text
stringlengths
481
13.8k
embedding
sequencelengths
1.02k
1.02k
Recommendation systems are unique as they show a conflation of compute and memory intensity due to their deep learning and massive embedding tables. Training these models typically involve a hybrid CPU-GPU mode, where GPUs accelerate the deep learning portion and the CPUs store and process the memory-intensive embedding tables. The hybrid mode incurs a substantial CPU-to-GPU transfer time and relies on main memory bandwidth to feed embeddings to GPU for deep learning acceleration. Alternatively, we can store the entire embeddings across GPUs to avoid the transfer time and utilize the GPU's High Bandwidth Memory (HBM). This approach requires GPU-to-GPU backend communication and scales the number of GPUs with the size of the embedding tables. To overcome these concerns, this paper offers a heterogeneous acceleration pipeline, called Hotline. Hotline leverages the insight that only a small number of embedding entries are accessed frequently, and can easily fit in a single GPU's HBM. Hotline implements a data-aware and model-aware scheduling pipeline that utilizes the (1) CPU main memory for not-frequently-accessed embeddings and (2) GPUs' local memory for frequently-accessed embeddings. Hotline improves the training throughput by dynamically stitching the execution of popular and not-popular inputs through a novel hardware accelerator and feeding to the GPUs. Results on real-world datasets and recommender models show that Hotline reduces the average training time by 3x and 1.8x in comparison to Intel-optimized CPU-GPU DLRM and HugeCTR-optimized GPU-only baseline, respectively. Hotline increases the overall training throughput to 35.7 epochs/hour in comparison to 5.3 epochs/hour for the Intel-optimized DLRM baseline
[ 0.0005735796876251698, -0.01670147106051445, -0.03719424083828926, 0.008642720058560371, 0.02722187153995037, -0.02129235491156578, -0.030078820884227753, 0.0425487756729126, -0.030132725834846497, 0.03322326019406319, 0.014105062000453472, 0.007681419141590595, -0.007488260976970196, -0.015416743233799934, -0.007555641699582338, 0.029845234006643295, -0.017896359786391258, 0.005323088727891445, 0.024023527279496193, -0.005278168246150017, 0.015398775227367878, -0.02628752402961254, -0.018363533541560173, -0.03272015228867531, 0.02925228141248226, 0.005147898569703102, -0.03261234238743782, 0.021993115544319153, -0.049232956022024155, -0.005543199833482504, 0.02909056842327118, 0.0007591578178107738, -0.013188682496547699, -0.020645499229431152, -0.06213414669036865, -0.05796551704406738, 0.06694963574409485, 0.03112097829580307, -0.015713218599557877, -0.012425032444298267, -0.005134422332048416, 0.000988252810202539, -0.055054664611816406, 0.011984811164438725, 0.006046310067176819, -0.04732832312583923, 0.0014149983180686831, 0.020411912351846695, 0.0008989731431938708, -0.03863169997930527, 0.03318732604384422, -0.04262064769864082, 0.018085025250911713, -0.026592982932925224, -0.056240566074848175, 0.030761614441871643, 0.020250197499990463, 0.03232485055923462, 0.061702910810709, 0.040644142776727676, -0.041578490287065506, 0.009150322526693344, -0.022963400930166245, -0.011894970200955868, 0.0034499005414545536, -0.01874086633324623, -0.0071872929111123085, 0.03730205073952675, -0.011517636477947235, -0.008346243761479855, -0.06662620604038239, -0.02707812562584877, 0.05997795984148979, -0.005071533378213644, -0.022388417273759842, -0.008157577365636826, 0.07309477031230927, 0.03555913269519806, 0.031875643879175186, 0.0028344886377453804, 0.012838302180171013, 0.032827962189912796, 0.02089705504477024, 0.03164205700159073, 0.08423507213592529, -0.04301594942808151, -0.010161035694181919, -0.06641058623790741, -0.02075330913066864, 0.0019899816252291203, -0.06062481552362442, -0.03126472607254982, 0.016782328486442566, -0.044920582324266434, -0.0850975513458252, 0.024041494354605675, -0.03599036857485771, -0.03255843743681908, -0.023196987807750702, 0.03798484429717064, -0.01697997935116291, -0.01845337450504303, 0.028874948620796204, 0.010664145462214947, 0.038308270275592804, -0.002573949284851551, 0.016126489266753197, 0.034013863652944565, 0.01969318278133869, 0.0871099904179573, -0.007959926500916481, -0.05818113684654236, -0.005646517034620047, -0.02224467135965824, -0.01630617119371891, -0.014769886620342731, -0.04215347394347191, 0.010745002888143063, 0.0503469854593277, -0.05440780892968178, 0.043195631355047226, 0.007223229389637709, -0.0064056748524308205, 0.005471326876431704, 0.01057430449873209, 0.03647551313042641, -0.017438169568777084, 0.0030321392696350813, 0.015012457966804504, 0.0024953382089734077, 0.020771276205778122, 0.03325919806957245, 0.001763132750056684, -0.03300764411687851, -0.016746392473578453, 0.009577067568898201, 0.04459715262055397, 0.07747901976108551, -0.028623394668102264, -0.02842574380338192, -0.023520415648818016, -0.030528027564287186, -0.03866763412952423, -0.02450866810977459, -0.003905844409018755, 0.04510026425123215, -0.035379450768232346, 0.032684214413166046, -0.024221176281571388, -0.008238434791564941, -0.06339192390441895, 0.031839706003665924, 0.0036228448152542114, 0.060696687549352646, -0.004927787929773331, -0.013862491585314274, -0.01476090308278799, -0.008858338929712772, -0.041973792016506195, -0.009208719246089458, 0.01556947361677885, -0.05404844135046005, -0.010403606109321117, 0.037517670542001724, 0.021885307505726814, 0.01454528421163559, 0.07043547183275223, 0.015515568666160107, -0.07726339995861053, 0.041147250682115555, -0.039242617785930634, 0.03519976884126663, -0.0022157076746225357, 0.015533536672592163, 0.006342785898596048, 0.039817601442337036, 0.058935802429914474, -0.033349040895700455, -0.05347345769405365, -0.01071805041283369, -0.007340022828429937, -0.016342107206583023, 0.03769735246896744, 0.011625446379184723, 0.05386875942349434, 0.036727067083120346, 0.036709100008010864, 0.03325919806957245, 0.026089873164892197, 0.030258502811193466, 0.03582865372300148, 0.03329513594508171, 0.007146864198148251, -0.008350735530257225, 0.004730137065052986, -0.030671771615743637, -0.011346939019858837, -0.014132014475762844, 0.03841608017683029, -0.008036292158067226, -0.05106571689248085, 0.000535116414539516, -0.028641361743211746, -0.0377332866191864, 0.016521789133548737, -0.0017013669712468982, 0.037912968546152115, 0.013853507116436958, 0.014931601472198963, -0.04147068038582802, 0.047076769173145294, -0.00044583677663467824, -0.025622699409723282, -0.06723712384700775, 0.03652941808104515, -0.0001264795137103647, 0.005704913754016161, -0.002162925899028778, -0.04111131653189659, -0.030689740553498268, -0.00003860362267005257, 0.033205293118953705, 0.061343543231487274, -0.00971182994544506, -0.010475479066371918, -0.049915749579668045, -0.006028342060744762, 0.020968927070498466, -0.00002221463182650041, -0.019459595903754234, -0.017824485898017883, 0.012110588140785694, -0.007290610112249851, -0.04499245434999466, 0.0015969265950843692, -0.024185240268707275, -0.03654738515615463, -0.04959231987595558, -0.06346379965543747, 0.015704235062003136, 0.00501313665881753, 0.06684182584285736, 0.013628903776407242, 0.0044044628739356995, -0.010475479066371918, 0.008701116777956486, -0.01642296463251114, 0.05821707099676132, 0.00963995698839426, -0.012919158674776554, -0.010825860314071178, -0.03599036857485771, -0.0027985521592199802, -0.006814451888203621, 0.03309748321771622, 0.05695929750800133, 0.033744338899850845, -0.051281336694955826, 0.013314460404217243, -0.0682433471083641, 0.011724271811544895, -0.007986878976225853, -0.009550115093588829, 0.029306186363101006, -0.03444509953260422, 0.03403183072805405, 0.07898835092782974, 0.019226009026169777, 0.04617835581302643, 0.013853507116436958, 0.009846591390669346, -0.04772362485527992, 0.006598833482712507, -0.0655481144785881, 0.048011116683483124, -0.05311409384012222, -0.022568099200725555, -0.018561184406280518, 0.04941263794898987, 0.03448103740811348, 0.01777956634759903, -0.028335902839899063, 0.027042189612984657, 0.013745698146522045, -0.06270913034677505, -0.041542552411556244, 0.01233519148081541, -0.03730205073952675, 0.025425048545002937, -0.04463309049606323, -0.024598510935902596, 0.00274464744143188, -0.0001667676551733166, 0.02409539930522442, 0.04323156550526619, 0.023682130500674248, -0.025892222300171852, 0.02048378437757492, 0.06076856330037117, -0.053832825273275375, -0.015237061306834221, 0.027976537123322487, -0.00969386100769043, -0.012829317711293697, -0.06716525554656982, 0.020447848364710808, -0.03232485055923462, 0.0695011243224144, 0.007560133934020996, -0.025568794459104538, 0.07438848167657852, -0.01219144556671381, 0.007425372023135424, -0.023358702659606934, 0.014715982601046562, 0.023250892758369446, -0.0008489989559166133, -0.0190103892236948, 0.006212516222149134, -0.08373196423053741, 0.03439119830727577, -0.007259165868163109, -0.12168087065219879, 0.026323460042476654, 0.011598493903875351, 0.03888325393199921, 0.034139640629291534, 0.03248656541109085, 0.007681419141590595, -0.0039035985246300697, -0.04625023156404495, -0.059187356382608414, -0.01980099268257618, 0.005372501444071531, 0.011796144768595695, -0.016935059800744057, -0.028785107657313347, 0.025532858446240425, -0.03625989332795143, 0.010736018419265747, -0.009397385641932487, -0.003530757734552026, 0.0021415886003524065, 0.02952180616557598, 0.006338294129818678, -0.01503042597323656, -0.042764391750097275, 0.0308514554053545, 0.023628225550055504, -0.008916735649108887, 0.0012173476861789823, 0.010789923369884491, -0.0215618796646595, 0.057318661361932755, 0.023412607610225677, -0.02979132905602455, -0.04215347394347191, 0.039961349219083786, -0.04118318855762482, 0.036044273525476456, 0.015803059563040733, -0.035505227744579315, -0.03690674901008606, 0.07187292724847794, -0.06004983186721802, 0.025389112532138824, -0.011805128306150436, -0.007133388426154852, 0.00869662407785654, 0.008714593015611172, -0.015210108831524849, -0.010340717621147633, -0.025694571435451508, 0.012946111150085926, -0.04326750338077545, 0.007708371616899967, 0.014392553828656673, -0.03230688348412514, -0.01292814314365387, 0.04272845759987831, -0.0045482087880373, 0.015398775227367878, 0.01063719391822815, 0.010322749614715576, 0.052898477762937546, 0.02089705504477024, 0.02454460598528385, -0.020681435242295265, -0.028731202706694603, 0.013601952232420444, 0.054084379225969315, -0.04567524790763855, 0.018776802346110344, -0.041973792016506195, -0.03378027677536011, 0.0022460289765149355, 0.047759562730789185, 0.0212743878364563, 0.013431253843009472, 0.008768497034907341, -0.04204566404223442, 0.02896478958427906, -0.0020977910608053207, 0.06389503180980682, -0.04024884104728699, -0.0016418471932411194, 0.01050243154168129, -0.041542552411556244, 0.02359228953719139, -0.015659313648939133, -0.002083191880956292, -0.05440780892968178, -0.01818385161459446, 0.024418827146291733, 0.022154830396175385, -0.0022022314369678497, -0.02614377811551094, 0.0007501736981794238, 0.02560473047196865, -0.03960198536515236, -0.05527028441429138, 0.04603461176156998, 0.03600833937525749, 0.025514889508485794, 0.005444374401122332, 0.02639533393085003, 0.015946805477142334, -0.008224958553910255, 0.00855287816375494, -0.028749171644449234, 0.02693437971174717, -0.013305475935339928, 0.02490396983921528, -0.06303256005048752, -0.014464426785707474, 0.016629599034786224, 0.02747342735528946, 0.03478649631142616, -0.05850456282496452, 0.004757089540362358, -0.03135456517338753, -0.05440780892968178, 0.015102298930287361, 0.019315849989652634, -0.009810654446482658, 0.0038384636864066124, 0.010403606109321117, -0.020573625341057777, -0.019441626965999603, -0.08006644248962402, -0.10320952534675598, -0.00136333960108459, -0.06673401594161987, -0.03273811936378479, 0.055989012122154236, 0.007968910969793797, 0.013745698146522045, -0.04103944078087807, -0.008844862692058086, -0.04269251972436905, -0.012892207130789757, 0.0366731621325016, 0.01965724676847458, -0.04725645110011101, -0.02655704692006111, 0.04973606765270233, -0.04607054591178894, -0.0476517528295517, 0.014024205505847931, -0.0039934394881129265, -0.011697319336235523, 0.015335885807871819, 0.024311019107699394, 0.018111977726221085, 0.0042786854319274426, -0.041686300188302994, 0.021597815677523613, -0.03245062753558159, -0.0011106613092124462, -0.019208040088415146, 0.007959926500916481, 0.022406386211514473, 0.06702150404453278, 0.03140847012400627, 0.027922632172703743, 0.054910916835069656, 0.0023021798115223646, 0.010745002888143063, 0.012649635784327984, -0.0488017201423645, -0.0018664501840248704, 0.026718761771917343, -0.011661382392048836, -0.014967537485063076, -0.04405810683965683, -0.008835878223180771, -0.024167273193597794, -0.006863864604383707, 0.057606153190135956, -0.013179698027670383, -0.03302561119198799, 0.019980674609541893, -0.03275608643889427, -0.010987574234604836, -0.010924684815108776, 0.027042189612984657, 0.03327716514468193, 0.016404995694756508, -0.026880474761128426, -0.035505227744579315, 0.0006990765105001628, 0.08049768209457397, 0.036601290106773376, -0.012218398042023182, 0.007456816267222166, 0.0020349023398011923, -0.03406776860356331, -0.06871052086353302, 0.029396027326583862, 0.013431253843009472, -0.008597799576818943, -0.01722254976630211, -0.051389142870903015, 0.0614154189825058, -0.08243825286626816, 0.01631515473127365, 0.008772989735007286, -0.0015082084573805332, 0.02086111716926098, -0.04542369022965431, -0.02005254663527012, 0.04395029693841934, -0.038452018052339554, -0.0020337793976068497, 0.01643194817006588, 0.0009500702726654708, 0.012901190668344498, 0.03909887373447418, 0.004460613708943129, -0.01911819912493229, -0.04732832312583923, 0.06659027189016342, 0.019154135137796402, 0.03888325393199921, -0.03112097829580307, 0.029396027326583862, 0.043842487037181854, -0.05703116953372955, -0.025910191237926483, -0.007834149524569511, -0.04395029693841934, -0.03155221417546272, -0.016198361292481422, -0.03189361095428467, -0.03726611286401749, -0.026197683066129684, -0.03625989332795143, -0.05591714009642601, -0.01725848764181137, 0.0026009015273302794, -0.013296491466462612, 0.009199734777212143, -0.012074652127921581, -0.03838014602661133, -0.01428474485874176, -0.00589358014985919, 0.044381532818078995, -0.001583450473845005, 0.020699404180049896, 0.007218737155199051, -0.035756781697273254, -0.006863864604383707, 0.003497067140415311, -0.021741561591625214, -0.04093163460493088, 0.00511645432561636, -0.03970979154109955, -0.04456121474504471, -0.009105402044951916, 0.027653109282255173, 0.010250876657664776, -0.048837654292583466, 0.026377364993095398, 0.001201625564135611, 0.041686300188302994, 0.01052040047943592, -0.03250453248620033, -0.06752461940050125, -0.0014397045597434044, -0.01547963172197342, -0.00522426376119256, 0.062421638518571854, -0.012443000450730324, 0.010816875845193863, -0.05548590049147606, -0.017536994069814682, 0.022711845114827156, -0.011885985732078552, 0.005426405929028988, -0.0350380539894104, 0.008242926560342312, 0.02292746491730213, 0.03399589657783508, 0.002383036771789193, -0.030743645504117012, -0.00795543473213911, 0.04136287048459053, -0.00703456299379468, -0.019154135137796402, 0.024275081232190132, -0.007366975303739309, -0.009702845476567745, 0.10083772242069244, 0.006158611737191677, 0.019297881051898003, -0.036691129207611084, 0.049628257751464844, -0.014033189043402672, 0.005628548562526703, -0.03033037669956684, 0.02343057468533516, -0.017159661278128624, 0.023125115782022476, 0.020411912351846695, -0.00403611408546567, 0.047076769173145294, 0.03633176535367966, -0.019854895770549774, 0.017069820314645767, -0.020573625341057777, -0.027042189612984657, -0.006814451888203621, -0.031983453780412674, -0.04380654916167259, 0.00187880324665457, -0.027850760146975517, -0.013009000569581985, 0.007703879382461309, 0.027976537123322487, 0.012002779170870781, -0.04862203821539879, -0.029306186363101006, -0.011535605415701866, 0.0805695503950119, -0.006167595740407705, 0.01817486621439457, 0.029072599485516548, 0.006652737967669964, 0.06400284171104431, 0.051281336694955826, 0.023502448573708534, 0.002989464672282338, 0.018138930201530457, 0.039673857390880585, 0.0018877873662859201, -0.009379417635500431, 0.035361479967832565, 0.00020789806148968637, 0.02948586829006672, -0.010223924182355404, 0.029593678191304207, 0.060157641768455505, 0.027401553466916084, -0.005637533031404018, 0.04463309049606323, 0.00916379876434803, -0.025425048545002937, 0.05519840866327286, -0.003223051782697439, 0.010529384016990662, -0.03392402082681656, -0.03385214880108833, -0.00854838639497757, 0.02249622717499733, 0.055989012122154236, -0.03559506684541702, 0.05146101862192154, 0.05670773983001709, 0.011814112775027752, 0.021364228799939156, 0.006167595740407705, -0.022604037076234818, -0.04427372291684151, -0.0404285229742527, -0.045351818203926086, -0.017617851495742798, -0.02964758314192295, 0.01779753342270851, -0.021849369630217552, -0.013035952113568783, -0.017069820314645767, -0.04646584764122963, 0.0226220041513443, 0.005951976869255304, 0.004433661233633757, 0.015803059563040733, -0.02021426148712635, 0.004267455078661442, 0.02898275852203369, -0.01576712355017662, -0.024221176281571388, 0.02440086007118225, 0.009999320842325687, -0.011544588953256607, -0.017995184287428856, 0.0374457947909832, -0.001199379563331604, -0.002984972670674324, -0.03794890642166138, -0.018076041713356972, -0.007569117937237024, -0.01043055858463049, -0.013377348892390728, 0.03525367006659508, -0.003919320646673441, 0.01654874160885811, 0.018794771283864975, -0.017069820314645767, -0.02519146166741848, -0.010475479066371918, -0.010107130743563175, 0.03978166729211807, 0.04632210358977318, -0.05904361233115196, -0.03564897179603577, -0.006005881819874048, 0.02882104553282261, 0.0019955968018621206, -0.033726371824741364, -0.002133727539330721, 0.041147250682115555, -0.02936009131371975, -0.013583983294665813, -0.01671045646071434, 0.0135480472818017, -0.053293775767087936, 0.021507974714040756, 0.022280607372522354, -0.004986184649169445, -0.006585357245057821, -0.011733255349099636, 0.004478581715375185, -0.002244906034320593, -0.0046088513918221, 0.004269701428711414, -0.019567405804991722, 0.03642160817980766, 0.03748173266649246, -0.024993810802698135, 0.0024167271330952644, 0.024454765021800995, 0.02573050931096077, 0.012137540616095066, -0.012550810351967812, -0.07481972128152847, 0.01507534645497799, 0.022298576310276985, -0.045495565980672836, 0.006612309720367193, -0.06022951379418373, 0.009927447885274887, 0.04970012977719307, -0.006131659261882305, 0.04244096577167511, 0.06698556989431381, -0.01023290865123272, -0.02952180616557598, -0.005830691196024418, -0.030006948858499527, -0.008368704468011856, -0.00012858516129199415, 0.03963791951537132, 0.025425048545002937, -0.020537689328193665, 0.0005878980737179518, 0.022460291162133217, 0.03370840474963188, 0.03945823758840561, -0.03351075202226639, 0.005713897757232189, -0.015183156356215477, 0.03848795220255852, 0.0026009015273302794, 0.02761717326939106, -0.019890833646059036, 0.024418827146291733, 0.020537689328193665, -0.038452018052339554, -0.0010966237168759108, 0.03812858834862709, 0.033762309700250626, 0.021795466542243958, 0.03945823758840561, 0.007816181518137455, 0.06166697293519974, -0.008404640480875969, -0.01616242527961731, -0.03004288487136364, -0.005022121127694845, -0.048442352563142776, 0.08962554484605789, -0.019854895770549774, 0.00990049634128809, 0.03787703439593315, -0.0016946288524195552, -0.0017238273285329342, -0.006616801489144564, -0.028192156925797462, 0.01070906687527895, 0.027796855196356773, -0.011742239817976952, -0.0000145816420626943, 0.014230839908123016, 0.022388417273759842, 0.03342091292142868, -0.01428474485874176, -0.05534215644001961, 0.012964079156517982, -0.019854895770549774, -0.04161442443728447, 0.005615072790533304, -0.015299949795007706, 0.01009814627468586, -0.014608172699809074, -0.027167966589331627, -0.008970639668405056, 0.012299255467951298, 0.04747207090258598, 0.07582593709230423, 0.029593678191304207, 0.029000727459788322, -0.014167951419949532, -0.0030793058685958385, 0.02817418798804283, -0.02598206326365471, 0.06252945214509964, -0.01618039235472679, 0.030474122613668442, -0.007007610518485308, 0.028497615829110146, 0.02626955509185791, -0.026341428980231285, -0.03564897179603577, -0.007052531000226736, 0.0024369414895772934, 0.009325512684881687, -0.026575015857815742, -0.002078699879348278, -0.006962690036743879, 0.03140847012400627, 0.042908139526844025, 0.020178325474262238, 0.008436084724962711, -0.002080945996567607, -0.023268861696124077, 0.0003865977341774851, -0.000701884098816663, 0.018085025250911713, 0.012164493091404438, -0.004123709164559841, 0.04474089667201042, -0.009666908532381058, -0.022568099200725555, 0.001574466354213655, 0.0014823791570961475, -0.029611647129058838, -0.0002835611521732062, 0.0018350057071074843, -0.0042023202404379845, -0.03733798488974571, -0.002526782685890794, 0.041973792016506195, -0.017824485898017883, 0.009226687252521515, -0.019028358161449432, -0.04941263794898987, 0.050454795360565186, -0.020645499229431152, -0.0032500040251761675, -0.03257640451192856, 0.02465241402387619, 0.030078820884227753, 0.013431253843009472, 0.026359396055340767, 0.07068702578544617, -0.022729814052581787, -0.013269539922475815, -0.020986896008253098, -0.01152662094682455, -0.04294407367706299, 0.005884596146643162, 0.029449932277202606, 0.017545979470014572, -0.010053225792944431, 0.025928158313035965, 0.001070232829079032, -0.03719424083828926, -0.0032208056654781103, 0.029342124238610268, -0.0008113780058920383, 0.0007889177068136632, -0.07201667875051498, -0.040212903171777725, -0.023107146844267845, 0.038200460374355316, -0.005403945688158274, -0.020717371255159378, -0.02222670428454876, 0.030815517529845238, -0.04096756875514984, -0.027132030576467514, -0.02991710603237152, 0.017590899020433426, -0.01428474485874176, 0.04740019515156746, -0.008993100374937057, 0.019369754940271378, 0.0007821795879863203, 0.03608021140098572, -0.039134811609983444, -0.011095383204519749, 0.023628225550055504, -0.0028232585173100233, 0.026772666722536087, -0.013673825189471245, 0.020519720390439034, -0.02454460598528385, 0.01564134657382965, -0.013413285836577415, -0.0047750575467944145, -0.06432627141475677, 0.002719941083341837, 0.0024683859664946795, -0.012820334173738956, 0.03974572941660881, 0.03841608017683029, -0.02452663704752922, -0.0028367347549647093, -0.022568099200725555, 0.01614445634186268, -0.0449565164744854, -0.0032028374262154102, 0.017680739983916283, 0.029467901214957237, -0.0014453197363764048, -0.049376703798770905, -0.008507957682013512, 0.018489310517907143, 0.008593306876718998, 0.006845896597951651, -0.041290998458862305, 0.01474293414503336, 0.00787907000631094, -0.013530079275369644, 0.007681419141590595, 0.008642720058560371, -0.021777497604489326, 0.0032567421440035105, 0.006908785551786423, 0.029431965202093124, -0.022334512323141098, -0.025550825521349907, 0.034139640629291534, -0.01447341125458479, 0.006302357651293278, 0.027275776490569115, -0.04474089667201042, 0.007712863851338625, -0.010080178268253803, 0.017752613872289658, -0.04488464444875717, -0.0226220041513443, 0.0485142283141613, 0.030815517529845238, 0.010753987357020378, 0.005111962091177702, -0.015794076025485992, -0.01806705817580223, 0.01601867936551571, 0.0309952013194561, 0.0635356679558754, -0.01792331226170063, 0.02301730588078499, 0.04218940809369087, 0.017734644934535027, -0.010403606109321117, 0.03838014602661133, -0.045998673886060715, -0.04280032962560654, 0.02600003220140934, -0.03949417546391487, 0.008530418388545513, 0.041290998458862305, -0.039961349219083786, -0.0425487756729126, -0.01992676965892315, 0.011670366860926151, -0.00481997849419713, -0.02371806651353836, -0.007447832264006138, -0.017545979470014572, -0.025640668347477913, 0.003490329021587968, 0.06684182584285736, 0.023466510698199272, 0.008683147840201855, 0.0312826931476593, 0.02531723864376545, -0.01926194503903389, 0.0587201826274395, 0.04757988080382347, -0.014060141518712044, -0.011167256161570549, -0.015488616190850735, 0.009033529087901115, 0.032935768365859985, 0.005754326470196247, 0.01476090308278799, 0.010367670096457005, -0.014401538297533989, 0.02979132905602455, -0.0076050544157624245, 0.019369754940271378, -0.03636770322918892 ]
Satellite-derived measurements are negatively impacted by cloud cover and surface reflectivity. These biases must be discarded and significantly increase the amount of missing data within remote sensing images. This paper expands the application of a partial convolutional neural network (PCNN) to incorporate depthwise convolution layers, conferring temporal dimensionality to the imputation process. The addition of a temporal dimension to the imputation process adds a state of successive existence within the dataset which spatial imputation cannot capture. The depthwise convolution process enables the PCNN to independently convolve the data for each channel. The deep learning system is trained with the Community Multiscale Air Quality model-simulated tropospheric column density of Nitrogen Dioxide (TCDNO2) to impute TROPOspheric Monitoring Instrument TCDNO2. The depthwise PCNN model achieves an index of agreement of 0.82 and outperforms the default PCNN models, with and without temporal dimensionality of data, and conventional data imputation methods such as inverse distance weighting by 3-11% and 8-15% in the index of agreement and correlation, respectively. The model demonstrates more consistency in the reconstruction of TROPOspheric Monitoring Instrument tropospheric column density of NO2 images. The model has also demonstrated the accurate imputation of remote sensing images with over 95% of the data missing. PCNN enables the accurate imputation of remote sensing data with large regions of missing data and will benefit future researchers conducting data assimilation for numerical models, emission studies, and human health impact analyses from air pollution.
[ -0.004888771567493677, -0.017641300335526466, -0.019917890429496765, -0.024144547060132027, 0.02539621666073799, -0.020443955436348915, -0.037949204444885254, 0.03161828964948654, -0.05775825306773186, 0.012371585704386234, 0.02581343986093998, -0.07078288495540619, 0.004612134303897619, -0.01263461820781231, -0.036479853093624115, 0.02938705123960972, 0.013976989313960075, -0.001891111140139401, 0.05957226827740669, -0.02887912653386593, -0.011772960424423218, -0.022384950891137123, -0.003612158354371786, -0.008961237035691738, 0.03406720981001854, 0.05630704015493393, 0.060297876596450806, 0.013641396537423134, -0.020552795380353928, 0.07727706432342529, 0.04295588657259941, 0.017795491963624954, 0.005464721936732531, 0.020988158881664276, -0.03424861282110214, -0.024090126156806946, 0.050864994525909424, 0.05213480442762375, -0.023382660001516342, -0.01554611325263977, -0.034321174025535583, 0.0015521170571446419, 0.02628508396446705, 0.000003011549097209354, 0.029568452388048172, -0.08823371678590775, -0.013596045784652233, -0.06581248342990875, 0.01842132769525051, 0.013632326386868954, -0.003394476603716612, -0.031146645545959473, -0.012407866306602955, -0.026248805224895477, -0.01165504939854145, 0.09353064000606537, 0.05111895874142647, 0.061821646988391876, 0.01647126115858555, -0.01291579008102417, 0.044661059975624084, 0.09882756322622299, -0.03007637709379196, -0.03889249265193939, -0.02372732199728489, -0.06893259286880493, -0.013351154513657093, -0.06759021431207657, -0.036044489592313766, -0.02949589304625988, -0.06330914050340652, -0.0674813762307167, 0.006163117475807667, 0.0007074660388752818, 0.03729615733027458, 0.03007637709379196, 0.0008321796194650233, 0.04397173598408699, 0.012063203379511833, -0.003657508874312043, 0.030185218900442123, 0.008126789703965187, -0.0355728454887867, 0.04701928049325943, 0.07205269485712051, -0.03582680597901344, 0.011999712325632572, -0.05383998155593872, -0.005827524699270725, -0.02955031208693981, -0.00009509409574093297, 0.06189420819282532, -0.012280885130167007, -0.00207704771310091, 0.05601679906249046, 0.011219685897231102, 0.0108206020668149, -0.013614186085760593, -0.06795302033424377, -0.03321462497115135, 0.008389821276068687, 0.0392552949488163, 0.0618579275906086, 0.06367194652557373, 0.06243841350078583, -0.0506473146378994, -0.0012210592394694686, -0.016498470678925514, 0.03141874819993973, 0.15919800102710724, -0.01727849803864956, 0.003943216055631638, -0.007546304725110531, 0.0033786038402467966, -0.02590414136648178, -0.026611607521772385, -0.04027114436030388, 0.009187988936901093, 0.019809048622846603, -0.024906432256102562, 0.05115523561835289, 0.05826617777347565, -0.010720831342041492, 0.07248806208372116, 0.01782270148396492, 0.03515562042593956, -0.014022340066730976, -0.08968492597341537, -0.00050112180178985, 0.011691330000758171, -0.017750142142176628, -0.022983577102422714, -0.014330722391605377, -0.005587167572230101, -0.0019908819813281298, 0.016552891582250595, -0.03684265539050102, 0.0034284892026335, -0.008317261002957821, -0.005237969569861889, -0.025976702570915222, -0.017097096890211105, -0.00239223288372159, -0.00445567537099123, 0.016171948984265327, 0.03515562042593956, -0.03511933982372284, 0.06515944004058838, -0.03620775043964386, -0.01808573491871357, -0.03702405467629433, 0.010539430193603039, 0.012997421436011791, -0.020480234175920486, 0.03218063339591026, 0.036461710929870605, 0.02327381819486618, -0.009056472219526768, -0.0527515709400177, -0.06577619910240173, -0.011918081901967525, -0.04698299989104271, 0.009183453395962715, 0.010249187238514423, 0.00687058363109827, -0.0025554944295436144, 0.0064125447534024715, 0.006929539144039154, -0.02334637939929962, 0.03214435651898384, 0.054855827242136, -0.0012913523241877556, -0.028788426890969276, 0.009378460235893726, 0.012834159657359123, 0.025994842872023582, 0.04799884930253029, -0.04600343480706215, -0.0227840356528759, 0.029695434495806694, -0.014684455469250679, -0.019010882824659348, 0.0017301172483712435, -0.014657245017588139, 0.017713861539959908, 0.01167318969964981, 0.03624403104186058, 0.007564444560557604, -0.023128697648644447, -0.008544012904167175, -0.03100152499973774, -0.01423095166683197, 0.07771242409944534, -0.040089741349220276, 0.039509259164333344, -0.022657053545117378, -0.04379033297300339, -0.032869961112737656, -0.02791769802570343, -0.023963144049048424, -0.05271529033780098, -0.03194481134414673, -0.0341760516166687, 0.0038774581626057625, 0.03096524439752102, 0.027065111324191093, 0.02018999308347702, 0.01866621896624565, 0.017831772565841675, -0.01789526268839836, -0.003655241336673498, -0.04818025231361389, 0.016870344057679176, -0.03223505616188049, 0.024017564952373505, -0.008376216515898705, -0.008371681906282902, -0.02229425124824047, -0.021550504490733147, 0.009015657007694244, -0.02374546229839325, 0.0015532508259639144, 0.014784226194024086, -0.011056424118578434, -0.06276493519544601, -0.0368063747882843, 0.013859078288078308, -0.009342179633677006, -0.04382661357522011, 0.0034874447155743837, -0.001270944601856172, -0.026575326919555664, 0.05634332075715065, -0.037550121545791626, 0.032797399908304214, -0.004603064153343439, -0.005473791621625423, -0.04194003716111183, -0.055726557970047, -0.03218063339591026, -0.00879797525703907, -0.001179110025987029, -0.04096046835184097, -0.009333109483122826, 0.03060244210064411, -0.040561385452747345, -0.026139963418245316, 0.08046972751617432, 0.03196295350790024, 0.007677820511162281, 0.015582392923533916, 0.03359556570649147, -0.03671567514538765, 0.04712812229990959, -0.048325374722480774, 0.005686938762664795, 0.01422188151627779, -0.01838504709303379, -0.02020813338458538, -0.04945006221532822, 0.03965437784790993, -0.012552987784147263, 0.009405670687556267, -0.002251646714285016, -0.020480234175920486, 0.024071985855698586, 0.017169656231999397, 0.012543917633593082, 0.03530074283480644, -0.00036110245855525136, -0.02423524670302868, -0.029840555042028427, 0.0299675352871418, -0.035971928387880325, 0.026611607521772385, -0.01964578777551651, 0.013777447864413261, -0.02641206607222557, 0.033922091126441956, -0.002264118054881692, 0.021042579784989357, -0.03261600062251091, -0.004467013292014599, -0.003816235112026334, -0.005047498270869255, 0.010992933996021748, -0.03566354513168335, 0.020570935681462288, -0.040525104850530624, -0.02639392577111721, -0.019772769883275032, 0.0011609699577093124, -0.09853732585906982, 0.05315065383911133, 0.043209850788116455, 0.004428465384989977, -0.04484246298670769, -0.058592699468135834, 0.013713956810534, 0.030656863003969193, -0.020788617432117462, 0.01012220699340105, 0.020316973328590393, 0.06316401809453964, 0.008398891426622868, 0.01339650433510542, 0.05213480442762375, 0.015455411747097969, -0.039073895663022995, -0.006612086668610573, 0.022638913244009018, 0.051518041640520096, 0.011836451478302479, -0.03709661588072777, -0.01601775735616684, 0.05793965607881546, -0.029169369488954544, -0.03524632006883621, -0.062257010489702225, -0.006457895040512085, -0.00010891179408645257, 0.011890871450304985, -0.027790717780590057, 0.010811532847583294, -0.015954267233610153, -0.0004158063675276935, -0.007691425736993551, 0.07524536550045013, 0.009369390085339546, 0.00034381262958049774, -0.029042387381196022, -0.012063203379511833, 0.009614282287657261, 0.025559479370713234, 0.011818311177194118, 0.043717775493860245, -0.015355641022324562, 0.01133759692311287, -0.014530263841152191, -0.020443955436348915, -0.029205650091171265, -0.06907770782709122, -0.006943144369870424, -0.04389917477965355, -0.018248995766043663, -0.04037998616695404, -0.0025554944295436144, -0.005056568421423435, -0.03051174059510231, 0.011246896348893642, 0.0010782054159790277, -0.014004199765622616, -0.011582489125430584, 0.035863086581230164, 0.06973075866699219, 0.005201689433306456, -0.053948819637298584, 0.006829768419265747, 0.01970020867884159, -0.026629747822880745, 0.04640251770615578, -0.039509259164333344, -0.034956078976392746, 0.03961809724569321, -0.07582584768533707, 0.035899367183446884, -0.02835306152701378, 0.002006754744797945, 0.022657053545117378, 0.01622636802494526, 0.02127840183675289, 0.08533129096031189, -0.04331868886947632, -0.0011813775636255741, -0.011927152052521706, -0.06269237399101257, 0.0121357636526227, 0.025069694966077805, 0.020806757733225822, 0.03140060976147652, -0.05267900973558426, 0.02227611094713211, 0.06341797858476639, -0.019228564575314522, -0.02434408850967884, 0.043246131390333176, 0.023437080904841423, -0.015174239873886108, 0.04585831239819527, 0.009759403765201569, -0.00866645947098732, -0.07894595712423325, -0.009895454160869122, -0.06983959674835205, 0.025595758110284805, 0.016289860010147095, -0.04175863787531853, 0.017378268763422966, 0.057105209678411484, 0.02791769802570343, -0.04342753067612648, 0.009110893122851849, -0.0034035465214401484, 0.023981284350156784, 0.0007097335765138268, 0.04284704476594925, -0.02116956189274788, -0.015727514401078224, -0.016453120857477188, -0.02477945201098919, 0.012045063078403473, 0.024144547060132027, -0.06051555648446083, -0.030384760349988937, 0.04455222189426422, -0.03537330403923988, -0.005795779637992382, 0.03103780560195446, 0.004979472607374191, 0.023382660001516342, 0.011600629426538944, 0.033359743654727936, 0.046801600605249405, -0.025051554664969444, 0.018394118174910545, 0.011464578099548817, 0.02017185278236866, 0.01791340298950672, 0.01290671993046999, 0.0086755296215415, -0.0026371250860393047, -0.04694672301411629, 0.011020144447684288, 0.011219685897231102, -0.014394213445484638, 0.026684168726205826, 0.0029477751813828945, 0.016961045563220978, -0.04607599228620529, -0.00607241690158844, -0.007201641798019409, -0.03722359985113144, -0.04955890402197838, 0.0024761310778558254, -0.02485201321542263, -0.047418367117643356, 0.017006395384669304, 0.0020781815983355045, -0.03929157555103302, -0.041613515466451645, -0.08163069933652878, 0.07375787198543549, -0.022929156199097633, -0.0035464002285152674, 0.008544012904167175, 0.049341220408678055, -0.0516994409263134, -0.039545539766550064, 0.014158391393721104, 0.005832059774547815, -0.028153520077466965, 0.05598051846027374, -0.047382086515426636, -0.023527780547738075, -0.04175863787531853, -0.014103970490396023, -0.05547259375452995, -0.0599350705742836, 0.026484627276659012, 0.047853730618953705, 0.0559079572558403, 0.01906530372798443, -0.015301221050322056, 0.012308095581829548, 0.02476131170988083, -0.005342275835573673, -0.02214912883937359, -0.05884666368365288, 0.010004295967519283, -0.041540954262018204, 0.06091463938355446, -0.004952262155711651, 0.011609699577093124, -0.022366810590028763, -0.028643304482102394, 0.042085159569978714, -0.002439850941300392, -0.02118770033121109, 0.006394404452294111, -0.02731907367706299, 0.04691044241189957, 0.02439850941300392, -0.004571319092065096, -0.02124212123453617, 0.012743459083139896, -0.005133663769811392, -0.04128699377179146, -0.014856787398457527, 0.07597097009420395, -0.00605427660048008, 0.018303416669368744, 0.003922808449715376, -0.03377696871757507, 0.026684168726205826, 0.00541030103340745, -0.010757111944258213, 0.06860606372356415, -0.0243622288107872, -0.06272865831851959, 0.015890775248408318, 0.03252529725432396, 0.047382086515426636, 0.00829005055129528, 0.011682259850203991, -0.00200902228243649, 0.025958562269806862, -0.020770477131009102, -0.011083634570240974, 0.001731251017190516, 0.030275918543338776, 0.027083251625299454, 0.026974409818649292, 0.01425816211849451, 0.010494079440832138, -0.04382661357522011, 0.024489209055900574, -0.019409965723752975, -0.015210520476102829, 0.05318693444132805, -0.0169973261654377, -0.010630130767822266, 0.05017567053437233, -0.00464841490611434, -0.0403074249625206, -0.008652853779494762, -0.008739019744098186, 0.02472503110766411, 0.029368910938501358, -0.03555470332503319, -0.06160396710038185, -0.023473361507058144, 0.04876073822379112, 0.03218063339591026, -0.011274106800556183, -0.0014387411065399647, 0.029568452388048172, 0.008607503958046436, -0.03305136412382126, 0.00865738932043314, -0.004040719475597143, -0.014312582090497017, -0.010693621821701527, 0.030185218900442123, 0.02122398093342781, -0.03842084854841232, -0.02637578547000885, 0.0278632789850235, -0.004412592854350805, -0.041577234864234924, 0.01469352561980486, -0.03472025692462921, -0.015183310024440289, -0.02537807635962963, 0.003891063155606389, 0.0012165241641923785, -0.019282985478639603, -0.008412497118115425, 0.06142256408929825, -0.017795491963624954, -0.0009438549168407917, 0.018548307940363884, -0.01499283779412508, -0.011301316320896149, 0.001129791489802301, 0.041033029556274414, 0.005532747134566307, 0.05013938993215561, -0.011818311177194118, -0.022929156199097633, 0.011029214598238468, -0.010158486664295197, 0.01347813569009304, 0.0020487038418650627, 0.06657437235116959, 0.027700016275048256, -0.02060721628367901, 0.02127840183675289, -0.021550504490733147, 0.017722930759191513, -0.027210231870412827, 0.04281076416373253, 0.02176818624138832, 0.025124114006757736, -0.003827572800219059, -0.019881609827280045, -0.0023446150589734316, 0.012843229807913303, 0.005065638106316328, 0.029804274439811707, -0.03686079382896423, 0.007754916325211525, 0.06505059450864792, 0.003934145905077457, -0.0013865880900993943, -0.0017187796765938401, 0.020806757733225822, -0.0026643353048712015, -0.009496371261775494, 0.04614855349063873, 0.023001717403531075, 0.014312582090497017, -0.004979472607374191, 0.016679871827363968, 0.008417031727731228, 0.020353253930807114, 0.010421519167721272, 0.019409965723752975, 0.001769798924215138, -0.02013557218015194, -0.04070650786161423, 0.036897074431180954, -0.04096046835184097, 0.06298261880874634, 0.005532747134566307, -0.043717775493860245, 0.023473361507058144, 0.008598433807492256, -0.039509259164333344, -0.052461329847574234, -0.058084774762392044, -0.023926865309476852, -0.021405382081866264, 0.027192091569304466, -0.011827381327748299, 0.0023162709549069405, -0.008045158348977566, -0.0012732121394947171, 0.04016230255365372, 0.004528236109763384, 0.009006586857140064, -0.020335113629698753, 0.023691043257713318, -0.015781935304403305, 0.015292150899767876, 0.005528212059289217, 0.020589075982570648, -0.05434790626168251, 0.02691999077796936, 0.020498374477028847, -0.002433048328384757, 0.005106453783810139, -0.0031155715696513653, 0.029151229187846184, 0.03239831700921059, 0.028697725385427475, -0.03706033527851105, 0.06047927588224411, -0.001590664847753942, -0.0253236573189497, -0.012244604527950287, 0.022457512095570564, -0.009441950358450413, 0.041033029556274414, -0.027845138683915138, 0.023981284350156784, -0.0033105784095823765, 0.013695817440748215, -0.010140346363186836, -0.014929347671568394, -0.028298642486333847, -0.014475843869149685, -0.06305518001317978, -0.04041626676917076, 0.044225696474313736, 0.03426675125956535, -0.06915026903152466, 0.0005118924891576171, 0.03368626907467842, 0.013523485511541367, -0.05492838844656944, -0.023981284350156784, -0.01134666707366705, -0.045713189989328384, 0.0336499884724617, -0.010729901492595673, 0.0019863469060510397, 0.03216249495744705, -0.014911207370460033, -0.0021586783695966005, -0.0010067785624414682, 0.018475748598575592, -0.004160898271948099, 0.025976702570915222, -0.014775156043469906, 0.031255487352609634, 0.013505345210433006, -0.01729663833975792, 0.01957322657108307, 0.016643593087792397, 0.017414549365639687, -0.021514223888516426, 0.00830819085240364, -0.04796256870031357, 0.05021195113658905, -0.041105590760707855, 0.042629364877939224, -0.005668798461556435, -0.018847621977329254, -0.03219877555966377, 0.01861179992556572, 0.008226560428738594, 0.03321462497115135, 0.030820123851299286, 0.0029409725684672594, 0.0258497204631567, 0.032307617366313934, -0.003829840337857604, -0.006503245793282986, 0.036897074431180954, -0.04143211245536804, 0.021296542137861252, 0.041577234864234924, -0.010403378866612911, -0.006190327927470207, 0.007097335532307625, 0.011582489125430584, -0.0018151492113247514, -0.01426723226904869, -0.04172235727310181, 0.016126597300171852, -0.011274106800556183, -0.00008772465662332252, 0.00673453276976943, -0.0004268605262041092, 0.0005728320684283972, -0.011500858701765537, -0.011437367647886276, 0.02280217409133911, 0.02434408850967884, -0.0108206020668149, 0.011854591779410839, -0.05079243332147598, 0.0169973261654377, -0.004038452170789242, 0.011101774871349335, -0.003714196849614382, -0.010648271068930626, 0.06251097470521927, -0.005986251402646303, -0.04186747968196869, -0.0008922689012251794, -0.017178727313876152, 0.0453866682946682, -0.028715865686535835, 0.014557474292814732, 0.009246944449841976, 0.013206033036112785, 0.0002685593208298087, 0.010530360043048859, -0.016126597300171852, 0.041649796068668365, 0.004292414057999849, -0.006122302263975143, -0.025541339069604874, 0.008970306254923344, -0.015174239873886108, -0.0373324379324913, 0.03457513451576233, 0.00875262450426817, -0.04897841811180115, -0.01959136687219143, 0.025069694966077805, 0.029804274439811707, -0.00431055435910821, -0.015165169723331928, 0.04745464399456978, 0.053041812032461166, 0.005387626122683287, -0.003913738299161196, -0.03718731924891472, -0.017151515930891037, -0.022384950891137123, -0.013142541982233524, 0.03929157555103302, 0.032343897968530655, 0.040633946657180786, 0.009659633040428162, -0.03140060976147652, -0.032869961112737656, -0.02851632423698902, -0.0067027872428298, -0.021459802985191345, 0.027718156576156616, -0.06363566219806671, 0.011791100725531578, 0.05438418313860893, -0.016217298805713654, -0.00609509227797389, 0.016834063455462456, -0.05910062417387962, 0.036443572491407394, -0.017777351662516594, -0.008457846939563751, -0.010339888744056225, -0.014938417822122574, -0.06066067889332771, -0.040996748954057693, -0.04335496947169304, 0.033831387758255005, -0.039545539766550064, 0.006807093042880297, -0.006571270991116762, 0.027119532227516174, 0.0020112895872443914, 0.014874926768243313, -0.021931447088718414, -0.029223790392279625, 0.02120584063231945, -0.06367194652557373, -0.05579911544919014, 0.02020813338458538, -0.009995225816965103, -0.01859365962445736, -0.029659153893589973, -0.03497421741485596, -0.013831867836415768, 0.010593850165605545, -0.004385382402688265, 0.0525701679289341, 0.004156363196671009, 0.03473839536309242, 0.00036988910869695246, -0.03216249495744705, 0.012208323925733566, -0.012262744829058647, 0.03288809955120087, -0.04190375655889511, -0.003065686207264662, 0.014684455469250679, 0.012625548057258129, -0.005160874221473932, 0.04698299989104271, -0.055508874356746674, -0.01263461820781231, 0.00879797525703907, 0.0037618146743625402, -0.010811532847583294, 0.020063010975718498, 0.004371777176856995, 0.046366237103939056, 0.01738733798265457, 0.05220736563205719, 0.016135668382048607, 0.0033990114461630583, -0.009641492739319801, -0.013868148438632488, 0.017813632264733315, -0.0010974793694913387, 0.03871108964085579, -0.035863086581230164, 0.030203357338905334, 0.024598050862550735, -0.006249283440411091, -0.003900133306160569, 0.023545920848846436, 0.010729901492595673, -0.01290671993046999, -0.008231095038354397, 0.018394118174910545, -0.029332630336284637, -0.005850200075656176, -0.028734005987644196, 0.03497421741485596, 0.04016230255365372, -0.0057458942756056786, -0.025468777865171432, -0.009958945214748383, 0.006358124315738678, 0.023890584707260132, -0.03617146983742714, 0.021586785092949867, 0.03713289648294449, 0.05779453366994858, 0.020951878279447556, 0.05213480442762375, -0.0629100576043129, -0.02637578547000885, -0.02739163488149643, -0.0016110725700855255, -0.05108267813920975, 0.023890584707260132, 0.04281076416373253, 0.01009499654173851, -0.008276445791125298, 0.026992550119757652, -0.0007783260080032051, 0.003537330310791731, -0.013577906414866447, 0.014929347671568394, -0.0035214575473219156, -0.008321796543896198, -0.010630130767822266, -0.014929347671568394, -0.03608077019453049, -0.007405718322843313, -0.026484627276659012, -0.014448633417487144, -0.07404810935258865, -0.02320125885307789, -0.008244700729846954, -0.026484627276659012, -0.0000641282822471112, 0.007101870607584715, 0.008734485134482384, -0.0413595549762249, 0.015727514401078224, 0.0031178391072899103, 0.0176140908151865, 0.011981572024524212, 0.0007063322700560093, 0.035391442477703094, 0.00876169465482235, -0.03787664324045181, 0.007251527160406113, -0.015954267233610153, -0.01626264862716198, 0.02887912653386593, 0.006131372414529324, -0.00849866308271885, 0.03252529725432396, 0.013550695963203907, 0.03658869117498398, 0.04876073822379112, 0.03990834206342697, 0.04720068350434303, 0.002251646714285016, -0.001663225470110774, -0.030783843249082565, -0.009387530386447906, 0.015636812895536423, -0.04429825767874718, -0.004600796848535538, -0.031708989292383194, 0.011446437798440456, -0.0029636479448527098, 0.009940804913640022, 0.0487244576215744, 0.0017992766806855798, 0.037513840943574905, 0.003655241336673498, 0.0217319056391716, -0.027210231870412827, 0.003913738299161196, -0.021822607144713402, -0.00622207298874855, -0.009133568033576012, -0.00686604855582118, -0.0455680713057518, -0.008154000155627728, 0.02477945201098919, 0.010466869920492172, -0.013042771257460117, -0.015292150899767876, -0.022366810590028763, -0.047890011221170425, 0.04535038769245148, -0.047817450016736984, -0.03669753298163414, -0.053549736738204956, 0.0045645167119801044, 0.04400801658630371, -0.014122110791504383, -0.015400991775095463, -0.03308764472603798, 0.008888675831258297, 0.013577906414866447, -0.00019089678244199604, -0.03940041735768318, -0.009242408908903599, 0.017641300335526466, -0.014475843869149685, 0.0017834040336310863, 0.030239637941122055, -0.007877361960709095, 0.04034370556473732, -0.03051174059510231, 0.009831964038312435, 0.014122110791504383, -0.06788045912981033, -0.004437535535544157, -0.02795397862792015, -0.03004009649157524, 0.014648174867033958, 0.009750333614647388, 0.013550695963203907, 0.07633377611637115, 0.0026892779860645533, -0.015165169723331928, 0.0032017373014241457, 0.01345999538898468, -0.03577238693833351, 0.002389965346083045, 0.00006416371616069227, 0.05648844316601753, -0.02746419422328472, 0.004675624892115593, 0.05735917016863823, 0.025523198768496513, -0.013804658316075802, 0.04999426752328873, -0.004142757970839739, -0.06827954202890396, -0.023509640246629715, -0.017940612509846687, -0.008571223355829716, -0.0121357636526227, -0.07894595712423325, 0.01677057333290577, 0.015990545973181725, -0.01373209711164236, 0.0013310338836163282, -0.0064125447534024715, 0.03245273604989052, -0.005791244562715292 ]
For many years now, understanding the brain mechanism has been a great research subject in many different fields. Brain signal processing and especially electroencephalogram (EEG) has recently known a growing interest both in academia and industry. One of the main examples is the increasing number of Brain-Computer Interfaces (BCI) aiming to link brains and computers. In this paper, we present a novel framework allowing us to retrieve the attention state, i.e degree of attention given to a specific task, from EEG signals. While previous methods often consider the spatial relationship in EEG through electrodes and process them in recurrent or convolutional based architecture, we propose here to also exploit the spatial and temporal information with a transformer-based network that has already shown its supremacy in many machine-learning (ML) related studies, e.g. machine translation. In addition to this novel architecture, an extensive study on the feature extraction methods, frequential bands and temporal windows length has also been carried out. The proposed network has been trained and validated on two public datasets and achieves higher results compared to state-of-the-art models. As well as proposing better results, the framework could be used in real applications, e.g. Attention Deficit Hyperactivity Disorder (ADHD) symptoms or vigilance during a driving assessment.
