6\%. At the same time, the newly generated samples of the GANs generator greatly enrich the sample diversity. And retraining malware detector can effectively improve the detection efficiency and robustness of traditional models.
[ -0.0363275520503521, -0.060760729014873505, -0.015843819826841354, -0.06451684981584549, 0.0444842204451561, 0.03680627420544624, -0.07328112423419952, -0.001270451582968235, 0.00920156855136156, 0.04220109060406685, 0.016681581735610962, -0.04194331541657448, 0.0076871528290212154, -0.028741667047142982, -0.04094905033707619, 0.03095114789903164, 0.02242623269557953, -0.059766463935375214, 0.030693374574184418, -0.08108795434236526, 0.0023211059160530567, -0.017261570319533348, -0.01779552921652794, 0.005583542864769697, 0.020253576338291168, 0.0653638169169426, 0.016377778723835945, -0.02124784328043461, -0.03347363695502281, 0.05067076534032822, 0.0067066955380141735, 0.0213214922696352, 0.0012221192009747028, -0.039512887597084045, -0.014969234354794025, -0.010384561493992805, 0.00741557078436017, 0.05873537436127663, -0.02811564691364765, 0.02321796305477619, 0.04735654592514038, -0.06665267795324326, -0.027250267565250397, 0.023015428334474564, -0.007733183912932873, -0.02303384058177471, -0.017657436430454254, -0.05089171603322029, -0.024654125794768333, -0.014923203736543655, -0.02850230596959591, 0.037432290613651276, -0.00985060352832079, 0.012400712817907333, 0.012704516761004925, 0.060208361595869064, 0.08086700737476349, 0.039070989936590195, 0.05560527369379997, -0.02732391655445099, 0.003507551271468401, 0.021082133054733276, 0.013339742086827755, 0.0208795964717865, -0.020032629370689392, -0.009408706799149513, 0.014867966994643211, -0.013993380591273308, 0.019001537933945656, 0.029625458642840385, -0.058403950184583664, 0.028355007991194725, -0.009556005708873272, -0.0024120169691741467, -0.03700880706310272, -0.0005469041061587632, 0.06602665781974792, 0.06547428667545319, 0.02713979221880436, -0.009371882304549217, 0.013625133782625198, 0.07578520476818085, -0.038702744990587234, 0.02060341089963913, 0.02076912298798561, -0.01889106258749962, -0.01760219968855381, -0.05070758983492851, -0.009012841619551182, -0.00678494805470109, -0.0029712917748838663, 0.058403950184583664, 0.053395792841911316, 0.011866754852235317, 0.009473150596022606, 0.03973383456468582, -0.09493403881788254, -0.024341117590665817, -0.07269192487001419, -0.010725189931690693, -0.015991119667887688, -0.028189295902848244, 0.012750547379255295, -0.02566680498421192, -0.010255674831569195, -0.032645083963871, -0.047945741564035416, 0.03573835641145706, -0.009970283135771751, 0.10178343206644058, -0.06190229579806328, 0.010255674831569195, -0.027158204466104507, 0.03503868728876114, -0.00911871250718832, 0.02504078671336174, -0.03848179429769516, -0.06131310015916824, -0.044778816401958466, -0.03601454198360443, -0.011121055111289024, 0.026605835184454918, -0.02060341089963913, -0.016000324860215187, -0.0707402229309082, 0.07228685915470123, 0.018311074003577232, 0.015125739388167858, -0.002017302205786109, -0.05107583850622177, -0.026348061859607697, -0.00811524037271738, 0.054868780076503754, 0.020713886246085167, 0.06024518609046936, 0.05461100861430168, 0.02748962678015232, 0.05210692808032036, 0.027287092059850693, 0.006748123560100794, 0.016580315306782722, -0.0009004786261357367, -0.03441266715526581, -0.011084230616688728, -0.014278771355748177, 0.02632964961230755, 0.0012014053063467145, 0.05763063207268715, -0.00503577571362257, 0.008957604877650738, -0.047135595232248306, 0.025298558175563812, 0.018651703372597694, 0.021008482202887535, 0.012538805603981018, -0.008036987856030464, 0.02585092931985855, 0.013579102233052254, -0.005141646601259708, -0.03665897250175476, 0.032810796052217484, -0.013864493928849697, 0.023641448467969894, 0.04047032818198204, 0.032976504415273666, -0.007190019823610783, 0.04562578350305557, 0.030233066529035568, -0.0020495238713920116, 0.05906679481267929, 0.0013912826543673873, 0.036787860095500946, 0.03231365978717804, 0.028631193563342094, -0.036714211106300354, 0.0204008761793375, 0.0444842204451561, -0.01716030389070511, 0.00898982584476471, 0.01833869330585003, -0.05056029185652733, 0.019167248159646988, 0.019185660406947136, 0.012907052412629128, 0.05777793005108833, 0.0698564276099205, 0.04566260799765587, -0.003111685859039426, -0.0007485768292099237, 0.021450379863381386, -0.01650666445493698, -0.0005558225675486028, 0.04492611438035965, -0.014232740737497807, 0.08027781546115875, 0.0018964712508022785, -0.061828646808862686, 0.01239150669425726, -0.047319721430540085, -0.012538805603981018, -0.04580990970134735, -0.019259309396147728, 0.05111266300082207, -0.03224001079797745, 0.03947606310248375, -0.006117500830441713, -0.0006225673132576048, 0.017215540632605553, -0.0014189011417329311, -0.02868643030524254, -0.044778816401958466, -0.047135595232248306, -0.06775742024183273, 0.02712137997150421, 0.06024518609046936, -0.0027181219775229692, 0.016221273690462112, 0.01570572890341282, -0.01397496834397316, 0.0028447068762034178, 0.01715109683573246, -0.014269565232098103, 0.026826782152056694, -0.038592271506786346, -0.021744975820183754, -0.026071876287460327, 0.024359529837965965, 0.016138417646288872, -0.0680151954293251, 0.020069453865289688, -0.06363305449485779, 0.015991119667887688, -0.013045144267380238, -0.021818626672029495, 0.04422644525766373, -0.04761431738734245, 0.020934833213686943, -0.00011953638022532687, 0.011452477425336838, -0.013385772705078125, -0.0035098528023809195, -0.03947606310248375, -0.06392765045166016, -0.04411597177386284, 0.05788840353488922, -0.0005256148288026452, -0.0019586130511015654, 0.022352583706378937, 0.0353701114654541, 0.039697010070085526, 0.015319068916141987, -0.05229105427861214, -0.03514916077256203, 0.007480014115571976, -0.008474281057715416, -0.010007108561694622, -0.0012439838610589504, -0.06227054074406624, 0.045957207679748535, -0.04385820031166077, 0.001270451582968235, -0.007507632486522198, -0.08845289051532745, -0.007190019823610783, -0.010973756201565266, 0.026789957657456398, 0.05063394084572792, 0.037616416811943054, 0.007765405345708132, 0.0027342329267412424, 0.011010580696165562, -0.043600428849458694, -0.05435323342680931, -0.0037469116505235434, -0.004985141567885876, -0.01852281577885151, 0.009878221899271011, -0.0013176333159208298, 0.08322378993034363, 0.0589931458234787, 0.02559315599501133, -0.010283293202519417, 0.017399663105607033, -0.01924089714884758, -0.026108702644705772, -0.026513773947954178, -0.03231365978717804, 0.025648392736911774, -0.07792103290557861, 0.05129678547382355, -0.01896471343934536, 0.022720830515027046, -0.0024442384019494057, 0.006287815049290657, -0.0066376496106386185, -0.0029666887130588293, 0.04220109060406685, 0.011378827504813671, -0.02686360850930214, -0.036143429577350616, -0.07674264162778854, -0.022113222628831863, -0.0016110800206661224, 0.025427445769309998, 0.016810469329357147, 0.007236050441861153, 0.002883833134546876, 0.06510604172945023, -0.01306355744600296, -0.010909313336014748, 0.026974081993103027, 0.010366149246692657, -0.05247517675161362, 0.013293711468577385, -0.006338448729366064, 0.012354682199656963, 0.006112897768616676, -0.013128000311553478, 0.005951789673417807, -0.019848505035042763, 0.021008482202887535, 0.017749497666954994, -0.005583542864769697, 0.02922038733959198, 0.02469095215201378, -0.007015102542936802, -0.005468465853482485, 0.010154406540095806, -0.055384326726198196, -0.00027834283537231386, -0.030601313337683678, 0.03314221650362015, -0.06934088468551636, -0.021026894450187683, -0.04404232278466225, 0.03918146342039108, -0.025427445769309998, 0.059950586408376694, 0.01614762470126152, 0.005496084224432707, -0.04234838858246803, -0.0019079790217801929, -0.0035098528023809195, -0.045036591589450836, -0.014334009028971195, -0.03656691312789917, -0.0281340591609478, 0.04952920228242874, -0.010992168448865414, -0.012455949559807777, 0.0008676816360093653, -0.04890318214893341, 0.008736656978726387, -0.015945088118314743, -0.04216426610946655, 0.005348785314708948, 0.03282920643687248, 0.008303966373205185, -0.008888558484613895, -0.004237140528857708, -0.03183494135737419, -0.02439635433256626, 0.018642496317625046, -0.05111266300082207, -0.013422598131000996, 0.0026905036065727472, -0.0009430571808479726, -0.002499475609511137, -0.04128047078847885, -0.0011329344706609845, 0.05096536502242088, 0.026256000623106956, -0.021376729011535645, 0.014867966994643211, -0.03914463892579079, 0.03376823663711548, 0.019480258226394653, 0.020732298493385315, -0.04945555329322815, 0.03829767182469368, 0.01931454800069332, 0.012179764918982983, -0.018983125686645508, -0.02023516409099102, 0.028925789520144463, 0.026716308668255806, 0.014941615983843803, -0.013846081681549549, 0.0626387894153595, 0.053579915314912796, 0.017270777374505997, 0.005795284640043974, -0.018384724855422974, 0.0020575793460011482, 0.025188084691762924, -0.025722041726112366, -0.033528875559568405, -0.038592271506786346, 0.0662476047873497, -0.06451684981584549, -0.017031416296958923, -0.005210692994296551, 0.0016064768424257636, -0.005799887701869011, -0.046509578824043274, -0.00603464525192976, 0.04728289693593979, -0.0014545751037076116, 0.020990069955587387, -0.049860622733831406, 0.012603248469531536, 0.04293758422136307, -0.04927142709493637, -0.0007180813699960709, 0.05770428106188774, 0.0140670295804739, -0.028281359001994133, -0.026458535343408585, 0.017906002700328827, -0.01374481339007616, 0.017169509083032608, 0.03376823663711548, 0.08226634562015533, 0.02767375111579895, -0.0041703954339027405, 0.04606768116354942, 0.07066657394170761, -0.012455949559807777, -0.0024396353401243687, -0.03474409133195877, 0.05582622438669205, 0.011811518110334873, 0.027618514373898506, -0.04374772682785988, -0.0066698710434138775, 0.006227974779903889, 0.00644432008266449, -0.001452273572795093, -0.009068078361451626, -0.021026894450187683, -0.005951789673417807, 0.01434321515262127, 0.01652507670223713, 0.031890176236629486, -0.06451684981584549, -0.04164871945977211, -0.03084067441523075, 0.0034546158276498318, -0.029699107632040977, -0.053506266325712204, -0.06330163031816483, 0.07740548998117447, -0.03739546611905098, -0.021303080022335052, 0.0626387894153595, -0.04131729528307915, -0.01689332351088524, -0.023015428334474564, 0.03067496232688427, -0.00944553129374981, 0.006209562532603741, 0.050044745206832886, -0.032000649720430374, 0.011139467358589172, -0.014444482512772083, 0.010182025842368603, 0.0032014460302889347, -0.06087120622396469, 0.012373094446957111, -0.01852281577885151, 0.04975014925003052, -0.017758704721927643, -0.0018918681889772415, -0.018439961597323418, 0.058477599173784256, 0.011397239752113819, -0.003680167021229863, -0.08705355226993561, 0.04938190430402756, -0.0007215336663648486, 0.019038362428545952, 0.027692163363099098, -0.017998063936829567, -0.018191395327448845, -0.005767666269093752, -0.04146459698677063, 0.03781895339488983, -0.04345312714576721, -0.028999440371990204, -0.007452395744621754, -0.006605427712202072, -0.0381135493516922, -0.027471214532852173, 0.002607648028060794, -0.006545587908476591, -0.033805061131715775, 0.017215540632605553, 0.024249054491519928, 0.04238521307706833, 0.01434321515262127, -0.019130423665046692, -0.05033934488892555, 0.00628321198746562, -0.032000649720430374, 0.013164824806153774, 0.01822821982204914, 0.020898008719086647, 0.03918146342039108, -0.025353794917464256, -0.02686360850930214, -0.0544637106359005, 0.009261407889425755, -0.02395445853471756, -0.032645083963871, -0.009500768966972828, 0.022481469437479973, -0.019019950181245804, 0.008419043384492397, 0.033620938658714294, 0.0024488414637744427, -0.009385691955685616, 0.010007108561694622, -0.05641541630029678, 0.03954971209168434, -0.003983970731496811, 0.012060084380209446, 0.024985548108816147, -0.008759671822190285, -0.010476622730493546, -0.005905759055167437, -0.04610450565814972, 0.030343540012836456, -0.02975434623658657, -0.011949609965085983, 0.00007444052607752383, -0.04433692246675491, 0.014048617333173752, -0.01002552080899477, -0.023291613906621933, -0.028723254799842834, 0.0032520799431949854, -0.0027158204466104507, -0.033897124230861664, -0.0018205203814432025, -0.015530810691416264, 0.009339660406112671, 0.009970283135771751, -0.02233417145907879, 0.017731085419654846, 0.005040378775447607, -0.01165501307696104, 0.022205285727977753, -0.005325770005583763, 0.0020817455369979143, -0.010955343954265118, 0.016479047015309334, -0.031061621382832527, 0.020750710740685463, 0.014619399793446064, -0.020087866112589836, -0.015180976130068302, 0.021376729011535645, 0.01360672153532505, -0.028723254799842834, 0.025151260197162628, 0.0213214922696352, 0.005459259729832411, 0.04511024057865143, 0.05774110555648804, 0.004030001349747181, -0.0001314037072006613, -0.08315014094114304, -0.06363305449485779, -0.009404104202985764, -0.00035961606772616506, -0.03012259304523468, 0.05096536502242088, -0.019480258226394653, -0.00516926497220993, -0.045773085206747055, -0.03413648158311844, -0.05869854986667633, 0.015392717905342579, 0.04452104493975639, 0.009266011416912079, -0.0048746676184237, -0.012124527245759964, -0.043784551322460175, -0.027728987857699394, -0.028189295902848244, 0.02331002615392208, 0.010274087078869343, -0.010218850336968899, -0.0099886953830719, -0.03549899533390999, -0.009767747484147549, 0.03873956948518753, -0.032166361808776855, 0.038260847330093384, -0.03732181712985039, -0.005339579191058874, 0.019351372495293617, 0.030693374574184418, 0.028447069227695465, -0.05236470326781273, -0.015346687287092209, 0.03468885272741318, -0.01641460321843624, -0.013091175816953182, -0.007387952413409948, 0.02649536170065403, 0.019738031551241875, 0.05243835225701332, -0.02820770815014839, -0.0008958755643106997, 0.004801018163561821, 0.050486642867326736, -0.012142939493060112, -0.031816527247428894, -0.012483567930758, 0.060134708881378174, -0.021579265594482422, 0.039881132543087006, 0.0053856102749705315, -0.01805330254137516, 0.014508926309645176, 0.003935638349503279, -0.03958653658628464, -0.01860567182302475, -0.04065445065498352, -0.018587259575724602, 0.01931454800069332, -0.04153824597597122, -0.0015075105475261807, -0.07578520476818085, 0.010642333887517452, 0.0006887366762384772, 0.0008199246367439628, -0.0335657000541687, 0.02695566974580288, 0.04938190430402756, 0.02605346404016018, -0.03205588832497597, -0.011388033628463745, -0.019811680540442467, 0.033528875559568405, -0.022610357031226158, -0.0034339018166065216, -0.007728580851107836, 0.06241784244775772, 0.013754019513726234, 0.016589520499110222, -0.0299568809568882, 0.022297346964478493, -0.03757959231734276, -0.026826782152056694, 0.026182351633906364, 0.00916014052927494, -0.0067020924761891365, 0.011737868189811707, 0.014729874208569527, 0.01434321515262127, -0.009712510742247105, -0.019019950181245804, 0.015724141150712967, 0.0032866031397134066, 0.03111685812473297, -0.010218850336968899, -0.016736818477511406, 0.000921192520763725, -0.016543488949537277, -0.07412809133529663, -0.05597352236509323, 0.0372113436460495, 0.019922154024243355, -0.043416302651166916, 0.029643870890140533, 0.02168973907828331, -0.012916258536279202, -0.018099332228302956, 0.028649605810642242, 0.00820730160921812, -0.03929194062948227, 0.06923040747642517, -0.028170883655548096, 0.00031703751301392913, 0.012419125065207481, -0.009878221899271011, -0.03896051645278931, -0.02441476657986641, -0.0253906212747097, -0.003620326751843095, 0.00014945643488317728, 0.035057101398706436, 0.05427958443760872, 0.004481103736907244, -0.022463057190179825, -0.020732298493385315, -0.034891389310359955, -0.014711461961269379, 0.002118570264428854, -0.0056295739486813545, -0.06223371624946594, 0.013965762220323086, -0.014702255837619305, 0.022463057190179825, 0.0028861346654593945, -0.029883231967687607, 0.01020043808966875, -0.019369784742593765, 0.00401619216427207, 0.030877498909831047, 0.004711258225142956, -0.0009280971135012805, 0.0020679361186921597, -0.0024488414637744427, 0.007816039025783539, 0.012879434041678905, -0.031172096729278564, 0.027710575610399246, 0.014748286455869675, 0.001575406058691442, -0.00889776460826397, -0.06882533431053162, -0.023733509704470634, 0.0069322469644248486, -0.006476541515439749, 0.0005469041061587632, -0.010854075662791729, -0.004034604411572218, 0.05100218951702118, -0.012962289154529572, -0.02231575921177864, 0.004333805292844772, -0.03386029973626137, -0.0015006059547886252, 0.025998227298259735, 0.01914883591234684, -0.002276225946843624, -0.005878140218555927, 0.027544863522052765, -0.012943876907229424, -0.01365275215357542, -0.03818719834089279, -0.0054040225222706795, -0.013256886973977089, -0.006536381784826517, 0.031337808817625046, -0.024911899119615555, -0.014103854075074196, 0.027636926621198654, -0.04249568656086922, 0.03463361784815788, -0.059471867978572845, -0.034339018166065216, 0.014582575298845768, 0.021266255527734756, 0.005463862791657448, -0.011912785470485687, -0.013091175816953182, -0.030509252101182938, -0.005463862791657448, 0.0037469116505235434, 0.008359203115105629, 0.07055609673261642, -0.010347736068069935, -0.03455996513366699, -0.026716308668255806, 0.02458047680556774, 0.019940566271543503, 0.05608399584889412, 0.003960954956710339, 0.027360741049051285, -0.009261407889425755, 0.03573835641145706, -0.02358621172606945, 0.03113527037203312, -0.03647485002875328, 0.04890318214893341, 0.0028493099380284548, -0.03529646247625351, -0.031337808817625046, -0.01732601411640644, 0.08454947918653488, -0.013385772705078125, 0.02259194478392601, -0.020916420966386795, 0.002455746289342642, -0.028336595743894577, 0.02122943103313446, -0.03146669268608093, -0.013128000311553478, 0.014729874208569527, -0.03873956948518753, 0.02750803902745247, 0.05037616938352585, -0.055384326726198196, 0.03984430804848671, -0.0462886281311512, -0.02794993668794632, 0.006246387027204037, 0.012225795537233353, -0.012188971042633057, 0.010550272651016712, -0.021929100155830383, -0.06179182231426239, -0.09058872610330582, 0.021100545302033424, -0.01061471551656723, -0.015309862792491913, 0.016285717487335205, -0.0018067110795527697, 0.008248729631304741, -0.00761810690164566, -0.0015316767385229468, 0.0004128392320126295, 0.00844666175544262, -0.007931116968393326, -0.03612501546740532, -0.03658532351255417, -0.0056894137524068356, -0.01740887016057968, -0.035075511783361435, 0.016736818477511406, -0.02677154541015625, 0.024083344265818596, 0.04709877073764801, 0.011452477425336838, 0.04035985469818115, 0.016672376543283463, 0.016110800206661224, -0.02450682781636715, 0.0053671980276703835, 0.0036180252209305763, -0.06996690481901169, 0.03131939470767975, -0.001693935482762754, 0.008759671822190285, 0.018550435081124306, 0.00870443508028984, 0.00707494281232357, 0.0026582819409668446, 0.003944844473153353, -0.0508180670440197, -0.040065258741378784, -0.01310958806425333, -0.013928936794400215, 0.0012439838610589504, 0.013229267671704292, 0.03395235911011696, 0.029920056462287903, 0.008741259574890137, 0.008639991283416748, 0.041427772492170334, -0.024249054491519928, 0.01278737187385559, 0.01115787960588932, -0.005910362116992474, 0.019903741776943207, -0.0236046239733696, -0.005353388376533985, 0.026513773947954178, 0.00512323435395956, -0.006108294706791639, 0.04908730462193489, 0.037340231239795685, -0.011986435391008854, -0.06105532869696617, -0.043342653661966324, -0.05405863747000694, -0.0019206374417990446, -0.02231575921177864, -0.030067354440689087, 0.06878851354122162, -0.0013360455632209778, 0.008893161080777645, 0.008501899428665638, -0.02058499865233898, -0.003583502257242799, -0.02196592465043068, 0.05542115122079849, -0.002798676025122404, 0.05310119688510895, -0.03557264432311058, 0.03726658225059509, -0.07873117923736572, 0.009454738348722458, -0.04209061339497566, 0.008607770316302776, -0.05398498848080635, -0.027839461341500282, -0.011259147897362709, -0.04319535568356514, -0.002290035132318735, 0.05774110555648804, 0.015724141150712967, 0.0018308772705495358, 0.00033401139080524445, -0.00962044857442379, 0.007346524856984615, -0.004407454282045364, -0.022997016087174416, 0.012373094446957111, -0.011507714167237282, 0.010927725583314896, 0.028005173429846764, 0.004782605916261673, -0.047319721430540085, -0.014757492579519749, -0.0399547815322876, -0.023843983188271523, -0.010421385988593102, -0.005832109600305557, 0.0003305590944364667, 0.018025683239102364, 0.0014027903089299798, 0.008976017124950886, 0.031006384640932083, -0.0002274212019983679, 0.0054178317077457905, -0.005799887701869011, 0.03465202823281288, -0.005555924493819475, -0.004801018163561821, -0.029901644214987755, -0.03321586549282074, -0.010099169798195362, 0.011222322471439838, -0.004649116657674313, -0.01995897851884365, -0.012465155683457851, 0.012879434041678905, 0.0194986704736948, 0.027102967724204063, 0.027968348935246468, 0.00594718661159277, -0.02829977124929428, 0.0013613625196740031, -0.018191395327448845, -0.03282920643687248, -0.011544538661837578, 0.008686022832989693, 0.024635713547468185, 0.009832191281020641, 0.03954971209168434, -0.05925091728568077, 0.04363725334405899, 0.017850765958428383, -0.05645224079489708, 0.008000162430107594, -0.02623758837580681, -0.041501421481370926, 0.03754276782274246, -0.019038362428545952, -0.041427772492170334, 0.0007842507329769433, 0.0023533275816589594, -0.02594299055635929, -0.0034707265440374613, 0.03866592049598694, 0.02277606725692749, 0.03130098059773445, -0.02623758837580681, 0.002874627010896802, -0.04779843986034393, 0.031816527247428894, 0.028005173429846764, 0.0299568809568882, -0.06683680415153503, -0.014315596781671047, 0.001470685820095241, -0.041759192943573, 0.005569733679294586, 0.0027066143229603767, -0.006504159886389971, 0.017988858744502068, 0.011388033628463745, -0.04426326975226402, -0.027544863522052765, 0.009694098494946957, 0.013487040996551514, -0.015558429062366486, 0.012492774054408073, 0.0004850501427426934, 0.037174519151449203, -0.0389973409473896, 0.004158888012170792, -0.011995641514658928, -0.06753647327423096, 0.027692163363099098, -0.01669078879058361, 0.009491562843322754, -0.025206496939063072, 0.019830092787742615, -0.0681256651878357, 0.005302754696458578, -0.015742553398013115, -0.038076724857091904, -0.007788421120494604, 0.0053856102749705315, -0.015622872859239578, 0.03323427960276604, -0.006554794032126665, 0.012750547379255295, 0.0013970364816486835, 0.014380039647221565, 0.03150351718068123, -0.030288303270936012, -0.04035985469818115, 0.010402973741292953, -0.03211112692952156, -0.021910687908530235, -0.0013579102233052254, 0.033179040998220444, 0.0066652679815888405, 0.007521442137658596, -0.06068708002567291, 0.04776161536574364, 0.0006369519978761673, 0.0030380364041775465, 0.05070758983492851, -0.028189295902848244, 0.018734559416770935, -0.015346687287092209 ]
We consider the problem of simultaneous learning in stochastic games with many players in the finite-horizon setting. While the typical target solution for a stochastic game is a Nash equilibrium, this is intractable with many players. We instead focus on variants of {\it correlated equilibria}, such as those studied for extensive-form games. We begin with a hardness result for the adversarial MDP problem: even for a horizon of 3, obtaining sublinear regret against the best non-stationary policy is \textsf{NP}-hard when both rewards and transitions are adversarial. This implies that convergence to even the weakest natural solution concept -- normal-form coarse correlated equilbrium -- is not possible via black-box reduction to a no-regret algorithm even in stochastic games with constant horizon (unless $\textsf{NP}\subseteq\textsf{BPP}$). Instead, we turn to a different target: algorithms which {\it generate} an equilibrium when they are used by all players. Our main result is algorithm which generates an {\it extensive-form} correlated equilibrium, whose runtime is exponential in the horizon but polynomial in all other parameters. We give a similar algorithm which is polynomial in all parameters for "fast-mixing" stochastic games. We also show a method for efficiently reaching normal-form coarse correlated equilibria in "single-controller" stochastic games which follows the traditional no-regret approach. When shared randomness is available, the two generative algorithms can be extended to give simultaneous regret bounds and converge in the traditional sense.
[ 0.016130326315760612, -0.040050048381090164, -0.05030014365911484, -0.015103619545698166, 0.02072080783545971, 0.028068972751498222, -0.06448736041784286, 0.004696546588093042, -0.07270101457834244, 0.014857549220323563, -0.037911780178546906, -0.003035572823137045, 0.019974112510681152, -0.04184890538454056, 0.010623444803059101, 0.02224813960492611, -0.0009678407805040479, 0.00029459482175298035, 0.03003753535449505, -0.01585880108177662, 0.037911780178546906, 0.024963397532701492, -0.012167747132480145, 0.09292968362569809, 0.0063299438916146755, 0.023198479786515236, -0.0062153940089046955, -0.019108623266220093, -0.09808867424726486, 0.03380495309829712, -0.007055426482111216, 0.024318523705005646, -0.038624536246061325, -0.018192224204540253, -0.019210446625947952, -0.009401578456163406, 0.022265110164880753, -0.03034300170838833, -0.01242230273783207, 0.05362633243203163, -0.036893561482429504, 0.019719555974006653, -0.026337996125221252, -0.03278673440217972, 0.022265110164880753, -0.024199731647968292, -0.0763666108250618, 0.01272776909172535, -0.0028679906390607357, -0.011633181013166904, 0.0012600491754710674, -0.025930708274245262, 0.028781728819012642, 0.024301553145051003, -0.00007192515477072448, -0.023843353614211082, 0.037708137184381485, -0.023741532117128372, 0.042493779212236404, 0.021467503160238266, 0.012184717692434788, 0.012583521194756031, -0.052166882902383804, 0.02866293676197529, 0.06706685572862625, -0.049519505351781845, 0.03176851198077202, 0.06150057911872864, 0.034042540937662125, 0.0047941263765096664, -0.0025116130709648132, -0.02672831527888775, -0.05121654272079468, -0.043104711920022964, 0.02122991904616356, -0.02245178446173668, -0.003892576089128852, 0.05912473052740097, 0.007971826009452343, 0.043410178273916245, -0.0773848369717598, 0.057529516518116, -0.013135057874023914, -0.006686321459710598, 0.041068267077207565, -0.07881034910678864, 0.020635956898331642, -0.057461634278297424, 0.060210831463336945, 0.020635956898331642, -0.016944903880357742, 0.004878978244960308, -0.0007451048004440963, -0.015638185665011406, -0.025777975097298622, 0.01545151136815548, 0.022417843341827393, 0.02637193724513054, -0.0442926362156868, 0.024369435384869576, 0.008968834765255451, 0.022825133055448532, 0.009757956489920616, 0.039642758667469025, 0.01025858148932457, -0.009868263266980648, -0.03293946757912636, 0.029918743297457695, 0.03229459375143051, 0.15463390946388245, -0.01636791042983532, 0.020500194281339645, -0.02010987512767315, 0.02209540642797947, -0.05922655388712883, -0.0026219203136861324, -0.05698646605014801, -0.052065059542655945, 0.0710039809346199, -0.07412652671337128, -0.054203324019908905, 0.038828179240226746, 0.016257604584097862, -0.04629513993859291, -0.01341506838798523, 0.03777601942420006, -0.03876030072569847, 0.028696876019239426, 0.012362906709313393, 0.021772969514131546, 0.011718032881617546, -0.038319069892168045, -0.0022846346255391836, -0.010555563494563103, 0.02229905128479004, -0.05437302961945534, 0.026898019015789032, -0.03198912739753723, -0.025489479303359985, -0.02891749143600464, -0.01560424454510212, -0.03886212036013603, 0.019380150362849236, 0.03285461291670799, 0.0036910530179739, -0.04649878293275833, -0.0007647267775610089, 0.03446679934859276, -0.029307808727025986, 0.004446234088391066, -0.04690607264637947, 0.09516977518796921, -0.0004133873444516212, 0.05932837352156639, -0.0009954175911843777, -0.016919447109103203, -0.02163720689713955, -0.004959587473422289, 0.03573957458138466, -0.07399076223373413, 0.028883550316095352, 0.02944357320666313, -0.007390591315925121, 0.03141213580965996, 0.04364776238799095, 0.02143356390297413, 0.0005393392057158053, 0.0008448056760244071, -0.03726690635085106, 0.03977851942181587, -0.011293773539364338, 0.007827578112483025, 0.019634705036878586, 0.03370313346385956, 0.031955186277627945, 0.048704929649829865, 0.022723309695720673, 0.032413385808467865, -0.000021942143575870432, 0.021043244749307632, 0.01558727491647005, -0.021467503160238266, -0.026898019015789032, 0.041237972676754, 0.09299756586551666, 0.039337292313575745, 0.0862773060798645, 0.007220887579023838, 0.04307077080011368, 0.004446234088391066, -0.018701335415244102, 0.046363018453121185, 0.05026620253920555, -0.02158629707992077, 0.022417843341827393, -0.0246918722987175, -0.02922295778989792, 0.02642284892499447, -0.031225459650158882, 0.04822976142168045, -0.04164525866508484, -0.03947305306792259, 0.02265542931854725, -0.013745990581810474, 0.02362274006009102, 0.005065652076154947, -0.0007382106268778443, -0.010199185460805893, 0.019414089620113373, 0.0030949690844863653, 0.04985891282558441, -0.01002948172390461, -0.007297254167497158, -0.04558238387107849, -0.03757237270474434, -0.02825564704835415, 0.003332554129883647, 0.001448844326660037, -0.01219320297241211, -0.050843194127082825, 0.0014074791688472033, 0.02683013677597046, -0.016452763229608536, -0.012693827971816063, 0.048806753009557724, 0.030936963856220245, -0.03655415400862694, -0.014373893849551678, 0.0030886053573340178, -0.03641838952898979, 0.025625241920351982, 0.008383356966078281, 0.0019484093645587564, 0.01832798682153225, 0.0013003537897020578, 0.006486919708549976, 0.005820833146572113, 0.038013603538274765, 0.0740586444735527, -0.06275638937950134, -0.012990809977054596, -0.05158989131450653, 0.001176257967017591, -0.013296276330947876, 0.006274790037423372, 0.005587490741163492, -0.030122386291623116, 0.03533228859305382, 0.04296894744038582, -0.0016058201435953379, -0.045242976397275925, -0.03692749887704849, -0.014161764644086361, -0.00962219387292862, -0.023962145671248436, 0.04113614931702614, 0.037097204476594925, -0.05362633243203163, 0.03268491104245186, -0.03899788483977318, 0.028035033494234085, 0.007144520990550518, -0.005646886769682169, 0.02199358493089676, 0.009707044810056686, 0.02112809754908085, 0.01776796579360962, 0.011853795498609543, 0.015027252957224846, 0.03489105775952339, -0.030020564794540405, -0.06730443984270096, -0.03865847736597061, -0.010589503683149815, 0.0173097662627697, -0.049926795065402985, -0.018548602238297462, -0.028883550316095352, 0.0014785424573346972, 0.028798699378967285, 0.045039333403110504, 0.02871384657919407, 0.05885320529341698, -0.00534566305577755, 0.004853522405028343, -0.022570576518774033, -0.031123638153076172, -0.040457334369421005, -0.09123264998197556, 0.04928192123770714, 0.015740007162094116, -0.04069491848349571, 0.020907482132315636, 0.041679199784994125, 0.0519292987883091, 0.034093450754880905, -0.028391409665346146, 0.0468381904065609, 0.015078163705766201, -0.00018534813716541976, -0.02459004893898964, 0.013737505301833153, 0.013296276330947876, 0.010589503683149815, -0.034398917108774185, -0.02372456155717373, -0.03543410822749138, 0.026745285838842392, 0.015714552253484726, 0.04425869509577751, 0.01878618635237217, -0.023894265294075012, -0.005511124152690172, -0.017581291496753693, 0.002252815058454871, 0.029698127880692482, 0.07595932483673096, -0.02403002791106701, -0.04466598480939865, -0.01326233521103859, 0.07147914916276932, -0.015570304356515408, -0.02336818352341652, 0.01338961347937584, -0.009511886164546013, -0.030427852645516396, 0.02586282603442669, 0.02733924798667431, -0.025574330240488052, 0.020075934007763863, -0.010275552049279213, -0.004637150559574366, -0.0336013101041317, 0.012278054840862751, -0.011896221898496151, 0.021654177457094193, 0.021212948486208916, 0.031904272735118866, 0.03692749887704849, -0.01751341111958027, -0.014246616512537003, -0.010479196906089783, 0.02840838022530079, 0.009885233826935291, -0.015239382162690163, -0.026847107335925102, -0.06248486042022705, 0.02693196013569832, 0.04113614931702614, -0.010368889197707176, 0.0008898832020349801, 0.01280413568019867, 0.022689370438456535, 0.037708137184381485, 0.07039304822683334, -0.04877281188964844, -0.009401578456163406, 0.00880761630833149, -0.0025816159322857857, 0.01491694524884224, 0.047788530588150024, -0.07419440895318985, -0.006779658142477274, 0.007161491550505161, 0.007246342953294516, -0.04130585491657257, -0.004011368378996849, 0.00673299003392458, -0.003033451735973358, 0.02189176343381405, -0.021874792873859406, -0.015918197110295296, 0.02667740359902382, 0.04571814462542534, -0.045853909105062485, 0.036995381116867065, -0.02509916014969349, -0.0002623776672407985, -0.08458026498556137, 0.01211683638393879, -0.003926516976207495, 0.06475888937711716, -0.0021053850650787354, 0.00534566305577755, 0.01364416815340519, 0.014501171186566353, 0.059599898755550385, 0.007823335006833076, 0.05871744081377983, -0.036791738122701645, 0.06971423327922821, -0.013474464416503906, -0.007988796569406986, 0.05162383243441582, 0.01529877819120884, -0.0004674803640227765, 0.0023737289011478424, -0.04001610726118088, -0.017683112993836403, 0.008637912571430206, -0.002768289763480425, -0.0034746809396892786, -0.014068427495658398, 0.038930002599954605, -0.04181496426463127, -0.0075008985586464405, -0.049621328711509705, -0.015697581693530083, 0.016910962760448456, 0.016020018607378006, -0.008277292363345623, -0.03293946757912636, -0.044224753975868225, -0.006957847159355879, -0.019159534946084023, -0.015095134265720844, -0.07860670238733292, 0.004518358036875725, 0.0065590436570346355, -0.06479282677173615, -0.03859059512615204, -0.021959643810987473, 0.06852630525827408, 0.011276802979409695, -0.007865761406719685, 0.017852816730737686, 0.02403002791106701, -0.027627743780612946, -0.0048704929649829865, -0.02066989615559578, 0.019159534946084023, 0.01369507983326912, -0.012905958108603954, -0.020907482132315636, -0.02357182838022709, -0.01685156673192978, -0.045242976397275925, 0.048399463295936584, 0.006618439685553312, -0.037300847470760345, 0.0014986947644501925, -0.011098614893853664, -0.011522873304784298, 0.013067176565527916, 0.05610400438308716, -0.01842981018126011, -0.022078435868024826, -0.0417470820248127, 0.031395163387060165, 0.03814936801791191, -0.04062703996896744, 0.01781887747347355, -0.033533427864313126, 0.006160240154713392, 0.0376741960644722, -0.00829850509762764, 0.02270633913576603, -0.056545235216617584, 0.035366225987672806, 0.03188730403780937, 0.0310557559132576, -0.013440524227917194, 0.05681676045060158, -0.012608976103365421, 0.04700789228081703, 0.03326190263032913, -0.045548442751169205, -0.04843340441584587, -0.0015708188293501735, -0.004011368378996849, 0.010861029848456383, -0.07643449306488037, -0.03468741476535797, -0.002908295253291726, 0.03227762132883072, 0.029664186760783195, -0.0023800928611308336, -0.09082535654306412, -0.010275552049279213, 0.020805660635232925, 0.05688464269042015, -0.004895948339253664, -0.022485725581645966, -0.001725673326291144, -0.04324047267436981, 0.044122934341430664, -0.004666848573833704, 0.0012971718097105622, -0.0004436157760210335, 0.002901931293308735, -0.02117900736629963, -0.0009641285287216306, -0.028035033494234085, 0.013118087314069271, 0.029239928349852562, -0.007360893301665783, 0.009240359999239445, -0.07724907249212265, 0.05355845391750336, 0.00047888231347315013, 0.000026317313313484192, -0.05199718102812767, 0.02418276108801365, 0.03400859981775284, 0.0272374264895916, -0.040253691375255585, 0.0070426990278065205, 0.013024750165641308, 0.0031458802986890078, 0.053490571677684784, -0.029867831617593765, 0.06251880526542664, -0.025744033977389336, 0.002113870345056057, 0.02148447372019291, 0.005150503944605589, -0.015918197110295296, 0.028951432555913925, 0.0628582090139389, -0.010818603448569775, 0.008366386406123638, -0.028883550316095352, -0.012982324697077274, 0.004552298691123724, -0.029545394703745842, 0.042290132492780685, 0.02158629707992077, -0.05254023149609566, 0.05291358008980751, -0.0529475174844265, -0.004000762011855841, 0.048806753009557724, -0.043715644627809525, -0.07276889681816101, -0.010674355551600456, -0.04833158105611801, 0.036893561482429504, 0.05749557539820671, 0.011930162087082863, 0.019719555974006653, 0.004145009908825159, 0.03529834747314453, 0.015239382162690163, -0.00399651937186718, -0.02077171951532364, 0.020618986338377, 0.007530596572905779, -0.02764471434056759, 0.011488933116197586, 0.06085570529103279, -0.024878546595573425, 0.010852544568479061, -0.0356377549469471, -0.044937510043382645, -0.03212488815188408, -0.028645966202020645, 0.014441775158047676, -0.031598806381225586, -0.0180734321475029, -0.030767260119318962, 0.05413544550538063, 0.011633181013166904, -0.006940876599401236, -0.03764025494456291, -0.0031310312915593386, 0.02418276108801365, 0.012668373063206673, 0.05858168005943298, -0.010453741066157818, 0.02484460547566414, -0.022825133055448532, -0.022519666701555252, 0.015290292911231518, -0.03458559140563011, 0.024420347064733505, 0.023249391466379166, -0.06601469218730927, 0.04103432595729828, -0.004628665279597044, -0.03662203252315521, 0.002199782757088542, -0.023198479786515236, 0.028934461995959282, 0.021314769983291626, -0.030258148908615112, -0.05057166889309883, -0.008247594349086285, -0.02250269614160061, 0.011005277745425701, -0.035264406353235245, -0.023843353614211082, 0.03590928018093109, -0.0014658147701993585, -0.00614751223474741, -0.05131836608052254, 0.004972314927726984, 0.012702313251793385, -0.055832479149103165, 0.019838349893689156, -0.03173457086086273, -0.03304128721356392, 0.006932391319423914, -0.006652380805462599, -0.06095752865076065, -0.0006401007412932813, 0.015544848516583443, 0.03417830169200897, 0.028679905459284782, 0.0008591244113631546, -0.022994836792349815, 0.030376942828297615, 0.007997281849384308, 0.031242430210113525, -0.04266348108649254, 0.04914616048336029, -0.04161132127046585, -0.012795650400221348, 0.023605769500136375, -0.019889259710907936, -0.016529129818081856, 0.0371650867164135, -0.023300303146243095, 0.004959587473422289, 0.001109437202103436, 0.0110731590539217, 0.00911308266222477, -0.0018041612347587943, -0.022536637261509895, -0.0054432423785328865, -0.02464096061885357, 0.03141213580965996, -0.01558727491647005, -0.036078982055187225, -0.001688550692051649, 0.01756432093679905, -0.032667942345142365, 0.03998216614127159, 0.05080925300717354, -0.01023312658071518, -0.003979549277573824, -0.011616210453212261, -0.015723036602139473, 0.023351212963461876, 0.049621328711509705, -0.006380855105817318, -0.015078163705766201, 0.03747055307030678, -0.038115426898002625, 0.02163720689713955, -0.001793554751202464, 0.01746249943971634, 0.00014742999337613583, 0.0110731590539217, 0.035977158695459366, 0.016257604584097862, 0.005532336886972189, 0.009749471209943295, -0.0070426990278065205, 0.027050752192735672, -0.02194267325103283, -0.004021975211799145, -0.030665438622236252, 0.011718032881617546, -0.006083873566240072, 0.053796038031578064, 0.015570304356515408, 0.073311947286129, 0.027118632569909096, -0.030478764325380325, 0.05607006698846817, -0.03950699418783188, -0.006499647628515959, -0.008748220279812813, -0.03290552645921707, 0.03940517455339432, -0.004108948167413473, 0.015663640573620796, 0.0580386258661747, 0.011624695733189583, -0.02229905128479004, -0.0173097662627697, 0.0203644298017025, -0.010699811391532421, -0.009316726587712765, 0.003697416977956891, -0.021314769983291626, 0.027763506397604942, 0.008251836523413658, -0.060414478182792664, 0.01543454173952341, -0.01369507983326912, -0.08559849113225937, -0.004552298691123724, -0.003041936783120036, -0.012965354137122631, 0.05932837352156639, -0.006351156625896692, -0.0099276602268219, -0.003705902025103569, 0.011930162087082863, -0.01346598006784916, -0.001334294443950057, 0.04093250632286072, 0.038013603538274765, 0.027678655460476875, 0.004505630116909742, 0.013729020021855831, 0.008756705559790134, -0.011327714659273624, 0.02530280500650406, -0.0009137477609328926, 0.036689914762973785, -0.0008458663360215724, 0.010572533123195171, 0.014543597586452961, -0.022214200347661972, 0.06302791088819504, -0.07480534166097641, -0.050435904413461685, 0.02270633913576603, 0.05162383243441582, 0.022621488198637962, 0.0034110420383512974, -0.024097910150885582, 0.03275279328227043, 0.0628582090139389, 0.03764025494456291, -0.014628449454903603, -0.009783411398530006, -0.008133044466376305, 0.016028502956032753, -0.054610613733530045, 0.005774164572358131, -0.00845123827457428, -0.0064614638686180115, -0.008133044466376305, 0.018463749438524246, 0.04184890538454056, 0.01160772517323494, -0.004862007685005665, 0.028679905459284782, 0.028900520876049995, 0.032464295625686646, 0.023503946140408516, -0.012328965589404106, 0.0063681271858513355, -0.017649173736572266, 0.004403808154165745, 0.026965899392962456, 0.014543597586452961, 0.039744582027196884, -0.003988034091889858, 0.03355040028691292, 0.04018580913543701, -0.02184085175395012, -0.0032073978800326586, 0.01641882210969925, 0.014390864409506321, 0.03896394371986389, 0.024097910150885582, 0.03736872971057892, 0.012337450869381428, 0.03344857692718506, 0.0027385917492210865, -0.021399622783064842, 0.012668373063206673, -0.029053254052996635, 0.01565515622496605, 0.0323285348713398, -0.00014968386676628143, 0.0077639389783144, 0.034653473645448685, -0.020483223721385002, 0.0025604029651731253, -0.016860051080584526, -0.014110852964222431, -0.02265542931854725, -0.013482949696481228, -0.02382638305425644, 0.033991627395153046, -0.007106337696313858, 0.014399349689483643, 0.0038565141148865223, 0.03153092786669731, -0.0018253742018714547, -0.008531847968697548, 0.016944903880357742, 0.006211151368916035, 0.018769217655062675, 0.022078435868024826, 0.01939712092280388, -0.013576286844909191, -0.043715644627809525, 0.05101289972662926, 0.02021169662475586, 0.009690075181424618, -0.002711014822125435, 0.018803156912326813, -0.007051183842122555, -0.014730270951986313, 0.004662605933845043, 0.00949491560459137, -0.0006332065095193684, 0.017123091965913773, -0.03509470075368881, -0.05362633243203163, -0.002367364941164851, -0.010606474243104458, 0.0180734321475029, 0.035875339061021805, -0.002649497240781784, 0.018090402707457542, 0.015824859961867332, -0.009469459764659405, 0.023402124643325806, -0.01695338822901249, -0.008434268645942211, 0.052166882902383804, -0.027016811072826385, -0.043206531554460526, -0.0376741960644722, -0.009206419810652733, 0.016919447109103203, 0.03069937974214554, 0.010716781951487064, -0.0060626608319580555, -0.004051673226058483, -0.02998662367463112, 0.013270820491015911, 0.015536363236606121, 0.016308514401316643, 0.07901398837566376, -0.03794572129845619, 0.039031825959682465, -0.04853522777557373, 0.012990809977054596, -0.02963024564087391, 0.0050614094361662865, -0.003529834561049938, 0.024861576035618782, 0.019023772329092026, -0.04164525866508484, 0.00089412578381598, -0.009291271679103374, -0.011998043395578861, 0.01537514477968216, -0.011667121201753616, 0.005897199735045433, -0.013126572594046593, -0.029850861057639122, 0.011718032881617546, -0.001764917280524969, 0.03148001432418823, -0.016893992200493813, -0.0076536317355930805, 0.01114952564239502, 0.018972860649228096, 0.06689715385437012, 0.03696143999695778, -0.016715804114937782, 0.01422964595258236, 0.01562970131635666, 0.036995381116867065, -0.033075228333473206, 0.05579853802919388, 0.03299037739634514, 0.026337996125221252, -0.054101504385471344, -0.004692304413765669, -0.05403362214565277, 0.018599513918161392, 0.023045746609568596, -0.03482317551970482, 0.0037334789521992207, 0.028119884431362152, 0.01786978729069233, 0.02932477928698063, -0.02845929190516472, -0.022587547078728676, -0.0402197502553463, 0.01827707700431347, -0.020635956898331642, -0.03706326335668564, -0.06306185573339462, 0.04256166145205498, 0.01929529756307602, 0.015095134265720844, -0.03509470075368881, -0.022740280255675316, -0.02418276108801365, -0.0110731590539217, -0.009503400884568691, -0.07154703140258789, 0.018243135884404182, 0.014730270951986313, 0.06513223797082901, -0.0402197502553463, -0.04368170350790024, 0.04436051845550537, 0.01288050226867199, -0.006970575079321861, -0.0188370980322361, 0.033737074583768845, -0.013381128199398518, 0.03417830169200897, 0.0010102667147293687, 0.03692749887704849, 0.02913810685276985, 0.06238303706049919, 0.010046452283859253, 0.0009450368816033006, -0.00838760007172823, 0.05366027355194092, -0.06360490620136261, 0.006198423448950052, 0.010810118168592453, -0.017174003645777702, -0.0010007208911702037, 0.03375404328107834, 0.009673104621469975, -0.005850531160831451, -0.004878978244960308, -0.02051716297864914, 0.024861576035618782, -0.010139789432287216, -0.0062323641031980515, -0.004531085956841707, 0.014297527261078358, -0.016563070937991142, -0.02041534148156643, -0.022027526050806046, 0.05060561001300812, 0.03305825963616371, 0.010504651814699173, 0.022078435868024826, 0.00416834419593215, -0.013075661845505238, 0.00972401537001133, 0.009749471209943295, -0.014255101792514324, -0.05657917633652687, 0.021467503160238266, 0.00008365856774616987, 0.026456790044903755, 0.04256166145205498, 0.021569326519966125, 0.01568061113357544, 0.007407561410218477, -0.022723309695720673, -0.009757956489920616, 0.0041386461816728115, -0.01000402681529522, 0.015171500854194164, -0.003697416977956891, -0.05790286511182785, 0.0014477837830781937, -0.024165790528059006, -0.0020831115543842316, 0.005455970298498869, 0.07154703140258789, 0.017734024673700333, 0.04527691751718521, -0.03321099281311035, -0.011692577041685581, -0.036893561482429504, 0.0534566305577755, 0.029511453583836555, 0.0038777270819991827, -0.015875769779086113, 0.0366559736430645, 0.00002210786988143809, -0.017343707382678986, -0.0074627152644097805, 0.01700429990887642, 0.03482317551970482, 0.00395833607763052, -0.014059942215681076, -0.0114549919962883, -0.04446233808994293, -0.011030733585357666, 0.04670242592692375, -0.013406583108007908, 0.029613276943564415, 0.002558281645178795, 0.003797117853537202, 0.02372456155717373, -0.011947132647037506, 0.01158227026462555, -0.02077171951532364, -0.026762256398797035, -0.013245364651083946, 0.041237972676754, 0.0003356949018780142, -0.0044632041826844215, -0.03573957458138466, -0.01537514477968216, 0.0011879251105710864, -0.0002861096290871501, 0.03438194841146469, -0.02922295778989792, 0.0009747349540702999, 0.0027152574621140957, -0.014051456935703754, 0.020941423252224922, 0.02209540642797947, 0.00941854901611805, 0.01786978729069233, 0.02688104845583439, -0.026813166216015816, -0.012362906709313393, -0.051861416548490524, -0.02840838022530079, -0.007738483604043722, 0.011514388024806976, -0.02005896344780922, 0.023605769500136375, -0.014059942215681076, 0.002199782757088542, -0.008765189908444881, -0.005298994481563568, -0.0037886325735598803, -0.01954985409975052, -0.02667740359902382, 0.012167747132480145 ]
Radio based positioning of a user equipment (UE) based on deep learning (DL) methods using channel state information (CSI) fingerprints have shown promising results. DL models are able to capture complex properties embedded in the CSI about a particular environment and map UE's CSI to the UE's position. However, the CSI fingerprints and the DL models trained on such fingerprints are highly dependent on a particular propagation environment, which generally limits the transfer of knowledge of the DL models from one environment to another. In this paper, we propose a DL model consisting of two parts: the first part aims to learn environment independent features while the second part combines those features depending on the particular environment. To improve transfer learning, we propose a meta learning scheme for training the first part over multiple environments. We show that for positioning in a new environment, initializing a DL model with the meta learned environment independent function achieves higher UE positioning accuracy compared to regular transfer learning from one environment to the new environment, or compared to training the DL model from scratch with only fingerprints from the new environment. Our proposed scheme is able to create an environment independent function which can embed knowledge from multiple environments and more effectively learn from a new environment.
[ 0.01584661565721035, -0.029161415994167328, -0.03380611166357994, -0.04382408782839775, 0.013797484338283539, 0.05369634926319122, -0.027849972248077393, 0.04764913395047188, -0.05016273632645607, -0.021912043914198875, -0.017212703824043274, -0.05427921190857887, 0.008829479105770588, -0.08305812627077103, -0.002367885084822774, -0.02378813736140728, 0.04866914451122284, -0.00006165181548567489, 0.0258281622081995, -0.06251216679811478, 0.03271324187517166, -0.03575506433844566, -0.02109239250421524, 0.02750389650464058, -0.021875616163015366, 0.009075375273823738, 0.017859317362308502, -0.008082685060799122, -0.06706579029560089, -0.0012704614782705903, 0.04914272204041481, 0.03329610824584961, -0.03996261581778526, -0.03340539336204529, -0.07369586825370789, 0.007631876040250063, 0.05059988424181938, 0.03744901344180107, -0.058432117104530334, 0.01789574697613716, 0.017740923911333084, -0.01683930680155754, 0.0131599772721529, 0.0561370924115181, 0.025099582970142365, -0.06998011469841003, -0.04702984169125557, -0.051547035574913025, 0.004867825191468, -0.023988498374819756, 0.0013091672444716096, -0.046264830976724625, 0.016037868335843086, -0.03659293055534363, -0.011456920765340328, 0.04794056713581085, 0.051947757601737976, 0.04841414466500282, 0.008201079443097115, 0.004977112170308828, -0.0039730379357934, -0.016766447573900223, -0.03610114008188248, -0.035554707050323486, 0.048304855823516846, -0.029926424846053123, 0.0055007790215313435, -0.06254859268665314, -0.0022449372336268425, 0.012012463063001633, -0.031966447830200195, 0.007153745274990797, 0.006429718807339668, -0.011711924336850643, -0.012067106552422047, -0.0003190383722539991, -0.006302217487245798, 0.03730329871177673, 0.036793291568756104, 0.008287597447633743, 0.049944162368774414, 0.06378718465566635, -0.006894188467413187, -0.013487838208675385, 0.06706579029560089, 0.011557100340723991, 0.019380228593945503, -0.06724793463945389, 0.013542481698095798, 0.03007214143872261, -0.048304855823516846, 0.03183894604444504, -0.02852390892803669, 0.023678850382566452, -0.03497184067964554, 0.050490595400333405, -0.01744949258863926, -0.027686040848493576, -0.04345979914069176, 0.004867825191468, -0.02473529241979122, 0.02912498638033867, 0.03156572952866554, -0.0206370297819376, -0.011156382039189339, -0.024043140932917595, -0.018405752256512642, 0.039889756590127945, -0.008110006339848042, 0.07482516765594482, 0.01747681386768818, 0.001308028819039464, 0.0004883763031102717, 0.052530620247125626, -0.002101497957482934, -0.03741258382797241, -0.046155545860528946, -0.09172822535037994, 0.047831278294324875, -0.011802996508777142, 0.017276454716920853, 0.019380228593945503, 0.0015766926808282733, -0.010172798298299313, -0.020964890718460083, 0.07143726944923401, 0.04131048917770386, -0.016046974807977676, 0.010719234123826027, -0.016547873616218567, -0.016757341101765633, -0.005960695445537567, 0.0030987418722361326, -0.0009938287548720837, 0.05486207455396652, 0.04498981684446335, -0.015163571573793888, 0.027649613097310066, 0.00025486070080660284, -0.013469623401761055, 0.06990725547075272, -0.02060060016810894, -0.00821929331868887, 0.01694859378039837, 0.04488053172826767, 0.03063679113984108, 0.003178430488333106, 0.000566357106436044, -0.01632019318640232, -0.013378551229834557, -0.07912379503250122, 0.026101378723978996, -0.00876572821289301, 0.009899580851197243, 0.07151012867689133, 0.019963093101978302, 0.01270461454987526, -0.029307132586836815, -0.034643981605768204, 0.02109239250421524, 0.03369682654738426, -0.0680493712425232, 0.007873217575252056, 0.03125608339905739, 0.02118346467614174, 0.013679089955985546, 0.028706053271889687, 0.012212823145091534, -0.04528125002980232, 0.03287717327475548, -0.018041463568806648, -0.04808628186583519, 0.030818935483694077, 0.01737663336098194, 0.009699221700429916, 0.02169346995651722, 0.013588017784059048, -0.02743103727698326, 0.058905694633722305, -0.002613780787214637, -0.021383823826909065, 0.014863032847642899, -0.018351109698414803, 0.010099940933287144, 0.04764913395047188, 0.013569802977144718, -0.02172989957034588, -0.012695507146418095, -0.029798923060297966, -0.07497088611125946, -0.005227561574429274, 0.0350082702934742, 0.07070869207382202, -0.029179630801081657, 0.0063932896591722965, -0.0711822658777237, -0.02322348766028881, 0.020873818546533585, 0.019708089530467987, -0.02486279420554638, -0.0005347663536667824, -0.011566207744181156, 0.022968485951423645, -0.012513361871242523, -0.015536969527602196, -0.0037886162754148245, 0.021256322041153908, 0.04477124288678169, -0.03324146568775177, -0.09019821137189865, -0.013551588170230389, 0.010109048336744308, -0.02646566927433014, 0.030436430126428604, 0.004849610850214958, 0.010409587062895298, 0.03970761224627495, -0.015673577785491943, -0.006903295870870352, 0.039306893944740295, 0.026028521358966827, 0.017695387825369835, 0.07227513939142227, 0.014061594381928444, -0.033551111817359924, -0.018833793699741364, 0.06939724832773209, 0.0065572201274335384, -0.008834033273160458, -0.0485234297811985, 0.013150869868695736, 0.00042348713031969965, 0.01745859906077385, -0.023569563403725624, 0.03522684425115585, -0.0018464949680492282, 0.024571361020207405, -0.016730019822716713, -0.019708089530467987, -0.008902337402105331, 0.013178191147744656, -0.009954224340617657, -0.057266391813755035, -0.02169346995651722, 0.04768556356430054, -0.035044699907302856, -0.03810473531484604, 0.05191132798790932, -0.012677292339503765, -0.012832115404307842, 0.004423846956342459, -0.005755782127380371, 0.011675494723021984, -0.013032475486397743, -0.020983105525374413, 0.020782744511961937, 0.020782744511961937, -0.07766663283109665, 0.021274536848068237, -0.053623490035533905, 0.02699388936161995, 0.028833555057644844, -0.027194250375032425, -0.00875206757336855, 0.03134715557098389, 0.0077912528067827225, 0.06681078672409058, 0.025518516078591347, -0.02542744390666485, 0.008392331190407276, -0.061528582125902176, -0.05325920134782791, 0.0066255247220396996, 0.02111060731112957, 0.02908855862915516, -0.03741258382797241, -0.022385621443390846, -0.008041702210903168, 0.012959617190063, 0.025117795914411545, 0.06061786040663719, 0.022330978885293007, 0.019380228593945503, -0.008260276168584824, -0.05325920134782791, -0.010400479659438133, -0.05824997276067734, 0.010764770209789276, 0.003847813233733177, -0.0040367888286709785, -0.027686040848493576, -0.02801390178501606, -0.05271276459097862, 0.03582792356610298, 0.027904614806175232, 0.022513123229146004, -0.04083691164851189, -0.05431564152240753, 0.012221929617226124, -0.04021761938929558, 0.0016313361702486873, 0.0007957459893077612, 0.03176609054207802, 0.0053914920426905155, 0.021402038633823395, 0.06090928986668587, 0.007732055615633726, -0.003925224766135216, -0.07008939981460571, -0.008128221146762371, 0.037776876240968704, 0.008451527915894985, 0.0066255247220396996, -0.04003547132015228, -0.0017485921271145344, 0.02060060016810894, -0.013078011572360992, 0.014380347914993763, 0.00210718996822834, -0.043569084256887436, -0.014899461530148983, 0.021565968170762062, -0.053149912506341934, 0.004835949745029211, 0.041929781436920166, 0.003406111616641283, 0.033022891730070114, 0.03156572952866554, -0.012030677869915962, -0.0005526962340809405, -0.02646566927433014, -0.020964890718460083, -0.06178358569741249, 0.008228400722146034, 0.0012397244572639465, 0.06619149446487427, 0.011302097700536251, 0.03635614365339279, 0.018260037526488304, -0.0026479330845177174, -0.021383823826909065, 0.01236764620989561, -0.07289443165063858, -0.021784542128443718, -0.013305692933499813, -0.04684769734740257, -0.03865117207169533, 0.025044938549399376, -0.030491074547171593, 0.02009059488773346, 0.0009260935476049781, -0.01113816723227501, 0.0047038947232067585, -0.000977891031652689, 0.07038082927465439, -0.03974404186010361, -0.05242133513092995, -0.020254524424672127, -0.03963475301861763, -0.02484457939863205, 0.00754535710439086, -0.023915639147162437, -0.03945260867476463, 0.013387657701969147, -0.0023997605312615633, 0.030217856168746948, 0.012759258039295673, 0.005227561574429274, -0.017094308510422707, 0.058359261602163315, 0.0592699870467186, -0.010427801869809628, 0.04058190807700157, 0.008779389783740044, -0.058395691215991974, 0.025573158636689186, 0.03497184067964554, 0.0040162974037230015, -0.016174476593732834, 0.05172918364405632, 0.029143201187253, 0.03183894604444504, 0.01479928195476532, -0.004799521062523127, 0.02961677871644497, 0.06393289566040039, 0.013196405954658985, -0.0004954913165420294, -0.02743103727698326, 0.015136250294744968, -0.00007812313560862094, -0.07540803402662277, -0.029780708253383636, -0.005569083616137505, 0.07158298790454865, -0.009662793017923832, 0.01908879727125168, 0.006324985530227423, -0.012804794125258923, -0.030891792848706245, -0.0379590205848217, 0.03550006076693535, -0.005605512764304876, 0.02803211659193039, -0.010263871401548386, -0.0263199545443058, 0.030436430126428604, -0.04972558841109276, -0.01999952271580696, -0.020800959318876266, 0.06761222332715988, -0.020363811403512955, -0.021292751654982567, -0.009152786806225777, 0.0358097068965435, -0.021219894289970398, -0.06695650517940521, 0.02329634688794613, 0.002443019999191165, -0.059998564422130585, 0.027758900076150894, 0.027613183483481407, 0.05245776101946831, -0.012376753613352776, 0.018642541021108627, 0.05857783555984497, 0.027176035568118095, -0.04524482041597366, 0.003000838914886117, -0.049871303141117096, -0.011875854805111885, -0.04899700731039047, 0.04906986653804779, -0.03639257326722145, -0.013214620761573315, 0.00018598712631501257, -0.005204793531447649, 0.005805871915072203, -0.05285848304629326, -0.03156572952866554, 0.02010880969464779, -0.03016321361064911, -0.017668066546320915, -0.017640743404626846, -0.0017895747441798449, 0.02267705276608467, 0.027904614806175232, 0.0036588378716260195, 0.012750150635838509, -0.01396141480654478, -0.02218526229262352, 0.05034488067030907, -0.02478993497788906, -0.009216537699103355, 0.0729672908782959, -0.028633195906877518, -0.025609588250517845, -0.045718397945165634, -0.0206370297819376, -0.06134643778204918, -0.011985141783952713, 0.05646495148539543, 0.05697495862841606, -0.0495070144534111, 0.003242181148380041, 0.007222049403935671, -0.04382408782839775, -0.06932438910007477, 0.02111060731112957, -0.018779151141643524, 0.030199643224477768, -0.07620947062969208, 0.040873341262340546, 0.024462074041366577, -0.03486255556344986, -0.006247573997825384, -0.027722470462322235, -0.06710222363471985, -0.018086999654769897, -0.0018704015528783202, 0.016283763572573662, 0.03418861702084541, 0.028815340250730515, -0.04316836595535278, 0.06440647691488266, -0.00008353056182386354, 0.004266746807843447, -0.027248892933130264, -0.0350082702934742, -0.021511325612664223, 0.034097544848918915, 0.034133974462747574, -0.029780708253383636, 0.007795806508511305, -0.0007866387604735792, -0.05548137053847313, -0.008342240937054157, -0.046155545860528946, 0.034042902290821075, 0.0289610568434, -0.026265310123562813, -0.02264062501490116, 0.0019136610208079219, 0.03733972832560539, 0.0032353505957871675, -0.016147155314683914, 0.09325824677944183, 0.0017895747441798449, -0.020782744511961937, 0.0622207336127758, 0.02593744918704033, 0.006639185361564159, 0.021802756935358047, -0.010209227912127972, 0.003943439573049545, 0.06072714552283287, 0.024061355739831924, -0.004048172850161791, 0.01452606450766325, 0.0381411649286747, 0.019362013787031174, 0.014261954464018345, -0.01397962961345911, 0.029981067404150963, -0.0036656681913882494, 0.015373039059340954, 0.048377715051174164, -0.0348261259496212, -0.012895866297185421, -0.05278562381863594, -0.029908210039138794, -0.004954344127327204, -0.004927022382616997, -0.05161989480257034, -0.03167501837015152, 0.00593337370082736, 0.017859317362308502, 0.00389334955252707, -0.009708329103887081, -0.004323666915297508, -0.02535458467900753, 0.0025067706592381, 0.011812103912234306, 0.002918873680755496, 0.022986700758337975, 0.01999952271580696, -0.021037748083472252, -0.011493350379168987, 0.05118274688720703, 0.0041665672324597836, 0.037704017013311386, -0.03682972118258476, -0.026684243232011795, 