[ 0.011078883893787861, 0.022718723863363266, -0.006924302317202091, -0.053921908140182495, 0.009720318019390106, -0.011306772008538246, 0.03546294569969177, 0.035480476915836334, -0.001200796803459525, 0.03954740986227989, 0.03621673211455345, -0.05441274493932724, -0.010868525132536888, -0.03712828457355499, 0.016609560698270798, -0.015128286555409431, 0.023174500092864037, -0.04477131366729736, -0.035568125545978546, -0.028380874544382095, -0.003979282919317484, -0.018494023010134697, -0.04161593317985535, -0.07664063572883606, 0.010158564895391464, 0.026662947610020638, 0.06850676983594894, 0.010903584770858288, -0.030028684064745903, 0.009729083627462387, -0.0014210158260539174, 0.019458167254924774, -0.011289242655038834, -0.03430597484111786, -0.04578804597258568, -0.03500717133283615, 0.014996811747550964, -0.0027609560638666153, 0.022631075233221054, 0.032850995659828186, 0.028310755267739296, 0.005386055447161198, -0.02341991849243641, -0.067735455930233, 0.004443824291229248, -0.048031870275735855, -0.03469163179397583, -0.06237131357192993, -0.004605975933372974, -0.024454182013869286, -0.00567091628909111, -0.07572907954454422, 0.016872508451342583, 0.051047008484601974, -0.029643027111887932, 0.01926533691585064, 0.016644621267914772, -0.020597608759999275, 0.07488764822483063, 0.06468525528907776, 0.03202709183096886, 0.054447807371616364, -0.041756171733140945, -0.01625019870698452, 0.026855776086449623, -0.04375458136200905, 0.0066920313984155655, -0.05367649346590042, 0.0048382468521595, 0.0028047808445990086, -0.0724334642291069, 0.026715537533164024, -0.040774501860141754, 0.006713944021612406, -0.011569720692932606, 0.005109959747642279, 0.004952190909534693, 0.05795378237962723, 0.010894820094108582, 0.0003733316552825272, 0.030642230063676834, 0.04578804597258568, -0.011578485369682312, 0.030414341017603874, 0.02478724904358387, -0.04747091606259346, -0.015496413223445415, -0.06230119243264198, -0.01707410253584385, -0.007064541336148977, -0.055885255336761475, 0.033534660935401917, -0.043193623423576355, -0.006972509436309338, 0.0032386453822255135, 0.005026692990213633, 0.030256573110818863, -0.010491632856428623, -0.03243027627468109, -0.0325179286301136, 0.003455577651038766, -0.0414055772125721, -0.01050039753317833, -0.03579601272940636, 0.04270278662443161, -0.01798565685749054, -0.04831234738230705, 0.032833464443683624, 0.002296414226293564, 0.09087489545345306, -0.05076653137803078, -0.01987888291478157, -0.002717131283134222, -0.007415139116346836, 0.005964541342109442, 0.018231075257062912, -0.03560318425297737, -0.02562868408858776, -0.023262150585651398, -0.01852908357977867, 0.008186453953385353, 0.05984700843691826, -0.042527489364147186, 0.025032667443156242, -0.02268366515636444, 0.07993625104427338, 0.017170516774058342, 0.03961752727627754, -0.011026293970644474, 0.022262947633862495, 0.018879679962992668, 0.06713943928480148, -0.032465338706970215, -0.04217689111828804, 0.016592031344771385, 0.007888445630669594, 0.0049872505478560925, 0.04158087447285652, -0.007419521454721689, -0.06479043513536453, 0.003477489808574319, -0.036917924880981445, -0.008383665233850479, 0.04536733031272888, 0.007204780355095863, 0.005618326365947723, 0.000646962143946439, 0.04634900018572807, -0.016083665192127228, 0.013129879720509052, -0.04144063591957092, 0.043719518929719925, -0.04662948101758957, -0.008449401706457138, 0.02243824675679207, -0.007888445630669594, -0.0010561752133071423, -0.00804621446877718, -0.024296414107084274, -0.017179282382130623, 0.045227088034152985, -0.0338677279651165, 0.04929402098059654, -0.009360956028103828, 0.05532430112361908, 0.017871713265776634, 0.02236812561750412, -0.004332071635872126, -0.07818326354026794, 0.056796811521053314, -0.0015820716507732868, 0.024173704907298088, 0.01769641414284706, 0.04217689111828804, -0.004925896413624287, 0.007476493716239929, 0.05760318413376808, -0.025593623518943787, -0.049854978919029236, 0.026768125593662262, -0.07818326354026794, 0.043579280376434326, 0.059286054223775864, 0.005210756789892912, 0.06524620950222015, 0.007160956040024757, 0.06577210873365402, -0.007954183034598827, 0.020509960129857063, 0.006280079483985901, -0.010947410017251968, 0.012086852453649044, 0.07320477813482285, -0.05700716748833656, 0.023525098338723183, -0.045156970620155334, -0.05897051468491554, 0.03477928042411804, 0.01790677197277546, -0.0027302787639200687, -0.04389481991529465, -0.026803186163306236, 0.004733067471534014, -0.018020715564489365, -0.04487649351358414, 0.008598405867815018, 0.016872508451342583, -0.05329083278775215, -0.00042263444629497826, -0.02781991846859455, -0.018651792779564857, -0.022315537557005882, -0.043789640069007874, 0.014102788642048836, -0.021579282358288765, -0.01296334620565176, 0.018984859809279442, -0.06598246842622757, 0.06749003380537033, 0.022613544017076492, 0.034866929054260254, 0.06664860248565674, 0.05511394143104553, -0.007051394321024418, -0.00723545765504241, 0.014830278232693672, -0.05826932191848755, -0.001135059748776257, -0.0009285358246415854, 0.018914740532636642, -0.0721529871225357, 0.0048382468521595, 0.006170517764985561, -0.013208764605224133, 0.0077394419349730015, -0.02366533689200878, 0.0485227070748806, -0.03574342653155327, 0.005833067465573549, -0.042527489364147186, -0.0020422309171408415, -0.03951234742999077, -0.04438565671443939, -0.013156174682080746, 0.03363984078168869, -0.009325896389782429, -0.033289242535829544, 0.0929083600640297, -0.00039387447759509087, 0.019528286531567574, -0.014795218594372272, 0.01814342476427555, -0.051888443529605865, 0.04073943942785263, -0.04715537652373314, 0.010570517741143703, 0.004570916295051575, -0.02697848528623581, 0.014646214433014393, -0.015137051232159138, 0.044035058468580246, -0.018651792779564857, 0.018949799239635468, 0.04603346437215805, -0.017643824219703674, 0.008300398476421833, 0.049469321966171265, -0.03527011722326279, 0.04161593317985535, -0.055885255336761475, -0.026943424716591835, -0.018353784456849098, -0.00559203140437603, -0.03574342653155327, 0.058830276131629944, -0.014356971718370914, 0.0388462133705616, -0.030887648463249207, -0.003942031878978014, 0.018353784456849098, -0.01114900317043066, 0.03379760682582855, 0.034656573086977005, 0.04308844357728958, -0.01376095600426197, -0.004209362436085939, 0.06871712952852249, -0.0127354571595788, -0.021894820034503937, -0.00797171238809824, -0.008304780349135399, -0.04361433908343315, -0.060583263635635376, -0.03462151065468788, 0.05199362337589264, -0.04981991648674011, -0.029309958219528198, -0.02296414226293564, -0.02221035771071911, -0.014690038748085499, -0.0512223094701767, -0.020843027159571648, 0.046068523079156876, 0.028626292943954468, -0.04634900018572807, 0.01541752927005291, 0.012253385968506336, 0.04943425953388214, -0.006893625017255545, -0.018756970763206482, 0.03015139326453209, -0.01812589541077614, 0.020352190360426903, -0.020054182037711143, -0.006358963903039694, 0.022929083555936813, 0.013287648558616638, -0.036988046020269394, 0.02994103543460369, -0.03490199148654938, -0.01299840584397316, -0.008519521914422512, -0.09949959814548492, 0.08638724684715271, -0.032465338706970215, -0.005101195070892572, 0.07706134766340256, 0.025716332718729973, 0.005092429928481579, 0.01578565686941147, -0.027188843116164207, 0.0037229082081466913, -0.048698004335165024, -0.04932907968759537, -0.015838246792554855, 0.008282868191599846, -0.015505178831517696, 0.0327984057366848, -0.014392031356692314, -0.015128286555409431, 0.00895776879042387, -0.03385019674897194, -0.0411250963807106, -0.030274102464318275, -0.04922390356659889, -0.030712349340319633, -0.005570119246840477, -0.011894023045897484, -0.02040478028357029, -0.03453386202454567, 0.000891832634806633, -0.00655617518350482, -0.020913146436214447, 0.014917927794158459, 0.010956174694001675, -0.018266133964061737, 0.0023139440454542637, -0.026189640164375305, 0.007954183034598827, -0.026733066886663437, -0.012367330491542816, -0.024699600413441658, -0.02373545803129673, 0.013191234320402145, -0.07593943923711777, -0.032535456120967865, -0.039337050169706345, -0.052554577589035034, -0.0007154382183216512, -0.01973864436149597, -0.011087648570537567, 0.07369561493396759, -0.042527489364147186, 0.011762549169361591, 0.006477290764451027, 0.010754581540822983, -0.011157768778502941, 0.038741033524274826, -0.008458167314529419, 0.06370358169078827, -0.002236155327409506, -0.04329880326986313, -0.002736852504312992, 0.03385019674897194, 0.01538246963173151, 0.0557800754904747, 0.001109312754124403, -0.033902786672115326, -0.05963665246963501, 0.07853385806083679, 0.020194420590996742, -0.06577210873365402, -0.004825099371373653, -0.09381991624832153, 0.007511553354561329, 0.01972111500799656, 0.004811951890587807, 0.016416732221841812, 0.03523505851626396, -0.045016732066869736, -0.05129242688417435, 0.00793665274977684, 0.0096063744276762, -0.006661354098469019, -0.014427090995013714, -0.005543824285268784, -0.0657370463013649, 0.019756173714995384, 0.05763824284076691, 0.021719520911574364, -0.03190438076853752, -0.024892428889870644, -0.03244780749082565, 0.021123504266142845, -0.001527290791273117, -0.0038916333578526974, -0.05329083278775215, 0.03227251023054123, -0.026417529210448265, -0.04217689111828804, -0.04715537652373314, 0.023998405784368515, 0.0244015920907259, -0.00952748954296112, -0.02857370302081108, -0.02631234936416149, 0.0175386443734169, -0.010176095180213451, -0.01980876363813877, -0.01723187230527401, 0.04740079492330551, -0.02320956066250801, 0.0176087636500597, -0.05911075323820114, -0.000984960119239986, -0.008291632868349552, -0.0006003984017297626, -0.030817529186606407, -0.04336892068386078, -0.03069481998682022, -0.02252589538693428, 0.005587649066001177, -0.0015722110401839018, -0.06272190809249878, 0.0015163345960900187, -0.0038828684482723475, 0.020001592114567757, 0.02994103543460369, 0.026855776086449623, -0.030501991510391235, -0.0290996003895998, 0.029678085818886757, -0.05735776573419571, -0.026890834793448448, -0.0019304780289530754, 0.010439042933285236, 0.011727489531040192, -0.037759359925985336, 0.04101992025971413, -0.039722707122564316, 0.013638246804475784, 0.034814342856407166, -0.0019414342241361737, -0.016767330467700958, 0.04073943942785263, 0.003874103305861354, -0.05395697057247162, -0.034814342856407166, 0.0044131469912827015, 0.02291155233979225, -0.01291952095925808, -0.005473705008625984, 0.012446214444935322, 0.038881272077560425, 0.007178485859185457, -0.008147011511027813, -0.004126095212996006, -0.03505976125597954, 0.0016620517708361149, 0.008002390153706074, 0.02538326568901539, -0.019756173714995384, 0.005811155308037996, -0.00798047799617052, -0.05872509628534317, 0.0009816732490435243, -0.003188246861100197, 0.02985338494181633, -0.013734661042690277, -0.018476493656635284, -0.005329083651304245, -0.020843027159571648, 0.01242868509143591, 0.016644621267914772, -0.0013717131223529577, -0.031027887016534805, 0.004303585272282362, 0.04189641401171684, 0.09501194953918457, 0.029047010466456413, 0.00566653348505497, -0.01216573640704155, 0.06412430107593536, 0.023682868108153343, -0.016451792791485786, 0.04042390361428261, -0.03484940156340599, -0.00007100970833562315, -0.052940238267183304, -0.02592669241130352, 0.053466133773326874, -0.0533609539270401, 0.030414341017603874, -0.03008127398788929, 0.008707967586815357, 0.010666931979358196, -0.02554103545844555, 0.018932269886136055, -0.016302788630127907, 0.014129082672297955, 0.029450198635458946, -0.01292828656733036, 0.025576094165444374, 0.05942629277706146, -0.028749002143740654, 0.024752190336585045, 0.03558565676212311, 0.01903744973242283, 0.012788047082722187, -0.021561751142144203, -0.03810995817184448, -0.005828685127198696, -0.034043025225400925, -0.009001593105494976, 0.000140649892273359, 0.009334661066532135, 0.007318724878132343, 0.0007313246605917811, -0.004430677276104689, -0.03407808765769005, -0.02706613391637802, 0.06107410043478012, -0.02992350421845913, 0.024471711367368698, -0.006161752622574568, -0.008817529305815697, 0.06244143098592758, -0.054447807371616364, 0.003999003674834967, 0.011604780331254005, 0.0032386453822255135, 0.0024454181548208, -0.012726692482829094, 0.021824700757861137, -0.027188843116164207, -0.047716330736875534, -0.010316334664821625, -0.02364780753850937, -0.035936255007982254, -0.008817529305815697, 0.03278087452054024, -0.004038446117192507, 0.01231474056839943, -0.0071872505359351635, 0.013874899595975876, -0.01830119453370571, 0.008975298143923283, 0.0389864519238472, 0.06387887895107269, 0.014295617118477821, 0.0009093625121749938, 0.011131473816931248, -0.0011854581534862518, 0.02727649360895157, -0.0059557766653597355, 0.050450995564460754, 0.04144063591957092, -0.006415936164557934, -0.000646962143946439, -0.01306852512061596, 0.0384254977107048, 0.0035169320181012154, 0.026592828333377838, 0.04592828452587128, 0.018476493656635284, -0.022315537557005882, -0.03460398316383362, -0.058549799025058746, -0.03248286619782448, -0.010351394303143024, 0.010991234332323074, 0.043649401515722275, 0.0035936252679675817, -0.006972509436309338, -0.0458231046795845, -0.03388525918126106, 0.01791553758084774, 0.02124621346592903, 0.059286054223775864, -0.0877896398305893, -0.019142629578709602, 0.02661035768687725, 0.005653386004269123, 0.05669163167476654, 0.004088844638317823, 0.0163290835916996, 0.023910755291581154, -0.013585656881332397, -0.006819123402237892, 0.01126294769346714, 0.012858166359364986, -0.0097816726192832, 0.05900557339191437, -0.005548207089304924, 0.015768127515912056, 0.026698006317019463, 0.036181673407554626, -0.016968922689557076, 0.005250198766589165, -0.035410355776548386, 0.027223903685808182, 0.005079282447695732, 0.04042390361428261, -0.0361466109752655, 0.0509418286383152, 0.02515537664294243, 0.029835855588316917, 0.01111394353210926, 0.0006672310410067439, -0.005469322670251131, -0.016372907906770706, -0.0058988044038414955, -0.03362230956554413, 0.0020937249064445496, 0.018388843163847923, -0.0032364539802074432, 0.002563745016232133, 0.001868027844466269, 0.014637449756264687, 0.011806374415755272, -0.005692828446626663, 0.026505177840590477, -0.044035058468580246, 0.03225497901439667, 0.0065912348218262196, 0.0008967628818936646, -0.024980079382658005, 0.001876792754046619, 0.08596652746200562, 0.0025462149642407894, 0.005697210785001516, 0.024541832506656647, 0.023016732186079025, 0.029362548142671585, -0.05115218833088875, -0.030133863911032677, -0.007511553354561329, 0.020457370206713676, 0.019247807562351227, 0.009150597266852856, -0.00020488047448452562, 0.009676493704319, 0.02797768823802471, -0.016074899584054947, 0.01784541830420494, -0.042527489364147186, -0.014558564871549606, 0.016530675813555717, 0.018178485333919525, 0.038670916110277176, -0.011473306454718113, -0.06016254797577858, -0.059741828590631485, 0.0024388444144278765, 0.004264143295586109, -0.032991234213113785, 0.027714740484952927, 0.032991234213113785, -0.01047410350292921, -0.03379760682582855, 0.0005888944142498076, -0.026873305439949036, -0.02259601466357708, -0.006323904264718294, 0.03349959850311279, -0.012709163129329681, 0.004728685133159161, 0.0047681271098554134, -0.0412653386592865, -0.03825019672513008, -0.006060956045985222, -0.013620716519653797, 0.003959561698138714, -0.030747409909963608, 0.022560955956578255, -0.007152190897613764, -0.04073943942785263, 0.025137847289443016, 0.024506771937012672, 0.005052987951785326, 0.013419123366475105, -0.010535458102822304, -0.0021693226881325245, -0.005009163171052933, 0.0017573704244568944, 0.039337050169706345, 0.012148207053542137, -0.018932269886136055, -0.022858962416648865, -0.0052414340898394585, 0.006188047584146261, -0.0017639441648498178, 0.019703585654497147, 0.03705816715955734, 0.01306852512061596, 0.007984859868884087, 0.007454581558704376, 0.038811154663562775, -0.038705974817276, 0.02047489956021309, -0.022578485310077667, 0.02222788706421852, 0.0028639440424740314, -0.0384254977107048, -0.016828684136271477, 0.0530804768204689, 0.02001912333071232, 0.020878085866570473, -0.013462947681546211, 0.0021222110372036695, 0.04683983698487282, 0.003768924158066511, -0.05602549389004707, 0.007353784516453743, 0.03097529709339142, -0.03385019674897194, 0.00023911851167213172, 0.03958246856927872, 0.002267928095534444, -0.022245418280363083, -0.012078086845576763, -0.012901991605758667, -0.027784859761595726, -0.004454780835658312, 0.008037449792027473, 0.04743585363030434, -0.025330675765872, 0.03192191198468208, -0.04557768628001213, -0.014216732233762741, 0.013349003158509731, -0.012086852453649044, 0.045682866126298904, -0.02001912333071232, -0.005828685127198696, 0.03360477834939957, -0.003207968082278967, -0.012121912091970444, 0.005995218642055988, 0.022315537557005882, -0.00914183259010315, -0.003319720970466733, -0.027469322085380554, 0.027714740484952927, 0.037373702973127365, 0.011438246816396713, 0.019335458055138588, 0.028608763590455055, -0.008068127557635307, -0.01994900219142437, 0.043053384870290756, 0.04091474041342735, 0.09501194953918457, -0.03393784537911415, 0.02298167161643505, 0.035112347453832626, 0.05003027617931366, -0.026873305439949036, -0.034200794994831085, 0.016819920390844345, -0.006784063298255205, 0.022315537557005882, 0.0030764939729124308, 0.023086851462721825, -0.003361354349181056, -0.02608446031808853, -0.0009778386447578669, -0.07706134766340256, -0.006639441940933466, 0.05602549389004707, -0.005009163171052933, -0.018196014687418938, 0.04063425958156586, 0.007467728573828936, 0.07264382392168045, -0.01662709005177021, -0.01425179187208414, 0.03954740986227989, -0.027609560638666153, -0.02894183062016964, 0.028468525037169456, -0.020282071083784103, -0.003407370299100876, 0.006994422059506178, -0.0030940237920731306, -0.054833464324474335, -0.05027569457888603, -0.005916334223002195, -0.005096812732517719, 0.006402788683772087, 0.003847808577120304, -0.025874102488160133, 0.023384859785437584, 0.03179920092225075, 0.0241211149841547, -0.028380874544382095, -0.06426453590393066, -0.005215139128267765, 0.014102788642048836, -0.07958565652370453, -0.014646214433014393, -0.05146772786974907, 0.008764940313994884, -0.02606693096458912, -0.044105175882577896, -0.05027569457888603, 0.033815138041973114, -0.004505178891122341, 0.05118724703788757, 0.021403983235359192, -0.014952987432479858, 0.008519521914422512, -0.04014342278242111, 0.02683824673295021, 0.01624143309891224, 0.05553465709090233, -0.03236015886068344, -0.011885258369147778, 0.018108366057276726, 0.017626294866204262, 0.0028376493137329817, 0.03516493737697601, -0.03255298733711243, 0.019002389162778854, -0.03846055641770363, -0.011315537616610527, 0.03150119259953499, -0.033376891165971756, -0.00559641420841217, 0.02759203128516674, 0.0023796812165528536, 0.020229481160640717, 0.05798884108662605, -0.0012051792582497, -0.003479681210592389, 0.020439838990569115, -0.01307729072868824, 0.03446374461054802, 0.025435855612158775, -0.022771313786506653, 0.0365673303604126, -0.00714342575520277, 0.025050198659300804, -0.00022939490736462176, 0.002254780847579241, -0.0020290836691856384, -0.01299840584397316, -0.01662709005177021, -0.013296414166688919, -0.023086851462721825, -0.03597131371498108, 0.028626292943954468, -0.04287808761000633, 0.012674103491008282, 0.022105177864432335, 0.02804780751466751, -0.016872508451342583, -0.008063744753599167, -0.006113545503467321, -0.0007422808557748795, 0.047576092183589935, 0.03567330539226532, 0.0065298802219331264, 0.007498405873775482, 0.054763343185186386, 0.01640796661376953, -0.02857370302081108, -0.012533864006400108, -0.031080476939678192, -0.05514900013804436, 0.007770119234919548, 0.03846055641770363, 0.033219121396541595, -0.022333066910505295, 0.012481274083256721, 0.002754382323473692, -0.0075203184969723225, 0.0010156374191865325, 0.019528286531567574, 0.026925895363092422, 0.035042230039834976, -0.026259759441018105, 0.028994420543313026, -0.042597606778144836, 0.004126095212996006, -0.011578485369682312, -0.02077290788292885, -0.002955975942313671, -0.0002278884348925203, -0.02994103543460369, -0.04466613382101059, -0.0204924289137125, 0.0192127488553524, -0.018038246780633926, 0.01126294769346714, -0.01462868507951498, -0.015522708185017109, -0.06240637227892876, 0.028906771913170815, -0.004960956051945686, 0.02592669241130352, 0.04778645187616348, -0.02615458145737648, 0.03807489946484566, -0.050976891070604324, 0.01812589541077614, -0.029537847265601158, 0.02820557728409767, 0.00816015899181366, -0.03190438076853752, 0.0005779382190667093, 0.039722707122564316, 0.028854181990027428, 0.02266613394021988, 0.03937210887670517, -0.028450995683670044, -0.040388841181993484, 0.030168922618031502, -0.013585656881332397, 0.01851155236363411, 0.024664539843797684, -0.006398405879735947, -0.005245816428214312, 0.013988844119012356, -0.011736254207789898, -0.06198565289378166, 0.031027887016534805, -0.03288605436682701, 0.019458167254924774, 0.044701192528009415, 0.01069322694092989, -0.003867529798299074, 0.011473306454718113, 0.011858963407576084, -0.041826292872428894, -0.027031075209379196, -0.026329878717660904, -0.036427091807127, 0.0036527886986732483, 0.00638964120298624, 0.00891832634806633, -0.0036243025679141283, -0.030887648463249207, -0.023314740508794785, -0.02093067578971386, 0.0011241035535931587, -0.03399043530225754, -0.036917924880981445, -0.050661351531744, -0.0036155376583337784, 0.007038246840238571, -0.04981991648674011, -0.015031872317194939, -0.009956971742212772, -0.00812509935349226, -0.0034665337298065424, 0.01601354591548443, -0.0241912342607975, -0.003394223051145673, 0.01578565686941147, -0.004785657394677401, -0.027486851438879967, 0.04827728867530823, -0.050836652517318726, 0.014786453917622566, -0.03225497901439667, 0.033832669258117676, -0.0070470115169882774, -0.044105175882577896, -0.0011931274784728885, -0.006100398022681475, 0.01571553759276867, -0.004750597290694714, -0.02268366515636444, -0.048101991415023804, -0.005701593589037657, -0.018792031332850456, -0.053325895220041275, 0.028538644313812256, 0.04073943942785263, -0.007340637035667896, -0.023174500092864037, -0.020229481160640717, 0.03220238909125328, -0.029345018789172173, 0.030887648463249207, 0.0042707170359790325, 0.020229481160640717, -0.031325895339250565, 0.020755376666784286, 0.023402389138936996, -0.043719518929719925, -0.048557765781879425, 0.02773226983845234, 0.031238244846463203, 0.002539641223847866, -0.013664540834724903, 0.022631075233221054, 0.00891832634806633, -0.04974979907274246, 0.014330676756799221, 0.00865537766367197, 0.02336733043193817, -0.033832669258117676 ]
Likelihood-based, or explicit, deep generative models use neural networks to construct flexible high-dimensional densities. This formulation directly contradicts the manifold hypothesis, which states that observed data lies on a low-dimensional manifold embedded in high-dimensional ambient space. In this paper we investigate the pathologies of maximum-likelihood training in the presence of this dimensionality mismatch. We formally prove that degenerate optima are achieved wherein the manifold itself is learned but not the distribution on it, a phenomenon we call manifold overfitting. We propose a class of two-step procedures consisting of a dimensionality reduction step followed by maximum-likelihood density estimation, and prove that they recover the data-generating distribution in the nonparametric regime, thus avoiding manifold overfitting. We also show that these procedures enable density estimation on the manifolds learned by implicit models, such as generative adversarial networks, hence addressing a major shortcoming of these models. Several recently proposed methods are instances of our two-step procedures; we thus unify, extend, and theoretically justify a large class of models.
[ 0.01788707822561264, -0.014408781193196774, -0.027018757537007332, -0.04456626623868942, 0.013573622331023216, 0.0235496386885643, -0.029349859803915024, 0.01407838799059391, -0.015069565735757351, -0.009709866717457771, 0.010076968930661678, 0.01997038722038269, 0.009067436680197716, -0.029056178405880928, 0.021328667178750038, 0.035462118685245514, 0.007057549431920052, 0.010177922435104847, 0.028248552232980728, -0.04129905253648758, 0.023586347699165344, -0.008737044408917427, -0.06405942142009735, 0.04074839875102043, 0.035351987928152084, 0.04776006191968918, 0.017620928585529327, -0.026945337653160095, -0.04596125707030296, 0.05620342120528221, 0.02134702168405056, 0.000617765006609261, -0.014601510018110275, -0.01859375089406967, -0.0403812974691391, -0.0030607187654823065, 0.0584060400724411, 0.009250988252460957, -0.01470246259123087, 0.06640888005495071, 0.05238555371761322, -0.007998249493539333, -0.009673155844211578, -0.0032213260419666767, 0.002815218875184655, -0.02538515068590641, -0.005956241395324469, 0.012655865401029587, 0.015308182686567307, -0.018300069496035576, -0.025458572432398796, -0.035462118685245514, -0.009608913213014603, -0.022099582478404045, -0.0743015855550766, 0.04757650941610336, 0.07092423737049103, 0.0010238724062219262, 0.07584341615438461, 0.017969677224755287, -0.004813633859157562, 0.018648816272616386, -0.08318547159433365, -0.028450459241867065, -0.03280062600970268, -0.014427135698497295, 0.057524994015693665, 0.005047662183642387, 0.037554606795310974, 0.009273931384086609, -0.04776006191968918, -0.017923789098858833, -0.002746386919170618, -0.0061030820943415165, -0.012940369546413422, 0.016657285392284393, 0.037664737552404404, 0.028890982270240784, 0.06802412867546082, -0.004423587583005428, 0.004267568700015545, -0.016712350770831108, -0.012499846518039703, 0.037114083766937256, 0.05275265872478485, 0.021952740848064423, 0.03770144656300545, -0.051284246146678925, 0.0066124373115599155, -0.0083102872595191, -0.05686420574784279, 0.09493275731801987, -0.040197744965553284, -0.01960328407585621, 0.0015188873512670398, 0.03463613986968994, 0.000448840408353135, 0.017253827303647995, -0.042069967836141586, 0.049925968050956726, -0.034782979637384415, 0.009719043970108032, 0.022209713235497475, 0.053119760006666183, -0.035260215401649475, -0.0823778435587883, 0.003932587802410126, 0.051761478185653687, 0.0505867525935173, 0.1718040555715561, 0.03318608179688454, -0.014674929901957512, -0.027183953672647476, 0.027275729924440384, -0.049338601529598236, 0.011462781578302383, -0.05484514310956001, -0.09867720305919647, 0.07026345282793045, -0.07606367766857147, -0.030763205140829086, 0.014785060659050941, -0.013509378768503666, -0.017813658341765404, -0.022760367020964622, 0.05458816885948181, -0.0392799898982048, -0.05212858319282532, 0.025348441675305367, 0.0129220150411129, -0.013637864962220192, -0.012986257672309875, 0.05598315969109535, -0.0015200346242636442, -0.00791106279939413, -0.002530714264139533, 0.015354069881141186, 0.010049436241388321, 0.004086311906576157, -0.022870497778058052, 0.016244294121861458, -0.03223161771893501, -0.0027119710575789213, 0.02283378690481186, 0.007108025718480349, 0.01973176933825016, -0.01126087550073862, 0.060645364224910736, -0.009663978591561317, -0.02378825470805168, -0.04607138782739639, 0.015142986550927162, -0.0024618825409561396, 0.032488588243722916, 0.08105627447366714, 0.014748350717127323, 0.0012687987182289362, -0.03234174847602844, 0.0066124373115599155, -0.06200364604592323, 0.06534428149461746, -0.024375619366765022, 0.013940724544227123, 0.04515363276004791, 0.032488588243722916, 0.055799610912799835, 0.03737105429172516, 0.020557750016450882, -0.02861565537750721, 0.032929111272096634, -0.06365560740232468, 0.0015762471593916416, 0.00303089153021574, -0.029937224462628365, -0.04493337124586105, 0.03983064368367195, 0.06813426315784454, 0.005846110638231039, 0.026725076138973236, 0.02019064873456955, 0.007305343635380268, -0.042290229350328445, 0.03683875501155853, 0.05051333084702492, 0.02086978778243065, 0.030194196850061417, 0.04526376351714134, 0.0219343863427639, 0.03425068035721779, -0.04673217236995697, -0.005887409672141075, 0.021438797935843468, 0.029955578967928886, -0.02435726299881935, 0.0008041843539103866, -0.04511692002415657, -0.0057864561676979065, -0.009911772795021534, -0.0028634010814130306, 0.029827093705534935, -0.007553137838840485, -0.09287697821855545, 0.0006980687030591071, -0.020392553880810738, 0.03669191524386406, -0.0019651465117931366, 0.0012183220824226737, 0.015280649997293949, -0.003813279327005148, 0.004421293269842863, 0.03920656815171242, -0.049668993800878525, -0.06336192786693573, -0.026357972994446754, -0.04085852950811386, -0.01200425811111927, -0.06563796103000641, 0.03637987747788429, -0.0007686212775297463, -0.03705901652574539, -0.011141566559672356, -0.0010732017690315843, 0.014564799144864082, -0.020906498655676842, 0.00030257293838076293, 0.029276439920067787, 0.018887434154748917, 0.016556331887841225, -0.008796698413789272, 0.002203763462603092, 0.023255955427885056, 0.0047493912279605865, 0.00148676591925323, -0.02101662941277027, 0.006217801943421364, -0.0027578589506447315, -0.024962984025478363, 0.02435726299881935, 0.04071168974041939, -0.054184358566999435, 0.012187809683382511, -0.006699624005705118, -0.049668993800878525, 0.015216406434774399, 0.01373881846666336, 0.053119760006666183, -0.010242165066301823, -0.011655510403215885, 0.010765286162495613, 0.022099582478404045, -0.0023609292693436146, -0.021493863314390182, 0.019291246309876442, 0.007892708294093609, -0.09008700400590897, -0.0061902692541480064, 0.01625347137451172, -0.04383205994963646, -0.011545379646122456, -0.034672848880290985, -0.0063462876714766026, 0.051284246146678925, -0.01835513487458229, 0.01914440467953682, 0.024632589891552925, 0.003870639018714428, 0.06472020596265793, 0.056717365980148315, 0.03469120338559151, 0.059690896421670914, -0.0004081149527337402, -0.04133576154708862, -0.0026660833973437548, 0.0043570501729846, 0.003512713825330138, -0.034544363617897034, 0.08810464292764664, 0.010581735521554947, 0.06193022429943085, -0.020374199375510216, 0.05425777658820152, 0.019438087940216064, -0.04324469715356827, 0.01373881846666336, -0.009535492397844791, 0.00018742313841357827, -0.01425276231020689, 0.0038614615332335234, -0.027789674699306488, -0.04787019267678261, -0.009099557995796204, 0.01149031426757574, -0.036067839711904526, 0.026119356974959373, 0.011545379646122456, -0.007686212658882141, -0.027037113904953003, -0.0024572936818003654, 0.07444842904806137, -0.042290229350328445, -0.018419377505779266, 0.05535908788442612, 0.021145114675164223, -0.0008971071802079678, -0.004664498381316662, -0.018768126145005226, 0.013078033924102783, 0.026449749246239662, -0.056827496737241745, 0.01344513613730669, 0.014234406873583794, 0.0705571398139, 0.002672966569662094, -0.03045116923749447, -0.013949902728199959, 0.018208293244242668, 0.05642368271946907, -0.0651240199804306, -0.009985193610191345, -0.05010951682925224, 0.020686237141489983, 0.008966483175754547, -0.06611519306898117, -0.013307472690939903, 0.056019872426986694, -0.00727322231978178, 0.026926983147859573, 0.03507666289806366, -0.0584060400724411, 0.014693285338580608, -0.05825919657945633, -0.0181073397397995, -0.05297292023897171, -0.023604704067111015, -0.027863094583153725, 0.018520331010222435, 0.010526670143008232, -0.004276746418327093, 0.003489769995212555, 0.008379119448363781, 0.020484330132603645, 0.027018757537007332, -0.026339618489146233, -0.04463968798518181, -0.013546089641749859, -0.03527856990695, -0.028450459241867065, 0.004717269446700811, -0.02169576846063137, -0.012986257672309875, 0.0010416539153084159, -0.0008816200424917042, -0.035131726413965225, 0.028670720756053925, 0.013610332272946835, -0.02158563770353794, -0.012206164188683033, 0.01326158456504345, -0.0032190317288041115, 0.020796367898583412, -0.016547154635190964, -0.05414764583110809, -0.023586347699165344, 0.002468765713274479, -0.05884656310081482, 0.012710930779576302, -0.018483620136976242, 0.011141566559672356, -0.005419353488832712, 0.004827400203794241, -0.01672152802348137, -0.010315585881471634, 0.003069896250963211, 0.008411240763962269, -0.004942120052874088, 0.006158147472888231, 0.024026870727539062, 0.035590607672929764, -0.005644204095005989, 0.04720940813422203, -0.016418667510151863, 0.05260581523180008, -0.007860586047172546, 0.005272512324154377, -0.0069290632382035255, -0.0016404901398345828, -0.0030010645277798176, 0.031680963933467865, 0.018997564911842346, 0.03522350266575813, 0.008553492836654186, -0.022007806226611137, 0.029955578967928886, -0.013876481913030148, 0.067840576171875, 0.0051302602514624596, -0.030304327607154846, -0.03221326321363449, 0.0017632400849834085, -0.0030400692485272884, -0.022778721526265144, 0.029698608443140984, 0.011270052753388882, 0.01177481934428215, -0.015675285831093788, 0.01879565790295601, 0.0029437048360705376, 0.02263188175857067, 0.03957366943359375, -0.022888852283358574, 0.011123212054371834, -0.04306114464998245, -0.0019754713866859674, 0.00997601542621851, 0.03140563517808914, -0.02376990020275116, -0.0629948228597641, -0.019823545590043068, -0.008727866224944592, -0.05249568447470665, 0.07264962047338486, -0.01239889394491911, 0.04456626623868942, -0.02859729900956154, -0.013977435417473316, 0.048274002969264984, 0.04284088313579559, 0.011802352033555508, -0.01067351084202528, -0.022062871605157852, 0.030139131471514702, 0.04504350200295448, -0.0011953781358897686, -0.03210313245654106, -0.020833078771829605, 0.004334106110036373, -0.040895238518714905, 0.03241516649723053, -0.009154623374342918, 0.021622348576784134, 0.0018217471661046147, -0.015941433608531952, 0.05836932733654976, 0.07628393918275833, -0.06196693331003189, -0.007410885766148567, -0.03540705516934395, -0.01741902343928814, -0.03727927803993225, -0.032139841467142105, -0.07305343449115753, 0.02226477861404419, -0.04647520184516907, -0.02202616073191166, 0.049889255315065384, -0.033424701541662216, 0.026945337653160095, -0.035131726413965225, 0.017822835594415665, -0.058112356811761856, 0.02252175100147724, 0.032818980515003204, 0.027404217049479485, -0.052789367735385895, -0.002551363781094551, 0.032818980515003204, 0.007855997420847416, -0.012720108032226562, 0.006080138497054577, 0.003567779203876853, 0.032837335020303726, -0.023017339408397675, -0.014977789483964443, -0.029111243784427643, 0.0033956998959183693, 0.043318118900060654, -0.06152641028165817, -0.09199593216180801, 0.028248552232980728, -0.056937627494335175, 0.011811529286205769, 0.020722948014736176, 0.03447094187140465, -0.030726496130228043, -0.03193793445825577, -0.0017035859636962414, 0.07334712147712708, 0.06490375846624374, 0.009255576878786087, 0.0009263607207685709, -0.00039090702193789184, 0.028578944504261017, -0.020227357745170593, -0.002989592496305704, -0.004331811796873808, -0.04640178009867668, 0.045851126313209534, 0.0004299116844777018, 0.021659059450030327, 0.06751018762588501, 0.01743737794458866, -0.06115930899977684, -0.0030721905641257763, -0.0007198654348030686, -0.008250633254647255, -0.015776237472891808, 0.022319843992590904, 0.0065068951807916164, 0.010572557337582111, -0.038252100348472595, 0.035241857171058655, -0.004347872454673052, -0.0274592824280262, -0.020025452598929405, 0.03276391699910164, 0.0071539138443768024, -0.024137001484632492, -0.002090191002935171, 0.03788499906659126, -0.02088814415037632, 0.014353714883327484, 0.014151808805763721, -0.06174667179584503, 0.03379180282354355, -0.03777486830949783, 0.05756170302629471, 0.029680252075195312, -0.022797077894210815, -0.005910353269428015, -0.00935194082558155, -0.0065711382776498795, 0.06534428149461746, -0.052679236978292465, -0.024026870727539062, -0.013995789922773838, -0.005327577702701092, -0.00912250205874443, 0.021603994071483612, -0.00246647116728127, -0.0008919448009692132, 0.0436117984354496, 0.03381015732884407, -0.003570073749870062, 0.014179341495037079, 0.009553847834467888, 0.00820015650242567, 0.01927289180457592, -0.029588477686047554, 0.012178631499409676, -0.01212356612086296, 0.022888852283358574, -0.05447803810238838, -0.016528798267245293, -0.0168316587805748, -0.06387586891651154, 0.01373881846666336, -0.027863094583153725, 0.00923722144216299, 0.022686947137117386, -0.05055003985762596, -0.01579459384083748, 0.040638267993927, -0.035829223692417145, 0.009627267718315125, -0.005841521546244621, -0.0025146533735096455, 0.0024366441648453474, 0.047135986387729645, -0.021530572324991226, 0.035939354449510574, -0.02228313311934471, -0.0054055871441960335, -0.033516477793455124, -0.009131679311394691, 0.0433548279106617, -0.00985670741647482, 0.04607138782739639, 0.0023999337572604418, 0.011407716199755669, 0.03197464346885681, 0.026137711480259895, -0.05550592765212059, 0.04970570653676987, 0.042730752378702164, -0.008558081462979317, 0.02017229236662388, 0.0010800849413499236, -0.04860439524054527, 0.041592735797166824, -0.0007353525725193322, 0.01697850041091442, 0.08590202778577805, -0.015739528462290764, -0.025899095460772514, -0.010333940386772156, -0.013417603448033333, 0.011325118131935596, -0.024889562278985977, 0.01395907998085022, -0.011444426141679287, 0.0015360952820628881, -0.04041800647974014, 0.031001823022961617, -0.010187099687755108, -0.0071952128782868385, 0.013812239281833172, -0.015280649997293949, -0.03665520250797272, -0.029698608443140984, -0.0026362561620771885, -0.03795841708779335, -0.01367457490414381, 0.023237600922584534, -0.04221681132912636, 0.012619155459105968, -0.010756108909845352, 0.023916739970445633, -0.03637987747788429, -0.014684108085930347, 0.042069967836141586, 0.037077371031045914, 0.028762497007846832, -0.01626264862716198, -0.004157437942922115, -0.02621113322675228, 0.041005369275808334, 0.028450459241867065, -0.012252052314579487, 0.01200425811111927, -0.030763205140829086, -0.022686947137117386, 0.05308305099606514, -0.01730889268219471, -0.012967902235686779, -0.0024022283032536507, 0.025642123073339462, -0.01639113575220108, 0.031111953780055046, 0.0015039738500490785, 0.014445491135120392, -0.024540815502405167, 0.038949597626924515, -0.020025452598929405, -0.0077137453481554985, -0.0056074936874210835, 0.05238555371761322, -0.021512217819690704, -0.015023677609860897, 0.06464678794145584, 0.03370002657175064, 0.017024386674165726, 0.0274592824280262, -0.012371361255645752, 0.04269404336810112, -0.017731059342622757, -0.018272535875439644, 0.017455732449889183, 0.011958369985222816, -0.01754750870168209, 0.01229794044047594, -0.0023437212221324444, -0.016895901411771774, -0.007007072679698467, -0.0052036806009709835, 0.0257155429571867, -0.00952631514519453, 0.043905481696128845, 0.010958014987409115, 0.0066858576610684395, 0.01798803173005581, 0.006479362491518259, -0.03079991601407528, -0.0320480652153492, 0.004946708679199219, 0.03355318680405617, -0.04353838041424751, -0.019015919417142868, -0.023971805348992348, 0.009388651698827744, 0.006194857880473137, -0.0038614615332335234, -0.022888852283358574, -0.0005331592983566225, 0.009058259427547455, -0.06754689663648605, -0.021053340286016464, 0.028909336775541306, 0.018410200253129005, -0.018410200253129005, 0.009044492617249489, -0.015133808366954327, -0.04306114464998245, 0.008259810507297516, 0.002592662815004587, 0.04445613548159599, -0.004485535901039839, 0.0038201624993234873, -0.003248858731240034, 0.029845448210835457, 0.01651044376194477, -0.01593225635588169, 0.008461717516183853, 0.022576816380023956, -0.026449749246239662, 0.030854981392621994, 0.02850552462041378, 0.0037375641986727715, 0.0013777823187410831, -0.0064334748312830925, 0.021328667178750038, 0.019933676347136497, 0.07026345282793045, 0.009315230883657932, 0.022558460012078285, 0.023714834824204445, 0.026284553110599518, -0.017510797828435898, 0.00952631514519453, 0.017685173079371452, 0.02767954394221306, 0.01356444414705038, -0.024522459134459496, 0.03265378624200821, -0.06438980996608734, 0.006438063457608223, 0.04544731229543686, -0.0032006765250116587, -0.03219490498304367, -0.007011661306023598, -0.002606429159641266, 0.03193793445825577, -0.006800577510148287, -0.0008919448009692132, 0.0017827424453571439, 0.027294084429740906, 0.0015120041789487004, -0.0037031483370810747, 0.00864985678344965, -0.018309246748685837, -0.021860964596271515, 0.027642833068966866, -0.04082182049751282, 0.03716914728283882, 0.011499491520226002, -0.06802412867546082, 0.04904491826891899, -0.0015475673135370016, 0.04383205994963646, 0.004028952214866877, 0.018602928146719933, 0.030726496130228043, -0.0080120163038373, 0.026982048526406288, -0.028780851513147354, -0.01971341483294964, 0.007117203436791897, 0.0009206247050315142, 0.0029138776008039713, -0.013344182632863522, -0.03968380019068718, 0.03046952374279499, 0.01199508085846901, 0.03950025141239166, 0.03412219509482384, 0.0449700802564621, 0.020502684637904167, -0.021659059450030327, -0.016684817150235176, -0.0031983822118490934, -0.015904724597930908, 0.02597251534461975, 0.03784828633069992, 0.005901176016777754, -0.04776006191968918, 0.015482556074857712, -0.029625186696648598, 0.019291246309876442, -0.026743430644273758, -0.010058613494038582, 0.01973176933825016, -0.03913314640522003, 0.019823545590043068, 0.023733189329504967, 0.05598315969109535, -0.04214338958263397, -0.012077678926289082, 0.003632022300735116, -0.019107695668935776, 0.012665042653679848, 0.02966189756989479, -0.02747763693332672, -0.03961038216948509, 0.01662975177168846, -0.022650236263871193, 0.005566194653511047, 0.03865591436624527, 0.0017345602391287684, 0.01786872372031212, 0.0137296412140131, -0.02711053378880024, 0.014684108085930347, -0.038729336112737656, -0.03140563517808914, 0.016437023878097534, -0.06762031465768814, -0.03219490498304367, -0.00922804418951273, -0.013004613108932972, 0.037077371031045914, 0.004841167014092207, 0.01986025646328926, 0.04478652775287628, 0.00014296929293777794, -0.0013846654910594225, -0.03469120338559151, 0.0281384214758873, -0.01055420283228159, 0.009966838173568249, -0.011912482790648937, -0.03716914728283882, -0.05829590931534767, -0.027165599167346954, 0.02573389932513237, -0.0332411490380764, -0.013252407312393188, 0.042657334357500076, -0.007011661306023598, -0.019015919417142868, 0.03994077444076538, 0.011527024209499359, 0.016299359500408173, -0.011793173849582672, -0.041702866554260254, 0.008461717516183853, -0.01824500411748886, 0.015225584618747234, -0.014500556513667107, 0.022558460012078285, -0.005070605780929327, 0.0030423635616898537, -0.008236866444349289, 0.010765286162495613, -0.01925453543663025, -0.02529337629675865, 0.01971341483294964, 0.02619277685880661, 0.009517136961221695, 0.02505475841462612, 0.016556331887841225, -0.003833928843960166, 0.030396103858947754, 0.016464555636048317, 0.008333231322467327, 0.023366086184978485, -0.018061453476548195, -0.04798032343387604, 0.015326537191867828, 0.017492443323135376, -0.006392175797373056, 0.019933676347136497, 0.02687191776931286, -0.004173498600721359, -0.008218511939048767, 0.0014121981803327799, 0.03035939298570156, -0.011426071636378765, 0.004184970632195473, -0.05880985036492348, 0.014509733766317368, -0.08685649931430817, -0.05322989076375961, -0.006525250617414713, -0.026798496022820473, 0.018492797389626503, 0.025311730802059174, 0.03509501740336418, 0.008929773233830929, -0.026798496022820473, 0.0014385837130248547, -0.056019872426986694, 0.03245187923312187, 0.04027116671204567, 0.06398599594831467, -0.022356554865837097, 0.015207229182124138, -0.040454715490341187, 0.015574331395328045, -0.03318608179688454, 0.024045227095484734, -0.03656342998147011, 0.004740213509649038, -0.017584219574928284, -0.02237490937113762, -0.009517136961221695, 0.025880739092826843, 0.023329375311732292, -0.012949547730386257, -0.00946207158267498, 0.010893772356212139, -0.025109823793172836, 0.01177481934428215, -0.020447619259357452, -0.025330085307359695, -0.01079281885176897, 0.022778721526265144, -0.0300106443464756, 0.04339153692126274, 0.014711640775203705, 0.041225630789995193, 0.00848925020545721, -0.03610454872250557, -0.06170996278524399, 0.02400851622223854, -0.039977483451366425, 0.05745157226920128, 0.04511692002415657, -0.0023517515510320663, -0.021750833839178085, 0.00151544576510787, -0.016703173518180847, -0.00904908124357462, 0.044602978974580765, -0.008406652137637138, 0.005235802382230759, -0.029735317453742027, -0.011435248889029026, 0.01177481934428215, 0.020521041005849838, -0.0023437212221324444, 0.046438489109277725, -0.029955578967928886, 0.009838351979851723, 0.0040037138387560844, 0.024485750123858452, 0.09845694154500961, -0.00801660493016243, -0.03994077444076538, 0.003829339984804392, 0.004586489405483007, 0.03968380019068718, -0.026229487732052803, 0.015647752210497856, 0.02734914980828762, 0.028303617611527443, 0.00364808295853436, -0.0281384214758873, 0.02641303837299347, -0.006355465389788151, -0.023017339408397675, -0.01903427392244339, -0.04662204161286354, -0.027973225340247154, 0.020814722403883934, 0.029735317453742027, 0.011719753965735435, 0.048530977219343185, 0.015574331395328045, 0.03590264171361923, -0.027863094583153725, 0.035462118685245514, 0.012784351594746113, 0.0014397308696061373, -0.02562376856803894, -0.006364643108099699, 0.000013640876204590313, 0.006020484026521444, 0.010737753473222256, -0.011875771917402744, -0.0026752608828246593, -0.0011466223513707519, -0.026725076138973236, -0.04878794774413109, -0.00975575391203165, 0.002365517895668745, 0.030634719878435135, 0.02944163605570793, 0.007080493029206991, -0.004877876956015825, -0.015253117308020592, 0.0007181446417234838, 0.04618151858448982, 0.018153227865695953, 0.026926983147859573, 0.02353128232061863, -0.030304327607154846, -0.03344305604696274, -0.00957220233976841, -0.044162455946207047, -0.041042082011699677, 0.013123921118676662, 0.01718958280980587, -0.010682688094675541, 0.010820351541042328, -0.02536679618060589, -0.021438797935843468, 0.014115098863840103, -0.007846820168197155, -0.013114743866026402, 0.041372474282979965, 0.0470992773771286, -0.014922724105417728, -0.016675639897584915, -0.012573267333209515, 0.009136267937719822, 0.03430574759840965, 0.010728576220571995, 0.05737815052270889, 0.009581380523741245, -0.017630107700824738, 0.02400851622223854, 0.023164179176092148, -0.030965112149715424, -0.05734144151210785, 0.01660222001373768, -0.056937627494335175, 0.008737044408917427, -0.09625432640314102, -0.017721882089972496, -0.017932966351509094, 0.005125671159476042, 0.03865591436624527, -0.04082182049751282, -0.002629372989758849, -0.049925968050956726 ]
Imitation learning is a promising approach to help robots acquire dexterous manipulation capabilities without the need for a carefully-designed reward or a significant computational effort. However, existing imitation learning approaches require sophisticated data collection infrastructure and struggle to generalize beyond the training distribution. One way to address this limitation is to gather additional data that better represents the full operating conditions. In this work, we investigate characteristics of such additional demonstrations and their impact on performance. Specifically, we study the effects of corrective and randomly-sampled additional demonstrations on learning a policy that guides a five-fingered robot hand through a pick-and-place task. Our results suggest that corrective demonstrations considerably outperform randomly-sampled demonstrations, when the proportion of additional demonstrations sampled from the full task distribution is larger than the number of original demonstrations sampled from a restrictive training distribution. Conversely, when the number of original demonstrations are higher than that of additional demonstrations, we find no significant differences between corrective and randomly-sampled additional demonstrations. These results provide insights into the inherent trade-off between the effort required to collect corrective demonstrations and their relative benefits over randomly-sampled demonstrations. Additionally, we show that inexpensive vision-based sensors, such as LeapMotion, can be used to dramatically reduce the cost of providing demonstrations for dexterous manipulation tasks. Our code is available at https://github.com/GT-STAR-Lab/corrective-demos-dexterous-manipulation.
[ 0.003252679482102394, 0.04699939116835594, -0.036565233021974564, -0.024431642144918442, 0.02108759619295597, 0.03232578560709953, 0.03148520737886429, 0.023645883426070213, -0.05112919583916664, 0.03618149086833, -0.019552623853087425, -0.03535918518900871, 0.02412099391222, -0.0527007170021534, 0.011905171908438206, 0.005518591031432152, 0.007377917412668467, 0.008583967573940754, -0.046597372740507126, -0.024029625579714775, 0.02845180779695511, 0.014088853262364864, -0.0316862128674984, 0.07711408287286758, 0.0068297130055725574, 0.005121142603456974, 0.030297430232167244, -0.03528609126806259, -0.046049170196056366, 0.07188787311315536, 0.027611227706074715, 0.008305296301841736, -0.003956208471208811, -0.007332233712077141, 0.011366104707121849, 0.037497181445360184, 0.010744806379079819, 0.026003161445260048, -0.02136169746518135, 0.05149466544389725, -0.03272780403494835, -0.010927541181445122, -0.0022887533996254206, -0.04506240040063858, -0.025637691840529442, -0.023956531658768654, -0.01627253368496895, 0.021270330995321274, -0.06267803907394409, 0.013440144248306751, 0.017908010631799698, -0.012937624007463455, -0.007336802314966917, -0.024541283026337624, -0.009392568841576576, 0.051385026425123215, 0.05887715145945549, 0.019296795129776, 0.05295654386281967, -0.028470082208514214, 0.02097795531153679, 0.019698811694979668, -0.067538782954216, 0.021197237074375153, 0.0056190951727330685, -0.05763455480337143, 0.05273726209998131, -0.006080500315874815, 0.0396169051527977, 0.020448023453354836, -0.03411658853292465, -0.025235675275325775, -0.03680278733372688, -0.010772216133773327, -0.014015759341418743, -0.008803249336779118, 0.07448270171880722, 0.022311918437480927, 0.017716139554977417, -0.039909280836582184, -0.009858542121946812, 0.0007183761917985976, 0.009840268641710281, 0.011731574311852455, 0.08742032945156097, -0.06136234477162361, 0.02233019284904003, -0.05288344994187355, 0.030827360227704048, -0.03526781499385834, -0.007035289891064167, 0.03177758306264877, -0.001976962201297283, 0.03800883889198303, -0.014390365220606327, 0.028707636520266533, 0.0047922199591994286, 0.011146822944283485, -0.032398879528045654, -0.024541283026337624, 0.0033965830225497484, 0.017880599945783615, -0.0315217524766922, -0.01863894984126091, 0.026642734184861183, 0.012316325679421425, -0.07009706646203995, -0.034226227551698685, -0.02731885202229023, 0.08244994282722473, 0.016555773094296455, -0.004415329545736313, -0.04009201377630234, 0.007336802314966917, -0.03884941712021828, -0.04074985906481743, -0.018501898273825645, -0.043637070804834366, 0.03468306362628937, -0.0885167345404625, 0.056136131286621094, 0.07609076797962189, 0.050105880945920944, 0.032051682472229004, -0.011996539309620857, 0.014289861544966698, -0.022860122844576836, 0.00580639811232686, 0.045464418828487396, -0.0025879815220832825, 0.0218733549118042, 0.0437467098236084, 0.012316325679421425, 0.02969440445303917, 0.02728230506181717, -0.0007412180420942605, 0.012480787001550198, 0.010160055011510849, -0.004394771996885538, 0.01142092514783144, -0.0047785150818526745, -0.045281682163476944, -0.0013865003129467368, 0.04184626787900925, -0.018273480236530304, -0.04400254040956497, -0.01441777590662241, 0.07484817504882812, -0.03568810597062111, -0.01720448210835457, -0.07020670920610428, 0.0013602321268990636, 0.004979523364454508, 0.057342179119586945, 0.07287463545799255, 0.00023541381233371794, -0.011018908582627773, 0.006304350681602955, 0.01926024816930294, -0.03269125521183014, 0.08983242511749268, -0.008003784343600273, 0.0030151242390275, 0.056099582463502884, 0.03645559400320053, 0.003369172802194953, 0.02081349305808544, 0.009995593689382076, -0.041115328669548035, 0.044112179428339005, -0.029365481808781624, -0.0031818696297705173, 0.03972654417157173, 0.010114370845258236, 0.0019952356815338135, 0.00026610755594447255, 0.0032892264425754547, 0.004687147680670023, -0.013019854202866554, -0.08011093735694885, -0.016902968287467957, -0.013613742776215076, -0.02381034381687641, -0.0009507919894531369, 0.059754278510808945, 0.02680719457566738, 0.04261375591158867, -0.02525394968688488, 0.060996875166893005, -0.007186045870184898, 0.006436833180487156, -0.010050414130091667, 0.009310337714850903, 0.03700379654765129, 0.011896035633981228, -0.04385635256767273, -0.04166353493928909, 0.014070579782128334, 0.011640206910669804, 0.056793976575136185, -0.06911030411720276, -0.048278532922267914, -0.011713300831615925, -0.034847527742385864, 0.02848835475742817, -0.0036250015255063772, -0.009620986878871918, -0.031503479927778244, 0.014911159873008728, -0.030169514939188957, 0.017295848578214645, 0.01272747851908207, -0.04688974842429161, -0.022823575884103775, -0.009155013598501682, 0.025089487433433533, -0.011082865297794342, 0.017834916710853577, -0.025655966252088547, -0.041151877492666245, -0.022695662453770638, -0.0027958424761891365, 0.0077982074581086636, -0.039361074566841125, -0.06410336494445801, 0.031850676983594894, 0.02077694609761238, -0.025546325370669365, -0.002871220465749502, -0.01017832849174738, 0.036565233021974564, -0.02645999938249588, 0.017323259264230728, -0.023024585098028183, 0.010041276924312115, 0.012453376315534115, 0.009223539382219315, -0.003047102829441428, -0.022476380690932274, 0.01035192608833313, 0.028122885152697563, -0.007793639320880175, 0.0038031679578125477, 0.012526470236480236, 0.059242621064186096, 0.07108383625745773, 0.009895089082419872, 0.07031635195016861, 0.007254571653902531, -0.004511265549808741, -0.05229869857430458, -0.0027478744741529226, -0.039872732013463974, 0.03490234538912773, -0.01677505485713482, 0.035706378519535065, 0.03852049633860588, -0.03347701579332352, 0.007268276531249285, -0.0850813239812851, 0.04389289766550064, 0.04206554964184761, -0.00974890124052763, 0.00961185060441494, -0.004401624668389559, -0.016409585252404213, 0.02121550962328911, 0.024212360382080078, -0.0007063841912895441, 0.040055468678474426, 0.0038031679578125477, -0.030151242390275, 0.0059206075966358185, 0.010900130495429039, -0.004527254495769739, -0.09436424821615219, 0.09619159996509552, -0.019296795129776, 0.05295654386281967, -0.005121142603456974, 0.027720868587493896, 0.03272780403494835, 0.017807506024837494, -0.0032892264425754547, -0.005760714411735535, -0.03643731772899628, -0.06472466886043549, 0.0575249157845974, -0.03455515205860138, -0.02214745804667473, 0.001989525044336915, -0.010699122212827206, -0.02952994406223297, 0.04407563433051109, 0.10379336774349213, -0.029603037983179092, -0.03027915582060814, 0.00198038830421865, -0.008689039386808872, 0.007167772389948368, 0.017679592594504356, -0.012371146120131016, -0.008538283407688141, 0.03300190344452858, -0.015532458201050758, 0.020722126588225365, -0.009356021881103516, 0.021416518837213516, -0.015441090799868107, -0.010827036574482918, -0.009191560558974743, 0.030681172385811806, -0.04860745742917061, 0.004602632950991392, -0.00016246266022790223, 0.043454334139823914, 0.041736628860235214, -0.0019952356815338135, -0.03910524770617485, 0.008922026492655277, -0.012946760281920433, -0.002180254552513361, -0.09451043605804443, 0.008095151744782925, 0.0565016008913517, 0.014125400222837925, -0.013111221604049206, -0.05584375560283661, -0.0420290045440197, -0.05690361559391022, -0.05412604659795761, -0.028360441327095032, -0.0230794046074152, 0.005842945072799921, -0.039397623389959335, 0.04579333961009979, -0.042394474148750305, 0.011155959218740463, -0.029054833576083183, -0.086835578083992, -0.042284831404685974, 0.035158175975084305, -0.06596726179122925, -0.0709741935133934, 0.015934474766254425, -0.026368631049990654, 0.019698811694979668, -0.006441401783376932, -0.00859767198562622, -0.04919220879673958, 0.001062146038748324, -0.03541400283575058, -0.023481421172618866, 0.024468189105391502, 0.0389225110411644, -0.07254571467638016, -0.04634154587984085, 0.027026476338505745, -0.02680719457566738, -0.02459610439836979, -0.012234094552695751, -0.060960330069065094, -0.022403286769986153, 0.030882181599736214, -0.03965345025062561, 0.008337275125086308, -0.05573411285877228, -0.007272845134139061, -0.020685579627752304, 0.02742849290370941, -0.008780406787991524, -0.039397623389959335, -0.0052125100046396255, 0.011183369904756546, -0.03643731772899628, -0.023371780291199684, 0.01715879701077938, 0.04367361590266228, -0.026167623698711395, 0.028543176129460335, 0.01720448210835457, -0.00035747495712712407, -0.04126151651144028, 0.01859326660633087, 0.02731885202229023, 0.07769883424043655, 0.010900130495429039, -0.010004729963839054, -0.004678010940551758, 0.016016704961657524, 0.017697865143418312, 0.0024623514618724585, -0.03968999907374382, 0.026021435856819153, -0.021160690113902092, 0.0004368503869045526, 0.01887650415301323, -0.01262697484344244, 0.04425836727023125, -0.041151877492666245, -0.050690632313489914, -0.04436801001429558, -0.03906869888305664, -0.0009096766589209437, 0.023755524307489395, 0.016482679173350334, -0.019936366006731987, 0.009209834039211273, 0.03203340992331505, 0.03428104892373085, -0.013677699491381645, 0.005372403189539909, -0.022202277556061745, -0.008547420613467693, -0.004266857635229826, -0.03256333991885185, 0.018383121117949486, 0.03685760870575905, 0.029840592294931412, -0.05905988812446594, 0.02887209877371788, -0.016555773094296455, 0.057890385389328, -0.004237163346260786, 0.019296795129776, 0.006628704722970724, -0.04034784436225891, 0.015733465552330017, -0.03311154618859291, -0.037606820464134216, 0.00721802469342947, 0.044806573539972305, 0.0011049745371565223, -0.02580215409398079, 0.03950726240873337, 0.040457483381032944, -0.005911470856517553, 0.03510335460305214, -0.006208414677530527, -0.002316163619980216, -0.011503155343234539, -0.026258990168571472, 0.01441777590662241, -0.00008201651507988572, -0.04016510769724846, -0.037223078310489655, -0.044185273349285126, -0.030370524153113365, 0.033952124416828156, -0.00015917913697194308, -0.06194709613919258, 0.004152648150920868, -0.03201513737440109, -0.013896981254220009, -0.004979523364454508, -0.0012677226914092898, 0.016354763880372047, -0.05697670951485634, -0.02233019284904003, -0.06735605001449585, -0.0006367165478877723, -0.0009313764167018235, -0.014353818260133266, -0.006144457496702671, 0.014664467424154282, 0.027519861236214638, -0.05818276107311249, -0.04572024568915367, 0.007642882876098156, 0.06011974811553955, -0.010379336774349213, -0.0378991961479187, -0.053175825625658035, 0.016318216919898987, 0.04908256605267525, 0.000856569386087358, -0.022275371477007866, -0.003369172802194953, 0.003853420028463006, -0.028415260836482048, 0.006532769184559584, -0.0006612715660594404, -0.006505358964204788, -0.06139889359474182, 0.03782610222697258, -0.004625474568456411, 0.0816459059715271, -0.01681160181760788, -0.022366739809513092, -0.04089604690670967, 0.0049109975807368755, -0.022385012358427048, -0.012535607442259789, 0.043417789041996, -0.0004948115674778819, -0.029749225825071335, -0.034226227551698685, -0.04572024568915367, 0.020685579627752304, -0.01619030348956585, 0.028269072994589806, -0.035779472440481186, -0.012215821072459221, 0.006231256760656834, -0.013476691208779812, -0.004205184523016214, 0.010744806379079819, -0.03958035632967949, 0.008885479532182217, -0.050142429769039154, -0.0097306277602911, 0.010516387410461903, -0.017186207696795464, -0.037223078310489655, 0.03186894953250885, -0.018501898273825645, -0.008954005315899849, 0.024194087833166122, 0.059279169887304306, 0.02242155931890011, -0.001570377149619162, 0.0475475937128067, -0.01960744336247444, -0.0041206697933375835, -0.053285468369722366, 0.04074985906481743, 0.0006498506409116089, -0.0071814777329564095, 0.04327160120010376, 0.06326279044151306, -0.017222754657268524, 0.03972654417157173, -0.04520858824253082, -0.056793976575136185, 0.009584439918398857, -0.022202277556061745, 0.06903720647096634, 0.00021956728596705943, 0.0010136071359738708, -0.014710151590406895, -0.013960938900709152, 0.0127457519993186, -0.012690931558609009, 0.059681184589862823, 0.01500252727419138, -0.016089798882603645, 0.016701960936188698, -0.007624609395861626, 0.02156270667910576, 0.024267181754112244, 0.009456525556743145, 0.021964723244309425, 0.008551988750696182, 0.005874923896044493, -0.026057982817292213, -0.038593590259552, -0.033769391477108, 0.001918715424835682, -0.0077845025807619095, 0.0029351776465773582, -0.038118477910757065, 0.017405489459633827, -0.010562071576714516, 0.03607184812426567, 0.03592566028237343, -0.060923781245946884, 0.042357925325632095, 0.07492126524448395, -0.0029922823887318373, -0.005948017816990614, -0.037223078310489655, -0.02883555181324482, -0.012371146120131016, -0.003766620997339487, 0.009849405847489834, 0.002133428817614913, -0.013239135965704918, -0.024340275675058365, -0.012718342244625092, -0.010680848732590675, -0.004639179911464453, -0.006203846540302038, -0.026003161445260048, 0.02965785749256611, -0.020575938746333122, 0.007409896235913038, -0.00010814188135555014, -0.004705421160906553, 0.0033508993219584227, 0.03958035632967949, -0.00856112502515316, 0.005582548212260008, 0.002331010764464736, 0.015733465552330017, -0.022074364125728607, 0.0076657249592244625, -0.021507885307073593, 0.03256333991885185, 0.021891629323363304, -0.0651266798377037, -0.01738721691071987, 0.015103030949831009, -0.0014710151590406895, -0.0021688337437808514, 0.016720233485102654, -0.024212360382080078, -0.013641152530908585, 0.019972912967205048, 0.02614934928715229, -0.0012151864357292652, -0.018748590722680092, 0.017770959064364433, -0.0036272858269512653, -0.021617526188492775, 0.03968999907374382, -0.010004729963839054, 0.01883995719254017, 0.030790813267230988, -0.0009182423818856478, 0.01438122894614935, 0.03841085359454155, -0.01441777590662241, 0.012398555874824524, -0.005948017816990614, -0.03534090891480446, 0.016647139564156532, -0.017231890931725502, -0.053248919546604156, -0.01580655947327614, 0.01743290014564991, 0.013705110177397728, -0.018766863271594048, 0.03296535834670067, 0.004764809738844633, -0.006573884282261133, 0.031814128160476685, -0.019442982971668243, 0.018584128469228745, 0.006144457496702671, 0.013604605570435524, -0.016327355057001114, 0.021306877955794334, 0.019442982971668243, 0.06066795438528061, -0.013220862485468388, 0.05814621224999428, -0.023517968133091927, 0.008437779732048512, 0.061106517910957336, 0.02700820378959179, -0.012690931558609009, 0.001617203000932932, -0.03170448914170265, 0.036126669496297836, 0.006742914207279682, -0.011640206910669804, 0.03641904518008232, -0.0067109353840351105, -0.01457310002297163, 0.006802302785217762, 0.058584775775671005, -0.03513990342617035, 0.018282616510987282, 0.008437779732048512, 0.057926930487155914, -0.02828734740614891, 0.03714998438954353, -0.0040704174898564816, 0.017725275829434395, 0.08654320240020752, 0.020027734339237213, 0.00908648781478405, -0.028396988287568092, 0.023938259109854698, 0.041188422590494156, -0.018492761999368668, 0.0637378990650177, 0.006555610802024603, 0.0016982915112748742, 0.0015829402254894376, -0.022914944216609, -0.03444550931453705, 0.03345874324440956, -0.021891629323363304, 0.00018387689488008618, -0.004413045477122068, 0.008017489686608315, 0.025363590568304062, -0.04572024568915367, 0.02642345242202282, -0.029895413666963577, -0.027410220354795456, 0.009250949136912823, 0.0012471650261431932, 0.01755167730152607, -0.010580345056951046, -0.0109366774559021, -0.027209211140871048, 0.038776323199272156, 0.01138437818735838, -0.08420419692993164, -0.016336491331458092, -0.022622568532824516, 0.03682106360793114, 0.05240834131836891, -0.007652019616216421, -0.008012920618057251, 0.024760564789175987, 0.019826725125312805, 0.04805925115942955, -0.005518591031432152, 0.04319850727915764, 0.0029237568378448486, 0.034500330686569214, -0.006911943666636944, 0.04824198782444, 0.0194612555205822, -0.048388175666332245, 0.059827372431755066, 0.0042440155521035194, 0.030772540718317032, 0.03470133990049362, 0.007606335915625095, -0.02156270667910576, -0.01572432927787304, 0.017304984852671623, 0.032234419137239456, -0.03232578560709953, 0.03925143554806709, -0.002862083725631237, 0.03314809128642082, -0.03183240070939064, -0.0029374619480222464, 0.008830659091472626, -0.050763726234436035, 0.02222055196762085, -0.004378782585263252, 0.05244488641619682, 0.006505358964204788, -0.011092002503573895, -0.003876261878758669, 0.007793639320880175, 0.07937999814748764, 0.02980404533445835, 0.011347831226885319, 0.003933366388082504, 0.0015920769656077027, 0.03855704143643379, 0.03979963809251785, -0.015614688396453857, 0.1037202700972557, 0.030480165034532547, 0.05591684952378273, 0.018858231604099274, -0.056867070496082306, -0.0330749973654747, 0.030955275520682335, 0.012106180191040039, 0.021580979228019714, -0.0065282005816698074, 0.055514831095933914, -0.0015189830446615815, 0.03619976341724396, 0.006573884282261133, -0.0071814777329564095, 0.020923133939504623, -0.004029302392154932, -0.004040723200887442, 0.029438575729727745, 0.01143919862806797, 0.010278832167387009, 0.017880599945783615, 0.04012856259942055, 0.0024280885700136423, 0.005824671592563391, 0.02938375622034073, -0.02697165682911873, 0.02618589624762535, -0.06059486046433449, -0.0028849255759269, -0.008099719882011414, 0.002150560263544321, -0.021818535402417183, -0.027410220354795456, -0.0032686686608940363, -0.001395637053065002, -0.012672658078372478, -0.0004662592546083033, -0.030809087678790092, 0.02583870105445385, -0.030681172385811806, 0.000012830695595766883, -0.022933216765522957, 0.02163580060005188, 0.041224971413612366, 0.0024395096115767956, 0.006555610802024603, -0.01502080075442791, -0.013494964689016342, -0.009721491485834122, -0.0102514224126935, -0.028415260836482048, 0.013759930618107319, 0.02501639351248741, -0.007825617678463459, 0.013339640572667122, -0.031229376792907715, -0.0038488516584038734, -0.005399813409894705, 0.034847527742385864, 0.020247016102075577, -0.016409585252404213, -0.009511345997452736, -0.03630940616130829, 0.010525524616241455, -0.00725913979113102, 0.030644625425338745, -0.005011501722037792, 0.036674875766038895, -0.019351614639163017, 0.02101450227200985, -0.015742603689432144, -0.02339005470275879, 0.0157608762383461, -0.004723694641143084, 0.0017736696172505617, -0.04520858824253082, 0.0006332902703434229, 0.05346820130944252, -0.04323505237698555, 0.03572465479373932, 0.043417789041996, -0.014774108305573463, 0.0018867368344217539, -0.021855082362890244, 0.004673442337661982, -0.02339005470275879, -0.02121550962328911, -0.0064094229601323605, 0.04915565997362137, -0.0006812581559643149, -0.036053575575351715, -0.05957154557108879, -0.029931960627436638, 0.0013099800562486053, -0.018511034548282623, -0.034536875784397125, 0.05350475013256073, -0.016875559464097023, 0.022202277556061745, 0.006468812003731728, 0.024340275675058365, 0.03206995874643326, -0.028853824362158775, -0.027684321627020836, 0.013979212380945683, 0.02424890734255314, 0.06611344963312149, -0.023682430386543274, 0.018026787787675858, -0.00009893376409308985, -0.009319474920630455, -0.061106517910957336, 0.009246380999684334, 0.053797125816345215, 0.07393450289964676, -0.03490234538912773, -0.04038438946008682, -0.022586021572351456, -0.054454971104860306, 0.005596253089606762, 0.03166794031858444, -0.0026336652226746082, 0.003718653228133917, -0.01017832849174738, 0.050763726234436035, -0.017697865143418312, -0.009342316538095474, -0.027647774666547775, -0.04699939116835594, -0.013504101894795895, 0.03917834162712097, 0.010379336774349213, -0.03965345025062561, 0.012553880922496319, -0.04433146119117737, 0.013695972971618176, -0.02945685014128685, 0.006948490627110004, -0.00010021861817222089, -0.02339005470275879, 0.0008582824957557023, -0.054345328360795975, -0.0547838918864727, 0.025984888896346092, 0.012736615724861622, -0.023901712149381638, -0.043563976883888245, -0.0151578513905406, 0.0033646044321358204, -0.005518591031432152, -0.013714246451854706, -0.0036661168560385704, 0.02039320394396782, -0.0067611876875162125, 0.04948458448052406, 0.01280057244002819, -0.005952585954219103, 0.05003278702497482, 0.03645559400320053, -0.027446767315268517, 0.02094140835106373, 0.06399372965097427, -0.013586332090198994, 0.023134225979447365, 0.0010016150772571564, -0.012215821072459221, -0.03914179280400276, 0.04257720708847046, -0.05449151620268822, -0.016976062208414078, 0.013010717928409576, -0.006688093766570091, 0.003908240702003241, -0.03830121457576752, 0.012316325679421425, -0.027684321627020836, 0.01219754759222269, 0.018821684643626213, 0.017560813575983047, -0.00030636630253866315, 0.025930067524313927, 0.0170491561293602, 0.02311595156788826, 0.022385012358427048, 0.023919984698295593, -0.045866433531045914, 0.006121615879237652, -0.008593103848397732, -0.007848459295928478, 0.027647774666547775, -0.01219754759222269, 0.014271588064730167, 0.006080500315874815, 0.0396169051527977, 0.04023820161819458, 0.009017962031066418, 0.018931325525045395, 0.02366415597498417, -0.03139383718371391, -0.020137375220656395, -0.03895905986428261, 0.0016468974063172936, -0.017131388187408447, -0.023554515093564987, -0.02183680795133114, -0.017953693866729736, 0.015614688396453857, -0.011192506179213524, 0.059863921254873276, 0.008917458355426788, 0.03283744305372238, -0.04279648885130882, 0.008839796297252178, -0.054966628551483154, 0.008296160027384758, -0.008784975856542587, -0.025930067524313927, 0.010562071576714516, 0.024778839200735092, 0.005313014145940542, -0.00260168663226068, 0.005582548212260008, -0.002594834193587303, -0.016327355057001114, -0.010105234570801258, -0.018465351313352585, -0.02817770652472973, -0.0558072067797184, 0.023956531658768654, 0.01615375652909279, -0.03289226442575455, -0.0014721571933478117, -0.003535918425768614, 0.005792693234980106, -0.02218400500714779, -0.003869409440085292, -0.02828734740614891, 0.00032635292154736817, 0.003567897016182542, -0.014545690268278122, -0.05533209815621376, 0.006587589625269175, 0.007711408659815788, -0.004988660104572773, 0.031138010323047638, -0.03665659949183464, 0.00918242335319519, 0.010726532898843288, 0.013668563216924667, -0.035633284598588943, 0.018154703080654144, -0.0037163689266890287, 0.049557678401470184, 0.019040966406464577, 0.022622568532824516, 0.039287980645895004, -0.0181729756295681, -0.06377444416284561, 0.03186894953250885, -0.00512571120634675, -0.028689363971352577, 0.030206061899662018, 0.003455971833318472, -0.010598618537187576, 0.03038879670202732, -0.04195591062307358, -0.03526781499385834, -0.00727741327136755, -0.05094646289944649, 0.004205184523016214, -0.0396169051527977, 0.038228120654821396, -0.06834281235933304 ]
An electrocardiogram (ECG) monitors the electrical activity generated by the heart and is used to detect fatal cardiovascular diseases (CVDs). Conventionally, to capture the precise electrical activity, clinical experts use multiple-lead ECGs (typically 12 leads). But in recent times, large-size deep learning models have been used to detect these diseases. However, such models require heavy compute resources like huge memory and long inference time. To alleviate these shortcomings, we propose a low-parameter model, named Low Resource Heart-Network (LRH-Net), which uses fewer leads to detect ECG anomalies in a resource-constrained environment. A multi-level knowledge distillation process is used on top of that to get better generalization performance on our proposed model. The multi-level knowledge distillation process distills the knowledge to LRH-Net trained on a reduced number of leads from higher parameter (teacher) models trained on multiple leads to reduce the performance gap. The proposed model is evaluated on the PhysioNet-2020 challenge dataset with constrained input. The parameters of the LRH-Net are 106x less than our teacher model for detecting CVDs. The performance of the LRH-Net was scaled up to 3.2% and the inference time scaled down by 75% compared to the teacher model. In contrast to the compute- and parameter-intensive deep learning techniques, the proposed methodology uses a subset of ECG leads using the low resource LRH-Net, making it eminently suitable for deployment on edge devices.