0.00042348713031969965, -0.02473529241979122, -0.02697567641735077, -0.01634751446545124, 0.005182025488466024, -0.03395183011889458, -0.010855842381715775, 0.05223918706178665, -0.028414621949195862, -0.012950509786605835, -0.011538886465132236, -0.0032717797439545393, -0.013988737016916275, -0.01632019318640232, 0.014671780169010162, -0.015946796163916588, 0.009148232638835907, 0.009198322892189026, 0.03278610110282898, -0.03843259811401367, -0.009881366975605488, 0.031948234885931015, -0.026137808337807655, 0.026265310123562813, -0.0432412251830101, 0.023132415488362312, 0.0037408031057566404, 0.003230797126889229, -0.032440025359392166, 0.0068167769350111485, 0.007194727659225464, 0.024115998297929764, -0.026611385866999626, -0.062184303998947144, -0.01215817965567112, -0.005701138637959957, 0.001919353031553328, 0.009307609871029854, 0.002099221106618643, -0.013688197359442711, -0.017240025103092194, 0.015955902636051178, -0.03529970347881317, -0.00017104553990066051, 0.0019660277757793665, 0.025973878800868988, -0.05657424032688141, 0.0015038347337394953, 0.0833495557308197, 0.006812223233282566, -0.0020878370851278305, -0.014717316254973412, -0.016265548765659332, 0.03857831284403801, 0.031420014798641205, 0.009389575570821762, -0.0064479331485927105, -0.009453325532376766, 0.0326768159866333, 0.0370665080845356, -0.020782744511961937, 0.015163571573793888, 0.017850210890173912, 0.05591851845383644, -0.011338526383042336, 0.016201797872781754, -0.020400241017341614, 0.008510725572705269, -0.038760457187891006, 0.03223966807126999, 0.020837388932704926, -0.05063631385564804, 0.046155545860528946, 0.01948951557278633, -0.02797747403383255, 0.01028208527714014, -0.02639281190931797, -0.0290521290153265, 0.010609947144985199, -0.021529540419578552, -0.04549982398748398, -0.04054547846317291, 0.013050689361989498, 0.0049088080413639545, -0.0026115039363503456, 0.022968485951423645, 0.0018066507764160633, -0.03489898517727852, 0.04582768306136131, -0.05107346177101135, 0.02801390178501606, 0.003624685574322939, -0.0079460758715868, -0.016666268929839134, 0.035081129521131516, 0.03282253071665764, 0.08815818279981613, -0.035153985023498535, 0.017677173018455505, -0.0170123428106308, 0.026247095316648483, -0.009002516977488995, -0.03136536851525307, 0.023952068760991096, -0.018214501440525055, 0.010673697106540203, -0.03342361003160477, 0.021493110805749893, 0.0485234297811985, -0.0013239665422588587, 0.023023128509521484, -0.004337328020483255, -0.03325967863202095, 0.016748232766985893, 0.004278130829334259, -0.027267107740044594, 0.008497064933180809, -0.0008788496488705277, -0.048887718468904495, -0.0010279809357598424, -0.014143560081720352, 0.04899700731039047, -0.03367861360311508, -0.002588735893368721, -0.027176035568118095, -0.02586459182202816, -0.022075975313782692, 0.0318753756582737, 0.020454883575439453, 0.028760695829987526, -0.013597125187516212, 0.05602780357003212, -0.02484457939863205, 0.005860515404492617, -0.0032991014886647463, -0.041456203907728195, -0.001685979776084423, -0.0495070144534111, 0.043532658368349075, 0.028906412422657013, -0.007326783146709204, 0.002397483680397272, -0.01746770553290844, -0.02703031897544861, 0.026301739737391472, 0.052530620247125626, -0.028268905356526375, -0.003995805978775024, 0.010291192680597305, -0.002342840190976858, 0.019708089530467987, 0.04382408782839775, 0.04972558841109276, 0.017158059403300285, -0.016629839316010475, -0.034607551991939545, -0.018287358805537224, 0.01948951557278633, -0.006712043657898903, 0.010901378467679024, 0.05482564866542816, 0.038323309272527695, -0.029889995232224464, -0.028214260935783386, -0.02697567641735077, -0.03123786859214306, 0.06262145191431046, -0.004266746807843447, 0.04451623931527138, 0.009116357192397118, -0.05657424032688141, 0.0005148442578501999, 0.06582720577716827, 0.01025476399809122, 0.012750150635838509, -0.007645536679774523, 0.018196286633610725, 0.012249251827597618, -0.01346051599830389, 0.009617256000638008, 0.014535171911120415, 0.036811504513025284, -0.025718875229358673, -0.0033104855101555586, 0.0024748952127993107, 0.016529658809304237, 0.018870223313570023, -0.0005162672605365515, -0.0317843034863472, 0.035099342465400696, -0.0034971842542290688, -0.015099821612238884, 0.07540803402662277, -0.00451264251023531, 0.008811264298856258, 0.01795949786901474, -0.02475350722670555, 0.029434632509946823, -0.038796886801719666, 0.030017497017979622, -0.0370665080845356, -0.03444362059235573, 0.030764291062951088, 0.016475016251206398, 0.0015721390955150127, 0.009872259572148323, -0.00409370893612504, 0.046774838119745255, 0.003679329063743353, 0.03123786859214306, 0.030928222462534904, 0.03662936016917229, 0.025591373443603516, -0.06131000816822052, 0.011475135572254658, 0.018615219742059708, -0.001113930600695312, 0.06032642722129822, -0.01559161301702261, 0.055736374109983444, -0.05242133513092995, -0.006671060808002949, 0.02010880969464779, 0.014662672765552998, -0.011757460422813892, -0.04502624645829201, -0.03919760510325432, 0.0012841223506256938, 0.019908448681235313, -0.011629958637058735, 0.010081726126372814, -0.021383823826909065, -0.03701186552643776, -0.0065025766380131245, 0.023369204252958298, -0.025518516078591347, -0.0317843034863472, -0.002118574222549796, 0.003963930532336235, 0.02642924152314663, 0.003911564126610756, 0.049944162368774414, 0.026684243232011795, 0.006976153701543808, 0.010081726126372814, -0.03586435317993164, -0.035117559134960175, -0.004202995914965868, -0.001159466803073883, -0.02948927693068981, 0.017795566469430923, -0.03424326330423355, 0.03846902400255203, -0.0027390054892748594, -0.012048892676830292, 0.004713002126663923, -0.0444069541990757, 0.005259437020868063, 0.0066528464667499065, 0.010983344167470932, 0.009708329103887081, 0.04167477786540985, -0.020819174125790596, -0.013651768676936626, 0.013988737016916275, -0.0038273220416158438, -0.029161415994167328, 0.016720911487936974, -0.03364218398928642, -0.012795686721801758, 0.04214835539460182, -0.05508065223693848, 0.016283763572573662, 0.014416777528822422, -0.0092666270211339, 0.038359738886356354, -0.01786842569708824, 0.05212990194559097, -0.02584637701511383, 0.010109048336744308, 0.011420492082834244, -0.02540922909975052, 0.02016345225274563, -0.009426004253327847, 0.036702219396829605, 0.003754463978111744, -0.00554631557315588, -0.009120911359786987, -0.011028880253434181, -0.02437100186944008, -0.024097785353660583, -0.05373277887701988, -0.02752211131155491, -0.004767645616084337, -0.013014260679483414, -0.00788687914609909, -0.018123427405953407, 0.036720432341098785, 0.028123188763856888, 0.04750341922044754, 0.009043499827384949, -0.01841486059129238, -0.0026661476586014032, -0.022895626723766327, 0.013078011572360992, 0.013114440254867077, -0.05322277173399925, 0.01899772509932518, 0.0034675856586545706, 0.003535890020430088, -0.04597340151667595, 0.03752187266945839, -0.002088975626975298, -0.008333134464919567, -0.038359738886356354, -0.059889279305934906, -0.00594703434035182, -0.007208388764411211, 0.0020320552866905928, -0.028687838464975357, 0.050927743315696716, 0.03125608339905739, -0.008123666979372501, -0.0015949072549119592, 0.0002673831768333912, 0.05453421548008919, -0.035135772079229355, 0.02435278706252575, 0.03905189037322998, 0.024534933269023895, -0.014189096167683601, 0.03397004306316376, -0.0010057819308713078, -0.004794967360794544, -0.012021570466458797, 0.017194489017128944, -0.06903295964002609, 0.005573637317866087, 0.058869265019893646, 0.024553146213293076, 0.0037772320210933685, 0.004587777424603701, 0.03284074366092682, -0.04418838024139404, -0.010619053617119789, 0.024589575827121735, 0.04437052458524704, -0.002827801275998354, -0.024152427911758423, 0.038942601531744, -0.06196573004126549, 0.01645680144429207, -0.0019421211909502745, -0.012813901528716087, 0.012440504506230354, 0.0077092875726521015, 0.027339965105056763, -0.007540803402662277, -0.02857855148613453, 0.004631036892533302, -0.015427682548761368, 0.02799568697810173, 0.00323307397775352, 0.0036041943822056055, -0.01748592033982277, 0.0485234297811985, 0.011429599486291409, 0.07526231557130814, -0.002834631595760584, 0.015946796163916588, 0.008469742722809315, 0.0002780557260848582, 0.0010308269411325455, 0.033059317618608475, 0.03945260867476463, -0.005059077404439449, 0.014362134039402008, -0.023041343316435814, 0.005459796637296677, 0.006006231531500816, 0.016793768852949142, 0.06116429343819618, -0.0032558420207351446, -0.0028938287869095802, -0.025609588250517845, -0.04269478842616081, 0.019143439829349518, -0.042039066553115845, -0.0003187537658959627, -0.004198442213237286, -0.018168965354561806, 0.034079331904649734, -0.03857831284403801, 0.0010911624412983656, 0.021565968170762062, -0.002531815553084016, 0.022895626723766327, -0.009936010465025902, -0.07861378788948059, -0.00796429067850113, -0.054169926792383194, -0.005122828297317028, 0.00686686672270298, 0.006666507106274366, -0.013806591741740704, 0.016520552337169647, 0.01958058774471283, -0.049434155225753784, 0.040436193346977234, -0.01738574169576168, 0.007773037999868393, 0.005783103872090578, 0.03690258041024208, -0.031456444412469864, 0.008405991829931736, -0.05719353258609772, 0.0528220534324646, 0.02595566399395466, -0.04138334468007088, -0.01632929965853691, 0.005988017190247774, 0.01905236765742302, 0.009571719914674759, 0.020892031490802765, -0.03712115436792374, 0.012012463063001633, 0.008023487403988838, 0.018888438120484352, 0.04214835539460182, 0.04899700731039047, 0.01111995242536068, -0.007089994382113218, -0.0316932313144207, 0.04750341922044754, -0.057229962199926376, -0.010382265783846378, 0.015737328678369522, -0.011711924336850643, -0.016602518036961555, 0.0001849910186138004, -0.026301739737391472, -0.03273145854473114, -0.020473098382353783, 0.007750269956886768, -0.03595542535185814, -0.018906651064753532, 0.037704017013311386, -0.03469862416386604, -0.03497184067964554, 0.007836788892745972, 0.056865669786930084, -0.019817376509308815, 0.0052503300830721855, 0.06112786382436752, -0.011356741189956665, 0.0070808869786560535, 0.00569203170016408, 0.05584565922617912, -0.043605513870716095, -0.031948234885931015, 0.018742721527814865, -0.014744638465344906, -0.012276573106646538, -0.06790366023778915, 0.023077772930264473, 0.01740395464003086, -0.04123762995004654, 0.026156023144721985, -0.051510609686374664, 0.005641941446810961, -0.016802877187728882 ]
Despite recent advances in Graph Neural Networks (GNNs), their training strategies remain largely under-explored. The conventional training strategy learns over all nodes in the original graph(s) equally, which can be sub-optimal as certain nodes are often more difficult to learn than others. Here we present TuneUp, a simple curriculum-based training strategy for improving the predictive performance of GNNs. TuneUp trains a GNN in two stages. In the first stage, TuneUp applies conventional training to obtain a strong base GNN. The base GNN tends to perform well on head nodes (nodes with large degrees) but less so on tail nodes (nodes with small degrees). Therefore, the second stage of TuneUp focuses on improving prediction on the difficult tail nodes by further training the base GNN on synthetically generated tail node data. We theoretically analyze TuneUp and show it provably improves generalization performance on tail nodes. TuneUp is simple to implement and applicable to a broad range of GNN architectures and prediction tasks. Extensive evaluation of TuneUp on five diverse GNN architectures, three types of prediction tasks, and both transductive and inductive settings shows that TuneUp significantly improves the performance of the base GNN on tail nodes, while often even improving the performance on head nodes. Altogether, TuneUp produces up to 57.6% and 92.2% relative predictive performance improvement in the transductive and the challenging inductive settings, respectively.
[ 0.012934749945998192, 0.017276547849178314, -0.027156630530953407, -0.01591690257191658, 0.06656818836927414, 0.027102243155241013, -0.009626282379031181, 0.041296929121017456, -0.008379940874874592, -0.01260843500494957, -0.026377100497484207, -0.014258136972784996, -0.028389373794198036, 0.010197332128882408, -0.007002168335020542, 0.015037666074931622, -0.006204510107636452, -0.03328409418463707, -0.034897539764642715, -0.047206852585077286, 0.013369835913181305, -0.08955524116754532, -0.00898271705955267, -0.019651392474770546, 0.00413558492437005, 0.018835606053471565, 0.04347236081957817, 0.02677593007683754, -0.035459525883197784, 0.031217433512210846, 0.024274183437228203, 0.04775070771574974, 0.05050625652074814, -0.018164848908782005, -0.02380284108221531, 0.0033265964593738317, 0.050107426941394806, 0.002013406716287136, -0.05946177989244461, -0.030655447393655777, 0.014910765923559666, 0.014620709232985973, 0.05612611770629883, -0.016460761427879333, 0.022769510746002197, -0.05953429266810417, -0.046880535781383514, -0.03288526460528374, 0.012989135459065437, -0.03576771169900894, -0.041151903569698334, 0.026123300194740295, 0.018282683566212654, -0.0073783365078270435, -0.059788092970848083, 0.06540795415639877, 0.005234630778431892, -0.008946459740400314, 0.04756942391395569, 0.042710959911346436, 0.006417521275579929, 0.013052585534751415, -0.020956652238965034, -0.013804921880364418, 0.052681684494018555, -0.04735188186168671, 0.019615136086940765, -0.012862235307693481, 0.042892247438430786, 0.014194686897099018, -0.051412682980298996, 0.013678021728992462, -0.060005635023117065, -0.020594079047441483, 0.020285893231630325, -0.029767146334052086, 0.005080537870526314, -0.0037752790376544, -0.0330846793949604, 0.0015352651244029403, 0.00721517950296402, 0.0066849179565906525, -0.018763091415166855, 0.00650816410779953, 0.047025565057992935, -0.02298705279827118, 0.05467583239078522, -0.04796825349330902, 0.04390744864940643, 0.005755827762186527, -0.04742439463734627, -0.034716252237558365, -0.059751834720373154, 0.010215461254119873, -0.028842588886618614, 0.039774127304553986, -0.0023295239079743624, -0.03513320907950401, -0.02126483805477619, 0.06740210205316544, 0.03781624138355255, 0.00317023741081357, 0.026304585859179497, -0.008765174075961113, 0.009834760800004005, -0.029966561123728752, 0.0060912068001925945, 0.000294872879749164, 0.08099854737520218, 0.09796690940856934, 0.05337057262659073, -0.04655422270298004, -0.018382390961050987, 0.04637293517589569, -0.036347825080156326, -0.026757800951600075, -0.05326180160045624, -0.061347153037786484, -0.00634047482162714, -0.006961379200220108, 0.033410992473363876, 0.04368990659713745, -0.029060130938887596, -0.03060106188058853, -0.07933071255683899, 0.02692095749080181, -0.06116586551070213, 0.0032744768541306257, 0.017494089901447296, -0.003480689600110054, 0.031217433512210846, 0.04597410559654236, 0.036239054054021835, -0.03462560847401619, 0.03540514037013054, -0.016188831999897957, 0.06769216060638428, 0.031924448907375336, -0.012019256129860878, -0.04597410559654236, 0.023113952949643135, -0.0028869782108813524, 0.0165423396974802, -0.03792501240968704, -0.012254927307367325, -0.0032200911082327366, 0.005329805891960859, 0.10253531485795975, -0.004196769092231989, 0.07940322905778885, -0.052899230271577835, 0.022098751738667488, 0.0026626368053257465, 0.03937530145049095, -0.00023666309425607324, 0.011167212389409542, -0.020177122205495834, 0.002857519080862403, -0.04180452972650528, -0.04368990659713745, 0.0438711903989315, 0.00307279615662992, -0.038287583738565445, 0.015862517058849335, 0.005651588086038828, 0.057250089943408966, 0.07218804955482483, 0.020358407869935036, -0.06519041210412979, 0.04376241937279701, 0.012780657038092613, 0.010587097145617008, -0.012227734550833702, 0.06221732497215271, -0.005257291253656149, 0.03558642417192459, -0.007795294281095266, -0.011022183112800121, -0.017530348151922226, -0.007219711318612099, -0.06250738352537155, -0.006857139524072409, 0.019542621448636055, 0.0302022323012352, 0.013505800627171993, 0.03649285435676575, 0.06979507952928543, 0.06540795415639877, -0.025579441338777542, 0.023712197318673134, 0.01340609323233366, 0.015454623848199844, 0.03148936107754707, -0.049636080861091614, 0.0005846470594406128, -0.01970577798783779, -0.017466897144913673, 0.004446037113666534, 0.029259545728564262, -0.01050551887601614, -0.012653756886720657, -0.048512108623981476, 0.019941451027989388, -0.023331496864557266, 0.0502161979675293, 0.05692377686500549, 0.002979887183755636, 0.037091098725795746, -0.03016597591340542, -0.03759869933128357, 0.009250113740563393, -0.045430250465869904, -0.05815652012825012, -0.03681916743516922, -0.021101679652929306, -0.008805963210761547, 0.028171829879283905, 0.03350163623690605, -0.005289016291499138, -0.0016666973242536187, 0.008098947815597057, 0.0540594607591629, 0.0462641641497612, -0.013487671501934528, -0.07004887610673904, -0.023530911654233932, 0.006843543145805597, -0.02376658283174038, 0.005162116140127182, 0.011992063373327255, -0.04648170620203018, 0.00561533123254776, 0.010396746918559074, -0.022696996107697487, 0.0013449148973450065, -0.01748502627015114, 0.020920393988490105, -0.03217824921011925, -0.004543478135019541, 0.016342924907803535, -0.0008293830323964357, 0.01613444648683071, 0.0372723825275898, 0.014403165318071842, 0.011937676928937435, 0.039556585252285004, 0.03379169479012489, 0.01970577798783779, 0.024564241990447044, 0.05173899978399277, -0.03217824921011925, -0.05786646157503128, 0.006050417199730873, 0.0022445463109761477, -0.04162324592471123, -0.006272492464631796, -0.0027351512107998133, -0.03518759459257126, 0.045611534267663956, -0.04912848398089409, 0.02186308056116104, 0.02334962598979473, -0.015255209058523178, 0.048403337597846985, 0.02889697439968586, -0.005134923383593559, 0.03745367005467415, 0.016043802723288536, 0.01045113243162632, -0.024201668798923492, 0.013369835913181305, -0.004645451437681913, -0.014031529426574707, -0.04173201695084572, -0.007586815394461155, -0.04445130378007889, 0.035568296909332275, -0.061455924063920975, 0.0029322996269911528, 0.017349062487483025, 0.05188402906060219, 0.027265401557087898, 0.020177122205495834, -0.024419212713837624, -0.036982327699661255, -0.04223961755633354, -0.024527983739972115, -0.005166648421436548, -0.0478232242166996, -0.0317612923681736, 0.00836634449660778, 0.03803378343582153, 0.033719178289175034, -0.018328005447983742, 0.02119232341647148, 0.05380566045641899, -0.049926139414310455, -0.04630042240023613, 0.027464816346764565, -0.038142554461956024, -0.010251718573272228, 0.011647620238363743, 0.02588762901723385, -0.010269846767187119, -0.009771310724318027, -0.01896250620484352, -0.006594275124371052, 0.06577052921056747, -0.04220335930585861, -0.0231320820748806, 0.019107535481452942, 0.012254927307367325, -0.028534403070807457, -0.0388314425945282, 0.003530543064698577, 0.010668676346540451, 0.06602432578802109, -0.010278911329805851, -0.021808695048093796, 0.000011250703209952917, -0.008932863362133503, -0.03745367005467415, -0.07686522603034973, 0.01610725373029709, 0.026449615135788918, 0.032667722553014755, 0.015291466377675533, 0.060041893273591995, -0.03440806642174721, 0.022298166528344154, -0.04336358979344368, -0.05112262815237045, -0.06780093163251877, -0.042493417859077454, 0.010587097145617008, -0.029205160215497017, -0.032486435025930405, 0.010614289902150631, -0.01927069202065468, -0.03228702023625374, -0.019288821145892143, 0.013215743005275726, -0.001312056789174676, -0.002934565767645836, 0.014502872712910175, -0.04949105530977249, -0.020757237449288368, -0.05344308540225029, 0.0020292692352086306, 0.004461899399757385, 0.0009166268864646554, 0.008502309210598469, 0.006014160346239805, 0.032450176775455475, 0.03759869933128357, 0.023567168042063713, -0.03406362235546112, 0.037091098725795746, -0.027102243155241013, 0.04615539312362671, 0.017466897144913673, -0.07033893465995789, -0.02461862750351429, 0.04144195839762688, -0.08694472163915634, -0.022842025384306908, -0.01658766157925129, -0.019252564758062363, -0.027827387675642967, 0.005406852345913649, -0.058809150010347366, 0.009426867589354515, 0.0077001191675662994, -0.020032092928886414, -0.002094985218718648, 0.009544703178107738, 0.00032376529998146, 0.019125664606690407, -0.0034738911781460047, 0.035459525883197784, -0.019941451027989388, -0.00518024479970336, 0.09354352951049805, 0.03147123381495476, 0.0003693700418807566, 0.08310145884752274, 0.031108662486076355, -0.024818040430545807, 0.002442827681079507, 0.00522556621581316, 0.0064855036325752735, -0.04644545167684555, -0.012164284475147724, 0.013968079350888729, 0.02699347212910652, 0.031743161380290985, -0.017602862790226936, -0.016596725210547447, 0.012209606356918812, -0.013460478745400906, -0.04448756203055382, -0.0013109237188473344, -0.010306104086339474, -0.04597410559654236, -0.009925403632223606, 0.019288821145892143, -0.00024501924053765833, -0.049962397664785385, 0.012100834399461746, -0.04514019191265106, 0.04006418585777283, -0.037018582224845886, -0.036656010895967484, 0.007500704377889633, 0.03504256531596184, 0.06638690084218979, -0.05656120553612709, -0.0048493980430066586, -0.018871864303946495, 0.004958169534802437, -0.003838729113340378, 0.02960398979485035, 0.02026776410639286, -0.012662820518016815, 0.007228775881230831, 0.011112825945019722, 0.012835042551159859, 0.028353117406368256, 0.015944095328450203, 0.019306950271129608, 0.04213084653019905, -0.016977425664663315, 0.036837298423051834, 0.018092334270477295, -0.025760728865861893, -0.038142554461956024, 0.01896250620484352, 0.015681231394410133, -0.03540514037013054, -0.03872267156839371, -0.0233133677393198, -0.06054949387907982, 0.000022572219677385874, -0.035568296909332275, -0.00786327663809061, -0.017358126118779182, -0.019651392474770546, -0.0027555457782000303, -0.021137937903404236, -0.008615612983703613, -0.05540097504854202, 0.029223289340734482, -0.05757640674710274, -0.033012162894010544, 0.042602188885211945, 0.00040874307160265744, -0.010777447372674942, -0.038432613015174866, 0.04767819494009018, -0.03810629993677139, 0.0014423560351133347, 0.03565894067287445, -0.05308051407337189, -0.10862652212381363, -0.06221732497215271, 0.002488149097189307, -0.013134164735674858, -0.04147821664810181, 0.007591347675770521, 0.04325481876730919, 0.06649567186832428, -0.06896115839481354, -0.019615136086940765, 0.04046301543712616, 0.03016597591340542, -0.032377663999795914, -0.02978527545928955, -0.08484181016683578, -0.006399392616003752, -0.0018649788107722998, -0.015826260671019554, -0.01662391796708107, 0.06450152397155762, 0.054277002811431885, -0.03745367005467415, -0.026975343003869057, 0.09057044237852097, -0.01646982505917549, -0.005112262908369303, -0.01009762566536665, -0.012835042551159859, -0.0022943997755646706, -0.05445828661322594, -0.0062588960863649845, 0.00738286878913641, -0.046953052282333374, 0.044088732451200485, -0.0013800390297546983, 0.034607481211423874, 0.01673268899321556, -0.020847879350185394, -0.030727962031960487, -0.03134433552622795, -0.0033039357513189316, -0.012490599416196346, -0.015935031697154045, 0.008642805740237236, 0.06392141431570053, 0.020594079047441483, -0.01662391796708107, -0.0348794087767601, 0.041369445621967316, 0.017122454941272736, 0.0022082889918237925, 0.002540268935263157, 0.006326878443360329, 0.01956075057387352, 0.0013279193080961704, 0.02625020034611225, 0.02231629565358162, 0.013578315265476704, -0.012128027155995369, -0.005851002875715494, 0.04804076626896858, -0.08404415100812912, 0.035314496606588364, 0.04216710478067398, -0.031670648604631424, 0.045393992215394974, 0.0027555457782000303, -0.03090924769639969, 0.008298362605273724, -0.014711352065205574, -0.04775070771574974, -0.024908684194087982, -0.01676894724369049, 0.00030053805676288903, -0.048330824822187424, -0.07360208034515381, -0.0002298648760188371, -0.05184777081012726, -0.004835801664739847, -0.023857226595282555, 0.011466333642601967, 0.00629515340551734, 0.0201952513307333, -0.0023567168973386288, -0.02875194512307644, -0.004310072399675846, 0.03759869933128357, -0.0659155547618866, 0.02079349383711815, -0.004804076626896858, 0.010070431977510452, -0.005733166821300983, -0.048367083072662354, -0.06214481219649315, -0.00825757347047329, 0.009861953556537628, 0.044124990701675415, 0.03696419671177864, 0.041333187371492386, -0.0014797463081777096, 0.01736718975007534, -0.009209324605762959, -0.013288257643580437, 0.048693396151065826, 0.03395485132932663, 0.01952449232339859, 0.013886501081287861, -0.025488799437880516, 0.0376349538564682, -0.010922476649284363, -0.012109898962080479, 0.030582932755351067, -0.035713326185941696, 0.02072097919881344, -0.031888190656900406, 0.004763287492096424, -0.009499382227659225, 0.02309582568705082, 0.01565403863787651, 0.008873945102095604, 0.02168179489672184, -0.014566322788596153, -0.019433850422501564, -0.041260674595832825, -0.056815005838871, 0.010478326119482517, -0.03540514037013054, -0.009762246161699295, 0.008728916756808758, 0.017711633816361427, -0.041188158094882965, -0.02953147515654564, -0.004799544345587492, -0.0313987210392952, -0.006444714032113552, 0.04053552821278572, -0.05696003511548042, 0.01837332732975483, 0.0032291552051901817, 0.033012162894010544, 0.027047857642173767, -0.029440831393003464, -0.004301008302718401, -0.0066531929187476635, -0.002934565767645836, -0.016451695933938026, -0.016859589144587517, 0.002775940578430891, 0.03730864077806473, 0.09869205206632614, -0.048403337597846985, 0.010813704691827297, -0.02320459671318531, -0.008493244647979736, -0.0005461238324642181, -0.008846752345561981, -0.03303029388189316, 0.04064430296421051, -0.013623636215925217, 0.05518343299627304, -0.006367667578160763, -0.05184777081012726, 0.04891093820333481, 0.011647620238363743, -0.04927350953221321, -0.00404494209215045, -0.019959578290581703, -0.04970859736204147, -0.028552530333399773, -0.048729654401540756, -0.004144649021327496, -0.015499945729970932, -0.008203187957406044, -0.014548194594681263, 0.06087581068277359, -0.011366626247763634, 0.014638837426900864, -0.04724310711026192, 0.003022942692041397, 0.0011353030567988753, 0.04049927368760109, -0.010686804540455341, 0.009562832303345203, 0.027682358399033546, -0.030927376821637154, 0.010614289902150631, 0.03362853825092316, -0.016506081447005272, 0.04078932851552963, 0.014294394291937351, 0.045611534267663956, -0.024002254009246826, -0.04448756203055382, 0.027754873037338257, 0.032812751829624176, -0.024673013016581535, 0.04452382028102875, 0.02440108358860016, 0.00041299196891486645, 0.02818995900452137, -0.010487389750778675, 0.006734771654009819, -0.03640221059322357, 0.01422187965363264, 0.01004323922097683, 0.029295803979039192, 0.039846643805503845, 0.003777545178309083, -0.039810385555028915, 0.016750818118453026, 0.05355186015367508, 0.030437905341386795, -0.026485871523618698, -0.04042675718665123, 0.02971276082098484, 0.0010344627080485225, -0.01446661539375782, 0.007985644042491913, 0.02956773154437542, 0.014276265166699886, -0.02157302387058735, -0.04329107701778412, 0.006666789297014475, -0.004359926097095013, 0.007265032734721899, -0.014892637729644775, 0.036275312304496765, 0.015055795200169086, 0.01043300423771143, 0.017276547849178314, -0.0060322885401546955, 0.019850807264447212, -0.017793212085962296, -0.012354634702205658, -0.012164284475147724, 0.06490035355091095, -0.026522129774093628, 0.0004747424682136625, -0.020811622962355614, -0.04321856051683426, -0.03130807727575302, 0.01372334361076355, 0.044124990701675415, -0.012989135459065437, 0.02193559519946575, -0.03317532315850258, -0.025162484496831894, 0.008624677546322346, -0.008470584638416767, -0.031634390354156494, 0.01331545040011406, 0.004627322778105736, 0.025343770161271095, 0.013759600929915905, 0.018545549362897873, -0.04028172791004181, 0.049853626638650894, -0.027265401557087898, 0.025615699589252472, 0.022805767133831978, -0.03723612800240517, -0.035387009382247925, -0.012916620820760727, 0.009744117967784405, -0.009490317665040493, -0.000244452734477818, -0.005121327005326748, 0.030075332149863243, -0.05061502754688263, -0.008783302269876003, -0.006163720972836018, 0.0034512304700911045, -0.01043300423771143, -0.006494567729532719, 0.026649029925465584, 0.018056076020002365, -0.05656120553612709, 0.021174194291234016, 0.01800169050693512, 0.01718590408563614, 0.034861281514167786, 0.012472470290958881, -0.007559622637927532, -0.00038778188172727823, 0.049962397664785385, -0.013170421123504639, 0.0004246055905241519, 0.022787639871239662, -0.03912150114774704, 0.0059280493296682835, -0.027609843760728836, -0.0658067837357521, -0.005805681459605694, 0.003043337259441614, -0.03455309569835663, -0.027918029576539993, -0.02610517106950283, -0.011783584021031857, 0.006802754011005163, -0.004536679945886135, 0.00810801237821579, 0.01340609323233366, 0.018137656152248383, -0.045393992215394974, 0.0024179008323699236, -0.011067504994571209, -0.02985779009759426, 0.0203765369951725, -0.015182695351541042, 0.08346403390169144, -0.027827387675642967, 0.006141060497611761, 0.045539021492004395, 0.07701025903224945, -0.034009236842393875, -0.03090924769639969, -0.023530911654233932, 0.008330088108778, 0.008642805740237236, 0.020847879350185394, 0.01478386577218771, 0.0276279728859663, -0.004831269383430481, -0.01814671978354454, -0.05623488873243332, -0.029132645577192307, -0.026014529168605804, -0.0478232242166996, -0.024382954463362694, 0.0049445731565356255, 0.004495890811085701, 0.012427149340510368, -0.0005752994911745191, 0.03168877586722374, 0.0036869023460894823, -0.013587378896772861, -0.03689168393611908, 0.025978270918130875, -0.03136246278882027, 0.0009069960797205567, 0.020503437146544456, 0.019107535481452942, -0.013859308324754238, -0.04637293517589569, -0.0009942399337887764, 0.008212251588702202, 0.024219797924160957, 0.055763546377420425, 0.02327711135149002, -0.017684441059827805, -0.020920393988490105, 0.0028099315240979195, -0.01658766157925129, 0.007464447524398565, -0.008543098345398903, -0.001783400191925466, -0.021355479955673218, 0.00457520317286253, 0.0118651632219553, -0.009154938161373138, -0.041151903569698334, -0.07555996626615524, -0.007024829275906086, 0.02197185344994068, -0.01365082897245884, 0.049781110137701035, 0.006476439069956541, 0.00970786064863205, 0.035387009382247925, -0.016388246789574623, 0.05221034213900566, -0.005628927610814571, 0.038360100239515305, -0.04017295688390732, 0.000015605814041919075, 0.018065141513943672, 0.042493417859077454, 0.006585210561752319, 0.006558017805218697, -0.01651514694094658, -0.016632981598377228, 0.0070792147889733315, -0.0031249159947037697, -0.02246132493019104, -0.022098751738667488, 0.0011217065621167421, -0.0017947305459529161, 0.03480689600110054, 0.02960398979485035, 0.03930278494954109, 0.001803794875741005, 0.01844584196805954, 0.006263428367674351, 0.0009438197594136, 0.061745982617139816, -0.01788385584950447, -0.01569029502570629, 0.058700378984212875, -0.026449615135788918, -0.03962910175323486, -0.004373522475361824, -0.0013539791107177734, 0.0003724858979694545, 0.008434327319264412, -0.026413356885313988, -0.012345570139586926, -0.013451415114104748, -0.017412511631846428, 0.03886770084500313, -0.030401647090911865, 0.06189101189374924, 0.025615699589252472, 0.009041635319590569, 0.022298166528344154, -0.028461888432502747, -0.0302022323012352, -0.03654723986983299, -0.005361530929803848, 0.014303458854556084, 0.032413922250270844, -0.027283528819680214, 0.031181177124381065, -0.0061546568758785725, 0.003893114859238267, -0.031634390354156494, -0.048294566571712494, -0.05344308540225029, -0.030963633209466934, 0.032522693276405334, -0.048620883375406265, 0.02298705279827118, 0.015228016301989555, 0.00525275943800807, -0.0006441315053962171, -0.02362155355513096, -0.0028643175028264523, 0.03529636561870575, 0.0023057302460074425, -0.012735335156321526, 0.02543441392481327, -0.033012162894010544, 0.03161626309156418, -0.005157584324479103, 0.0008820692892186344, 0.009979789145290852, -0.01752128265798092, -0.023077696561813354, -0.023820968344807625, 0.008253040723502636, 0.008520437404513359, -0.0502161979675293, -0.012653756886720657, -0.010306104086339474, -0.014684159308671951, 0.005402320064604282, 0.007727311924099922, -0.027899902313947678, 0.022678866982460022, 0.04637293517589569, -0.004346329718828201, 0.02818995900452137, 0.004525349475443363, 0.024092897772789, 0.0239116121083498, 0.026304585859179497, -0.01269907783716917, 0.003906711470335722, -0.02978527545928955, 0.013587378896772861, -0.030891118571162224, -0.019125664606690407, 0.03136246278882027, 0.031924448907375336, -0.024709269404411316, 0.019923321902751923, -0.028552530333399773, 0.02402038313448429, -0.038505129516124725, -0.03915775567293167, 0.004717966075986624, 0.01859993487596512, 0.026467742398381233, -0.008883009664714336, 0.013369835913181305, 0.015817195177078247, -0.06203603744506836, 0.036057766526937485, -0.015363981015980244, -0.017077133059501648, -0.0023635150864720345, 0.006988571956753731, -0.011094697751104832, 0.01171107031404972, -0.013514865189790726, 0.013678021728992462, -0.006009628064930439, 0.014285329729318619, 0.017530348151922226, -0.004690772853791714, -0.021772438660264015, -0.022370681166648865, -0.00014318754256237298, 0.018173912540078163, -0.04920099675655365, -0.01550900936126709, 0.00019913124560844153, 0.03194257616996765, 0.03216012194752693, -0.000805589254014194, 0.05677874758839607, -0.00851590558886528, -0.0011466334108263254, 0.0025357366539537907, 0.019325077533721924, -0.017077133059501648, 0.008389005437493324, 0.02681218646466732, 0.04923725500702858, 0.03335660696029663, 0.061637211591005325, -0.015146438032388687, 0.0010423939675092697, -0.012726270593702793, -0.03658349812030792, 0.014321587048470974, -0.05054251104593277, -0.017566604539752007, -0.02376658283174038, 0.023476526141166687, 0.026232071220874786, -0.012191477231681347, -0.0151917589828372, 0.02224378101527691, 0.042783476412296295, -0.0022649408783763647, 0.025452541187405586, 0.03303029388189316, -0.03203321993350983, -0.031924448907375336, -0.02090226486325264, 0.0497448556125164, 0.036239054054021835, -0.004638653248548508, 0.026159556582570076, -0.004595597740262747, -0.03143497556447983, 0.033338479697704315, 0.012889428064227104, -0.006902460940182209, -0.0203765369951725, -0.007836083881556988, -0.02164553850889206, 0.007872340269386768, 0.0005447075236588717, 0.038215070962905884, 0.004477762151509523, -0.029259545728564262, 0.008987248875200748, -0.008996313437819481, 0.0012871299404650927, -0.0403905026614666 ]
Deep learning-based adversarial malware detectors have yielded promising results in detecting never-before-seen malware executables without relying on expensive dynamic behavior analysis and sandbox. Despite their abilities, these detectors have been shown to be vulnerable to adversarial malware variants - meticulously modified, functionality-preserving versions of original malware executables generated by machine learning. Due to the nature of these adversarial modifications, these adversarial methods often use a \textit{single view} of malware executables (i.e., the binary/hexadecimal view) to generate adversarial malware variants. This provides an opportunity for the defenders (i.e., malware detectors) to detect the adversarial variants by utilizing more than one view of a malware file (e.g., source code view in addition to the binary view). The rationale behind this idea is that while the adversary focuses on the binary view, certain characteristics of the malware file in the source code view remain untouched which leads to the detection of the adversarial malware variants. To capitalize on this opportunity, we propose Adversarially Robust Multiview Malware Defense (ARMD), a novel multi-view learning framework to improve the robustness of DL-based malware detectors against adversarial variants. Our experiments on three renowned open-source deep learning-based malware detectors across six common malware categories show that ARMD is able to improve the adversarial robustness by up to seven times on these malware detectors.