[ 0.03231683000922203, 0.04537596181035042, -0.014353006146848202, -0.0030767188873142004, -0.011775282211601734, -0.014122314751148224, 0.025696996599435806, 0.03095274418592453, -0.0027682946529239416, 0.02651946060359478, -0.004704094957560301, -0.051474232226610184, 0.010340984910726547, -0.006930766627192497, 0.041564542800188065, 0.020842451602220535, -0.03486446663737297, -0.05275807902216911, 0.029468296095728874, -0.025014953687787056, 0.014272766187787056, -0.02549639530479908, 0.006825451273471117, -0.024854471907019615, 0.04930774122476578, 0.04457355663180351, 0.05079219117760658, -0.007958847098052502, -0.055807217955589294, 0.03464380279183388, 0.06976905465126038, 0.014553607441484928, -0.04533584043383598, -0.030150340870022774, -0.016599738970398903, -0.0511532723903656, 0.04661968722939491, 0.0463789664208889, -0.020160406827926636, 0.01840514875948429, -0.007467374671250582, -0.03434290364384651, -0.019498424604535103, -0.015045080333948135, 0.043530430644750595, -0.03596777096390724, -0.024272728711366653, -0.02200593613088131, 0.025516455993056297, 0.007908697240054607, -0.012216605246067047, -0.012005973607301712, 0.013831443153321743, 0.02166491560637951, -0.013721113093197346, 0.020521489903330803, 0.062025848776102066, 0.06499474495649338, 0.09428250044584274, 0.039598651230335236, 0.007352028973400593, 0.03843516483902931, -0.04722148925065994, 0.006188543047755957, -0.013380090706050396, -0.04682029038667679, -0.0001202822822961025, 0.07358047366142273, 0.010471375659108162, 0.008706086315214634, -0.06503486633300781, -0.03947829082608223, -0.007146412972360849, 0.06030068174004555, -0.016830429434776306, -0.01612832583487034, -0.012698047794401646, 0.04248730465769768, 0.004681527614593506, 0.03139406815171242, 0.0504712276160717, 0.050872430205345154, 0.0030065085738897324, 0.019809355959296227, 0.05484433099627495, -0.000981691526249051, 0.006048121955245733, -0.08473388850688934, -0.03803396224975586, -0.006900676526129246, -0.03548632934689522, 0.04268790781497955, -0.03668993338942528, 0.04613824561238289, -0.0038465254474431276, -0.03394170105457306, -0.0030165384523570538, -0.0165395587682724, -0.04782329499721527, -0.050350867211818695, 0.00967900175601244, 0.011544591747224331, -0.022748161107301712, 0.016148386523127556, 0.05283832177519798, -0.0579737089574337, -0.03658963367342949, 0.04188550263643265, -0.0005431900499388576, 0.13769257068634033, -0.02738204598426819, 0.0017502442933619022, -0.018966831266880035, -0.041323818266391754, -0.05440301075577736, -0.030029980465769768, -0.024252668023109436, -0.019418183714151382, 0.007407194469124079, -0.010892638005316257, -0.0002045190631179139, 0.017863525077700615, 0.0076178256422281265, 0.055726975202560425, -0.046178366988897324, 0.04272802546620369, 0.002543872222304344, 0.025516455993056297, -0.016479376703500748, 0.05761262774467468, 0.0003388277254998684, 0.001722661661915481, 0.02164485491812229, -0.050511348992586136, 0.035245608538389206, 0.024172428995370865, -0.008686026558279991, 0.012808377854526043, 0.02720150537788868, -0.04272802546620369, 0.0027783247642219067, 0.0051078046672046185, -0.028344931080937386, -0.04068189486861229, 0.022206537425518036, -0.010792337357997894, -0.00006433339149225503, 0.05063170939683914, -0.018806349486112595, -0.01832490786910057, -0.08084222674369812, 0.07117325812578201, 0.018826410174369812, 0.027582647278904915, 0.060701884329319, -0.02011025696992874, -0.020060107111930847, 0.0023470325395464897, -0.04826461523771286, -0.05279820039868355, 0.041063036769628525, 0.048144254833459854, 0.01586754433810711, -0.01970905438065529, 0.023129303008317947, 0.04014027491211891, 0.0020611758809536695, -0.02310924232006073, -0.08345004171133041, 0.04304898902773857, -0.014553607441484928, 0.0021063112653791904, 0.013741172850131989, 0.027682946994900703, -0.03189557045698166, 0.03291863575577736, 0.05364072695374489, -0.007477404549717903, -0.04060165584087372, -0.029969800263643265, -0.04457355663180351, -0.009006988257169724, 0.014122314751148224, -0.014172465540468693, 0.03051142208278179, 0.017973855137825012, 0.06150428578257561, 0.029568597674369812, 0.017241662368178368, 0.046178366988897324, -0.020080165937542915, 0.004551136866211891, 0.061424046754837036, -0.05993960052728653, -0.01959872432053089, -0.05480420961976051, 0.021002931520342827, -0.0023871527519077063, 0.02234695851802826, 0.012768258340656757, -0.020090196281671524, -0.02533591538667679, -0.0017552593490108848, 0.009363055229187012, 0.02198587730526924, -0.005185537505894899, 0.07727152854204178, 0.016098234802484512, 0.0491071417927742, -0.017010970041155815, -0.05083230882883072, 0.024312850087881088, -0.038495343178510666, -0.01487456914037466, -0.011073178611695766, 0.010004978626966476, 0.024152368307113647, -0.029729077592492104, 0.06086236238479614, 0.05616829916834831, 0.05159459263086319, -0.010391135700047016, 0.044814277440309525, -0.03941810876131058, -0.053600605577230453, 0.02667994238436222, 0.0042677875608205795, 0.01943824253976345, 0.030912624672055244, -0.03628873452544212, 0.009177498519420624, -0.011153419502079487, 0.02625867910683155, 0.03707107529044151, -0.02056160941720009, -0.017883585765957832, 0.022868521511554718, -0.012718107551336288, -0.020421188324689865, -0.04529571905732155, -0.02591765858232975, 0.0055817244574427605, -0.01637907698750496, 0.012367055751383305, 0.022226598113775253, -0.07462359964847565, -0.000556981423869729, 0.08842495083808899, 0.025717057287693024, 0.01019053440541029, -0.0810428336262703, -0.061424046754837036, 0.06375101953744888, -0.0021689990535378456, -0.07426251471042633, -0.03468392416834831, 0.008214613422751427, -0.05616829916834831, 0.04268790781497955, 0.0072868335992097855, 0.032276712357997894, -0.048304736614227295, -0.09797356277704239, 0.027662886306643486, -0.0010393642587587237, -0.008194553665816784, 0.06166476756334305, 0.025255674496293068, 0.0525173582136631, -0.03504500538110733, 0.008164463564753532, -0.03520548716187477, -0.01611829549074173, -0.03763275966048241, -0.018876560032367706, -0.06286837160587311, -0.008154433220624924, -0.039097148925065994, 0.011293839663267136, 0.025175433605909348, -0.011965853162109852, -0.013159429654479027, 0.02846529148519039, 0.015035049989819527, -0.00445334380492568, -0.05825455114245415, -0.030170399695634842, -0.005215627606958151, -0.04537596181035042, -0.008119327947497368, 0.017973855137825012, -0.050431109964847565, -0.02302900329232216, -0.021705035120248795, 0.013209580443799496, -0.011554621160030365, -0.06226656958460808, -0.015285801142454147, -0.01749241352081299, -0.003505503525957465, -0.06351029872894287, -0.04461367800831795, 0.023430204018950462, 0.04730173200368881, -0.012186515145003796, -0.05516529455780983, 0.008821431547403336, 0.04529571905732155, -0.029147334396839142, 0.013580692000687122, 0.0030340910889208317, -0.028284750878810883, 0.026760181412100792, -0.05576709657907486, -0.01840514875948429, -0.03701089695096016, -0.0029162380378693342, -0.009157438762485981, 0.034563563764095306, 0.016679977998137474, 0.037211496382951736, -0.007948817685246468, -0.09853524714708328, 0.04738197103142738, 0.012326935306191444, -0.04866581782698631, 0.06334981322288513, -0.0011522023705765605, -0.04674004763364792, -0.03919744864106178, -0.024192487820982933, 0.013951804488897324, -0.052477240562438965, 0.014704057946801186, -0.005055146757513285, -0.002373361261561513, -0.012728137895464897, -0.018966831266880035, 0.02397182770073414, 0.02575717680156231, -0.0107421875, -0.03656957298517227, -0.07045109570026398, -0.03297881409525871, 0.006524549797177315, 0.018365027382969856, -0.06198573112487793, 0.045496322214603424, -0.016750188544392586, -0.017091210931539536, 0.0010487674735486507, 0.03608813136816025, 0.01202603429555893, 0.026760181412100792, -0.006128362379968166, 0.006690045353025198, -0.029107214882969856, 0.006755240727216005, -0.031674906611442566, -0.019719084724783897, -0.0061484226025640965, -0.03085244446992874, -0.014001954346895218, 0.0368303544819355, -0.06503486633300781, -0.010200563818216324, 0.030130280181765556, -0.012728137895464897, 0.0014794329181313515, 0.04180526360869408, -0.016649888828396797, 0.03000991977751255, -0.02224665880203247, 0.009317919611930847, 0.018876560032367706, -0.01834496669471264, -0.002861072774976492, -0.003994468599557877, -0.0344432033598423, 0.029789257794618607, -0.022467318922281265, 0.02643921971321106, -0.02686048299074173, -0.0012336965883150697, 0.03981931135058403, 0.042166344821453094, 0.0005949075566604733, -0.08361052721738815, -0.001138410996645689, 0.0443328358232975, -0.01747235283255577, -0.06824447959661484, 0.012818408198654652, -0.06098272278904915, 0.032958753407001495, 0.007998967543244362, 0.025275735184550285, 0.02300894260406494, 0.04312922805547714, -0.0538814477622509, -0.05235688015818596, 0.04312922805547714, 0.0024360492825508118, 0.017713073641061783, -0.03538602963089943, -0.020862510427832603, -0.02694072388112545, 0.002861072774976492, 0.03699083626270294, -0.048224497586488724, 0.02880631387233734, -0.0007798366714268923, 0.001905710087157786, -0.05841502919793129, 0.0199497751891613, 0.025355974212288857, -0.02667994238436222, -0.053079042583703995, -0.025295794010162354, -0.01539613213390112, -0.07253734767436981, 0.033640798181295395, 0.05484433099627495, 0.011695042252540588, -0.016900639981031418, -0.0025150359142571688, 0.0416046604514122, -0.026820363476872444, 0.013139369897544384, 0.013370061293244362, -0.017081180587410927, 0.010501465760171413, 0.009282814338803291, -0.01066194660961628, -0.0028986854013055563, 0.0009346755687147379, 0.03388151898980141, 0.03685041517019272, -0.07847514003515244, 0.045135241001844406, -0.005255748052150011, -0.02047133818268776, -0.012587716802954674, -0.01402201410382986, -0.020822390913963318, -0.008114312775433064, 0.011083208955824375, 0.06724147498607635, 0.0012324427952989936, -0.05428265035152435, -0.057010821998119354, 0.016920700669288635, -0.03767288103699684, 0.018395118415355682, -0.01637907698750496, 0.007642900571227074, 0.004159964621067047, -0.053600605577230453, -0.005666980054229498, -0.03317941725254059, 0.008294854313135147, 0.09067168086767197, 0.02318948321044445, -0.015295831486582756, 0.0067953611724078655, 0.04136393964290619, -0.05532577261328697, -0.05644914135336876, 0.006840496324002743, 0.04445319622755051, -0.008635875768959522, -0.004400685895234346, 0.00026610985514707863, -0.0024059589486569166, 0.0015157917514443398, 0.009899662807583809, -0.020922690629959106, -0.03145424649119377, -0.016479376703500748, -0.0009998709429055452, 0.03797378018498421, 0.04517535865306854, 0.0058324760757386684, 0.03554650768637657, 0.01601799577474594, -0.009247709065675735, 0.014744178391993046, 0.03526566922664642, -0.00522565795108676, -0.037652820348739624, -0.008510500192642212, 0.008154433220624924, -0.031333886086940765, -0.040039971470832825, 0.0035456237383186817, -0.03544620797038078, -0.020320888608694077, -0.0038364953361451626, -0.007552630268037319, 0.029989859089255333, 0.038234561681747437, -0.030912624672055244, -0.009348009712994099, 0.014423216693103313, -0.04288850724697113, 0.018354997038841248, 0.0035456237383186817, 0.019137341529130936, 0.0070912474766373634, 0.023470325395464897, 0.06659955531358719, 0.0368303544819355, -0.02062178961932659, -0.032958753407001495, 0.0011102015851065516, 0.012898648157715797, -0.020521489903330803, 0.011604771949350834, 0.005175507627427578, 0.05949827656149864, 0.007101277820765972, 0.05516529455780983, -0.025014953687787056, 0.001905710087157786, -0.062106091529130936, 0.014262735843658447, -0.013660932891070843, 0.00273820455186069, 0.030651843175292015, -0.006860556546598673, 0.025696996599435806, 0.012818408198654652, -0.02174515649676323, -0.0026078138034790754, -0.0586557537317276, -0.015265741385519505, -0.024954773485660553, 0.046860408037900925, -0.0018442760920152068, -0.02028076723217964, -0.034503381699323654, 0.07265770435333252, 0.03757258132100105, 0.0035957740619778633, 0.0034403083845973015, 0.020762210711836815, 0.016920700669288635, -0.042086102068424225, -0.01953854411840439, 0.03225665166974068, 0.0022993898019194603, -0.024714050814509392, 0.01679030992090702, -0.0012330696918070316, -0.03037100099027157, -0.03213629126548767, 0.02838505059480667, -0.022728100419044495, -0.030972804874181747, -0.010712097398936749, 0.01902701146900654, 0.003999483771622181, 0.004395670723170042, -0.018284786492586136, -0.04669992998242378, -0.03309917449951172, -0.0022404631599783897, 0.03787348046898842, -0.014694028533995152, 0.009197559207677841, 0.019749175757169724, -0.06563667207956314, -0.03725161775946617, -0.013801353052258492, 0.004927263595163822, 0.01774316467344761, 0.03420248255133629, -0.026479341089725494, 0.02216641791164875, 0.033801279962062836, -0.0016913177678361535, 0.03368091955780983, 0.005396168678998947, -0.008500469848513603, -0.03301893547177315, -0.029026973992586136, 0.004516031593084335, -0.03424260392785072, 0.009759241715073586, 0.01308922003954649, 0.0138113833963871, 0.044051993638277054, -0.029107214882969856, 0.004242712631821632, -0.009257739409804344, -0.01603805460035801, 0.026579640805721283, -0.0027331896126270294, 0.015125320293009281, -0.05897671356797218, -0.03404200077056885, 0.06018032133579254, 0.04328970983624458, 0.05721142515540123, -0.006333978846669197, -0.028625771403312683, 0.02166491560637951, 0.02641916088759899, -0.011815402656793594, 0.016910670325160027, 0.016499437391757965, 0.00006691925955237821, -0.018124306574463844, 0.010812397114932537, 0.040722016245126724, 0.0009917215211316943, 0.020681969821453094, 0.002843520138412714, 0.004490956198424101, -0.022186478599905968, 0.04268790781497955, -0.0024159890599548817, 0.045656803995370865, 0.007768276147544384, 0.020531518384814262, -0.008510500192642212, -0.03121352568268776, -0.012186515145003796, -0.0010280804708600044, -0.048906538635492325, 0.009017017669975758, -0.001466895337216556, -0.036108192056417465, -0.022788280621170998, 0.011855523101985455, 0.004596272017806768, -0.08176499605178833, 0.03600789234042168, -0.007241698447614908, 0.024152368307113647, -0.021384073421359062, 0.029026973992586136, -0.03685041517019272, 0.01763283461332321, 0.0007585227722302079, -0.01749241352081299, 0.010772277601063251, 0.04016033187508583, 0.05219639837741852, 0.003372605424374342, 0.032537493854761124, 0.05099279060959816, 0.022025996819138527, 0.03291863575577736, 0.0050902520306408405, -0.02908715419471264, 0.007622840348631144, 0.01969902403652668, -0.03043118119239807, -0.02539609558880329, -0.015225620940327644, 0.006940796971321106, 0.048986781388521194, -0.049588583409786224, 0.005190552677959204, -0.008686026558279991, 0.03793366253376007, 0.015576672740280628, -0.01014038361608982, 0.018204547464847565, -0.038675885647535324, -0.06094260513782501, -0.03271803259849548, -0.007597765419632196, 0.009192544035613537, 0.006213617976754904, 0.030130280181765556, 0.022547559812664986, -0.01696082018315792, -0.0026529491879045963, -0.04782329499721527, -0.0398995503783226, 0.029347935691475868, 0.017281781882047653, -0.011384110897779465, -0.013861533254384995, 0.025215554982423782, 0.010832457803189754, -0.029789257794618607, -0.039357930421829224, -0.007878607138991356, -0.015586703084409237, 0.006559655070304871, -0.026238620281219482, 0.027843428775668144, -0.013711082749068737, -0.030651843175292015, 0.028264690190553665, 0.012577686458826065, -0.013249700888991356, -0.06302885711193085, 0.0197792649269104, -0.009754226543009281, 0.015576672740280628, -0.011223630048334599, 0.056489259004592896, 0.010411195456981659, 0.0018680974608287215, -0.025937717407941818, -0.013209580443799496, 0.008485425263643265, 0.017412172630429268, -0.004172502085566521, 0.010752216912806034, 0.04457355663180351, -0.006835481151938438, -0.040782198309898376, 0.01198591385036707, -0.031093165278434753, 0.05596769601106644, -0.00626878347247839, 0.01402201410382986, -0.006083227228373289, -0.05123351141810417, -0.023249663412570953, 0.053079042583703995, 0.04577716439962387, -0.0010725888423621655, 0.0005068311584182084, 0.018284786492586136, 0.04798377677798271, 0.0235305055975914, -0.02778324857354164, 0.0098896324634552, 0.031494367867708206, -0.0020624296739697456, 0.032015930861234665, 0.015105260536074638, 0.032958753407001495, 0.03291863575577736, -0.031855449080467224, -0.004363073036074638, 0.00545634888112545, -0.016158415004611015, 0.0075425999239087105, 0.02974913828074932, -0.0185856893658638, 0.045054998248815536, -0.03199587017297745, -0.022567620500922203, 0.017863525077700615, -0.017753195017576218, 0.020340947434306145, -0.013500452041625977, -0.047702934592962265, 0.053199402987957, 0.024433210492134094, -0.005491454154253006, -0.013741172850131989, 0.011705072596669197, -0.014904659241437912, 0.04060165584087372, -0.06334981322288513, 0.0036935671232640743, 0.03622855246067047, 0.06419233977794647, -0.03777318075299263, 0.011364050209522247, 0.027602706104516983, -0.004789350554347038, 0.010641886852681637, 0.05263771861791611, 0.07181518524885178, -0.060501281172037125, 0.00984951201826334, 0.01808418706059456, 0.0024134814739227295, -0.007492450065910816, 0.02641916088759899, -0.014714088290929794, -0.02780330739915371, -0.0018530524102970958, 0.009257739409804344, 0.015907663851976395, -0.015967844054102898, -0.00300400098785758, -0.009433264844119549, -0.0378534197807312, -0.03259767219424248, 0.02020052820444107, 0.01766292378306389, 0.0005328466068021953, 0.039016906172037125, 0.019989896565675735, 0.024693991988897324, -0.01893674023449421, -0.012858528643846512, 0.02355056442320347, -0.0635504201054573, -0.02190563641488552, 0.04048129543662071, -0.028284750878810883, 0.0025463798083364964, -0.006198572926223278, -0.01748238317668438, -0.003816435346379876, -0.010371075011789799, -0.04100285843014717, -0.017181482166051865, -0.0484250970184803, 0.031073104590177536, 0.01910725235939026, 0.005175507627427578, -0.00024746020790189505, 0.017462322488427162, -0.027843428775668144, -0.039337869733572006, -0.01015041396021843, -0.0463789664208889, -0.048826299607753754, 0.011023028753697872, -0.021885575726628304, 0.000627191795501858, -0.01356063224375248, -0.005857551004737616, -0.02056160941720009, 0.04850533604621887, 0.006775300949811935, 0.01670003868639469, 0.004255250096321106, -0.01731187291443348, 0.028505410999059677, -0.007477404549717903, 0.0029613731894642115, -0.032015930861234665, 0.043530430644750595, -0.0015045079635456204, 0.01867595873773098, 0.0013565646950155497, 0.035085126757621765, -0.006043107248842716, -0.01857565902173519, -0.007347014266997576, 0.010280804708600044, -0.022788280621170998, -0.0024962294846773148, -0.010491435416042805, -0.006048121955245733, -0.013691022992134094, -0.009162453934550285, 0.031715027987957, -0.024874532595276833, -0.024433210492134094, -0.023129303008317947, -0.0025564099196344614, -0.004132382106035948, 0.038575585931539536, -0.015817394480109215, -0.024573631584644318, -0.00674019567668438, -0.0074222395196557045, -0.021484375, -0.0010431255213916302, 0.028204509988427162, 0.019989896565675735, -0.0017339454498142004, 0.009709091857075691, 0.011384110897779465, 0.00839515496045351, -0.03586747124791145, -0.0334201380610466, 0.009839482605457306, 0.009488430805504322, 0.015997935086488724, -0.010290835052728653, -0.024874532595276833, -0.029729077592492104, 0.008114312775433064, 0.028786253184080124, 0.004704094957560301, 0.052998803555965424, 0.043610673397779465, 0.025436215102672577, -0.005566679406911135, 0.06334981322288513, 0.03181532770395279, -0.014603757299482822, -0.020942751318216324, -0.0002842893300112337, -0.020942751318216324, -0.0014167450135573745, 0.001157844322733581, 0.058615632355213165, -0.0019370540976524353, 0.005692055448889732, -0.00007890831329859793, -0.014784298837184906, 0.011113299056887627, -0.016419196501374245, 0.010822427459061146, 0.02403200790286064, -0.03733185678720474, -0.04176514223217964, -0.06363065540790558, 0.012698047794401646, 0.012076184153556824, 0.011444291099905968, -0.014944779686629772, 0.005797370802611113, -0.005742205306887627, -0.02984943799674511, -0.0076178256422281265, -0.009137379005551338, -0.01857565902173519, 0.07165469974279404, 0.021043051034212112, 0.039277687668800354, -0.02565687708556652, 0.03915732726454735, -0.015646882355213165, -0.019317882135510445, 0.04790353402495384, -0.04665980860590935, 0.015406161546707153, -0.03763275966048241, -0.0094633549451828, 0.0037938677705824375, -0.011945793405175209, -0.030210521072149277, 0.029608717188239098, -0.007592750247567892, 0.023309843614697456, 0.029688958078622818, 0.00945834070444107, 0.0710529014468193, 0.022286778315901756, 0.008635875768959522, -0.015225620940327644, -0.054603610187768936, 0.010521525517106056, -0.013450301252305508, 0.03544620797038078, -0.02822457067668438, 0.024854471907019615, 0.01825469732284546, -0.05608805641531944, 0.04794365540146828, -0.011384110897779465, 0.03843516483902931, -0.005807400681078434, -0.006409204099327326, -0.012146394699811935, -0.011534561403095722, 0.028706012293696404, 0.04268790781497955, 0.011143389157950878, -0.0058324760757386684, -0.04268790781497955, 0.010902668349444866, 0.03225665166974068, 0.004400685895234346, -0.004784335382282734, -0.01823463663458824, -0.000022606800484936684, -0.0053259581327438354, 0.026579640805721283, -0.003823957871645689, -0.06700075417757034, -0.016409168019890785, -0.006449324078857899, 0.007898666895925999, -0.021043051034212112, -0.0146639384329319, 0.007472389843314886, 0.0056569501757621765, 0.03464380279183388, 0.004516031593084335, -0.010501465760171413, -0.024192487820982933, 0.004485941492021084, 0.03925762698054314, 0.006950826849788427, 0.004611317068338394, -0.022788280621170998, 0.02164485491812229, -0.030050039291381836, -0.024573631584644318, -0.00031281227711588144, -0.05681022256612778, 0.02192569710314274, -0.000732193875592202, 0.041484300047159195, 0.048826299607753754, -0.02796378917992115, -0.02029079757630825, 0.002400944009423256, -0.04066183790564537, -0.034583624452352524, 0.009839482605457306, -0.006118332501500845, -0.017943765968084335, 0.014092224650084972, 0.032096169888973236, 0.030591662973165512, -0.05055147036910057, 0.022708041593432426, 0.0265997014939785, -0.015496432781219482, -0.016770249232649803, 0.017612773925065994, 0.031494367867708206, -0.04998978599905968, -0.02310924232006073, 0.002209119265899062, -0.01704106107354164, 0.01765289343893528, -0.008224643766880035, 0.01440315693616867, -0.00810428336262703, -0.017612773925065994, 0.00432796822860837, -0.009744197130203247, -0.01908719167113304, 0.01389162428677082 ]
Given entities and their interactions in the web data, which may have occurred at different time, how can we find communities of entities and track their evolution? In this paper, we approach this important task from graph clustering perspective. Recently, state-of-the-art clustering performance in various domains has been achieved by deep clustering methods. Especially, deep graph clustering (DGC) methods have successfully extended deep clustering to graph-structured data by learning node representations and cluster assignments in a joint optimization framework. Despite some differences in modeling choices (e.g., encoder architectures), existing DGC methods are mainly based on autoencoders and use the same clustering objective with relatively minor adaptations. Also, while many real-world graphs are dynamic, previous DGC methods considered only static graphs. In this work, we develop CGC, a novel end-to-end framework for graph clustering, which fundamentally differs from existing methods. CGC learns node embeddings and cluster assignments in a contrastive graph learning framework, where positive and negative samples are carefully selected in a multi-level scheme such that they reflect hierarchical community structures and network homophily. Also, we extend CGC for time-evolving data, where temporal graph clustering is performed in an incremental learning fashion, with the ability to detect change points. Extensive evaluation on real-world graphs demonstrates that the proposed CGC consistently outperforms existing methods.
[ -0.01367020420730114, -0.045706238597631454, -0.03525726497173309, 0.008541874587535858, 0.03503290191292763, 0.028317995369434357, -0.04048175364732742, 0.017131825909018517, -0.05561032518744469, 0.013710268773138523, 0.02509676292538643, 0.004843867849558592, 0.0030609718523919582, -0.05371925234794617, -0.0076283905655145645, 0.031090497970581055, 0.00827744510024786, 0.0008879422675818205, 0.0015815688529983163, -0.01639462821185589, 0.009094771929085255, -0.07121967524290085, 0.00636233389377594, 0.010032295249402523, 0.08128402382135391, 0.009086758829653263, 0.07686083763837814, -0.0033955152612179518, -0.058142438530921936, 0.07006580382585526, 0.02852633409202099, 0.01402277685701847, 0.03952018916606903, -0.0245999563485384, -0.06288614124059677, 0.008121190592646599, 0.06993759423494339, 0.03272515535354614, 0.042725395411252975, 0.0056171235628426075, 0.005597091279923916, 0.044071584939956665, -0.01958380825817585, -0.004551392514258623, 0.017756842076778412, -0.0009275064803659916, -0.020304979756474495, -0.03359055891633034, 0.012900954112410545, 0.011250273324549198, 0.005384746007621288, -0.023526212200522423, 0.01818954385817051, -0.025112789124250412, -0.03791758790612221, 0.017676711082458496, 0.03980866074562073, -0.03852657601237297, 0.027628876268863678, 0.05163586884737015, 0.011538742110133171, 0.016234368085861206, -0.0582706443965435, 0.003072991268709302, 0.03573804721236229, -0.010865648277103901, -0.016490785405039787, -0.012876915745437145, 0.03046548366546631, -0.03091421164572239, -0.05352694168686867, -0.01113809086382389, -0.01993638090789318, -0.015296845696866512, 0.058430906385183334, -0.014775999821722507, 0.05371925234794617, 0.003441590117290616, 0.013293592259287834, -0.05205254629254341, 0.03285336121916771, 0.012860889546573162, -0.03349440172314644, 0.016811305657029152, 0.0929509773850441, -0.058238595724105835, 0.04419979080557823, -0.05439234524965286, 0.013085253536701202, 0.009831969626247883, 0.0034315737430006266, -0.02634679339826107, 0.026026273146271706, -0.07186072319746017, 0.0003861271543428302, -0.001160885556600988, 0.03599446266889572, 0.007888813503086567, -0.05945657193660736, 0.02594614215195179, -0.05032173544168472, -0.029744312167167664, 0.05025763064622879, -0.002514083404093981, -0.005004127975553274, -0.03580215200781822, -0.01367020420730114, 0.0631425604224205, -0.02854236029088497, 0.12884928286075592, 0.0012049571378156543, 0.06506568193435669, -0.01616225205361843, 0.03637908771634102, -0.03509700670838356, -0.01091372687369585, -0.058623217046260834, -0.015192676335573196, 0.04323823004961014, -0.07301459461450577, 0.012804797850549221, 0.004940023645758629, -0.010392880998551846, -0.018526090309023857, -0.05323847383260727, 0.031843721866607666, -0.02908724546432495, 0.004282956477254629, -0.060129664838314056, 0.02192360907793045, -0.06686060130596161, -0.0028426172211766243, -0.003417551051825285, 0.010889687575399876, 0.08083529770374298, 0.016827331855893135, 0.07955321669578552, -0.009150863625109196, -0.013686229474842548, 0.019567782059311867, -0.0018620244227349758, -0.004427190870046616, 0.004647548776119947, -0.028943011537194252, 0.018750455230474472, 0.0317155122756958, -0.00009759602107806131, 0.07128378003835678, -0.005749338306486607, 0.011362455785274506, -0.0389753058552742, 0.028959035873413086, 0.0197280440479517, -0.007367967627942562, -0.0026523079723119736, 0.007400019560009241, -0.0017899072263389826, -0.07897627353668213, -0.040577907115221024, -0.0783352330327034, 0.09000218659639359, -0.020353058353066444, 0.01396668516099453, 0.03769322484731674, -0.04301386699080467, 0.00994415208697319, 0.03618677705526352, -0.057982176542282104, -0.04150741919875145, 0.040193285793066025, 0.03474443405866623, 0.0073319086804986, -0.017260035499930382, 0.026282690465450287, -0.009078745730221272, 0.04663574695587158, 0.030641769990324974, -0.03403928875923157, -0.005216472782194614, 0.050738412886857986, -0.009679722599685192, -0.02937571331858635, 0.040289439260959625, 0.032628998160362244, 0.033975183963775635, 0.04602675884962082, 0.039295826107263565, 0.01396668516099453, 0.024567903950810432, -0.008389626629650593, 0.03242065757513046, 0.038398370146751404, 0.11275915056467056, -0.029616104438900948, -0.004956049844622612, -0.0532064214348793, -0.017820945009589195, 0.003886312246322632, -0.03666755557060242, 0.012732680886983871, -0.0032993589993566275, -0.05496928468346596, 0.03278925642371178, 0.014030789956450462, 0.08154044300317764, -0.015985965728759766, 0.025433309376239777, -0.03891120105981827, -0.015192676335573196, -0.040834326297044754, -0.02043318934738636, -0.015489158220589161, -0.05115509033203125, 0.008461743593215942, 0.005869533400982618, -0.021458854898810387, 0.028350047767162323, 0.0068751671351492405, 0.003171150805428624, -0.03669960796833038, 0.015505184419453144, 0.00996819045394659, 0.08634825050830841, 0.018429934978485107, -0.03027317114174366, -0.025737805292010307, 0.02177937515079975, -0.02897506207227707, -0.033686716109514236, 0.015120559372007847, -0.009126824326813221, 0.022147973999381065, -0.007896826602518559, -0.020417163148522377, -0.02251657284796238, -0.049039654433727264, 0.006166015285998583, 0.006827089004218578, 0.011963431723415852, 0.017211956903338432, -0.016843358054757118, -0.005004127975553274, -0.09128426760435104, -0.022228103131055832, 0.0775659829378128, 0.003123072674497962, -0.005224485881626606, 0.016779253259301186, 0.0034676322247833014, 0.020000485703349113, 0.007708520628511906, -0.015777627006173134, 0.00986402202397585, -0.00872617308050394, 0.00026618235278874636, 0.04301386699080467, 0.01834980398416519, -0.024279436096549034, 0.021346671506762505, -0.09186120331287384, 0.04474467784166336, -0.008934511803090572, -0.05961683392524719, 0.050385840237140656, 0.009279071353375912, -0.002966818865388632, 0.038847096264362335, 0.022212078794836998, -0.006642789579927921, 0.032340530306100845, -0.011402520351111889, -0.031539227813482285, -0.06634776294231415, -0.039199668914079666, -0.019872277975082397, 0.00814923644065857, 0.03112255036830902, -0.04012918099761009, 0.012965058907866478, 0.0321001373231411, -0.005496928468346596, -0.02400699257850647, 0.016891436651349068, -0.008445718325674534, -0.05593084543943405, -0.005440837237983942, 0.00019055951270274818, -0.05019352585077286, -0.04195614904165268, -0.05096277594566345, -0.03272515535354614, -0.03096229024231434, 0.007095525041222572, -0.012933006510138512, -0.02365441992878914, -0.03702012822031975, -0.024824321269989014, -0.001968196826055646, 0.007243765518069267, -0.06961707770824432, -0.035866256803274155, 0.00607787212356925, 0.044263895601034164, 0.013045188970863819, -0.03836631774902344, 0.0006685859407298267, 0.03833426535129547, 0.015160624869167805, -0.003044945653527975, -0.08121991902589798, -0.02251657284796238, -0.032132189720869064, -0.02331787347793579, 0.013525969348847866, 0.020000485703349113, -0.027260277420282364, 0.06980938464403152, -0.016338538378477097, 0.026955783367156982, -0.07692494243383408, 0.03628293424844742, 0.013998737558722496, -0.08763033151626587, 0.002455989131703973, -0.01709977351129055, 0.03081805631518364, -0.00857392605394125, 0.029792390763759613, -0.04718063399195671, 0.0291834007948637, -0.05766165629029274, -0.01859019510447979, -0.007099531590938568, 0.028414152562618256, -0.004775756970047951, 0.017756842076778412, -0.022532599046826363, 0.064007967710495, -0.007536240853369236, 0.004030546639114618, -0.010352815501391888, -0.020449215546250343, -0.030946264043450356, 0.040289439260959625, 0.0393599309027195, -0.01750042475759983, -0.018029283732175827, -0.010104412212967873, 0.05577058717608452, 0.002429946791380644, 0.0007717535481788218, 0.036314982920885086, -0.0339110791683197, 0.00328132975846529, 0.05134740099310875, 0.0010356821585446596, 0.004080628044903278, -0.0021655173040926456, 0.037308599799871445, 0.04718063399195671, 0.023125560954213142, -0.06147585064172745, 0.018718402832746506, 0.028959035873413086, -0.06192458048462868, -0.013662191107869148, -0.02549741417169571, -0.005549013148993254, -0.04474467784166336, -0.008285457268357277, -0.05125124379992485, 0.027773110195994377, -0.03846247121691704, 0.008549886755645275, -0.0012209832202643156, 0.04051380604505539, 0.045257508754730225, -0.0032612972427159548, 0.0078327227383852, 0.03846247121691704, -0.031491149216890335, 0.02227618172764778, 0.0388791486620903, 0.01036884170025587, -0.0108416099101305, 0.03810989856719971, 0.022740937769412994, 0.022484520450234413, 0.0009585569496266544, 0.005020154174417257, 0.039648398756980896, -0.06387975811958313, -0.05413592979311943, 0.021795401349663734, 0.04006507620215416, 0.023446083068847656, 0.010673335753381252, 0.022580675780773163, 0.020513318479061127, 0.009311123751103878, -0.013686229474842548, 0.014727922156453133, 0.004431197419762611, -0.010064346715807915, -0.022292207926511765, -0.0064023989252746105, 0.027228225022554398, -0.013598086312413216, 0.015393001958727837, 0.019407521933317184, 0.0054328241385519505, 0.01245222520083189, -0.042981814593076706, 0.021795401349663734, -0.002694376278668642, 0.009094771929085255, -0.07827112823724747, 0.015425054356455803, 0.026731418445706367, 0.02525702305138111, -0.00039213692070916295, -0.014703882858157158, 0.0730786994099617, -0.024696113541722298, -0.007275817915797234, 0.050385840237140656, 0.029247505590319633, -0.020048564299941063, 0.008958551101386547, -0.014840103685855865, 0.042276669293642044, 0.03137896582484245, 0.0030569653026759624, -0.005889566149562597, -0.02251657284796238, -0.006482529453933239, 0.0022296214010566473, -0.025785882025957108, -0.023301847279071808, -0.015513197518885136, -0.0064544836059212685, -0.023446083068847656, -0.022292207926511765, -0.04166767746210098, -0.04644343629479408, -0.010224607773125172, -0.031731538474559784, -0.014327270910143852, -0.025192920118570328, -0.006226112600415945, -0.05673214793205261, 0.029551999643445015, -0.04311002045869827, -0.033622611314058304, 0.020657552406191826, -0.0019521708600223064, -0.0053687202744185925, -0.005484908819198608, 0.06141174957156181, -0.029055193066596985, 0.015384988859295845, 0.011378481052815914, -0.031250759959220886, -0.026426924392580986, -0.04115484654903412, 0.08192506432533264, 0.01513658557087183, -0.004687613807618618, -0.00911881122738123, -0.01292499341070652, 0.051026880741119385, -0.04000097140669823, 0.03637908771634102, 0.013758347369730473, -0.02092999592423439, 0.01918315887451172, -0.014431440271437168, -0.07628390192985535, 0.04577034339308739, -0.0005103289149701595, 0.023237744346261024, 0.03435980901122093, 0.0028726658783853054, 0.016290459781885147, -0.05269358679652214, 0.03753296285867691, 0.03275720775127411, -0.0010286708129569888, -0.052373066544532776, -0.015929874032735825, 0.014655804261565208, 0.07045043259859085, -0.027500668540596962, -0.026827573776245117, 0.03320593386888504, 0.013830464333295822, -0.008185295388102531, -0.034872643649578094, 0.08057887852191925, 0.00023150102060753852, 0.006057839374989271, -0.017885049805045128, -0.011041934601962566, -0.009415293112397194, -0.018205570057034492, -0.00018705382535699755, 0.015569288283586502, 0.017227983102202415, -0.024311488494277, -0.003068984718993306, -0.02580190822482109, 0.028718646615743637, -0.033077728003263474, -0.01576160080730915, 0.010424932464957237, 0.018510064110159874, 0.031154602766036987, -0.0028866888023912907, 0.0036399122327566147, 0.01814146712422371, 0.004218852613121271, -0.02703591249883175, -0.03266105055809021, 0.01600199192762375, -0.05871937423944473, 0.035962410271167755, 0.04586649686098099, 0.04811014235019684, 0.02043318934738636, -0.00480780890211463, 0.005869533400982618, 0.00312507594935596, -0.018413908779621124, -0.013726294972002506, 0.0023037418723106384, 0.0073198894970119, 0.02466406114399433, -0.005613117013126612, -0.01690746285021305, -0.030193040147423744, -0.0011869278969243169, 0.040834326297044754, -0.07378384470939636, 0.018926741555333138, -0.0033614598214626312, 0.004066605120897293, 0.02201976627111435, -0.007251778617501259, 0.002506070537492633, 0.0027925358153879642, 0.0053807394579052925, -0.007852754555642605, 0.024888424202799797, -0.010609231889247894, -0.015697496011853218, -0.007063472643494606, 0.017227983102202415, -0.0070915184915065765, 0.021859506145119667, -0.027853241190314293, -0.027067964896559715, 0.013165383599698544, 0.013918607495725155, -0.011570793576538563, -0.030994342640042305, -0.012316004373133183, 0.023670446127653122, 0.0539756715297699, 0.03580215200781822, 0.018526090309023857, -0.002097406657412648, -0.02833402156829834, -0.028766725212335587, -0.04240487515926361, -0.001566544407978654, -0.025112789124250412, 0.05295000225305557, 0.010232619941234589, -0.0036178764421492815, 0.015881795436143875, 0.0007752592209726572, 0.01823762245476246, 0.03666755557060242, 0.03554573655128479, 0.002199572743847966, -0.021699244156479836, -0.04304591566324234, -0.0012750710593536496, -0.008405652828514576, -0.022196052595973015, 0.008237379603087902, 0.04400748014450073, 0.00750418845564127, -0.002451982581987977, 0.03843041881918907, -0.013189422897994518, -0.04121895134449005, 0.006302236579358578, 0.034327756613492966, -0.05304615944623947, 0.036058567464351654, 0.006218099966645241, 0.0031951898708939552, -0.008397639729082584, -0.0052645509131252766, -0.05323847383260727, 0.04907170310616493, -0.05420003458857536, 0.028350047767162323, 0.0009465374168939888, -0.015352937392890453, 0.01830172725021839, 0.038943253457546234, -0.034616224467754364, -0.012965058907866478, 0.020801788195967674, 0.024680087342858315, 0.04493698850274086, -0.041090741753578186, -0.10788723826408386, 0.0837840884923935, -0.008565912954509258, 0.09045091271400452, 0.048046037554740906, 0.026475001126527786, 0.019471626728773117, 0.01584974303841591, -0.03660345450043678, -0.014960299246013165, -0.005981715861707926, -0.03107447363436222, 0.04487288370728493, -0.06654007732868195, -0.018478013575077057, -0.012243887409567833, -0.04032149165868759, -0.018766481429338455, 0.03525726497173309, 0.01665104553103447, 0.015184663236141205, -0.03197193145751953, -0.02658718451857567, -0.021635141223669052, 0.029055193066596985, -0.005296602845191956, 0.01839788258075714, 0.004290969576686621, 0.0036759707145392895, 0.01242818683385849, 0.029199426993727684, 0.022708885371685028, -0.0006570672267116606, 0.004298982676118612, 0.036571402102708817, -0.052180755883455276, -0.032292451709508896, 0.007191681303083897, -0.023830706253647804, -0.0024339533410966396, 0.020016511902213097, 0.02604229934513569, -0.049231965094804764, 0.00899861566722393, 0.0011568790068849921, 0.007520214654505253, -0.000010227549864794128, 0.0025180899538099766, -0.008405652828514576, 0.025577545166015625, 0.04791783168911934, -0.009655683301389217, 0.0003247775312047452, -0.01443945337086916, -0.014223101548850536, 0.011073986999690533, -0.011202194727957249, -0.004306995775550604, -0.014607726596295834, 0.020946022123098373, -0.0005443842383101583, -0.003667957615107298, -0.04125100374221802, -0.05801422894001007, -0.012243887409567833, -0.039295826107263565, -0.006226112600415945, -0.04378311336040497, -0.040642011910676956, -0.0009901082376018167, -0.0006390379858203232, -0.011025908403098583, -0.017388243228197098, -0.006482529453933239, -0.026555132120847702, 0.007732559461146593, 0.007840734906494617, -0.01679527945816517, 0.005589078180491924, 0.021186411380767822, 0.0011709018144756556, -0.008461743593215942, 0.005729306023567915, -0.0027164120692759752, 0.08519437909126282, -0.024471748620271683, 0.04359080269932747, -0.00044347031507641077, 0.03126678615808487, -0.03554573655128479, -0.009807930327951908, 0.0012199815828353167, 0.03112255036830902, -0.012836850248277187, 0.019551757723093033, 0.04926401749253273, -0.007944904267787933, -0.022196052595973015, -0.020801788195967674, -0.002175533678382635, 0.02296530082821846, -0.02972828596830368, 0.025673700496554375, 0.020962048321962357, -0.04077022150158882, -0.025112789124250412, 0.023446083068847656, -0.009928125888109207, 0.013830464333295822, -0.01674720086157322, 0.008742199279367924, 0.040577907115221024, -0.05054609850049019, -0.02121846377849579, 0.005737318657338619, 0.045257508754730225, 0.00528057711198926, -0.004218852613121271, 0.03852657601237297, 0.0086460430175066, -0.05461671203374863, 0.006017774343490601, -0.029295584186911583, -0.01794915460050106, 0.007940897718071938, 0.0194876529276371, 0.032244373112916946, 0.008950538001954556, 0.022532599046826363, -0.0048118154518306255, -0.017115799710154533, 0.02734040841460228, 0.007500182371586561, 0.0037621106021106243, -0.03724449500441551, -0.04737294465303421, 0.0016086128307506442, 0.025433309376239777, 0.006891192868351936, 0.007772624492645264, -0.0040766214951872826, 0.0009906089399009943, -0.004154748283326626, -0.01471189595758915, 0.053815409541130066, -0.03807784616947174, 0.006590704899281263, -0.025016633793711662, 0.004395138937979937, -0.0071436031721532345, -0.011033921502530575, 0.04246897995471954, -0.016122186556458473, 0.10057936608791351, -0.005609110463410616, 0.014150984585285187, 0.03282130882143974, 0.005949663929641247, 0.005813442636281252, -0.008317509666085243, -0.018862636759877205, -0.048590924590826035, -0.011875288560986519, 0.00290271476842463, 0.03394313156604767, -0.020321005955338478, 0.02698783576488495, -0.016026029363274574, -0.0391676165163517, -0.006326275411993265, 0.019119054079055786, -0.0343918614089489, -0.0489114448428154, 0.03056163899600506, 0.039295826107263565, 0.02554549276828766, 0.02048126608133316, -0.013734308071434498, 0.05176407843828201, -0.030994342640042305, -0.043622855097055435, 0.023542238399386406, -0.006811062805354595, 0.005424811039119959, -0.01083359681069851, -0.0042108395136892796, -0.042533084750175476, -0.007924871519207954, -0.014703882858157158, 0.007267804816365242, 0.026667313650250435, 0.026635263115167618, 0.042821552604436874, -0.007484156172722578, -0.020817812532186508, -0.009142850525677204, -0.014583687297999859, -0.03817400336265564, -0.05230896174907684, -0.015673456713557243, -0.05740524083375931, -0.008445718325674534, -0.06436053663492203, -0.007343928329646587, -0.01849403977394104, -0.054264139384031296, -0.014191050082445145, 0.019151106476783752, -0.014727922156453133, 0.02171527035534382, -0.012436199933290482, 0.0069593037478625774, 0.0385906808078289, -0.007271811366081238, 0.06208484247326851, -0.017179904505610466, 0.02937571331858635, 0.027003860101103783, -0.007408032659441233, 0.04663574695587158, 0.018558142706751823, 0.034520070999860764, 0.011699002236127853, -0.021603088825941086, -0.05448850244283676, -0.002209588885307312, 0.008950538001954556, -0.05420003458857536, -0.02218002639710903, 0.0338149257004261, -0.004879926331341267, 0.015184663236141205, 0.043751060962677, 0.017580555751919746, 0.005128329619765282, 0.00242393696680665, 0.004871913231909275, 0.013517956249415874, -0.0030910205096006393, 0.022548625245690346, -0.01873442903161049, 0.023702498525381088, 0.01401476375758648, -0.014679843559861183, 0.0389753058552742, 0.04169972985982895, -0.008822329342365265, 0.021202437579631805, -0.025978194549679756, 0.027676954865455627, -0.011009883135557175, 0.01601000502705574, 0.017756842076778412, -0.03823810815811157, 0.07820703089237213, 0.022356312721967697, 0.0010446968954056501, -0.00107775058131665, 0.01650681160390377, -0.035321369767189026, -0.04775756970047951, 0.022147973999381065, 0.009222980588674545, 0.0069392709992825985, -0.00927105825394392, 0.06904014199972153, -0.011162130162119865, 0.014183036983013153, -0.026827573776245117, -0.0344880186021328, -0.025481387972831726, -0.04214845970273018, 0.01863827370107174, -0.04945632815361023, -0.0027544740587472916, 0.0012740694219246507, -0.009255032055079937, 0.0015134582063183188, 0.03968045115470886, -0.010969817638397217, -0.009647670201957226, -0.01155476737767458, -0.04583444818854332, 0.027917344123125076, 0.012219848111271858, 0.060129664838314056, 0.002502063987776637, 0.009359201416373253, -0.03573804721236229, -0.0011178156128153205, 0.007051453460007906, -0.01056115422397852, -0.013093266636133194, 0.006310249213129282, -0.04564213380217552, 0.02261272817850113, -0.01833377778530121, -0.031731538474559784, -0.03266105055809021, 0.010881674475967884, 0.012340043671429157, 0.02788529358804226, 0.05775781348347664, -0.011634898371994495, 0.04025738686323166, -0.01362212561070919, 0.01913508027791977, 0.010432945564389229, -0.032981570810079575, -0.007696500979363918, 0.04291770979762077, -0.029808416962623596, 0.029648156836628914, -0.006863147486001253, 0.018910715356469154, 0.04000097140669823, 0.004487288650125265, -0.020865891128778458, -0.025289075449109077, 0.006282203830778599, -0.0025240997783839703, -0.0018960797460749745, -0.0390714630484581, -0.01734016463160515, 0.025625621899962425, 0.038302212953567505, -0.017179904505610466, 0.029439818114042282, 0.03121870756149292, 0.005901585798710585, -0.010160502977669239, -0.05144355818629265, 0.002333790762349963, -0.023702498525381088, -0.014784012921154499, -0.0016917478060349822, -0.007916859351098537, -0.032981570810079575, 0.02147488109767437, -0.003036932786926627, 0.008814316242933273, 0.033782873302698135, 0.017308112233877182, 0.019551757723093033, -0.019952407106757164, 0.02306145802140236, 0.011354442685842514, 0.01894276775419712, 0.0109858438372612, -0.005096277687698603, 0.04022533446550369, 0.0313308909535408, -0.002820581430569291, -0.01774081587791443, -0.007900833152234554, -0.036956027150154114, 0.04368695989251137, -0.029103271663188934, 0.004915984813123941, -0.02003253810107708, -0.03150717541575432, 0.014183036983013153, 0.028446203097701073, -0.003048952203243971, 0.022212078794836998, 0.04070611670613289, -0.018205570057034492, 0.03977660834789276, -0.006470509804785252, -0.021458854898810387, 0.0023618361447006464, -0.020593449473381042, 0.018702376633882523, 0.021555010229349136, -0.004751718137413263, -0.04278950020670891, 0.012588446959853172, 0.009150863625109196, 0.0019010878168046474, 0.036859869956970215, 0.009639657102525234, 0.004651555325835943, -0.011049947701394558, 0.0013521963264793158, 0.008565912954509258, 0.00884636864066124, -0.06317461282014847, 0.03036932647228241, 0.041186898946762085, -0.018910715356469154, 0.022596701979637146, -0.02549741417169571, -0.03174756467342377, 0.015945900231599808, -0.013301605358719826, -0.013846490532159805, -0.007812689989805222, -0.05673214793205261, 0.01396668516099453, -0.005933637730777264, -0.03314182907342911, 0.009487410075962543, -0.05272563919425011, -0.032244373112916946, -0.02570575289428234 ]
Model-based reinforcement learning (RL) algorithms designed for handling complex visual observations typically learn some sort of latent state representation, either explicitly or implicitly. Standard methods of this sort do not distinguish between functionally relevant aspects of the state and irrelevant distractors, instead aiming to represent all available information equally. We propose a modified objective for model-based RL that, in combination with mutual information maximization, allows us to learn representations and dynamics for visual model-based RL without reconstruction in a way that explicitly prioritizes functionally relevant factors. The key principle behind our design is to integrate a term inspired by variational empowerment into a state-space model based on mutual information. This term prioritizes information that is correlated with action, thus ensuring that functionally relevant factors are captured first. Furthermore, the same empowerment term also promotes faster exploration during the RL process, especially for sparse-reward tasks where the reward signal is insufficient to drive exploration in the early stages of learning. We evaluate the approach on a suite of vision-based robot control tasks with natural video backgrounds, and show that the proposed prioritized information objective outperforms state-of-the-art model based RL approaches with higher sample efficiency and episodic returns. https://sites.google.com/view/information-empowerment
[ 0.01906859502196312, -0.005832863971590996, -0.03108210861682892, -0.053578879684209824, -0.002464310498908162, 0.030863501131534576, -0.01433870941400528, 0.028617799282073975, -0.040482260286808014, 0.04908747225999832, 0.012579907663166523, 0.015610611997544765, 0.03205591067671776, -0.021185120567679405, -0.06415156275033951, 0.035335030406713486, 0.01298731379210949, 0.06562220305204391, -0.01546156033873558, -0.009420025162398815, 0.009131859987974167, -0.02285449206829071, -0.03670630231499672, 0.031320590525865555, 0.003281606826931238, 0.02386803925037384, 0.005013083107769489, -0.0028270012699067593, -0.08958961069583893, 0.06287965923547745, 0.034738827496767044, 0.012391109019517899, -0.013623264618217945, 0.03386439383029938, -0.008282269351184368, 0.05043886974453926, -0.0027226656675338745, -0.003077903762459755, -0.023510316386818886, 0.08386604487895966, -0.020708156749606133, -0.014070417732000351, -0.010532939806580544, -0.040323272347450256, -0.017518464475870132, 0.003641813527792692, -0.048769500106573105, 0.0013774799881502986, -0.021940311416983604, -0.03108210861682892, 0.004921168088912964, -0.05393660068511963, 0.036805666983127594, -0.010373951867222786, -0.045470502227544785, 0.010175216943025589, 0.05985889583826065, -0.01816435344517231, 0.025616904720664024, 0.0645490363240242, 0.01677320897579193, 0.007000430021435022, -0.09237189590930939, -0.01639561355113983, 0.06474776566028595, -0.05497002229094505, 0.04348315671086311, -0.02078765071928501, 0.016634095460176468, 0.01210294384509325, -0.07599615305662155, 0.03535490483045578, -0.04264846816658974, 0.023927658796310425, 0.03054552525281906, 0.03682554140686989, 0.007661222945898771, 0.021662084385752678, 0.024523863568902016, 0.0006440246943384409, 0.030803879722952843, 0.04566923528909683, -0.01292769331485033, -0.0023127752356231213, 0.0919744223356247, -0.06049484759569168, 0.07345234602689743, -0.07524096220731735, 0.009181543253362179, 0.00936537329107523, -0.03501705452799797, 0.020847272127866745, -0.009539266116917133, 0.01928720436990261, 0.020807525143027306, -0.044794805347919464, 0.02019144594669342, -0.0046503921039402485, -0.04396011680364609, 0.010950282216072083, -0.016087574884295464, -0.0034778574481606483, 0.0019463581265881658, -0.03966744989156723, 0.060892317444086075, -0.022695504128932953, -0.06375409662723541, -0.044158853590488434, 0.04121758043766022, 0.12067171931266785, -0.0119141461327672, -0.012132754549384117, -0.021224867552518845, 0.043999865651130676, -0.04980291798710823, 0.04797456040978432, -0.031658440828323364, -0.048888739198446274, 0.015978271141648293, -0.048133548349142075, 0.01602795533835888, 0.04821304231882095, 0.029253749176859856, -0.022993605583906174, -0.044755056500434875, 0.058308765292167664, -0.04455632343888283, 0.02132423408329487, 0.054811034351587296, 0.027643999084830284, 0.0322745181620121, 0.004809380043298006, -0.007999071851372719, 0.017498591914772987, 0.014795799739658833, 0.015938524156808853, -0.012649464420974255, 0.003502699313685298, -0.0013203436974436045, -0.002623298205435276, 0.00416597630828619, -0.04487429931759834, -0.021145373582839966, 0.0457884781062603, 0.03217514976859093, 0.022616010159254074, 0.014368520118296146, 0.02871716581285, -0.039647575467824936, -0.0039746942929923534, -0.0334073044359684, 0.046662911772727966, -0.024782218039035797, 0.047457847744226456, 0.06212447211146355, 0.012838262133300304, -0.032373882830142975, -0.0007017819443717599, -0.02961147204041481, -0.0491669662296772, 0.0795733779668808, -0.01446788664907217, -0.013722632080316544, 0.07603590190410614, 0.10238812118768692, 0.0010582623071968555, 0.008798979222774506, -0.023728923872113228, -0.02353019081056118, 0.044119104743003845, -0.052147988229990005, -0.015401939861476421, -0.014616938307881355, 0.03547414764761925, 0.02800172008574009, -0.002695339499041438, 0.06132953241467476, -0.030128182843327522, -0.0536583736538887, -0.01729985699057579, -0.03748136758804321, 0.005186975933611393, -0.024066774174571037, 0.02353019081056118, 0.07023284584283829, 0.006111092399805784, 0.0697956308722496, -0.015700042247772217, -0.030803879722952843, 0.006240270100533962, 0.024861712008714676, 0.040442515164613724, 0.034102875739336014, -0.04018415883183479, 0.062243711203336716, -0.037322379648685455, -0.04515252634882927, -0.022417275235056877, 0.010105660185217857, 0.014358582906425, 0.014756052754819393, -0.03455996513366699, -0.0008154333918355405, 0.045589741319417953, -0.0019562947563827038, -0.054930273443460464, 0.01617700606584549, -0.014000860042870045, 0.010284521616995335, -0.033268190920352936, -0.007432678248733282, -0.04972342401742935, -0.05524824932217598, -0.03704414889216423, -0.03159881755709648, 0.011367625556886196, -0.022953858599066734, 0.02500082738697529, -0.01932695135474205, -0.029631346464157104, -0.01677320897579193, -0.007437646389007568, 0.0405418798327446, -0.004511278122663498, -0.036388326436281204, 0.004955946933478117, 0.00555463507771492, -0.012709084898233414, 0.031161602586507797, 0.025577157735824585, -0.005539730191230774, 0.03487794101238251, 0.04769632965326309, 0.01876055635511875, -0.02724652923643589, 0.032970089465379715, 0.015302572399377823, -0.013603391125798225, 0.00594713632017374, -0.011218574829399586, 0.018532011657953262, -0.02146334946155548, -0.009042429737746716, -0.007517140358686447, 0.0773078054189682, -0.005649034399539232, 0.0390314981341362, 0.04451657459139824, 0.0491669662296772, 0.036686427891254425, -0.00855552963912487, -0.05922294408082962, -0.03599085658788681, -0.007268722169101238, -0.03350667282938957, 0.0185717586427927, -0.008943062275648117, -0.045430753380060196, -0.03658705949783325, -0.03823655843734741, 0.031141730025410652, 0.009762843139469624, 0.0686827152967453, 0.045430753380060196, -0.028776787221431732, -0.011457055807113647, 0.03348679840564728, 0.014646748080849648, 0.022655757144093513, 0.025020699948072433, -0.009921830147504807, -0.016822893172502518, -0.02706766687333584, -0.02012188918888569, -0.060256365686655045, -0.010254710912704468, 0.01172534842044115, 0.018144479021430016, 0.02034049853682518, -0.023132720962166786, 0.02690868079662323, -0.03758073225617409, 0.005803053732961416, 0.030466031283140182, 0.008426351472735405, 0.00439203716814518, 0.026928553357720375, 0.008754263631999493, -0.061647508293390274, 0.020648537203669548, -0.030565397813916206, 0.024603357538580894, -0.028399189934134483, -0.01943625509738922, 0.056957367807626724, 0.019148088991642, -0.05910370498895645, -0.02601437456905842, 0.029432611539959908, 0.027445264160633087, -0.007368089631199837, 0.0450332872569561, -0.009618760086596012, 0.0016706136520951986, -0.017578085884451866, 0.030485905706882477, -0.020429927855730057, 0.05397634953260422, 0.004645423963665962, -0.02804146707057953, -0.033049583435058594, 0.04173428937792778, -0.030187802389264107, -0.027027921751141548, 0.008610181510448456, 0.038455165922641754, 0.023510316386818886, 0.0062899538315832615, -0.04908747225999832, 0.03614984452724457, 0.02289423905313015, 0.013335099443793297, -0.02004239521920681, -0.04968367889523506, -0.009901956655085087, 0.00998641923069954, 0.055645719170570374, -0.023132720962166786, -0.04300619289278984, -0.002097893273457885, -0.06625815480947495, -0.023768670856952667, -0.0360306017100811, 0.01835315115749836, 0.014736179262399673, -0.03811731934547424, -0.016494981944561005, 0.017140869051218033, -0.05862674117088318, -0.06295915693044662, -0.03607035055756569, -0.03467920795083046, -0.0185717586427927, -0.01075154822319746, 0.017776820808649063, -0.04554999619722366, -0.018074922263622284, 0.022715376690030098, 0.009444867260754108, -0.011278195306658745, 0.0012222185032442212, -0.027564505115151405, -0.0033139013685286045, -0.017558211460709572, 0.05914345011115074, -0.0167036522179842, 0.01722036302089691, 0.004533635452389717, -0.05163127928972244, 0.015938524156808853, 0.0386539027094841, -0.05838825926184654, -0.05310191586613655, 0.02716703526675701, -0.04125732555985451, 0.04491404443979263, -0.021085752174258232, -0.012858135625720024, 0.050876084715127945, 0.0439203716814518, -0.011784967966377735, 0.03358616679906845, -0.028915900737047195, 0.0016544664977118373, -0.04364214092493057, -0.013434466905891895, -0.011268258094787598, -0.0065979924984276295, -0.052108243107795715, 0.03024742379784584, -0.021363981068134308, 0.021264614537358284, -0.06315789371728897, -0.015789473429322243, 0.006096187513321638, 0.04233049228787422, 0.045510247349739075, -0.014587127603590488, -0.002203471027314663, 0.021344108507037163, -0.006697359960526228, -0.058348510414361954, -0.019863534718751907, -0.017468780279159546, 0.012669337913393974, 0.05807028338313103, 0.0070352088660001755, -0.05977940186858177, 0.01655460149049759, -0.013742505572736263, -0.026888806372880936, -0.008515782654285431, 0.022715376690030098, 0.010493192821741104, -0.01015534345060587, 0.026888806372880936, -0.004931104835122824, 0.011625980958342552, 0.016335994005203247, -0.0009433688246645033, 0.029074888676404953, -0.05942167714238167, -0.017270047217607498, 0.014239341951906681, 0.010831042192876339, -0.041376568377017975, -0.019207710400223732, -0.01527276262640953, 0.019336886703968048, -0.07985160499811172, 0.0002831969759427011, 0.04173428937792778, 0.03485807031393051, 0.08601238578557968, -0.03692490980029106, 0.028061341494321823, -0.017627768218517303, -0.004516246262937784, -0.03213540464639664, -0.048093799501657486, 0.05858699232339859, -0.0040343147702515125, 0.04491404443979263, -0.08036831766366959, -0.0009576528682373464, -0.0029313371051102877, 0.0018805272411555052, 0.06272067874670029, -0.030784007161855698, -0.026332348585128784, -0.02315259352326393, -0.02142360247671604, -0.015252889133989811, -0.026034247130155563, 0.015282698906958103, 0.00893312506377697, 0.004014441277831793, -0.06180649623274803, 0.007194196805357933, 0.020211320370435715, -0.0619257353246212, 0.031618691980838776, -0.028737040236592293, -0.05047861859202385, 0.02867741882801056, -0.03217514976859093, 0.020469674840569496, -0.028101088479161263, -0.011784967966377735, -0.01715080626308918, -0.0027326021809130907, 0.0039821467362344265, 0.028240201994776726, -0.0577920526266098, 0.01993309147655964, 0.025080321356654167, -0.035633135586977005, -0.026709945872426033, -0.015958396717905998, 0.0450332872569561, -0.0012011028593406081, -0.0577920526266098, 0.005020535551011562, 0.02529892884194851, 0.021999932825565338, 0.08736377954483032, -0.014567254111170769, -0.06896094232797623, 0.004163492005318403, -0.009221290238201618, 0.05071709677577019, -0.027345895767211914, 0.006344605702906847, -0.041297074407339096, -0.027127288281917572, -0.0015774568310007453, 0.04459606856107712, 0.004551025107502937, -0.0315391980111599, 0.008406477980315685, -0.026789439842104912, -0.05433407053351402, -0.03726276010274887, 0.03257261961698532, -0.002546288538724184, -0.040104664862155914, -0.008813884109258652, -0.022099299356341362, 0.025040574371814728, -0.01290781982243061, -0.005350932013243437, -0.018452517688274384, -0.02454373612999916, 0.01805504783987999, 0.036388326436281204, 0.018333276733756065, 0.04511278122663498, -0.010274584405124187, -0.0059570730663836, -0.014845483005046844, 0.0037461493629962206, 0.058149777352809906, 0.017766883596777916, -0.056957367807626724, 0.011337815783917904, 0.02188069187104702, 0.017279982566833496, -0.029512105509638786, 0.03521579131484032, -0.00009354505164083093, 0.0010272100334987044, 0.048054054379463196, 0.014905103482306004, 0.012937629595398903, -0.03768010064959526, 0.05528799816966057, 0.013752441853284836, -0.010612433776259422, 0.03734225407242775, 0.04225099831819534, -0.042807456105947495, 0.07233943790197372, -0.03831605240702629, -0.05477128550410271, -0.004528667312115431, -0.008808916434645653, 0.011884335428476334, 0.007785432506352663, 0.0002474868088029325, -0.04586797207593918, -0.0009098323644138873, 0.027087541297078133, 0.03915073722600937, 0.0023525222204625607, -0.025418169796466827, -0.05413533374667168, 0.07182272523641586, -0.018363086506724358, -0.01617700606584549, 0.0094746770337224, 0.004312543198466301, -0.019823787733912468, -0.04026365280151367, 0.02154284343123436, -0.04157530143857002, -0.0322745181620121, -0.004938557744026184, 0.0058080218732357025, -0.04229074716567993, -0.02728627622127533, 0.0283395703881979, -0.03847504034638405, 0.018184226006269455, 0.037660226225852966, 0.03430161252617836, -0.00398711534217, 0.026729818433523178, 0.03211553022265434, 0.03531515970826149, 0.006011724937707186, -0.04193302243947983, -0.014855419285595417, -0.008818852715194225, -0.004759696312248707, 0.024345003068447113, 0.05043886974453926, 0.02192043885588646, -0.0008104650187306106, -0.01605776511132717, 0.01427908893674612, -0.03589148819446564, -0.0006402984145097435, 0.004116292577236891, 0.04121758043766022, -0.005380742251873016, -0.0502798818051815, -0.05111456662416458, -0.029114635661244392, 0.022397402673959732, -0.028498558327555656, -0.0110695231705904, 0.06057434156537056, 0.035414524376392365, 0.037362124770879745, -0.011119207367300987, -0.025875259190797806, 0.00016286931349895895, -0.0012545128120109439, 0.05791129544377327, -0.04125732555985451, -0.030644891783595085, 0.025080321356654167, -0.029094761237502098, 0.02180119790136814, 0.008356794714927673, 0.011407372541725636, 0.03704414889216423, 0.017538338899612427, 0.026471463963389397, -0.005882547702640295, 0.02221854031085968, 0.031141730025410652, 0.009658507071435452, -0.02094663865864277, 0.05063760280609131, -0.0060663772746920586, -0.029432611539959908, -0.0017699809977784753, 0.007929515093564987, -0.058348510414361954, 0.03016792982816696, -0.0170812476426363, 0.05401609465479851, -0.03036666475236416, -0.0245834831148386, -0.03616971895098686, 0.001955052837729454, -0.050836339592933655, 0.0020457254722714424, -0.008247490972280502, 0.0043945214711129665, 0.02728627622127533, -0.014626874588429928, -0.04777582362294197, -0.012748831883072853, -0.0008353068260475993, 0.01077142171561718, 0.04463581740856171, 0.03700440376996994, -0.00658805575221777, -0.04237024113535881, 0.03583186864852905, -0.013593453913927078, 0.042727962136268616, -0.0013029545079916716, 0.00837169960141182, -0.003055546199902892, 0.010542876087129116, 0.04348315671086311, 0.021383855491876602, -0.003915073815733194, 0.043443407863378525, 0.01409029122442007, 0.04109833762049675, -0.057474080473184586, -0.008247490972280502, 0.010473319329321384, -0.025100193917751312, -0.006344605702906847, 0.031400084495544434, 0.036428071558475494, -0.008197806775569916, -0.000677561154589057, 0.010840978473424911, 0.03479844704270363, -0.011427246034145355, 0.04523202031850815, 0.02056904323399067, -0.01353383343666792, 0.07834122329950333, -0.011983702890574932, 0.006265111733227968, -0.02015169896185398, 0.012778641656041145, 0.03328806534409523, -0.012897882610559464, 0.0004164113197475672, 0.0202610045671463, -0.02500082738697529, 0.00791957788169384, 0.020161636173725128, 0.008863568305969238, 0.017091184854507446, -0.010602496564388275, 0.01685270294547081, -0.009956609457731247, -0.00277234916575253, 0.03893212974071503, -0.02132423408329487, 0.051472291350364685, -0.029114635661244392, -0.035414524376392365, 0.011377561837434769, -0.0023897849023342133, 0.03783908858895302, 0.0018867376493290067, -0.03505680337548256, 0.0036716237664222717, 0.03839554637670517, -0.017508527263998985, -0.030505778267979622, -0.005162134300917387, 0.009390215389430523, 0.032373882830142975, 0.0645490363240242, -0.0008483487763442099, 0.004610645119100809, 0.017031565308570862, 0.007392931263893843, 0.006096187513321638, -0.022993605583906174, 0.03764035552740097, 0.02319234050810337, 0.004024378024041653, 0.02390778623521328, 0.029074888676404953, -0.01189427264034748, -0.007338279392570257, 0.013444403186440468, -0.0033859426621347666, 0.0517902672290802, 0.029472358524799347, 0.008659864775836468, -0.02800172008574009, -0.009787684306502342, 0.02669007144868374, 0.055486731231212616, 0.0028891058173030615, 0.0283395703881979, 0.0002645655767992139, 0.04181378334760666, 0.00494352588430047, -0.034361232072114944, 0.025040574371814728, 0.0187704935669899, 0.010473319329321384, -0.02559703029692173, 0.013891556300222874, 0.029134508222341537, -0.011407372541725636, 0.044158853590488434, 0.013315225951373577, 0.04507303237915039, 0.02086714468896389, -0.007268722169101238, 0.062203966081142426, -0.0032642176374793053, 0.010264648124575615, 0.014497697353363037, -0.010850915685296059, 0.07444602251052856, 0.023669304326176643, 0.02120499312877655, -0.008148123510181904, -0.02593488059937954, -0.02724652923643589, 0.026173360645771027, -0.010552813299000263, 0.04777582362294197, -0.04451657459139824, 0.04396011680364609, 0.013086680322885513, 0.01444801315665245, 0.05115431547164917, 0.0533006489276886, -0.029412737116217613, -0.0060912189073860645, 0.016803020611405373, 0.034917689859867096, -0.016842767596244812, 0.008247490972280502, 0.0027624124195426702, 0.026372095569968224, -0.054850779473781586, -0.04566923528909683, 0.009762843139469624, 0.006344605702906847, 0.007243880070745945, -0.030863501131534576, 0.03358616679906845, -0.0315391980111599, 0.031618691980838776, -0.012112881056964397, 0.002605909015983343, -0.022576263174414635, 0.004141134675592184, 0.004876452963799238, -0.017518464475870132, 0.002340101171284914, -0.035712629556655884, -0.013494087383151054, -0.021264614537358284, 0.004198270849883556, -0.008262395858764648, 0.03358616679906845, 0.013494087383151054, -0.040144409984350204, -0.014438076876103878, 0.012013513594865799, -0.034540094435214996, 0.016981881111860275, 0.01298731379210949, 0.020767778158187866, 0.018442580476403236, -0.046821899712085724, -0.0038008014671504498, 0.0036219400353729725, -0.02012188918888569, 0.016683779656887054, 0.004151071421802044, -0.0010793779511004686, -0.0055695404298603535, -0.0013414593413472176, 0.011457055807113647, -0.02353019081056118, -0.06188599020242691, 0.015938524156808853, 0.03869364783167839, 0.008023913949728012, 0.000852696131914854, 0.042052265256643295, -0.028816532343626022, -0.019575368613004684, 0.019227582961320877, -0.04570898413658142, -0.021821070462465286, -0.026968300342559814, 0.02563677728176117, 0.018790366128087044, 0.007666191551834345, 0.03481832146644592, 0.048729751259088516, -0.026471463963389397, -0.01328541524708271, 0.0034728890750557184, 0.011546486988663673, -0.022119173780083656, -0.021006258204579353, -0.002481699688360095, 0.060256365686655045, -0.033983636647462845, -0.011019839905202389, -0.022616010159254074, -0.01993309147655964, 0.009896988980472088, -0.0074724252335727215, 0.01073167473077774, 0.025954753160476685, 0.0015426782192662358, -0.035633135586977005, -0.01225199457257986, 0.015859030187129974, 0.03805769607424736, 0.009971514344215393, -0.008023913949728012, -0.0034405947662889957, 0.005246596410870552, 0.030446158722043037, 0.0007850021356716752, 0.007790400646626949, 0.0022593652829527855, -0.020728031173348427, -0.03412275016307831, -0.026849059388041496, 0.01546156033873558, -0.012937629595398903, 0.029134508222341537, -0.035374779254198074, -0.05262495204806328, -0.06518498808145523, 0.015233015641570091, 0.025616904720664024, -0.034917689859867096, 0.03054552525281906, -0.025994500145316124, 0.04785531759262085, -0.001851959154009819, -0.013961113058030605, 0.01647510752081871, -0.026292601600289345, 0.018830113112926483, 0.00040926929796114564, 0.03585174307227135, -0.03354641795158386, 0.0472988598048687, -0.02353019081056118, -0.0305852722376585, -0.04292669892311096, 0.034997183829545975, 0.0010650937911123037, 0.002355006290599704, 0.017925871536135674, -0.03255274519324303, -0.03764035552740097, 0.024563610553741455, 0.021443475037813187, -0.028498558327555656, -0.02386803925037384, 0.02142360247671604, 0.014626874588429928, 0.009082176722586155, -0.01943625509738922, -0.0072488486766815186, -0.013364909216761589, 0.005504951346665621, 0.03728263080120087, 0.015928586944937706, -0.0029412738513201475, 0.039806563407182693, -0.0469013936817646, -0.010294457897543907, -0.020181510597467422, 0.028697293251752853, -0.02086714468896389, 0.006250206846743822, -0.023927658796310425, -0.04733860865235329, -0.04713987186551094, -0.004056672099977732, 0.018005365505814552, 0.0060912189073860645, 0.029472358524799347, 0.035076677799224854, 0.04972342401742935, -0.024742471054196358, 0.011447119526565075, -0.003192176343873143, 0.03444072604179382, -0.007417772896587849, 0.019923154264688492, -0.024027027189731598, 0.003289059503003955, 0.01681295596063137, 0.029969194903969765, -0.01550130732357502, -0.003783412044867873, -0.02323208749294281, -0.002174902940168977, 0.006761948578059673, 0.009270974434912205, -0.00854062382131815, -0.027604252099990845, -0.005768274888396263, 0.002427047584205866, 0.01605776511132717, 0.006697359960526228, 0.03921036049723625, -0.001319101662375033, -0.00149423663970083, -0.01231161504983902, -0.016296247020363808, -0.009489582851529121, -0.0034530155826359987, -0.002759928349405527, -0.0020891986787319183, -0.013046934269368649, -0.016693715006113052, -0.028458811342716217, -0.03193666785955429, 0.05858699232339859, -0.0010477046016603708, -0.0142592154443264, -0.04980291798710823, -0.033526547253131866, -0.013961113058030605, 0.004178397357463837, -0.06657613068819046, -0.020131826400756836, -0.02120499312877655, 0.020092079415917397, 0.022317908704280853, 0.006593023892492056, 0.023331455886363983, 0.005658971145749092, 0.060932062566280365, -0.0003788380417972803, -0.00795435719192028, -0.014199594967067242, -0.03285084664821625, -0.011685601435601711, 0.05175051838159561, -0.05373786762356758, 0.06280016899108887, -0.01981385052204132, 0.0016258984105661511, 0.02386803925037384, 0.006573150400072336, 0.014159847982227802, -0.016236625611782074, 0.005847768858075142, -0.012589843943715096, 0.0009893262758851051, 0.019426317885518074, -0.0577920526266098, -0.005634129047393799, -0.0037014340050518513, -0.006662581115961075, -0.0048491270281374454, 0.03990593180060387, 0.0016842767363414168, -0.00932562630623579, -0.03215527534484863, -0.015014407224953175, 0.04821304231882095, 0.027445264160633087, 0.01813454180955887, 0.048928484320640564, -0.003164850175380707, -0.03712364286184311, 0.04960418492555618, 0.012550096958875656, 0.0019165478879585862, 0.024265509098768234, 0.000716065987944603, -0.016564538702368736, -0.01962505280971527, -0.005067734979093075, -0.007676128298044205, 0.02653108350932598, -0.03404325619339943, 0.010562749579548836, -0.032711733132600784, 0.03104236163198948, -0.05771255865693092 ]
Integration of multi-omics data provides opportunities for revealing biological mechanisms related to certain phenotypes. We propose a novel method of multi-omics integration called supervised deep generalized canonical correlation analysis (SDGCCA) for modeling correlation structures between nonlinear multi-omics manifolds, aiming for improving classification of phenotypes and revealing biomarkers related to phenotypes. SDGCCA addresses the limitations of other canonical correlation analysis (CCA)-based models (e.g., deep CCA, deep generalized CCA) by considering complex/nonlinear cross-data correlations and discriminating phenotype groups. Although there are a few methods for nonlinear CCA projections for discriminant purposes of phenotypes, they only consider two views. On the other hand, SDGCCA is the nonlinear multiview CCA projection method for discrimination. When we applied SDGCCA to prediction of patients of Alzheimer's disease (AD) and discrimination of early- and late-stage cancers, it outperformed other CCA-based methods and other supervised methods. In addition, we demonstrate that SDGCCA can be used for feature selection to identify important multi-omics biomarkers. In the application on AD data, SDGCCA identified clusters of genes in multi-omics data, which are well known to be associated with AD.
[ 0.02474534511566162, -0.02358916960656643, -0.04480176046490669, -0.002320377854630351, 0.02413514070212841, -0.010261048562824726, -0.02024911157786846, 0.004056646954268217, 0.0017332580173388124, 0.03886030614376068, 0.011023801751434803, -0.03738297522068024, 0.0876123309135437, -0.017471080645918846, -0.013079223223030567, 0.0325816385447979, -0.04666448384523392, 0.003203566651791334, 0.016989341005682945, -0.0036431539338082075, -0.02957879565656185, -0.05671678110957146, 0.02344464883208275, -0.0007226090529002249, 0.013882122002542019, 0.0491374135017395, 0.04762796312570572, -0.001977138686925173, -0.035648711025714874, 0.06281881034374237, 0.026864998042583466, 0.006443263962864876, 0.02418331615626812, -0.03497427701950073, -0.04322807863354683, -0.022834444418549538, 0.05202785134315491, 0.03972743824124336, 0.022400880232453346, 0.02419937402009964, 0.016074037179350853, -0.022288473322987556, 0.01898053102195263, 0.07104049623012543, 0.01877177692949772, -0.0009238355560228229, -0.022593574598431587, 0.003051015781238675, -0.03230865299701691, 0.005403509829193354, 0.004893668927252293, -0.006768438033759594, 0.000530415098182857, -0.04486599192023277, -0.035648711025714874, 0.030751029029488564, 0.024873808026313782, 0.05267016962170601, 0.06699388474225998, 0.06731504201889038, -0.011160294525325298, 0.02497015707194805, -0.011007743887603283, -0.007137771230190992, 0.006896901875734329, -0.0766286700963974, 0.036291029304265976, 0.030253231525421143, 0.02892041951417923, 0.015793021768331528, -0.06712234765291214, -0.017744066193699837, -0.07688560336828232, 0.030381694436073303, -0.02498621493577957, 0.01926957443356514, -0.025837287306785583, 0.040337640792131424, -0.03853914886713028, -0.03378598764538765, 0.054950401186943054, 0.045444078743457794, -0.017808297649025917, 0.06362170726060867, 0.03754355385899544, -0.06962739676237106, 0.0010437685996294022, -0.05462924391031265, 0.031056130304932594, -0.012276324443519115, 0.0023003052920103073, -0.010839135386049747, -0.014275542460381985, 0.03818587213754654, -0.0023926387075334787, -0.018466675654053688, 0.007081568241119385, 0.0011652070097625256, -0.04419155791401863, 0.021758560091257095, -0.014556556940078735, -0.020441805943846703, 0.005937437526881695, 0.05748756229877472, -0.002886421512812376, -0.031104303896427155, -0.009161076508462429, -0.01944621093571186, -0.01970313861966133, 0.13244619965553284, -0.040787264704704285, 0.02427966333925724, -0.0753440335392952, -0.008024974726140499, 0.007571336813271046, 0.0006408137269318104, -0.08947505801916122, -0.04181497544050217, 0.031409405171871185, -0.09930253773927689, 0.011818671599030495, 0.01193107757717371, -0.015487920492887497, -0.022015487775206566, -0.04878413677215576, 0.03738297522068024, 0.012886527925729752, 0.007089597638696432, 0.011168324388563633, 0.040658801794052124, -0.02853502705693245, -0.0015315297059714794, -0.01592148467898369, 0.0018627254758030176, 0.0371902771294117, 0.015455803833901882, 0.025564301759004593, 0.01013258472084999, -0.045508310198783875, -0.03908511996269226, 0.008952323347330093, -0.04663236811757088, -0.026029983535408974, 0.014428093098104, -0.011457367800176144, -0.004636741243302822, 0.017037514597177505, 0.08362995088100433, -0.0003605517849791795, 0.01851484924554825, -0.07007701694965363, 0.04486599192023277, 0.026784708723425865, -0.010582207702100277, 0.03385021910071373, 0.059864144772291183, 0.050839558243751526, -0.04053033888339996, -0.006985220592468977, -0.040915727615356445, 0.04990819841623306, 0.026640186086297035, 0.027073752135038376, 0.04493022337555885, 0.030269289389252663, 0.01930169016122818, -0.02371763437986374, -0.0007682738942094147, -0.0006262611714191735, 0.060410115867853165, 0.021389227360486984, 0.03796106204390526, 0.00583707494661212, 0.04432002082467079, -0.05880431830883026, 0.08118914067745209, 0.07572942227125168, 0.010710671544075012, -0.0007602449040859938, 0.03433195874094963, -0.049811847507953644, -0.04399885982275009, 0.0122040631249547, 0.025162851437926292, 0.061084549874067307, -0.006623915862292051, 0.0672508105635643, 0.027764244005084038, 0.035520248115062714, -0.007707829587161541, 0.040723033249378204, -0.017246268689632416, 0.03279039263725281, -0.01192304864525795, 0.005548031534999609, 0.007374626584351063, -0.02872772328555584, 0.004114856943488121, -0.00718193082138896, -0.027908766642212868, -0.008125336840748787, -0.046825066208839417, -0.00012702112144324929, 0.036708537489175797, 0.025981808081269264, 0.010421628132462502, 0.02415119856595993, -0.026383258402347565, 0.015255079604685307, -0.03821798786520958, -0.0241672582924366, 0.017085688188672066, -0.05861162021756172, -0.03237288445234299, 0.05299132689833641, -0.005933423060923815, 0.0020614429377019405, -0.030060535296797752, 0.005275045987218618, -0.028101462870836258, 0.014709108509123325, 0.03542390093207359, 0.055721186101436615, -0.036098334938287735, 0.036130450665950775, -0.02352493815124035, -0.026768648996949196, -0.03413926064968109, 0.027378853410482407, 0.055849649012088776, 0.07720676064491272, -0.011730353347957134, -0.001247504143975675, -0.021967314183712006, -0.024873808026313782, -0.018000993877649307, 0.020618444308638573, -0.025580359622836113, 0.017037514597177505, -0.017037514597177505, -0.01920534297823906, -0.05302344262599945, -0.0378325954079628, -0.035873524844646454, 0.017278384417295456, 0.060474347323179245, -0.0013498738408088684, 0.04814181849360466, 0.08741963654756546, 0.0791979506611824, -0.022465111687779427, -0.022738097235560417, -0.0009549479000270367, 0.017631659284234047, -0.04428790509700775, -0.007270249538123608, -0.01606600731611252, -0.022577516734600067, 0.026383258402347565, -0.05909335985779762, 0.020843256264925003, 0.04804547131061554, -0.00025843307957984507, 0.051064372062683105, 0.01012455578893423, -0.014813484624028206, 0.07007701694965363, 0.02458476461470127, 0.0486556738615036, 0.0077600181102752686, -0.013504759408533573, -0.011184382252395153, -0.0491374135017395, 0.010903366841375828, 0.008430439047515392, -0.01973525620996952, 0.02972331829369068, -0.06166263669729233, 0.007639583200216293, 0.02394244633615017, 0.04396674409508705, 0.011088034138083458, 0.015584267675876617, -0.03232470899820328, -0.041236888617277145, -0.003382211783900857, -0.01962284930050373, 0.0055841621942818165, -0.026254795491695404, -0.0035869509447366, -0.006202394142746925, -0.0198797769844532, -0.03876395896077156, -0.0074629453010857105, 0.003956284373998642, -0.04374193400144577, -0.0068246410228312016, 0.0027679940685629845, -0.021614039316773415, -0.04717833921313286, -0.025548243895173073, -0.030911607667803764, 0.009072757326066494, 0.02975543402135372, -0.008566931821405888, 0.045090802013874054, 0.007719872985035181, 0.051257066428661346, -0.07065510749816895, -0.04232883080840111, -0.0031232768669724464, -0.0094581488519907, 0.046279095113277435, 0.02402273565530777, -0.014034672640264034, 0.06574136018753052, 0.027571549639105797, -0.027137983590364456, -0.027475200593471527, -0.013906208798289299, 0.0006689151632599533, -0.027234330773353577, -0.06400710344314575, -0.007695786189287901, -0.009281511418521404, 0.031248826533555984, -0.07258205860853195, 0.03892454132437706, -0.04480176046490669, 0.04685718193650246, 0.00961070042103529, -0.01949438638985157, -0.029867839068174362, 0.020152762532234192, -0.0029064940754324198, -0.0050743212923407555, -0.010285135358572006, 0.04814181849360466, -0.01213983166962862, -0.011465396732091904, 0.013922267593443394, -0.0564277358353138, -0.05793718621134758, -0.009859598241746426, -0.03757566958665848, 0.0052951183170080185, -0.025227084755897522, -0.03548813238739967, 0.006929017603397369, 0.027186157181859016, 0.0006623915978707373, -0.026142388582229614, -0.0879334881901741, 0.0010317250853404403, -0.03250134736299515, 0.01960679143667221, 0.006483408622443676, -0.011240584775805473, 0.03349694237112999, -0.0007471978315152228, 0.05417961999773979, -0.07181128114461899, -0.011256642639636993, 0.017053572461009026, -0.055624835193157196, 0.00988368596881628, 0.010012149810791016, -0.027700012549757957, 0.022063661366701126, 0.006957119330763817, -0.055400025099515915, 0.05250959098339081, 0.017326558008790016, 0.03291885554790497, -0.03706181421875954, 0.030927665531635284, 0.022689923644065857, 0.01918928325176239, -0.001607805024832487, 0.045990049839019775, -0.0586758516728878, 0.013215715996921062, -0.04942645877599716, -0.04313173145055771, 0.005114465951919556, 0.025130735710263252, 0.006627930328249931, 0.026640186086297035, -0.008061105385422707, 0.036708537489175797, -0.011071976274251938, -0.04653602093458176, 0.04807758703827858, -0.016218557953834534, 0.07521557062864304, -0.013906208798289299, 0.0020815155003219843, 0.03256557881832123, 0.06333266943693161, -0.0004275436804164201, -0.004668856970965862, 0.011361019685864449, -0.006631945259869099, 0.013287977315485477, 0.01983160339295864, -0.023027140647172928, -0.0578729547560215, 0.0060096983797848225, 0.031040072441101074, 0.030269289389252663, -0.008687366731464863, -0.03346482664346695, -0.0026094214990735054, 0.02935398370027542, 0.001787453657016158, 0.02423148974776268, -0.03712604567408562, 0.03404291346669197, -0.011441309936344624, 0.010108496993780136, -0.008872033096849918, -0.040466103702783585, 0.05382634326815605, -0.004841480404138565, 0.016700297594070435, 0.03516697138547897, 0.025082562118768692, -0.004821408074349165, 0.005331248976290226, -0.0015154717257246375, 0.025114677846431732, 0.02938609942793846, -0.01192304864525795, -0.016844818368554115, 0.012605513446033001, -0.005327234510332346, 0.012043483555316925, -0.00936180166900158, -0.02501833066344261, 0.03857126459479332, -0.016684239730238914, 0.012750035151839256, 0.0015797036467120051, -0.011176353320479393, -0.09063123166561127, -0.06291516125202179, -0.021870967000722885, -0.041461698710918427, -0.045765239745378494, -0.022673865780234337, -0.05703793838620186, 0.027394911274313927, -0.045122917741537094, -0.03271010145545006, -0.002499022986739874, -0.016732413321733475, -0.021854909136891365, 0.006812597159296274, 0.03352905809879303, -0.012332526966929436, 0.013633223250508308, 0.020650560036301613, 0.010646440088748932, -0.040979959070682526, -0.0024046823382377625, 0.11080005019903183, -0.03773624822497368, -0.06975585967302322, -0.012067570351064205, 0.00962675828486681, 0.016041919589042664, 0.0011993302032351494, 0.03413926064968109, -0.010927454568445683, -0.03500639274716377, 0.05395480617880821, 0.036130450665950775, -0.07155434787273407, 0.02476140297949314, 0.03372175619006157, 0.03853914886713028, 0.0069531043991446495, -0.026559896767139435, -0.004660828039050102, -0.010526005178689957, 0.020345458760857582, -0.022995024919509888, 0.02419937402009964, 0.002302312757819891, -0.03715816140174866, 0.01867542788386345, -0.0007983826217241585, -0.026575954630970955, -0.025724880397319794, 0.040979959070682526, 0.016395196318626404, -0.02442418597638607, 0.01869148761034012, 0.08928235620260239, 0.018017051741480827, 0.027940882369875908, -0.050711095333099365, -0.00943406205624342, -0.006483408622443676, 0.015214934013783932, -0.013440527953207493, 0.03808952495455742, -0.035777173936367035, -0.0018316131317988038, 0.022641750052571297, 0.020441805943846703, 0.022738097235560417, -0.014990122988820076, -0.040369756519794464, -0.022272415459156036, -0.01954255998134613, -0.009586612693965435, 0.025660648941993713, 0.03234076872467995, -0.025114677846431732, 0.04049822315573692, -0.030574390664696693, -0.01213180273771286, 0.06815005838871002, -0.030172942206263542, -0.010461772792041302, 0.025371605530381203, 0.012830324470996857, 0.06474576890468597, -0.009779308922588825, -0.03940627723932266, 0.026559896767139435, -0.017246268689632416, -0.01885206624865532, 0.005720654968172312, -0.016989341005682945, 0.030879491940140724, 0.014773339964449406, -0.014171166345477104, -0.013528847135603428, -0.045668888837099075, 0.02842262201011181, -0.00026244757464155555, -0.02421543188393116, 0.016700297594070435, 0.0243278369307518, 0.016989341005682945, -0.05363364890217781, 0.0005519930273294449, 0.0400807149708271, 0.014524441212415695, 0.013528847135603428, 0.013986499048769474, -0.0386354960501194, 0.013504759408533573, -0.06924200057983398, -0.010847164317965508, -0.016282789409160614, -0.01857908070087433, -0.013296006247401237, 0.007483018096536398, 0.010839135386049747, 0.00495790084823966, -0.015841195359826088, 0.01936592161655426, -0.02456870675086975, 0.004741118289530277, 0.05189938470721245, 0.021662212908267975, 0.00495790084823966, -0.026078157126903534, -0.0199600663036108, -0.020602386444807053, -0.029964188113808632, -0.02330012619495392, -0.010004120878875256, 0.050293587148189545, -0.005263002589344978, 0.007715858519077301, 0.02890436165034771, 0.04480176046490669, -0.02903282456099987, 0.02938609942793846, 0.015375514514744282, 0.00920122116804123, -0.0023765808437019587, 0.0029044868424534798, -0.036997582763433456, -0.03198749199509621, 0.014933919534087181, -0.00940997526049614, -0.04807758703827858, 0.0026054070331156254, -0.045893702656030655, -0.02447235956788063, -0.012597483582794666, 0.007141785696148872, 0.03423561155796051, 0.020409690216183662, -0.07701406627893448, 0.04313173145055771, -0.005058262962847948, 0.026543838903307915, -0.0038338422309607267, 0.014949977397918701, 0.006419176701456308, -0.013095281086862087, -0.015664556995034218, 0.045990049839019775, 0.06731504201889038, -0.01210771594196558, -0.009594641625881195, 0.011336932890117168, -0.05186726897954941, -0.022079721093177795, -0.01857908070087433, 0.018161574378609657, 0.020281227305531502, 0.010935483500361443, -0.0037334798835217953, 0.03404291346669197, 0.005154611077159643, 0.02938609942793846, -0.04297114908695221, 0.08395110815763474, 0.03725450858473778, -0.007503090426325798, -0.0014662941684946418, 0.0008816833724267781, -0.003422356676310301, -0.014492325484752655, 0.0014492325717583299, -0.05800141766667366, -0.03394656628370285, 0.01922140084207058, -0.02892041951417923, -0.010782932862639427, -0.01409087609499693, -0.017599543556571007, -0.008446496911346912, -0.04521926864981651, 0.06583771109580994, -0.02479351870715618, 0.0024468344636261463, -0.015656528994441032, 0.0370296984910965, -0.006916974205523729, -0.01867542788386345, 0.027924824506044388, 0.02347676455974579, 0.025435836985707283, -0.022368764504790306, -0.008269858546555042, 0.035199087113142014, 0.0029827693942934275, -0.011449338868260384, 0.041269004344940186, 0.032035667449235916, 0.016636066138744354, 0.02002429962158203, -0.009016554802656174, -0.026415374130010605, 0.010670526884496212, 0.011521599255502224, 0.01930169016122818, -0.036387380212545395, -0.012043483555316925, 0.006969162728637457, 0.009153047576546669, -0.012966817244887352, 0.026062099263072014, -0.05289497971534729, -0.040305525064468384, -0.013825919479131699, 0.06272246688604355, -0.03320790082216263, 0.0397595539689064, -0.009209251031279564, 0.000886199704837054, -0.027459142729640007, -0.015487920492887497, -0.07316014915704727, -0.035199087113142014, 0.012750035151839256, -0.012613542377948761, 0.007218061480671167, -0.04489810764789581, 0.009988062083721161, -0.029996303841471672, 0.022400880232453346, -0.006290712859481573, 0.01184275932610035, 0.055207330733537674, -0.017984936013817787, -0.003000834723934531, -0.005957509856671095, -0.0028964579105377197, -0.04049822315573692, -0.017808297649025917, 0.012982875108718872, 0.006033785175532103, -0.005752770695835352, 0.006648003123700619, 0.04852721095085144, -0.021132299676537514, 0.03725450858473778, 0.007382655516266823, 0.024873808026313782, -0.01906082034111023, -0.017294442281126976, 0.007936655543744564, 0.021405285224318504, -0.022930793464183807, -0.008414380252361298, 0.0069410610012710094, 0.015809079632163048, 0.036644306033849716, -0.01971919648349285, 0.05144976079463959, -0.004496234003454447, -0.0038398641627281904, 0.020955661311745644, -0.022449053823947906, -0.030895549803972244, 0.0025652621407061815, -0.00997200421988964, 0.008209641091525555, -0.06111666560173035, -0.050775326788425446, -0.007314409129321575, 0.01952650211751461, -0.0402412936091423, -0.0031373274978250265, 0.012709889560937881, 0.03343271091580391, -0.05687735974788666, 0.015447774901986122, 0.045668888837099075, -0.015391572378575802, -0.016138268634676933, 0.012926672585308552, -0.031441520899534225, -0.004072704818099737, -0.008253800682723522, 0.01959073357284069, 0.04322807863354683, 0.0387960746884346, 0.021485574543476105, -0.015455803833901882, -0.0018215769669041038, 0.006379032041877508, -0.012725947424769402, 0.07052663713693619, -0.0000608446825935971, -0.005519930273294449, -0.021822793409228325, 0.0062184520065784454, -0.031698450446128845, -0.031666334718465805, -0.045604657381772995, -0.008719482459127903, 0.013906208798289299, 0.018225805833935738, 0.02427966333925724, 0.035937756299972534, 0.012051512487232685, -0.015744848176836967, -0.010445714928209782, 0.002673653420060873, -0.01433174591511488, -0.016716355457901955, -0.007603452540934086, 0.031746622174978256, 0.0004139947413932532, 0.02407090924680233, -0.023251952603459358, 0.020682675763964653, 0.011481454595923424, 0.0322604775428772, 0.05604234337806702, 0.01870754547417164, 0.026110272854566574, -0.007149814628064632, -0.006138162221759558, 0.004175074398517609, -0.025789113715291023, 0.011585831642150879, -0.04264999181032181, 0.011794584803283215, -0.00803300365805626, -0.03227653726935387, -0.016844818368554115, 0.05257382243871689, -0.026238735765218735, 0.060217417776584625, 0.01840244233608246, 0.016090095043182373, 0.017711950466036797, 0.011328903958201408, -0.04406309127807617, -0.0006598825566470623, -0.025403721258044243, -0.00359899434261024, 0.02366946078836918, 0.005744741763919592, -0.035648711025714874, -0.0050903791561722755, 0.006182321812957525, -0.01912505179643631, -0.0282138679176569, 0.005367379169911146, 0.013978470116853714, 0.018306095153093338, -0.008783713914453983, 0.021260762587189674, -0.006379032041877508, -0.050614748150110245, 0.021453458815813065, -0.01188290398567915, 0.0012655694736167789, -0.03404291346669197, -0.027667896822094917, -0.020233051851391792, -0.016234615817666054, -0.045829471200704575, -0.03744720667600632, 0.03979166969656944, -0.007695786189287901, 0.03433195874094963, 0.026399316266179085, 0.03324001654982567, 0.0373508557677269, -0.03706181421875954, 0.022288473322987556, -0.030221115797758102, 0.07752791792154312, 0.0378325954079628, 0.0247292872518301, 0.03747932240366936, 0.008189569227397442, 0.0028061317279934883, -0.013239802792668343, -0.0381537564098835, -0.06323631852865219, 0.026495663449168205, 0.042071904987096786, 0.022866562008857727, 0.015423688106238842, 0.03481369838118553, 0.016684239730238914, -0.002703762147575617, -0.012212092988193035, 0.027635781094431877, 0.013898179866373539, -0.013103310018777847, 0.0148696880787611, 0.027202215045690536, -0.008928235620260239, 0.02928975224494934, -0.006603843532502651, 0.07495864480733871, 0.03417137637734413, 0.02395850419998169, -0.012597483582794666, 0.0009238355560228229, -0.01954255998134613, 0.03709392994642258, -0.04435213655233383, -0.00469294423237443, -0.001987174851819873, -0.016732413321733475, 0.007097626570612192, -0.01165006309747696, 0.0675719752907753, -0.0116420341655612, -0.011160294525325298, 0.006503481417894363, -0.012966817244887352, -0.016539717093110085, -0.030461985617876053, 0.0003334539651405066, -0.0074669597670435905, -0.023412533104419708, -0.005363364703953266, 0.03494216129183769, -0.021935198456048965, -0.012838353402912617, 0.0029566753655672073, -0.015070412307977676, -0.060474347323179245, -0.030686795711517334, -0.007860380224883556, 0.0027358781080693007, -0.007049452513456345, 0.008639192208647728, 0.06680119037628174, -0.02408696711063385, 0.021212588995695114, -0.055303677916526794, -0.04335654154419899, -0.01957467570900917, -0.024889865890145302, 0.008743569254875183, -0.030654679983854294, 0.006796539295464754, -0.006884858012199402, 0.08054681867361069, -0.036997582763433456, 0.017021456733345985, 0.022914735600352287, 0.035616595298051834, 0.005877220071852207, 0.0373508557677269, 0.004436016548424959, 0.030510159209370613, 0.03918146714568138, -0.01190699078142643, -0.0004671867936849594, 0.036580074578523636, -0.01464487612247467, -0.004279451444745064, -0.03834645077586174, -0.004022523760795593, 0.05459712818264961, -0.018482733517885208, -0.0034845813643187284, -0.03706181421875954, 0.0026435446925461292, 0.02479351870715618, 0.02371763437986374, -0.0048655676655471325, 0.014982094056904316, 0.020634502172470093, 0.007515133824199438, 0.055014632642269135, -0.030349578708410263, -0.022481169551610947, -0.02402273565530777, 0.008229713886976242, -0.006965148262679577, -0.014291600324213505, 0.05263805389404297, -0.017278384417295456, 0.027908766642212868, 0.0069410610012710094, -0.05777660757303238, 0.012701860629022121, -0.00028176733758300543, -0.017246268689632416, -0.04486599192023277, -0.03979166969656944, -0.027812417596578598, -0.03731874004006386, -0.008310004137456417, 0.012926672585308552, 0.008631163276731968, -0.014452180825173855, 0.0010307214688509703, -0.0022581531666219234, -0.017342615872621536, 0.021999429911375046, 0.022047603502869606, 0.013384324498474598, 0.004323610570281744, -0.012300411239266396, 0.036130450665950775, 0.015849225223064423, -0.013617165386676788, -0.004126900341361761, -0.0003786170273087919, -0.0011029824381694198, 0.001977138686925173, -0.003404291346669197, 0.05318402498960495, -0.015447774901986122, 0.008141394704580307, -0.009843540377914906, -0.0013338158605620265, -0.031152477487921715, -0.01865937002003193, 0.002274211263284087, -0.013713513500988483, 0.02402273565530777, -0.025548243895173073, -0.020233051851391792, -0.035552363842725754, 0.03709392994642258, -0.015760906040668488, -0.0476921945810318, 0.011537657119333744, 0.004407914821058512, 0.017149921506643295, 0.02946639060974121, 0.02880801260471344, -0.025451894849538803, 0.0015355441719293594, 0.008478612639009953, -0.015295224264264107, 0.04711410775780678, 0.011577802710235119, -0.004777248483151197, -0.020313343033194542, 0.008823859505355358, 0.011553714983165264, -0.010301193222403526, -0.00358293647877872, 0.009787337854504585, 0.03805740922689438, -0.040723033249378204, 0.05758390948176384, 0.008310004137456417, -0.021100183948874474, -0.01209968701004982, 0.04814181849360466, -0.007876438088715076, 0.02961091138422489, -0.026704417541623116, 0.010558120906352997, 0.020891429856419563, -0.046825066208839417, 0.003065066644921899, -0.04891260340809822, -0.03722239285707474, 0.016555774956941605 ]
Neural networks have had discernible achievements in a wide range of applications. The wide-spread adoption also raises the concern of their dependability and reliability. Similar to traditional decision-making programs, neural networks can have defects that need to be repaired. The defects may cause unsafe behaviors, raise security concerns or unjust societal impacts. In this work, we address the problem of repairing a neural network for desirable properties such as fairness and the absence of backdoor. The goal is to construct a neural network that satisfies the property by (minimally) adjusting the given neural network's parameters (i.e., weights). Specifically, we propose CARE (\textbf{CA}usality-based \textbf{RE}pair), a causality-based neural network repair technique that 1) performs causality-based fault localization to identify the `guilty' neurons and 2) optimizes the parameters of the identified neurons to reduce the misbehavior. We have empirically evaluated CARE on various tasks such as backdoor removal, neural network repair for fairness and safety properties. Our experiment results show that CARE is able to repair all neural networks efficiently and effectively. For fairness repair tasks, CARE successfully improves fairness by $61.91\%$ on average. For backdoor removal tasks, CARE reduces the attack success rate from over $98\%$ to less than $1\%$. For safety property repair tasks, CARE reduces the property violation rate to less than $1\%$. Results also show that thanks to the causality-based fault localization, CARE's repair focuses on the misbehavior and preserves the accuracy of the neural networks.