[ -0.020956438034772873, 0.0025382169988006353, -0.02252577804028988, -0.03686036542057991, 0.05132891982793808, 0.06717543303966522, -0.04903232306241989, 0.017157485708594322, 0.00399751216173172, 0.041147343814373016, 0.0028563912492245436, -0.021683692932128906, 0.028554342687129974, -0.03881246969103813, -0.04987441003322601, 0.008990216068923473, -0.01783689484000206, -0.02706155553460121, -0.03663070499897003, -0.06541470438241959, 0.05733834579586983, -0.011607378721237183, -0.03710916265845299, 0.05197962000966072, -0.008870601654052734, 0.05297481268644333, 0.012726969085633755, -0.0478840246796608, -0.02945384383201599, 0.047156769782304764, 0.017970863729715347, 0.021052129566669464, 0.00505729578435421, -0.0076074739918112755, -0.04424775019288063, 0.014487693086266518, 0.01882251724600792, 0.05707040801644325, -0.025683598592877388, 0.04390325769782066, 0.030640417709946632, -0.05397000536322594, -0.03835315257310867, 0.010191144421696663, -0.004801320843398571, 0.013588192872703075, -0.0149565814062953, -0.04451568424701691, -0.022793713957071304, 0.005885026883333921, -0.02784622646868229, 0.008727064356207848, -0.04057319462299347, -0.03793210908770561, 0.03531016409397125, 0.03848712146282196, 0.04547259956598282, -0.0046171145513653755, 0.037798140197992325, -0.012908782809972763, 0.0037176148034632206, 0.0022463579662144184, 0.061816707253456116, 0.016114449128508568, -0.008329944685101509, -0.048343345522880554, 0.041721493005752563, -0.03875505551695824, 0.012583431787788868, 0.013530777767300606, -0.06675438582897186, -0.0027822302654385567, -0.012707831338047981, -0.00712423212826252, -0.005004665348678827, 0.05592210963368416, 0.028535204008221626, 0.02187507599592209, -0.033453747630119324, -0.04417119547724724, -0.00363149237819016, 0.05775938928127289, -0.010372958146035671, 0.00028094425215385854, 0.08061052113771439, -0.03555896133184433, -0.015033134259283543, -0.054850365966558456, -0.025032896548509598, -0.054658982902765274, -0.014870459213852882, 0.032898735255002975, 0.06579747051000595, -0.028994522988796234, -0.026162056252360344, 0.00769359664991498, -0.08780651539564133, -0.0179612934589386, -0.052362386137247086, -0.030429895967245102, -0.023214757442474365, -0.022028183564543724, 0.002380325924605131, 0.007358676288276911, -0.023616662248969078, -0.03402789682149887, -0.04642951488494873, 0.023023374378681183, -0.025530491024255753, 0.15157532691955566, -0.04972130060195923, 0.007521351799368858, -0.04589364305138588, 0.05098443105816841, -0.02359752357006073, 0.009971054270863533, -0.06970168650150299, -0.06135739013552666, -0.03437238559126854, -0.03567378968000412, 0.0029520827811211348, 0.04646779224276543, -0.0014054689090698957, -0.02220042794942856, -0.04359704628586769, 0.04918542876839638, 0.027922779321670532, 0.03242027759552002, -0.008009378798305988, 0.04015215113759041, -0.03831487521529198, -0.020841607823967934, 0.033109258860349655, -0.060936346650123596, 0.02329131029546261, 0.035712067037820816, 0.004095596261322498, 0.04233391955494881, 0.023616662248969078, 0.04057319462299347, 0.0014772374415770173, -0.03205665200948715, -0.0587545782327652, -0.010660032741725445, 0.0072486307471990585, -0.01147341076284647, 0.04581708833575249, 0.06778785586357117, 0.006650559138506651, 0.02589411847293377, -0.014698213897645473, 0.03923351317644119, 0.01675558090209961, 0.027712257578969002, 0.04015215113759041, -0.007449583150446415, 0.037702448666095734, 0.0007314418908208609, 0.03502308949828148, -0.03307098150253296, 0.08972034603357315, 0.0015669482527300715, 0.024707544595003128, 0.055080026388168335, 0.04730987548828125, -0.011645655147731304, 0.04608502611517906, -0.021473171189427376, -0.0336834080517292, 0.05450587719678879, -0.034640323370695114, 0.01825793832540512, 0.025626182556152344, 0.043864984065294266, -0.03287959843873978, 0.028650034219026566, 0.03287959843873978, -0.018028277903795242, -0.03454463183879852, -0.013856128789484501, -0.035826895385980606, -0.02032487466931343, -0.013128873892128468, -0.022985097020864487, 0.024956341832876205, 0.01092796865850687, 0.042563579976558685, -0.005841965787112713, -0.007593120448291302, 0.009363412857055664, -0.0073730298317968845, -0.03467859700322151, 0.039539728313684464, -0.01191359106451273, 0.04838162288069725, 0.0056553673930466175, -0.06269706785678864, -0.0032248033676296473, -0.016822565346956253, 0.020076075568795204, 0.0033994405530393124, -0.032803043723106384, 0.019865555688738823, 0.03864022716879845, 0.022678885608911514, -0.012200665660202503, 0.014860889874398708, 0.011320304125547409, 0.016726873815059662, -0.07264898717403412, -0.0069280643947422504, -0.016497213393449783, -0.07084998488426208, 0.000013428581951302476, 0.002003540750592947, 0.0005430492456071079, -0.02731035277247429, -0.01695653423666954, -0.028860555961728096, 0.021377481520175934, -0.008722280152142048, -0.021894214674830437, -0.012813091278076172, -0.012325065210461617, -0.04554915428161621, -0.01478433609008789, -0.013750867918133736, 0.035731203854084015, -0.002865960355848074, -0.0065740058198571205, -0.028745725750923157, 0.00968397967517376, -0.00541135435923934, -0.013291548937559128, 0.06441951543092728, 0.006229516584426165, 0.06702232360839844, 0.012143251486122608, -0.006196024361997843, -0.0007780914893373847, -0.014746059663593769, -0.022219566628336906, -0.03653501346707344, -0.07689768821001053, 0.05282170698046684, 0.016612043604254723, -0.017100071534514427, 0.036477599292993546, 0.02436305582523346, 0.06763475388288498, 0.04742470756173134, 0.0068132346495985985, -0.018344059586524963, -0.023961151018738747, -0.051290642470121384, -0.03217148035764694, -0.004315686412155628, -0.03465946018695831, 0.03242027759552002, -0.04493672773241997, 0.010229420848190784, 0.012114543467760086, -0.038984715938568115, 0.035195332020521164, -0.005679290276020765, 0.000702136370819062, 0.0511375367641449, 0.028133301064372063, 0.01990383118391037, 0.006315638776868582, 0.009932777844369411, -0.0760938823223114, -0.05990287661552429, 0.03676467388868332, 0.04547259956598282, -0.0358651727437973, 0.03961627930402756, 0.021339204162359238, 0.023329587653279305, 0.00024326573475264013, 0.03565465286374092, -0.01091840025037527, 0.04118562117218971, -0.03439152613282204, 0.0233870018273592, 0.00139231130015105, -0.018985193222761154, 0.017875172197818756, -0.06292673200368881, 0.007942394353449345, -0.015722112730145454, 0.008750987239181995, 0.0033994405530393124, -0.028803139925003052, 0.013492501340806484, -0.029511258006095886, 0.02685103379189968, -0.0003851582878269255, -0.03358771651983261, -0.048343345522880554, -0.05477381497621536, -0.017970863729715347, 0.003282218473032117, -0.0004407789674587548, -0.03228631243109703, 0.0288222786039114, -0.007191216107457876, 0.1283797174692154, -0.01283222995698452, -0.03196096047759056, -0.039080407470464706, -0.005038157571107149, -0.042678408324718475, -0.028343820944428444, -0.023520970717072487, 0.05167340859770775, -0.00684672687202692, -0.024286502972245216, 0.030200237408280373, 0.022755438461899757, 0.00907633826136589, -0.00858352705836296, -0.03087007626891136, 0.0271955244243145, 0.0478074736893177, -0.024937205016613007, -0.0163058303296566, 0.0201143529266119, -0.047233324497938156, -0.038334015756845474, -0.03709002584218979, 0.023865459486842155, -0.04091768339276314, 0.007865841500461102, -0.027214661240577698, -0.0072534154169261456, -0.02390373684465885, 0.08841894567012787, 0.030468173325061798, -0.015635991469025612, -0.04175977036356926, -0.039845939725637436, -0.0445539616048336, 0.0021147821098566055, -0.02706155553460121, -0.06028564274311066, -0.013224565424025059, 0.004652998875826597, -0.019980384036898613, 0.026927586644887924, 0.0010250951163470745, -0.04210425913333893, 0.018860794603824615, 0.024075981229543686, -0.024439608678221703, -0.015377623960375786, -0.009243798442184925, 0.015951773151755333, -0.027272077277302742, 0.011645655147731304, -0.029109353199601173, -0.03988421708345413, -0.0019485180964693427, -0.03021937422454357, 0.003260687692090869, -0.01576995849609375, 0.0011626516934484243, -0.026831895112991333, -0.01554986834526062, 0.027214661240577698, 0.015348915942013264, 0.04505155608057976, -0.012143251486122608, 0.025702735409140587, -0.02415253408253193, 0.015167102217674255, 0.06177842989563942, -0.002545393770560622, -0.022334394976496696, 0.03458290547132492, -0.020611949265003204, 0.07050549238920212, -0.05010406672954559, -0.023406140506267548, -0.011655224487185478, -0.001947321929037571, 0.044630516320466995, -0.011703070253133774, 0.06143394112586975, 0.02294682152569294, 0.008258176036179066, -0.00720556965097785, -0.043558768928050995, 0.018774671480059624, 0.0467357262969017, -0.027348630130290985, -0.0005032774643041193, 0.00012447370681911707, 0.0337025448679924, -0.042793236672878265, 0.0018013924127444625, 0.0337025448679924, 0.013473362661898136, 0.0015155141009017825, -0.028305545449256897, -0.007109878119081259, 0.0499892383813858, -0.06717543303966522, 0.008808402344584465, -0.006081194616854191, 0.02229611948132515, 0.022793713957071304, -0.009932777844369411, 0.02489892765879631, 0.058792855590581894, 0.01061218697577715, 0.02750173583626747, 0.009942346252501011, -0.042142536491155624, -0.02315734326839447, 0.018248368054628372, -0.005597952753305435, 0.06005598232150078, -0.01752111315727234, 0.007329968735575676, 0.036707259714603424, 0.03645846247673035, -0.02348269335925579, 0.006789311766624451, -0.0684385597705841, 0.08734720200300217, -0.014171910472214222, 0.025281693786382675, -0.04623813182115555, -0.020401427522301674, -0.032248035073280334, 0.031157150864601135, -0.0111384904012084, -0.02893710881471634, -0.020592810586094856, -0.005674505606293678, 0.013004474341869354, 0.02359752357006073, -0.004109949804842472, -0.0662950724363327, -0.07976843416690826, -0.0054209232330322266, 0.005263032391667366, -0.016908688470721245, -0.01827707700431347, -0.04141528159379959, 0.05722351744771004, -0.06797923892736435, -0.0019772255327552557, 0.06361570954322815, 0.004229564219713211, -0.028209853917360306, -0.025492215529084206, 0.01904260739684105, -0.0006871845689602196, 0.019214853644371033, 0.07961532473564148, 0.01391354389488697, 0.0244778860360384, -0.015167102217674255, 0.0641515776515007, -0.0718451738357544, -0.0685533881187439, 0.0048563433811068535, -0.01641109213232994, -0.0014796297764405608, -0.027673982083797455, 0.010076315142214298, -0.015626421198248863, 0.032343726605176926, 0.005463984329253435, 0.01643979921936989, -0.06020909175276756, 0.0266596507281065, -0.01935838907957077, 0.07234277576208115, -0.014698213897645473, -0.009152892045676708, -0.029300736263394356, 0.0026171624194830656, -0.025492215529084206, 0.019530635327100754, -0.021396618336439133, 0.004277409985661507, -0.04110906645655632, -0.00771751906722784, -0.011923160403966904, -0.020056938752532005, 0.010420803911983967, -0.005258247721940279, -0.026831895112991333, -0.01478433609008789, 0.031807854771614075, 0.07636181265115738, 0.04765436425805092, -0.004590799566358328, -0.03837228938937187, 0.01484175119549036, -0.0012134878197684884, 0.005841965787112713, 0.005707997828722, -0.025798426941037178, 0.00371043779887259, 0.02271716110408306, 0.0015573791461065412, 0.004667352885007858, -0.0163058303296566, -0.005975934211164713, 0.0006501041352748871, 0.009018924087285995, -0.04470706731081009, 0.018411044031381607, 0.008387359790503979, 0.02598981000483036, 0.019214853644371033, 0.043864984065294266, 0.0004542355891317129, -0.03892730176448822, 0.037779003381729126, 0.014918304048478603, 0.006090763956308365, 0.040611471980810165, -0.027252938598394394, 0.003026243532076478, -0.030716970562934875, -0.024286502972245216, 0.03226717188954353, -0.028114162385463715, -0.0435204915702343, 0.009253367781639099, -0.0347742885351181, 0.024420469999313354, 0.027980193495750427, -0.009052415378391743, 0.016812996938824654, -0.02183680050075054, 0.01456424593925476, 0.003521447069942951, -0.007660104427486658, -0.04417119547724724, 0.03651587665081024, 0.026353439316153526, -0.024229086935520172, -0.0035142702981829643, 0.051405470818281174, -0.03460204601287842, -0.010325112380087376, 0.0033874791115522385, -0.02838209830224514, -0.052783429622650146, -0.02631516195833683, 0.021607140079140663, 0.04221908748149872, -0.023616662248969078, -0.02956867218017578, 0.0024903712328523397, 0.0026458699721843004, 0.008449559099972248, 0.025300832465291023, 0.012822660617530346, -0.024075981229543686, -0.0011632497189566493, 0.03764503449201584, 0.0326499380171299, 0.0008295256993733346, -0.007928040809929371, -0.06078324094414711, -0.004686491098254919, -0.014592953026294708, -0.01098538376390934, 0.004810890182852745, 0.019731586799025536, -0.04260185360908508, 0.021817661821842194, -0.009100261144340038, -0.03303270414471626, -0.024382194504141808, -0.009430397301912308, 0.004889835603535175, 0.007650535088032484, -0.021492309868335724, -0.033319778740406036, -0.025798426941037178, -0.041912876069545746, -0.04064974933862686, 0.0087031414732337, 0.015616852790117264, -0.02141575701534748, 0.018650272861123085, -0.002044209511950612, 0.028401236981153488, 0.0424487479031086, -0.027348630130290985, 0.04260185360908508, -0.006396976765245199, -0.02426736429333687, -0.004385062959045172, 0.044745344668626785, 0.04665917530655861, -0.02099471539258957, -0.013081028126180172, 0.011837038211524487, 0.018851224333047867, -0.015731683000922203, 0.005200833082199097, 0.020363150164484978, -0.012152819894254208, 0.02480323612689972, -0.009396905079483986, -0.0015023564919829369, -0.03657329082489014, 0.031922683119773865, -0.021798523142933846, 0.0004060907813254744, 0.020152630284428596, 0.04367360100150108, -0.020726777613162994, 0.02738690748810768, 0.013961389660835266, 0.009478243067860603, -0.020056938752532005, 0.0006345542497001588, 0.005334801040589809, -0.016583336517214775, -0.051367197185754776, -0.02132006548345089, 0.0358651727437973, 0.00199756002984941, -0.015521161258220673, -0.03946317359805107, 0.012506878934800625, 0.05446759983897209, 0.01999952271580696, -0.010420803911983967, 0.009980623610317707, -0.014162342064082623, 0.012526016682386398, -0.03980766236782074, 0.022812852635979652, -0.026123778894543648, 0.00836822111159563, -0.010372958146035671, -0.009540442377328873, 0.028841417282819748, 0.005310878157615662, -0.00720556965097785, 0.01104279886931181, -0.05205617472529411, 0.03927179053425789, -0.02045884169638157, 0.004952034913003445, 0.00499988067895174, 0.00016387169307563454, -0.005521399434655905, -0.0004715796676464379, -0.002801368711516261, 0.019827278330922127, -0.004440085496753454, -0.01249730959534645, 0.022583194077014923, -0.04443913325667381, 0.016688596457242966, 0.03450635448098183, 0.001319346483796835, 0.07058204710483551, 0.0074974289163947105, -0.05787421762943268, -0.0016518745105713606, 0.04979785531759262, -0.010870554484426975, -0.009884932078421116, 0.06082151457667351, 0.03351116180419922, 0.023138204589486122, -0.03309011831879616, 0.0030525587499141693, 0.03054472617805004, 0.000559197214897722, 0.019961247220635414, -0.03841056674718857, -0.014975719153881073, 0.0023839145433157682, 0.005942441988736391, -0.010746154934167862, -0.040496643632650375, -0.04057319462299347, -0.039654556661844254, 0.016946963965892792, -0.008559604175388813, 0.01456424593925476, 0.010535634122788906, -0.035635512322187424, -0.034085310995578766, -0.0026865387335419655, -0.027654843404889107, -0.015109687112271786, -0.03226717188954353, -0.049300260841846466, 0.01310973521322012, 0.012736538425087929, -0.007703165523707867, 0.013463793322443962, 0.006774958223104477, 0.012449463829398155, 0.0233870018273592, 0.010870554484426975, 0.05427621677517891, 0.02055453322827816, 0.026449130848050117, 0.024669267237186432, -0.0013779575238004327, 0.04156838729977608, 0.005545322317630053, -0.02001866139471531, 0.029530396685004234, 0.08512715995311737, 0.0500275157392025, -0.029434705153107643, -0.07341451942920685, -0.03798952326178551, -0.005617090966552496, 0.0017643120372667909, -0.025855842977762222, -0.020937299355864525, -0.016257984563708305, 0.05201789736747742, -0.013176719658076763, -0.023846320807933807, 0.0033946558833122253, -0.06330949813127518, -0.046812281012535095, 0.03351116180419922, 0.04329083487391472, -0.0014927873853594065, 0.011875314638018608, 0.014602522365748882, 0.01828664541244507, 0.019597617909312248, -0.07444798201322556, -0.0033659483306109905, -0.0061194715090096, -0.001696131774224341, -0.009650487452745438, 0.013511639088392258, 0.018439751118421555, 0.02729121595621109, -0.022430086508393288, 0.03668811917304993, -0.04738643020391464, -0.01730102300643921, 0.009961484931409359, 0.06024736538529396, 0.033893927931785583, 0.012392048723995686, -0.02271716110408306, -0.03188440576195717, 0.05125236511230469, -0.007133801002055407, -0.017042655497789383, 0.0891079232096672, 0.0021662162616848946, -0.017243608832359314, -0.005827612243592739, 0.05320447310805321, 0.05668764188885689, 0.02403770387172699, -0.009554795920848846, -0.01890864036977291, -0.021454034373164177, -0.016765151172876358, -0.013626469299197197, 0.02970264106988907, -0.039539728313684464, 0.010296405293047428, 0.028535204008221626, -0.05075477063655853, -0.0026985001750290394, -0.06396019458770752, 0.030295928940176964, 0.004294156096875668, 0.007966317236423492, -0.02317648008465767, -0.006722327787429094, -0.017138347029685974, 0.010143298655748367, -0.027922779321670532, -0.020631086081266403, -0.026353439316153526, -0.02369321510195732, 0.026372576132416725, 0.008999785408377647, -0.0651850476861, 0.033530302345752716, -0.039654556661844254, -0.033664267510175705, 0.06556781381368637, 0.002248750301077962, -0.020860746502876282, 0.0056649367325007915, -0.02868831157684326, -0.04110906645655632, -0.023310448974370956, -0.013569054193794727, 0.017980432137846947, -0.023884598165750504, 0.018985193222761154, -0.012315495871007442, -0.014104926958680153, 0.03299442678689957, 0.024497022852301598, -0.007741441950201988, 0.00649745250120759, 0.015301070176064968, -0.0011626516934484243, -0.05611349269747734, 0.02001866139471531, -0.01539676170796156, -0.024630991742014885, 0.03707088530063629, -0.026028087362647057, -0.006100332830101252, 0.05772111192345619, -0.0032893952447921038, 0.04394153505563736, -0.0033133181277662516, 0.017635943368077278, 0.023980289697647095, -0.022238703444600105, 0.04068802669644356, -0.05948183685541153, 0.04558742791414261, -0.03316667303442955, 0.029530396685004234, -0.01082270871847868, 0.018832087516784668, -0.029664363712072372, 0.013827421702444553, -0.0016530706780031323, -0.050065793097019196, 0.009894500486552715, -0.028975386172533035, -0.0031554270535707474, 0.02861175872385502, 0.014315447770059109, -0.008908878080546856, 0.01249730959534645, -0.005023803561925888, 0.027233799919486046, 0.02641085349023342, -0.040955960750579834, -0.023865459486842155, -0.005870673339813948, 0.0037080454640090466, 0.0035884312819689512, -0.027004141360521317, 0.002447310136631131, 0.01005717646330595, -0.012698261998593807, -0.03402789682149887, 0.049759577959775925, 0.051175814121961594, 0.013865698128938675, -0.01599004864692688, -0.011741346679627895, -0.014458985067903996, 0.029185906052589417, -0.005009450018405914, -0.016468506306409836, 0.042908068746328354, 0.029721779748797417, -0.03282218426465988, 0.004303724970668554, -0.0011752111604437232, 0.016602475196123123, 0.005440061446279287, 0.03881246969103813, -0.013636038638651371, 0.05209445208311081, -0.030315065756440163, 0.04045836627483368, -0.04612330347299576, 0.004483146592974663, -0.027673982083797455, 0.005406569689512253, -0.022123875096440315, -0.030831800773739815, -0.015502022579312325, 0.010669602081179619, 0.007956747896969318, 0.023099927231669426, 0.004612330347299576, 0.01098538376390934, -0.03391306847333908, -0.024669267237186432, 0.01674601249396801, -0.003310925792902708, -0.06005598232150078, -0.03467859700322151, -0.013750867918133736, 0.0022164543624967337, 0.05814215540885925, 0.022219566628336906, -0.000873782963026315, 0.02717638574540615, -0.031367674469947815, 0.007506997790187597, -0.05393172800540924, 0.0014413532335311174, 0.029951438307762146, 0.042678408324718475, -0.01654505915939808, -0.0033587715588510036, -0.0043109022080898285, -0.002345637883991003, 0.021817661821842194, 0.03731968253850937, 0.02273629978299141, -0.021281789988279343, 0.0018946916097775102, -0.0337408222258091, 0.004002296831458807, -0.07969187945127487, 0.014143203385174274, 0.004554915241897106, 0.014516400173306465, -0.029817471280694008, -0.003088443074375391, -0.003504701191559434, 0.04118562117218971, 0.034869980067014694, 0.015856081619858742, -0.046161577105522156, 0.02292768284678459, -0.013224565424025059, -0.01848759688436985, -0.01947321929037571, 0.025090310722589493, -0.010296405293047428, -0.0024186025839298964, 0.02870745025575161, -0.06177842989563942, -0.00799502432346344, 0.021147821098566055, -0.04765436425805092, -0.011664793826639652, -0.03531016409397125, -0.04198943078517914, 0.010698309168219566, 0.013167150318622589, -0.03255424648523331, 0.02426736429333687, 0.0006991460104472935, -0.007286907639354467, 0.014966149814426899, 0.027769671753048897, 0.018430182710289955, 0.013176719658076763, -0.0005107533652335405, -0.00620080903172493, -0.0511375367641449, 0.02294682152569294, 0.03243941813707352, -0.011760485358536243, -0.04053491726517677, 0.016564197838306427, 0.00399272795766592, -0.04206598177552223, -0.03205665200948715, -0.0038970361929386854, 0.045931920409202576, 0.022870268672704697, 0.033759959042072296, -0.03163560852408409, -0.0028850985690951347, 0.0012547547230497003, 0.011961436830461025, -0.04064974933862686, 0.02348269335925579, 0.033645130693912506, -0.022334394976496696, -0.006951987277716398, 0.0532810278236866, 0.04294634237885475, -0.03906127065420151, -0.016152724623680115, -0.04646779224276543, -0.000982034020125866, -0.028860555961728096, 0.010937537997961044, -0.012047559954226017, -0.02761656604707241, -0.008822755888104439, -0.01567426696419716, -0.015530729666352272, 0.010459080338478088, -0.001723643159493804, 0.01430587936192751, 0.010975814424455166, 0.010621756315231323, 0.005736705381423235, 0.011549963615834713, 0.04003732278943062, -0.0013325040927156806, -0.051711685955524445, -0.00919595267623663, -0.03465946018695831, -0.018946915864944458, 0.008014163002371788, 0.02654482237994671, 0.02076505497097969, 0.020286597311496735, -0.035271886736154556, 0.013521208427846432, -0.035195332020521164, 0.0025190787855535746, 0.03282218426465988, -0.040075600147247314, 0.006741466000676155, -0.0222769808024168 ]
How can we recommend existing bundles to users accurately? How can we generate new tailored bundles for users? Recommending a bundle, or a group of various items, has attracted widespread attention in e-commerce owing to the increased satisfaction of both users and providers. Bundle matching and bundle generation are two representative tasks in bundle recommendation. The bundle matching task is to correctly match existing bundles to users while the bundle generation is to generate new bundles that users would prefer. Although many recent works have developed bundle recommendation models, they fail to achieve high accuracy since they do not handle heterogeneous data effectively and do not learn a method for customized bundle generation. In this paper, we propose BundleMage, an accurate approach for bundle matching and generation. BundleMage effectively mixes user preferences of items and bundles using an adaptive gate technique to achieve high accuracy for the bundle matching. BundleMage also generates a personalized bundle by learning a generation module that exploits a user preference and the characteristic of a given incomplete bundle to be completed. BundleMage further improves its performance using multi-task learning with partially shared parameters. Through extensive experiments, we show that BundleMage achieves up to 6.6% higher nDCG in bundle matching and 6.3x higher nDCG in bundle generation than the best competitors. We also provide qualitative analysis that BundleMage effectively generates bundles considering both the tastes of users and the characteristics of target bundles.
[ -0.027913186699151993, -0.0444650873541832, -0.025807900354266167, 0.006098069250583649, 0.030798880383372307, 0.0349913015961647, -0.04163384065032005, 0.017568247392773628, -0.043593935668468475, 0.06424751877784729, 0.02261367440223694, -0.0447554737329483, 0.024210786446928978, -0.028003931045532227, -0.019328702241182327, 0.021688073873519897, 0.028457656502723694, 0.002583966124802828, -0.033285293728113174, -0.045517731457948685, -0.06500977277755737, -0.04021821916103363, 0.023357784375548363, 0.02918361686170101, 0.026624606922268867, 0.002279970096424222, 0.005485540255904198, 0.004859399050474167, -0.035971350967884064, 0.04493696242570877, -0.0023525662254542112, 0.030199961736798286, -0.016225220635533333, 0.004065379500389099, -0.07226938009262085, 0.006379378959536552, -0.0058984300121665, 0.04174273833632469, 0.023357784375548363, 0.0029310660902410746, -0.0036388777662068605, -0.017368609085679054, -0.03923817351460457, 0.007699720095843077, 0.04424729943275452, -0.03767735883593559, -0.0013282811269164085, -0.012450224719941616, -0.03167003393173218, -0.009069970808923244, 0.0328134223818779, 0.015481110662221909, -0.005889355670660734, 0.0020678534638136625, -0.027042033150792122, 0.026152731850743294, -0.005490077193826437, -0.025499368086457253, 0.046062201261520386, 0.04192422702908516, 0.011270538903772831, 0.018502920866012573, -0.058476127684116364, 0.013094514608383179, 0.01768621616065502, -0.025263430550694466, 0.013648060150444508, 0.04286797717213631, 0.08755085617303848, -0.005880281329154968, -0.057750169187784195, 0.03034515492618084, 0.037278078496456146, 0.007713331840932369, -0.039310768246650696, -0.005562673322856426, 0.03589875251054764, 0.012722460553050041, 0.024483023211359978, 0.02936510741710663, 0.026679053902626038, 0.032287098467350006, 0.01058995071798563, 0.005326736252754927, 0.013430272229015827, -0.011388507671654224, 0.0011133287334814668, -0.07528211921453476, 0.027023885399103165, -0.04780450835824013, 0.016225220635533333, -0.00908358208835125, -0.021252498030662537, -0.023012952879071236, 0.0159983579069376, 0.10098112374544144, -0.0040608420968055725, 0.012395777739584446, -0.020054662600159645, 0.02787688933312893, -0.013457495719194412, -0.0028493953868746758, 0.03466461971402168, -0.009047284722328186, 0.015825942158699036, -0.020272450521588326, -0.004886622540652752, 0.0212887953966856, 0.02600754052400589, 0.01744120381772518, -0.02408374473452568, -0.007359426002949476, 0.006615316495299339, 0.046824462711811066, -0.017604544758796692, -0.01920165866613388, -0.053575895726680756, -0.0832676813006401, 0.010299566201865673, -0.024936748668551445, 0.01361176185309887, 0.049183834344148636, -0.027078332379460335, -0.05600786209106445, -0.05491892248392105, 0.08602633327245712, -0.03343048691749573, -0.00510441092774272, 0.0431220605969429, -0.0112523902207613, -0.06148886680603027, 0.02589864656329155, -0.05168839544057846, 0.013312303461134434, -0.0031170935835689306, 0.00861170794814825, 0.033448636531829834, -0.019891321659088135, -0.0307807307690382, -0.035190943628549576, -0.032232653349637985, -0.01616169884800911, 0.01147017814218998, -0.022069202736020088, -0.04696965217590332, 0.012350405566394329, 0.01996391825377941, 0.07216048985719681, -0.002100748475641012, 0.018802380189299583, -0.0349913015961647, 0.010453833267092705, -0.018094569444656372, 0.019274255260825157, 0.024392277002334595, 0.01225966028869152, -0.007949269376695156, -0.03230524808168411, 0.036298032850027084, -0.001975974068045616, 0.05310402065515518, 0.0314522460103035, 0.04018191993236542, 0.04911123588681221, 0.02655201032757759, 0.015717048197984695, 0.005399332381784916, 0.020345047116279602, -0.07324942946434021, 0.0414886511862278, -0.031688183546066284, 0.017268788069486618, -0.04678816348314285, -0.01346656959503889, 0.02212364971637726, -0.008670692332088947, 0.09807728230953217, -0.012640789151191711, -0.007422947324812412, 0.047877103090286255, -0.03927446901798248, 0.03237784281373024, 0.07862153649330139, 0.04377542808651924, 0.08631671965122223, 0.009972884319722652, 0.057859063148498535, -0.030653687193989754, 0.04925642907619476, -0.026461265981197357, 0.008443829603493214, 0.05230546370148659, 0.0639934316277504, -0.012550044804811478, 0.05038166791200638, -0.01767714135348797, -0.11259649693965912, 0.021143604069948196, 0.02205105498433113, 0.03956485539674759, -0.03341233730316162, -0.024428576231002808, 0.05691531300544739, -0.004457851871848106, 0.08246912807226181, 0.00024742214009165764, 0.028929531574249268, -0.03515464439988136, 0.0010220165131613612, -0.04010932520031929, 0.007327665109187365, -0.011089048348367214, -0.05118022486567497, 0.056661225855350494, 0.028929531574249268, -0.013158036395907402, -0.02205105498433113, 0.002804022980853915, -0.06177924945950508, 0.000024175056751118973, -0.012695237062871456, -0.0021585985086858273, 0.02820357121527195, -0.008684304542839527, 0.023720763623714447, -0.016579126939177513, 0.03072628378868103, 0.025063790380954742, -0.04061749577522278, -0.024265233427286148, 0.008062700740993023, 0.04007302597165108, -0.004221914801746607, -0.020871369168162346, -0.007441096473485231, -0.014827745966613293, -0.04399321600794792, -0.009918437339365482, -0.020345047116279602, 0.036406926810741425, 0.00306491507217288, -0.04290427267551422, -0.052486952394247055, -0.01346656959503889, 0.022904058918356895, -0.002774530788883567, -0.011279613710939884, -0.01012715045362711, 0.019510192796587944, 0.001660634996369481, -0.00839392002671957, -0.05186988785862923, -0.025045642629265785, 0.04352134093642235, -0.015853164717555046, 0.03486425802111626, 0.050998736172914505, -0.008870331570506096, 0.026297923177480698, -0.01341212261468172, -0.029238063842058182, 0.03261378034949303, -0.026951288804411888, 0.03620728850364685, -0.016969330608844757, 0.027749845758080482, 0.027350567281246185, 0.016933031380176544, -0.016415784135460854, 0.036788053810596466, 0.014092710800468922, -0.07372130453586578, -0.019020168110728264, -0.005730551667511463, -0.02782244049012661, -0.02283146232366562, 0.08718787133693695, -0.006701523903757334, 0.031071115285158157, 0.024537470191717148, 0.004432897083461285, 0.031470391899347305, 0.010181598365306854, 0.018257910385727882, -0.06744174659252167, -0.03595320135354996, -0.0030399600509554148, -0.031034817919135094, -0.028439508751034737, 0.000863779743667692, -0.005644343793392181, -0.037278078496456146, -0.04025451838970184, 0.014600883238017559, 0.08101720362901688, 0.023339634761214256, 0.011787786148488522, 0.0020360928028821945, 0.023357784375548363, 0.01284042838960886, -0.047550421208143234, 0.011406656354665756, 0.004364838358014822, 0.037278078496456146, -0.018375879153609276, -0.0011195674305781722, -0.005290437955409288, 0.06018213555216789, -0.02513638697564602, -0.01744120381772518, 0.01681506261229515, -0.017695290967822075, -0.015662601217627525, 0.01110719796270132, -0.01974612846970558, 0.04493696242570877, 0.05386627838015556, 0.027205374091863632, 0.04199682176113129, -0.04533624276518822, -0.04675186425447464, 0.007813150994479656, -0.07455615699291229, 0.0072641437873244286, -0.030871475115418434, -0.012423001229763031, 0.009863990359008312, 0.05263214558362961, -0.01985502429306507, 0.03804033622145653, -0.031688183546066284, -0.007023669313639402, 0.0008518694085069001, -0.016887659206986427, -0.00774962967261672, -0.0028062916826456785, 0.0055989716202020645, 0.05208767578005791, -0.013185259886085987, -0.014110859483480453, -0.02003651298582554, 0.01903831772506237, -0.025826049968600273, 0.029346957802772522, 0.007005520164966583, -0.0336301252245903, -0.02134324237704277, 0.007418410386890173, 0.026479413732886314, -0.047187440097332, 0.0010707919718697667, -0.02381150797009468, -0.04457398131489754, 0.002244806382805109, 0.028566550463438034, -0.019237956032156944, 0.053975172340869904, 0.03666101396083832, -0.004196960013359785, 0.027640951797366142, -0.049074940383434296, -0.0390566810965538, -0.039419662207365036, 0.01903831772506237, -0.05745978280901909, 0.01787678152322769, 0.00932859443128109, 0.006356692872941494, 0.00560804596170783, -0.00607538316398859, -0.033720873296260834, 0.017041925340890884, 0.03455572575330734, -0.008312249556183815, -0.06729654967784882, 0.05735088884830475, -0.008902092464268208, 0.014491989277303219, -0.05059945583343506, 0.0444650873541832, -0.003949679434299469, -0.04613479971885681, -0.014491989277303219, -0.033339742571115494, 0.057967957109212875, 0.035100195556879044, 0.010544578544795513, -0.003112556179985404, -0.012776907533407211, -0.004614387173205614, 0.025971241295337677, -0.015635376796126366, -0.018185313791036606, 0.0004769788356497884, -0.011706115677952766, -0.0094919353723526, 0.0038339796010404825, 0.019800575450062752, 0.02961919456720352, -0.005485540255904198, 0.04580811783671379, 0.030308855697512627, -0.04054490104317665, 0.03183337301015854, -0.04526364430785179, -0.00706450454890728, 0.0642838180065155, -0.014392169192433357, 0.049474216997623444, -0.0079991789534688, -0.03484611213207245, 0.01974612846970558, -0.020925816148519516, 0.015789642930030823, 0.025336025282740593, -0.006424751598387957, -0.03197856619954109, 0.0212887953966856, -0.0014814133755862713, -0.06522756069898605, -0.030490346252918243, 0.0009635993046686053, 0.013239706866443157, -0.00568064209073782, -0.059456177055835724, 0.0221055019646883, -0.03978264331817627, 0.02255922742187977, -0.047877103090286255, 0.0030240798369050026, 0.04323095455765724, 0.01805827021598816, 0.023194441571831703, -0.04007302597165108, 0.04105307534337044, 0.04235980287194252, -0.023303335532546043, 0.013620836660265923, -0.021651776507496834, -0.035136494785547256, 0.044900666922330856, -0.050018686801195145, -0.007436559069901705, -0.02392040379345417, -0.04083528742194176, 0.029056575149297714, -0.029346957802772522, 0.01492756512016058, -0.0022266574669629335, 0.013239706866443157, -0.08900277316570282, 0.03767735883593559, -0.10446573793888092, -0.008607170544564724, 0.07426577061414719, -0.030962221324443817, 0.027731696143746376, -0.036243584007024765, 0.052051376551389694, -0.008834033273160458, -0.010662546381354332, -0.004950143862515688, 0.004727818537503481, -0.023775210604071617, -0.03902038559317589, 0.04486436769366264, -0.01434679701924324, 0.034483131021261215, 0.011515550315380096, 0.047332633286714554, -0.03303121030330658, 0.013339526951313019, 0.01963723450899124, 0.0181671641767025, 0.012069095857441425, 0.011025527492165565, -0.012377629056572914, -0.08697008341550827, 0.01714174635708332, 0.024392277002334595, -0.005190618336200714, 0.030980370938777924, -0.02595309354364872, 0.0253541748970747, 0.033267147839069366, -0.05041796714067459, 0.015435737557709217, 0.036570265889167786, 0.003368911100551486, 0.043376147747039795, -0.06526385992765427, -0.02337593212723732, -0.022849611937999725, 0.03177892789244652, -0.022686269134283066, -0.020871369168162346, 0.005090799182653427, -0.014083635993301868, 0.0261708814650774, -0.005580822471529245, -0.012831354513764381, 0.0026202641893178225, 0.023684466257691383, 0.05103503167629242, 0.04279537871479988, -0.010562727227807045, -0.014991086907684803, 0.022686269134283066, -0.01998206600546837, -0.011542773805558681, -0.03675175830721855, 0.07789557427167892, 0.0051497831009328365, 0.03408385068178177, -0.004868473391979933, -0.010145300067961216, 0.04265018552541733, -0.019455745816230774, -0.006583555601537228, 0.026951288804411888, 0.01037216279655695, -0.024827852845191956, -0.038766298443078995, 0.04406581073999405, -0.048966046422719955, -0.014600883238017559, 0.04018191993236542, 0.034646470099687576, 0.05157950147986412, -0.00683310441672802, -0.03825812414288521, 0.05274103954434395, -0.008516425266861916, -0.015789642930030823, -0.038330722600221634, -0.015127204358577728, 0.018511995673179626, 0.006379378959536552, -0.004389793146401644, -0.026733500882983208, -0.029836982488632202, 0.03450128063559532, 0.018511995673179626, 0.035535771399736404, -0.03847591206431389, 0.0027836053632199764, 0.027132779359817505, -0.05996434763073921, 0.009746021591126919, -0.031688183546066284, 0.03916557505726814, -0.03573541343212128, 0.002214179839938879, -0.029836982488632202, -0.03252303600311279, 0.014845894649624825, -0.024011148139834404, -0.05059945583343506, 0.020345047116279602, -0.058585021644830704, -0.015417588874697685, 0.03676990792155266, 0.033285293728113174, 0.03600764647126198, -0.00004643595821107738, 0.012359479442238808, -0.005181543994694948, 0.032958611845970154, -0.02551751583814621, 0.04395691677927971, -0.001279505668208003, 0.02212364971637726, -0.028185421600937843, -0.010635322891175747, -0.007722406182438135, 0.008421143516898155, 0.02353927306830883, 0.011542773805558681, -0.004777728579938412, 0.034319788217544556, 0.0003629803250078112, -0.030109217390418053, 0.009197013452649117, 0.0002960558340419084, 0.018303282558918, -0.03555392101407051, -0.03704214096069336, -0.013702507130801678, -0.0058303712867200375, 0.007518230006098747, 0.02177881821990013, 0.059891752898693085, -0.03359382972121239, -0.022141799330711365, -0.012586342170834541, -0.011179793626070023, 0.009310444816946983, 0.02738686464726925, 0.033267147839069366, -0.051434312015771866, 0.014519212767481804, -0.008566335774958134, 0.015898538753390312, 0.02869359403848648, -0.01990947127342224, 0.008929315954446793, 0.07190640270709991, 0.00124547618906945, 0.047223739326000214, -0.00008585335308453068, -0.03535428270697594, 0.015462961979210377, 0.04922012984752655, -0.05579007416963577, -0.021379541605710983, -0.028620997443795204, 0.055390797555446625, -0.03771365433931351, -0.015535557642579079, -0.01388399675488472, 0.022522928193211555, -0.03858480602502823, 0.03395680710673332, -0.00370239932090044, -0.04461028054356575, 0.057750169187784195, 0.013294153846800327, -0.026751648634672165, -0.014029189012944698, -0.0033076582476496696, -0.035481326282024384, 0.013865848071873188, -0.04108937084674835, -0.02408374473452568, 0.059891752898693085, -0.03771365433931351, -0.015453887172043324, 0.03996413201093674, 0.01773158833384514, 0.03265007957816124, -0.026207178831100464, 0.027677249163389206, -0.02117990143597126, 0.0873330608010292, -0.01941944658756256, 0.04232350364327431, -0.004151587374508381, -0.012286883778870106, 0.036025796085596085, 0.0414886511862278, -0.02402929775416851, 0.0029151856433600187, 0.008942927233874798, 0.027622802183032036, -0.012250585481524467, -0.04424729943275452, -0.05277733877301216, 0.04170643910765648, 0.04003673046827316, -0.002418356481939554, -0.03428349271416664, 0.005399332381784916, 0.0072732181288301945, -0.0008921375847421587, 0.02936510741710663, 0.0009891213849186897, -0.0436665304005146, 0.04471917450428009, 0.0199276190251112, 0.027731696143746376, -0.014328648336231709, -0.03088962472975254, -0.06392083317041397, 0.06116218492388725, 0.019401298835873604, -0.022486630827188492, 0.012804131023585796, 0.02226884290575981, -0.010707919485867023, -0.0212887953966856, -0.019655384123325348, -0.026025688275694847, 0.0010220165131613612, -0.012087244540452957, 0.015308694913983345, -0.012141691520810127, 0.001097448286600411, 0.024610064923763275, -0.021633626893162727, 0.03814923018217087, -0.01440124399960041, -0.0054129441268742085, 0.009124417789280415, 0.00341655220836401, 0.0279313363134861, 0.006039084866642952, -0.04457398131489754, -0.004650685470551252, -0.002708740532398224, -0.0166789460927248, -0.012450224719941616, -0.004986442159861326, -0.0046075815334916115, 0.0222325436770916, -0.0112523902207613, 0.013874922879040241, 0.0034301639534533024, -0.0004846354422625154, -0.0054401676170527935, -0.043485041707754135, -0.018729783594608307, 0.005707865580916405, -0.03771365433931351, -0.016089102253317833, 0.020345047116279602, -0.006660688668489456, 0.03814923018217087, 0.014673478901386261, -0.036878801882267, 0.03137964755296707, 0.013766028918325901, 0.04232350364327431, 0.06693357229232788, -0.051325418055057526, -0.015898538753390312, -0.011388507671654224, 0.003629803191870451, 0.01963723450899124, 0.020726175978779793, -0.02468266151845455, -0.01470070332288742, -0.012722460553050041, -0.01887497678399086, 0.00746378256008029, -0.03555392101407051, 0.012758757919073105, -0.02738686464726925, 0.021851414814591408, -0.01500923652201891, 0.004203765653073788, 0.049074940383434296, 0.0034029404632747173, -0.010381236672401428, -0.02194216102361679, 0.0011490596225485206, 0.0023208053316920996, 0.005167932249605656, 0.008203355595469475, 0.013929369859397411, 0.022849611937999725, -0.01168796606361866, 0.023502975702285767, 0.03495500609278679, 0.007422947324812412, -0.015907611697912216, 0.02392040379345417, -0.0039995894767344, -0.012114468030631542, 0.019219808280467987, -0.05074464902281761, -0.010553652420639992, 0.02014540694653988, 0.011923903599381447, 0.0290202759206295, 0.019455745816230774, 0.008366696536540985, -0.033503081649541855, 0.005530912429094315, -0.02188771404325962, -0.010907558724284172, 0.024483023211359978, -0.027205374091863632, 0.003446044400334358, -0.057096805423498154, 0.00677865743637085, -0.057750169187784195, 0.012332255952060223, -0.011887605302035809, -0.026134582236409187, 0.009215163066983223, 0.015508334152400494, 0.015381290577352047, 0.020345047116279602, 0.031361497938632965, -0.014582734555006027, 0.038112934678792953, 0.014909416437149048, -0.025880496948957443, 0.03511834517121315, 0.021869564428925514, -0.016070954501628876, -0.015099980868399143, -0.012776907533407211, 0.003652489511296153, 0.021161751821637154, -0.014147157780826092, -0.007146175019443035, 0.036606565117836, -0.015680748969316483, -0.01743212901055813, 0.028983978554606438, -0.03666101396083832, -0.0033280758652836084, 0.024555617943406105, -0.03778625279664993, -0.03568096458911896, -0.01757732219994068, 0.023031100630760193, -0.02952844835817814, 0.04954681172966957, 0.021542882546782494, 0.03197856619954109, -0.012595416978001595, -0.02261367440223694, 0.009573605842888355, -0.004201496951282024, -0.037169184535741806, 0.03170632943511009, -0.031034817919135094, -0.003657026682049036, -0.00382036785595119, -0.043593935668468475, 0.016942106187343597, 0.011660742573440075, -0.025444921106100082, -0.004172005224972963, -0.019891321659088135, 0.025172684341669083, 0.018856827169656754, 0.009246923960745335, 0.0033280758652836084, -0.03872999921441078, -0.009455637075006962, -0.005408406723290682, -0.015290546230971813, -0.008167057298123837, -0.006615316495299339, 0.029165469110012054, -0.02611643448472023, 0.07600808143615723, -0.01632503978908062, 0.014428467489778996, -0.03622543439269066, -0.023992998525500298, -0.00043245701817795634, 0.04504585638642311, -0.011315911076962948, 0.018729783594608307, 0.007041817996650934, 0.050454262644052505, 0.015544632449746132, 0.06199703738093376, 0.03237784281373024, 0.024755258113145828, -0.042940571904182434, -0.01996391825377941, 0.02990957908332348, 0.0052450657822191715, 0.0026021150406450033, 0.028276165947318077, 0.04352134093642235, -0.030962221324443817, -0.025699006393551826, -0.024591917172074318, 0.02974623627960682, 0.017323235049843788, -0.017051000148057938, -0.036733608692884445, -0.004922920372337103, -0.020835069939494133, -0.02722352370619774, 0.01157907210290432, -0.020816920325160027, 0.04261389002203941, -0.012241511605679989, -0.028221718966960907, 0.010471981950104237, -0.001684455550275743, 0.0072641437873244286, -0.04511845484375954, -0.0012715654447674751, -0.03825812414288521, 0.028512103483080864, -0.012323182076215744, 0.07840374857187271, -0.06707876175642014, -0.015426663681864738, -0.047332633286714554, -0.011170719750225544, -0.06352155655622482, -0.003260016907006502, 0.020163556560873985, -0.02036319673061371, -0.029437704011797905, 0.04580811783671379, -0.03462832048535347, -0.07259606570005417, 0.0011099257972091436, -0.028221718966960907, 0.04344874247908592, 0.011533699929714203, 0.02194216102361679, -0.01841217651963234, -0.0222325436770916, 0.05372108891606331, 0.010952930897474289, 0.01827605813741684, -0.01597113348543644, 0.025499368086457253, -0.04653407633304596, -0.02096211351454258, 0.007940194569528103, 0.06137997284531593, -0.03272267431020737, -0.04613479971885681, 0.02381150797009468, -0.022087352350354195, -0.052051376551389694, 0.014773298986256123, 0.0010316581465303898, 0.010181598365306854, 0.027296120300889015, -0.0010702247964218259, -0.011397581547498703, -0.0225047804415226, 0.011842233128845692, -0.04341244697570801, 0.03406570106744766, 0.017994748428463936, -0.018893126398324966, -0.04736893251538277, 0.02261367440223694, 0.009827692061662674, 0.009800468571484089, 0.03707844018936157, 0.053975172340869904, -0.05502781644463539, 0.008362159132957458, 0.006229649763554335, 0.012069095857441425, 0.02842135913670063, -0.018838679417967796, 0.007509155198931694, 0.031415946781635284, -0.019056467339396477, 0.014301424846053123, 0.009337668307125568, 0.013493793085217476, -0.02546306885778904, 0.009147103875875473, -0.055281903594732285, 0.01925610564649105, -0.006225112359970808, -0.0014281007461249828, -0.012277808971703053, 0.021161751821637154, -0.027132779359817505, 0.029982173815369606, -0.005943802651017904, 0.021869564428925514, -0.0005654552951455116, 0.015381290577352047, -0.04105307534337044, -0.011733339168131351, -0.036788053810596466, -0.0067514339461922646, -0.04105307534337044, -0.012604491785168648, -0.05096243694424629, 0.004063110798597336, 0.009528233669698238, -0.027749845758080482, 0.0033621052280068398, 0.046279989182949066, 0.0027200838085263968, 0.030000323429703712, -0.005526375491172075, 0.02947400137782097, 0.004786802921444178, 0.03793144226074219, 0.024283383041620255, 0.00735488859936595, 0.023775210604071617, 0.016524678096175194, 0.017994748428463936, -0.015036460012197495, 0.0124048525467515, -0.02936510741710663, -0.02497304603457451, 0.02177881821990013, -0.021052857860922813, -0.05433815345168114, 0.020780622959136963, -0.04791340231895447, -0.05252325162291527, 0.01871163584291935, -0.02096211351454258, 0.029274363070726395, 0.020726175978779793, 0.005612583365291357, -0.06050881743431091, -0.04087158292531967, -0.056153055280447006, 0.03778625279664993, 0.048530466854572296, -0.006828567013144493, 0.0593835785984993, 0.047550421208143234, -0.02348482608795166, 0.06261410564184189, 0.0005767983966507018, -0.004001858178526163, 0.04450138658285141, 0.013348600827157497, -0.025263430550694466, 0.015462961979210377, -0.039201874285936356, 0.047332633286714554, 0.020653579384088516, -0.039528556168079376, 0.031524840742349625, 0.006805880926549435, 0.023466678336262703, -0.02749575860798359 ]
In this paper, we propose a Joint Semantic Transfer Network (JSTN) towards effective intrusion detection for large-scale scarcely labelled IoT domain. As a multi-source heterogeneous domain adaptation (MS-HDA) method, the JSTN integrates a knowledge rich network intrusion (NI) domain and another small-scale IoT intrusion (II) domain as source domains, and preserves intrinsic semantic properties to assist target II domain intrusion detection. The JSTN jointly transfers the following three semantics to learn a domain-invariant and discriminative feature representation. The scenario semantic endows source NI and II domain with characteristics from each other to ease the knowledge transfer process via a confused domain discriminator and categorical distribution knowledge preservation. It also reduces the source-target discrepancy to make the shared feature space domain-invariant. Meanwhile, the weighted implicit semantic transfer boosts discriminability via a fine-grained knowledge preservation, which transfers the source categorical distribution to the target domain. The source-target divergence guides the importance weighting during knowledge preservation to reflect the degree of knowledge learning. Additionally, the hierarchical explicit semantic alignment performs centroid-level and representative-level alignment with the help of a geometric similarity-aware pseudo-label refiner, which exploits the value of unlabelled target II domain and explicitly aligns feature representations from a global and local perspective in a concentrated manner. Comprehensive experiments on various tasks verify the superiority of the JSTN against state-of-the-art comparing methods, on average a 10.3% of accuracy boost is achieved. The statistical soundness of each constituting component and the computational efficiency are also verified.