[ -0.009994348511099815, -0.04654710739850998, -0.011252379044890404, -0.016485434025526047, 0.042283784598112106, 0.04598798230290413, -0.03613341599702835, 0.01146205049008131, 0.00830823928117752, 0.03394933417439461, 0.00767485611140728, -0.03760111704468727, 0.0008872823673300445, -0.034036699682474136, -0.009356597438454628, -0.03354746475815773, -0.0048530250787734985, -0.051788896322250366, -0.0022157488856464624, -0.05769464746117592, 0.012824916280806065, -0.00834755226969719, 0.0033307215198874474, 0.031206130981445312, 0.002363174222409725, 0.058218829333782196, 0.05720541626214981, 0.0186607763171196, -0.05751992389559746, 0.025195542722940445, 0.02348322421312332, 0.017778409644961357, 0.00033662127680145204, -0.006827433127909899, 0.013759702444076538, -0.018835503607988358, -0.002380646765232086, 0.03193997964262962, -0.016066091135144234, 0.08477723598480225, 0.0296685378998518, -0.034386150538921356, 0.025230487808585167, 0.002765044802799821, 0.015541911125183105, -0.023605532944202423, -0.06164346635341644, -0.055807605385780334, -0.01596998982131481, 0.010736935772001743, 0.03770595043897629, -0.034735605120658875, 0.05402539670467377, -0.0035775224678218365, -0.014668279327452183, 0.07792796194553375, 0.03906881809234619, -0.02145639806985855, 0.0344560407102108, -0.02301146276295185, 0.004385631997138262, 0.042283784598112106, -0.06919164210557938, -0.0012110722018405795, 0.013698548078536987, -0.008662059903144836, -0.008784368634223938, -0.0038723733741790056, 0.0013366567436605692, -0.031677890568971634, -0.08883088827133179, -0.0028021743055433035, -0.06817822903394699, -0.04616270959377289, -0.00867516454309225, 0.00851354282349348, 0.02051287703216076, 0.03973277658224106, -0.0187830850481987, 0.01573411002755165, 0.021613651886582375, 0.021264199167490005, 0.012274527922272682, 0.027798965573310852, 0.01783956214785576, -0.06548744440078735, 0.03941826894879341, -0.06360039860010147, 0.04050157219171524, -0.04556863754987717, -0.023640478029847145, 0.019289791584014893, 0.020914746448397636, 0.006106686778366566, 0.02503828890621662, -0.015603065490722656, 0.00331980106420815, -0.004691403359174728, -0.04874865710735321, 0.04392620921134949, -0.027397096157073975, 0.004442417994141579, 0.022050468251109123, 0.00207705982029438, -0.002033378230407834, -0.019551880657672882, -0.04032684862613678, 0.04144509509205818, 0.04822447896003723, 0.15767307579517365, -0.035172417759895325, -0.018241433426737785, -0.04619765281677246, 0.012851124629378319, -0.013436458073556423, -0.0281134732067585, -0.018643304705619812, -0.025143126025795937, -0.018887920305132866, 0.0016489801928400993, -0.005482039880007505, 0.09749731421470642, 0.026453573256731033, 0.024514110758900642, -0.02975590154528618, 0.027536876499652863, -0.00710262730717659, -0.027816439047455788, 0.005464567337185144, 0.006521661765873432, 0.012737552635371685, -0.005578139331191778, 0.022696956992149353, -0.026925334706902504, 0.04361170157790184, -0.04326225072145462, 0.041689712554216385, -0.011112597770988941, -0.02336091734468937, -0.05717046931385994, 0.03169536590576172, -0.013882010243833065, 0.012099801562726498, 0.01576031930744648, 0.00906829908490181, -0.0022889154497534037, 0.03057711571455002, 0.06936637312173843, -0.010798090137541294, 0.03136338293552399, -0.07646026462316513, 0.04099080711603165, 0.011863920837640762, 0.023553116247057915, 0.08876100182533264, -0.008897940628230572, -0.0031669156160205603, 0.014930368401110172, -0.05259263888001442, -0.006609024945646524, 0.07618069648742676, -0.05098515748977661, -0.019237374886870384, 0.03836991265416145, 0.0684228464961052, 0.06304127722978592, -0.016310706734657288, -0.015008995309472084, -0.07946555316448212, 0.06471864879131317, 0.02184079773724079, 0.005403412971645594, -0.02732720598578453, 0.01711444929242134, 0.015498229302465916, 0.04326225072145462, 0.05951180309057236, 0.005713552702218294, -0.013095742091536522, -0.021002110093832016, -0.06290149688720703, 0.03690221160650253, 0.026051701977849007, -0.030245136469602585, 0.01602240838110447, 0.004464258905500174, 0.020967165008187294, -0.021491345018148422, 0.08142249286174774, -0.0032957762014120817, -0.015568120405077934, 0.014292617328464985, 0.0440310463309288, -0.0398026667535305, -0.010204019956290722, -0.011540677398443222, -0.035347145050764084, -0.059476859867572784, 0.05175395309925079, -0.010204019956290722, -0.03131096810102463, -0.038963980972766876, 0.011514468118548393, -0.032883502542972565, 0.0012307289289310575, -0.015174985863268375, 0.07555168122053146, -0.0011914154747501016, 0.02530037984251976, -0.02309882640838623, -0.02797369286417961, -0.013593711890280247, 0.020390568301081657, -0.023465752601623535, -0.03164294734597206, -0.010780617594718933, -0.023168716579675674, -0.01539339404553175, -0.012964696623384953, 0.0395580530166626, 0.01144457794725895, 0.0022430499084293842, 0.01696593128144741, 0.003920422866940498, -0.020408039912581444, -0.006604657042771578, 0.01405673660337925, -0.01717560365796089, -0.03312812000513077, -0.006141632329672575, -0.08302997052669525, -0.02676808089017868, -0.0035010797437280416, -0.013261731714010239, -0.003671437967568636, -0.0029026418924331665, -0.02486356347799301, -0.036552757024765015, -0.050460975617170334, 0.0024090399965643883, -0.052487801760435104, 0.01731538400053978, -0.01908012107014656, -0.03185261785984039, 0.05888278782367706, 0.004138831049203873, -0.035853851586580276, 0.0702749490737915, 0.028777433559298515, -0.0037500648759305477, -0.022399920970201492, 0.01135721430182457, 0.024514110758900642, 0.023168716579675674, -0.06772394478321075, -0.018852975219488144, -0.0050758011639118195, -0.015987463295459747, 0.028165891766548157, 0.016546588391065598, 0.029354030266404152, -0.0074957613833248615, -0.005132587160915136, 0.026069175451993942, -0.009400279261171818, -0.040256958454847336, -0.061888083815574646, 0.021211782470345497, 0.029091941192746162, 0.020215841010212898, 0.0162932351231575, -0.0006284689297899604, -0.011802766472101212, -0.03606352210044861, 0.0015856418758630753, -0.03181767463684082, 0.014327562414109707, 0.04724601283669472, -0.004560358356684446, 0.013672338798642159, -0.0020748756360262632, -0.04431061074137688, 0.007945681922137737, 0.006884219124913216, -0.03492780402302742, -0.05720541626214981, -0.055632878094911575, 0.00643429858610034, -0.0480148084461689, -0.013576239347457886, 0.00865769200026989, -0.0148342689499259, -0.036762431263923645, -0.005783442873507738, 0.08673417568206787, 0.01062336377799511, 0.016135981306433678, -0.04472995176911354, -0.0024767464492470026, 0.020111005753278732, -0.069401316344738, -0.02647104673087597, 0.07006527483463287, 0.03718177229166031, -0.04308752343058586, 0.007993731647729874, 0.0437864288687706, 0.05720541626214981, -0.030839204788208008, -0.0004916909383609891, 0.004370343405753374, 0.004874865990132093, -0.020303204655647278, -0.053640998899936676, -0.018451105803251266, 0.031101295724511147, -0.023605532944202423, -0.03366977348923683, -0.03419395163655281, -0.013453930616378784, -0.007989363744854927, 0.021613651886582375, -0.05905751511454582, 0.03082173317670822, -0.04696644842624664, 0.002671129535883665, 0.01410041842609644, 0.04361170157790184, -0.012816179543733597, -0.005438358522951603, -0.02664577215909958, 0.0386844202876091, -0.0204604584723711, -0.008229612372815609, -0.046651940792798996, -0.010308856144547462, -0.07499255985021591, 0.034822966903448105, -0.020215841010212898, -0.056331783533096313, -0.0014196517877280712, -0.020530348643660545, -0.06307622045278549, 0.022766847163438797, -0.02659335359930992, -0.05720541626214981, -0.039138708263635635, -0.040676299482584, -0.002837119624018669, -0.03648286685347557, 0.0008414167095907032, -0.034997694194316864, -0.001612942898645997, 0.01605735346674919, 0.032586470246315, -0.016651423647999763, 0.015620538033545017, 0.017131920903921127, -0.041130587458610535, 0.04521918669342995, 0.04658205062150955, -0.03496274724602699, -0.017411483451724052, 0.0009801057167351246, -0.02902205102145672, -0.04770030081272125, 0.0020279178861528635, 0.0029878211207687855, 0.009924458339810371, 0.026995224878191948, -0.04595303535461426, 0.07132330536842346, -0.012510408647358418, -0.013820855878293514, 0.014991522766649723, -0.03959299623966217, 0.016773732379078865, 0.012073592282831669, -0.03372219204902649, 0.048469096422195435, -0.05217329412698746, -0.03492780402302742, -0.026174010708928108, 0.036727484315633774, -0.03850969299674034, 0.050321195274591446, 0.009950666688382626, -0.009810886345803738, -0.018852975219488144, 0.006670179311186075, -0.029546231031417847, -0.03812529519200325, -0.011549413204193115, -0.055458150804042816, 0.008081095293164253, -0.008609642274677753, -0.044240716844797134, -0.04640732705593109, 0.021124418824911118, -0.05587749555706978, -0.03770595043897629, 0.011732876300811768, 0.0366925373673439, 0.014030528254806995, -0.02758929505944252, 0.04546380415558815, -0.007810269016772509, -0.039488159120082855, -0.008692637085914612, 0.019674189388751984, -0.006875482853502035, 0.017682308331131935, 0.030978986993432045, -0.03864947333931923, 0.04431061074137688, 0.03298833966255188, -0.0004930559662170708, -0.01684362255036831, 0.04123542457818985, -0.05154428258538246, 0.02028573304414749, -0.0010696530807763338, 0.05458451807498932, -0.03830002248287201, -0.0013770622899755836, -0.03527725487947464, -0.024077294394373894, -0.011610567569732666, 0.046651940792798996, -0.06664063781499863, 0.0022692587226629257, -0.009199343621730804, 0.03125854954123497, 0.019621772691607475, -0.011479523032903671, -0.022137831896543503, 0.0312236025929451, -0.02439180202782154, -0.03847474977374077, -0.005368467886000872, 0.03899892792105675, -0.013314150273799896, -0.0008375945617444813, -0.007604965474456549, -0.04343697801232338, -0.047909971326589584, 0.0073297712951898575, -0.03962794318795204, 0.004361607134342194, -0.05084537714719772, -0.049377672374248505, 0.06349556148052216, -0.03739144280552864, -0.055597931146621704, 0.009461433626711369, 0.005621821153908968, -0.009382806718349457, -0.06153862923383713, 0.024723781272768974, -0.024933453649282455, 0.0009637251496315002, 0.04459017142653465, -0.02115936391055584, -0.016564060002565384, -0.02206794172525406, 0.04948250949382782, -0.006657075136899948, -0.045533694326877594, 0.014519762247800827, 0.013576239347457886, 0.058777954429388046, -0.014082945883274078, 0.010387483052909374, -0.029843265190720558, 0.05098515748977661, 0.015279821120202541, -0.0017603682354092598, -0.05566782504320145, 0.015017732046544552, -0.0375661700963974, 0.01569916494190693, 0.025195542722940445, 0.0065391347743570805, 0.006307621952146292, -0.042213890701532364, -0.003896398236975074, 0.02219025045633316, -0.023989930748939514, -0.027903802692890167, -0.06052521616220474, -0.01684362255036831, -0.034997694194316864, -0.008137880824506283, -0.024252021685242653, 0.005468935705721378, -0.02495092712342739, 0.007635542657226324, -0.023378388956189156, 0.05259263888001442, -0.021351562812924385, 0.05402539670467377, -0.04144509509205818, 0.0065391347743570805, 0.024688836187124252, 0.009662368334829807, -0.04368159547448158, -0.031241076067090034, 0.027187423780560493, -0.0017603682354092598, -0.027606766670942307, 0.02996557392179966, -0.01817154325544834, -0.007950049825012684, -0.01939462684094906, -0.009723522700369358, -0.016118507832288742, 0.025492578744888306, -0.0426681824028492, -0.0003257008793298155, 0.04745568335056305, 0.06415952742099762, -0.00048431966570205986, -0.029546231031417847, 0.028777433559298515, 0.008972199633717537, 0.05786937475204468, 0.02025078609585762, 0.005931960418820381, -0.03994245082139969, -0.01637186110019684, 0.05608716607093811, 0.072895847260952, -0.0025466368533670902, -0.06052521616220474, -0.00022905535297468305, -0.01669510453939438, 0.034997694194316864, -0.00066123012220487, -0.055597931146621704, -0.044065993279218674, -0.08610516041517258, 0.05696079879999161, 0.007910736836493015, 0.02206794172525406, 0.009146925993263721, 0.01972660794854164, 0.02353564277291298, -0.05849839001893997, 0.025894448161125183, -0.007993731647729874, 0.00590575160458684, -0.024898508563637733, -0.02676808089017868, -0.001784393098205328, 0.031590528786182404, -0.026069175451993942, 0.0025925026275217533, 0.026436099782586098, -0.0038832935970276594, -0.056366730481386185, -0.02327355369925499, -0.015140040777623653, -0.00024147730437107384, 0.014170309528708458, 0.00513695552945137, -0.05751992389559746, -0.014755642041563988, 0.05902256816625595, 0.029354030266404152, -0.021229254081845284, -0.02591192163527012, 0.006809960585087538, 0.00990698579698801, -0.006801224313676357, 0.00047148819430731237, 0.002561925444751978, -0.01742895506322384, -0.03700704500079155, -0.02210288681089878, 0.021473871544003487, -0.033827025443315506, -0.014318826608359814, 0.0075132339261472225, 0.0686674639582634, 0.010920398868620396, 0.017123185098171234, -0.03043733537197113, 0.00763117428869009, -0.006617761682718992, -0.04217894747853279, -0.03899892792105675, 0.039662886410951614, -0.0026405523531138897, -0.003186572343111038, -0.027606766670942307, 0.03216712549328804, 0.017367802560329437, 0.0005391946760937572, 0.062237534672021866, -0.048853494226932526, 0.0007354888366535306, -0.004534149542450905, 0.03496274724602699, 0.008526647463440895, 0.007967522367835045, -0.001652256236411631, 0.02556246891617775, 0.05014646798372269, -0.0575898140668869, 0.030384916812181473, 0.015594328753650188, -0.00855722464621067, 0.021037055179476738, -0.048469096422195435, 0.021438926458358765, -0.007465184200555086, 0.013550030067563057, -0.012326945550739765, -0.035818908363580704, 0.0398026667535305, 0.020373094826936722, -0.014502288773655891, 0.05776454135775566, -0.01182897575199604, -0.003717303741723299, 0.02136903628706932, -0.00043162875226698816, -0.04071124643087387, 0.00840870663523674, -0.005556298885494471, -0.03850969299674034, -0.011470786295831203, -0.016275761649012566, -0.019289791584014893, 0.022696956992149353, 0.010378746315836906, 0.015061413869261742, 0.011863920837640762, 0.0052592637948691845, 0.0013191840844228864, -0.011794030666351318, -0.01103397086262703, -0.010265174321830273, 0.04567347466945648, -0.015524438582360744, -0.006010587327182293, 0.038055405020713806, -0.025492578744888306, 0.020023642107844353, -0.011261114850640297, -0.042633235454559326, 0.0366925373673439, -0.007570020388811827, 0.04797986149787903, -0.002029010094702244, 0.004368159454315901, 0.04804975166916847, -0.007045841310173273, -0.015559383668005466, 0.05077548325061798, 0.024898508563637733, -0.007098258938640356, -0.011243642307817936, 0.04472995176911354, 0.0366925373673439, -0.010457373224198818, 0.018084179610013962, 0.03169536590576172, 0.02547510527074337, 0.06761910766363144, -0.04948250949382782, -0.04308752343058586, -0.01426640897989273, 0.037286609411239624, 0.014345035888254642, -0.015498229302465916, 0.01135721430182457, 0.029563702642917633, 0.040676299482584, -0.008024308830499649, -0.003793746465817094, -0.016599005088210106, -0.029336558654904366, 0.0034442937467247248, -0.013148159720003605, 0.00034535760642029345, -0.0048355525359511375, 0.0019121618242934346, -0.025807086378335953, 0.007399661932140589, -0.035818908363580704, -0.051579225808382034, 0.002363174222409725, 0.004175960551947355, 0.02245233952999115, -0.0069235325790941715, 0.016590269282460213, -0.04368159547448158, 0.0009855659445747733, -0.013410249724984169, -0.0344560407102108, -0.017979344353079796, -0.017603682354092598, 0.02715247869491577, -0.0036474131047725677, 0.027047643437981606, 0.004442417994141579, -0.00553882634267211, 0.029808320105075836, -0.009915721602737904, 0.005355363246053457, 0.04137520492076874, 0.011654249392449856, 0.029843265190720558, -0.008164090104401112, 0.0460229255259037, 0.012510408647358418, 0.000635567179415375, -0.029249195009469986, 0.03690221160650253, 0.018940338864922523, -0.02608664706349373, 0.016948457807302475, -0.041864439845085144, -0.02746698632836342, -0.013252995908260345, 0.028043583035469055, 0.0008266741642728448, -0.005036487709730864, 0.006578448228538036, -0.0009555348660796881, 0.008749423548579216, -0.03854463994503021, -0.011147542856633663, -0.005364099517464638, 0.04085102677345276, 0.018293851986527443, 0.011147542856633663, 0.005569403059780598, 0.021648598834872246, 0.013462667353451252, -0.014048000797629356, 0.0468965582549572, -0.009933194145560265, 0.011252379044890404, 0.013934428803622723, -0.06401974707841873, -0.005486408248543739, 0.013200577348470688, 0.007019632030278444, 0.047735244035720825, -0.010282646864652634, 0.045533694326877594, 0.011348478496074677, -0.03777584061026573, 0.014126627705991268, 0.003018398070707917, 0.03686726465821266, 0.021945632994174957, -0.004892338532954454, -0.015952518209815025, 0.06534766405820847, -0.011951284483075142, 0.013218049891293049, 0.0513695552945137, -0.04598798230290413, -0.04127037152647972, 0.008583432994782925, 0.020582767203450203, -0.030297553166747093, 0.011994965374469757, -0.011365951038897038, 0.04860887676477432, -0.027432041242718697, -0.0015321319224312901, 0.00030822824919596314, 0.03634308651089668, -0.03394933417439461, 0.01658153347671032, 0.012082329019904137, 0.01972660794854164, 0.02184079773724079, -0.01146205049008131, 0.009417751803994179, 0.0017199628055095673, -0.018922867253422737, -0.03424637019634247, -0.019027702510356903, -0.031013932079076767, 0.04493962228298187, -0.027991164475679398, -0.03522483631968498, 0.001259121927432716, -0.025929393246769905, -0.011977492831647396, -0.016861096024513245, -0.05793926492333412, 0.005787811242043972, 0.00632509496062994, -0.01825890690088272, 0.02418212965130806, 0.005726656876504421, -0.00222666934132576, -0.009374069981276989, -0.013654866255819798, -0.0006142724305391312, -0.012082329019904137, -0.011252379044890404, -0.054689355194568634, -0.03143327683210373, 0.016013672575354576, 0.0386844202876091, -0.012685135006904602, 0.008089831098914146, -0.02219025045633316, -0.010422428138554096, -0.006919164676219225, 0.048643823713064194, 0.0076486472971737385, -0.07048462331295013, -0.018328797072172165, -0.05283725634217262, -0.007967522367835045, -0.06454392522573471, -0.037111882120370865, -0.024723781272768974, 0.015664219856262207, 0.008382498286664486, 0.06908681243658066, 0.02362300641834736, -0.03290097787976265, 0.05566782504320145, -0.013156896457076073, 0.0018662960501387715, -0.036552757024765015, 0.01670384220778942, 0.021316617727279663, -0.007687960751354694, -0.035469453781843185, -0.0008064714493229985, 0.042283784598112106, 0.020565293729305267, -0.0006841629510745406, -0.0053728362545371056, -0.025143126025795937, -0.016188398003578186, -0.024199603125452995, -0.013087005354464054, 0.0004269875935278833, -0.006355672143399715, -0.008081095293164253, 0.07946555316448212, 0.027344677597284317, -0.01852099597454071, 0.011697931215167046, 0.0028808012139052153, 0.03281361237168312, 0.012047383934259415, -0.018328797072172165, -0.048853494226932526, -0.016913512721657753, 0.012755025178194046, 0.02729225903749466, 0.01451102551072836, 0.02136903628706932, 0.019656717777252197, 0.005661134608089924, -0.06384501606225967, 0.009522587060928345, -0.03487538546323776, -0.0015736294444650412, -0.025579940527677536, -0.01887044869363308, 0.06859757751226425, 0.013121950440108776, 0.0022277613170444965, 0.03994245082139969, -0.01934221014380455, -0.015480756759643555, -0.005621821153908968, 0.016450488939881325, 0.027222368866205215, 0.05028625205159187, 0.002996557392179966, 0.02870754338800907, -0.045743364840745926, 0.022644538432359695, -0.03816024214029312, -0.02788632921874523, -0.09987359493970871, -0.01981397159397602, 0.04270312562584877, -0.03155558183789253, -0.019971225410699844, 0.025510050356388092, -0.00410170154646039, 0.02301146276295185, 0.009155661799013615, -0.02720489725470543, -0.02673313580453396, 0.013785910792648792, -0.014048000797629356, -0.04504445940256119, -0.013156896457076073, 0.015865154564380646, 0.01012539304792881, -0.00943522434681654, -0.015358448028564453, -0.018451105803251266, -0.001603114535100758, -0.013951901346445084, -0.03997739404439926, -0.020495403558015823, 0.022417394444346428, 0.004778766538947821, 0.031328439712524414, -0.028445454314351082, 0.016162190586328506, 0.0032346220687031746, -0.01064083632081747, -0.0004384540079627186, 0.009155661799013615, -0.04284290596842766, 0.020373094826936722, 0.029109414666891098, 0.012816179543733597, -0.03185261785984039, 0.034560877829790115, -0.019184956327080727, 0.025055762380361557, -0.03920859843492508, 0.029773375019431114, -0.0033154329285025597, 0.018713194876909256, 0.015568120405077934, 0.03513747453689575, -0.038404855877161026, -0.01176782138645649, -0.007906368933618069, -0.03700704500079155, -0.035853851586580276, -0.00627267686650157, -0.0065566073171794415, -0.006014955695718527, 0.04252839833498001, -0.03994245082139969, 0.03934837877750397, -0.012798707000911236, -0.03005293570458889, 0.028165891766548157, -0.03040239028632641, -0.01640680618584156, 0.04141015186905861, -0.03061206080019474, -0.019883861765265465, 0.0437864288687706, -0.019097592681646347, -0.03255152329802513, -0.02820083685219288, 0.01646796055138111, 0.0009205896058119833, -0.05430495738983154, -0.042807962745428085, -0.03293592110276222, -0.02107200026512146, 0.03138085827231407, -0.009740995243191719, -0.0029266667552292347, -0.02788632921874523, 0.015454547479748726, 0.027257313951849937, -0.0017953135538846254, 0.012108538299798965, -0.005377204157412052, 0.037636060267686844, 0.013523821718990803, 0.05227813124656677, -0.027781493961811066, 0.005556298885494471, 0.038230132311582565, 0.03484043851494789, -0.00590575160458684, 0.010806825943291187, -0.0016555323963984847, 0.019184956327080727, -0.01342772226780653, 0.0052767363376915455, 0.0032346220687031746, -0.02556246891617775, 0.0023304130882024765, -0.048119645565748215, -0.011837711557745934, 0.0023544379509985447, 0.02535279653966427, -0.018503522500395775, 0.010396219789981842, -0.012947224080562592, -0.04623259976506233, 0.02629631944000721, 0.03183514624834061, -0.01297343336045742, -0.010544736869633198, 0.013471403159201145, 0.053990449756383896, -0.0006049900548532605, -0.023640478029847145, 0.04595303535461426, -0.008006836287677288, 0.0076661198399960995, -0.0189053937792778, -0.03718177229166031, -0.01817154325544834, 0.023937514051795006, 0.025405215099453926, -0.015576856210827827, 0.01265018992125988, -0.06992549449205399, 0.014642070047557354, 0.007137572392821312, -0.024601474404335022, -0.006224627140909433, 0.02362300641834736, 0.030507225543260574, -0.039523106068372726 ]
A fundamental problem in drug discovery is to design molecules that bind to specific proteins. To tackle this problem using machine learning methods, here we propose a novel and effective framework, known as GraphBP, to generate 3D molecules that bind to given proteins by placing atoms of specific types and locations to the given binding site one by one. In particular, at each step, we first employ a 3D graph neural network to obtain geometry-aware and chemically informative representations from the intermediate contextual information. Such context includes the given binding site and atoms placed in the previous steps. Second, to preserve the desirable equivariance property, we select a local reference atom according to the designed auxiliary classifiers and then construct a local spherical coordinate system. Finally, to place a new atom, we generate its atom type and relative location w.r.t. the constructed local coordinate system via a flow model. We also consider generating the variables of interest sequentially to capture the underlying dependencies among them. Experiments demonstrate that our GraphBP is effective to generate 3D molecules with binding ability to target protein binding sites. Our implementation is available at https://github.com/divelab/GraphBP.
[ -0.015676235780119896, -0.013521847315132618, -0.015168290585279465, -0.006901046726852655, 0.01531717088073492, 0.03646695241332054, 0.0017351140268146992, 0.029268143698573112, -0.039654746651649475, 0.0030345339328050613, 0.011332429014146328, 0.04182664677500725, 0.009721017442643642, -0.02534470707178116, -0.0066558318212628365, 0.018426144495606422, 0.014134884811937809, -0.025800105184316635, -0.04659082368016243, -0.06098843738436699, 0.02073817141354084, -0.07181292027235031, 0.0032162554562091827, 0.05254603922367096, 0.030371611937880516, -0.0206505935639143, 0.0012873780215159059, 0.008087711408734322, -0.058326106518507004, 0.07016647607088089, 0.03765799477696419, 0.025292159989476204, 0.018408630043268204, 0.012269500643014908, -0.046135421842336655, 0.010307781398296356, 0.004891160409897566, 0.03947959095239639, -0.025204584002494812, -0.005061935167759657, 0.018986636772751808, 0.011971739120781422, 0.012365834787487984, -0.028077101334929466, 0.013697001151740551, 0.016219211742281914, -0.0006732461624778807, -0.008057059720158577, -0.022349582985043526, -0.012654838152229786, 0.04438388720154762, -0.014923075214028358, -0.01728764735162258, -0.03450523316860199, -0.010623057372868061, 0.03755290433764458, 0.024048570543527603, 0.041861679404973984, 0.047046221792697906, 0.014327554032206535, -0.010386601090431213, -0.041126035153865814, -0.027569156140089035, -0.0034373868256807327, 0.013390482403337955, -0.01453773770481348, 0.01736646704375744, -0.04816720262169838, -0.013048933818936348, 0.019424520432949066, -0.029881181195378304, 0.00466346088796854, 0.02315528877079487, -0.02000252529978752, 0.002922873478382826, 0.013267875649034977, 0.023190319538116455, 0.061443835496902466, 0.023628203198313713, -0.06011267006397247, 0.04266738519072533, 0.006795954424887896, 0.01224322710186243, 0.03396225720643997, 0.07804838567972183, -0.022367097437381744, 0.02385590225458145, -0.047466591000556946, -0.01854875311255455, -0.015001894906163216, -0.061128560453653336, 0.031545139849185944, -0.032771214842796326, -0.01772553101181984, 0.0001387543888995424, -0.0018686685943976045, 0.04046045243740082, -0.003341052448377013, -0.04032032936811447, 0.041336219757795334, -0.012549745850265026, -0.009554621763527393, -0.021841637790203094, 0.07181292027235031, -0.02429378591477871, -0.031860414892435074, 0.028795229271054268, 0.026202958077192307, -0.008924068883061409, 0.12239724397659302, -0.039654746651649475, 0.014047307893633842, 0.012033043429255486, 0.05198555067181587, -0.06732898950576782, -0.01825099065899849, -0.09941710531711578, -0.02637811191380024, -0.051670271903276443, -0.06659334897994995, 0.0360465832054615, 0.006866015959531069, -0.04781689494848251, -0.06235463544726372, -0.03175532445311546, 0.009090464562177658, -0.0681697279214859, -0.05636438727378845, -0.023523110896348953, 0.03338425233960152, -0.059902485460042953, 0.02856753021478653, 0.03166774660348892, -0.03585391491651535, 0.00784249696880579, 0.0016891362611204386, 0.01048293523490429, 0.011201064102351665, -0.03482050821185112, 0.00757976621389389, 0.002714878646656871, -0.041861679404973984, -0.05731021612882614, -0.045925240963697433, 0.02657078020274639, -0.01307520642876625, -0.02587016671895981, 0.06309027969837189, -0.007627933751791716, 0.03667713701725006, -0.06557745486497879, 0.01043038908392191, 0.03180786967277527, 0.0029338204767555, -0.010474177077412605, 0.02939075231552124, -0.029460813850164413, -0.031632717698812485, 0.03772805631160736, -0.011962981894612312, 0.06701371818780899, -0.030459187924861908, 0.05089959874749184, 0.03583639860153198, 0.010658088140189648, 0.06547236442565918, 0.022804981097579002, 0.01048293523490429, -0.07489562034606934, 0.03734271973371506, 0.05471794307231903, 0.0023755189031362534, 0.00863068737089634, 0.043403029441833496, -0.0508645661175251, 0.0252396147698164, 0.01673591323196888, -0.024679124355316162, 0.006055931095033884, -0.01804080791771412, -0.02960093691945076, -0.0037044959608465433, 0.05177536606788635, 0.03305146098136902, 0.012961356900632381, 0.04077572748064995, 0.047046221792697906, 0.0004775668785441667, 0.04536474868655205, 0.03291133791208267, 0.045715056359767914, -0.009659714065492153, 0.06477174907922745, -0.040390390902757645, 0.0162542425096035, -0.06095340847969055, -0.04119609668850899, 0.002741151722148061, -0.022156912833452225, -0.00010180795652559027, -0.01715628243982792, -0.039339467883110046, -0.0029929347801953554, -0.005136375315487385, 0.015842631459236145, 0.037167567759752274, -0.004306585993617773, -0.029145536944270134, -0.013259117491543293, -0.02553737536072731, 0.02052798680961132, -0.008565004914999008, -0.09058937430381775, -0.0466608852148056, 0.025081977248191833, -0.02103593200445175, -0.003700117114931345, 0.005876398645341396, -0.02522210031747818, -0.005836989264935255, -0.05787070468068123, 0.06694365292787552, 0.09955722838640213, -0.023277895525097847, 0.05657457187771797, 0.019512096419930458, -0.014056066051125526, 0.021719029173254967, -0.010623057372868061, -0.009204315021634102, 0.045609962195158005, 0.07044672220945358, 0.02292758971452713, 0.015063198283314705, -0.011437521316111088, -0.0055830166675150394, -0.01585138961672783, -0.03366449475288391, -0.026290535926818848, 0.00030268708360381424, -0.013224086724221706, 0.009213072247803211, -0.018268506973981857, -0.013679485768079758, 0.05878150463104248, 0.06862512975931168, -0.030196458101272583, 0.08029034733772278, 0.0305467639118433, 0.03702744469046593, -0.02086077816784382, 0.003067375160753727, 0.020475439727306366, -0.006349313072860241, -0.04046045243740082, -0.015947723761200905, 0.00023960447288118303, -0.036642104387283325, 0.03688732162117958, -0.05724015459418297, 0.021841637790203094, 0.014905559830367565, -0.0008035165374167264, 0.027744309976696968, 0.040705665946006775, -0.030091365799307823, 0.025659983977675438, 0.018986636772751808, 0.009344437159597874, 0.05867641046643257, -0.032473452389240265, -0.07573635876178741, 0.02835734561085701, 0.03447020426392555, 0.0012786203296855092, -0.04375333711504936, 0.012987629510462284, -0.002474042819812894, 0.07538605481386185, -0.032263267785310745, -0.007387097459286451, -0.004107348620891571, 0.006922940723598003, 0.08008016645908356, -0.015466051176190376, -0.05587395653128624, -0.028007039800286293, -0.04578511789441109, -0.04722137376666069, 0.003196550766006112, -0.0233304426074028, 0.029250629246234894, -0.04000505059957504, -0.014380100183188915, 0.027901947498321533, 0.023067710921168327, -0.06298518925905228, -0.04221198707818985, 0.03052924945950508, -0.025099491700530052, -0.04354315251111984, -0.036326829344034195, -0.014292523264884949, 0.02844492346048355, 0.00018979520245920867, -0.003146194154396653, 0.007518462836742401, 0.09654459357261658, -0.04224701598286629, 0.009178041480481625, 0.06918562203645706, 0.022892558947205544, -0.016858521848917007, -0.023838387802243233, 0.0055129555985331535, 0.01846117526292801, 0.04004008322954178, -0.06704875081777573, -0.024416392669081688, -0.020808231085538864, -0.04203683137893677, -0.022980134934186935, -0.07090212404727936, 0.039864927530288696, 0.013626939617097378, 0.056434448808431625, 0.027849402278661728, 0.007811844814568758, -0.021211085841059685, -0.020790716633200645, -0.0027126893401145935, -0.041441310197114944, -0.08554495126008987, 0.01031653955578804, -0.026395628228783607, -0.03916431590914726, -0.00964219868183136, 0.03692235052585602, -0.00959840975701809, 0.021438784897327423, -0.020247740671038628, 0.006349313072860241, -0.03364698216319084, 0.0016497267642989755, 0.022349582985043526, -0.05016395449638367, 0.012829991988837719, 0.024223724380135536, 0.01787441223859787, -0.01553611271083355, 0.0009206504328176379, -0.00041407375829294324, -0.026308050379157066, 0.03450523316860199, 0.03503069281578064, -0.048097141087055206, 0.003170277690514922, -0.04105597361922264, -0.018110869452357292, 0.04641566798090935, -0.02220945991575718, -0.05475297570228577, 0.010421630926430225, 0.03968977555632591, -0.03397977352142334, 0.015658719465136528, -0.025099491700530052, 0.003605972044169903, -0.022174429148435593, 0.023523110896348953, -0.04568002372980118, 0.03608161583542824, 0.007785571739077568, 0.04126615822315216, 0.010710634291172028, 0.003700117114931345, -0.02844492346048355, 0.003093648236244917, -0.052160702645778656, 0.033629465848207474, -0.003816156182438135, 0.03475044667720795, 0.009677229449152946, -0.056434448808431625, -0.029688512906432152, 0.007360824383795261, -0.0007252448122017086, -0.026010289788246155, 0.015860145911574364, 0.018163414672017097, 0.00008100848208414391, -0.05468291416764259, -0.027358971536159515, -0.01884651370346546, 0.0034373868256807327, -0.07016647607088089, 0.045715056359767914, -0.0031921719200909138, 0.04214192554354668, -0.0004209156904835254, 0.00959840975701809, -0.0367121659219265, -0.0441737063229084, 0.014143642969429493, -0.0021806606091558933, 0.0007558966754004359, -0.018005777150392532, -0.09619428217411041, 0.03828854858875275, -0.026202958077192307, 0.01896912045776844, -0.06508702784776688, 0.00008860302477842197, -0.02385590225458145, 0.0342775322496891, -0.0008511363994330168, -0.03334921970963478, 0.018286021426320076, 0.005928944796323776, 0.013250360265374184, 0.04046045243740082, 0.025887683033943176, 0.0070674424059689045, -0.0019879918545484543, -0.03503069281578064, 0.018688874319195747, 0.01812838390469551, -0.019669733941555023, -0.022594796493649483, -0.05587395653128624, 0.05815095081925392, -0.0005867641302756965, -0.0427374467253685, -0.04259732365608215, -0.0713224932551384, 0.00669962028041482, 0.010421630926430225, -0.00028900321922264993, -0.06347561627626419, 0.002859380329027772, 0.03243842348456383, -0.010132628493010998, -0.024346331134438515, -0.019879918545484543, -0.008232212625443935, 0.013206571340560913, -0.014765437692403793, -0.012488442473113537, 0.002962283091619611, -0.033629465848207474, -0.026080351322889328, -0.0004633356584236026, -0.05209064111113548, -0.018286021426320076, 0.007877526804804802, 0.0342775322496891, -0.05576886236667633, 0.028269769623875618, 0.06473672389984131, -0.04515456408262253, -0.01083324197679758, 0.005902671720832586, -0.0017756182933226228, -0.031089739874005318, -0.013355451636016369, 0.030914587900042534, -0.024433908984065056, -0.041966769844293594, 0.018215959891676903, -0.017383981496095657, 0.03259605914354324, 0.019021667540073395, 0.026430658996105194, -0.013775819912552834, 0.015220836736261845, -0.023838387802243233, 0.0044926865957677364, -0.05198555067181587, 0.02960093691945076, 0.03772805631160736, 0.03636185824871063, 0.019967494532465935, 0.03084452636539936, -0.019109243527054787, -0.05983242392539978, -0.03117731772363186, 0.06098843738436699, -0.018286021426320076, 0.05468291416764259, 0.024363847449421883, -0.00817966740578413, 0.009011645801365376, -0.07139255106449127, 0.04459407180547714, 0.037973273545503616, -0.025257129222154617, 0.000960059929639101, 0.001540255849249661, 0.0652972161769867, 0.041231125593185425, 0.0162542425096035, -0.06736402213573456, 0.0030608067754656076, 0.028900321573019028, 0.039444562047719955, -0.012094346806406975, 0.018075838685035706, 0.014721648767590523, 0.018303537741303444, 0.0024433908984065056, -0.01734895072877407, -0.005307150073349476, -0.04939327761530876, 0.004387594293802977, -0.014231218956410885, -0.019932463765144348, -0.03086204081773758, -0.02054550126194954, -0.018093353137373924, 0.005197679158300161, 0.023207833990454674, -0.020090103149414062, -0.04095087945461273, 0.05534849688410759, -0.04928818717598915, 0.03639689087867737, 0.014458918944001198, -0.027761824429035187, 0.03417244181036949, 0.014239977113902569, 0.010141385719180107, 0.0020350643899291754, -0.0026995528023689985, -0.020352832973003387, -0.016026541590690613, -0.013013903051614761, 0.020510470494627953, -0.00672589335590601, -0.011376217938959599, 0.004619672894477844, -0.03243842348456383, 0.006038415711373091, -0.03618670627474785, 0.06515709310770035, -0.0064149959944188595, -0.004584642127156258, 0.03790321201086044, -0.02711375616490841, -0.031317438930273056, 0.03233332931995392, 0.0013913753209635615, -0.005022525787353516, 0.033944740891456604, -0.02711375616490841, 0.006918562110513449, -0.04116106405854225, 0.05103972181677818, -0.05566377192735672, -0.009151768870651722, 0.01614915020763874, 0.019266881048679352, 0.022980134934186935, -0.0314575619995594, -0.05345683917403221, -0.004238713998347521, -0.022664858028292656, 0.0014789521228522062, 0.028690138831734657, 0.026605810970067978, 0.024118632078170776, 0.021701514720916748, -0.01151634007692337, 0.008727021515369415, 0.04014517366886139, -0.007334551308304071, 0.03989996016025543, 0.044348858296871185, -0.019266881048679352, -0.006927319802343845, 0.014327554032206535, 0.02532719075679779, -0.04680100828409195, -0.01022020447999239, 0.002703931648284197, 0.001089235651306808, -0.0062135690823197365, -0.03856879472732544, -0.08253231644630432, -0.038708917796611786, -0.028830260038375854, -0.02627301961183548, 0.040600575506687164, 0.001527119311504066, -0.02492433786392212, -0.0360465832054615, -0.01980985701084137, 0.0448392890393734, 0.02814716286957264, 0.025992775335907936, -0.05293137952685356, 0.0048517510294914246, -0.007391476538032293, 0.02012513391673565, 0.008144636638462543, -0.022664858028292656, -0.02544979937374592, 0.019056696444749832, 0.013504331931471825, -0.018583783879876137, -0.016070330515503883, -0.007225080393254757, 0.02010761760175228, 0.01958215795457363, -0.019722281023859978, -0.01161267515271902, -0.006042794790118933, -0.02625550515949726, 0.008197181858122349, -0.004424814600497484, -0.03136998787522316, 0.04557493329048157, -0.04228204861283302, 0.06827481836080551, 0.0391993448138237, 0.04711628332734108, 0.009143010713160038, -0.0007706752512603998, -0.0019748553168028593, -0.007487810682505369, -0.012076831422746181, -0.01762043870985508, -0.007811844814568758, -0.09248103201389313, 0.0006245315889827907, 0.02513452246785164, -0.02357565611600876, -0.0413011871278286, 0.04462910443544388, -0.01318905595690012, 0.031002163887023926, -0.03170277923345566, 0.00291630532592535, 0.0009118927409872413, -0.01781310699880123, -0.021403754130005836, 0.011463794857263565, 0.01251471508294344, 0.009607167914509773, 0.00620481139048934, 0.02690357342362404, -0.007846875116229057, 0.014686618000268936, 0.031842902302742004, 0.0151069862768054, 0.0013629129389300942, -0.03228078410029411, -0.02867262251675129, 0.027761824429035187, 0.0074790529906749725, 0.008438018150627613, -0.000692403526045382, 0.027078725397586823, -0.02114102430641651, 0.003246907377615571, 0.006787196733057499, 0.0005443441332317889, 0.003159330692142248, 0.05646947771310806, 0.021456299349665642, 0.043613214045763016, 0.0005383232492022216, -0.03044167347252369, -0.042912598699331284, 0.021946730092167854, 0.00943201407790184, -0.006222326774150133, 0.03536348417401314, 0.01802329160273075, -0.05370205268263817, -0.032998912036418915, -0.007119988556951284, -0.014064823277294636, -0.03536348417401314, 0.004553989972919226, 0.00022085757518652827, -0.009493318386375904, -0.027761824429035187, -0.0151069862768054, -0.023715779185295105, 0.040390390902757645, 0.013040175661444664, -0.026395628228783607, 0.0066514527425169945, -0.015360958874225616, 0.0012567261001095176, 0.016744671389460564, 0.02961845137178898, -0.027043694630265236, 0.03254351392388344, -0.017024917528033257, -0.010500450618565083, -0.001474573276937008, -0.01844366081058979, -0.004860508721321821, 0.018163414672017097, 0.02544979937374592, -0.002279184525832534, -0.019669733941555023, 0.002502505201846361, -0.004203683231025934, 0.0402502678334713, 0.012593534775078297, -0.0036650863476097584, 0.015229593962430954, -0.017988260835409164, -0.01614915020763874, -0.009186799637973309, 0.0031374364625662565, 0.0236632339656353, 0.016639579087495804, -0.039654746651649475, -0.0066339378245174885, 0.007943210192024708, -0.06571757793426514, 0.007408991921693087, -0.0032666120678186417, 0.018321052193641663, 0.009221830405294895, 0.01172652468085289, -0.015579900704324245, 0.0353284552693367, -0.020790716633200645, -0.02094835415482521, 0.022051822394132614, 0.019459551200270653, -0.00081774772843346, -0.019722281023859978, 0.03982989862561226, 0.009037919342517853, -0.0370975062251091, 0.012961356900632381, -0.003516205819323659, 0.02700866386294365, -0.012339562177658081, -0.006366828456521034, 0.05566377192735672, 0.001843490288592875, 0.001077741151675582, -0.04046045243740082, 0.017699258401989937, 0.06873022019863129, -0.02322535030543804, 0.05037413910031319, -0.0011757176835089922, -0.04364824295043945, -0.000812274229247123, 0.02271740511059761, 0.024206209927797318, -0.028847776353359222, -0.008529974147677422, 0.022542251273989677, 0.02513452246785164, 0.014949348755180836, 0.04736149683594704, 0.019336942583322525, -0.008092090487480164, -0.022156912833452225, -0.00445765582844615, -0.016587033867836, -0.02835734561085701, 0.006270494312047958, 0.0030345339328050613, 0.04105597361922264, 0.020282771438360214, 0.020825747400522232, 0.004359132144600153, -0.011630190536379814, 0.012322046793997288, -0.05135499686002731, 0.06351064890623093, -0.023295411840081215, -0.02751660905778408, 0.008753294125199318, 0.023733295500278473, -0.0030717540066689253, -0.035906460136175156, 0.02262982726097107, -0.037377748638391495, -0.001345397555269301, -0.020773202180862427, 0.006401859223842621, -0.0233304426074028, 0.013749547302722931, 0.015457293950021267, 0.06659334897994995, 0.028935352340340614, 0.003708874573931098, -0.026763450354337692, -0.013224086724221706, -0.013828366063535213, 0.02229703590273857, -0.013644455000758171, 0.00515826977789402, 0.039864927530288696, -0.0203178022056818, -0.0723734125494957, -0.04088081791996956, 0.026518234983086586, 0.017436528578400612, -0.006703998893499374, 0.016972370445728302, -0.03301642835140228, 0.02898789942264557, 0.03012639656662941, 0.030389126390218735, -0.025502344593405724, -0.03291133791208267, -0.01026399340480566, 0.002732394030317664, -0.014275007881224155, -0.023470563814044, -0.024994399398565292, 0.007133124861866236, 0.001824880251660943, 0.013048933818936348, -0.02397850900888443, 0.012593534775078297, -0.010255235247313976, 0.015711266547441483, -0.006082204170525074, 0.08309280872344971, 0.006134750321507454, -0.030879557132720947, 0.042176954448223114, -0.039339467883110046, 0.04266738519072533, -0.024153662845492363, 0.0059464601799845695, 0.0013705758610740304, 0.02305019646883011, -0.02951335906982422, 0.010798211209475994, -0.05075947567820549, -0.005009389016777277, -0.012488442473113537, 0.03573130816221237, -0.002714878646656871, 0.004328479990363121, 0.022647343575954437, 0.04918309301137924, -0.029758574441075325, -0.0261504128575325, 0.001906983437947929, 0.03343679755926132, -0.01751534640789032, 0.002194891916587949, 0.04816720262169838, 0.020615562796592712, -0.00009831856732489541, -0.026973634958267212, 0.04263235256075859, 0.003093648236244917, 0.011656463146209717, -0.010526723228394985, 0.01178782805800438, -0.0203178022056818, 0.0013224086724221706, -0.027849402278661728, -0.0252396147698164, -0.004860508721321821, 0.0013935647439211607, -0.007619176059961319, -0.058641381561756134, 0.06526218354701996, 0.03510075435042381, 0.02000252529978752, 0.01470413338392973, -0.01766422763466835, -0.04869266226887703, -0.02576507441699505, 0.014966864138841629, -0.0044401404447853565, 0.006261736620217562, 0.0023295411374419928, 0.04158143326640129, 0.0012271689483895898, -0.012164408341050148, -0.023715779185295105, -0.06708377599716187, -0.02688605710864067, -0.04865763336420059, 0.011560129001736641, -0.009090464562177658, -0.004615293815732002, -0.0007071821019053459, 0.014905559830367565, 0.020510470494627953, 0.0019190252060070634, -0.0016716208774596453, 0.0249068234115839, 0.0033454312942922115, -0.03793824091553688, -0.015965238213539124, -0.01715628243982792, 0.01673591323196888, -0.025975259020924568, 0.01587766222655773, -0.031825385987758636, 0.03482050821185112, 0.016911067068576813, -0.021438784897327423, -0.02979360520839691, 0.0023886554408818483, -0.024731669574975967, 0.05033910647034645, 0.037377748638391495, 0.036957383155822754, -0.005044419784098864, 0.00964219868183136, 0.019985010847449303, -0.0006781723350286484, 0.04596026986837387, 0.00034100189805030823, 0.010693118907511234, -0.021859152242541313, -0.012330804020166397, -0.035170815885066986, 0.0677843913435936, 0.0012621997157111764, -0.004895539488643408, -0.02867262251675129, -0.011595159769058228, 0.0110434265807271, 0.029495844617486, 0.028602560982108116, -0.05079450458288193, -0.04189670830965042, -0.0391993448138237, 0.03189544752240181, 0.010719392448663712, -0.016201695427298546, 0.027341457083821297, -0.02700866386294365, 0.01877645216882229, 0.0039803627878427505, -0.02492433786392212, 0.04452401027083397, 0.08988875895738602, -0.035678762942552567, 0.012024285271763802, 0.010964606888592243, -0.012794961221516132, 0.000754254637286067, 0.009747290052473545, -0.045084502547979355, 0.013250360265374184, -0.008639444597065449, 0.03793824091553688, -0.011253610253334045, 0.002460906282067299, 0.012917567975819111, 0.04459407180547714, -0.020808231085538864, -0.01162143237888813, -0.01854875311255455, 0.0107806958258152, -0.010395358316600323, -0.016998644918203354, -0.020563017576932907, -0.014380100183188915, -0.019021667540073395, -0.029320690780878067, 0.009983747266232967, 0.06564752012491226, -0.018180929124355316, 0.014178672805428505, -0.017130009829998016, 0.021806607022881508, -0.012952598743140697, -0.007115609478205442, 0.04855254292488098, 0.005762549117207527, 0.006866015959531069, -0.0011888542212545872, -0.036326829344034195, -0.05667966231703758, -0.008048301562666893, -0.018110869452357292, -0.04753665253520012, 0.002294510370120406, 0.007514083757996559, 0.003378272522240877, -0.010167659260332584, -0.060077641159296036, -0.005267740692943335, 0.022997651249170303, 0.014686618000268936, -0.01459028385579586, 0.01958215795457363, -0.03347182646393776, 0.02138623781502247, -0.043823398649692535, -0.007938831113278866, 0.04834235832095146, 0.06785445660352707, 0.031422533094882965, 0.04396352171897888, 0.02000252529978752, -0.011008395813405514, 0.04578511789441109, -0.012146892957389355, -0.022156912833452225, -0.03937450051307678, 0.002977608935907483, -0.013364209793508053, -0.021648969501256943, -0.0458902083337307, 0.0498136468231678, 0.04462910443544388, 0.013740789145231247, 0.013732031919062138, -0.03315655142068863, -0.0032162554562091827, -0.020387863740324974 ]
Audio-based classification techniques on body sounds have long been studied to aid in the diagnosis of respiratory diseases. While most research is centered on the use of cough as the main biomarker, other body sounds also have the potential to detect respiratory diseases. Recent studies on COVID-19 have shown that breath and speech sounds, in addition to cough, correlate with the disease. Our study proposes Fused Audio Instance and Representation (FAIR) as a method for respiratory disease detection. FAIR relies on constructing a joint feature vector from various body sounds represented in waveform and spectrogram form. We conducted experiments on the use case of COVID-19 detection by combining waveform and spectrogram representation of body sounds. Our findings show that the use of self-attention to combine extracted features from cough, breath, and speech sounds leads to the best performance with an Area Under the Receiver Operating Characteristic Curve (AUC) score of 0.8658, a sensitivity of 0.8057, and a specificity of 0.7958. Compared to models trained solely on spectrograms or waveforms, the use of both representations results in an improved AUC score, demonstrating that combining spectrogram and waveform representation helps to enrich the extracted features and outperforms the models that use only one representation.
[ 0.0003958023153245449, 0.06727708131074905, -0.028199750930070877, 0.017396675422787666, 0.022779587656259537, -0.018514234572649002, -0.06276959180831909, 0.015468886122107506, -0.048613838851451874, 0.038332290947437286, -0.03501686453819275, -0.005550545174628496, 0.01003940962255001, -0.049284372478723526, -0.04667673259973526, -0.012255902402102947, -0.007222228217869997, -0.036208927631378174, 0.008446887135505676, -0.03870480880141258, 0.0022968174889683723, 0.05129598081111908, 0.008935819379985332, -0.043137796223163605, 0.014928732067346573, 0.03345227986574173, 0.029056545346975327, 0.01520812138915062, -0.07264136523008347, 0.05226453021168709, 0.06671830266714096, 0.007664595264941454, -0.023021725937724113, -0.057144541293382645, 0.002616951707750559, -0.0012933422112837434, 0.04108893498778343, 0.05978943035006523, 0.008754216134548187, -0.020861109718680382, -0.002782257506623864, 0.0005817711935378611, 0.0009702977258712053, 0.009536507539451122, -0.014891480095684528, -0.02244431897997856, -0.05226453021168709, 0.0035389382392168045, 0.006323523819446564, 0.012516666203737259, -0.012302467599511147, -0.02399027720093727, -0.014928732067346573, -0.02259332686662674, 0.020041566342115402, 0.04298878833651543, 0.060310959815979004, 0.023915773257613182, 0.05036468058824539, -0.01953866519033909, 0.026020510122179985, 0.027044938877224922, -0.013149949721992016, -0.01677270419895649, -0.03948710113763809, -0.03743824362754822, -0.004472566302865744, -0.01582277938723564, -0.0593424066901207, 0.026169518008828163, -0.035389382392168045, -0.006649478804320097, -0.014826289378106594, 0.060273706912994385, 0.02179240994155407, 0.045521922409534454, 0.030732885003089905, 0.04660223051905632, 0.0020325612276792526, 0.007189632393419743, 0.0419829823076725, 0.05207827314734459, -0.04578268527984619, 0.08120932430028915, 0.03741961717605591, 0.0021629431284964085, -0.05975218117237091, -0.06623402237892151, -0.0387420617043972, -0.006360775791108608, -0.059528667479753494, 0.017908889800310135, 0.011259411461651325, 0.01247010100632906, 0.03509136661887169, -0.015962474048137665, -0.01857011392712593, -0.005559858400374651, -0.04410634562373161, -0.05066269636154175, 0.0030988992657512426, -0.0387420617043972, -0.017554996535182, -0.049209870398044586, 0.015776215121150017, -0.007101159077137709, -0.03877931460738182, 0.03661869838833809, 0.0032083268743008375, 0.13924790918827057, -0.03622755408287048, -0.002686799271032214, -0.002350367372855544, -0.06615952402353287, -0.015375755727291107, 0.04343581199645996, -0.01434201281517744, -0.007315358147025108, -0.054089877754449844, 0.009396812878549099, 0.03164555877447128, 0.08746765553951263, -0.04432985931634903, 0.04988040402531624, 0.003296800423413515, 0.10199593007564545, 0.027734100818634033, 0.001295670517720282, -0.024642186239361763, 0.04760803282260895, 0.02868402563035488, 0.016269803047180176, -0.011734374798834324, 0.007403831463307142, 0.039971377700567245, -0.014872853644192219, -0.033806174993515015, 0.02568524144589901, 0.03134754300117493, -0.00680779991671443, 0.014071936719119549, -0.01474247220903635, 0.004451612010598183, 0.052488043904304504, 0.025349974632263184, -0.008842688985168934, -0.01170643512159586, 0.07688809186220169, 0.014043997041881084, -0.02890753746032715, -0.047906048595905304, 0.010663379915058613, 0.0280507430434227, -0.010300173424184322, -0.0023142793215811253, -0.05025292560458183, 0.059491414576768875, -0.04600619897246361, 0.028367385268211365, 0.01948278769850731, 0.030900519341230392, -0.023580504581332207, 0.018020646646618843, -0.028274254873394966, 0.05345659330487251, 0.010924143716692924, -0.036823585629463196, 0.01753637008368969, -0.0358736589550972, 0.05882088094949722, 0.03356403484940529, 0.07986824959516525, 0.015068426728248596, 0.016530567780137062, -0.05390361696481705, 0.08731864392757416, 0.0187004953622818, 0.03499823808670044, -0.058709125965833664, 0.03717747703194618, -0.050066664814949036, 0.04138695076107979, -0.008754216134548187, -0.003939397167414427, 0.06493020802736282, 0.04187122732400894, 0.07800564914941788, 0.010924143716692924, -0.025461729615926743, 0.004067450761795044, 0.014295448549091816, -0.0038695496041327715, 0.008344444446265697, 0.008679712191224098, -0.046266961842775345, 0.0002430109743727371, -0.033042509108781815, 0.004339856095612049, 0.029708456248044968, 0.015468886122107506, -0.06880441308021545, 0.0036646637599915266, 0.001798572251573205, -0.015413007698953152, -0.03719610348343849, -0.002593669341877103, 0.055579956620931625, -0.019073015078902245, -0.019985688850283623, -0.0435103140771389, -0.029782960191369057, 0.01091483049094677, -0.049396127462387085, -0.009834523312747478, 0.021419890224933624, -0.0037298547104001045, 0.022015921771526337, -0.027417458593845367, 0.0093502476811409, 0.07048074901103973, -0.018877442926168442, 0.008400321938097477, 0.030025098472833633, 0.04406909644603729, -0.0024446614552289248, 0.02412065863609314, -0.00700337253510952, -0.01662369631230831, -0.004279321525245905, 0.004588978365063667, -0.04298878833651543, 0.0006379401893354952, -0.016446750611066818, -0.012898499146103859, 0.006272302474826574, -0.05140773579478264, -0.011101090349256992, -0.03030448779463768, 0.03501686453819275, -0.02734295465052128, -0.014220944605767727, -0.0012316437205299735, -0.005094208754599094, -0.013271018862724304, 0.01206032931804657, 0.021922791376709938, -0.004996422212570906, 0.07837817072868347, 0.022891342639923096, -0.006146577186882496, -0.0167913306504488, 0.025871502235531807, -0.035519763827323914, 0.00188820983748883, -0.05774057283997536, -0.04585719108581543, 0.006579631473869085, -0.00235153129324317, 0.0016134764300659299, -0.048539333045482635, 0.06079523637890816, 0.01248872745782137, 0.011967198923230171, 0.05144498869776726, -0.005182682070881128, -0.03656281903386116, 0.0667928010225296, -0.015832092612981796, 0.03402968496084213, -0.030621130019426346, -0.01587865687906742, 0.029838837683200836, -0.05446239933371544, 0.005303751211613417, 0.04261626675724983, 0.005946347489953041, 0.03162693232297897, -0.03125441446900368, 0.04205748811364174, 0.01773194409906864, 0.013392088003456593, -0.001706606475636363, 0.05196651443839073, -0.036842212080955505, -0.03734511137008667, -0.018234845250844955, 0.010532998479902744, -0.03132891654968262, -0.05535644665360451, -0.027007687836885452, 0.006747265346348286, -0.07059250771999359, -0.041573211550712585, -0.021457141265273094, 0.025964632630348206, 0.030192730948328972, 0.032204337418079376, -0.015068426728248596, -0.024679439142346382, -0.01759224943816662, -0.03494235873222351, 0.0032502354588359594, 0.01935240440070629, 0.02734295465052128, -0.0035459231585264206, 0.012768116779625416, 0.03198082745075226, 0.04444161430001259, -0.027491962537169456, -0.055468201637268066, 0.01287987269461155, -0.004244397860020399, -0.029373187571763992, 0.012479414232075214, 0.026895930990576744, 0.03352678567171097, -0.023655008524656296, -0.08113481849431992, 0.03479335084557533, -0.0421692430973053, 0.024400047957897186, 0.031589679419994354, -0.08106031268835068, 0.08627559244632721, -0.0005005734856240451, -0.04600619897246361, 0.03112403117120266, -0.00017170835053548217, 0.07435495406389236, -0.022760961204767227, 0.007366579491645098, 0.0019568931311368942, 0.007212914992123842, -0.0034085563383996487, 0.007981237024068832, 0.0034504649229347706, -0.068320132791996, -0.008619177155196667, -0.012200023978948593, -0.005550545174628496, 0.013224453665316105, -0.021308133378624916, -0.025070583447813988, -0.026020510122179985, 0.0028940134216099977, 0.008190779946744442, 0.004090733360499144, -0.0202278271317482, -0.03503549098968506, -0.02788310870528221, 0.0010238474933430552, -0.023152107372879982, -0.0077763511799275875, 0.013559721410274506, -0.03822053223848343, -0.0025447760708630085, -0.019650420174002647, -0.058783628046512604, 0.017620187252759933, -0.0034551213029772043, 0.007352610118687153, -0.04257901757955551, -0.0021850615739822388, -0.03402968496084213, -0.06843189150094986, -0.02397165074944496, 0.017452552914619446, 0.02730570361018181, 0.02801349014043808, 0.002838135464116931, -0.02803211659193039, 0.042243748903274536, -0.01952003873884678, -0.011017274111509323, -0.013243080116808414, 0.016130108386278152, -0.028181124478578568, -0.041610464453697205, -0.010188417509198189, 0.05215277522802353, -0.04459062218666077, 0.03566877171397209, 0.024698063731193542, -0.01797408238053322, 0.0057600876316428185, 0.05464865639805794, 0.02650478482246399, 0.0216620285063982, -0.054127130657434464, 0.05956592038273811, -0.009052231907844543, -0.017685377970337868, -0.01208826806396246, -0.04179672524333, 0.04380832985043526, -0.00971345417201519, -0.0032455790787935257, 0.05543094873428345, 0.03738236427307129, 0.00048514886293560266, -0.03252097964286804, -0.013801859691739082, -0.009122079238295555, 0.007515587378293276, -0.031422048807144165, -0.009704140946269035, -0.009494598954916, -0.020637597888708115, -0.0019021793268620968, -0.005899782758206129, -0.012274527922272682, 0.009033605456352234, -0.01125009823590517, 0.027789978310465813, 0.011743687093257904, 0.017247667536139488, 0.0018719121580943465, 0.018830876797437668, -0.02408340573310852, 0.012283841148018837, -0.030844641849398613, 0.0887342244386673, 0.03266998752951622, -0.025033332407474518, -0.005331689957529306, 0.016726139932870865, 0.05315857753157616, -0.02646753378212452, 0.03445808216929436, -0.049396127462387085, -0.026244021952152252, -0.03477472439408302, 0.06053446978330612, -0.034160066395998, -0.004109359346330166, 0.035408008843660355, -0.007990550249814987, -0.004572680685669184, -0.023878520354628563, 0.03106815367937088, -0.060310959815979004, 0.033061135560274124, 0.003671648446470499, -0.04134970158338547, -0.05341934412717819, -0.056399501860141754, 0.039338093250989914, 0.0009621488861739635, 0.0072315409779548645, -0.0050103915855288506, 0.003010425716638565, 0.02864677459001541, -0.039226338267326355, 0.021568898111581802, -0.04105168581008911, 0.021885540336370468, 0.04738452285528183, -0.05107246711850166, 0.020600346848368645, -0.018421106040477753, -0.040120385587215424, 0.06299310177564621, -0.003422525944188237, 0.022220807150006294, -0.034607090055942535, 0.030732885003089905, -0.061838291585445404, -0.0593424066901207, 0.0000380886958737392, -0.028143873438239098, -0.032278843224048615, -0.02648616023361683, -0.03602266684174538, 0.011212846264243126, 0.021270882338285446, -0.030677007511258125, 0.022779587656259537, -0.04090267792344093, 0.0324464775621891, -0.0014004417462274432, 0.04116344079375267, -0.037810761481523514, -0.010728570632636547, -0.03877931460738182, 0.013056820258498192, 0.001355040818452835, -0.013271018862724304, 0.004151267930865288, -0.038555800914764404, -0.0051268041133880615, 0.04406909644603729, -0.023561878129839897, 0.021513020619750023, -0.03904007747769356, 0.0023713214322924614, -0.02343149669468403, 0.02408340573310852, 0.0033596630673855543, 0.07148655503988266, -0.00387187791056931, 0.028590897098183632, -0.01515224389731884, 0.029913341626524925, -0.017340797930955887, -0.04440436139702797, 0.053978122770786285, -0.009182613343000412, 0.015794839709997177, -0.0062583331018686295, 0.03494235873222351, 0.06053446978330612, 0.022686457261443138, 0.019706299528479576, -0.020414086058735847, -0.022798214107751846, -0.03963610902428627, -0.00012630749552045017, 0.046304214745759964, 0.020544467493891716, 0.013112697750329971, 0.008018488995730877, 0.021960044279694557, -0.004570352379232645, 0.06839463859796524, -0.050811704248189926, 0.00409771827980876, 0.009177956730127335, 0.015226747840642929, -0.010691318660974503, -0.005871843546628952, -0.03732648491859436, -0.01773194409906864, -0.016120795160531998, -0.00003621518408181146, 0.026691045612096786, -0.012768116779625416, -0.03194357454776764, 0.037792135030031204, 0.02009744383394718, -0.04403184354305267, -0.02320798486471176, -0.0035692055243998766, -0.00097087980248034, -0.008693681098520756, -0.052413538098335266, 0.019948435947299004, 0.04976864904165268, -0.060161951929330826, -0.030080975964665413, 0.04365932196378708, 0.012162772007286549, 0.0075388699769973755, -0.012768116779625416, 0.020600346848368645, -0.00013234639482107013, 0.0004575009224936366, 0.004758940543979406, 0.034551214426755905, -0.05971492826938629, -0.013252392411231995, -0.0032083268743008375, 0.011408419348299503, 0.0328189954161644, 0.00048194752889685333, 0.0009458510903641582, -0.036264803260564804, 0.01198582537472248, 0.05986393615603447, -0.012768116779625416, -0.00027313269674777985, -0.012907811440527439, -0.036804959177970886, -0.02555486001074314, -0.03043486922979355, 0.02792036160826683, 0.009955592453479767, 0.03941259905695915, -0.05531919375061989, 0.01873774640262127, 0.04682574048638344, 0.018178967759013176, 0.030062349513173103, -0.00978795811533928, 0.007487648632377386, -0.009778645820915699, -0.019724924117326736, -0.015301251783967018, -0.058001335710287094, -0.048613838851451874, 0.008465512655675411, 0.011753000319004059, 0.039189085364341736, -0.005429476499557495, -0.03503549098968506, -0.055505454540252686, -0.0005922483396716416, -0.02946631796658039, 0.0030500059947371483, 0.015385068953037262, -0.0591561496257782, -0.00505695678293705, -0.004558711312711239, 0.0328189954161644, 0.026616541668772697, -0.009201239794492722, 0.00791138969361782, 0.04824131727218628, 0.0031966858077794313, 0.021438516676425934, 0.03488648310303688, 0.05688377842307091, -0.03246510401368141, 0.021289508789777756, -0.02484707161784172, 0.029112424701452255, -0.013960180804133415, 0.054015375673770905, 0.03725198283791542, 0.004076763987541199, -0.002595997415482998, 0.05960317328572273, -0.05818759649991989, 0.021252255886793137, 0.009243148379027843, 0.04436711221933365, 0.0166982002556324, -0.03736373782157898, -0.04436711221933365, -0.0034644342958927155, 0.018877442926168442, -0.02251882292330265, -0.02961532585322857, -0.010020783171057701, -0.018234845250844955, 0.028535017743706703, -0.014034684747457504, 0.026709672063589096, 0.039263591170310974, 0.06511646509170532, -0.015832092612981796, -0.01395086757838726, 0.024362796917557716, -0.020786605775356293, 0.02099149115383625, -0.005392224527895451, 0.04581993818283081, -0.042318250983953476, 0.012451475486159325, 0.012023077346384525, 0.018821563571691513, -0.001328265992924571, 0.002668173285201192, 0.014751785434782505, 0.04328680410981178, -0.01940828189253807, 0.018234845250844955, 0.061093252152204514, 0.009555133059620857, -0.019557291641831398, -0.013736668042838573, 0.05613873898983002, 0.013010255061089993, 0.02577837184071541, -0.02629989944398403, -0.009843836538493633, 0.0029894716572016478, -0.01597178727388382, 0.01597178727388382, -0.001509869354777038, 0.03393655642867088, 0.028497766703367233, -0.037680380046367645, -0.04496314376592636, -0.02402752824127674, 0.015087053179740906, -0.05375460907816887, 0.007673908490687609, 0.023506000638008118, -0.011576053686439991, -0.047012001276016235, -0.04038114845752716, -0.012991628609597683, -0.05882088094949722, 0.012460787780582905, 0.0032618767581880093, 0.0032711897511035204, 0.057144541293382645, 0.021978668868541718, 0.005308407358825207, -0.0061698597855865955, -0.01016979105770588, -0.00024519371800124645, 0.0032595484517514706, -0.016800643876194954, -0.005913752131164074, 0.036059919744729996, -0.035426635295152664, 0.01479834970086813, 0.011911321431398392, -0.006030164659023285, -0.04213199391961098, 0.0004225771699566394, 0.01748049259185791, -0.019222022965550423, 0.019836680963635445, -0.004160580690950155, -0.009150017984211445, 0.00034428981598466635, -0.007715817075222731, -0.01667957566678524, -0.0033689760603010654, 0.0025890127290040255, 0.0006088371155783534, 0.007990550249814987, 0.024493178352713585, 0.015887970104813576, 0.0036111141089349985, 0.017201103270053864, -0.052562545984983444, 0.01441651675850153, -0.0011804221430793405, 0.009410781785845757, -0.037754885852336884, -0.01090551819652319, 0.01658644527196884, 0.033154264092445374, -0.008609864860773087, 0.013271018862724304, -0.0025238217785954475, 0.022109052166342735, 0.04559642821550369, -0.04578268527984619, -0.024455927312374115, -0.0019906528759747744, -0.008237344212830067, 0.019222022965550423, -0.005042986944317818, 0.05882088094949722, 0.04179672524333, 0.028292881324887276, 0.006658792030066252, -0.014081249013543129, 0.0265234112739563, -0.023152107372879982, 0.000720593030564487, 0.030546626076102257, -0.01627911627292633, 0.045559175312519073, 0.005452759098261595, -0.010439868085086346, 0.014276822097599506, -0.014183692634105682, 0.026597915217280388, -0.03341502696275711, -0.014481708407402039, -0.0047193607315421104, -0.017508432269096375, -0.010486433282494545, -0.04902360960841179, -0.00008483557030558586, 0.013839111663401127, -0.024549055844545364, -0.0003701915848068893, 0.016549192368984222, 0.04533566161990166, -0.023114854469895363, -0.08083680272102356, 0.0020174277015030384, 0.008037115447223186, -0.028386009857058525, 0.025275470688939095, 0.004225771874189377, 0.05975218117237091, -0.03274449333548546, 0.0018707480048760772, -0.02015332318842411, 0.020414086058735847, -0.027454711496829987, 0.030751511454582214, -0.00681245606392622, 0.0028660744428634644, 0.03173868730664253, -0.03499823808670044, 0.014351326040923595, -0.006607570219784975, -0.010989334434270859, -0.040083132684230804, -0.04667673259973526, -0.008055740967392921, 0.04608070105314255, 0.022351188585162163, -0.0018358242232352495, 0.002877715742215514, -0.026560664176940918, 0.042355503886938095, 0.01093345694243908, -0.016167359426617622, 0.026989061385393143, -0.03959885612130165, -0.01816965453326702, 0.013438652269542217, -0.014556212350726128, -0.0007962611271068454, 0.017908889800310135, 0.016120795160531998, -0.019631795585155487, -0.03166418522596359, -0.014993922784924507, 0.00719428900629282, -0.01004872191697359, 0.004386420827358961, 0.011957886628806591, 0.033005256205797195, -0.010411929339170456, -0.0097320806235075, -0.00007090245344443247, -0.05997569113969803, 0.059528667479753494, -0.04526115953922272, -0.04060466215014458, -0.029820211231708527, -0.025890126824378967, -0.008037115447223186, -0.03952435404062271, -0.02097286656498909, -0.019277900457382202, 0.020525842905044556, 0.02033958211541176, 0.04581993818283081, 0.03021135739982128, 0.012432849034667015, -0.01740598864853382, -0.012516666203737259, -0.026113640516996384, -0.008744902908802032, 0.03576190397143364, 0.05226453021168709, 0.033862050622701645, 0.008037115447223186, 0.05602698028087616, -0.005038330797106028, 0.021233629435300827, -0.032241590321063995, -0.0025145087856799364, -0.009825210087001324, -0.0017322171479463577, 0.011520175263285637, -0.02259332686662674, -0.015711024403572083, -0.04220649600028992, 0.010188417509198189, -0.034551214426755905, 0.004279321525245905, 0.00002299145853612572, 0.04254176467657089, 0.0009318816009908915, 0.02413928508758545, -0.037028469145298004, 0.029969219118356705, -0.010421241633594036, 0.05423888564109802, -0.022220807150006294, -0.028497766703367233, 0.023561878129839897, 0.011305976659059525, -0.007543526589870453, -0.006533066276460886, -0.039300840348005295, -0.048502080142498016, -0.0715610608458519, -0.025908753275871277, -0.002859089756384492, 0.0035505795385688543, 0.009424751624464989, 0.008032458834350109, -0.020767979323863983, -0.024604935199022293, 0.009909027256071568, -0.005285125225782394, -0.0010942770168185234, 0.021215004846453667, 0.04183397442102432, 0.036078546196222305, -0.021196378394961357, 0.08456200361251831, -0.033135637640953064, -0.023114854469895363, 0.008493452332913876, 0.04533566161990166, -0.0280507430434227, -0.02941044047474861, 0.027585092931985855, 0.043063290417194366, -0.025070583447813988, 0.05211552232503891, 0.0080138323828578, 0.0006524917553178966, 0.028609521687030792, -0.009834523312747478, -0.03022998385131359, 0.010179104283452034, -0.03110540471971035, -0.02967120334506035, -0.07267861813306808, 0.0010977693600580096, 0.03423457220196724, 0.029205555096268654, -0.023878520354628563, -0.006658792030066252, -0.0072315409779548645, -0.040120385587215424, -0.05453690141439438, -0.0038369542453438044, 0.05587797239422798, 0.014509647153317928, 0.0059510041028261185, 0.020022939890623093, 0.04894910380244255, 0.025014705955982208, 0.050103917717933655, 0.017284920439124107, 0.013652851805090904, -0.017722630873322487, 0.02726845070719719, -0.006137263961136341, -0.012693612836301327, -0.0016367590287700295, 0.032316096127033234, 0.0057600876316428185, -0.017303545027971268, 0.02246294543147087, 0.03896557539701462, 0.01722904108464718, -0.033005256205797195, 0.02944769151508808, 0.015217434614896774, -0.012963689863681793, -0.012051016092300415, 0.020749354735016823, -0.032912127673625946, -0.002051187213510275, 0.04447886720299721, -0.02399027720093727, 0.0011507370509207249, 0.012339719571173191, -0.024493178352713585, 0.06265783309936523, -0.0265234112739563, -0.03512861952185631, 0.02724982425570488, -0.029224179685115814, -0.029950594529509544, 0.016614384949207306, -0.004747299477458, -0.005187338683754206, 0.0014935716753825545, -0.032260216772556305, -0.0007054593879729509, 0.04593169316649437, 0.02633715234696865, -0.027771353721618652, -0.006882303860038519, -0.030732885003089905, 0.007394518703222275, -0.036134421825408936, -0.013485217466950417, 0.006384058389812708, -0.031403422355651855, 0.010980022139847279, -0.009927653707563877, 0.01392292883247137, -0.03825778514146805, -0.020693475380539894, -0.0003652440500445664, -0.010626127943396568, -0.00965757668018341, -0.002465615514665842, -0.04373382776975632, -0.02646753378212452, -0.005122147500514984, -0.02179240994155407, -0.014500333927571774, 0.04719826206564903, -0.027436085045337677, 0.010318798944354057, -0.02257470041513443, 0.008763528428971767, -0.019557291641831398, -0.055542707443237305, 0.025219591334462166, -0.004768253769725561, 0.025070583447813988, -0.010672693140804768, -0.0009027785272337496, -0.02415790967643261, 0.01589728333055973, -0.012134833261370659, -0.026895930990576744, 0.003639053087681532, 0.00580199621617794, 0.0326327383518219, -0.029149675741791725, 0.033862050622701645, 0.05502117797732353, -0.06377539038658142, 0.03948710113763809, 0.044739630073308945, 0.008242000825703144, -0.03430907428264618, 0.042281001806259155, 0.012581856921315193, -0.013699416071176529, 0.0019010151736438274, -0.01392292883247137, 0.04257901757955551, 0.005923065356910229, -0.017359424382448196, -0.02553623355925083, 0.04488863795995712, -0.02549898251891136, 0.005983599461615086, -0.0543878935277462, 0.04451612010598183, 0.027659596875309944 ]
Full-precision deep learning models are typically too large or costly to deploy on edge devices. To accommodate to the limited hardware resources, models are adapted to the edge using various edge-adaptation techniques, such as quantization and pruning. While such techniques may have a negligible impact on top-line accuracy, the adapted models exhibit subtle differences in output compared to the original model from which they are derived. In this paper, we introduce a new evasive attack, DIVA, that exploits these differences in edge adaptation, by adding adversarial noise to input data that maximizes the output difference between the original and adapted model. Such an attack is particularly dangerous, because the malicious input will trick the adapted model running on the edge, but will be virtually undetectable by the original model, which typically serves as the authoritative model version, used for validation, debugging and retraining. We compare DIVA to a state-of-the-art attack, PGD, and show that DIVA is only 1.7-3.6% worse on attacking the adapted model but 1.9-4.2 times more likely not to be detected by the the original model under a whitebox and semi-blackbox setting, compared to PGD.
[ -0.030287668108940125, -0.030362917110323906, -0.028368821367621422, -0.008728868328034878, 0.009391998872160912, 0.050002869218587875, -0.04688004031777382, 0.02129542827606201, -0.014325502328574657, 0.019940948113799095, -0.013742323964834213, -0.04157499596476555, 0.01473937090486288, -0.047707777470350266, -0.03038172796368599, 0.0053473724983632565, -0.012952210381627083, -0.03692837804555893, 0.026487600058317184, -0.06324666738510132, 0.010233845561742783, -0.020486503839492798, -0.05466829985380173, 0.015350768342614174, 0.014560654759407043, 0.06719723343849182, 0.0025866797659546137, 0.0039058863185346127, -0.02613016776740551, 0.02671334706246853, 0.005394402891397476, 0.019809262827038765, -0.011080395430326462, -0.014504218474030495, -0.014353720471262932, 0.03371148928999901, -0.004162202589213848, 0.042741354554891586, -0.011720010079443455, 0.04560081288218498, -0.019122617319226265, -0.07088442891836166, -0.03465210273861885, 0.022762781009078026, 0.00025293612270615995, -0.006960520055145025, -0.026412351056933403, -0.02127661556005478, -0.018943902105093002, 0.012256158515810966, -0.016507718712091446, -0.05647427216172218, -0.009307343512773514, 0.04721866175532341, -0.017702294513583183, 0.05207221210002899, 0.01789041794836521, -0.02338358387351036, 0.055571284145116806, -0.004775951150804758, 0.009678885340690613, -0.00733206095173955, -0.02050531469285488, 0.03446397930383682, -0.012801713310182095, 0.018699342384934425, 0.050529610365629196, 0.008103362284600735, 0.0015167349483817816, 0.023665767163038254, 0.002683092374354601, -0.04917513206601143, -0.02430538274347782, -0.014043319039046764, -0.00893580261617899, -0.0556841604411602, 0.0020328951068222523, 0.038282860070466995, -0.015077991411089897, -0.03222532570362091, -0.023421209305524826, 0.04070963338017464, -0.04710578918457031, -0.017881011590361595, 0.03897891193628311, -0.0031980767380446196, -0.003698952030390501, -0.06241893023252487, 0.03194314241409302, -0.06576750427484512, -0.05297520011663437, -0.05233558267354965, -0.00020443586981855333, -0.03702244162559509, -0.004521986469626427, 0.056737642735242844, -0.04774540290236473, -0.03175501897931099, -0.08743917942047119, -0.048422642052173615, -0.0163666270673275, 0.00855015218257904, 0.027804454788565636, 0.035461027175188065, -0.010403155349195004, -0.04906225949525833, -0.05572178214788437, 0.06437540054321289, 0.0019564705435186625, 0.16780497133731842, 0.01898152567446232, 0.05527029186487198, 0.0029817360918968916, 0.02665690891444683, -0.014071537181735039, 0.03198076784610748, -0.037436310201883316, -0.07137354463338852, 0.011371984146535397, -0.05064248666167259, -0.002763044089078903, 0.02338358387351036, 0.028067825362086296, 0.05323857069015503, -0.039054159075021744, 0.032770879566669464, 0.026355914771556854, 0.0003280380042269826, 0.01715674065053463, 0.024738064035773277, 0.0003950565296690911, 0.0025537582114338875, 0.013121520169079304, -0.006546651013195515, 0.025133119896054268, -0.019959760829806328, 0.006048127543181181, 0.0061421883292496204, -0.004919394385069609, 0.02810545079410076, 0.06253180652856827, -0.023458832874894142, -0.003468502312898636, 0.014513624832034111, -0.03540458902716637, 0.015350768342614174, 0.03790661320090294, 0.054329678416252136, -0.023364771157503128, 0.02599848248064518, -0.04812164977192879, 0.028914375230669975, 0.011644762009382248, 0.03766205534338951, 0.062042687088251114, 0.05259895697236061, 0.05395343527197838, -0.0037530369590967894, 0.011955163441598415, -0.059822846204042435, 0.03472734987735748, -0.038677915930747986, 0.02547173947095871, 0.017627045512199402, -0.014560654759407043, 0.04022051766514778, 0.07464687526226044, 0.003931752871721983, -0.004458494950085878, 0.05241083353757858, 0.026092544198036194, 0.0036095939576625824, -0.0056295557878911495, -0.01165416743606329, -0.02665690891444683, 0.025565801188349724, 0.029497554525732994, -0.03181145712733269, -0.03615707904100418, -0.005770646966993809, -0.07916180044412613, 0.014127974398434162, 0.009876413270831108, -0.044697824865579605, 0.0231202132999897, 0.009363780729472637, 0.03779374063014984, -0.0021951503586024046, 0.021765733137726784, -0.021238991990685463, 0.020467691123485565, -0.00030599243473261595, 0.02724008820950985, -0.03924228250980377, 0.015538889914751053, -0.05925847962498665, 0.003560211742296815, -0.028406444936990738, 0.06682099401950836, 0.001373291714116931, -0.0008971075294539332, -0.03371148928999901, -0.026750970631837845, 0.020072633400559425, 0.035724397748708725, 0.007143938913941383, 0.009420217014849186, -0.021765733137726784, 0.02945992909371853, -0.056022778153419495, -0.014748777262866497, -0.0022856842260807753, -0.03920465707778931, 0.02069343812763691, 0.0003897655988112092, 0.006245655473321676, -0.029986672103405, -0.025057870894670486, -0.019959760829806328, -0.01802210323512554, -0.011400203220546246, 0.026374725624918938, -0.024719251319766045, -0.012557153590023518, -0.07728058099746704, 0.01045018620789051, -0.027917327359318733, 0.04289185255765915, -0.026826219633221626, 0.028331197798252106, -0.036646194756031036, -0.04232748597860336, 0.05959710106253624, 0.009100409224629402, 0.042214613407850266, -0.021784545853734016, -0.00043591432040557265, 0.012858149595558643, -0.01696861907839775, 0.0029723301995545626, -0.04977712407708168, -0.03564915060997009, -0.02193504385650158, -0.058054499328136444, 0.023421209305524826, -0.004623102024197578, 0.02594204619526863, 0.05692576617002487, -0.01359182596206665, 0.025641050189733505, 0.014184410683810711, -0.015830479562282562, -0.03465210273861885, 0.030663911253213882, -0.048234522342681885, 0.002906487323343754, 0.013450734317302704, 0.004705405328422785, 0.0055307913571596146, -0.03830167278647423, 0.06576750427484512, 0.012237346731126308, -0.03566795960068703, 0.07637759298086166, -0.02528361789882183, 0.024587566033005714, 0.024117261171340942, -0.005930550862103701, 0.004557259380817413, 0.01939539425075054, -0.027146026492118835, -0.004674835596233606, -0.07652809470891953, -0.04040864109992981, -0.0076095410622656345, 0.008465496823191643, 0.030475789681077003, 0.01313092652708292, 0.041349250823259354, -0.016564156860113144, 0.020937995985150337, -0.005850599147379398, 0.03818879649043083, 0.0036119455471634865, 0.03211245313286781, -0.02037362940609455, -0.006711258087307215, 0.016451282426714897, -0.046992916613817215, -0.014720559120178223, -0.018407752737402916, 0.01303686574101448, -0.013836384750902653, -0.0072003756649792194, 0.06742297857999802, -0.04387008771300316, -0.019734013825654984, -0.05876936390995979, 0.05241083353757858, -0.047256287187337875, -0.07299140095710754, -0.045676060020923615, 0.06358528882265091, 0.01800329051911831, 0.005093407351523638, 0.001055835629813373, -0.01215269137173891, 0.06584275513887405, -0.004761842079460621, -0.04259085655212402, 0.014786401763558388, 0.0032780286855995655, -0.024850936606526375, -0.05944660305976868, -0.05244845896959305, -0.023270711302757263, -0.004526689648628235, -0.013742323964834213, -0.008625401183962822, -0.009015754796564579, -0.01008334755897522, -0.00040652023744769394, -0.051695968955755234, 0.026901468634605408, 0.0628328025341034, -0.012369032017886639, 0.003816528245806694, -0.01823844388127327, -0.07269040495157242, -0.006283279974013567, -0.07871031016111374, -0.06110207736492157, -0.06877746433019638, -0.024474693462252617, 0.00277480180375278, 0.05128210037946701, -0.05263657867908478, -0.0010323203168809414, 0.01549185998737812, -0.008686540648341179, -0.016084443777799606, 0.018097352236509323, -0.00894991122186184, 0.0041198753751814365, -0.050717733800411224, -0.024587566033005714, -0.0636981651186943, -0.037229374051094055, -0.028519319370388985, 0.025659862905740738, 0.0010376112768426538, 0.039656151086091995, 0.0016331354854628444, 0.010854648426175117, 0.004143390338867903, -0.024192510172724724, 0.009867006912827492, -0.017805762588977814, 0.007063987199217081, -0.03295900300145149, 0.026995530351996422, -0.026807406917214394, 0.007769444957375526, 0.020524127408862114, -0.037492744624614716, -0.0790865570306778, -0.006377341225743294, -0.04225223511457443, -0.04721866175532341, 0.06659524142742157, -0.023797452449798584, 0.052222710102796555, -0.019489455968141556, 0.024343008175492287, -0.019696390256285667, -0.04277897998690605, 0.014316095970571041, -0.057866375893354416, -0.041236378252506256, 0.06625662744045258, -0.04631567373871803, 0.035009533166885376, -0.012632402591407299, 0.007054580841213465, 0.05297520011663437, 0.035254091024398804, -0.008098659105598927, -0.027785642072558403, 0.015473047271370888, 0.03117184154689312, 0.032319385558366776, -0.051583096385002136, -0.037699680775403976, -0.002683092374354601, 0.053539566695690155, -0.015369580127298832, -0.021652860566973686, -0.038470979779958725, 0.02534005418419838, -0.043192848563194275, -0.042666103690862656, 0.03647688776254654, 0.0010041020577773452, 0.016978025436401367, 0.008122174069285393, 0.02744702249765396, -0.0009453138336539268, -0.01810675859451294, 0.011165049858391285, -0.023552894592285156, 0.015999790281057358, -0.03502834588289261, -0.049476128071546555, 0.009302640333771706, 0.011155644431710243, 0.02882031537592411, -0.0038071221206337214, -0.007219187915325165, -0.015134427696466446, 0.00022354203974828124, 0.020486503839492798, 0.03711650148034096, 0.04736915975809097, 0.021427113562822342, -0.004329161252826452, 0.01752357929944992, -0.050002869218587875, 0.002271575154736638, 0.061064451932907104, 0.06456352770328522, 0.012632402591407299, -0.028143074363470078, 0.030607474967837334, -0.050303865224123, -0.03935515508055687, -0.008832335472106934, 0.0197152029722929, 0.024869749322533607, -0.043380968272686005, 0.025227181613445282, 0.004016408231109381, -0.02140830084681511, 0.009514277800917625, 0.006800616160035133, -0.06478927284479141, -0.05658714473247528, -0.001920021721161902, -0.011014552786946297, -0.020994432270526886, -0.0029723301995545626, -0.10166121274232864, 0.024907372891902924, -0.04688004031777382, -0.0667833685874939, 0.07024481147527695, 0.004152796696871519, -0.01430669054389, -0.02214197814464569, 0.04988999664783478, -0.039392780512571335, -0.0005664240452460945, 0.037812553346157074, 0.00762835331261158, -0.0020622890442609787, 0.03544221445918083, 0.046729542315006256, -0.03491547331213951, -0.05165834352374077, -0.017692888155579567, 0.0586564876139164, -0.0006302092224359512, -0.02835000865161419, -0.0015649412525817752, 0.03540458902716637, 0.017476549372076988, 0.030626287683844566, -0.04883651062846184, -0.06994381546974182, 0.01202100608497858, -0.035329341888427734, 0.04477307200431824, 0.05372769013047218, -0.008056331425905228, -0.023101400583982468, -0.002882972126826644, 0.0012051576049998403, 0.026732157915830612, -0.0395432785153389, -0.03988189622759819, -0.042402733117341995, 0.005469651892781258, -0.015087396837770939, 0.03433229401707649, -0.011080395430326462, -0.018407752737402916, -0.0640367791056633, -0.011277923360466957, 0.008286780677735806, 0.08217176049947739, 0.08826691657304764, 0.006537245120853186, -0.02409844845533371, -0.014889868907630444, 0.010271470062434673, 0.028331197798252106, -0.041612621396780014, -0.012622997164726257, 0.010817023925483227, 0.08217176049947739, 0.0176834836602211, 0.009495466016232967, -0.010610089637339115, -0.0008741801721043885, -0.043192848563194275, 0.00707339309155941, 0.004620750434696674, -0.018351316452026367, 0.03000548481941223, -0.0070922053419053555, 0.046466171741485596, 0.016780495643615723, -0.013140332885086536, -0.013620044104754925, 0.006240952759981155, -0.023007340729236603, 0.1032414436340332, 0.041612621396780014, -0.02116374298930168, 0.005526088178157806, 0.01283933687955141, 0.0065231360495090485, 0.023590518161654472, -0.006193921901285648, 0.023741016164422035, 0.004477307200431824, 0.01109920721501112, -0.014560654759407043, -0.011409608647227287, -0.01765526458621025, 0.006546651013195515, -0.031190654262900352, 0.011381390504539013, -0.0016107959672808647, 0.0006901731831021607, 0.021107306703925133, 0.032451070845127106, 0.0000746977239032276, -0.04616517573595047, 0.00094766536494717, 0.04387008771300316, 0.039392780512571335, -0.03732343763113022, -0.01689337007701397, -0.0016343112802132964, -0.030833221971988678, 0.0005099874106235802, 0.0020716951694339514, 0.005422621034085751, -0.006762991659343243, -0.036194704473018646, 0.008352624252438545, 0.0033438713289797306, 0.053012825548648834, -0.009006348438560963, -0.026092544198036194, -0.06354766339063644, -0.0035578603856265545, 0.05606040358543396, 0.0028594566974788904, -0.013544795103371143, -0.01939539425075054, -0.026769783347845078, -0.05617327615618706, -0.012500717304646969, 0.035329341888427734, -0.03920465707778931, 0.002960572484880686, -0.024324195459485054, 0.03563033789396286, 0.032056014984846115, -0.005441433284431696, -0.009217985905706882, -0.0312470905482769, 0.02848169393837452, -0.0035508056171238422, -0.0224617850035429, -0.03143521398305893, -0.01063830778002739, -0.032733254134655, -0.02428657002747059, 0.014908680692315102, 0.06098920479416847, 0.007684790063649416, 0.012566559948027134, 0.013055677525699139, 0.014353720471262932, 0.017504766583442688, 0.025509364902973175, 0.02644997462630272, 0.0011787029216066003, -0.004014056641608477, -0.013930445536971092, 0.04040864109992981, 0.07408250868320465, -0.02797376550734043, 0.03438873216509819, 0.006574869621545076, -0.004317403305321932, -0.019179053604602814, -0.013864602893590927, 0.0628328025341034, 0.0010476052993908525, 0.06520313769578934, -0.03732343763113022, 0.02443706803023815, 0.0325639471411705, 0.02383507788181305, 0.0059822844341397285, -0.0015567108057439327, -0.0009799988474696875, 0.02972330152988434, -0.04970187321305275, 0.05767825245857239, 0.033749114722013474, -0.000146676495205611, 0.024079635739326477, -0.01879340410232544, -0.00866772886365652, -0.018511220812797546, 0.007096908520907164, -0.024926185607910156, -0.0033744412939995527, -0.035931333899497986, 0.01109920721501112, 0.001615499029867351, 0.029967859387397766, 0.04729390889406204, 0.011550700291991234, -0.028989624232053757, -0.01662999950349331, 0.012162097729742527, 0.009095706045627594, 0.013337860815227032, -0.011729416437447071, -0.012604184448719025, -0.0011957514798268676, 0.053012825548648834, 0.005469651892781258, 0.03534815460443497, 0.060537710785865784, -0.03173620626330376, 0.022743968293070793, 0.003080500289797783, 0.027860891073942184, -0.013366078957915306, 0.00003077193468925543, 0.034746162593364716, -0.00884174183011055, 0.005610743537545204, 0.04138687625527382, 0.04428395628929138, -0.039994772523641586, -0.008216234855353832, 0.011118019931018353, 0.0010352598037570715, -0.06388628482818604, 0.0640367791056633, -0.01733545772731304, -0.007727117743343115, 0.06843884289264679, -0.0007519007776863873, -0.022969715297222137, -0.029046060517430305, 0.017627045512199402, 0.053802937269210815, -0.0059728785417973995, 0.05011574178934097, 0.001240430516190827, 0.005234498996287584, -0.019019149243831635, -0.006715961266309023, 0.02298852801322937, -0.006236249580979347, 0.01601860113441944, -0.011400203220546246, -0.0258103609085083, 0.02129542827606201, 0.004707756917923689, -0.04127399995923042, -0.0001260271528735757, 0.00830089021474123, -0.0019940948113799095, 0.01863349974155426, 0.02330833487212658, 0.003386198775842786, 0.0059164417907595634, 0.0034496900625526905, -0.012425468303263187, 0.0009023984894156456, 0.031867895275354385, 0.004489065147936344, 0.008277375251054764, -0.06441302597522736, 0.0326768197119236, 0.01889687031507492, -0.018360722810029984, 0.005737725645303726, -0.021991480141878128, -0.019414206966757774, 0.016930993646383286, 0.001027617254294455, 0.05519504100084305, 0.029648052528500557, 0.03882841393351555, 0.05764063075184822, -0.0003762443084269762, 0.03156689926981926, -0.002471454907208681, -0.01723198965191841, 0.025189556181430817, 0.037549182772636414, 0.022518223151564598, 0.004815927240997553, -0.05715151131153107, -0.02148354984819889, 0.026619285345077515, -0.0046254536136984825, 0.019677577540278435, -0.007976379245519638, 0.0012263213284313679, 0.013177957385778427, -0.03122827783226967, -0.025039060041308403, 0.00022383597388397902, 0.014156192541122437, -0.007275624666363001, 0.023402396589517593, 0.024343008175492287, 0.06475164741277695, -0.0014426617417484522, 0.03194314241409302, -0.055119793862104416, 0.012942804023623466, 0.01733545772731304, 0.00028188928263261914, 0.014033912681043148, 0.016216130927205086, 0.010563058778643608, -0.014786401763558388, 0.03489666059613228, 0.023477645590901375, -0.003216888988390565, 0.026995530351996422, -0.039317529648542404, -0.02101324498653412, -0.012923992238938808, 0.02882031537592411, 0.0013638855889439583, 0.02797376550734043, -0.01244428101927042, -0.01489927526563406, 0.02122017927467823, -0.01529433112591505, -0.019527079537510872, 0.07167454063892365, -0.007854100316762924, -0.0002307435788679868, 0.014748777262866497, 0.015557702630758286, 0.005850599147379398, -0.010929897427558899, 0.019790450111031532, 0.006673633586615324, -0.0027912624645978212, -0.029760925099253654, -0.013986882753670216, 0.023985575884580612, -0.04616517573595047, -0.015303737483918667, 0.002229247475042939, -0.05391580983996391, -0.003668382065370679, 0.005267420317977667, -0.006946410518139601, -0.032056014984846115, 0.009297938086092472, 0.02325189858675003, -0.02697671763598919, 0.005159249994903803, 0.006259765010327101, -0.02122017927467823, 0.0034214716870337725, 0.019357770681381226, -0.006791209802031517, 0.03549865260720253, 0.010563058778643608, -0.022029105573892593, 0.021126117557287216, 0.026374725624918938, -0.0557970330119133, 0.06715960800647736, -0.02607373148202896, -0.020448878407478333, -0.038677915930747986, -0.04710578918457031, -0.030795596539974213, 0.011945757083594799, 0.0005802392843179405, -0.001040550647303462, -0.024211321026086807, 0.04846026748418808, -0.016028007492423058, -0.01447600033134222, 0.010647714138031006, -0.012519530020654202, -0.02127661556005478, 0.01430669054389, 0.013488358817994595, -0.0006619548657909036, -0.03734224662184715, -0.007477855775505304, 0.016686435788869858, 0.013431922532618046, -0.015021554194390774, 0.01008334755897522, -0.06509026885032654, -0.002871214412152767, -0.015830479562282562, 0.013497765175998211, 0.0010899327462539077, -0.010205627419054508, 0.007760039065033197, -0.0024855639785528183, 0.047971151769161224, -0.026167791336774826, 0.023327147588133812, -0.052222710102796555, 0.023722203448414803, -0.013253206387162209, -0.00643377797678113, 0.014635903760790825, 0.03640163689851761, -0.010280875489115715, -0.044697824865579605, 0.03222532570362091, -0.03484022244811058, -0.0028594566974788904, 0.0008694771095179021, -0.011663573794066906, -0.024079635739326477, 0.013478952459990978, -0.01680871471762657, 0.015077991411089897, -0.002164580626413226, -0.009203876368701458, -0.00045707804383710027, 0.0015696441987529397, -0.006071642506867647, -0.02494499832391739, -0.04477307200431824, -0.012679433450102806, 0.028199510648846626, 0.02238653600215912, -0.013779948465526104, 0.03764324262738228, -0.012980428524315357, 0.022160790860652924, -0.029102498665452003, 0.01984688825905323, -0.05692576617002487, -0.0023950301110744476, -0.016507718712091446, 0.010732369497418404, 0.07923705130815506, 0.018972119316458702, 0.019677577540278435, 0.03438873216509819, -0.004707756917923689, -0.0007695371750742197, -0.019564704969525337, -0.008465496823191643, 0.03719175234436989, 0.014457187615334988, -0.0009382592397741973, 0.025114307180047035, 0.010722963139414787, 0.00864421296864748, -0.04232748597860336, -0.036646194756031036, 0.0259232334792614, -0.015482453629374504, 0.020147882401943207, -0.0018083242466673255, 0.03158571198582649, 0.032262951135635376, -0.024907372891902924, -0.011814071796834469, 0.013328454457223415, -0.01554829627275467, 0.006208031438291073, 0.020674625411629677, -0.01309330202639103, -0.004524338059127331, -0.0038870740681886673, -0.011842289939522743, 0.05775350332260132, 0.021521175280213356, -0.03344811871647835, 0.005648367572575808, -0.0029817360918968916, -0.006734773050993681, -0.010976928286254406, -0.02945992909371853, -0.01240665651857853, 0.06294567137956619, -0.030607474967837334, 0.0006302092224359512, -0.01678990200161934, 0.037887804210186005, -0.00031334097729995847, -0.0019799857400357723, 0.05113160237669945, -0.026148980483412743, 0.035197656601667404, 0.01392104011029005, -0.0014050373574718833, 0.0013239097315818071, 0.05267420411109924, 0.009349671192467213, 0.038677915930747986, -0.018614687025547028, 0.03357980400323868, 0.016479501500725746, 0.009246204048395157, 0.028199510648846626, 0.010233845561742783, -0.041424497961997986, 0.01087346114218235, -0.05120685324072838, -0.0019164944533258677, -0.0065419478341937065, -0.00906748790293932, 0.0014167949557304382, 0.007915239781141281, 0.030833221971988678, -0.05737725645303726, 0.02742820978164673, -0.004989940207451582, -0.022875653579831123, 0.018727561458945274, -0.007186266593635082, -0.0013156792847439647, -0.00736968545243144, 0.011183862574398518, -0.03692837804555893, 0.026431163772940636, -0.007760039065033197, 0.0037953646387904882, -0.021521175280213356, 0.04180074483156204, 0.027879703789949417, 0.034482792019844055, -0.010487810708582401, -0.008385545574128628, -0.02409844845533371, 0.0033932533115148544, 0.00860658846795559, -0.016987431794404984, -0.03158571198582649, 0.033824365586042404, -0.02037362940609455, -0.03467091545462608, 0.01734486222267151, -0.007524886168539524, 0.02861338108778, -0.01789982244372368, 0.029911423102021217, -0.03491547331213951, -0.020524127408862114, -0.01080761756747961, 0.015501265414059162, 0.005258014425635338, 0.028180699795484543, 0.030682723969221115, -0.0034755568485707045, 0.009669478982686996, 0.02744702249765396, 0.008244453929364681, -0.03286493942141533, 0.03380555287003517, -0.0422898605465889, 0.003922346979379654, 0.00024000271514523774, -0.026882655918598175, 0.001362709910608828, 0.02797376550734043, -0.02710840292274952, -0.030701536685228348, -0.012510123662650585, 0.04078488424420357, -0.014344314113259315, 0.00952838733792305, 0.020486503839492798, 0.052937574684619904, -0.017758730798959732, 0.029102498665452003, 0.057603005319833755, -0.0042891851626336575, -0.042666103690862656, -0.027729205787181854, -0.019414206966757774, -0.039656151086091995, 0.018012696877121925, 0.07385675609111786, -0.05037911236286163, 0.041875991970300674, -0.04729390889406204, 0.03623232617974281, -0.04251560941338539, 0.03177383169531822, 0.055496037006378174, -0.009782352484762669, -0.020937995985150337, -0.029760925099253654 ]
Risk assessment is a substantial problem for financial institutions that has been extensively studied both for its methodological richness and its various practical applications. With the expansion of inclusive finance, recent attentions are paid to micro and small-sized enterprises (MSEs). Compared with large companies, MSEs present a higher exposure rate to default owing to their insecure financial stability. Conventional efforts learn classifiers from historical data with elaborate feature engineering. However, the main obstacle for MSEs involves severe deficiency in credit-related information, which may degrade the performance of prediction. Besides, financial activities have diverse explicit and implicit relations, which have not been fully exploited for risk judgement in commercial banks. In particular, the observations on real data show that various relationships between company users have additional power in financial risk analysis. In this paper, we consider a graph of banking data, and propose a novel HIDAM model for the purpose. Specifically, we attempt to incorporate heterogeneous information network with rich attributes on multi-typed nodes and links for modeling the scenario of business banking service. To enhance feature representation of MSEs, we extract interactive information through meta-paths and fully exploit path information. Furthermore, we devise a hierarchical attention mechanism respectively to learn the importance of contents inside each meta-path and the importance of different metapahs. Experimental results verify that HIDAM outperforms state-of-the-art competitors on real-world banking data.
[ -0.051610395312309265, 0.055238671600818634, -0.035838495939970016, -0.01901143416762352, 0.04368742182850838, -0.017030689865350723, 0.005641416180878878, 0.01802106201648712, -0.03189552202820778, -0.046834398061037064, 0.05298025533556938, -0.004259986337274313, -0.007293578237295151, -0.07049224525690079, -0.01619766652584076, 0.022787803784012794, 0.038911424577236176, -0.05882992595434189, 0.03195105493068695, -0.04054044559597969, 0.01827096752822399, -0.013698598369956017, -0.019363153725862503, 0.04635309427976608, -0.0009504559566266835, 0.028322778642177582, 0.02513877861201763, 0.022287989035248756, -0.06804871559143066, 0.0543501153588295, 0.04690844565629959, -0.021732641384005547, -0.0024111384991556406, -0.04316909611225128, -0.027008453384041786, -0.012162134051322937, 0.021566037088632584, 0.046945467591285706, 0.007163996808230877, 0.03754156455397606, 0.06264331936836243, -0.010172135196626186, -0.018354270607233047, 0.008242298848927021, 0.023879989981651306, 0.003984625916928053, -0.030285010114312172, -0.006502206437289715, -0.003357545007020235, 0.022898873314261436, 0.00016776155098341405, 0.0007271595532074571, -0.016669712960720062, -0.04490919038653374, -0.04838937520980835, 0.042354583740234375, 0.08619009703397751, 0.011847436428070068, 0.02065896801650524, 0.025046221911907196, -0.008015531115233898, 0.05401690676808357, 0.018474595621228218, 0.024379802867770195, 0.033894773572683334, -0.03730091452598572, 0.006761368829756975, -0.019788920879364014, 0.004523776937276125, -0.022787803784012794, -0.08915195614099503, 0.00892722886055708, 0.013485714793205261, 0.010986646637320518, -0.005192509386688471, 0.017400922253727913, 0.011579018086194992, 0.013300598599016666, 0.010847808793187141, 0.047871049493551254, 0.04838937520980835, 0.03245086967945099, -0.020899618044495583, 0.0006097264704294503, 0.05446118488907814, -0.022362036630511284, 0.002695754636079073, -0.08056256920099258, 0.005784881301224232, -0.009186390787363052, -0.0019286794122308493, -0.0070714387111365795, -0.009431670419871807, -0.014392783865332603, -0.00552109070122242, 0.0020744584035128355, 0.005868183448910713, -0.009427042677998543, -0.059644438326358795, -0.006307834293693304, -0.023750407621264458, -0.0015376213705167174, 0.012773017399013042, -0.036838121712207794, 0.03465375304222107, -0.041614118963479996, -0.06412424892187119, 0.03406137973070145, -0.008408903144299984, 0.15994039177894592, -0.04690844565629959, 0.04513132944703102, -0.012088087387382984, 0.04239160940051079, -0.01853013038635254, 0.014985156245529652, -0.006460555363446474, -0.02563859336078167, 0.0198814794421196, -0.06279141455888748, -0.02815617248415947, 0.005419276654720306, -0.011884459294378757, -0.012847064062952995, -0.06460554897785187, 0.05153634771704674, -0.021010687574744225, -0.022824827581644058, -0.037078775465488434, 0.0031307777389883995, -0.08796721696853638, 0.012615668587386608, 0.006367997266352177, -0.05775625258684158, 0.004003137815743685, 0.03961486741900444, 0.07278768718242645, -0.037023238837718964, 0.009436298161745071, -0.03158082440495491, 0.016780782490968704, -0.018780037760734558, -0.05127718672156334, -0.033469006419181824, 0.0254534762352705, 0.014587156474590302, -0.012495343573391438, 0.0389854721724987, -0.012152878567576408, 0.03557933121919632, -0.03600509837269783, 0.04457597807049751, 0.044501934200525284, 0.023713383823633194, 0.019714875146746635, 0.009302088990807533, 0.007524973247200251, 0.0062893228605389595, -0.06053299456834793, -0.013957761228084564, 0.07341708242893219, -0.026971429586410522, -0.005470183677971363, -0.004014707636088133, 0.0001504069077782333, 0.041243888437747955, -0.061791785061359406, -0.06619755178689957, -0.0962604209780693, 0.04813021048903465, -0.00843204278498888, 0.0030497892294079065, 0.00708532240241766, -0.012134366668760777, -0.01687334105372429, 0.05472034588456154, 0.023046966642141342, -0.015957016497850418, -0.05734899640083313, 0.014466830529272556, -0.021010687574744225, -0.021936269477009773, 0.028600452467799187, 0.007751740515232086, 0.03709728643298149, 0.010190646164119244, 0.05312834680080414, 0.024083616212010384, 0.007529601454734802, -0.0032048241700977087, 0.01834501512348652, 0.019474223256111145, 0.01613287627696991, -0.003734719241037965, 0.012143622152507305, -0.07071438431739807, -0.018187666311860085, 0.00018019904382526875, 0.013365388847887516, -0.06008871644735336, -0.017428690567612648, -0.049463048577308655, 0.020436827093362808, 0.05920016020536423, 0.02460194192826748, -0.010755251161754131, 0.04557560756802559, -0.016965899616479874, 0.022676734253764153, -0.056571509689092636, -0.016780782490968704, 0.029674125835299492, -0.01699366606771946, -0.00023081676044967026, -0.0474637933075428, 0.03163635730743408, 0.028730032965540886, 0.015373899601399899, 0.03370966017246246, -0.03715281933546066, 0.02300994284451008, -0.006557741202414036, 0.03491291403770447, 0.03385775163769722, -0.019899990409612656, 0.021084735170006752, -0.024028081446886063, 0.03457970544695854, 0.005437788087874651, 0.0009371507330797613, 0.006113462150096893, -0.010144367814064026, 0.0038388471584767103, 0.005937601905316114, 0.008297833614051342, 0.0035079519730061293, -0.01380041241645813, -0.040873654186725616, 0.005743229761719704, -0.01691962033510208, 0.024435337632894516, -0.0028808708302676678, -0.05279513821005821, -0.032043613493442535, 0.03828202933073044, 0.0061921365559101105, 0.007020531687885523, 0.06749336421489716, 0.010079576633870602, 0.05261002108454704, 0.006284694653004408, -0.03678258880972862, 0.01349497027695179, 0.008626414462924004, 0.007089950144290924, 0.001383743598125875, 0.04276183992624283, -0.0312846377491951, 0.024990687146782875, -0.014272458851337433, 0.05427606776356697, 0.004162800498306751, 0.004928718786686659, 0.028248731046915054, -0.04468705132603645, 0.020714502781629562, 0.07856331020593643, -0.028748545795679092, 0.03839309886097908, 0.012819296680390835, 0.04483514279127121, -0.063087597489357, -0.01594776101410389, 0.03406137973070145, -0.017632316797971725, -0.03233980014920235, 0.0734541043639183, 0.00289012654684484, 0.02606436051428318, 0.04850044474005699, -0.003875870257616043, 0.012217668816447258, 0.05975550785660744, -0.01656789891421795, -0.05401690676808357, -0.04335421323776245, -0.04316909611225128, 0.014179900288581848, -0.09966655820608139, -0.018243201076984406, -0.03809691220521927, -0.028748545795679092, -0.030747799202799797, 0.0021843709982931614, -0.012310227379202843, 0.045538585633039474, -0.010468320921063423, 0.031303148716688156, 0.02049236372113228, -0.04635309427976608, -0.04457597807049751, 0.01588296890258789, -0.0026031965389847755, 0.061495598405599594, -0.03831905126571655, -0.004081812221556902, -0.008052554912865162, 0.06530899554491043, 0.004026277456432581, -0.056830670684576035, -0.0044312188401818275, 0.0373934730887413, -0.003866614541038871, 0.002894754521548748, -0.07012201100587845, 0.02256566472351551, 0.02317654713988304, -0.01269897073507309, 0.05575699731707573, -0.041058771312236786, 0.017123248428106308, 0.008899461477994919, -0.08870767802000046, -0.007682322058826685, -0.044613003730773926, 0.0055072070099413395, -0.05882992595434189, 0.028433848172426224, -0.029600080102682114, -0.01300441287457943, -0.005187881179153919, -0.0324878916144371, -0.036190215498209, -0.0020686734933406115, -0.04350230470299721, 0.007779507897794247, 0.04513132944703102, 0.035301659256219864, -0.014374272897839546, 0.028045102953910828, -0.033469006419181824, -0.012041808106005192, -0.08004423975944519, 0.008242298848927021, -0.011671575717628002, 0.023879989981651306, -0.03200659155845642, -0.021121757104992867, 0.007210275623947382, -0.042539700865745544, 0.0010412785923108459, 0.0033876262605190277, -0.023158036172389984, 0.021695617586374283, 0.016401294618844986, -0.04494621232151985, 0.04624202474951744, -0.005789509043097496, -0.025342406705021858, 0.008820787072181702, 0.0065623689442873, -0.07226936519145966, -0.032302774488925934, 0.014004040509462357, -0.040947701781988144, -0.01306920312345028, -0.02497217431664467, -0.022213943302631378, 0.0027188940439373255, -0.018141387030482292, -0.05331346392631531, 0.03343198448419571, -0.016031062230467796, 0.005854299757629633, 0.0010592116741463542, 0.04079961031675339, -0.01386520266532898, 0.03139570727944374, -0.03374668210744858, 0.044983234256505966, -0.028322778642177582, -0.0009151682024821639, -0.0018338073277845979, 0.010098088532686234, -0.013976273126900196, -0.02728612720966339, 0.0440206304192543, 0.007043671328574419, 0.0015515050617977977, 0.054979510605335236, 0.0376526340842247, -0.0229358971118927, -0.009690833278000355, -0.04794509336352348, 0.017761899158358574, -0.04857448861002922, -0.010801530443131924, -0.016466084867715836, 0.06371699273586273, -0.04975923150777817, -0.010718227364122868, 0.04727867618203163, 0.01969636231660843, 0.03134017065167427, -0.029729660600423813, -0.017743388190865517, 0.09722302854061127, -0.007719345390796661, 0.02741570770740509, -0.022954408079385757, 0.010357251390814781, -0.03072928823530674, -0.02882259152829647, -0.007089950144290924, -0.010014786384999752, 0.02987775392830372, -0.02299143187701702, -0.007964624091982841, -0.0011783803347498178, -0.0056738113053143024, -0.011403157375752926, -0.025360919535160065, 0.10425744205713272, 0.018817061558365822, -0.026878871023654938, 0.04916686192154884, -0.030247986316680908, -0.02232501283288002, 0.029100265353918076, -0.02600882574915886, 0.07375029474496841, 0.01417064480483532, -0.005599765107035637, -0.011541995219886303, -0.057867322117090225, -0.010042553767561913, 0.006446671672165394, 0.01722506247460842, -0.037615612149238586, -0.013957761228084564, -0.0051462301053106785, -0.033894773572683334, -0.05820053070783615, 0.05597913637757301, 0.018307991325855255, 0.0077008334919810295, -0.000327424262650311, -0.010412786155939102, -0.0019495049491524696, -0.018354270607233047, -0.04390956088900566, 0.023158036172389984, -0.05053672194480896, -0.03200659155845642, 0.0397629588842392, -0.01195850595831871, 0.043095048516988754, -0.03226575255393982, 0.0872267484664917, -0.014457575045526028, -0.02937794104218483, 0.08581987023353577, -0.012319482862949371, -0.015957016497850418, 0.0342094711959362, 0.01938166655600071, -0.04783402383327484, 0.015845946967601776, 0.014670458622276783, 0.04546453803777695, -0.002024708315730095, -0.019400177523493767, 0.04724165424704552, 0.013161761686205864, 0.023528268560767174, -0.0205478984862566, -0.001840749173425138, -0.03409840166568756, 0.0042322189547121525, 0.06697504222393036, 0.0067197177559137344, 0.02889663726091385, 0.00966306496411562, 0.042724817991256714, 0.01644757390022278, 0.005099951289594173, 0.020455339923501015, 0.0018083538161590695, -0.05149932578206062, 0.0029109520837664604, -0.0058265323750674725, 0.016586411744356155, -0.0025916267186403275, -0.054239045828580856, 0.013282086700201035, -0.027378685772418976, -0.028989195823669434, 0.034635238349437714, 0.02232501283288002, 0.00536836963146925, 0.015438690781593323, 0.0035658006090670824, -0.020510874688625336, -0.008834670297801495, 0.009311344474554062, 0.054683323949575424, 0.015401666983962059, 0.005053672008216381, 0.0063911364413797855, -0.005229532718658447, 0.03006286919116974, -0.012782272882759571, -0.0035773704294115305, -0.008228414691984653, 0.002834591781720519, 0.019788920879364014, -0.00443353271111846, 0.019363153725862503, 0.030581194907426834, 0.015512737445533276, -0.00041708993376232684, 0.01680855080485344, -0.00499813724309206, 0.04857448861002922, -0.05405392870306969, -0.031192079186439514, 0.06579029560089111, 0.001060368726029992, 0.025490500032901764, -0.07215829193592072, 0.0030544172041118145, 0.04624202474951744, -0.024324268102645874, -0.03656044974923134, -0.005266555584967136, 0.015475713647902012, -0.01069971639662981, 0.036523424088954926, -0.014744505286216736, -0.04975923150777817, -0.015512737445533276, 0.029526032507419586, -0.008145112544298172, -0.002570801181718707, 0.015475713647902012, 0.03200659155845642, 0.04379849135875702, -0.03741198405623436, -0.01949273608624935, 0.01649385318160057, -0.0043756840750575066, -0.023842966184020042, 0.052239790558815, -0.003466300666332245, -0.016975155100226402, -0.01193073857575655, 0.00157927256077528, -0.062347132712602615, 0.017891479656100273, -0.012412040494382381, 0.018909620121121407, 0.005831160116940737, 0.0037208355497568846, -0.02686036005616188, 0.00029170262860134244, 0.010440553538501263, 0.00616436917334795, 0.05942229926586151, 0.041614118963479996, 0.02980370819568634, -0.008654181845486164, -0.025101756677031517, -0.02262119948863983, -0.06249522790312767, -0.00840427540242672, 0.02630501054227352, -0.0032580450642853975, -0.0021936269477009773, 0.03454268351197243, -0.0014334935694932938, -0.009440925903618336, -0.007992391474545002, 0.004521463066339493, 0.027989568188786507, -0.001909010810777545, -0.0020166095346212387, 0.010042553767561913, -0.04013318940997124, 0.007020531687885523, 0.0000385417697543744, -0.01220841333270073, 0.0593852736055851, 0.014383528381586075, -0.03520910069346428, 0.005248044151812792, -0.005599765107035637, -0.009015158750116825, -0.031377196311950684, 0.029174312949180603, 0.0063309739343822, -0.013735621236264706, 0.020140642300248146, 0.012152878567576408, 0.06986285001039505, -0.0014809295535087585, -0.0060810670256614685, 0.01853013038635254, -0.037504542618989944, 0.016114365309476852, -0.03017394058406353, 0.07086247950792313, -0.021547524258494377, 0.006835415493696928, -0.07526824623346329, 0.012088087387382984, 0.004405765328556299, 0.0389854721724987, -0.0045723700895905495, -0.04801914095878601, -0.01927059516310692, 0.06978880614042282, 0.002547661541029811, 0.04542751610279083, 0.03215468302369118, 0.010866320692002773, -0.000021548681615968235, -0.006460555363446474, -0.015623806975781918, -0.0006664182874374092, 0.004479811992496252, -0.033024728298187256, 0.023139525204896927, -0.03519058972597122, -0.00578025309368968, 0.011699343100190163, -0.012282459996640682, 0.010570134967565536, 0.03968891128897667, 0.030136916786432266, -0.012921110726892948, -0.013161761686205864, 0.02330612950026989, -0.0045515443198382854, 0.029340917244553566, -0.002947975415736437, 0.0009180606575682759, 0.007552740629762411, 0.02097366563975811, 0.02423170953989029, 0.054794393479824066, 0.011301343329250813, 0.016262458637356758, 0.020770037546753883, 0.009126228280365467, 0.00554885808378458, -0.04079961031675339, -0.010857065208256245, 0.006761368829756975, -0.025860732421278954, 0.00877450779080391, 0.023046966642141342, -0.017928503453731537, 0.0024227083195000887, 0.0026749290991574526, 0.02417617477476597, 0.027508266270160675, -0.019548270851373672, 0.00837650801986456, 0.036523424088954926, 0.02447236143052578, -0.004172056447714567, -0.07134377956390381, -0.06797466427087784, 0.0654941126704216, 0.04994434863328934, -0.055534858256578445, 0.03163635730743408, 0.028193196281790733, 0.004017021507024765, -0.027674870565533638, -0.0002039170649368316, -0.029118778184056282, -0.05335048586130142, 0.026767801493406296, -0.034986961632966995, -0.020881107077002525, -0.014985156245529652, 0.0022908130194991827, 0.004030905198305845, -0.0000037240172332531074, -0.01300441287457943, -0.04098472744226456, 0.04901876673102379, 0.019344642758369446, 0.038170959800481796, -0.048722583800554276, -0.0029757427982985973, -0.05501653254032135, 0.024453848600387573, 0.04213244467973709, -0.008635670877993107, 0.005798764992505312, 0.005442416295409203, 0.017761899158358574, -0.011171762831509113, 0.019029945135116577, 0.0033714286983013153, 0.0014045691350474954, -0.020992176607251167, -0.006034787744283676, -0.0014207668136805296, 0.01704920083284378, -0.060570020228624344, 0.0086495541036129, -0.010542367585003376, 0.03589402884244919, 0.0027235220186412334, 0.024546407163143158, -0.019159525632858276, 0.012402785010635853, 0.005678439512848854, 0.009589019231498241, 0.003700010012835264, -0.05679364874958992, -0.020992176607251167, -0.0037809982895851135, 0.013115482404828072, 0.02017766609787941, -0.012800784781575203, 0.0035287775099277496, 0.025305384770035744, -0.028915150091052055, -0.005363741889595985, 0.0038295912090688944, -0.01606808602809906, -0.018974410369992256, 0.008589391596615314, 0.056016162037849426, 0.002707324456423521, 0.0027350918389856815, 0.014911109581589699, -0.007312089670449495, -0.02906324341893196, -0.04524239897727966, 0.02649012766778469, 0.022047339007258415, -0.02115878090262413, -0.009774135425686836, -0.016392039135098457, -0.011255064979195595, 0.006983508355915546, -0.03691216930747032, 0.021695617586374283, -0.049463048577308655, -0.02680482529103756, -0.01808585226535797, 0.00845981016755104, -0.015281341969966888, -0.021695617586374283, -0.01919654943048954, -0.04857448861002922, 0.019418688490986824, -0.010051809251308441, 0.012449064292013645, 0.05660853162407875, -0.011541995219886303, -0.041058771312236786, -0.03759709745645523, -0.014105853624641895, -0.04820425808429718, 0.016715992242097855, 0.014309481717646122, 0.0705292671918869, -0.037004727870225906, 0.057015787810087204, -0.021547524258494377, 0.012458319775760174, -0.03159933537244797, -0.017808178439736366, -0.0010314442915841937, 0.006469810847193003, 0.0018187665846198797, -0.026582686230540276, 0.039948076009750366, 0.011856691911816597, 0.03004435822367668, -0.03417244926095009, -0.052721090614795685, -0.023528268560767174, -0.012162134051322937, -0.004387253895401955, 0.012004785239696503, 0.0014126679161563516, -0.0018662026850506663, 0.022232454270124435, 0.01352273765951395, 0.008626414462924004, -0.0039337193593382835, -0.03096994012594223, -0.009746368043124676, 0.054683323949575424, -0.015225807204842567, 0.01864120177924633, 0.03165486827492714, -0.02717505767941475, 0.007899833843111992, -0.023102501407265663, 0.018206177279353142, 0.0029086382128298283, 0.012884086929261684, -0.0002260442270198837, -0.00615048548206687, -0.004794509615749121, 0.016512364149093628, 0.01606808602809906, -0.005280439276248217, -0.05268406867980957, -0.042650770395994186, -0.03293216973543167, -0.028193196281790733, 0.01193073857575655, -0.015096225775778294, -0.04102174937725067, -0.006617904175072908, -0.02299143187701702, -0.007617531344294548, 0.028730032965540886, -0.020196177065372467, 0.04350230470299721, -0.02943347580730915, 0.016031062230467796, 0.036393843591213226, 0.0006079910090193152, 0.007876694202423096, -0.03165486827492714, -0.009829670190811157, -0.008742112666368484, 0.03905951604247093, 0.0020652024541050196, 0.034079890698194504, -0.004165114369243383, -0.013115482404828072, -0.08885577321052551, -0.015540504828095436, -0.0002769511775113642, -0.0054100207053124905, -0.006488322746008635, -0.0408366322517395, -0.001706539886072278, 0.06268034130334854, 0.015984782949090004, 0.0009284734260290861, 0.009607530198991299, 0.03674556314945221, 0.002096440875902772, 0.010783018544316292, 0.04457597807049751, -0.004479811992496252, 0.049277931451797485, -0.02299143187701702, 0.05294323340058327, -0.00536836963146925, -0.0197518989443779, -0.012689715251326561, 0.024861104786396027, 0.006238415837287903, 0.008080322295427322, -0.037023238837718964, 0.0008330228738486767, -0.033154308795928955, 0.0036537309642881155, -0.0009556623408570886, -0.02330612950026989, 0.02948901057243347, 0.01932612992823124, -0.013319110497832298, 0.01601255126297474, 0.0021542897447943687, -0.04009616747498512, -0.03509803116321564, 0.0304886382073164, -0.014152132906019688, 0.009922227822244167, -0.018372781574726105, 0.04379849135875702, -0.0035704285837709904, 0.015003667213022709, -0.021547524258494377, -0.053202394396066666, -0.030377566814422607, -0.002165859565138817, 0.007487949915230274, 0.008908716961741447, -0.010412786155939102, 0.03454268351197243, 0.009329856373369694, 0.03706026077270508, -0.007895206101238728, -0.010820041410624981, -0.01594776101410389, 0.0007636043010279536, -0.05372072011232376, -0.0011997843394055963, 0.003748602932319045, 0.0342094711959362, -0.00012864128802902997, 0.00249906862154603, -0.04202137514948845, 0.005113834980875254, -0.07708238065242767, -0.01355050504207611, -0.0546092763543129, 0.009468693286180496, -0.019233573228120804, 0.01938166655600071, 0.0064559271559119225, 0.0077100894413888454, 0.006585508584976196, -0.021917756646871567, 0.008311716839671135, 0.06556815654039383, 0.027619335800409317, -0.053091324865818024, 0.0029965683352202177, -0.04716760665178299, 0.02797105722129345, -0.004706579260528088, 0.06286545842885971, 0.018298735842108727, -0.011301343329250813, -0.018594922497868538, 0.022972919046878815, 0.021010687574744225, 0.02145496755838394, -0.005576625466346741, -0.02698994055390358, -0.03667151927947998, -0.007515717297792435, -0.0413549579679966, -0.022139897570014, -0.03150677680969238, 0.06367997080087662, 0.0027050103526562452, 0.028989195823669434, 0.024379802867770195, -0.03213617205619812, 0.026175430044531822, -0.049463048577308655, -0.05349858105182648, 0.002501382492482662, -0.015114737674593925, -0.02558305859565735, -0.013791156932711601, 0.0055072070099413395, -0.02152901329100132, -0.023954035714268684, -0.03096994012594223, -0.007487949915230274, 0.00011656535207293928, 0.06479066610336304, -0.004641788545995951, -0.02619394101202488, -0.021195804700255394, -0.014550132676959038, -0.0328766368329525, 0.027434220537543297, -0.050203513354063034, -0.038059890270233154, -0.020992176607251167, 0.012319482862949371, 0.006867810618132353, -0.01748422533273697, 0.03306175395846367, 0.024509383365511894, -0.010412786155939102, -0.010708971880376339, 0.035357192158699036, -0.015133248642086983, -0.015688598155975342, 0.01582743413746357, -0.0028068243991583586, 0.029766684398055077, 0.05494248494505882, -0.015225807204842567, -0.01693813130259514, -0.024009570479393005, 0.0424286313354969, -0.014698226004838943, -0.05009244382381439, -0.023879989981651306, -0.027563801035284996, 0.017919247969985008, 0.011347622610628605, -0.040762584656476974, -0.07885950058698654, 0.03920761123299599, -0.003861986566334963, -0.03295068442821503, -0.0030521033331751823, 0.02478705905377865, 0.012624924071133137, -0.018307991325855255, 0.019048456102609634, 0.028748545795679092, -0.019788920879364014, -0.006266183219850063, 0.024009570479393005, 0.021640082821249962, 0.007779507897794247, -0.017752643674612045, 0.013781900517642498, 0.026471616700291634, -0.014068830758333206, 0.030025847256183624, -0.0270454753190279, -0.028470870107412338, -0.019548270851373672, -0.019585292786359787, -0.002871614880859852, -0.06638266891241074, 0.012578645721077919, 0.0031446614302694798, -0.026952918618917465, -0.01901143416762352 ]
We describe a general approach for maximum a posteriori (MAP) inference in a class of discrete-continuous factor graphs commonly encountered in robotics applications. While there are openly available tools providing flexible and easy-to-use interfaces for specifying and solving inference problems formulated in terms of either discrete or continuous graphical models, at present, no similarly general tools exist enabling the same functionality for hybrid discrete-continuous problems. We aim to address this problem. In particular, we provide a library, DC-SAM, extending existing tools for inference problems defined in terms of factor graphs to the setting of discrete-continuous models. A key contribution of our work is a novel solver for efficiently recovering approximate solutions to discrete-continuous inference problems. The key insight to our approach is that while joint inference over continuous and discrete state spaces is often hard, many commonly encountered discrete-continuous problems can naturally be split into a "discrete part" and a "continuous part" that can individually be solved easily. Leveraging this structure, we optimize discrete and continuous variables in an alternating fashion. In consequence, our proposed work enables straightforward representation of and approximate inference in discrete-continuous graphical models. We also provide a method to approximate the uncertainty in estimates of both discrete and continuous variables. We demonstrate the versatility of our approach through its application to distinct robot perception applications, including robust pose graph optimization, and object-based mapping and localization.