[ 0.016563011333346367, 0.01548860128968954, -0.022857334464788437, -0.020119018852710724, 0.07918298244476318, 0.008105606772005558, -0.016867266967892647, 0.03131949156522751, -0.04183538630604744, 0.011866037733852863, 0.002714546164497733, -0.04917559772729874, 0.033107005059719086, -0.024892056360840797, 0.006465469021350145, 0.007035951595753431, 0.006779234390705824, -0.02384617179632187, 0.051685720682144165, -0.06317143887281418, 0.04837692156434059, 0.03744267299771309, -0.008638056926429272, 0.01805577240884304, 0.012693236581981182, 0.03696727007627487, 0.037499722093343735, 0.015298441052436829, -0.049327727407217026, 0.08085639774799347, -0.0344000980257988, 0.00223201303742826, 0.013339783996343613, -0.019272802397608757, -0.002193980850279331, -0.01081064436584711, 0.053891588002443314, 0.1359269767999649, -0.06682252138853073, 0.005609745159745216, 0.009821807965636253, -0.05860757455229759, -0.0468176007270813, 0.048034630715847015, 0.01836002990603447, -0.005162867251783609, -0.053168974816799164, -0.07275554537773132, -0.005044016521424055, 0.02517729625105858, 0.02015705034136772, -0.023199623450636864, 0.004647056106477976, 0.01916821487247944, -0.04301438480615616, 0.051685720682144165, 0.08078032732009888, 0.028333967551589012, 0.08671335130929947, 0.0263372790068388, -0.008319537155330181, 0.07077787071466446, 0.01111490186303854, 0.00643694493919611, 0.006993165239691734, -0.042329806834459305, 0.04750218242406845, -0.02428354136645794, 0.08131278306245804, -0.025823844596743584, -0.043356675654649734, 0.015659745782613754, -0.0058712163008749485, -0.01724758930504322, -0.032992906868457794, 0.0038531343452632427, 0.0452963151037693, 0.009393946267664433, 0.04662744328379631, 0.03154768422245979, 0.02091769315302372, 0.05351126566529274, 0.021697353571653366, -0.03114834800362587, 0.03101523593068123, 0.01140965148806572, -0.0035560079850256443, -0.06050918251276016, 0.04563860595226288, -0.03285979479551315, 0.0018885349854826927, 0.03818430006504059, 0.013539453037083149, -0.02692677639424801, -0.031813912093639374, 0.03042573668062687, -0.00967443361878395, -0.04008590802550316, -0.057999059557914734, -0.020271146669983864, 0.012541108764708042, -0.013843710534274578, -0.04647531360387802, 0.047312021255493164, 0.037670865654945374, 0.023047495633363724, -0.007872659713029861, 0.013339783996343613, -0.0193488672375679, 0.15311752259731293, 0.0395154245197773, 0.027706436812877655, -0.025614667683839798, 0.0511532686650753, -0.03263160213828087, -0.019244277849793434, -0.023865187540650368, -0.08975592255592346, 0.04179735481739044, -0.018417079001665115, 0.016182688996195793, 0.007872659713029861, 0.004002885892987251, -0.032821763306856155, -0.010126065462827682, 0.07811807841062546, 0.019624600186944008, 0.00519614527001977, 0.01563122309744358, 0.022457996383309364, -0.027991678565740585, 0.011257522739470005, 0.036206625401973724, -0.01886395737528801, 0.04046623036265373, 0.04632318392395973, 0.053435198962688446, 0.02192554622888565, -0.015260408632457256, -0.009983444586396217, 0.013130607083439827, 0.0030996219720691442, -0.0424058698117733, 0.01185652893036604, 0.008647564798593521, 0.05442403629422188, -0.000758266425691545, 0.10245867073535919, -0.014651893638074398, -0.001889723469503224, -0.027839548885822296, 0.08176916837692261, 0.013805678114295006, 0.038526590913534164, 0.03565515950322151, 0.03249849006533623, 0.04913756623864174, 0.008832971565425396, -0.004271488171070814, -0.02236291579902172, 0.004252471961081028, -0.04735005274415016, -0.004877625964581966, 0.05617351457476616, 0.03858363628387451, 0.009374930523335934, 0.03921116888523102, 0.014861070550978184, -0.04020000621676445, 0.05237029865384102, 0.036891207098960876, 0.01726660504937172, -0.010629992000758648, 0.03424796834588051, -0.026850713416934013, -0.006223014090210199, 0.03778496012091637, -0.028333967551589012, -0.011076869443058968, 0.025329425930976868, -0.0057523660361766815, 0.01358699332922697, -0.0018362407572567463, -0.008989854715764523, 0.010297209955751896, 0.035883352160453796, 0.051533591002225876, -0.009175261482596397, 0.05442403629422188, -0.005837938282638788, -0.032232265919446945, 0.03324011713266373, 0.027154970914125443, -0.04506812244653702, -0.0015129672829061747, -0.01067753229290247, -0.014100427739322186, 0.01249356847256422, 0.0039957547560334206, -0.027154970914125443, 0.020556388422846794, -0.017998725175857544, -0.000023305847207666375, -0.05712432041764259, -0.009351160377264023, 0.018103312700986862, -0.00924657192081213, -0.0012491190573200583, -0.02761135622859001, -0.026983825489878654, -0.03116736374795437, -0.008661827072501183, -0.01593547873198986, -0.05434797331690788, 0.0013014134019613266, -0.010164097882807255, 0.02647039107978344, 0.030653929337859154, -0.0014951396733522415, 0.030007382854819298, 0.034742388874292374, -0.03702431917190552, 0.014480749145150185, -0.0031566701363772154, -0.06986510008573532, -0.044383544474840164, -0.009241817519068718, -0.002574302488937974, -0.010240161791443825, 0.005091556813567877, -0.007411519531160593, -0.026698583737015724, 0.017694467678666115, -0.03010246343910694, 0.035179756581783295, -0.04518222063779831, 0.02483500726521015, -0.029950333759188652, -0.03274570032954216, -0.018806908279657364, -0.011799480766057968, -0.009227555245161057, -0.04841495305299759, -0.0497460812330246, 0.026527438312768936, -0.01661054976284504, -0.011390634812414646, 0.051267366856336594, -0.00753036979585886, 0.0511532686650753, -0.034571241587400436, -0.010629992000758648, 0.05423387512564659, -0.020423276349902153, -0.045258283615112305, -0.004901396110653877, 0.008200686424970627, -0.03713841363787651, 0.04069442301988602, -0.07271751016378403, 0.0193488672375679, 0.03478042036294937, 0.027250049635767937, 0.004057557322084904, 0.011133917607367039, 0.04442157596349716, 0.06381798535585403, 0.014965659007430077, 0.012322423048317432, -0.029436901211738586, -0.0024067233316600323, -0.03814626857638359, -0.08602876961231232, 0.011789972893893719, -0.0021000888664275408, -0.0036059252452105284, 0.04035213217139244, -0.02439763769507408, -0.010173605754971504, 0.07039754837751389, 0.006028098985552788, -0.05092507600784302, 0.006774480454623699, -0.010506386868655682, -0.012075214646756649, -0.01440468430519104, -0.042900290340185165, -0.012712253257632256, -0.03403879329562187, -0.01081064436584711, -0.019966889172792435, -0.007829872891306877, -0.003829364199191332, -0.004967952147126198, 0.03753775358200073, 0.007435289211571217, -0.0071785724721848965, 0.013035526499152184, 0.020366227254271507, -0.009103951044380665, -0.08093246072530746, -0.04339470714330673, 0.02749725989997387, 0.022743238136172295, -0.050088368356227875, 0.020670484751462936, -0.02179243415594101, 0.08260587602853775, -0.0031328999903053045, -0.021602272987365723, -0.0068077584728598595, -0.0026860220823436975, -0.04487796127796173, -0.03622564300894737, -0.05309291183948517, 0.014166983775794506, -0.0024578289594501257, 0.0029379851184785366, 0.03616859391331673, -0.03420993685722351, 0.007406765129417181, -0.006703170016407967, -0.07849840074777603, 0.04404125362634659, -0.012446028180420399, -0.019462963566184044, 0.054918453097343445, 0.04164522886276245, -0.03730956092476845, 0.012113246135413647, -0.030482785776257515, -0.023332737386226654, -0.10200228542089462, -0.04206358268857002, -0.01975771225988865, 0.029779190197587013, -0.03156670182943344, 0.04183538630604744, -0.03550302982330322, 0.003204210428521037, 0.0009626893443055451, -0.0037865780759602785, -0.009132474660873413, -0.060623280704021454, 0.00014737466699443758, 0.01987180858850479, -0.016933824867010117, 0.03599745035171509, -0.0027811024338006973, 0.004359437618404627, 0.0009395134984515607, -0.02177341841161251, 0.004737382289022207, -0.009707711637020111, 0.005319749936461449, -0.060623280704021454, -0.02297143079340458, -0.023028479889035225, 0.005486140493303537, 0.009032640606164932, -0.014756482094526291, -0.034438129514455795, 0.021963579580187798, 0.0033064219169318676, -0.05879773572087288, -0.001032216940075159, 0.007649220526218414, 0.021754402667284012, -0.017238082364201546, 0.03888789564371109, -0.006817266810685396, 0.004048048984259367, 0.007192834280431271, 0.031034251675009727, -0.008723629638552666, 0.025215329602360725, 0.02162128873169422, 0.0022854958660900593, -0.016800710931420326, 0.03727152571082115, 0.021126870065927505, -0.004295258317142725, 0.008923297747969627, -0.017276113852858543, 0.009218047372996807, 0.03702431917190552, 0.08093246072530746, 0.018264949321746826, -0.02823888696730137, 0.03740464150905609, 0.01212275493890047, -0.007535123731940985, -0.06701268255710602, -0.04750218242406845, 0.05001230537891388, -0.02721201814711094, -0.02968410961329937, -0.018702320754528046, 0.03666301444172859, -0.023903219029307365, -0.0701313242316246, 0.018150852993130684, 0.01002147700637579, -0.03377256914973259, -0.03247947245836258, -0.035331886261701584, -0.02515828050673008, -0.01687677577137947, -0.028543144464492798, -0.023009464144706726, -0.005571713205426931, -0.033107005059719086, -0.008319537155330181, -0.011552272364497185, 0.05716235190629959, 0.04210161417722702, -0.016867266967892647, 0.022553076967597008, 0.021164903417229652, -0.02922772243618965, -0.04426944628357887, -0.019462963566184044, 0.05164768919348717, 0.0033468310721218586, -0.04693169891834259, 0.06195440515875816, -0.01184702105820179, -0.0096839414909482, 0.0138912508264184, -0.0017471028259024024, 0.019662631675601006, -0.02922772243618965, 0.08610483258962631, -0.020727533847093582, -0.019795745611190796, -0.011057853698730469, 0.024036331102252007, -0.024378621950745583, -0.032536521553993225, 0.007368733175098896, -0.018093805760145187, -0.03609253093600273, -0.01652497798204422, -0.009588860906660557, -0.01566925458610058, -0.0336584709584713, 0.03626367449760437, 0.027364147827029228, 0.0024744682013988495, -0.01689579151570797, -0.054157812148332596, 0.018721336498856544, -0.04586679860949516, -0.005647777579724789, 0.04457370564341545, -0.004986968357115984, -0.012075214646756649, -0.02937985211610794, 0.042025547474622726, 0.002828642725944519, 0.004706481005996466, 0.0847356766462326, -0.03997180983424187, -0.019985904917120934, 0.022324884310364723, 0.010858184657990932, -0.013919774442911148, -0.03316405415534973, 0.008443142287433147, 0.020100003108382225, 0.05035459250211716, -0.030083447694778442, 0.05069688335061073, -0.022477012127637863, -0.03261258825659752, 0.01903510093688965, 0.019928857684135437, -0.03088212199509144, 0.036605965346097946, -0.047312021255493164, 0.007449551485478878, 0.008471665903925896, 0.007996263913810253, 0.01359650120139122, 0.06347569078207016, 0.05191391333937645, 0.006465469021350145, 0.011333586648106575, -0.002479222137480974, -0.03468533977866173, 0.02181144990026951, -0.017076443880796432, -0.01888297311961651, -0.0482628233730793, -0.023617977276444435, -0.04023803770542145, -0.0351036936044693, 0.02268618904054165, 0.04518222063779831, 0.0386977344751358, -0.0350656621158123, -0.05309291183948517, 0.047273989766836166, 0.048186760395765305, 0.0313955582678318, -0.003948214929550886, -0.005604991223663092, 0.054918453097343445, 0.006703170016407967, 0.06028098985552788, -0.011381126940250397, -0.011799480766057968, -0.004140752833336592, -0.021374080330133438, -0.015203360468149185, 0.03386764973402023, -0.0555269680917263, -0.03352535888552666, 0.03276471421122551, 0.035160742700099945, 0.031376540660858154, 0.005272209644317627, -0.019187230616807938, -0.022343900054693222, 0.0005966296885162592, 0.01672464795410633, 0.0285241287201643, 0.000773716950789094, 0.0020073854830116034, -0.026850713416934013, -0.0380702018737793, 0.017589878290891647, -0.01176144927740097, 0.01324470341205597, -0.008894774131476879, 0.002259348751977086, -0.04198751598596573, 0.05590729042887688, -0.018968544900417328, -0.0061992439441382885, -0.02485402300953865, 0.023047495633363724, -0.023028479889035225, -0.023636994883418083, -0.004264357034116983, -0.0021713993046432734, 0.02181144990026951, -0.020442292094230652, 0.030197544023394585, 0.03498959541320801, 0.021735385060310364, 0.014290587976574898, 0.0012752662878483534, 0.03609253093600273, -0.0008159088902175426, -0.020594419911503792, -0.024663863703608513, 0.021393096074461937, -0.009859840385615826, -0.018417079001665115, 0.018787892535328865, 0.06461665779352188, -0.01676267944276333, -0.061498019844293594, -0.004285750444978476, -0.03687218949198723, 0.017133492976427078, 0.04297635331749916, 0.042748160660266876, 0.013872234150767326, -0.019700665026903152, -0.028314951807260513, -0.059710510075092316, -0.038944944739341736, 0.015593189746141434, 0.026527438312768936, 0.024169445037841797, 0.010915232822299004, 0.005728595890104771, -0.025918925181031227, -0.054195843636989594, -0.055336806923151016, 0.0030758518259972334, 0.0322132483124733, -0.019700665026903152, 0.020974742248654366, -0.031490638852119446, -0.0599767342209816, 0.004742136225104332, 0.017323654145002365, 0.03599745035171509, -0.008585762232542038, -0.026983825489878654, -0.008428880013525486, 0.0029522471595555544, -0.005348274018615484, 0.017390210181474686, -0.028448063880205154, 0.0423678383231163, -0.024093380197882652, 0.01886395737528801, 0.03626367449760437, 0.037195462733507156, 0.05031656101346016, 0.007568402215838432, 0.030958186835050583, -0.006218260154128075, -0.007996263913810253, 0.012655205093324184, -0.01286438200622797, 0.01763741858303547, -0.02222980372607708, 0.0438891239464283, -0.03318306803703308, 0.00936542171984911, 0.0380702018737793, 0.027858564630150795, 0.0056287613697350025, -0.022400949150323868, 0.009935904294252396, 0.03810823708772659, -0.021545223891735077, 0.040732454508543015, 0.016401372849941254, -0.018654780462384224, -0.028124790638685226, 0.02648940682411194, -0.046437282115221024, -0.03466632217168808, -0.04168326035141945, -0.011828005313873291, -0.01593547873198986, -0.01294995378702879, -0.0034038792364299297, -0.021012773737311363, 0.007948723621666431, 0.03447616472840309, 0.003822233062237501, -0.010135573334991932, 0.00817691721022129, -0.01178046502172947, 0.02327568829059601, 0.003510844660922885, 0.0307299941778183, -0.008471665903925896, 0.04909953102469444, -0.032954875379800797, -0.03382961452007294, 0.004095589276403189, 0.05229423567652702, 0.003620187286287546, 0.017219064757227898, -0.020575404167175293, 0.028562160208821297, -0.021145887672901154, -0.009793284349143505, -0.00020947406301274896, 0.008476420305669308, -0.007639712188392878, 0.01183751318603754, 0.028581175953149796, -0.07218506187200546, 0.020974742248654366, 0.010563435032963753, 0.054766327142715454, -0.007839380763471127, 0.022457996383309364, 0.009916888549923897, 0.009156244806945324, 0.010715563781559467, 0.007577910088002682, -0.052712589502334595, -0.054043713957071304, 0.03453321009874344, 0.015792859718203545, -0.03445714712142944, 0.013710597530007362, 0.02894248254597187, 0.01565023884177208, -0.09660171717405319, -0.023503880947828293, 0.03639678657054901, -0.01214177068322897, -0.0005594888934865594, 0.003208964364603162, -0.015745319426059723, 0.015279424376785755, 0.02209669165313244, -0.012037182226777077, -0.009745744056999683, -0.037366606295108795, 0.012484059669077396, -0.012731269001960754, 0.02179243415594101, 0.016886284574866295, -0.012902414426207542, 0.01219881884753704, 0.004915657918900251, 0.014832546934485435, -0.05062082037329674, -0.017561355605721474, 0.012968970462679863, -0.03335421532392502, 0.03276471421122551, 0.04206358268857002, 0.0453723780810833, 0.015403029508888721, -0.005595483351498842, 0.01755184680223465, -0.011095886118710041, -0.0073402090929448605, 0.02411239594221115, 0.012550616636872292, 0.03552204743027687, 0.028562160208821297, 0.0022771761287003756, -0.011599811725318432, -0.014490257017314434, -0.033563390374183655, 0.039249200373888016, 0.012693236581981182, 0.01755184680223465, -0.016952840611338615, -0.058683641254901886, -0.021982595324516296, -0.00816265493631363, -0.02500615268945694, 0.0025505325756967068, -0.016258753836154938, 0.009878856129944324, 0.05039262771606445, -0.04792053624987602, -0.029284771531820297, 0.011923085898160934, -0.019206246361136436, -0.006151703651994467, 0.03055884875357151, 0.020404260605573654, 0.004830085672438145, -0.028333967551589012, -0.011209982447326183, -0.0672789067029953, 0.00463517103344202, 0.040123939514160156, 0.014566321857273579, -0.015393521636724472, 0.003289782674983144, 0.02732611447572708, -0.03479943796992302, 0.013548960909247398, 0.04396519064903259, -0.03759480267763138, -0.031642764806747437, -0.057542674243450165, -0.007059721741825342, -0.0007291480433195829, 0.018835432827472687, -0.03154768422245979, 0.02820085547864437, 0.021564241498708725, -0.0030188036616891623, 0.022591110318899155, 0.02483500726521015, 0.0328788124024868, 0.03112933225929737, -0.051571622490882874, -0.05218013748526573, -0.00938919186592102, 0.026660552248358727, 0.030349671840667725, 0.03637777268886566, 0.00003227534762118012, 0.0380702018737793, -0.0248730406165123, 0.0068933311849832535, 0.006227768026292324, 0.03681514039635658, -0.04445960745215416, -0.0010940191568806767, -0.0026693830732256174, -0.0157358106225729, 0.016819726675748825, -0.019643615931272507, 0.021278999745845795, -0.019092150032520294, 0.040428198873996735, 0.03554106503725052, 0.004409354645758867, -0.021678337827324867, 0.010211638174951077, -0.006959887221455574, -0.01785610429942608, 0.03055884875357151, -0.01635383442044258, 0.03921116888523102, 0.00935591384768486, -0.014357144944369793, 0.030615897849202156, 0.005947280675172806, -0.03540795296430588, 0.042481936514377594, -0.003415764309465885, 0.009869348257780075, 0.031661782413721085, -0.019443947821855545, -0.030159510672092438, -0.04879527539014816, -0.026109084486961365, -0.010839168913662434, -0.019776728004217148, 0.021240968257188797, 0.0029308542143553495, -0.02631826139986515, 0.02821987122297287, 0.04312848299741745, -0.01650596223771572, -0.03616859391331673, -0.04039016366004944, -0.01468992605805397, -0.09675384312868118, -0.00288569089025259, 0.0026289739180356264, -0.015250900760293007, -0.0017150131752714515, -0.07001722604036331, 0.03846954181790352, 0.04400322213768959, 0.022762253880500793, 0.04792053624987602, -0.021830465644598007, -0.04210161417722702, -0.0011445306008681655, -0.01534598134458065, -0.015193852595984936, -0.06925658136606216, 0.05438600480556488, -0.03386764973402023, 0.012683728709816933, -0.0038412492722272873, 0.03040672093629837, 0.023332737386226654, 0.01903510093688965, 0.014176491647958755, -0.016410881653428078, 0.029570013284683228, -0.02266717329621315, -0.026698583737015724, 0.008443142287433147, 0.044954024255275726, -0.009393946267664433, 0.04046623036265373, 0.011333586648106575, 0.0037366608157753944, 0.021412111818790436, -0.006636613979935646, 0.06762120127677917, -0.006936117075383663, 0.012322423048317432, 0.025386473163962364, -0.026641536504030228, 0.004751644562929869, 0.011219490319490433, -0.002398403827100992, 0.011067361570894718, 0.0006495181587524712, 0.0322132483124733, -0.018768876791000366, -0.05537484213709831, -0.020100003108382225, -0.03420993685722351, 0.03997180983424187, -0.055488936603069305, -0.05773283541202545, 0.035464998334646225, -0.01185652893036604, -0.017123984172940254, -0.020708516240119934, 0.01390075869858265, 0.003439534455537796, -0.024911072105169296, -0.01220832671970129, 0.011999149806797504, 0.030501801520586014, -0.05027852952480316, 0.03396273031830788, 0.027839548885822296, 0.010259178467094898, 0.0012003903975710273, 0.005766627844423056, -0.024644846096634865, -0.018968544900417328, 0.0009454559767618775, -0.036339737474918365, 0.019206246361136436, 0.01891149766743183, 0.0033444541040807962, -0.043927159160375595, -0.045676637440919876, -0.004121736623346806, -0.013729613274335861, 0.015374504961073399, -0.07408666610717773, 0.011495223268866539, -0.017846595495939255, 0.05575516074895859, 0.019928857684135437, -0.007197588216513395, -0.03892592713236809, -0.008352815173566341, -0.003168555209413171, 0.01322568766772747, -0.03388666361570358, -0.016344325616955757, -0.024911072105169296, -0.012027674354612827, -0.014823039062321186, -0.02443566918373108, 0.015906956046819687, 0.009265587665140629, 0.028124790638685226, 0.04373699799180031, 0.017171524465084076, -0.027002841234207153, 0.03086310625076294, -0.016277769580483437, -0.003701005596667528, 0.019833777099847794, 0.015602698549628258, -0.01140965148806572, 0.010915232822299004, -0.019624600186944008, 0.04849101975560188, -0.010430322960019112, 0.01462337002158165, 0.022419964894652367, -0.020670484751462936, 0.041759323328733444, 0.008248226717114449, -0.04077048599720001, -0.010411307215690613, -0.004948936402797699, 0.011875545606017113, 0.02133604697883129, 0.036491867154836655, 0.026090068742632866, 0.008937560021877289, 0.048034630715847015, -0.019187230616807938, 0.003848380409181118, -0.009189523756504059, -0.03280274569988251, -0.01854068413376808, -0.007943970151245594, -0.013767645694315434, -0.022762253880500793, 0.03715743124485016, -0.02106982283294201, 0.01783708855509758, -0.027573324739933014, 0.011799480766057968, 0.04267209395766258, 0.02034721150994301, -0.035464998334646225, -0.011970626190304756, -0.04164522886276245, 0.024606814607977867, 0.00030633725691586733, -0.016534486785531044, -0.01632530987262726, 0.035312872380018234, -0.030026398599147797, -0.03171883150935173, 0.023351753130555153, -0.011628336273133755, -0.006489239167422056, -0.02264815755188465, 0.02146916091442108, -0.019624600186944008, 0.015307948924601078, -0.022400949150323868, 0.04754021391272545, 0.006223014090210199, 0.0032256036065518856, -0.005780890118330717, -0.0018184131477028131, -0.03704333305358887, 0.032954875379800797, 0.0009430790087208152, -0.06598581373691559, 0.018245933577418327, -0.0007701514405198395, 0.011533255688846111, 0.00972672738134861, 0.022115707397460938, -0.026793664321303368, 0.013815185986459255, -0.030311640352010727, -0.0025885645300149918, -0.027078906074166298, -0.005828430410474539, -0.01468992605805397, -0.011637844145298004, 0.0010161721147596836, 0.06313340365886688, -0.01613514870405197, -0.006474976893514395, 0.032232265919446945, 0.013149622827768326, -0.017561355605721474, 0.014566321857273579, 0.03639678657054901, -0.0424058698117733, 0.01827445812523365, 0.026261214166879654, -0.004423616919666529, 0.038260363042354584, -0.024663863703608513, -0.00500598456710577, -0.010924740694463253, -0.015022707171738148, -0.019928857684135437, -0.009265587665140629, 0.023865187540650368, -0.013615516945719719 ]
In this work, we propose a self-improving artificial intelligence system to enhance the safety performance of reinforcement learning (RL)-based autonomous driving (AD) agents using black-box verification methods. RL algorithms have become popular in AD applications in recent years. However, the performance of existing RL algorithms heavily depends on the diversity of training scenarios. A lack of safety-critical scenarios during the training phase could result in poor generalization performance in real-world driving applications. We propose a novel framework in which the weaknesses of the training set are explored through black-box verification methods. After discovering AD failure scenarios, the RL agent's training is re-initiated via transfer learning to improve the performance of previously unsafe scenarios. Simulation results demonstrate that our approach efficiently discovers safety failures of action decisions in RL-based adaptive cruise control (ACC) applications and significantly reduces the number of vehicle collisions through iterative applications of our method. The source code is publicly available at https://github.com/data-and-decision-lab/self-improving-RL.
[ -0.018148809671401978, 0.006368412636220455, -0.018447402864694595, -0.06274169683456421, 0.01443506870418787, 0.05818816274404526, -0.011243863962590694, 0.01737433671951294, -0.06890016049146652, 0.010189460590481758, 0.012382247485220432, -0.01569475419819355, 0.04990222677588463, -0.02646273747086525, 0.010404073633253574, 0.055314213037490845, -0.008808471262454987, -0.011719745583832264, -0.003142216708511114, -0.045199401676654816, -0.01273682527244091, -0.028814151883125305, -0.061920564621686935, 0.0737149566411972, -0.006102479062974453, 0.023439491167664528, 0.015284189954400063, -0.00808531790971756, -0.08853259682655334, 0.04911842569708824, 0.04113108292222023, 0.024689845740795135, 0.013166051357984543, 0.017934195697307587, 0.007357499562203884, 0.028926122933626175, 0.02864619344472885, 0.04728954657912254, -0.01974441111087799, 0.07248326390981674, 0.030773663893342018, -0.03693212941288948, -0.00923303235322237, 0.00016168886213563383, -0.0020656518172472715, -0.0018487059278413653, -0.007544119842350483, 0.017243701964616776, -0.06759382039308548, -0.0001541074161650613, -0.022133149206638336, -0.020752161741256714, 0.03807051107287407, -0.019800398498773575, 0.01799018308520317, 0.035569801926612854, 0.038928963243961334, 0.01963244006037712, 0.04303460568189621, -0.012372915633022785, 0.0379585400223732, 0.007674753665924072, -0.060203660279512405, 0.040683191269636154, 0.03558846190571785, -0.03325571119785309, 0.052141670137643814, -0.0004548866127151996, 0.030922958627343178, -0.00040356608224101365, -0.04254939407110214, -0.003123554866760969, -0.02959795668721199, -0.005528621841222048, 0.043631792068481445, 0.017029087990522385, -0.03215465322136879, 0.039078257977962494, -0.0025753581430763006, 0.0038793664425611496, 0.019427157938480377, 0.018550043925642967, -0.022245122119784355, 0.0036927461624145508, 0.07356566190719604, 0.0006625015521422029, 0.030773663893342018, -0.06546635180711746, 0.048409268260002136, -0.0836058259010315, -0.022095825523138046, -0.008267272263765335, -0.003907359205186367, 0.012708832509815693, 0.0009605105733498931, 0.007777394726872444, -0.03506592661142349, -0.007124224212020636, -0.0836058259010315, 0.004404235631227493, 0.0255482979118824, -0.008169297128915787, 0.032024018466472626, 0.023439491167664528, 0.013837884180247784, -0.0339462049305439, -0.07576777786016464, -0.01443506870418787, -0.028664855286478996, 0.1383228600025177, -0.007912694476544857, -0.01430443488061428, -0.016151973977684975, 0.008533206768333912, -0.029299363493919373, -0.03765994682908058, -0.010730658657848835, -0.05587407201528549, 0.018438071012496948, -0.050163496285676956, -0.011906365863978863, 0.03277049958705902, 0.03036309778690338, -0.028160979971289635, -0.0062704370357096195, -0.004397237207740545, 0.028366263955831528, 0.03243458271026611, -0.009023084305226803, -0.010590693913400173, 0.03116556443274021, -0.00863118190318346, -0.033666275441646576, 0.00175656215287745, 0.028347600251436234, -0.005178709048777819, -0.014201793819665909, -0.030195141211152077, 0.004054322838783264, 0.0070495763793587685, -0.02496977709233761, -0.03620430827140808, -0.0016982434317469597, 0.06266704946756363, 0.03993671387434006, 0.016515882685780525, 0.030829649418592453, 0.06259240210056305, -0.03652156516909599, 0.03310641646385193, -0.038593046367168427, 0.048707857728004456, -0.01645989716053009, 0.02196519263088703, 0.07199805229902267, 0.01758894883096218, 0.005668587051331997, 0.03402085229754448, -0.01226094365119934, -0.06464522331953049, 0.0836058259010315, 0.013147389516234398, -0.014603027142584324, 0.08099314570426941, 0.03751065209507942, 0.02069617435336113, 0.015125563368201256, -0.02379406988620758, -0.06501846015453339, 0.043855734169483185, -0.0507233589887619, -0.01350196823477745, -0.010450728237628937, 0.02200251631438732, 0.0152375353500247, 0.0008607854251749814, 0.05744168162345886, -0.018932614475488663, 0.0021461318247020245, -0.029224716126918793, -0.07087833434343338, -0.02489512786269188, 0.050163496285676956, 0.04113108292222023, 0.0558367483317852, 0.04273601621389389, 0.06419733166694641, -0.002985922386869788, 0.022898292168974876, -0.010553369298577309, -0.00368108251132071, 0.04777475818991661, 0.04788672924041748, 0.013940525241196156, 0.016040002927184105, -0.002032993361353874, -0.05915858969092369, -0.03435676917433739, 0.020565541461110115, -0.02058420330286026, 0.016842469573020935, -0.023887379094958305, -0.014155138283967972, 0.010180129669606686, 0.006503712385892868, -0.011803724803030491, 0.020938780158758163, 0.036334943026304245, 0.029915209859609604, -0.05904661491513252, 0.00006345814472297207, -0.04945433884859085, -0.06740719825029373, -0.02452188730239868, -0.025156395509839058, -0.006909611169248819, -0.017318349331617355, 0.01743965409696102, -0.023700758814811707, -0.030045844614505768, -0.010273439809679985, -0.018550043925642967, 0.002177623799070716, -0.020154977217316628, -0.021050753071904182, -0.028664855286478996, 0.01434175856411457, 0.018223457038402557, -0.03402085229754448, -0.019296523183584213, -0.03372226282954216, -0.03025112673640251, 0.020210962742567062, -0.007464806083589792, 0.020565541461110115, 0.03252789378166199, 0.042250800877809525, -0.009359000250697136, 0.03700677677989006, -0.006648343056440353, -0.019371172413229942, -0.027713092043995857, 0.004590855911374092, -0.041914887726306915, 0.0726325660943985, 0.024465901777148247, -0.0012865127064287663, 0.04393038526177406, 0.034076839685440063, 0.025977525860071182, -0.04941701516509056, -0.004992089234292507, -0.050387442111968994, -0.015405493788421154, -0.025007100775837898, 0.012764818035066128, 0.029038095846772194, -0.03975009173154831, -0.005094730295240879, -0.024503225460648537, 0.006069820374250412, 0.02252505160868168, 0.011682421900331974, 0.036148324608802795, -0.057105764746665955, -0.004693496972322464, 0.03639093041419983, 0.06113675981760025, 0.021106738597154617, -0.045423343777656555, 0.008626516908407211, -0.018092824146151543, -0.005276684649288654, 0.004754148423671722, 0.0017483975971117616, -0.04008600860834122, -0.013128727674484253, -0.006657673977315426, 0.03514057397842407, 0.014192462898790836, -0.011598442681133747, -0.009573614224791527, 0.03680149465799332, -0.016665179282426834, -0.009890868328511715, -0.08091849833726883, -0.03937685117125511, 0.015125563368201256, -0.07050509005784988, 0.023850055411458015, 0.0010614021448418498, -0.025193721055984497, -0.040309954434633255, -0.001999168423935771, 0.06901213526725769, 0.03178141266107559, -0.013389996252954006, -0.055351536720991135, -0.035159237682819366, -0.013231368735432625, -0.00778206018730998, -0.05830013379454613, 0.05288815125823021, 0.03150148317217827, 0.04396770894527435, 0.034618038684129715, -0.007432147394865751, 0.01686113141477108, -0.03127753734588623, -0.048931803554296494, -0.031053593382239342, 0.037062760442495346, -0.05397054925560951, -0.02295427955687046, 0.0019373504910618067, 0.001253854134120047, 0.006200454663485289, -0.02230110764503479, -0.06419733166694641, -0.014369751326739788, -0.030680352821946144, -0.003221530467271805, -0.0594945028424263, 0.06707128137350082, 0.009601606987416744, 0.025137733668088913, 0.006102479062974453, -0.0035061261150985956, -0.08950302749872208, 0.008383910171687603, -0.02890746109187603, 0.000878281076438725, -0.08912978321313858, -0.018298106268048286, -0.006750984117388725, -0.03273317590355873, -0.04449024423956871, 0.06453324854373932, -0.013604609295725822, -0.060203660279512405, -0.01590936817228794, 0.009928192012012005, -0.03631628304719925, -0.0397874154150486, -0.017784900963306427, -0.06688465923070908, 0.05165645852684975, -0.010049494914710522, 0.026910625398159027, -0.026257455348968506, 0.0009231865406036377, 0.003884031902998686, 0.02200251631438732, 0.0014474726049229503, 0.001729735522530973, 0.004856789484620094, -0.040459249168634415, 0.0017239036969840527, -0.03183739632368088, 0.014789647422730923, 0.0525522343814373, -0.06449592113494873, -0.030493732541799545, -0.010572031140327454, 0.02043490670621395, 0.03930220380425453, 0.016562538221478462, -0.020490892231464386, 0.030960282310843468, -0.0026033511385321617, -0.027358513325452805, 0.06904945522546768, 0.053858574479818344, 0.005458639468997717, 0.004047324415296316, -0.01491095032542944, -0.01920321397483349, -0.05296279862523079, 0.004996754694730043, 0.03642825409770012, 0.006629680749028921, -0.020248286426067352, -0.028627531602978706, 0.0011803724337369204, -0.030997607856988907, 0.06617550551891327, 0.011439815163612366, -0.027545133605599403, 0.018848635256290436, 0.024465901777148247, 0.002659337129443884, -0.023010265082120895, -0.009251694194972515, -0.03765994682908058, 0.031445495784282684, 0.038891639560461044, 0.04430362582206726, -0.02627611719071865, -0.0055239563807845116, -0.0737149566411972, -0.006951600778847933, 0.020957443863153458, -0.006946935318410397, -0.03594304248690605, -0.03282648324966431, 0.056881822645664215, -0.008243945427238941, 0.018270112574100494, -0.000982088502496481, -0.003886364633217454, 0.04277333989739418, -0.06221915781497955, -0.010851961560547352, 0.01122520212084055, 0.07266988605260849, -0.03135218471288681, 0.009032415226101875, -0.004754148423671722, -0.030493732541799545, -0.014043166302144527, -0.013492637313902378, 0.02237575687468052, 0.03510325029492378, 0.005705911200493574, -0.0008024666458368301, 0.012783480808138847, -0.0478120818734169, 0.021293358877301216, -0.05117124691605568, -0.045162077993154526, 0.022637024521827698, -0.018008844926953316, 0.011962351389229298, -0.04646841809153557, -0.02161061391234398, -0.012540874071419239, 0.016077326610684395, 0.007847377099096775, -0.04575926065444946, 0.0029229382053017616, -0.0006490882369689643, -0.03807051107287407, -0.023196885362267494, -0.011831717565655708, -0.03021380305290222, -0.05800154432654381, 0.029915209859609604, -0.052290964871644974, -0.007800722494721413, -0.014976266771554947, -0.04803602769970894, 0.05393322557210922, -0.036876142024993896, -0.027507809922099113, 0.029541969299316406, -0.020864132791757584, -0.025753580033779144, -0.04422897472977638, 0.033516980707645416, -0.006359081715345383, 0.04568461328744888, 0.04934236779808998, 0.0434451699256897, -0.02993387170135975, 0.0036834152415394783, 0.02803034707903862, -0.04911842569708824, -0.07091565430164337, -0.007646760903298855, -0.031258873641490936, 0.011178547516465187, -0.04482616111636162, 0.033666275441646576, -0.03915290907025337, 0.015396162867546082, 0.011206540279090405, -0.015713416039943695, -0.048558562994003296, -0.014024504460394382, -0.0401606559753418, 0.014966935850679874, 0.061547327786684036, 0.031445495784282684, -0.027657106518745422, 0.01353929191827774, 0.056993793696165085, 0.09875938296318054, -0.007553450763225555, -0.03222930058836937, -0.03596170246601105, -0.050536736845970154, -0.02080814726650715, -0.04788672924041748, -0.014323096722364426, -0.014659012667834759, -0.009918861091136932, -0.0008666173089295626, 0.013557953760027885, 0.062032539397478104, -0.005486632231622934, 0.026630695909261703, -0.009806889109313488, 0.006205120123922825, -0.024428578093647957, -0.00745547516271472, 0.03989939019083977, -0.021629275754094124, -0.033050429075956345, -0.0041989535093307495, -0.02580956742167473, 0.01116921566426754, 0.04400503262877464, -0.0067743114195764065, -0.03674550727009773, 0.02054687961935997, -0.011085237376391888, 0.03491663187742233, -0.025417665019631386, 0.038966286927461624, 0.02280498296022415, 0.024260619655251503, 0.021013429388403893, 0.018298106268048286, 0.02668668143451214, 0.006923607550561428, 0.01645989716053009, 0.0383317805826664, -0.021050753071904182, 0.060129012912511826, 0.00956428237259388, -0.02080814726650715, 0.04990222677588463, -0.0416162945330143, -0.07184875756502151, -0.01061868667602539, 0.005883200094103813, 0.02803034707903862, 0.03956347331404686, -0.018997931852936745, 0.016002677381038666, -0.027787741273641586, 0.040683191269636154, 0.03040042333304882, 0.015386831946671009, -0.005687248893082142, 0.011999676004052162, 0.03478599712252617, -0.028590207919478416, -0.0037370685022324324, 0.037790581583976746, 0.01693577878177166, 0.013138058595359325, -0.0022802650928497314, 0.035345856100320816, -0.012251612730324268, -0.020192300900816917, -0.021144062280654907, -0.016665179282426834, -0.027022598311305046, -0.02982190065085888, 0.005323339719325304, -0.04434094950556755, -0.0051880404353141785, 0.033628951758146286, 0.005150716286152601, -0.03543916717171669, 0.010889286175370216, 0.016553208231925964, -0.04157897084951401, 0.020957443863153458, -0.06509310752153397, -0.002293095225468278, -0.003121222136542201, -0.05762830376625061, -0.006690332666039467, -0.02868351712822914, -0.01138382963836193, -0.059979718178510666, -0.017206378281116486, -0.006960931699723005, -0.020285610109567642, -0.050126172602176666, 0.0011074739741161466, 0.02004300430417061, -0.024148646742105484, -0.023271532729268074, -0.03551381453871727, -0.008327924646437168, 0.03043774701654911, -0.04187756031751633, -0.02295427955687046, -0.02944866009056568, -0.0038280459120869637, 0.046990953385829926, -0.033013105392456055, -0.024204634130001068, -0.0018988600932061672, -0.01202766876667738, -0.0008666173089295626, -0.01729968748986721, 0.006853625178337097, 0.019688425585627556, 0.012858128175139427, 0.02142399363219738, 0.027619782835245132, 0.004364578984677792, 0.007791391108185053, 0.0270039364695549, 0.02153596468269825, -0.012018337845802307, -0.03471134975552559, -0.009331007488071918, 0.0397874154150486, 0.014276441186666489, 0.03306908905506134, 0.0001352996041532606, 0.03997403755784035, 0.045386020094156265, 0.04128037765622139, -0.01617063581943512, -0.0005105810705572367, -0.019100572913885117, 0.019147228449583054, -0.014836302027106285, -0.00020440739172045141, 0.06300296634435654, -0.019800398498773575, -0.017831554636359215, 0.007058907300233841, -0.008607854135334492, -0.015498803928494453, -0.03185606002807617, 0.02332751825451851, -0.03424479812383652, 0.004987423773854971, 0.0017262364272028208, -0.012484888546168804, 0.03456205129623413, 0.016366587951779366, -0.0010987261775881052, -0.009125725366175175, 0.003032577456906438, -0.026947949081659317, 0.0792015939950943, -0.0006776644149795175, -0.01494827400892973, 0.038705021142959595, -0.035532478243112564, 0.017169054597616196, -0.01832609809935093, -0.03808917477726936, 0.04001136124134064, 0.009055742993950844, 0.037753257900476456, -0.01850338838994503, 0.008729157969355583, 0.03288247063755989, -0.005029412917792797, 0.0394141748547554, 0.011869041249155998, 0.0074508097022771835, -0.011085237376391888, 0.023308856412768364, 0.004856789484620094, 0.05497829616069794, 0.005976510234177113, 0.07785792648792267, 0.0030045844614505768, 0.014005842618644238, 0.05318674445152283, -0.03825712949037552, -0.024204634130001068, -0.052104346454143524, 0.03711874783039093, 0.03334902226924896, -0.020304271951317787, 0.04113108292222023, 0.042288124561309814, 0.01993103139102459, -0.011654428206384182, -0.0379585400223732, 0.0019058582838624716, -0.012718163430690765, -0.0029672603122889996, -0.029392674565315247, -0.013977848924696445, 0.0042246137745678425, 0.03762262314558029, -0.03043774701654911, -0.02364477328956127, -0.048931803554296494, 0.004035660997033119, 0.025884214788675308, -0.013968518003821373, 0.02043490670621395, 0.033050429075956345, -0.04463953897356987, -0.03592437878251076, 0.010600024834275246, -0.015153556130826473, 0.019651101902127266, -0.02084547095000744, -0.025492312386631966, 0.008477220311760902, 0.028198305517435074, -0.01839141547679901, 0.0026430077850818634, 0.031034931540489197, -0.012335591949522495, -0.012130309827625751, 0.014295103959739208, 0.053485333919525146, 0.007595440372824669, 0.013278023339807987, 0.046990953385829926, 0.01638524979352951, 0.022972941398620605, -0.05830013379454613, 0.007726074196398258, 0.032061342149972916, 0.024148646742105484, 0.006853625178337097, 0.0005662754992954433, -0.07177411019802094, -0.04941701516509056, -0.0011967017780989408, 0.01235425379127264, 0.006872287020087242, -0.02864619344472885, -0.008015335537493229, 0.016562538221478462, -0.008971763774752617, 0.008150635287165642, 0.008817802183330059, -0.011047912761569023, -0.01628260873258114, 0.0094896350055933, 0.04172826558351517, -0.011159884743392467, -0.0022429409436881542, 0.01518154889345169, -0.02062152698636055, 0.05617266520857811, -0.008029332384467125, 0.015069576911628246, 0.0026266786735504866, -0.020957443863153458, 0.029187392443418503, -0.008654509671032429, 0.016338594257831573, 0.061547327786684036, 0.00495476508513093, 0.05244026333093643, -0.02142399363219738, -0.037174735218286514, 0.012531543150544167, 0.024036675691604614, 0.007399489171802998, -0.001362327137030661, -0.011859710328280926, -0.0023315856233239174, 0.06987058371305466, -0.006279767956584692, 0.0034408089704811573, 0.016291938722133636, -0.06371212005615234, 0.02054687961935997, -0.006359081715345383, 0.03361028805375099, 0.011495801620185375, 0.05411984398961067, -0.008607854135334492, -0.008645178750157356, -0.006051158532500267, 0.01796218939125538, 0.0027596454601734877, 0.02616414614021778, -0.0028879467863589525, 0.006988924462348223, -0.010973264463245869, -0.0175236314535141, 0.004012333229184151, -0.04564728960394859, 0.009834881871938705, -0.012522212229669094, 0.029541969299316406, -0.043743763118982315, -0.03405817598104477, 0.03239725902676582, 0.03820114582777023, 0.0064943814650177956, 0.01701042614877224, -0.010170797817409039, -0.006485050078481436, 0.0011407156707718968, 0.0032985112629830837, -0.03491663187742233, -0.0015232870355248451, -0.007796057034283876, -0.043631792068481445, 0.016795814037322998, 0.028590207919478416, -0.03443141654133797, -0.006363747175782919, -0.03254655376076698, -0.022786321118474007, -0.013100734911859035, -0.020229624584317207, 0.005262688267976046, 0.019501805305480957, 0.007133555132895708, 0.024185972288250923, 0.004775143228471279, -0.00939632486552, 0.008043328300118446, -0.05404519662261009, 0.04650574177503586, 0.06143535301089287, 0.020341595634818077, -0.004870785865932703, 0.005729238502681255, -0.020341595634818077, -0.007982676848769188, 0.04072051867842674, -0.046916306018829346, -0.03620430827140808, 0.0037090755067765713, 0.008425899781286716, 0.005985841155052185, -0.030176479369401932, 0.0006047659553587437, 0.07147552073001862, -0.01452837884426117, 0.01781289279460907, -0.028086332604289055, 0.04329587519168854, 0.01359527837485075, -0.0328638069331646, -0.032024018466472626, -0.015442817471921444, -0.005351332947611809, 0.02577224373817444, -0.0015617774333804846, -0.0067743114195764065, -0.06998255848884583, -0.0281049944460392, -0.010861292481422424, -0.010478721931576729, 0.01619862951338291, -0.02131202071905136, 0.00843056570738554, 0.0034734676592051983, 0.018195465207099915, -0.026593372225761414, -0.006792973726987839, 0.04471419006586075, 0.04923039674758911, 0.07815651595592499, 0.001302841934375465, -0.008948436006903648, -0.0011897034710273147, 0.015312183648347855, 0.03226662427186966, -0.0302884504199028, 0.04445292055606842, 0.04736419394612312, -0.011467807926237583, -0.04993955418467522, -0.0016830804524943233, -0.0273771770298481, 0.012400909326970577, 0.0017215708503499627, -0.02566027082502842, -0.0083045968785882, -0.01729968748986721, 0.02088279463350773, 0.033591628074645996, 0.011337174102663994, 0.006872287020087242, -0.04923039674758911, 0.028086332604289055, 0.006368412636220455, 0.010161466896533966, -0.0173370111733675, 0.009284352883696556, -0.007894032634794712, -0.017682259902358055, -0.05669520050287247, -0.0009698416106402874, -0.013194045051932335, 0.0004633428470697254, -0.013828553259372711, -0.03196803107857704, -0.015993347391486168, 0.03424479812383652, 0.05490364879369736, -0.030139153823256493, 0.017840886488556862, -0.03433810919523239, 0.009247028268873692, -0.008892450481653214, 0.0024703843519091606, -0.030605705454945564, 0.00956428237259388, 0.0024913789238780737, 0.007133555132895708, 0.023887379094958305, -0.017169054597616196, 0.03109091706573963, -0.021218711510300636, -0.024839142337441444, -0.014463061466813087, 0.027638444676995277, -0.008407237939536572, 0.03303176537156105, -0.025529636070132256, -0.0558367483317852, -0.015825388953089714, 0.03609233722090721, -0.00939632486552, -0.014173800125718117, 0.0002688496606424451, -0.05594872310757637, 0.0317627489566803, -0.038779668509960175, 0.012372915633022785, 0.0046445089392364025, -0.009475638158619404, -0.005990507081151009, -0.009372997097671032, -0.03271451219916344, 0.0191658902913332, 0.020341595634818077, 0.007735405117273331, 0.0009383494616486132, 0.017766239121556282, -0.008691833354532719, -0.02375674620270729, -0.023962028324604034, -0.013044748455286026, -0.048931803554296494, -0.031034931540489197, -0.020192300900816917, -0.0016235953662544489, 0.012204958125948906, -0.01071199681609869, 0.0025636942591518164, 0.01283013541251421, 0.000060432852478697896, -0.020173639059066772, -0.05393322557210922, -0.040608543902635574, -0.026108158752322197, -0.030960282310843468, -0.014005842618644238, 0.013903201557695866, -0.016926446929574013, -0.0368574783205986, -0.048521239310503006, 0.10017769783735275, -0.03441275656223297, 0.028384925797581673, -0.04411700367927551, -0.027563797309994698, -0.027563797309994698, 0.04172826558351517, -0.028776828199625015, 0.002876283135265112, -0.03659621253609657, 0.0069982558488845825, 0.019315185025334358, -0.008108645677566528, 0.011635766364634037, 0.02875816449522972, -0.004604852292686701, 0.02284230664372444, -0.01981906034052372, -0.05718041583895683, -0.0361296609044075, 0.026779992505908012, 0.006620349828153849, -0.023364843800663948, 0.000059084231907036155, -0.021106738597154617, -0.031333524733781815, -0.03508459031581879, 0.024316605180501938, 0.03241591900587082, 0.001998001942411065, 0.014285773038864136, -0.001362327137030661, -0.010282770730555058, -0.011271856725215912, 0.008953101933002472, -0.010562700219452381, -0.01536816917359829, 0.013987180776894093, -0.021405331790447235, 0.01321270689368248, 0.02646273747086525, -0.034543391317129135, 0.048707857728004456, -0.010488052852451801, 0.03741734102368355, 0.006116475444287062, 0.003543450031429529, 0.03340500593185425, 0.034039516001939774, -0.02989654801785946, 0.0032915128394961357, -0.018512718379497528, -0.03769727051258087, 0.033703599125146866, -0.0009360166732221842, -0.02941133640706539, 0.0010718995472416282, -0.048819832503795624, -0.022748995572328568, 0.04075784236192703, -0.018745994195342064, 0.003149215131998062, -0.01631060056388378, 0.055351536720991135, 0.01693577878177166 ]
In the past few years, Softmax has become a common component in neural network frameworks. In this paper, a gradient decay hyperparameter is introduced in Softmax to control the probability-dependent gradient decay rate during training. By following the theoretical analysis and empirical results of a variety of model architectures trained on MNIST, CIFAR-10/100 and SVHN, we find that the generalization performance depends significantly on the gradient decay rate as the confidence probability rises, i.e., the gradient decreases convexly or concavely as the sample probability increases. Moreover, optimization with the small gradient decay shows a similar curriculum learning sequence where hard samples are in the spotlight only after easy samples are convinced sufficiently, and well-separated samples gain a higher gradient to reduce intra-class distance. Based on the analysis results, we can provide evidence that the large margin Softmax will affect the local Lipschitz constraint of the loss function by regulating the probability-dependent gradient decay rate. This paper provides a new perspective and understanding of the relationship among concepts of large margin Softmax, local Lipschitz constraint and curriculum learning by analyzing the gradient decay rate. Besides, we propose a warm-up strategy to dynamically adjust Softmax loss in training, where the gradient decay rate increases from over-small to speed up the convergence rate.
[ -0.044223640114068985, -0.005650798324495554, -0.029591619968414307, 0.018526611849665642, 0.06515251845121384, 0.012621026486158371, 0.008712785318493843, 0.030137591063976288, -0.052085619419813156, 0.031575314700603485, -0.03132052719593048, 0.004424638580530882, 0.019309168681502342, 0.009745580144226551, 0.04469681531190872, 0.04793624207377434, 0.05386912450194359, -0.016097040846943855, 0.0387275330722332, 0.007184066344052553, 0.01032794825732708, -0.07825582474470139, 0.016852300614118576, 0.0170160923153162, -0.022657791152596474, 0.05252239480614662, 0.012020458467304707, 0.006992976646870375, -0.04906458035111427, 0.037235211580991745, 0.015905950218439102, -0.022202813997864723, -0.028900057077407837, -0.044369231909513474, -0.0794205591082573, 0.018599407747387886, 0.07978454232215881, 0.06191309541463852, -0.03667104244232178, -0.009090414270758629, 0.015396378003060818, -0.017088888213038445, 0.012930409982800484, -0.014750312082469463, 0.0036921279970556498, -0.0409478135406971, -0.03370460122823715, -0.0449879989027977, -0.013321688398718834, -0.08771931380033493, -0.011683776043355465, -0.023986319079995155, 0.012375338934361935, -0.02571522630751133, -0.025169257074594498, 0.0073205591179430485, 0.04375046491622925, -0.013339887373149395, 0.07985733449459076, -0.029464226216077805, -0.005127576179802418, -0.010664630681276321, -0.06566209346055984, -0.01677040383219719, -0.0162972304970026, -0.06788237392902374, 0.0371624156832695, -0.023203760385513306, 0.012957707978785038, 0.03330422192811966, -0.08225961029529572, 0.0044928849674761295, -0.028918256983160973, 0.005737243685871363, 0.02547864057123661, -0.03412317857146263, 0.08400671184062958, 0.03059256635606289, 0.017088888213038445, 0.030101193115115166, 0.021038077771663666, -0.0020428409334272146, -0.01722538098692894, 0.008021221496164799, 0.07195895910263062, -0.025405842810869217, 0.007316009607166052, -0.03774478659033775, 0.03173910453915596, -0.02069229446351528, -0.040183454751968384, 0.006506152451038361, -0.0059055848978459835, 0.037963174283504486, -0.013330788351595402, 0.029245838522911072, -0.04200335592031479, 0.030465174466371536, -0.050666093826293945, 0.011519985273480415, -0.02635219320654869, 0.03499673306941986, 0.05477907508611679, -0.03661644458770752, 0.03661644458770752, -0.06016598641872406, -0.03678023815155029, -0.039309900254011154, 0.040911417454481125, 0.12025918066501617, 0.009113163687288761, -0.010755625553429127, -0.034013982862234116, 0.029609819874167442, -0.021602246910333633, 0.042622122913599014, -0.0265341829508543, -0.06977507472038269, 0.019108979031443596, -0.02593361586332321, 0.028681669384241104, 0.0257516261190176, -0.017334574833512306, 0.04709908738732338, -0.05019291862845421, 0.02387712523341179, 0.030192188918590546, -0.02833588793873787, 0.022184615954756737, -0.059037648141384125, 0.06038437783718109, 0.046152736991643906, 0.01828092336654663, -0.004160752985626459, 0.061294328421354294, -0.02354954369366169, 0.09084954857826233, 0.0038286205381155014, -0.032867446541786194, -0.010801123455166817, 0.0009002831648103893, -0.006428806576877832, 0.051175668835639954, -0.012247946113348007, 0.032812848687171936, -0.0003270137822255492, -0.025460440665483475, 0.046662308275699615, -0.022184615954756737, 0.04320449382066727, -0.0322122797369957, 0.0615491159260273, -0.02309456653892994, 0.050993677228689194, 0.07920217514038086, 0.00181080331094563, -0.007202265318483114, 0.017152585089206696, 0.005973831284791231, -0.04895538464188576, 0.038982320576906204, -0.006583498325198889, 0.024040916934609413, 0.05481547489762306, -0.0058873859234154224, 0.029828207567334175, 0.03960108757019043, 0.011046810075640678, -0.07239573448896408, 0.03334062173962593, -0.02584262005984783, -0.008981220424175262, 0.01909078098833561, -0.0017050214810296893, -0.018744999542832375, 0.04957415163516998, 0.004972884431481361, 0.02869986742734909, -0.021311061456799507, 0.025060061365365982, -0.03375919908285141, 0.012957707978785038, -0.00915411114692688, 0.06449735909700394, 0.03814516216516495, -0.049646951258182526, 0.04174857214093208, 0.026206601411104202, -0.015450974926352501, -0.013858560472726822, 0.02704375609755516, 0.010455342009663582, 0.05044770613312721, 0.027844512835144997, 0.030701760202646255, 0.0075844451785087585, 0.0054779076017439365, 0.0033577207941561937, -0.02243940159678459, -0.013139698654413223, -0.00031507067615166306, -0.0668996274471283, 0.006660844199359417, -0.010428043082356453, 0.01881779544055462, 0.005441509652882814, -0.03665284439921379, -0.014459128491580486, 0.022548595443367958, 0.011283397674560547, 0.028572475537657738, -0.049100980162620544, -0.05237680301070213, -0.04444202780723572, -0.046662308275699615, -0.02626119740307331, 0.05514305457472801, 0.012793917208909988, -0.03698042407631874, -0.018526611849665642, 0.021311061456799507, 0.01554197072982788, 0.058309685438871384, 0.002015542471781373, 0.010846621356904507, -0.02746233344078064, 0.009295153431594372, -0.05725414305925369, 0.03062896430492401, 0.004818192683160305, 0.0027799014933407307, 0.01602424494922161, -0.003899141913279891, -0.0499381348490715, 0.06136712431907654, -0.0033463463187217712, -0.011492686346173286, 0.007206815294921398, -0.006251366343349218, -0.025678828358650208, 0.0017391446745023131, -0.016997892409563065, 0.024641484022140503, -0.06453375518321991, -0.04083862155675888, 0.041457388550043106, 0.025587834417819977, 0.042622122913599014, -0.010873919352889061, 0.004638477228581905, 0.006847384385764599, -0.06773678213357925, 0.031848300248384476, 0.06395138800144196, -0.0577637143433094, 0.016115238890051842, -0.0016822726465761662, -0.025242052972316742, -0.021820634603500366, -0.02433210052549839, 0.04662591218948364, 0.0036807535216212273, 0.026424989104270935, 0.012166050262749195, 0.047863446176052094, 0.005850987508893013, 0.04131179302930832, 0.053614336997270584, 0.008544444106519222, 0.013876759447157383, 0.04098421335220337, -0.009076765738427639, 0.0045156339183449745, -0.041602980345487595, -0.0031893798150122166, -0.030428774654865265, 0.05452428758144379, -0.017325475811958313, 0.009882071986794472, -0.026570580899715424, 0.04447842389345169, 0.011001313105225563, 0.0061285230331122875, 0.015696661546826363, 0.016643011942505836, -0.049100980162620544, -0.010983113199472427, 0.0076117436401546, -0.11873046308755875, -0.02427750453352928, -0.010792023502290249, -0.0018244525417685509, -0.02939143031835556, -0.00012966807116754353, 0.029154842719435692, 0.01658841408789158, -0.048773396760225296, -0.022111820057034492, 0.008599041029810905, -0.06333261728286743, -0.049428559839725494, 0.04007425904273987, 0.04269491881132126, -0.054997462779283524, 0.016888698562979698, -0.006547100376337767, 0.01037344615906477, 0.006888332311064005, -0.044369231909513474, 0.035488106310367584, 0.04480600729584694, 0.013057802803814411, 0.01794424280524254, -0.006610797252506018, 0.005036581307649612, 0.01665211096405983, 0.0443328320980072, -0.006538000889122486, -0.04258572682738304, -0.02819029428064823, -0.007793733850121498, -0.01329439040273428, -0.05321395769715309, -0.010728327557444572, -0.01478671096265316, -0.013094200752675533, -0.009918470866978168, -0.015878653153777122, -0.04102060943841934, 0.042658522725105286, -0.005800940096378326, -0.04382326081395149, -0.04757225885987282, -0.02737133949995041, -0.02189343050122261, 0.018472013995051384, 0.007397904992103577, 0.0198187418282032, -0.048227425664663315, 0.0009958280716091394, 0.007593544665724039, 0.026606978848576546, 0.012320742011070251, -0.028918256983160973, -0.017061589285731316, 0.006255915854126215, -0.06227707490324974, 0.023331154137849808, 0.010846621356904507, 0.017571162432432175, 0.0009446433396078646, 0.042112551629543304, 0.024623285979032516, 0.006406058091670275, -0.01331258937716484, 0.006415157578885555, 0.02087428607046604, 0.011574582196772099, -0.05994759872555733, 0.02939143031835556, 0.010719227604568005, -0.016697607934474945, -0.013667470775544643, -0.025041863322257996, 0.001220472389832139, -0.014586521312594414, -0.012894012033939362, 0.0023726983927190304, 0.0043677669018507, 0.012730220332741737, -0.0006898569408804178, -0.03132052719593048, -0.015332681126892567, 0.024823475629091263, 0.052740782499313354, -0.008576292544603348, 0.004561131354421377, -0.020965280011296272, -0.07279611378908157, 0.06278664618730545, -0.03707142174243927, 0.04375046491622925, 0.060457173734903336, 0.0418577641248703, 0.016406424343585968, 0.03894592076539993, -0.0014684341149404645, -0.04294970631599426, 0.030738158151507378, 0.025424042716622353, 0.02354954369366169, -0.02930043637752533, -0.005509756039828062, -0.018926989287137985, 0.063114233314991, 0.031102139502763748, -0.015077895484864712, 0.004247198347002268, 0.03239427134394646, -0.03308583423495293, -0.011410790495574474, -0.007689089514315128, 0.007625393103808165, -0.06322342157363892, -0.03526971861720085, 0.003014214104041457, -0.021147271618247032, -0.0011209463700652122, 0.049974530935287476, -0.01996433362364769, 0.0324670672416687, 0.0028481478802859783, 0.02469608187675476, 0.008107666857540607, 0.021038077771663666, 0.03206668794155121, -0.04819102585315704, -0.0069565786980092525, -0.00986387301236391, 0.05918323993682861, 0.016097040846943855, -0.013813062570989132, 0.05070249363780022, 0.00888567604124546, 0.006374209653586149, 0.003141607390716672, -0.007379706017673016, -0.018062535673379898, 0.03719881549477577, 0.014277137815952301, 0.023331154137849808, 0.030246784910559654, 0.03619786724448204, -0.08109486848115921, -0.014850406907498837, -0.024859873577952385, -0.054160308092832565, 0.03122953325510025, 0.007552596740424633, 0.01800793781876564, 0.008644538931548595, -0.038472745567560196, 0.046662308275699615, -0.03590668365359306, -0.058710064738988876, 0.005400561727583408, -0.00532321585342288, -0.008771931752562523, -0.014986899681389332, -0.04149378463625908, -0.08247799426317215, 0.03215768188238144, -0.027771716937422752, -0.05314116179943085, 0.06522531807422638, -0.06213148310780525, 0.0022282435093075037, -0.016970593482255936, 0.009204158559441566, -0.06882872432470322, 0.03133872523903847, 0.0012636950705200434, 0.0038286205381155014, -0.03490573540329933, -0.010509938932955265, 0.02837228588759899, -0.020892484113574028, -0.018326422199606895, -0.029227640479803085, -0.015123392455279827, -0.019982533529400826, -0.06391498446464539, -0.0427677184343338, 0.029446028172969818, 0.03425057232379913, 0.049610551446676254, -0.043495677411556244, -0.08575382083654404, 0.027480533346533775, -0.0007268236950039864, 0.07563516497612, -0.05350514501333237, -0.009481693617999554, 0.017052490264177322, -0.03041057661175728, -0.012202448211610317, 0.061658307909965515, 0.012420836836099625, 0.042986106127500534, -0.041930560022592545, -0.020255519077181816, 0.011874865740537643, -0.029646217823028564, -0.02156584896147251, -0.006078475620597601, -0.06886512041091919, 0.021638644859194756, -0.014231639914214611, 0.048591405153274536, -0.00044246387551538646, -0.0020940257236361504, -0.014986899681389332, 0.042986106127500534, 0.024550490081310272, -0.02535124681890011, 0.007188616320490837, 0.0002948811452370137, -0.02032831497490406, 0.0013364912010729313, -0.02354954369366169, 0.04116620123386383, 0.006829185411334038, -0.000030284320018836297, -0.041093405336141586, 0.018708601593971252, 0.019745945930480957, 0.027171149849891663, -0.03605227544903755, 0.051212064921855927, 0.013076001778244972, -0.01058273483067751, 0.011720173992216587, -0.042840514332056046, 0.033777397125959396, -0.04567956179380417, 0.08276917785406113, 0.05532504618167877, -0.029173042625188828, 0.06085754930973053, -0.00516397412866354, -0.022293809801340103, 0.007420653942972422, -0.03554270416498184, -0.07650871574878693, 0.005282267928123474, 0.04007425904273987, -0.02465968392789364, 0.014167943969368935, -0.03354080766439438, 0.013166996650397778, -0.015978746116161346, 0.02884545922279358, -0.003232602495700121, 0.06773678213357925, -0.023476745933294296, -0.026097407564520836, 0.026970960199832916, -0.03570649400353432, 0.011483587324619293, 0.0409478135406971, -0.008362453430891037, -0.036725640296936035, -0.015005098655819893, 0.007479800842702389, -0.03850914537906647, -0.007629942614585161, -0.035124123096466064, -0.0055006565526127815, -0.016706708818674088, -0.02695276029407978, -0.012621026486158371, 0.01165647804737091, -0.021602246910333633, -0.0085080461576581, 0.022384805604815483, -0.06660844385623932, 0.03439616411924362, -0.006451555527746677, 0.02351314388215542, 0.02400451898574829, -0.01644282229244709, 0.0003855919057969004, 0.021966226398944855, -0.002513740910217166, -0.04291331022977829, 0.01963675208389759, 0.021693242713809013, 0.0020109927281737328, 0.0304469745606184, 0.0016117515042424202, 0.018926989287137985, -0.028226692229509354, -0.0007734586833976209, -0.002420470817014575, -0.012466334737837315, 0.03472374752163887, -0.020291917026042938, -0.0393826961517334, -0.007033924572169781, -0.04502439498901367, 0.028590673580765724, 0.02640679106116295, -0.009536290541291237, 0.004365492146462202, -0.0015912775415927172, 0.00724321324378252, 0.06187669560313225, -0.015614766627550125, 0.029009250923991203, -0.06529811024665833, 0.030192188918590546, -0.0056416988372802734, 0.007684539537876844, 0.031211333349347115, -0.04345928132534027, 0.002434120047837496, 0.032230477780103683, 0.03550630435347557, 0.005418760702013969, 0.001498007564805448, 0.049100980162620544, -0.0028868208173662424, 0.03474194556474686, -0.03275825083255768, 0.016615713015198708, -0.010764725506305695, 0.028954654932022095, 0.014823108911514282, 0.04426003620028496, 0.031848300248384476, 0.019836941733956337, 0.01918177679181099, -0.009167760610580444, -0.004718098323792219, -0.015114293433725834, 0.03923710435628891, -0.01403145119547844, -0.029500624164938927, 0.041238997131586075, -0.041093405336141586, -0.04669870808720589, -0.0053960117511451244, -0.01117420382797718, -0.008844727650284767, -0.020637698471546173, -0.003528336528688669, 0.03195749223232269, -0.0010902355425059795, -0.031575314700603485, -0.01619713567197323, -0.03667104244232178, -0.007734586950391531, -0.0018722250824794173, 0.005719044711440802, -0.014204341918230057, 0.018199028447270393, 0.004790894221514463, -0.025405842810869217, 0.032230477780103683, 0.02544224262237549, -0.006724541075527668, 0.042148951441049576, -0.0026183852460235357, 0.015214387327432632, 0.001756206271238625, -0.027717120945453644, 0.03192109614610672, 0.014331734739243984, -0.0009082452743314207, 0.0010430318070575595, 0.044733211398124695, -0.021820634603500366, -0.01791694387793541, 0.025405842810869217, -0.0034760143607854843, -0.04236733913421631, 0.02478707581758499, 0.02391352318227291, -0.012147851288318634, -0.0039810375310480595, 0.00638330914080143, -0.012903111055493355, -0.02544224262237549, 0.03745359927415848, 0.018062535673379898, -0.02571522630751133, 0.011692875996232033, 0.08662737160921097, 0.02222101390361786, -0.0017334574367851019, 0.008512595668435097, -0.019345566630363464, 0.019400164484977722, -0.012775718234479427, -0.05186723172664642, -0.014795809984207153, 0.03756279498338699, -0.004483785480260849, -0.06125792860984802, 0.009185959585011005, -0.01232984196394682, -0.03026498481631279, -0.0007342170574702322, -0.03508772701025009, 0.015141591429710388, -0.001347865560092032, 0.009163211099803448, 0.0022976272739470005, -0.019855139777064323, 0.003764923894777894, 0.006779137998819351, -0.012803016230463982, -0.0002879143285099417, 0.013785763643682003, 0.03113853745162487, -0.008676386438310146, -0.0015366805018857121, -0.027353139594197273, -0.02262139320373535, -0.040911417454481125, 0.029864605516195297, 0.048773396760225296, -0.008753732778131962, 0.03552450239658356, 0.013558275997638702, 0.014750312082469463, 0.02240300364792347, -0.016888698562979698, -0.016979694366455078, 0.043422881513834, -0.027207547798752785, 0.056926559656858444, 0.012275245040655136, -0.028736265376210213, 0.024404896423220634, 0.023858925327658653, 0.029409630224108696, 0.009131362661719322, 0.006906531285494566, -0.0033872942440211773, 0.0019336467375978827, -0.024131910875439644, 0.005241320002824068, -0.008649088442325592, 0.03667104244232178, -0.013403584249317646, 0.004304070025682449, 0.052413202822208405, -0.027243945747613907, 0.0011294771684333682, 0.0028731715865433216, -0.007188616320490837, -0.010482640005648136, 0.027080154046416283, -0.03432336822152138, 0.007793733850121498, -0.0014115620870143175, 0.01963675208389759, -0.03945549204945564, 0.0081486152485013, 0.030556168407201767, -0.05212201923131943, 0.00410388084128499, -0.05663537606596947, -0.033922988921403885, 0.0015992396511137486, -0.03619786724448204, -0.030610766261816025, -0.030647164210677147, 0.04287691041827202, -0.006883782334625721, 0.03164811059832573, 0.01740737073123455, 0.022748785093426704, 0.05004732683300972, 0.04695349186658859, -0.04502439498901367, 0.03839994966983795, 0.015996946021914482, 0.0023749731481075287, 0.04731747508049011, -0.018199028447270393, -0.009690982289612293, -0.04149378463625908, -0.015460074879229069, 0.04273131862282753, 0.006051177158951759, 0.012056856416165829, 0.03647085279226303, 0.041238997131586075, -0.04051103815436363, 0.008922073990106583, 0.040183454751968384, 0.0633690133690834, -0.028481479734182358, -0.01090121828019619, -0.02478707581758499, 0.017207181081175804, 0.030010197311639786, 0.017006991431117058, -0.004904638044536114, -0.03008299320936203, -0.003824070794507861, -0.0005505206063389778, 0.05368713289499283, 0.05732693895697594, -0.03981947526335716, 0.07818302512168884, 0.03366820141673088, -0.025697028264403343, 0.054305899888277054, 0.0023954471107572317, 0.0024272953160107136, -0.012402637861669064, -0.042658522725105286, 0.02662517875432968, -0.025405842810869217, -0.018563009798526764, -0.02262139320373535, -0.016579315066337585, 0.0032030290458351374, 0.02487807162106037, 0.012894012033939362, -0.007079422008246183, 0.008048520423471928, 0.011046810075640678, 0.011347094550728798, 0.014022351242601871, 0.031666308641433716, -0.05113926902413368, -0.029773609712719917, -0.02566063031554222, -0.01112870592623949, -0.031484320759773254, -0.025151057168841362, -0.02078329026699066, -0.014231639914214611, -0.00017559218395035714, 0.04203975573182106, 0.00904946681112051, 0.011620080098509789, 0.021766038611531258, -0.026825368404388428, 0.04182136803865433, -0.011374392546713352, 0.023385751992464066, -0.02092888206243515, 0.03887312486767769, -0.013703868724405766, 0.016479220241308212, -0.022330207750201225, -0.037781182676553726, -0.03619786724448204, 0.008630889467895031, 0.025169257074594498, -0.02400451898574829, -0.016752205789089203, 0.029973799362778664, 0.03288564458489418, -0.03992866724729538, 0.026188401505351067, 0.02544224262237549, 0.05008372664451599, 0.019345566630363464, -0.04880979284644127, 0.010955815203487873, -0.014076948165893555, 0.025314848870038986, -0.02041931077837944, -0.012939509004354477, -0.014122446067631245, 0.036634642630815506, 0.006114873569458723, -0.01918177679181099, 0.0004566818824969232, -0.012193349190056324, -0.028954654932022095, -0.02369513548910618, -0.04607994109392166, -0.04222174733877182, 0.01607884094119072, 0.008589941076934338, -0.012630125507712364, 0.029609819874167442, -0.01474121306091547, -0.03652545064687729, 0.044405627995729446, 0.021584047004580498, -0.018926989287137985, -0.02866346947848797, 0.005063879769295454, -0.014331734739243984, 0.005814589560031891, -0.019327368587255478, -0.02677077054977417, 0.003325872356072068, -0.015359980054199696, 0.01032794825732708, -0.0324670672416687, -0.013603773899376392, -0.028263092041015625, 0.016515618190169334, 0.00553250452503562, 0.010619132779538631, 0.02529664896428585, 0.05146685242652893, 0.03330422192811966, -0.0014991449424996972, 0.014559222385287285, -0.01798064075410366, -0.013621972873806953, -0.005582551937550306, 0.028991052880883217, -0.03554270416498184, 0.028390483930706978, 0.002386347623541951, 0.03375919908285141, 0.006365110166370869, 0.03399578481912613, -0.02662517875432968, 0.02493266947567463, 0.010983113199472427, -0.009122262708842754, -0.015396378003060818, 0.04673510417342186, 0.04626192897558212, 0.0284268818795681, 0.008398851379752159, 0.018180828541517258, 0.026188401505351067, -0.00820776168256998, 0.013813062570989132, 0.006460655014961958, 0.043168094009160995, -0.01223884616047144, -0.010300650261342525, 0.010409844107925892, -0.0062877642922103405, 0.002525115152820945, 0.011893064714968204, -0.029591619968414307, 0.03137512505054474, -0.029955601319670677, 0.0024841674603521824, 0.0029323184862732887, 0.004151653498411179, -0.027535129338502884, 0.03146611899137497, -0.030829153954982758, 0.02194802835583687, 0.026006411761045456, -0.02713475190103054, 0.04677150398492813, 0.03303123638033867, 0.03850914537906647, -0.05248599871993065, 0.044405627995729446, 0.012693822383880615, -0.04870060086250305, -0.005982930772006512, 0.000029875553082092665, -0.06056636571884155, 0.01106500905007124, -0.04731747508049011, 0.028463279828429222, 0.003578383941203356, -0.0014320360496640205, -0.002289665164425969, 0.02806290239095688, 0.03767198696732521, 0.048736996948719025, 0.005127576179802418, -0.0304469745606184, -0.0017254953272640705, -0.014768511988222599, -0.016979694366455078, 0.02496906742453575, -0.015387278981506824, -0.03721701353788376, 0.004556581843644381, 0.004288146272301674, -0.033831994980573654, -0.0012534580891951919, 0.021929828450083733, -0.003767198882997036, 0.015769457444548607, 0.020219121128320694, -0.006660844199359417, -0.024441294372081757, -0.015241686254739761, 0.08378832787275314, -0.03104754164814949, 0.02185703255236149, 0.042804114520549774, -0.016706708818674088, -0.028572475537657738, -0.0034782893490046263, -0.030574368312954903, -0.03192109614610672, 0.043677669018507004, -0.017125286161899567, 0.03201209008693695, 0.05299557000398636, -0.03206668794155121, -0.016524717211723328, -0.007466151379048824, -0.04287691041827202, -0.009709181264042854, -0.019946135580539703, -0.013166996650397778, 0.012803016230463982, -0.0035419859923422337, -0.0012614201987162232, 0.04065662994980812, 0.0241865087300539, 0.0017675806302577257, 0.011146904900670052, 0.015551069751381874, -0.014886804856359959, -0.006701792124658823, -0.0022691914346069098, 0.0118020698428154, -0.032357871532440186, 0.05055690184235573, -0.007557146716862917, 0.017398271709680557, 0.0065152524039149284, -0.027444135397672653, -0.022512197494506836, -0.010519038885831833, 0.03239427134394646, -0.001215922529809177, -0.02589721791446209, -0.01614253781735897 ]
GNN-based methods have achieved excellent results as a mainstream task in drug response prediction tasks in recent years. Traditional GNN methods use only the atoms in a drug molecule as nodes to obtain the representation of the molecular graph through node information passing, whereas the method using the transformer can only extract information about the nodes. However, the covalent bonding and chirality of a drug molecule have a great influence on the pharmacological properties of the molecule, and these information are implied in the chemical bonds formed by the edges between the atoms. In addition, CNN methods for modelling cell lines genomics sequences can only perceive local rather than global information about the sequence. In order to solve the above problems, we propose the decoupled dual transformer structure with edge embedded for drug respond prediction (TransEDRP), which is used for the representation of cell line genomics and drug respectively. For the drug branch, we encoded the chemical bond information within the molecule as the embedding of the edge in the molecular graph, extracted the global structural and biochemical information of the drug molecule using graph transformer. For the branch of cell lines genomics, we use the multi-headed attention mechanism to globally represent the genomics sequence. Finally, the drug and genomics branches are fused to predict IC50 values through the transformer layer and the fully connected layer, which two branches are different modalities. Extensive experiments have shown that our method is better than the current mainstream approach in all evaluation indicators.