[ 0.039128951728343964, 0.039775118231773376, -0.04142643138766289, -0.005667415913194418, 0.056324150413274765, 0.0592677965760231, -0.049395814538002014, 0.044621363282203674, -0.06468841433525085, 0.0569344200193882, 0.020695267245173454, -0.01423360500484705, 0.06264222413301468, -0.01719520054757595, -0.048641953617334366, -0.01766187511384487, -0.006959747988730669, 0.04135463386774063, 0.013784877955913544, -0.017186224460601807, -0.03270318731665611, 0.013093839399516582, -0.011280984617769718, 0.05233946070075035, 0.05718570575118065, 0.003334037959575653, 0.0033968596253544092, -0.04404699429869652, -0.03898536041378975, 0.02841336280107498, 0.005021249875426292, 0.02704923413693905, -0.04910862818360329, 0.02204144559800625, -0.02466200850903988, -0.004639832302927971, 0.00793797243386507, 0.0018700677901506424, -0.017886238172650337, 0.07240650802850723, -0.005039198789745569, 0.022149140015244484, -0.01134380605071783, -0.017670849338173866, -0.018487531691789627, -0.04749321565032005, -0.0015447409823536873, 0.032918576151132584, -0.04271876439452171, 0.021108094602823257, 0.008184771984815598, -0.049611203372478485, -0.01574132591485977, -0.02916722372174263, -0.004958427976816893, -0.0430777445435524, 0.05065224692225456, 0.057293400168418884, 0.030782638117671013, 0.020264489576220512, 0.07186803966760635, 0.02177220955491066, -0.05761648342013359, -0.00422027288004756, 0.02128758653998375, -0.09046326577663422, 0.013479744084179401, -0.0015133301494643092, 0.014556688256561756, -0.04663166031241417, -0.020031152293086052, -0.0011291081318631768, 0.0033721798099577427, -0.013111788779497147, 0.06623203307390213, 0.024231230840086937, -0.0036728265695273876, -0.004343672655522823, -0.0011072326451539993, -0.0011936124647036195, 0.07768353074789047, 0.022920949384570122, 0.0019721530843526125, -0.03679557517170906, 0.017697773873806, -0.04067257046699524, 0.05241125822067261, -0.060596026480197906, 0.06472431123256683, 0.002876336919143796, -0.05097533017396927, 0.034067317843437195, 0.02058757282793522, 0.029328765347599983, 0.022920949384570122, 0.009656594134867191, -0.02699538692831993, -0.010060448199510574, 0.010195066221058369, 0.002943645929917693, -0.0066725630313158035, -0.0017556424718350172, 0.033833980560302734, 0.0020933090709149837, -0.0022301706485450268, -0.0649397000670433, -0.004036294762045145, -0.03762122988700867, 0.005236638244241476, 0.10489431023597717, -0.01601056195795536, 0.002434341236948967, -0.02484150044620037, 0.0041439891792833805, -0.0759604200720787, 0.01699776016175747, -0.015597733668982983, -0.038841765373945236, 0.051011230796575546, -0.07667838782072067, -0.022292733192443848, 0.025218429043889046, 0.024697907269001007, -0.03643659129738808, -0.02889798767864704, 0.033151913434267044, 0.017787517979741096, -0.026618456467986107, -0.0017904187552630901, -0.006959747988730669, -0.03203907236456871, -0.005299460142850876, -0.006246272940188646, -0.06257042288780212, 0.029813390225172043, -0.0180298313498497, 0.023746607825160027, 0.0032824345398694277, -0.018191372975707054, 0.0018509968649595976, -0.018020857125520706, -0.02703128568828106, -0.01723109744489193, 0.03185958042740822, -0.020946552976965904, 0.010518149472773075, -0.03361859172582626, 0.06924747675657272, -0.05689852312207222, 0.06989364326000214, -0.0430777445435524, 0.023315830156207085, -0.04519573599100113, 0.057508789002895355, 0.04630857706069946, 0.056288253515958786, -0.04009820148348808, -0.0337262861430645, 0.0033116017002612352, -0.033098068088293076, 0.06870900094509125, -0.042934153228998184, 0.035054516047239304, 0.07524245977401733, -0.02058757282793522, 0.010042499750852585, 0.024033792316913605, -0.05908830836415291, -0.036687880754470825, 0.004980864468961954, 0.002586908405646682, -0.021808108314871788, 0.01983371190726757, 0.0030535839032381773, -0.0064078145660459995, 0.028359515592455864, 0.062283240258693695, 0.04092385619878769, 0.0011700544273480773, 0.0004627492162398994, -0.042934153228998184, -0.009710441343486309, 0.03966742381453514, 0.053093321621418, 0.04113924503326416, 0.02010294795036316, 0.06041653826832771, -0.03544939309358597, 0.07725275307893753, -0.040780264884233475, 0.03988281264901161, 0.017643926665186882, 0.061098601669073105, -0.005775110330432653, 0.06048833206295967, -0.06468841433525085, -0.07811430841684341, 0.0009002575534395874, -0.030064675956964493, 0.013156660832464695, -0.03304421901702881, -0.020479878410696983, -0.004013858735561371, 0.006798206828534603, 0.018702920526266098, 0.011433551087975502, 0.005438565276563168, -0.03010057471692562, 0.012600240297615528, -0.07617580890655518, 0.024446619674563408, 0.009889932349324226, -0.04404699429869652, -0.08206310123205185, -0.00853926595300436, -0.025774851441383362, -0.007305267732590437, 0.009988652542233467, -0.02317223697900772, -0.02320813573896885, 0.05646774545311928, 0.016656728461384773, 0.0332237109541893, -0.014018216170370579, 0.04907273128628731, 0.04734962061047554, 0.0077719432301819324, -0.01890036091208458, -0.008193746209144592, -0.0013865649234503508, 0.03970332071185112, 0.024805601686239243, 0.012366903014481068, -0.014027190394699574, -0.006138578522950411, -0.019743965938687325, 0.035772476345300674, -0.014574636705219746, 0.008889271877706051, 0.0132733304053545, -0.03157239779829979, 0.03318781405687332, -0.0059187025763094425, -0.028072331100702286, 0.013623337261378765, 0.0659448504447937, 0.0364006944000721, 0.021610667929053307, 0.03148265182971954, 0.002586908405646682, -0.03609555959701538, -0.02387225069105625, 0.047457315027713776, -0.013452820479869843, -0.018774718046188354, 0.03180573508143425, 0.018290093168616295, 0.01773367077112198, 0.021215789020061493, -0.05445744842290878, 0.04882144555449486, 0.04734962061047554, 0.019672170281410217, -0.0016558008501306176, -0.021377330645918846, 0.0171144288033247, 0.04885734245181084, 0.03110572136938572, -0.004204567521810532, 0.016154155135154724, -0.038410987704992294, -0.019546527415513992, -0.014440018683671951, 0.013048967346549034, 0.02460816130042076, -0.056288253515958786, 0.028539005666971207, 0.0262953732162714, 0.01435924880206585, -0.003751353593543172, -0.002017025602981448, 0.01732981763780117, 0.003529234090819955, 0.02272351086139679, 0.007601426914334297, -0.021826056763529778, -0.005689851939678192, 0.025451768189668655, -0.04239568114280701, 0.01052712369710207, -0.025164581835269928, 0.010033524595201015, -0.034354500472545624, 0.04989838972687721, 0.019241392612457275, -0.028090279549360275, -0.06888849288225174, -0.056324150413274765, 0.004980864468961954, 0.011909201741218567, 0.0060981931164860725, 0.0024478030391037464, -0.004076680168509483, 0.015140032395720482, 0.04325723648071289, 0.0020742383785545826, -0.008714268915355206, 0.057544685900211334, -0.0033116017002612352, -0.051298413425683975, 0.03081853687763214, 0.0058244699612259865, -0.06957055628299713, 0.015938766300678253, 0.02771334908902645, 0.04849836230278015, 0.016064409166574478, 0.001692820806056261, -0.0282159224152565, -0.017177250236272812, -0.0008935266523621976, 0.0023356215097010136, -0.09089404344558716, -0.0024971631355583668, -0.0016860899049788713, 0.0224542748183012, -0.02512868493795395, -0.006892438977956772, -0.013165635988116264, 0.032882679253816605, 0.001680480781942606, -0.0038007134571671486, -0.045841898769140244, -0.032416004687547684, -0.02868259884417057, -0.0023423524107784033, 0.011245086789131165, 0.03483912721276283, -0.030764689669013023, -0.009719416499137878, -0.009050813503563404, -0.0602729432284832, 0.000828461314085871, 0.008593112230300903, 0.019043952226638794, -0.014125910587608814, 0.004516432527452707, -0.02031833678483963, -0.04828297346830368, -0.03157239779829979, 0.0010090736905112863, -0.05898061394691467, 0.015418242663145065, -0.0028404388576745987, 0.044836752116680145, -0.04088795930147171, -0.008377724327147007, -0.053416404873132706, -0.04297005012631416, 0.015938766300678253, 0.0410674512386322, -0.016486212611198425, -0.04828297346830368, -0.005842419341206551, -0.036939166486263275, 0.03325960785150528, -0.0131476866081357, -0.0008099513361230493, -0.05047275871038437, 0.02006704919040203, 0.016916990280151367, 0.057544685900211334, 0.01591184176504612, -0.03412116318941116, -0.013766929507255554, -0.01680929586291313, 0.03988281264901161, 0.015965688973665237, -0.02534407377243042, 0.018361888825893402, -0.0382314994931221, 0.03227240964770317, -0.006542432587593794, -0.029723644256591797, 0.028323616832494736, 0.048211175948381424, 0.008902734145522118, -0.02722872421145439, 0.0015739082591608167, 0.04239568114280701, 0.04968300089240074, -0.038410987704992294, 0.003966742195188999, 0.0022570942528545856, 0.002376006916165352, -0.012339979410171509, 0.0347314327955246, -0.03780072182416916, 0.008377724327147007, 0.014045139774680138, 0.02699538692831993, -0.015956714749336243, -0.03394167497754097, 0.06616023927927017, 0.0005760526400990784, -0.010598920285701752, -0.0025397920981049538, -0.012510495260357857, 0.01915164664387703, 0.02243632636964321, 0.026115883141756058, 0.0018117332365363836, 0.0011134026572108269, -0.021179892122745514, 0.00879952684044838, 0.005618055816739798, -0.06328839063644409, 0.03494682163000107, 0.006178963929414749, -0.04297005012631416, -0.005819982849061489, -0.02132348343729973, 0.0672730803489685, -0.025882545858621597, -0.01783239096403122, 0.058944713324308395, 0.031662143766880035, -0.023567115887999535, -0.043652113527059555, -0.03945203498005867, 0.040313590317964554, 0.028377464041113853, 0.03819559887051582, -0.08823758363723755, 0.007134751416742802, 0.019438832998275757, -0.007511681877076626, 0.0928325429558754, -0.02293889969587326, -0.003834367962554097, -0.049826592206954956, -0.0018633368890732527, -0.011936125345528126, -0.009118122979998589, 0.023244032636284828, -0.043400827795267105, -0.0597703717648983, -0.019510628655552864, -0.016755448654294014, 0.014493865892291069, -0.06192426010966301, 0.07473988831043243, -0.02295684814453125, -0.067452572286129, 0.005631517618894577, -0.024715855717658997, -0.012223309837281704, -0.013955394737422466, -0.002871849574148655, -0.06382685899734497, 0.047708600759506226, 0.0410674512386322, -0.01540926843881607, -0.04350852221250534, 0.012636138126254082, 0.07075519859790802, 0.0007454468868672848, 0.028144126757979393, -0.001024218276143074, -0.0029122349806129932, -0.020713215693831444, -0.049359917640686035, 0.052267663180828094, 0.02177220955491066, -0.038626376539468765, 0.056288253515958786, 0.0008884784765541553, -0.11422782391309738, 0.04185720905661583, -0.03509041294455528, 0.028862088918685913, 0.019654221832752228, 0.016916990280151367, -0.01471822988241911, -0.026546660810709, -0.04016999900341034, 0.04731372371315956, 0.04709833487868309, -0.008741192519664764, 0.016432365402579308, -0.004213541746139526, -0.0004268510965630412, -0.02916722372174263, -0.029974929988384247, 0.006847566459327936, -0.009961728937923908, -0.02604408748447895, -0.06633972376585007, 0.04910862818360329, 0.025703053921461105, -0.013219483196735382, -0.013793853111565113, -0.00263402471318841, 0.003966742195188999, 0.008745679631829262, -0.024500466883182526, 0.031446754932403564, -0.009548899717628956, -0.0155259370803833, 0.020982451736927032, 0.04282645881175995, 0.033816028386354446, 0.01493361871689558, -0.0420725978910923, 0.030944179743528366, -0.015220803208649158, -0.010482251644134521, -0.05452924594283104, 0.014287452213466167, 0.03729814663529396, 0.004552330356091261, -0.019672170281410217, 0.006452687084674835, 0.045770104974508286, -0.08773500472307205, 0.03184163197875023, -0.0008250958635471761, -0.04020589590072632, 0.051047127693891525, -0.011657915078103542, 0.00877260323613882, 0.06321658939123154, -0.023782504722476006, -0.02722872421145439, -0.009360435418784618, -0.03273908793926239, -0.0014471430331468582, 0.053703587502241135, 0.011460474692285061, 0.018828565254807472, -0.0303877592086792, -0.004980864468961954, -0.015095159411430359, 0.04167771711945534, 0.00932453665882349, -0.03494682163000107, 0.02223888598382473, -0.02317223697900772, 0.010545073077082634, 0.017751621082425117, 0.005923190154135227, -0.012716908939182758, -0.02148502506315708, -0.009180944412946701, -0.03544939309358597, -0.01641441509127617, -0.05004198104143143, -0.019223444163799286, 0.031949326395988464, -0.04232388362288475, 0.002020391169935465, -0.001762373372912407, 0.03566478192806244, 0.0037378917913883924, -0.015938766300678253, -0.04164182022213936, -0.010643793269991875, 0.03419296070933342, 0.027390265837311745, -0.03151854872703552, -0.04329313337802887, -0.014484891667962074, -0.001527913729660213, -0.05377538502216339, 0.036687880754470825, -0.04325723648071289, 0.0035516703501343727, -0.0037984699010849, -0.0014998683473095298, -0.035054516047239304, 0.006412301678210497, -0.021449126303195953, 0.03776482492685318, 0.05165739730000496, 0.03561093658208847, 0.024338925257325172, -0.025882545858621597, -0.026636404916644096, 0.014772077091038227, 0.02769540064036846, -0.002510624937713146, -0.004648806527256966, 0.03830329328775406, 0.00764629989862442, -0.007884125225245953, -0.0525907464325428, 0.0056135687045753, -0.0015301574021577835, 0.026151781901717186, -0.07409372180700302, 0.0017803224036470056, 0.0046757301315665245, -0.05277023836970329, 0.01890036091208458, -0.03248779848217964, 0.00877260323613882, -0.010904054157435894, -0.005478950683027506, -0.036687880754470825, -0.00027021748246625066, -0.03017237037420273, -0.009405307471752167, 0.05187278613448143, -0.035790424793958664, 0.04415468871593475, -0.0046757301315665245, 0.016674676910042763, 0.01820034720003605, -0.024087639525532722, -0.006371916271746159, 0.044836752116680145, -0.04860605672001839, -0.002802297007292509, 0.007251420523971319, -0.0029638386331498623, -0.03351089730858803, -0.03273908793926239, -0.04849836230278015, 0.013542566448450089, 0.010150193236768246, 0.05531900376081467, 0.014269502833485603, -0.006340505555272102, -0.016199026256799698, -0.007439885754138231, 0.022346580401062965, -0.009360435418784618, 0.06913977861404419, 0.008781577460467815, 0.00813092477619648, -0.06576535850763321, -0.03392372280359268, 0.025721004232764244, 0.04738552123308182, -0.008252080529928207, 0.03898536041378975, 0.004819322843104601, 0.018702920526266098, 0.05689852312207222, -0.006174476817250252, -0.005407154560089111, 0.019205493852496147, -0.013183584436774254, 0.03650838881731033, -0.024949194863438606, 0.0034484632778912783, 0.0002498845860827714, -0.0439034029841423, -0.02895183488726616, -0.0006815033848397434, 0.0193670354783535, -0.020659368485212326, 0.004126040264964104, 0.015463115647435188, -0.022903000935912132, 0.009889932349324226, 0.01435924880206585, 0.004363865125924349, -0.002728257095441222, 0.02607998438179493, 0.004918042570352554, 0.01814649999141693, -0.023046594113111496, -0.0032577544916421175, -0.002322159707546234, -0.018972156569361687, -0.0023737631272524595, 0.01444899383932352, -0.04655986279249191, -0.032146766781806946, 0.0310518741607666, -0.020372183993458748, -0.03591607138514519, -0.00993480533361435, 0.012519469484686852, 0.009216842241585255, 0.007022569887340069, 0.006654614116996527, -0.007516168989241123, -0.00466675590723753, -0.030190318822860718, -0.03080058842897415, 0.00598601158708334, 0.007928997278213501, -0.0047699627466499805, 0.011442526243627071, -0.01574132591485977, -0.01985166035592556, -0.007359114941209555, -0.033133964985609055, -0.02893388457596302, -0.011622016318142414, 0.055139511823654175, -0.02223888598382473, 0.055103614926338196, 0.01696186140179634, -0.00896555557847023, 0.02249017357826233, -0.04117514565587044, 0.00723795872181654, -0.007493732497096062, 0.0028471697587519884, -0.028646700084209442, 0.0052949730306863785, 0.04275466129183769, 0.0037827645428478718, 0.025056889280676842, -0.038590479642152786, 0.023800455033779144, -0.0016041973140090704, 0.00920786801725626, -0.010545073077082634, -0.01207074336707592, -0.03586222231388092, 0.058693427592515945, 0.03351089730858803, -0.015561835840344429, -0.052447155117988586, 0.05384718254208565, -0.01940293423831463, 0.04347262531518936, -0.0365622378885746, -0.00824759341776371, 0.023603014647960663, 0.00639435276389122, -0.027910789474844933, 0.03426475450396538, 0.062067851424217224, 0.00543407816439867, -0.007722583133727312, 0.0030535839032381773, -0.04016999900341034, 0.013057941570878029, 0.040277693420648575, 0.0038792407140135765, 0.02466200850903988, 0.02012089639902115, 0.049647100269794464, -0.03182368353009224, -0.035036567598581314, 0.06770385801792145, -0.02363891340792179, 0.02056962251663208, 0.00030064675956964493, 0.021143993362784386, -0.004491752479225397, 0.004265145398676395, -0.0579395666718483, 0.006968722678720951, -0.03424680605530739, 0.02058757282793522, 0.03876997157931328, 0.035036567598581314, 0.0474214181303978, 0.004348159767687321, 0.016216976568102837, -0.03254164755344391, 0.026726150885224342, 0.020623469725251198, -0.012375877238810062, 0.04828297346830368, 0.03586222231388092, 0.030782638117671013, -0.026923591271042824, -0.007125777192413807, -0.023854300379753113, -0.028880037367343903, 0.033367302268743515, -0.09067865461111069, 0.010428404435515404, -0.013775903731584549, 0.03566478192806244, 0.009970703162252903, 0.05427796021103859, -0.02126963622868061, 0.013569490052759647, -0.025685105472803116, 0.014852847903966904, 0.022113243117928505, -0.00598601158708334, -0.021879903972148895, 0.01088610477745533, 0.01706058159470558, -0.030064675956964493, 0.07176034152507782, -0.03483912721276283, -0.016504161059856415, -0.03132111206650734, -0.052985627204179764, -0.004227003548294306, -0.003870266256853938, 0.0015065992483869195, 0.011604067869484425, 0.020982451736927032, -0.001426950329914689, -0.011442526243627071, 0.00741744926199317, -0.005478950683027506, 0.01888241246342659, 0.012645113281905651, -0.013013068586587906, 0.014386171475052834, 0.010607894510030746, 0.011191239580512047, 0.02652871049940586, -0.03704686090350151, -0.002997493138536811, 0.024679958820343018, 0.020479878410696983, -0.01888241246342659, -0.023620963096618652, -0.04128284007310867, 0.022903000935912132, -0.009629670530557632, -0.02150297351181507, -0.0009226938709616661, -0.016988785937428474, -0.011532271280884743, 0.01435924880206585, -0.007897586561739445, 0.02753385901451111, 0.05327280983328819, -0.03568273037672043, -0.022633764892816544, -0.03293652459979057, -0.0023468397557735443, 0.0196183230727911, 0.0031859581358730793, 0.026869744062423706, 0.045052140951156616, -0.025487665086984634, -0.008189259096980095, -0.010832257568836212, -0.023064542561769485, 0.007592452690005302, -0.018173424527049065, 0.014422070235013962, 0.018155474215745926, 0.026205629110336304, 0.006205887533724308, 0.047026537358760834, 0.06738077104091644, 0.020282438024878502, -0.008543753065168858, -0.022149140015244484, -0.01507721096277237, 0.008961068466305733, 0.013093839399516582, 0.036490440368652344, 0.016216976568102837, 0.019205493852496147, -0.004693679511547089, -0.040528979152441025, -0.032146766781806946, 0.03160829469561577, 0.012393826618790627, -0.01915164664387703, -0.06174476817250252, -0.00439976342022419, -0.04810348153114319, -0.008287978358566761, 0.007578990887850523, -0.020443979650735855, 0.04910862818360329, -0.013838725164532661, 0.014484891667962074, -0.008611061610281467, 0.013497693464159966, 0.019510628655552864, -0.0029997366946190596, 0.004572523292154074, -0.020946552976965904, 0.051765091717243195, -0.0876632109284401, 0.04587779939174652, -0.02344147302210331, -0.030764689669013023, -0.009880958124995232, 0.0075565543957054615, -0.013542566448450089, -0.034085266292095184, -0.0033744233660399914, -0.04713423177599907, -0.027426164597272873, 0.04034948721528053, 0.00525458762422204, -0.04910862818360329, 0.020928604528307915, -0.02107219770550728, -0.0382314994931221, -0.019295239821076393, -0.006870002951472998, 0.02148502506315708, 0.013327177613973618, 0.008777090348303318, 0.016890065744519234, -0.006775770336389542, -0.019923457875847816, 0.018702920526266098, -0.02489534765481949, 0.004882144276052713, -0.009827110916376114, -0.011891252361238003, 0.003520259400829673, -0.008934144861996174, -0.00278210430406034, -0.06070372089743614, -0.028987731784582138, 0.02466200850903988, 0.029113376513123512, -0.0039644986391067505, 0.02195170149207115, 0.02394404634833336, 0.0044020069763064384, -0.03607761114835739, 0.005505874287337065, 0.01884651370346546, 0.0057392120361328125, 0.05251895263791084, 0.023279931396245956, -0.05639594793319702, 0.0222029872238636, 0.007749506738036871, 0.012357927858829498, 0.01589389331638813, -0.035305801779031754, -0.029131324961781502, -0.022185038775205612, 0.0005614690599031746, 0.006120629608631134, -0.0198696106672287, 0.00867388304322958, 0.011397653259336948, 0.03762122988700867, -0.020228590816259384, 0.011568169109523296, -0.010571996681392193, 0.007538605481386185, -0.009100173600018024, -0.01707853190600872, 0.007982844486832619, -0.024195333942770958, -0.007062955293804407, -0.06325248628854752, -0.001090405392460525, -0.026744099333882332, -0.0050706095062196255, -0.011092519387602806, -0.022579917684197426, 0.06601664423942566, -0.011630991473793983, 0.007520656101405621, -0.030423657968640327, -0.0196183230727911, -0.017222123220562935, 0.010500200092792511, -0.0477445013821125, -0.046954743564128876, -0.04121104255318642, -0.020156795158982277, 0.04142643138766289, -0.02150297351181507, 0.013318202458322048, 0.002665435429662466, 0.005088558420538902, 0.010841232724487782, -0.008853374049067497, -0.03236215561628342, -0.04979069530963898, -0.050113778561353683, 0.00844054576009512, -0.02392609789967537, 0.018990105018019676, -0.007727070711553097, -0.0011902470141649246, -0.0034955795854330063, 0.0402417927980423, 0.013937445357441902, 0.017697773873806, 0.015624657273292542, -0.04246747866272926, -0.003338525304570794, 0.005636005196720362, -0.02584664709866047, -0.019277291372418404, 0.007637325208634138, 0.0044244434684515, -0.035539139062166214, 0.029974929988384247, -0.01074251253157854, 0.026726150885224342, -0.013407948426902294, -0.033080119639635086, 0.048677850514650345, 0.012465622276067734, 0.0023086979053914547, 0.03783661872148514, 0.003630197374150157, -0.018451634794473648, -0.012016896158456802, -0.03352884575724602, -0.01470925472676754, 0.009059788659214973, -0.0047206031158566475, -0.028162075206637383, 0.014054113999009132, -0.031949326395988464, 0.02704923413693905, 0.0348929725587368, -0.027318470180034637, -0.0032263435423374176, -0.04203670099377632, -0.014009241946041584, -0.029328765347599983 ]
The Reinforcement Learning (RL) paradigm has been an essential tool for automating robotic tasks. Despite the advances in RL, it is still not widely adopted in the industry due to the need for an expensive large amount of robot interaction with its environment. Curriculum Learning (CL) has been proposed to expedite learning. However, most research works have been only evaluated in simulated environments, from video games to robotic toy tasks. This paper presents a study for accelerating robot learning of contact-rich manipulation tasks based on Curriculum Learning combined with Domain Randomization (DR). We tackle complex industrial assembly tasks with position-controlled robots, such as insertion tasks. We compare different curricula designs and sampling approaches for DR. Based on this study, we propose a method that significantly outperforms previous work, which uses DR only (No CL is used), with less than a fifth of the training time (samples). Results also show that even when training only in simulation with toy tasks, our method can learn policies that can be transferred to the real-world robot. The learned policies achieved success rates of up to 86\% on real-world complex industrial insertion tasks (with tolerances of $\pm 0.01~mm$) not seen during the training.
[ 0.04664761200547218, -0.017571769654750824, -0.03116270899772644, -0.03865087777376175, -0.010460639372467995, 0.015712879598140717, -0.026638241484761238, -0.0002912735508289188, -0.031408220529556274, 0.050821345299482346, 0.011223485693335533, -0.04776996001601219, 0.0046779136173427105, -0.08691186457872391, -0.016782617196440697, 0.056503232568502426, 0.03409133478999138, 0.0014632180100306869, -0.004809438716620207, -0.04384173825383186, 0.05909866467118263, -0.009881927631795406, -0.01416965015232563, 0.049839287996292114, -0.000377312971977517, 0.014958801679313183, 0.039527710527181625, 0.002026584465056658, -0.08059865236282349, 0.03591515123844147, 0.022429434582591057, 0.03721286728978157, -0.0035643333103507757, -0.004294298589229584, -0.02228914014995098, 0.009627645835280418, 0.037774041295051575, 0.07190044969320297, -0.07386456429958344, 0.03840536251664162, 0.024884570389986038, 0.03503831848502159, -0.021377231925725937, -0.04296490550041199, 0.0014369130367413163, -0.04100079461932182, -0.03647632524371147, 0.008641206659376621, -0.043105196207761765, 0.03289883956313133, -0.011986331082880497, -0.025077475234866142, 0.09883681684732437, -0.028497129678726196, -0.07060273736715317, 0.02297307178378105, 0.023113364353775978, 0.02128954790532589, 0.024376006796956062, 0.010749994777143002, 0.029952676966786385, -0.003257441334426403, -0.0608874075114727, 0.0191851444542408, 0.04149182140827179, -0.07316309213638306, 0.03258318081498146, -0.0391068309545517, 0.05324140936136246, -0.03121531754732132, -0.04720878601074219, -0.05401302129030228, -0.026427799835801125, -0.016773849725723267, -0.012003867886960506, -0.008066879585385323, 0.007448711432516575, 0.013292815536260605, -0.006098385900259018, -0.0006494057597592473, 0.03407379984855652, 0.01885194703936577, -0.004813822917640209, -0.05853749066591263, 0.11665409803390503, -0.04755951836705208, 0.06316717714071274, -0.05527566373348236, 0.021464915946125984, -0.00558105343952775, -0.02300814539194107, -0.005366228986531496, 0.0340387262403965, 0.011276095174252987, -0.01770329475402832, 0.017142120748758316, -0.015835635364055634, -0.0191851444542408, -0.03335479646921158, -0.005646815989166498, 0.01913253590464592, -0.0026239280123263597, -0.00043786937021650374, -0.015178009867668152, -0.006891921628266573, 0.025586038827896118, -0.05390780419111252, -0.021149255335330963, -0.040965721011161804, 0.1297014057636261, -0.033512625843286514, -0.05289067327976227, 0.0190974622964859, 0.04384173825383186, -0.041877631098032, 0.019062388688325882, -0.03830014169216156, -0.0728825107216835, 0.03605544567108154, -0.010925361886620522, 0.03288130462169647, 0.02272755838930607, 0.014555457048118114, -0.03012804314494133, -0.046612538397312164, 0.03721286728978157, -0.00252966838888824, 0.0014632180100306869, 0.04710356518626213, 0.017887430265545845, -0.04264924302697182, -0.004353484604507685, 0.00923307053744793, -0.010942897759377956, 0.05997550114989281, 0.008435150608420372, 0.0056380475871264935, -0.029637016355991364, -0.04640209674835205, 0.03393350541591644, 0.006098385900259018, -0.020044442266225815, -0.021096644923090935, 0.06158887594938278, 0.029303818941116333, 0.03370552882552147, -0.056117426604032516, 0.0773017555475235, -0.006940147373825312, 0.00868943240493536, -0.04598121717572212, 0.033530160784721375, -0.03724794089794159, 0.03082951158285141, 0.04868186637759209, 0.012258150614798069, -0.010153747163712978, 0.04282461106777191, 0.01082890946418047, -0.03012804314494133, 0.11370793730020523, 0.001897251233458519, -0.021008960902690887, 0.03011050634086132, 0.04566555470228195, 0.03114517219364643, 0.020693300291895866, -0.027462465688586235, -0.032811157405376434, 0.044122327119112015, -0.03815985098481178, -0.0013404611963778734, 0.02905830554664135, 0.04138660058379173, 0.02872510813176632, 0.018255699425935745, 0.020482860505580902, -0.021079108119010925, -0.01703689992427826, -0.06891921162605286, -0.02800610288977623, -0.0013273087097331882, 0.028532203286886215, 0.06046652793884277, 0.03374060243368149, 0.02442861720919609, 0.029531795531511307, -0.01731748692691326, -0.017115814611315727, -0.007830134592950344, -0.0033297801855951548, 0.039457567036151886, -0.006983988918364048, 0.03512600064277649, -0.010565859265625477, -0.03861580416560173, -0.02306075394153595, 0.05843226984143257, 0.005103178322315216, -0.00030744020477868617, -0.04398203268647194, 0.008351851254701614, 0.01594962552189827, -0.016230212524533272, 0.006085233297199011, 0.027164341881871223, -0.009145386517047882, 0.004055360797792673, -0.0069182263687253, -0.05362721532583237, -0.012529969215393066, 0.006979604717344046, -0.03298652544617653, -0.009636414237320423, -0.020640691742300987, 0.000918484409339726, -0.0040400163270533085, -0.02940903790295124, 0.003090842626988888, -0.060431454330682755, -0.012442285194993019, -0.023288732394576073, 0.011100728064775467, -0.011810964904725552, -0.03612559288740158, 0.05324140936136246, 0.023481635376811028, -0.012819324620068073, 0.0213070847094059, -0.000388273416319862, -0.023534245789051056, 0.02733970806002617, 0.03510846570134163, -0.0020879628136754036, -0.010267735458910465, 0.03658154606819153, 0.017808513715863228, -0.0033297801855951548, -0.0041627730242908, 0.03512600064277649, 0.04086050018668175, 0.0031105712987482548, -0.01776467263698578, -0.0037155873142182827, 0.018904557451605797, 0.01310868002474308, 0.020640691742300987, 0.08130012452602386, 0.03161866217851639, 0.016089918091893196, 0.012766714207828045, -0.05769572779536247, 0.006549955811351538, 0.011407620273530483, -0.033863358199596405, 0.07737190276384354, 0.05636294186115265, -0.032863765954971313, 0.05208398774266243, -0.03481034189462662, 0.011302400380373001, 0.014686983078718185, 0.06600812077522278, 0.02053547091782093, -0.009618877433240414, -0.00038251918158493936, -0.009715329855680466, 0.049102749675512314, 0.020307494327425957, -0.012784251011908054, -0.0038449205458164215, -0.03675691410899162, -0.01772959902882576, -0.010486943647265434, -0.02981238253414631, -0.026006920263171196, 0.04506930708885193, -0.015011411160230637, 0.025936773046851158, 0.063658207654953, 0.018887020647525787, 0.009724097326397896, 0.026147212833166122, 0.019728783518075943, 0.0031193397007882595, -0.0475945919752121, -0.04426262155175209, -0.023692075163125992, -0.05745021626353264, 0.009539962746202946, 0.006668328773230314, -0.02867249771952629, -0.023920053616166115, 0.024533838033676147, 0.0573800690472126, -0.00009658883209340274, -0.003448152681812644, -0.012828093022108078, -0.009382132440805435, -0.009653951041400433, 0.029935140162706375, -0.024551374837756157, 0.0010691904462873936, -0.037037502974271774, -0.020307494327425957, -0.004125507548451424, -0.022517116740345955, 0.010057294741272926, -0.013020996935665607, -0.04671775922179222, -0.011758354492485523, 0.010188819840550423, -0.011030581779778004, -0.0188168752938509, -0.04636702314019203, 0.04636702314019203, 0.044823795557022095, 0.015861941501498222, -0.02167535573244095, -0.026497947052121162, -0.015370913781225681, 0.020763447508215904, -0.0863506868481636, 0.07793307304382324, 0.07281236350536346, -0.021727966144680977, 0.01878180168569088, -0.0431753434240818, -0.05576669052243233, -0.037423308938741684, -0.04289475828409195, 0.01238090731203556, -0.03461743891239166, 0.01489742286503315, -0.006742859724909067, -0.04443798586726189, -0.08607010543346405, 0.056117426604032516, -0.03963293135166168, -0.062150049954652786, -0.03886131942272186, -0.013012228533625603, -0.025358062237501144, 0.003579678013920784, 0.01943065971136093, -0.047664739191532135, 0.026410263031721115, -0.0029220518190413713, -0.03575732186436653, -0.02202608995139599, 0.0009864391759037971, 0.020272420719265938, 0.030320946127176285, -0.02060561813414097, 0.019062388688325882, -0.0643947497010231, -0.003491994459182024, -0.0007491456926800311, -0.053276482969522476, -0.02160520851612091, 0.0004877393366768956, -0.06029115989804268, -0.02332380600273609, 0.02691882848739624, -0.05706440657377243, 0.0320044681429863, -0.00870696920901537, 0.007830134592950344, 0.05660845339298248, -0.013845221139490604, 0.0083255460485816, -0.013248973526060581, 0.04503423348069191, -0.05566147342324257, -0.012451053597033024, -0.0013152521569281816, -0.007247039582580328, 0.019290365278720856, -0.028760181739926338, 0.022394360974431038, -0.022096237167716026, 0.019220218062400818, -0.03868595138192177, 0.005252240225672722, 0.03114517219364643, 0.06853340566158295, 0.011284863576292992, -0.011135801672935486, 0.025077475234866142, 0.015791794285178185, 0.07765249162912369, -0.015125400386750698, -0.0011793427402153611, -0.000492123537696898, -0.029601942747831345, -0.003825191641226411, 0.026129676029086113, -0.0006768068415112793, 0.03298652544617653, -0.039562784135341644, -0.04461335390806198, 0.015853172168135643, -0.006514882668852806, 0.028058713302016258, 0.016598481684923172, -0.049418408423662186, 0.030005285516381264, -0.009478583931922913, -0.0027225720696151257, 0.009084008634090424, 0.01630912721157074, -0.022815240547060966, 0.025708796456456184, -0.029268745332956314, -0.010662310756742954, -0.019255291670560837, 0.009794244542717934, -0.001941093010827899, -0.03717779368162155, -0.059729985892772675, -0.0030996110290288925, 0.024253251031041145, 0.03589761629700661, 0.01594962552189827, -0.03125039115548134, 0.04029932618141174, 0.011363779194653034, 0.016563409939408302, -0.052259352058172226, -0.014599299058318138, 0.027848273515701294, 0.06029115989804268, -0.007496937643736601, 0.009443510323762894, 0.017948808148503304, 0.040264252573251724, 0.008132643066346645, 0.060080718249082565, -0.0018402569694444537, 0.007431174628436565, -0.0006351572228595614, -0.04461335390806198, -0.023218585178256035, -0.005098794121295214, 0.001405127695761621, -0.013547097332775593, -0.038124777376651764, -0.0013064838713034987, -0.010004685260355473, -0.00015714523033238947, -0.057625580579042435, -0.01731748692691326, -0.0878237709403038, -0.004121123347431421, 0.033091746270656586, -0.004081666003912687, 0.00885164737701416, -0.03801955655217171, -0.015309534966945648, -0.00745747983455658, 0.019676173105835915, 0.0411410890519619, 0.004528851713985205, -0.006957684177905321, -0.00043841739534400403, 0.03503831848502159, -0.02332380600273609, -0.03872102499008179, 0.006418430712074041, 0.03963293135166168, -0.02626997046172619, -0.0640089362859726, -0.028163934126496315, 0.00531800277531147, 0.0190974622964859, -0.0014215684495866299, 0.031723883002996445, -0.035599492490291595, -0.012968386523425579, -0.026760997250676155, -0.043035052716732025, -0.012521200813353062, -0.01238090731203556, -0.048015471547842026, 0.013117448426783085, 0.003428424010053277, 0.05846734344959259, -0.01630035787820816, 0.012582579627633095, 0.021482452750205994, 0.01599346660077572, -0.005830951500684023, -0.05481971055269241, 0.008492144756019115, -0.010250198654830456, -0.035652101039886475, -0.0062211425974965096, -0.0673409104347229, 0.03731808811426163, -0.02088620513677597, -0.018887020647525787, -0.04082542657852173, 0.013213899917900562, -0.01809787005186081, -0.0333898700773716, -0.008934946730732918, 0.05033031851053238, -0.015046484768390656, 0.03154851496219635, 0.006677096709609032, -0.027515076100826263, 0.053662288933992386, -0.017185961827635765, -0.0030842663254588842, 0.016238979995250702, 0.016905374825000763, 0.01011867355555296, -0.025954309850931168, 0.02800610288977623, 0.02088620513677597, 0.011302400380373001, 0.035301368683576584, -0.00005795330071123317, 0.005401302129030228, -0.025287915021181107, 0.01135501079261303, 0.04454320669174194, -0.02939150109887123, 0.07596896588802338, 0.026655778288841248, -0.02835683710873127, 0.017975112423300743, -0.03163620084524155, -0.06811252981424332, -0.022604800760746002, 0.016870301216840744, 0.0651312842965126, -0.03398611769080162, 0.007023446727544069, -0.011214717291295528, -0.002367453882470727, 0.05033031851053238, -0.0071900454349815845, 0.019220218062400818, 0.01804525963962078, 0.004647224210202694, 0.007295265328139067, 0.0018830026965588331, 0.022131310775876045, 0.028777718544006348, -0.00033949947101064026, 0.00012392141798045486, -0.009776707738637924, 0.02479688823223114, -0.026760997250676155, -0.02974223531782627, -0.006756011862307787, -0.015835635364055634, 0.004743676166981459, -0.002757645444944501, -0.00848337635397911, 0.006791085470467806, -0.016054844483733177, 0.01770329475402832, 0.01988661289215088, -0.08901626616716385, 0.001162902102805674, 0.059694912284612656, 0.01846614107489586, -0.017527926713228226, -0.015861941501498222, 0.008229094557464123, 0.011600524187088013, -0.0318291038274765, -0.00036333841853775084, 0.04706849157810211, -0.003825191641226411, -0.022218992933630943, -0.03822999820113182, 0.020114589482545853, 0.003246480831876397, 0.00027072275406681, 0.027585221454501152, 0.0058134146966040134, 0.002930820221081376, 0.003656401066109538, -0.03637110814452171, -0.02586662583053112, 0.007887128740549088, -0.009092777036130428, -0.042298510670661926, 0.020675763487815857, -0.007895897142589092, 0.022955534979701042, -0.0258315522223711, 0.009136618115007877, 0.005418838933110237, -0.021447379142045975, 0.019062388688325882, -0.03609051927924156, 0.018711654469370842, 0.024376006796956062, 0.019272828474640846, 0.0326533280313015, -0.0024047193583101034, -0.011995099484920502, 0.015546280890703201, -0.002908899448812008, 0.008101953193545341, -0.016440652310848236, -0.0014982913853600621, 0.042017921805381775, 0.037037502974271774, -0.0374583825469017, 0.017212266102433205, -0.0030448087491095066, 0.04542004317045212, 0.03970307856798172, -0.00745747983455658, -0.028637424111366272, -0.02379729598760605, -0.01454668864607811, 0.02760275825858116, 0.011644366197288036, -0.013748769648373127, 0.005300466436892748, 0.022096237167716026, -0.029145987704396248, -0.0276729054749012, 0.010618469677865505, 0.04219328984618187, 0.008601749315857887, -0.022762630134820938, -0.023621929809451103, -0.0004217027162667364, -0.005515290889889002, 0.017869893461465836, 0.08880582451820374, 0.04398203268647194, 0.0014237604336813092, -0.042438805103302, 0.015116631984710693, -0.018325846642255783, 0.06060681864619255, -0.005923018790781498, 0.05569654703140259, 0.005545979831367731, -0.006177301052957773, 0.03391597047448158, -0.0056380475871264935, -0.030583998188376427, 0.01628282107412815, 0.014117039740085602, 0.05250486731529236, -0.0190974622964859, -0.015765490010380745, 0.01948326826095581, 0.013310352340340614, -0.008746426552534103, 0.04713863879442215, -0.004276761785149574, -0.01627405360341072, -0.01220554020255804, -0.010057294741272926, 0.017834819853305817, 0.037107646465301514, 0.04398203268647194, 0.03431931510567665, 0.016124991700053215, 0.0632724016904831, 0.006922610569745302, -0.025638649240136147, -0.017975112423300743, -0.010934129357337952, 0.007119898684322834, -0.005111946724355221, -0.00976793933659792, 0.026305044069886208, -0.008224709890782833, -0.0057257311418652534, -0.022867850959300995, 0.0038668413180857897, 0.02521776780486107, -0.012643957510590553, 0.017773441970348358, -0.015572586096823215, -0.026094602420926094, 0.033880896866321564, -0.044087253510951996, 0.018360920250415802, -0.029707161709666252, -0.014686983078718185, 0.010048526339232922, -0.023867443203926086, -0.001275794580578804, 0.040264252573251724, -0.026743460446596146, -0.05559132620692253, 0.06867370009422302, -0.034582365304231644, -0.02230667695403099, -0.021850723773241043, -0.008470224216580391, -0.00013892351125832647, 0.0918922871351242, 0.014616835862398148, -0.011118264868855476, 0.027567686513066292, 0.0066990177147090435, 0.018887020647525787, -0.006514882668852806, 0.024305859580636024, 0.011188412085175514, 0.009557499550282955, 0.0034240398090332747, 0.009873159229755402, 0.020675763487815857, -0.02335887961089611, 0.029181061312556267, 0.01951834186911583, -0.0010039758635684848, 0.018711654469370842, 0.02263987436890602, -0.07183030247688293, -0.04257909581065178, 0.0023630696814507246, 0.0019783584866672754, -0.050119876861572266, 0.009084008634090424, -0.018571360036730766, 0.006216758396476507, -0.019009778276085854, 0.014643141068518162, -0.0025603575631976128, 0.005054952576756477, -0.014090735465288162, 0.015309534966945648, 0.019220218062400818, 0.022745095193386078, 0.008220326155424118, -0.021359695121645927, -0.00888233631849289, 0.0667797401547432, -0.03770389407873154, 0.011749586090445518, -0.029338892549276352, 0.016019770875573158, 0.016931679099798203, 0.02839191071689129, -0.011723280884325504, 0.08719245344400406, -0.03770389407873154, 0.0453849695622921, 0.03977322578430176, -0.05246979370713234, -0.02486703358590603, 0.006422814913094044, -0.02193840593099594, 0.028549740090966225, 0.002214007778093219, -0.019728783518075943, 0.04173733666539192, -0.00350295496173203, 0.016493262723088264, 0.010767531581223011, 0.005221551284193993, 0.011100728064775467, 0.03570471331477165, 0.03661661967635155, 0.007124282419681549, 0.04748937115073204, -0.015695342794060707, 0.07035722583532333, -0.025322988629341125, -0.018325846642255783, 0.04854157194495201, 0.0012385291047394276, 0.010039757937192917, -0.049067676067352295, -0.020412713289260864, 0.005879177246242762, 0.025778941810131073, 0.03370552882552147, 0.007887128740549088, -0.027146805077791214, 0.05699425935745239, 0.0233413428068161, -0.017878660932183266, 0.023183511570096016, 0.009610109031200409, -0.027111731469631195, 0.006286905612796545, 0.002867249771952629, 0.016440652310848236, 0.042368657886981964, -0.01951834186911583, -0.028128860518336296, 0.011241021566092968, 0.0016199522651731968, -0.0404045470058918, -0.00003053508771699853, 0.007843286730349064, 0.008185252547264099, 0.04036947339773178, -0.006317594554275274, 0.03300406038761139, 0.0166949350386858, -0.0325656421482563, 0.0019498612964525819, 0.025621112436056137, 0.04222836345434189, 0.023534245789051056, -0.011083191260695457, -0.03612559288740158, -0.01599346660077572, -0.07109376788139343, 0.02128954790532589, 0.026725923642516136, 0.023218585178256035, -0.02085113152861595, 0.016054844483733177, -0.0368972085416317, 0.025726333260536194, 0.026059530675411224, -0.0389314629137516, -0.0004088242130819708, -0.0010248007019981742, -0.007255807984620333, 0.032092154026031494, 0.02947918511927128, 0.03714272007346153, 0.057555437088012695, -0.012722873128950596, -0.012126625515520573, -0.0049935742281377316, 0.02509501203894615, -0.00601508654654026, 0.01114457007497549, -0.0030448087491095066, 0.06200975552201271, 0.0013547097332775593, -0.03924712538719177, -0.028426984325051308, -0.03361784666776657, -0.03305667266249657, -0.00415619695559144, -0.0213070847094059, 0.025077475234866142, -0.011153338477015495, 0.0244461540132761, 0.02125447429716587, 0.046963270753622055, 0.013371730223298073, 0.01628282107412815, -0.041351526975631714, 0.019027315080165863, -0.015686573460698128, 0.08438657969236374, -0.021745502948760986, -0.018255699425935745, -0.016572177410125732, -0.0005644623888656497, -0.00848337635397911, 0.012100320309400558, 0.017606843262910843, 0.03509092703461647, -0.017571769654750824, 0.0028409447986632586, -0.05057583004236221, -0.05292574688792229, 0.019342975690960884, 0.04748937115073204, -0.06193960830569267, 0.03540658950805664, -0.013248973526060581, 0.005629279185086489, 0.008956867270171642, -0.038054630160331726, -0.02939150109887123, -0.034231629222631454, 0.004888353869318962, 0.023937590420246124, -0.006852463819086552, -0.04296490550041199, 0.043420858681201935, 0.006585029419511557, -0.005545979831367731, -0.04706849157810211, 0.00296370149590075, -0.011214717291295528, -0.026340117678046227, 0.02483196184039116, -0.040194105356931686, -0.009987148456275463, 0.014572993852198124, -0.007645999547094107, -0.02299060858786106, 0.017299950122833252, -0.014494079165160656, 0.02374468557536602, 0.004296490456908941, -0.01990414969623089, -0.002551589161157608, -0.02697143889963627, 0.023236121982336044, 0.0276729054749012, -0.0035073391627520323, -0.017948808148503304, 0.01149530429393053, -0.019360512495040894, -0.025358062237501144, -0.0191851444542408, 0.038756098598241806, -0.007865208201110363, 0.018571360036730766, 0.025656186044216156, -0.02697143889963627, -0.05145266652107239, 0.03475772961974144, -0.0341264083981514, 0.009084008634090424, -0.015362145379185677, -0.0018084717448800802, -0.0052083986811339855, -0.05857256427407265, 0.020342567935585976, 0.0013821108732372522, -0.00798358116298914, 0.01274040900170803, -0.017589306458830833, -0.012968386523425579, 0.036651693284511566, 0.007391717284917831, -0.002733532339334488, 0.011635597795248032, -0.002301691332831979, 0.003428424010053277, -0.03833521530032158, -0.04499915987253189, -0.03167127072811127, -0.050856418907642365, -0.025989383459091187, 0.031303003430366516, -0.053030967712402344, 0.022201456129550934, -0.005497754085808992, -0.005655584391206503, 0.07344368100166321, -0.03928219899535179, -0.007501321379095316, 0.007685456890612841, 0.003461305284872651, 0.05250486731529236, -0.01330158393830061, -0.012003867886960506, -0.005024263169616461, -0.02165781892836094, 0.016177602112293243, -0.030285874381661415, 0.047629665583372116, -0.010837677866220474, 0.013547097332775593, -0.020780984312295914, -0.006795469671487808, -0.06846325844526291, 0.01065354235470295, -0.008023038506507874, -0.01330158393830061, -0.017650684341788292, 0.031408220529556274, -0.001941093010827899, 0.035950224846601486, 0.022517116740345955, 0.028286689892411232, 0.005817798897624016, 0.03323203697800636, -0.04433276504278183, -0.046612538397312164, -0.030619069933891296, 0.01983400247991085, 0.013205131515860558, -0.06271122395992279, 0.012766714207828045, -0.011837269179522991, -0.020833594724535942, 0.0038295758422464132, 0.008952483534812927, -0.020640691742300987, 0.004318411462008953, -0.01509032677859068, -0.04005381464958191, 0.01556381769478321, 0.013845221139490604, -0.054749563336372375, 0.011091959662735462, -0.01065354235470295, 0.037738967686891556, 0.00019893189892172813, 0.02511254884302616, -0.00341527140699327, -0.018536288291215897, 0.008378156460821629, -0.007970428094267845, 0.04331563785672188, 0.029338892549276352, 0.009987148456275463, 0.045560333877801895, 0.0007190045434981585, -0.029970213770866394, 0.06537680327892303, -0.008952483534812927, 0.02549835480749607, 0.03822999820113182, -0.003763813292607665, 0.028076250106096268, 0.015546280890703201, -0.031039951369166374, 0.01698428951203823, -0.020360102877020836, -0.0732332393527031, 0.05706440657377243, -0.03282869607210159, 0.050505682826042175, -0.041982848197221756 ]
To act safely and ethically in the real world, agents must be able to reason about harm and avoid harmful actions. However, to date there is no statistical method for measuring harm and factoring it into algorithmic decisions. In this paper we propose the first formal definition of harm and benefit using causal models. We show that any factual definition of harm must violate basic intuitions in certain scenarios, and show that standard machine learning algorithms that cannot perform counterfactual reasoning are guaranteed to pursue harmful policies following distributional shifts. We use our definition of harm to devise a framework for harm-averse decision making using counterfactual objective functions. We demonstrate this framework on the problem of identifying optimal drug doses using a dose-response model learned from randomized control trial data. We find that the standard method of selecting doses using treatment effects results in unnecessarily harmful doses, while our counterfactual approach allows us to identify doses that are significantly less harmful without sacrificing efficacy.