[ -0.03850090131163597, -0.004428967833518982, -0.022694729268550873, -0.037307340651750565, 0.006023225840181112, -0.025661583989858627, -0.012174333445727825, 0.007374508306384087, -0.017460107803344727, 0.0365229994058609, 0.023069849237799644, -0.04211568832397461, -0.021023742854595184, -0.04637841135263443, -0.03360729664564133, 0.022967543452978134, -0.017528312280774117, -0.01819329522550106, 0.00124471471644938, -0.05821172520518303, 0.031015561893582344, -0.014979204162955284, 0.003606262616813183, 0.011296212673187256, 0.057563792914152145, 0.02416110597550869, 0.012080552987754345, -0.010179379023611546, -0.04061521217226982, 0.04201338440179825, 0.00919042807072401, 0.011679857037961483, 0.023462019860744476, -0.01420338824391365, -0.04593508690595627, -0.02199564315378666, 0.0065475404262542725, 0.027093859389424324, -0.011918569914996624, 0.03877371549606323, 0.014893949031829834, 0.017383377999067307, -0.0016390164382755756, 0.018892383202910423, 0.006381294224411249, -0.019352756440639496, -0.009872463531792164, -0.03795527294278145, 0.043241050094366074, -0.02022235095500946, -0.03577275946736336, -0.023121003061532974, -0.008099171333014965, 0.015712391585111618, -0.06677126884460449, 0.1016232818365097, 0.045525867491960526, 0.04037649929523468, 0.041638266295194626, 0.06366801261901855, -0.015388425439596176, -0.033419739454984665, -0.009420614689588547, -0.013103606179356575, 0.017579464241862297, -0.017835227772593498, 0.016564935445785522, -0.013521352782845497, 0.015252018347382545, 0.045389458537101746, -0.04866322875022888, 0.013683336786925793, -0.0005882555851712823, -0.004983121529221535, -0.0013907129177823663, -0.004273378290235996, -0.02047811448574066, 0.045764580368995667, 0.05070933699607849, -0.039251141250133514, 0.03792117163538933, 0.09780388325452805, -0.025133006274700165, 0.008674638345837593, 0.06615743786096573, -0.03188515827059746, 0.03966036066412926, -0.053676191717386246, -0.041024431586265564, 0.013308216817677021, -0.04010368511080742, 0.0006735100178048015, -0.055483583360910416, -0.037273239344358444, -0.03812578320503235, 0.004330925177782774, 0.037409644573926926, 0.010571549646556377, -0.06237214431166649, -0.06905609369277954, -0.019659671932458878, 0.02025645412504673, -0.021245405077934265, 0.03292526304721832, 0.017494209110736847, -0.009829835966229439, -0.011611653491854668, 0.0657823234796524, -0.0017018916551023722, 0.135929673910141, -0.029941357672214508, -0.013112131506204605, 0.025371719151735306, 0.033163975924253464, -0.04484383016824722, -0.04593508690595627, -0.08593647181987762, -0.03232848271727562, 0.005179206840693951, -0.05268723890185356, 0.022916391491889954, -0.005891081411391497, -0.04890194162726402, -0.015456628985702991, -0.03379485756158829, 0.055551789700984955, -0.05452873557806015, -0.009633750654757023, 0.004288298077881336, 0.020887335762381554, -0.0847088024020195, 0.02658233232796192, 0.001040104078128934, -0.002894388046115637, 0.06837405264377594, 0.047299157828092575, 0.00600191205739975, 0.02034170739352703, -0.05793891102075577, 0.02610490657389164, 0.027025654911994934, 0.006257675588130951, -0.014390948228538036, -0.01643705554306507, 0.011040449142456055, 0.023734834045171738, -0.00918190274387598, 0.09664442390203476, 0.04262721538543701, 0.011023398488759995, -0.016837749630212784, 0.0032268802169710398, 0.013205911964178085, -0.029958408325910568, -0.0075705936178565025, 0.005272986833006144, 0.02419520728290081, -0.047571972012519836, -0.023274460807442665, -0.013896472752094269, 0.037307340651750565, -0.00025509725674055517, 0.006948236376047134, 0.017579464241862297, -0.018892383202910423, 0.04453691467642784, 0.03208976984024048, -0.002636493416503072, -0.05500616133213043, 0.06346339732408524, 0.03222617506980896, 0.014493254013359547, 0.0003748530871234834, 0.04617379978299141, -0.035363540053367615, 0.029600339010357857, 0.00459095137193799, -0.049788590520620346, -0.012890470214188099, 0.021057844161987305, -0.04307053983211517, 0.0019171590683981776, -0.0006495321867987514, 0.0018404300790280104, 0.0161898173391819, 0.06435004621744156, 0.03843269869685173, 0.04177467152476311, -0.007331881206482649, 0.04204748570919037, -0.0022869501262903214, 0.0019406040664762259, 0.017698820680379868, -0.03239668533205986, 0.006253412459045649, -0.04303643852472305, -0.00023724710626993328, -0.00007233305950649083, 0.027724741026759148, -0.039046529680490494, -0.017562413588166237, 0.001837233081459999, 0.0042541963048279285, -0.005507436580955982, 0.03278885409235954, -0.008661850355565548, 0.02194449119269848, -0.027673589065670967, 0.03205566853284836, -0.05446053296327591, -0.0322943776845932, -0.04692403972148895, -0.05708636716008186, 0.017434531822800636, 0.003815135918557644, -0.012506824918091297, -0.029856102541089058, -0.012737012468278408, 0.0024745098780840635, -0.0019256845116615295, -0.0160619355738163, 0.031578242778778076, 0.04085392504930496, -0.02409290336072445, 0.01822739839553833, 0.010869939811527729, -0.0439571850001812, -0.0260367039591074, -0.030793901532888412, -0.007276465650647879, -0.005247410386800766, 0.03483496233820915, 0.01839790679514408, -0.03224322572350502, -0.03451099619269371, -0.043513864278793335, 0.0303505789488554, -0.025388769805431366, -0.05101625248789787, -0.011577552184462547, -0.022797035053372383, 0.012515351176261902, 0.003335579764097929, -0.043616168200969696, 0.06250855326652527, 0.010486295446753502, -0.016829224303364754, 0.11867417395114899, 0.03483496233820915, 0.049686282873153687, 0.023615477606654167, -0.03396536782383919, 0.027571283280849457, 0.0073702456429600716, -0.023206256330013275, -0.004744409117847681, -0.003420834196731448, -0.001772226532921195, 0.0142886433750391, -0.0818442553281784, 0.05432412400841713, -0.0404106006026268, -0.009113699197769165, 0.045423563569784164, -0.00817590020596981, -0.01599373109638691, 0.06083756312727928, -0.009403564035892487, 0.011722484603524208, 0.0490383505821228, -0.025167109444737434, -0.055176667869091034, -0.051220864057540894, 0.005153630394488573, -0.014561457559466362, -0.025491075590252876, 0.013956150971353054, -0.0242634117603302, 0.07154551893472672, 0.0009969440288841724, 0.0005999780842103064, -0.045116644352674484, -0.011372941546142101, 0.01419486291706562, -0.009863938204944134, -0.006867244374006987, 0.001756241312250495, -0.0008466831059195101, -0.02017119899392128, -0.020682726055383682, -0.005784513428807259, -0.006828879937529564, -0.023837139829993248, -0.043616168200969696, 0.010153803043067455, -0.02615606039762497, 0.004565374925732613, -0.004090081434696913, -0.003855631686747074, -0.07713820785284042, -0.059678103774785995, -0.06738510727882385, 0.012234010733664036, 0.02639477327466011, -0.0024169632233679295, 0.011355890892446041, -0.0003732545592356473, 0.12958674132823944, -0.03476675599813461, -0.010128227062523365, 0.025252362713217735, -0.02453622594475746, -0.005162155721336603, -0.028560234233736992, -0.019096992909908295, -0.009360936470329762, 0.010759109631180763, -0.07441006600856781, -0.002041843719780445, 0.0006857653497718275, 0.0021846448071300983, -0.02032465673983097, -0.07365982979536057, 0.0027686376124620438, 0.05094804987311363, 0.05313056334853172, -0.002595997415482998, 0.035602252930402756, 0.004791299346834421, 0.022899340838193893, -0.004693256691098213, -0.0034336221870034933, -0.022694729268550873, -0.0002717485185712576, -0.047674279659986496, -0.016684291884303093, -0.03679581359028816, 0.007412872742861509, -0.02431456372141838, -0.027093859389424324, 0.0037554576992988586, 0.049481671303510666, -0.021518219262361526, -0.0328059047460556, -0.03771656006574631, -0.047606077045202255, -0.041638266295194626, 0.045082543045282364, -0.015388425439596176, 0.006666896864771843, 0.0008168440544977784, -0.0029220955912023783, -0.021040793508291245, 0.0009532511467114091, 0.018687771633267403, -0.03700042515993118, 0.01803983747959137, -0.05899606645107269, 0.002295475685968995, 0.03826218843460083, 0.0031267062295228243, -0.007238101214170456, -0.01600225642323494, 0.03509072586894035, -0.07802485674619675, 0.0018670720746740699, 0.0022762934677302837, 0.022711781784892082, 0.029822001233696938, -0.014987729489803314, -0.016752496361732483, 0.02392239309847355, -0.005724835209548473, -0.003868419909849763, 0.0012063502799719572, -0.014680813066661358, 0.015686815604567528, 0.013606607913970947, -0.008666113018989563, 0.06240624561905861, -0.025525176897644997, -0.005349715705960989, -0.04238850250840187, -0.000929273315705359, 0.007971289567649364, -0.0071571096777915955, 0.05282364785671234, -0.015482204966247082, -0.07461468130350113, 0.039523955434560776, 0.01617276668548584, -0.041194941848516464, 0.020597470924258232, -0.028833048418164253, 0.021091947332024574, 0.0008173768874257803, 0.016957106068730354, 0.03856910392642021, 0.03839859738945961, -0.007114482577890158, -0.05398310720920563, -0.0028261845000088215, -0.027724741026759148, 0.004252064973115921, 0.000994279864244163, -0.053266968578100204, 0.01776702329516411, -0.05783660709857941, 0.05466514080762863, 0.005886818747967482, 0.014842797070741653, -0.04692403972148895, 0.017698820680379868, -0.0409221276640892, 0.05265313759446144, 0.019131094217300415, -0.03812578320503235, -0.0164029523730278, -0.0021345578134059906, -0.012839317321777344, 0.01797163486480713, 0.06363391131162643, 0.008580858819186687, -0.008516917936503887, -0.021006692200899124, 0.03405062109231949, 0.021126048639416695, -0.03290821239352226, 0.0068501937203109264, 0.03411882370710373, 0.010418091900646687, -0.02030760608613491, 0.0011370809515938163, 0.00044012602302245796, -0.06128088757395744, -0.028815997764468193, 0.02214910089969635, -0.010656803846359253, -0.013333793729543686, 0.06697588413953781, -0.0028688115999102592, 0.007847670465707779, -0.029583288356661797, -0.03792117163538933, -0.04078572243452072, -0.014493254013359547, -0.01815919391810894, -0.011918569914996624, -0.03829628974199295, -0.051084455102682114, -0.047367364168167114, 0.026514127850532532, -0.041160840541124344, -0.06639615446329117, 0.03829628974199295, 0.013384945690631866, -0.03198746219277382, -0.013811218552291393, 0.0857318565249443, -0.017494209110736847, -0.02639477327466011, 0.028833048418164253, -0.03226027637720108, 0.007233838550746441, 0.02027350477874279, 0.05623382329940796, -0.07215934991836548, -0.03287411108613014, 0.011620178818702698, 0.0010976508492603898, 0.018977636471390724, -0.022831136360764503, 0.05875735357403755, 0.01022200658917427, 0.006036013830453157, 0.011560501530766487, 0.04440050944685936, -0.08095760643482208, 0.00020993904036004096, 0.0409221276640892, 0.023837139829993248, -0.025269413366913795, 0.031578242778778076, 0.016505258157849312, -0.015456628985702991, 0.015013305470347404, 0.05067523568868637, -0.008116221986711025, 0.009710479527711868, 0.012438621371984482, 0.037102729082107544, -0.03812578320503235, -0.06789662688970566, -0.019284551963210106, 0.027179112657904625, -0.04081982374191284, -0.02027350477874279, -0.0319533608853817, 0.06816944479942322, 0.0184320081025362, 0.016513783484697342, -0.020836183801293373, 0.05797301605343819, 0.023820089176297188, 0.0316123440861702, 0.03002661094069481, 0.07052246481180191, 0.018773026764392853, -0.01595962978899479, 0.00555006368085742, 0.006786252837628126, -0.004727358464151621, -0.030810952186584473, 0.0032972150947898626, -0.055824603885412216, -0.0028709429316222668, -0.003382469527423382, 0.03485201299190521, -0.03435753658413887, 0.029020609334111214, 0.025593381375074387, 0.0014642449095845222, -0.006168158259242773, 0.015354323200881481, -0.03655710071325302, -0.013325267471373081, 0.05316466465592384, 0.0072594149969518185, 0.0782976746559143, 0.033198077231645584, -0.0007278597331605852, -0.0163176991045475, 0.02794640325009823, 0.007003651466220617, -0.019250450655817986, -0.002242191694676876, -0.015755020081996918, -0.03785296902060509, -0.05036832019686699, 0.03236258402466774, 0.03812578320503235, 0.06015552952885628, -0.006027488503605127, 0.012796690687537193, 0.00555858900770545, 0.0102305319160223, 0.05855274572968483, -0.05030011385679245, -0.045491766184568405, 0.043616168200969696, -0.023837139829993248, 0.005179206840693951, -0.009684903547167778, 0.011560501530766487, 0.01110865268856287, -0.064077228307724, -0.031339529901742935, -0.018755976110696793, -0.04303643852472305, -0.01642000302672386, 0.02235371246933937, 0.039182938635349274, -0.0045525869354605675, -0.02809986099600792, 0.007783729583024979, -0.02859433740377426, -0.01633474975824356, 0.04828811064362526, 0.02231961116194725, 0.026633484289050102, 0.0005498910904861987, -0.025644533336162567, -0.051084455102682114, 0.03891012445092201, -0.0072594149969518185, 0.013367895036935806, 0.037102729082107544, 0.0000460906776424963, -0.00452701048925519, -0.012327791191637516, 0.06271316111087799, -0.03775066137313843, -0.00995771773159504, 0.004492908716201782, 0.0004931436269544065, -0.04883373901247978, -0.04027419537305832, -0.06564591079950333, -0.0164029523730278, -0.009258631616830826, -0.01836380548775196, 0.015405476093292236, 0.0301800686866045, -0.01844905875623226, -0.0070590670220553875, -0.03053813800215721, 0.01007707417011261, -0.012984249740839005, 0.059916816651821136, -0.045764580368995667, 0.001625162665732205, 0.012668808922171593, 0.023700732737779617, 0.005694996099919081, -0.005507436580955982, -0.007250889670103788, -0.01317180972546339, 0.031390681862831116, 0.03597737103700638, -0.02833857387304306, 0.03645479679107666, 0.006901346147060394, -0.0013406259240582585, -0.02850908227264881, 0.017596514895558357, 0.04610559716820717, 0.03665940463542938, 0.005579902790486813, -0.019540315493941307, -0.051357269287109375, 0.02462148107588291, -0.031305428594350815, 0.07400085031986237, 0.0328059047460556, -0.0008642668253742158, 0.014928051270544529, 0.030589289963245392, -0.0527554415166378, -0.030810952186584473, -0.01587437465786934, -0.033556144684553146, -0.029003558680415154, -0.04641251266002655, -0.055551789700984955, 0.024655582383275032, -0.039251141250133514, -0.02445097081363201, 0.01785227842628956, -0.003367550205439329, 0.05377849563956261, -0.0601896308362484, 0.03031647577881813, 0.003361155977472663, -0.03244783729314804, 0.011586077511310577, -0.01110012736171484, 0.021552320569753647, 0.05916657671332359, 0.06646435707807541, 0.02202974632382393, 0.012839317321777344, 0.029480982571840286, -0.006487862206995487, 0.02042696252465248, -0.01613866351544857, -0.06056474894285202, 0.016726920381188393, -0.0012820134870707989, -0.004211569204926491, 0.020853234454989433, -0.017332226037979126, 0.026616433635354042, 0.039251141250133514, -0.0019107649568468332, 0.010477770119905472, -0.06206522881984711, 0.022745883092284203, 0.015635663643479347, -0.0011317526223137975, 0.04262721538543701, 0.025235312059521675, 0.009821310639381409, -0.006845931056886911, 0.030896207317709923, 0.009625225327908993, -0.008329357951879501, 0.03778476640582085, 0.014817220158874989, -0.026701688766479492, 0.0021175069268792868, -0.029532136395573616, -0.007728314492851496, -0.06100807338953018, -0.0027366674039512873, 0.03850090131163597, -0.0010406369110569358, 0.011679857037961483, -0.03413587436079979, 0.002034383825957775, 0.05868915095925331, 0.010605651885271072, -0.04197928309440613, -0.010733532719314098, 0.0281510129570961, -0.026923349127173424, 0.012651758268475533, 0.007323355879634619, -0.01586584933102131, -0.011696908622980118, 0.011790688149631023, 0.025866195559501648, -0.02042696252465248, 0.007344669196754694, -0.025763889774680138, -0.03359024599194527, 0.037614256143569946, 0.03655710071325302, -0.023189205676317215, -0.020512215793132782, -0.009539971128106117, 0.0328911617398262, 0.01795458421111107, -0.01521791610866785, 0.004428967833518982, 0.0027110909577459097, 0.014561457559466362, 0.01300982665270567, 0.0486973337829113, -0.043616168200969696, 0.009028444066643715, -0.029702644795179367, 0.0361819826066494, 0.020972590893507004, -0.01109160203486681, 0.045594070106744766, 0.01393909938633442, -0.008900563232600689, 0.03253309056162834, 0.008525443263351917, -0.0033547619823366404, 0.04259311407804489, 0.020767979323863983, -0.04893604293465614, 0.017195818945765495, 0.02608785592019558, -0.026769891381263733, 0.004087950102984905, 0.021364761516451836, 0.031151968985795975, -0.0090881222859025, 0.03427228331565857, 0.005729097872972488, 0.004603739362210035, -0.014868373051285744, 0.01197824813425541, 0.02838972583413124, -0.005055587738752365, 0.06547540426254272, -0.009880988858640194, -0.027758844196796417, 0.02414405532181263, -0.033283330500125885, 0.05040242150425911, 0.009650802239775658, -0.03473265469074249, 0.006223573815077543, 0.006705261301249266, 0.0013321004807949066, -0.002312526572495699, -0.01583174802362919, -0.02015414834022522, 0.004991646856069565, -0.001727467984892428, 0.014740491285920143, 0.023649578914046288, 0.037614256143569946, -0.033283330500125885, 0.006432447116822004, -0.02185923606157303, -0.03031647577881813, 0.019779028370976448, 0.008738579228520393, 0.07925251871347427, -0.017443057149648666, 0.0014333401340991259, 0.03244783729314804, -0.0199495367705822, -0.023700732737779617, -0.033061668276786804, 0.057802505791187286, -0.025133006274700165, -0.035022519528865814, 0.008892036974430084, 0.0009276748169213533, -0.012643232010304928, -0.017818177118897438, 0.04037649929523468, -0.030691595748066902, -0.031032614409923553, -0.04208158701658249, -0.008401824161410332, -0.06656666100025177, -0.0035295335110276937, 0.025252362713217735, 0.04054700955748558, 0.03488611429929733, 0.012182858772575855, 0.02453622594475746, -0.03798937425017357, -0.05285774916410446, 0.03594326972961426, -0.03214092180132866, 0.02453622594475746, 0.03587506711483002, -0.00919042807072401, -0.055176667869091034, -0.023376764729619026, -0.011057499796152115, -0.01981312967836857, -0.013240013271570206, -0.0018148537492379546, 0.028560234233736992, -0.01602783426642418, -0.0121317058801651, 0.01584027335047722, -0.022728832438588142, -0.02825331874191761, 0.051084455102682114, -0.03597737103700638, 0.0059422338381409645, 0.01790343038737774, -0.027008604258298874, 0.0025448447559028864, -0.00998329371213913, -0.00658164219930768, -0.06230393797159195, 0.045594070106744766, -0.0012010218342766166, 0.041672367602586746, 0.00808638334274292, 0.00920747872442007, 0.008069331757724285, -0.011475246399641037, 0.004642103798687458, -0.0019352756207808852, 0.04893604293465614, 0.013197386637330055, -0.025678634643554688, 0.006112742703408003, 0.004341581836342812, -0.0005019354866817594, 0.02828742004930973, -0.05671124905347824, -0.024757888168096542, -0.017391905188560486, -0.015260543674230576, 0.007216787897050381, -0.029259322211146355, -0.0008839818765409291, 0.021126048639416695, -0.01420338824391365, -0.016863327473402023, 0.033283330500125885, 0.02796345390379429, -0.0031586766708642244, 0.019318655133247375, 0.029429830610752106, 0.009275682270526886, -0.009019918739795685, -0.019591469317674637, 0.029208168387413025, 0.025661583989858627, 0.013419047929346561, -0.023393817245960236, 0.00818442553281784, -0.01125358510762453, -0.0360114723443985, 0.012216960079967976, -0.02035875804722309, -0.007732577156275511, -0.028935354202985764, -0.004200912080705166, -0.013325267471373081, 0.029088811948895454, 0.02213205024600029, -0.005950759630650282, 0.05094804987311363, -0.007455500308424234, -0.06953351199626923, -0.01619834266602993, 0.02231961116194725, -0.0409221276640892, -0.0017711608670651913, 0.02209794893860817, 0.02018824964761734, -0.025525176897644997, 0.009267156943678856, -0.04873143509030342, -0.025763889774680138, -0.017178768292069435, -0.030725697055459023, 0.01629212126135826, 0.005716309882700443, -0.002325314562767744, -0.012651758268475533, -0.02196154184639454, 0.02235371246933937, 0.009437665343284607, -0.02006889320909977, 0.0005384350079111755, 0.006892820820212364, -0.06291776895523071, 0.005976335611194372, -0.0011456063948571682, 0.04388898238539696, -0.02642887458205223, 0.003557241288945079, -0.045116644352674484, 0.04600329324603081, -0.013853845186531544, 0.03183400630950928, -0.04259311407804489, -0.0009409958147443831, -0.001371530699543655, -0.0007502390071749687, 0.020699776709079742, 0.027264367789030075, -0.002139886375516653, 0.051391370594501495, -0.06445235013961792, -0.05244852602481842, 0.025610432028770447, -0.0026748578529804945, 0.027792945504188538, -0.021279506385326385, 0.01328264083713293, -0.023001646623015404, 0.027503080666065216, 0.006006174720823765, 0.035636354237794876, -0.009011393412947655, 0.01851726323366165, 0.000262024172116071, 0.001060884795151651, 0.009386513382196426, -0.03174874931573868, -0.011031923815608025, 0.00561400456354022, -0.016974156722426414, 0.008256891742348671, -0.003307871986180544, 0.05701816454529762, -0.03183400630950928, -0.012063502334058285, 0.03046993352472782, -0.011424094438552856, 0.000994812697172165, 0.025576330721378326, -0.011586077511310577, 0.005191994830965996, -0.037409644573926926, 0.011892993003129959, -0.0031160495709627867, 0.011534924618899822, -0.021398862823843956, 0.04157005995512009, -0.02044401317834854, 0.006206522695720196, 0.039558056741952896, -0.027008604258298874, 0.03174874931573868, 0.027809996157884598, -0.047230955213308334, -0.015720916911959648, -0.010025921277701855, -0.013112131506204605, 0.053301069885492325, -0.04276362434029579, -0.02191038988530636, 0.01404140517115593, 0.005409393925219774, -0.03265244886279106, 0.021006692200899124, -0.013615133240818977, -0.022950492799282074, 0.02854318358004093, 0.027844097465276718, -0.01520086545497179, -0.02047811448574066, -0.008026705123484135, 0.033368583768606186, 0.004047454334795475, 0.007579118944704533, 0.01418633759021759, -0.013947625644505024, -0.023376764729619026, 0.04184287413954735, 0.003589211730286479, -0.03901242837309837, -0.011534924618899822, 0.0028197902720421553, 0.027690639719367027, -0.017528312280774117, -0.0324648879468441, -0.023308562114834785, -0.003970724996179342, -0.0015260543441399932, -0.01824444904923439, 0.0034783808514475822, 0.019864283502101898, 0.005972072947770357, -0.008691688999533653, -0.0005669419770129025, 0.0444687120616436, 0.002619442529976368, 0.047026343643665314, 0.021143099293112755, 0.049686282873153687, -0.0316975973546505, 0.021126048639416695, 0.011483771726489067, 0.02392239309847355, -0.025763889774680138, 0.007830619812011719, -0.04883373901247978, -0.028833048418164253, -0.009531445801258087, 0.00511526595801115, -0.02414405532181263, -0.03208976984024048, 0.03611377626657486, -0.02433161437511444, -0.0303505789488554, 0.0013150495942682028 ]