[ 0.0047470335848629475, -0.02995947375893593, -0.014782140031456947, 0.009136510081589222, 0.0004081319784745574, 0.02677910216152668, -0.06590331345796585, -0.001012684777379036, -0.04700927436351776, 0.024803131818771362, 0.009498771280050278, 0.03323394060134888, 0.019477421417832375, -0.00231823674403131, -0.03425015136599541, 0.02555588260293007, -0.03488999232649803, -0.030354667454957962, -0.009042416699230671, -0.03438188508152962, -0.00021612175623886287, 0.017426175996661186, -0.006473655346781015, 0.08355531841516495, 0.027569491416215897, 0.029846562072634697, -0.009748120792210102, -0.0011338306358084083, -0.02666619047522545, 0.019477421417832375, -0.0051986840553581715, 0.029808923602104187, -0.05273018032312393, -0.03219890594482422, -0.011027796193957329, 0.00530218705534935, -0.019533878192305565, 0.04569196328520775, -0.026101626455783844, 0.0646236389875412, -0.004253040999174118, 0.025104232132434845, -0.028792710974812508, 0.003900189185515046, 0.0005451561301015317, -0.03020411729812622, -0.023993926122784615, -0.025499427691102028, -0.03389259800314903, -0.0037025921046733856, 0.000949171488173306, -0.10282573103904724, 0.03921830654144287, -0.059806037694215775, -0.04174002259969711, 0.019740885123610497, 0.0036673068534582853, -0.05216561630368233, 0.052015066146850586, -0.01802837662398815, -0.030862774699926376, -0.004986973013728857, -0.00668066181242466, -0.007085265126079321, -0.029526643455028534, -0.015892447903752327, -0.02924436144530773, 0.032914020121097565, 0.012053418904542923, 0.007908586412668228, -0.05032137781381607, 0.03669659048318863, -0.005974958185106516, 0.03123915009200573, -0.04215403273701668, 0.012514478527009487, 0.0557035468518734, 0.05950493738055229, 0.01879994571208954, -0.00018098359578289092, 0.021660398691892624, 0.017868418246507645, -0.0063654473051428795, 0.0037849240470677614, 0.08287784457206726, -0.036395490169525146, 0.04057325795292854, -0.061951376497745514, 0.006779460236430168, -0.030411124229431152, -0.03603793680667877, 0.01331427600234747, -0.0011467684525996447, 0.029432548210024834, -0.034099601209163666, 0.022977711632847786, 0.004544731695204973, -0.018668215721845627, -0.021603941917419434, 0.01856471225619316, 0.019402146339416504, 0.04437464848160744, -0.00939997285604477, -0.004055443685501814, -0.009926898404955864, -0.056418657302856445, -0.05660684406757355, 0.042906783521175385, 0.02674146555364132, 0.22311528027057648, -0.03120151348412037, 0.03152143210172653, -0.06793574243783951, -0.013775336556136608, -0.04667053744196892, -0.04030979424715042, -0.05799943581223488, -0.04219167307019234, 0.051902156323194504, 0.01509264949709177, -0.04283151030540466, 0.03775044158101082, 0.03545455262064934, -0.0008456682553514838, -0.02668500877916813, 0.020324265584349632, -0.030467581003904343, -0.024953681975603104, 0.008374350145459175, 0.0034414816182106733, 0.004836422856897116, 0.017125075682997704, 0.021754492074251175, 0.007414593361318111, 0.001979498891159892, -0.06631732732057571, 0.023109443485736847, 0.006097279954701662, -0.01732267253100872, 0.03253764659166336, -0.03466416522860527, -0.04584251344203949, -0.07294153422117233, -0.03233063966035843, -0.019590334966778755, -0.054198045283555984, -0.007607485633343458, 0.01669224537909031, -0.015214971266686916, 0.0046741110272705555, -0.023128261789679527, 0.01741676777601242, 0.0011285378132015467, 0.028190510347485542, 0.04776202514767647, -0.028755072504281998, -0.028359878808259964, -0.0151585154235363, 0.015440796501934528, -0.006492474116384983, 0.05671975761651993, -0.03125796839594841, 0.00930117443203926, 0.07926464080810547, 0.10357848554849625, 0.04377244785428047, 0.01401057094335556, -0.03918066993355751, -0.025499427691102028, 0.04700927436351776, -0.019853796809911728, -0.011441809125244617, -0.06010713428258896, 0.032801106572151184, 0.05359584465622902, 0.0404227077960968, 0.05502606928348541, 0.02581934630870819, -0.010736105963587761, -0.0376751683652401, -0.006412494461983442, 0.0044130003079771996, 0.03940649330615997, -0.017501451075077057, -0.020625365898013115, 0.0313144251704216, 0.017030982300639153, -0.019609153270721436, 0.12134339660406113, 0.02118992991745472, 0.015930084511637688, 0.0156572125852108, -0.0010767861967906356, 0.008214390836656094, -0.015177333727478981, -0.018743490800261497, -0.04358426108956337, -0.060859885066747665, -0.0012961424654349685, -0.0026863787788897753, -0.015600756742060184, -0.04930516332387924, 0.03163434565067291, 0.031032143160700798, 0.002808700781315565, -0.028717435896396637, 0.04117545858025551, -0.02677910216152668, -0.02214968577027321, -0.03381732106208801, -0.025028957054018974, 0.0038202092982828617, -0.03598148003220558, 0.005066952668130398, -0.028717435896396637, -0.023711644113063812, 0.010378548875451088, 0.04463811218738556, -0.025405332446098328, -0.020888829603791237, 0.03784453868865967, 0.013116679154336452, 0.08671686798334122, 0.003072163322940469, 0.011931097134947777, 0.04384772479534149, -0.0036531928926706314, -0.005838521756231785, -0.014923281036317348, -0.05476260557770729, 0.013765926472842693, 0.02132166177034378, 0.0029498415533453226, 0.005885568913072348, 0.030467581003904343, 0.019176321104168892, 0.0019877320155501366, 0.05050956457853317, 0.01181818451732397, -0.04019688069820404, -0.002128872787579894, 0.008557833731174469, 0.030862774699926376, -0.0517139658331871, 0.044035911560058594, 0.010943111963570118, -0.04027215763926506, 0.03441952168941498, 0.019477421417832375, 0.030542856082320213, 0.008364940993487835, -0.05178924277424812, 0.015186743810772896, 0.0009756353683769703, -0.003641430987045169, 0.026421546936035156, 0.001236157608218491, -0.05043429136276245, 0.022845981642603874, -0.03652722388505936, 0.013398961164057255, -0.022733068093657494, 0.01584540121257305, 0.020738279446959496, -0.027174297720193863, 0.0065912725403904915, 0.029884198680520058, -0.017755504697561264, 0.0313144251704216, 0.062101926654577255, -0.0398581437766552, -0.013351913541555405, 0.01003981102257967, 0.02237551100552082, -0.004765852354466915, -0.04264332354068756, 0.048401862382888794, 0.0626288503408432, 0.02013607881963253, -0.011197165586054325, -0.05141286551952362, -0.03884193301200867, 0.009710483253002167, -0.011460628360509872, -0.01996671035885811, -0.06579039990901947, -0.015346703119575977, -0.0338737778365612, -0.07881298661231995, -0.00014760969497729093, -0.011197165586054325, -0.011479446664452553, 0.0015396102098748088, -0.0001162205808213912, 0.046407073736190796, -0.0055750589817762375, -0.0027381302788853645, 0.015403158962726593, 0.04550377279520035, 0.007536915596574545, -0.05393458157777786, -0.030825138092041016, 0.054009854793548584, 0.03899248316884041, -0.04535322263836861, 0.004598835948854685, 0.04885351285338402, 0.0398581437766552, -0.006544225383549929, 0.049606263637542725, 0.02660973370075226, -0.024069201201200485, 0.04486393555998802, -0.04113782197237015, 0.013126088306307793, -0.012730894610285759, 0.0008256733417510986, -0.039707593619823456, -0.02668500877916813, -0.023899832740426064, -0.013154316693544388, -0.018941087648272514, -0.05058484151959419, -0.002115934854373336, -0.031013324856758118, -0.00132437061984092, -0.05107412859797478, 0.007061741780489683, -0.053106553852558136, -0.03543573617935181, -0.0628170371055603, 0.0032109518069773912, -0.017068620771169662, 0.022168505936861038, -0.05404749512672424, 0.003987225703895092, -0.040874358266592026, 0.012646210379898548, -0.02122756652534008, -0.026515640318393707, 0.04132600873708725, 0.014114073477685452, -0.05235380306839943, 0.03108859993517399, 0.011328896507620811, -0.009381154552102089, -0.04132600873708725, 0.027588309720158577, 0.015064421109855175, -0.004944630432873964, 0.0011297139571979642, -0.04155183210968971, -0.02344818226993084, 0.02568761445581913, 0.0422293096780777, 0.006078461185097694, 0.02905617281794548, -0.0059702531434595585, -0.05032137781381607, 0.03814563527703285, 0.029413729906082153, -0.031916625797748566, -0.02580052800476551, -0.015948902815580368, -0.0818992629647255, 0.011545312590897083, 0.019778521731495857, 0.015516071580350399, 0.00038343234336934984, -0.02118992991745472, -0.049568627029657364, 0.03248118981719017, 0.09206140041351318, 0.011291258968412876, -0.07026927173137665, -0.0493428036570549, -0.0006721827667206526, -0.05017082765698433, -0.014189348556101322, 0.02802114188671112, -0.030956868082284927, 0.007028808817267418, -0.0151585154235363, -0.0055515356361866, 0.0014749207766726613, -0.04448756203055382, 0.01346482615917921, 0.013191954232752323, 0.04253040999174118, 0.022168505936861038, 0.013229591771960258, -0.03504054248332977, -0.007847425527870655, -0.029263179749250412, 0.05513898283243179, 0.007518096826970577, 0.03822091221809387, -0.05449914559721947, 0.04452519863843918, -0.027456577867269516, 0.051036491990089417, -0.04689636453986168, 0.017652001231908798, 0.04034743085503578, 0.004812899045646191, 0.021923862397670746, -0.0008556657121516764, -0.024332663044333458, -0.005607991944998503, 0.027531852945685387, 0.011451218277215958, 0.012749713845551014, 0.009832805022597313, 0.021886223927140236, -0.022864799946546555, 0.032857563346624374, 0.004758795257657766, -0.025461789220571518, 0.03210481256246567, -0.06149972602725029, -0.02452085167169571, -0.004883469548076391, 0.05242908000946045, 0.0016795748379081488, -0.03263173997402191, 0.02367400750517845, -0.016466420143842697, -0.023071806877851486, -0.008788363076746464, -0.06409671157598495, 0.017106257379055023, 0.0826520174741745, -0.03707296773791313, -0.026383908465504646, -0.028585704043507576, 0.03759989142417908, -0.018715262413024902, 0.011837003752589226, -0.007536915596574545, -0.019853796809911728, 0.0578865222632885, -0.025461789220571518, -0.04271859675645828, 0.05062247812747955, -0.05713377147912979, -0.014923281036317348, -0.009343517012894154, -0.019609153270721436, -0.004043682012706995, -0.003930769395083189, -0.09085699915885925, 0.0673711821436882, -0.02341054379940033, -0.04339607432484627, 0.05581645667552948, 0.017444996163249016, 0.04836422577500343, -0.05378403142094612, 0.05905328691005707, -0.04776202514767647, -0.01613709144294262, 0.010999567806720734, -0.002271189820021391, -0.008247324265539646, -0.01125362142920494, 0.05461205542087555, -0.07090910524129868, -0.023052986711263657, 0.0005154577665962279, 0.026534458622336388, -0.006713594309985638, 0.003580270102247596, -0.03583092987537384, -0.09093227237462997, -0.007414593361318111, 0.029601918533444405, -0.003159200306981802, -0.021509848535060883, 0.03144615516066551, -0.05717140808701515, 0.07433412224054337, 0.03014766238629818, -0.019308052957057953, -0.04475102201104164, 0.011310078203678131, -0.008129706606268883, 0.05374639481306076, 0.024182112887501717, 0.014960918575525284, -0.05284309387207031, -0.0424174964427948, -0.06669370085000992, -0.02583816461265087, -0.005396280903369188, -0.015271428041160107, -0.005231616552919149, -0.040610894560813904, -0.011498265899717808, 0.040987271815538406, 0.02681674063205719, 0.0511494055390358, -0.025969896465539932, -0.02461494505405426, 0.008722498081624508, 0.014763321727514267, -0.029601918533444405, -0.0009579927427694201, -0.015262018889188766, -0.012984948232769966, -0.013144907541573048, 0.06112334877252579, -0.008463739417493343, -0.019740885123610497, -0.017313264310359955, -0.02226259931921959, -0.005151636898517609, 0.020343085750937462, -0.03650840371847153, 0.05592937022447586, 0.026289815083146095, 0.024182112887501717, -0.040610894560813904, -0.050735391676425934, 0.016428781673312187, -0.0446004718542099, 0.01672988198697567, 0.02807759679853916, -0.0017607307527214289, 0.007762740831822157, -0.030768681317567825, 0.040648531168699265, 0.07215114682912827, -0.013126088306307793, -0.05766069516539574, -0.019458603113889694, -0.034287791699171066, -0.006087870337069035, 0.020380722358822823, -0.02792704850435257, -0.008858934044837952, -0.017529679462313652, 0.08581356704235077, 0.037486981600522995, 0.014763321727514267, -0.023730462417006493, 0.015883037820458412, 0.03340330719947815, -0.0014490449102595448, -0.016645198687911034, 0.011827593669295311, -0.0023488171864300966, -0.02583816461265087, -0.007880358025431633, 0.008623698726296425, -0.008571947924792767, -0.013276638463139534, 0.023899832740426064, 0.0005869102315045893, -0.013577738776803017, -0.012354519218206406, 0.02796468511223793, -0.029281998053193092, 0.011460628360509872, 0.02139693684875965, 0.018997542560100555, -0.019571516662836075, 0.017021572217345238, 0.05656920745968819, -0.014716274105012417, 0.018291840329766273, -0.0033709113486111164, -0.039820507168769836, -0.029583098366856575, -0.02561233937740326, -0.03472062200307846, 0.0032579987309873104, -0.012100465595722198, -0.016974525526165962, -0.02689201571047306, -0.019308052957057953, -0.011902868747711182, -0.009691664017736912, 0.016485238447785378, 0.02023017220199108, -0.0007115845801308751, 0.027418941259384155, -0.014377536252140999, -0.025499427691102028, 0.0006810040795244277, 0.0005228088120929897, -0.04000869393348694, 0.04452519863843918, -0.01058555580675602, 0.0018618815811350942, -0.03560510277748108, 0.00390959857031703, -0.01181818451732397, -0.013624786399304867, -0.0005572118679992855, -0.03652722388505936, 0.03677186742424965, -0.010312682949006557, 0.004314201883971691, 0.03033584915101528, -0.021886223927140236, 0.0184329804033041, 0.02128402329981327, -0.0016372326062992215, -0.03342212736606598, 0.02026781067252159, 0.04704691469669342, -0.03703533113002777, -0.010858427733182907, -0.021754492074251175, -0.0030792204197496176, 0.002764006145298481, 0.018978724256157875, -0.003072163322940469, -0.02566879615187645, -0.02117111161351204, 0.0026158082764595747, -0.026421546936035156, 0.037336431443691254, 0.02361755073070526, -0.008190867491066456, 0.02901853621006012, -0.006177259609103203, -0.00841198768466711, 0.020888829603791237, -0.05129995569586754, -0.020907647907733917, -0.02811523526906967, 0.0036437835078686476, -0.002472315216436982, 0.03921830654144287, -0.018790537491440773, 0.0059937769547104836, 0.02798350341618061, 0.019402146339416504, -0.037336431443691254, -0.018771719187498093, 0.02004198543727398, 0.006407789420336485, 0.046519987285137177, -0.007245224434882402, 0.02566879615187645, 0.0031450861133635044, 0.010077448561787605, 0.03583092987537384, 0.02689201571047306, -0.011037205345928669, 0.03447597846388817, 0.05717140808701515, 0.04358426108956337, 0.02888680435717106, -0.022526061162352562, 0.007762740831822157, -0.015271428041160107, 0.0054856701754033566, 0.050660114735364914, -0.0010226822923868895, 0.0022065001539885998, 0.025330057367682457, 0.04508976265788078, 0.02105819806456566, -0.0008556657121516764, 0.020926466211676598, 0.013615376316010952, 0.030505217611789703, 0.046331800520420074, -0.012156922370195389, -0.026346271857619286, -0.05480024591088295, 0.021942680701613426, 0.0179342832416296, -0.016090044751763344, 0.00021082897728774697, 0.06108571216464043, 0.003813152201473713, -0.008280256763100624, -0.0013561273226514459, -0.026365090161561966, -0.041890572756528854, 0.03133324533700943, 0.0015925379702821374, -0.012702666223049164, -0.024784313514828682, 0.035134635865688324, -0.03504054248332977, -0.04046034440398216, -0.018169518560171127, -0.047536201775074005, -0.013276638463139534, 0.03362913429737091, -0.002398216398432851, -0.002549942582845688, 0.014255214482545853, -0.047573838382959366, 0.01613709144294262, -0.02920672297477722, -0.019853796809911728, 0.009555228054523468, -0.007414593361318111, 0.035096995532512665, -0.028698617592453957, -0.0018501199083402753, 0.020794736221432686, -0.010801970958709717, -0.006224306765943766, -0.02137811668217182, 0.005081066396087408, 0.052956003695726395, -0.025951078161597252, 0.03498408570885658, -0.004142480902373791, 0.0005501548293977976, 0.06292995065450668, 0.009870442561805248, 0.00830848515033722, 0.0031780190765857697, 0.020305447280406952, -0.018696444109082222, 0.0447886623442173, -0.03144615516066551, 0.02474667690694332, 0.005038724280893803, 0.042944423854351044, 0.03498408570885658, 0.0014419879298657179, -0.006238420493900776, 0.013916476629674435, 0.003504995023831725, 0.004224812611937523, -0.00236410740762949, -0.007329909130930901, 0.0145186772570014, 0.0014537496026605368, -0.0036673068534582853, -0.015233790501952171, 0.015214971266686916, 0.01669224537909031, -0.01445281133055687, 0.03218008950352669, -0.021942680701613426, -0.027701223269104958, 0.024803131818771362, -0.011611178517341614, -0.0019947891123592854, -0.020813554525375366, 0.010331502184271812, 0.0578865222632885, -0.03711060434579849, 0.06451072543859482, 0.00838376022875309, -0.007668646983802319, -0.020399540662765503, -0.009103577584028244, 0.034231334924697876, -0.022695431485772133, -0.046407073736190796, -0.023128261789679527, 0.04610597342252731, 0.012053418904542923, 0.007235815282911062, 0.03381732106208801, -0.013888249173760414, -0.062101926654577255, 0.02792704850435257, 0.018997542560100555, -0.005612696520984173, 0.014970327727496624, -0.0002315590245416388, 0.020606547594070435, -0.031916625797748566, -0.0050528384745121, -0.001035032095387578, 0.008858934044837952, -0.019148092716932297, -0.0033285690005868673, 0.017906054854393005, 0.007781559601426125, -0.022751886397600174, -0.01885640248656273, 0.04162710905075073, 0.01657933183014393, 0.013860020786523819, -0.002239433117210865, -0.00045870739268139005, 0.004855241626501083, 0.03483353555202484, -0.021905042231082916, -0.029903018847107887, -0.004888174124062061, -0.013079041615128517, -0.03016648069024086, -0.009635208174586296, -0.08972787111997604, 0.001923042582347989, 0.01394470501691103, -0.026459183543920517, 0.0626288503408432, 0.006483064498752356, 0.028736254200339317, 0.02335408702492714, -0.017106257379055023, -0.021698037162423134, -0.01457513403147459, -0.0015984189230948687, 0.002582875546067953, -0.013709470629692078, 0.003930769395083189, 0.06356979161500931, -0.0025076004676520824, 0.011611178517341614, -0.011357124894857407, -0.03720469772815704, -0.010002173483371735, 0.011197165586054325, 0.005410395096987486, -0.011140708811581135, -0.008186162449419498, -0.04444992169737816, -0.0034861762542277575, -0.017040392383933067, -0.0224884245544672, 0.005951434373855591, 0.03218008950352669, 0.00032785817165859044, 0.027569491416215897, -0.03551100939512253, 0.02568761445581913, 0.057359594851732254, -0.02555588260293007, -0.006238420493900776, -0.04019688069820404, 0.0402345210313797, -0.02670382708311081, -0.035322822630405426, 0.02798350341618061, 0.005636220332235098, 0.00023317626619245857, -0.034043144434690475, -0.012185150757431984, -0.019891435280442238, 0.018131880089640617, -0.0021935622207820415, -0.02905617281794548, 0.008120297454297543, 0.005208093207329512, -0.023956287652254105, 0.0010279749985784292, -0.003954293206334114, 0.028585704043507576, 0.016127681359648705, -0.026252176612615585, 0.02122756652534008, 0.04482629895210266, 0.006407789420336485, -0.009564637206494808, 0.007842720486223698, -0.04275623336434364, 0.012345110066235065, 0.02911262959241867, -0.04373481124639511, 0.025141870602965355, -0.0370541475713253, -0.002582875546067953, -0.05227852985262871, 0.005462146829813719, -0.07328027486801147, 0.00203830748796463, 0.034005507826805115, -0.028322242200374603, 0.012091056443750858, -0.01569485105574131, 0.008313189260661602, 0.02235669270157814, 0.014274033717811108, -0.010933702811598778, 0.0016101805958896875, 0.0315026119351387, 0.011959325522184372, 0.018790537491440773, -0.02911262959241867, 0.017689639702439308, -0.06801101565361023, -0.01281557884067297, -0.02218732424080372, -0.004062500782310963, -0.012072238139808178, -0.03466416522860527, -0.0002080355625366792, -0.0073252045549452305, -0.00026904954575002193, 0.037524618208408356, 0.01657933183014393, 0.002879271050915122, -0.0003025704645551741, -0.01833888702094555, 0.007809787523001432, 0.013841201551258564, -0.02668500877916813, -0.03660249710083008, 0.04926752671599388, 0.013653013855218887, 0.008129706606268883, 0.02779531665146351, 0.016955707222223282, 0.03665895387530327, -0.03144615516066551, -0.0024629058316349983, -0.043094974011182785, 0.019947892054915428, -0.04369717463850975, 0.0041824704967439175, -0.0006945300265215337, -0.009014188311994076, -0.0030909820925444365, 0.018536483868956566, -0.01123480312526226, -0.005471555981785059, 0.01887522079050541, -0.004902288317680359, 0.0027757678180933, -0.01898813433945179, -0.005156341474503279, -0.0017136838287115097, 0.04365953430533409, -0.005113999359309673, 0.00953170470893383, -0.01289085391908884, 0.0024040972348302603, 0.028303422033786774, 0.013182545080780983, 0.0011667634826153517, 0.018216565251350403, -0.02333526872098446, -0.03475825861096382, -0.04606833681464195, -0.03310220688581467, -0.020719461143016815, 0.0360567532479763, 0.005283368285745382, -0.011422990821301937, 0.012128693982958794, -0.02909381128847599, 0.018047194927930832, -0.004659996833652258, -0.05273018032312393, -0.012025190517306328, -0.06059642508625984, 0.0058808643370866776, 0.015920676290988922, -0.013050813227891922, -0.058676909655332565, 0.0336855910718441, -0.003241532249376178, 0.018668215721845627, -0.04576723650097847, 0.03011002391576767, 0.013916476629674435, -0.027381302788853645, 0.02250724285840988, -0.015534890815615654, -0.027042565867304802, 0.004725862294435501, 0.008529605343937874, -0.01797192171216011, -0.0818992629647255, 0.009795167483389378, 0.007715693674981594, -0.029394911602139473, -0.011046615429222584, 0.009611683897674084, -0.022940075024962425, 0.0008803653763607144, 0.05833817273378372, 0.008045022375881672, -0.038578469306230545, -0.011771137826144695, 0.015403158962726593, -0.014292852021753788, 0.038653742522001266, -0.00953170470893383, -0.01617472805082798, 0.026534458622336388, 0.013737699016928673, -0.0016372326062992215, -0.016852203756570816, -0.007094674278050661, 0.025424152612686157, 0.004624711349606514, 0.02440793812274933, -0.054198045283555984, -0.03778808191418648, -0.0372423380613327, -0.001245566993020475, 0.008247324265539646, 0.009870442561805248, 0.02024899050593376, -0.011931097134947777, 0.0011720561888068914, 0.005156341474503279, 0.012119284830987453, 0.03690359741449356, 0.014725684188306332, 0.05385930463671684, -0.005363347940146923, -0.029470186680555344, -0.02254488132894039, 0.039782870560884476, -0.018235383555293083, -0.0005795591860078275, -0.008190867491066456, -0.04373481124639511, 0.008741316385567188, -0.042003482580184937, -0.051864515990018845, 0.0072593386285007, -0.05483788251876831, 0.02435148134827614, -0.03598148003220558, 0.00864251796156168, -0.021942680701613426 ]
In recommendation systems, the choice of loss function is critical since a good loss may significantly improve the model performance. However, manually designing a good loss is a big challenge due to the complexity of the problem. A large fraction of previous work focuses on handcrafted loss functions, which needs significant expertise and human effort. In this paper, inspired by the recent development of automated machine learning, we propose an automatic loss function generation framework, AutoLossGen, which is able to generate loss functions directly constructed from basic mathematical operators without prior knowledge on loss structure. More specifically, we develop a controller model driven by reinforcement learning to generate loss functions, and develop iterative and alternating optimization schedule to update the parameters of both the controller model and the recommender model. One challenge for automatic loss generation in recommender systems is the extreme sparsity of recommendation datasets, which leads to the sparse reward problem for loss generation and search. To solve the problem, we further develop a reward filtering mechanism for efficient and effective loss generation. Experimental results show that our framework manages to create tailored loss functions for different recommendation models and datasets, and the generated loss gives better recommendation performance than commonly used baseline losses. Besides, most of the generated losses are transferable, i.e., the loss generated based on one model and dataset also works well for another model or dataset. Source code of the work is available at https://github.com/rutgerswiselab/AutoLossGen.
[ -0.006298852618783712, -0.019053500145673752, -0.022887952625751495, -0.010222380980849266, -0.0162370428442955, 0.011096160858869553, -0.009950914420187473, 0.01594861038029194, -0.03895532712340355, 0.015736527740955353, 0.0444185771048069, -0.03009876050055027, -0.029691562056541443, -0.0354602076113224, 0.03875172883272171, 0.014379199594259262, 0.00021380576072260737, -0.017212621867656708, 0.009993331506848335, -0.03225351870059967, 0.006260677706450224, -0.036647871136665344, 0.02353268302977085, 0.058365125209093094, 0.029063796624541283, 0.02887716516852379, 0.019375864416360855, -0.005437797401100397, -0.020393861457705498, 0.017560437321662903, 0.08306850492954254, 0.014150150120258331, -0.00852147862315178, 0.006489727180451155, -0.05632913485169411, -0.00936556700617075, 0.029946060851216316, 0.08754768967628479, -0.01042598020285368, 0.036478202790021896, 0.04981395602226257, 0.0046191588044166565, -0.036749668419361115, 0.011240377090871334, 0.043977443128824234, -0.0543610081076622, 0.01145245973020792, -0.013785367831587791, -0.015889227390289307, -0.018273035064339638, 0.02648487314581871, -0.016347326338291168, 0.009246801026165485, -0.06158878281712532, -0.009340116754174232, 0.04160211980342865, 0.017950668931007385, -0.007371990475803614, 0.028028834611177444, 0.019833963364362717, -0.004307397175580263, -0.010052714496850967, -0.026400040835142136, -0.008797185495495796, 0.01783190295100212, -0.06162271648645401, 0.05341087654232979, 0.017509538680315018, 0.008788702078163624, -0.002782523399218917, -0.07662119716405869, -0.039532192051410675, 0.0027040529530495405, 0.00010471577843418345, -0.044011376798152924, 0.039328593760728836, 0.025517776608467102, 0.030879223719239235, 0.02533114328980446, 0.005480214022099972, 0.024448880925774574, 0.012674055062234402, -0.01359025202691555, -0.015439611859619617, 0.02675633877515793, -0.016924189403653145, 0.009662482887506485, -0.04587770625948906, 0.043977443128824234, -0.04139852151274681, -0.04621703550219536, 0.05181601643562317, -0.026739371940493584, -0.0048482078127563, -0.013742951676249504, 0.03766586631536484, -0.025636542588472366, -0.0057135047391057014, -0.0967775210738182, 0.04306124895811081, -0.03471367806196213, 0.00735078239813447, 0.0047548916190862656, 0.0007550140144303441, 0.0014411011943593621, -0.022328054532408714, -0.010188447311520576, 0.006633943412452936, -0.0008525719749741256, 0.10485363006591797, 0.02707870490849018, -0.016550924628973007, -0.022582553327083588, -0.019477663561701775, 0.011851174756884575, -0.0048312414437532425, -0.05897592380642891, -0.03966792672872543, 0.042484384030103683, -0.036647871136665344, 0.028130633756518364, 0.07784279435873032, 0.012674055062234402, -0.049372825771570206, -0.02843603305518627, 0.06036718562245369, -0.005306306295096874, 0.025212377309799194, 0.04716716706752777, 0.03250801935791969, -0.023396950215101242, 0.022921886295080185, -0.005730471573770046, -0.00783857237547636, -0.018306968733668327, 0.03193115442991257, 0.019613398239016533, -0.01744167134165764, -0.031116757541894913, -0.01581287756562233, -0.036613937467336655, -0.05110342055559158, -0.03827666491270065, 0.02025812864303589, -0.01331030298024416, -0.026705438271164894, 0.0020158449187874794, 0.03973579406738281, -0.022158388048410416, -0.017051439732313156, -0.03691933676600456, 0.06589829921722412, -0.02141185849905014, -0.008101554587483406, 0.02675633877515793, 0.021700289100408554, -0.04842269420623779, -0.008258495479822159, 0.07533173263072968, -0.0014474636409431696, 0.08306850492954254, 0.008546927943825722, -0.018120335415005684, 0.07512813061475754, 0.06321757286787033, -0.008080346509814262, 0.005115431733429432, 0.029521895572543144, -0.08944795280694962, 0.034459177404642105, -0.013064286671578884, 0.016813907772302628, -0.0185614675283432, 0.03688540309667587, 0.03569773957133293, 0.004377384670078754, 0.07003815472126007, 0.04604737088084221, -0.006795126013457775, 0.01720413938164711, -0.035188741981983185, -0.008211838081479073, 0.03344118222594261, -0.012385622598230839, 0.03610493987798691, -0.0026764823123812675, 0.06145304813981056, -0.01740773767232895, 0.026281272992491722, -0.015329329296946526, -0.022294120863080025, 0.05704173073172569, 0.004337088670581579, 0.01717020571231842, -0.003331817453727126, -0.020071495324373245, -0.04988182336091995, -0.0005991333164274693, -0.0421111173927784, 0.0018111852696165442, -0.006765434518456459, -0.09487726539373398, 0.05164635181427002, 0.015286912210285664, -0.03193115442991257, 0.004572500474750996, 0.06352297216653824, -0.0036838743835687637, -0.03583347424864769, -0.05483607202768326, -0.02960672788321972, -0.0031642720568925142, -0.061011917889118195, 0.03255891799926758, -0.002078409306704998, -0.010748345404863358, -0.0038047614507377148, 0.001619250513613224, -0.015380228869616985, -0.002117644529789686, -0.01730593852698803, 0.013420585542917252, 0.07037748396396637, -0.026128573343157768, 0.015244496054947376, -0.03603707253932953, -0.003043384989723563, 0.0066466680727899075, 0.01428588293492794, -0.027621636167168617, -0.0500514879822731, 0.010485363192856312, 0.013581768609583378, -0.011893590912222862, 0.03417074680328369, 0.04166998714208603, -0.0063794441521167755, -0.055107537657022476, 0.01601647585630417, -0.04689570143818855, -0.0318293534219265, -0.012928553856909275, 0.019206197932362556, -0.06559289991855621, 0.04506330564618111, -0.002411379013210535, -0.03437434509396553, 0.052325014024972916, 0.043977443128824234, 0.016856323927640915, -0.026535773649811745, -0.015422645024955273, -0.034425243735313416, 0.01845966838300228, -0.07336360961198807, 0.0020349323749542236, 0.08496876806020737, -0.04553837329149246, 0.02203962206840515, -0.036546070128679276, -0.009102584794163704, -0.01158819254487753, 0.022429853677749634, 0.029097730293869972, 0.03065865859389305, 0.003976548556238413, 0.0842222347855568, -0.0016701503191143274, 0.031744521111249924, 0.06586436927318573, 0.028419066220521927, -0.04139852151274681, 0.0064345854334533215, -0.04604737088084221, -0.0021483965683728456, -0.029691562056541443, 0.016033442690968513, -0.021327024325728416, 0.005526872351765633, 0.0046191588044166565, 0.005246923305094242, -0.011995390988886356, 0.045165106654167175, 0.004245893098413944, 0.011698475107550621, -0.06325151026248932, -0.016067376360297203, -0.06406590342521667, -0.02940312959253788, 0.0037114452570676804, -0.0025280243717134, -0.0024453122168779373, -0.030081793665885925, 0.036478202790021896, 0.055277206003665924, 0.014845781028270721, -0.0019341931911185384, -0.0071005248464643955, 0.0280118677765131, -0.07322787493467331, -0.02774040214717388, 0.0006802548887208104, 0.03255891799926758, -0.0016828753286972642, -0.0560237355530262, -0.032932184636592865, 0.03895532712340355, 0.024007748812437057, -0.021785123273730278, 0.01671210676431656, 0.04285764694213867, -0.009255283512175083, -0.003522691782563925, -0.017747070640325546, 0.006905409041792154, 0.07546746730804443, 0.06213171407580376, -0.007121732924133539, -0.022090522572398186, -0.032474085688591, -0.004324364010244608, 0.0263491403311491, -0.09060168266296387, 0.0015704715624451637, -0.06633943319320679, 0.0005630792584270239, -0.012758888304233551, 0.012317756190896034, 0.03892139717936516, 0.013564801774919033, -0.02237895503640175, -0.020495660603046417, -0.007232015952467918, 0.004271343350410461, 0.0076095229014754295, 0.016152208670973778, 0.006765434518456459, 0.017882803454995155, -0.0606725849211216, -0.04122885316610336, 0.0027188987005501986, -0.02360055036842823, -0.024601580575108528, 0.0626407116651535, 0.006727259606122971, -0.018120335415005684, -0.021734222769737244, 0.01935889758169651, 0.02293885312974453, 0.021920856088399887, 0.000923089450225234, 0.0035163292195647955, -0.007486515212804079, -0.0041589392349123955, 0.04197538644075394, -0.021836021915078163, 0.017560437321662903, 0.018680233508348465, -0.05313941091299057, 0.10790761560201645, 0.02512754499912262, 0.016720591112971306, -0.07309214025735855, 0.009085617959499359, -0.03542627394199371, 0.039226796478033066, -0.030013926327228546, -0.013352719135582447, -0.004593708552420139, -0.0005418710061348975, -0.0280118677765131, 0.011664542369544506, 0.03262678533792496, 0.017577404156327248, -0.01766223832964897, 0.012224440462887287, 0.028351198881864548, -0.04462217539548874, -0.06124944984912872, 0.05069622024893761, 0.026467906311154366, -0.011130093596875668, -0.03742833435535431, -0.00451735919341445, 0.020665327087044716, 0.031099790707230568, -0.03542627394199371, -0.00677815917879343, 0.026909038424491882, 0.032372284680604935, 0.0195624977350235, -0.027502870187163353, -0.01766223832964897, -0.05565046891570091, -0.011113127693533897, -0.010536262765526772, 0.017161723226308823, 0.018340902402997017, -0.006358236074447632, 0.015626244246959686, -0.008258495479822159, -0.025908008217811584, 0.015855293720960617, 0.06969881802797318, -0.08496876806020737, 0.005229956470429897, -0.010069681331515312, -0.003433617064729333, 0.013191537000238895, 0.017882803454995155, 0.01508331298828125, -0.011902074329555035, -0.061011917889118195, 0.03566380590200424, 0.03218565136194229, 0.010824695229530334, -0.03685146942734718, -0.0273501705378294, 0.004398592747747898, 0.004364659544080496, -0.007287157699465752, 0.013047320768237114, 0.04577590525150299, 0.016067376360297203, 0.005140881985425949, 0.02300671860575676, 0.0023286668583750725, 0.009815181605517864, -0.020631393417716026, -0.02356661669909954, 0.0500514879822731, 0.09134820848703384, -0.010485363192856312, -0.05313941091299057, -0.023973815143108368, 0.037767667323350906, -0.029063796624541283, -0.030387192964553833, -0.056498799473047256, 0.019867897033691406, 0.006833300925791264, -0.0401090569794178, -0.01317457016557455, 0.08612249791622162, 0.017781004309654236, -0.03858206421136856, 0.002737986156716943, -0.028164567425847054, -0.02741803601384163, -0.02008846215903759, -0.0742458701133728, 0.009085617959499359, -0.010926494374871254, -0.01766223832964897, 0.02999696135520935, -0.022192321717739105, 0.0530376136302948, -0.017280489206314087, 0.03763193264603615, -0.0550396703183651, 0.002455916255712509, 0.012029323726892471, 0.015524445101618767, -0.01704295724630356, -0.01783190295100212, 0.062369246035814285, -0.031744521111249924, -0.026603639125823975, -0.010519295930862427, -0.027536801993846893, 0.002243833616375923, 0.03848026320338249, 0.01598254404962063, 0.024669446051120758, -0.011062227189540863, 0.04482577368617058, -0.033169716596603394, -0.07709626108407974, 0.036546070128679276, -0.018188202753663063, 0.056736331433057785, -0.02008846215903759, 0.03749620169401169, -0.040787722915410995, 0.02449977956712246, -0.026603639125823975, 0.045131172984838486, 0.029946060851216316, 0.013658118434250355, -0.027553768828511238, -0.07913225144147873, 0.02025812864303589, -0.0397697277367115, 0.0073762321844697, -0.03552807494997978, -0.04051625728607178, 0.02203962206840515, -0.026111608371138573, 0.010154513642191887, -0.02377021685242653, 0.023413917049765587, -0.026366107165813446, -0.025500809773802757, 0.0193928312510252, 0.04621703550219536, -0.028130633756518364, 0.017059922218322754, 0.009246801026165485, -0.0008743104408495128, 0.003794157411903143, 0.02860569953918457, 0.0026425488758832216, 0.001182360458187759, -0.029148630797863007, -0.0028843232430517673, -0.01800156943500042, 0.0036350954324007034, 0.004322242923080921, 0.05476820468902588, 0.008627519942820072, -0.011469426564872265, -0.0012237165356054902, -0.046759966760873795, 0.05622733384370804, -0.027825234457850456, 0.03488334268331528, 0.08381503820419312, 0.03252498432993889, 0.09019447863101959, 0.04974609240889549, -0.011571225710213184, 0.06352297216653824, -0.006659393198788166, -0.08048958331346512, -0.00030990567756816745, -0.04200931638479233, 0.020241161808371544, 0.04757436364889145, -0.011978424154222012, -0.03262678533792496, -0.021089492365717888, 0.0281815342605114, 0.016084343194961548, 0.005866204388439655, 0.011308243498206139, -0.01266557164490223, 0.04903349280357361, -0.027027804404497147, 0.0010259494883939624, 0.018951699137687683, 0.005140881985425949, 0.0024474330712109804, 0.003361508948728442, 0.01793370395898819, -0.014268916100263596, 0.007024175021797419, -0.07499240338802338, -0.03318668156862259, -0.031676653772592545, -0.037462268024683, -0.040889523923397064, -0.02728230319917202, -0.017916737124323845, 0.004793066531419754, 0.027604669332504272, -0.02724836952984333, 0.03542627394199371, -0.0036817537620663643, -0.008440886624157429, 0.007456823717802763, -0.028402099385857582, 0.003976548556238413, -0.01704295724630356, 0.012521355412900448, -0.033695679157972336, 0.019409798085689545, -0.0019405556377023458, 0.002530145226046443, -0.012182023376226425, -0.0004965383559465408, -0.022718286141753197, -0.05405560880899429, -0.0030030894558876753, 0.004188631195574999, -0.00704538356512785, 0.025212377309799194, -0.03875172883272171, -0.008381503634154797, 0.006286127958446741, -0.015549895353615284, -0.011520326137542725, 0.030370226129889488, -0.005611705128103495, -0.008856568485498428, -0.08456156402826309, -0.011206443421542645, 0.007461065426468849, 0.004644608590751886, 0.002542870119214058, -0.0520535483956337, 0.0016086463583633304, 0.02134399116039276, 0.018306968733668327, 0.029063796624541283, -0.02774040214717388, -0.02923346310853958, 0.07662119716405869, -0.013751435093581676, 0.015252979472279549, 0.013997450470924377, -0.011528809554874897, 0.0035078460350632668, 0.031184623017907143, -0.05134095251560211, 0.008160937577486038, -0.03705506771802902, 0.007431373931467533, 0.001715748105198145, 0.02526327781379223, 0.00735078239813447, 0.03427254408597946, 0.0067824008874595165, 0.023549649864435196, -0.01859540119767189, 0.007711322512477636, 0.044995442032814026, 0.018544500693678856, -0.028758399188518524, -0.0044367676600813866, -0.004580983892083168, -0.02214142121374607, 0.006841784343123436, -0.009560682810842991, -0.003467550268396735, 0.012258373200893402, 0.011791791766881943, -0.0008329543634317815, 0.027502870187163353, 0.02078409306704998, -0.00936556700617075, -0.04119491949677467, 0.003461187705397606, -0.003463308559730649, 0.08266130834817886, -0.017713136970996857, 0.02224322222173214, -0.005111190490424633, 0.0018398164538666606, 0.0404483899474144, 0.01859540119767189, -0.0193928312510252, 0.024177415296435356, 0.02606070786714554, 0.021191291511058807, 0.007948854938149452, -0.042586181312799454, 0.02947099506855011, 0.035392340272665024, 0.020071495324373245, -0.026332173496484756, 0.03905712813138962, -0.012419556267559528, -0.02154759131371975, -0.03142215684056282, 0.029708528891205788, -0.016169175505638123, 0.02505967766046524, 0.011800275184214115, 0.06633943319320679, -0.0037284118589013815, -0.042484384030103683, -0.010799244977533817, -0.02509361132979393, 0.04156818613409996, -0.011070710606873035, -0.02127612568438053, 0.020801059901714325, 0.04414711147546768, -0.02363448217511177, -0.000666469510179013, -0.028419066220521927, 0.020444761961698532, -0.0035608664620667696, -0.001315972418524325, -0.04156818613409996, -0.02137792482972145, 0.027502870187163353, 0.04832089692354202, -0.026162507012486458, -0.010230863466858864, -0.06382837146520615, -0.007991272024810314, -0.01030721329152584, -0.018323935568332672, 0.006786642596125603, -0.004347693175077438, -0.01141852606087923, -0.0005556563846766949, 0.011155543848872185, -0.015668660402297974, 0.0050730155780911446, 0.006841784343123436, 0.008975334465503693, 0.017221106216311455, -0.018239101395010948, -0.010239346884191036, 0.0018472393276169896, 0.033033981919288635, -0.015863778069615364, 0.005221473053097725, 0.02373628318309784, 0.03549414128065109, -0.05280008167028427, 0.024007748812437057, -0.01322546973824501, 0.012156574055552483, 0.024313148111104965, 0.012937037274241447, -0.031540922820568085, 0.022056588903069496, -0.019816996529698372, 0.03026842698454857, 0.060333251953125, -0.09698112308979034, -0.03211778774857521, 0.011579709127545357, 0.015855293720960617, 0.026094641536474228, -0.006659393198788166, -0.011316726915538311, -0.005912862252444029, 0.015371745452284813, -0.042314715683460236, -0.00415257690474391, 0.006608493160456419, -0.020495660603046417, -0.02877536416053772, -0.007130216341465712, -0.0210555586963892, -0.02665453962981701, 0.006358236074447632, -0.014905164018273354, 0.025432944297790527, -0.014947580173611641, -0.05151061713695526, 0.034951210021972656, 0.0019288910552859306, 0.02287098579108715, 0.01918923296034336, 0.0052893394604325294, 0.03902319446206093, 0.0048482078127563, 0.06688236445188522, 0.0185614675283432, -0.03138822317123413, 0.035053011029958725, -0.013658118434250355, -0.020207228139042854, -0.009764282032847404, -0.056668467819690704, 0.014099250547587872, 0.05334301292896271, -0.000297445832984522, -0.006913891993463039, -0.016347326338291168, -0.010536262765526772, -0.01783190295100212, 0.019715197384357452, 0.005883170757442713, -0.032270487397909164, 0.008856568485498428, 0.010205414146184921, 0.037835534662008286, -0.046522434800863266, 0.04994969069957733, -0.00019259749387856573, 0.05704173073172569, 0.022480754181742668, -0.039226796478033066, 0.03552807494997978, -0.014599764719605446, -0.0019511597929522395, -0.024669446051120758, 0.06026538833975792, -0.003448462812229991, 0.007520448416471481, -0.0328134186565876, -0.014175599440932274, 0.0162455253303051, 0.025738341733813286, 0.015015446580946445, -0.013853234238922596, -0.022328054532408714, 0.017144756391644478, -0.003961702808737755, -0.00366266630589962, 0.05744893103837967, 0.005285097751766443, 0.005374172702431679, -0.03003089316189289, 0.04489364102482796, 0.03459491208195686, -0.0022692836355417967, 0.03576560690999031, -0.00621401984244585, -0.006443068850785494, -0.022056588903069496, 0.024211347103118896, -0.01001029834151268, 0.02940312959253788, -0.007499240338802338, 0.015515961684286594, -0.014574315398931503, -0.019341930747032166, -0.0263491403311491, -0.01001029834151268, -0.007605281658470631, 0.03145609050989151, -0.04139852151274681, -0.03155788779258728, -0.023821115493774414, -0.03691933676600456, -0.02843603305518627, 0.005522630643099546, -0.011299760080873966, -0.019070465117692947, -0.012852204963564873, 0.013200020417571068, 0.014438582584261894, -0.005064532160758972, 0.002426224760711193, 0.02363448217511177, -0.008368778973817825, 0.007936130277812481, 0.008415437303483486, 0.028928063809871674, 0.00001528485881863162, 0.015753494575619698, 0.02075015939772129, -0.004207718651741743, -0.016152208670973778, -0.016355808824300766, 0.04916922748088837, -0.03444221243262291, -0.008453612215816975, 0.00348027516156435, -0.016355808824300766, 0.028062768280506134, -0.003974427469074726, -0.006739984732121229, -0.0055311135947704315, 0.029097730293869972, 0.010069681331515312, -0.03474761173129082, -0.03763193264603615, -0.02019026130437851, -0.0301666259765625, 0.05707566440105438, -0.003942615352571011, -0.011197960004210472, 0.027553768828511238, 0.011936007998883724, 0.015015446580946445, -0.00812276266515255, 0.02741803601384163, -0.020410828292369843, -0.010035747662186623, -0.04614917188882828, -0.03254195302724838, -0.0556844025850296, -0.017424704506993294, 0.04326484724879265, -0.04991575703024864, 0.01915529929101467, 0.0034548253752291203, 0.005285097751766443, -0.018510567024350166, -0.0018376955995336175, 0.028656598180532455, -0.04302731528878212, 0.009993331506848335, 0.011944491416215897, 0.03769979998469353, -0.011681508272886276, 0.03294914960861206, -0.02964066155254841, -0.0477440319955349, -0.04428284242749214, -0.03398411348462105, -0.05286794528365135, 0.03361084684729576, 0.053750209510326385, -0.0410931222140789, -0.0217172559350729, 0.02672240510582924, 0.0013488451950252056, -0.035256609320640564, 0.0013286974281072617, 0.0024792454205453396, 0.03627460449934006, -0.004281947389245033, -0.006829059217125177, -0.019545530900359154, -0.007787672337144613, 0.048083364963531494, -0.005200264975428581, 0.013768400996923447, -0.03274555131793022, 0.024754278361797333, 0.004924557637423277, 0.018849899992346764, 0.009721865877509117, 0.043943509459495544, -0.06552503257989883, 0.006812092382460833, 0.014065316878259182, 0.043604180216789246, 0.02012239582836628, 0.039362527430057526, -0.03736046701669693, 0.03736046701669693, 0.01650850847363472, 0.00006852918158983812, 0.06650909781455994, -0.04984788969159126, 0.021174324676394463, -0.027502870187163353, 0.04411317780613899, -0.019681263715028763, -0.02992909401655197, -0.050831954926252365, 0.023057619109749794, 0.016220076009631157, -0.0027082946617156267, 0.03566380590200424, 0.061079785227775574, -0.018748100847005844, -0.017475605010986328, -0.005378414411097765, -0.003794157411903143, -0.020342960953712463, 0.0030476266983896494, 0.008309395983815193, 0.017127789556980133, 0.023278184235095978, -0.03864993155002594, 0.03238925337791443, 0.013123670592904091, -0.010663512162864208, -0.0070156920701265335, -0.04896562546491623, 0.015185113064944744, -0.02943706326186657, 0.004390109330415726, -0.0017411980079486966, 0.013463002629578114, -0.0019331327639520168, 0.0286735650151968, 0.00020293652778491378, 0.012818271294236183, -0.00263194483704865, 0.0075246901251375675, -0.028554799035191536, -0.013420585542917252, -0.03837846592068672, 0.048253029584884644, -0.02960672788321972, 0.008322120644152164, -0.04452037438750267, -0.011656058952212334, -0.02210748940706253, -0.0026892072055488825, -0.025704409927129745, -0.005492938682436943, 0.03254195302724838, 0.026993870735168457, -0.011113127693533897, 0.01879899948835373, -0.04621703550219536, 0.03966792672872543, 0.04787976294755936, -0.0061673615127801895, 0.02175118960440159, 0.0036096456460654736, -0.010230863466858864, -0.024313148111104965, -0.01029024738818407, 0.018052469938993454, -0.07214201241731644, -0.006205536425113678, -0.027536801993846893, -0.019274065271019936, 0.026705438271164894, -0.05341087654232979, -0.02853783220052719, 0.009204383939504623, 0.003887473838403821, 0.001676512765698135, 0.005196023266762495, 0.025110578164458275, -0.024313148111104965, -0.035154808312654495, 0.0024834871292114258, 0.025941941887140274, -0.0062734028324484825, -0.008822635747492313, 0.06535536795854568, 0.008364536799490452, -0.014828814193606377, 0.05565046891570091, 0.020868925377726555, -0.00533599779009819, 0.0023626000620424747, 0.010230863466858864, -0.018256068229675293, 0.04445251077413559, -0.05860266089439392, -0.0027782819233834743, 0.027859168127179146, -0.0248560793697834, 0.06152091547846794, -0.0281815342605114, 0.016983572393655777, 0.010001814924180508 ]
Many real-world multi-objective optimisation problems rely on computationally expensive function evaluations. Multi-objective Bayesian optimisation (BO) can be used to alleviate the computation time to find an approximated set of Pareto optimal solutions. In many real-world problems, a decision-maker has some preferences on the objective functions. One approach to incorporate the preferences in multi-objective BO is to use a scalarising function and build a single surrogate model (mono-surrogate approach) on it. This approach has two major limitations. Firstly, the fitness landscape of the scalarising function and the objective functions may not be similar. Secondly, the approach assumes that the scalarising function distribution is Gaussian, and thus a closed-form expression of an acquisition function e.g., expected improvement can be used. We overcome these limitations by building independent surrogate models (multi-surrogate approach) on each objective function and show that the distribution of the scalarising function is not Gaussian. We approximate the distribution using Generalised value distribution. We present an a-priori multi-surrogate approach to incorporate the desirable objective function values (or reference point) as the preferences of a decision-maker in multi-objective BO. The results and comparison with the existing mono-surrogate approach on benchmark and real-world optimisation problems show the potential of the proposed approach.
[ 0.054798025637865067, 0.014013098552823067, -0.03592872619628906, -0.06185833364725113, 0.05035397410392761, 0.05476218834519386, -0.041609227657318115, 0.016656234860420227, -0.06913367658853531, 0.0032120817340910435, 0.03877793624997139, -0.037451889365911484, 0.03162803128361702, -0.01994447410106659, -0.0627901554107666, 0.0778425857424736, 0.021180924028158188, 0.0024482603184878826, -0.000025496879970887676, 0.0005857457290403545, 0.013439672999083996, -0.008534192107617855, 0.003635431407019496, 0.08106810599565506, -0.007239503785967827, 0.052396804094314575, 0.009685523808002472, -0.01694294810295105, -0.07483209669589996, 0.02662847191095352, 0.0364125519990921, 0.053902048617601395, -0.051285792142152786, 0.012364499270915985, -0.00722158420830965, 0.01770452968776226, 0.052898552268743515, -0.029441842809319496, 0.003964703530073166, 0.05347197875380516, -0.0010673339711502194, -0.013520310632884502, 0.008829864673316479, 0.009174816310405731, -0.0007201424450613558, 0.01348447147756815, -0.0026991344057023525, 0.06949207186698914, 0.028689222410321236, 0.0047128451988101006, 0.010339587926864624, 0.0004692685906775296, 0.012902085669338703, 0.023259593173861504, -0.002347462810575962, 0.029155129566788673, 0.02876090072095394, 0.02999735064804554, 0.03626919537782669, 0.030821649357676506, 0.009067298844456673, 0.0257324930280447, 0.0007996605127118528, -0.024890273809432983, 0.008753706701099873, -0.016396401450037956, 0.04970886930823326, -0.020607497543096542, -0.0063076866790652275, -0.004287255462259054, -0.01981903798878193, -0.032308973371982574, -0.030463257804512978, 0.041967619210481644, -0.031180040910840034, 0.009900558739900589, 0.04318615049123764, -0.00722158420830965, -0.042863596230745316, 0.01317087933421135, 0.02671806886792183, 0.03177138790488243, -0.017023585736751556, 0.010805496945977211, 0.02922680787742138, -0.019532324746251106, 0.026072965934872627, -0.05436795577406883, -0.008888103999197483, -0.023116236552596092, -0.04630415141582489, 0.004717325326055288, -0.008072763681411743, 0.04232601076364517, 0.035211943089962006, 0.0071991849690675735, 0.009076259098947048, 0.015903612598776817, -0.0564466267824173, 0.029280567541718483, 0.008166841231286526, -0.011808992363512516, 0.022668248042464256, 0.034943148493766785, -0.010402306914329529, -0.04590992256999016, 0.018743863329291344, -0.0071095870807766914, -0.033688779920339584, 0.10945269465446472, -0.04214681312441826, 0.005411708261817694, -0.012678091414272785, -0.010563583113253117, -0.07977789640426636, -0.01820627599954605, -0.04569488763809204, -0.06110571324825287, 0.013600949198007584, -0.07382860034704208, -0.012516815215349197, 0.06343525648117065, 0.03250608965754509, -0.1229282096028328, -0.03497898951172829, -0.0009082978940568864, -0.013179839588701725, -0.02057165838778019, 0.06293350458145142, -0.0251053087413311, -0.014362530782818794, -0.005456507205963135, -0.04064157232642174, -0.022184420377016068, 0.0150524340569973, 0.04379541426897049, 0.06203753128647804, -0.02184394747018814, -0.046375829726457596, -0.00048634817358106375, -0.035319458693265915, -0.07164241373538971, 0.034584756940603256, -0.024442285299301147, 0.0219514649361372, 0.012248021550476551, 0.010267909616231918, 0.07171409577131271, -0.019120175391435623, 0.0064196838065981865, -0.03200434148311615, 0.037451889365911484, 0.012463056482374668, 0.0753338485956192, 0.024818595498800278, 0.04504978284239769, -0.010760698467493057, -0.006881112698465586, 0.024424364790320396, -0.0219514649361372, 0.050389815121889114, 0.04243352636694908, -0.028026197105646133, 0.07612230628728867, 0.05096323788166046, 0.019048497080802917, -0.026520954445004463, -0.03827618807554245, -0.11654884368181229, 0.03981726989150047, -0.06920535862445831, -0.010572542436420918, 0.0011070930631831288, 0.0639370009303093, -0.03603624179959297, 0.06891864538192749, 0.05963630974292755, 0.008556591346859932, 0.005496826022863388, 0.036430474370718, -0.048382822424173355, 0.024890273809432983, 0.009380891919136047, 0.03300783783197403, 0.046124957501888275, 0.0029388084076344967, 0.10651388764381409, -0.005725300870835781, 0.018672185018658638, 0.005210113245993853, 0.0477018803358078, 0.011629796586930752, 0.06873944401741028, -0.027004782110452652, 0.06304102391004562, 0.022184420377016068, -0.06866776943206787, -0.0001864754594862461, -0.01706838421523571, -0.011638756841421127, 0.018492989242076874, -0.06089067831635475, 0.020249107852578163, 0.01085029635578394, 0.008413235656917095, 0.03178930655121803, 0.017381977289915085, 0.027882840484380722, -0.015769215300679207, -0.06085483729839325, 0.010877175256609917, -0.02851002663373947, -0.0865873321890831, -0.028796739876270294, -0.005756659898906946, -0.003915424924343824, -0.004495570436120033, 0.002549058059230447, -0.024191411212086678, -0.04935047775506973, -0.001458204467780888, 0.0552280955016613, 0.03956639766693115, 0.003041845979169011, 0.015715457499027252, 0.04569488763809204, 0.029441842809319496, 0.003281520213931799, 0.031072523444890976, -0.0003354318323545158, -0.008081723004579544, 0.018779702484607697, 0.002139147836714983, -0.025015711784362793, 0.008265398442745209, -0.003973663318902254, 0.0018927538767457008, -0.02109132707118988, -0.006536161061376333, 0.03503274545073509, -0.0021279482170939445, -0.00953320786356926, -0.001336127519607544, -0.012946885079145432, 0.080351322889328, 0.03435180336236954, 0.014371490105986595, 0.021557236090302467, 0.02033870480954647, 0.01706838421523571, -0.007190225180238485, -0.05386620759963989, -0.025660814717411995, 0.03902880847454071, 0.002256745006889105, -0.000058553574490360916, 0.03001526929438114, -0.01009767409414053, 0.04329366609454155, -0.10973940789699554, 0.020159509032964706, 0.06924119591712952, -0.0005028677405789495, 0.05687669664621353, 0.00010569742880761623, -0.003606312209740281, 0.06461794674396515, -0.016521837562322617, -0.05752180144190788, 0.03616167977452278, 0.005107075907289982, -0.018672185018658638, 0.023134157061576843, -0.007866688072681427, 0.000018269554857397452, -0.028205392882227898, 0.024926112964749336, -0.00998119730502367, 0.04752268269658089, -0.007360460702329874, -0.0020506700966507196, 0.033581264317035675, 0.0014033258194103837, -0.0007459018379449844, 0.010653181001543999, -0.03324079141020775, -0.02548161894083023, -0.02019534818828106, -0.01595737226307392, -0.02497987262904644, -0.017758287489414215, -0.0015634819865226746, 0.018725944682955742, -0.02635967917740345, 0.0602455735206604, 0.0074231792241334915, -0.03465643525123596, -0.006912471726536751, 0.044117964804172516, -0.030427418649196625, -0.01300064381211996, -0.01607384905219078, 0.03574952855706215, 0.002907449146732688, 0.0031471233814954758, -0.00025591376470401883, 0.011235566809773445, 0.034208446741104126, -0.01744469627737999, -0.017794126644730568, -0.03159219026565552, 0.03415468707680702, -0.04214681312441826, -0.06368613243103027, 0.013224638067185879, 0.045121461153030396, 0.02799035795032978, -0.003189682262018323, -0.04967303201556206, -0.03605416417121887, 0.01593945175409317, 0.02913721092045307, -0.07755587249994278, -0.045013945549726486, 0.000085817911894992, 0.00022595449991058558, -0.026180483400821686, 0.02924472838640213, -0.02609088458120823, -0.022793686017394066, -0.02937016449868679, -0.04856201633810997, 0.030194465070962906, -0.045981600880622864, -0.01499867532402277, -0.005886576604098082, -0.01731029897928238, 0.0015567621449008584, -0.026305919513106346, -0.02671806886792183, 0.006455522961914539, -0.04978054761886597, 0.012597453780472279, 0.02146763727068901, 0.010760698467493057, -0.03938720002770424, -0.02834874950349331, -0.017292378470301628, 0.004753164481371641, 0.015213709324598312, 0.0010018156608566642, -0.02333127148449421, -0.0338858962059021, -0.016638314351439476, -0.006482402328401804, -0.012310740537941456, 0.009649685584008694, 0.005335550289601088, -0.03845538571476936, 0.008278838358819485, 0.010267909616231918, -0.048382822424173355, -0.039709754288196564, 0.02684350684285164, -0.07042388617992401, 0.06408035755157471, 0.003026166232302785, 0.028187474235892296, 0.036090001463890076, -0.03539113700389862, -0.04340118542313576, 0.04834698140621185, 0.07049556076526642, 0.009318172931671143, -0.041214995086193085, 0.033581264317035675, -0.013609908521175385, -0.010285829193890095, -0.02922680787742138, 0.02032078616321087, -0.020249107852578163, 0.012122584506869316, -0.03239857032895088, -0.02987191267311573, 0.026288000866770744, 0.009649685584008694, 0.01654871739447117, -0.00299480720423162, 0.007131986320018768, 0.04877705127000809, -0.003395757405087352, 0.007490377873182297, 0.006692957133054733, -0.042110975831747055, -0.008431155234575272, -0.009810960851609707, 0.03526570275425911, -0.04859785735607147, -0.060173895210027695, 0.004381333477795124, 0.026771828532218933, -0.016351601108908653, -0.02560705691576004, 0.08142650127410889, -0.03476395457983017, 0.02598336711525917, -0.02196938544511795, 0.003906465135514736, -0.0019957914482802153, 0.017032545059919357, 0.026538874953985214, -0.029316406697034836, -0.050999078899621964, 0.0071409461088478565, -0.002916408935561776, 0.0389212928712368, -0.009004580788314342, -0.018421310931444168, 0.0257324930280447, -0.027273576706647873, -0.05379452928900719, 0.019263532012701035, 0.028259152546525, -0.01593945175409317, 0.02558913640677929, 0.011199727654457092, -0.03981726989150047, 0.0072529432363808155, -0.0034315965604037046, -0.027667807415127754, -0.01141476258635521, 0.041107479482889175, 0.04684174060821533, -0.05684085562825203, 0.033455826342105865, 0.009264414198696613, -0.000124386977404356, 0.040498215705156326, -0.0074814180843532085, -0.04157338663935661, 0.006800474599003792, -0.023671744391322136, -0.004896520636975765, 0.01060838159173727, 0.01594841107726097, -0.0651913732290268, -0.029190968722105026, -0.037846118211746216, 0.005823858082294464, 0.018905140459537506, -0.00979304127395153, 0.006298726890236139, -0.06709084659814835, -0.008901542983949184, 0.040964122861623764, -0.03727269172668457, 0.048956248909235, 0.00476660393178463, 0.011262445710599422, -0.001533242641016841, -0.04504978284239769, 0.03189682215452194, 0.031538430601358414, -0.05060485005378723, -0.022417373955249786, 0.06662493944168091, -0.02836667001247406, -0.0351044237613678, 0.0064062438905239105, -0.01719382219016552, 0.020643336698412895, -0.023922618478536606, 0.027775323018431664, 0.005676021799445152, 0.03413676843047142, 0.02433476783335209, -0.03723685443401337, -0.014891157858073711, 0.023438788950443268, 0.00199467153288424, 0.036448393017053604, -0.036573830991983414, 0.05254016071557999, -0.023420870304107666, 0.024030135944485664, 0.03727269172668457, -0.024424364790320396, 0.02512322925031185, -0.0147478012368083, 0.022005224600434303, -0.05071236565709114, -0.018994737416505814, -0.018994737416505814, 0.0069707101210951805, -0.005823858082294464, -0.0009262174717150629, -0.001376446452923119, -0.03026614338159561, 0.07870272547006607, 0.03499690815806389, 0.029316406697034836, -0.03574952855706215, -0.03279280290007591, 0.007759171072393656, 0.03159219026565552, 0.013753265142440796, 0.0030194465070962906, 0.015590020455420017, 0.0017852365272119641, 0.01499867532402277, 0.028796739876270294, 0.03198642283678055, 0.012409297749400139, -0.016521837562322617, 0.035946644842624664, 0.03159219026565552, -0.006939351093024015, -0.01792852394282818, 0.05759347975254059, 0.007871168665587902, 0.024513963609933853, 0.0021996265277266502, -0.013905581086874008, 0.053149424493312836, 0.007772610988467932, 0.009327133186161518, -0.002963447943329811, -0.0010846935911104083, 0.038957130163908005, 0.01830483414232731, -0.06479714065790176, 0.027918679639697075, -0.05092740058898926, -0.04203929752111435, -0.03845538571476936, -0.05655414238572121, 0.004056541249155998, 0.027076460421085358, -0.01592153310775757, -0.030158625915646553, -0.013188798911869526, 0.040856607258319855, 0.027882840484380722, -0.03931552171707153, -0.01023207139223814, 0.01292000524699688, 0.03252400830388069, -0.06074732169508934, -0.01167459599673748, 0.05823858082294464, 0.001079093781299889, 0.024442285299301147, 0.001290208543650806, -0.0052907513454556465, -0.061320748180150986, -0.039208006113767624, -0.005268351640552282, -0.06171497702598572, -0.013412793166935444, -0.07762754708528519, 0.01679959148168564, 0.009927438572049141, 0.00721710454672575, -0.016360562294721603, 0.0018031561048701406, 0.014066857285797596, 0.02322375401854515, 0.04444051906466484, -0.014362530782818794, 0.008453554473817348, -0.009748242795467377, 0.019371047616004944, -0.04802443087100983, -0.025642896071076393, -0.03447724133729935, 0.011665635742247105, 0.011692515574395657, 0.005917936097830534, -0.026180483400821686, -0.04530065879225731, 0.028438348323106766, -0.04250520467758179, 0.004164058715105057, 0.019173933193087578, 0.039100486785173416, -0.03798947483301163, -0.034817714244127274, 0.0009418971021659672, -0.01317087933421135, -0.034459322690963745, -0.0023967416491359472, 0.024639399722218513, -0.017023585736751556, -0.03198642283678055, 0.013466551899909973, -0.021270522847771645, 0.006742235738784075, -0.019371047616004944, -0.010518783703446388, -0.006957270670682192, 0.03114420175552368, -0.0042805359698832035, 0.013269437476992607, 0.030929166823625565, -0.024675238877534866, 0.020392464473843575, 0.044117964804172516, 0.0017303578788414598, 0.01908433623611927, -0.011298284865915775, -0.021431798115372658, 0.007830849848687649, 0.018295874819159508, -0.03440556302666664, 0.05132162943482399, 0.022309856489300728, -0.011092210188508034, 0.012722889892756939, -0.0056849815882742405, 0.01255265437066555, 0.06454627215862274, -0.03148467466235161, 0.03223729506134987, -0.042720239609479904, 0.020428303629159927, 0.022184420377016068, 0.02610880509018898, -0.03668134659528732, -0.010465024970471859, -0.00527283176779747, -0.027506530284881592, 0.024424364790320396, 0.0058417776599526405, 0.00028755300445482135, 0.000050258775445399806, 0.028922175988554955, -0.011289325542747974, 0.03953055664896965, 0.004381333477795124, 0.017238620668649673, -0.0219514649361372, 0.01783892512321472, -0.012472016736865044, 0.029585199430584908, -0.007105106953531504, 0.02811579592525959, -0.023564226925373077, -0.010536703281104565, 0.04350870102643967, 0.00839979574084282, -0.03677094355225563, 0.005169793963432312, -0.00671087671071291, 0.04730764776468277, 0.008372915908694267, -0.03492522984743118, -0.03587496653199196, -0.0025199386291205883, -0.030552856624126434, 0.04300695285201073, 0.01933520846068859, -0.007284302730113268, -0.023169996216893196, 0.016996705904603004, -0.01833171397447586, 0.04056989401578903, 0.014425248838961124, 0.04967303201556206, 0.007821889594197273, 0.05845361575484276, 0.013663667254149914, 0.03702181950211525, -0.016011130064725876, 0.018036041408777237, 0.033079516142606735, -0.00998119730502367, -0.010554622858762741, 0.05336445942521095, -0.026270080357789993, -0.05203841254115105, 0.00389078538864851, 0.004177498165518045, -0.02521282620728016, -0.020051991567015648, -0.025571217760443687, -0.0004653486830648035, -0.01809876039624214, -0.007665093522518873, -0.00804140418767929, 0.005510265938937664, -0.012445136904716492, -0.04917128384113312, 0.043365344405174255, 0.009273374453186989, 0.01255265437066555, 0.01908433623611927, -0.01743573509156704, 0.0007106226985342801, -0.003241201164200902, -0.03664550930261612, -0.01705942489206791, 0.0026453756727278233, -0.024173490703105927, -0.006540640722960234, 0.04429716244339943, -0.028581704944372177, 0.0028850496746599674, 0.014461087994277477, -0.014953875914216042, -0.006840793415904045, 0.016091767698526382, 0.025374101474881172, -0.057055890560150146, 0.005555064883083105, -0.0077636511996388435, 0.0008634990081191063, 0.04103580117225647, -0.009900558739900589, 0.01557210087776184, 0.006370404735207558, 0.061177391558885574, 0.022256098687648773, 0.025499539449810982, -0.03476395457983017, -0.0013294076779857278, 0.056769177317619324, 0.018672185018658638, -0.017910603433847427, 0.0067019169218838215, -0.005460986867547035, 0.0043790931813418865, 0.009300253354012966, -0.02809787541627884, -0.003001526929438114, -0.026449276134371758, -0.00961384642869234, -0.02809787541627884, 0.02220233902335167, -0.02759612910449505, -0.016898149624466896, 0.029907751828432083, -0.025033630430698395, 0.0002728533581830561, -0.006253927946090698, -0.001779636717401445, 0.034065090119838715, 0.0103575075045228, -0.0011871710885316133, -0.005891056731343269, 0.009362972341477871, 0.08006460964679718, 0.025141147896647453, -0.014658203348517418, 0.0035055147018283606, -0.05820274353027344, -0.01996239461004734, 0.02811579592525959, 0.015643779188394547, 0.026682229712605476, -0.047773558646440506, 0.00921961572021246, 0.033563341945409775, 0.037201013416051865, 0.048275306820869446, 0.054009564220905304, -0.014272932894527912, -0.016011130064725876, 0.006034413352608681, 0.028778819367289543, 0.004193177912384272, 0.0024840994738042355, -0.014980755746364594, 0.017722448334097862, -0.09146145731210709, 0.02786492183804512, 0.021037567406892776, -0.013090241700410843, 0.004981638863682747, -0.03187890350818634, 0.05834610015153885, 0.008480433374643326, 0.06709084659814835, 0.004450771491974592, 0.011764193885028362, -0.016038009896874428, -0.02270408719778061, -0.014926997013390064, -0.024818595498800278, 0.03300783783197403, 0.016745831817388535, -0.03592872619628906, 0.0023317832965403795, -0.02148555777966976, 0.006522721145302057, 0.053543657064437866, -0.012463056482374668, -0.015339146368205547, -0.02987191267311573, 0.012328660115599632, -0.028079956769943237, -0.014255013316869736, -0.013717425987124443, 0.006903511937707663, 0.031180040910840034, -0.03241649270057678, -0.04433299973607063, -0.0040968600660562515, -0.014398369938135147, 0.012982724234461784, -0.03924384340643883, -0.0213242806494236, 0.015849854797124863, -0.0036287116818130016, 0.014470048248767853, 0.031807225197553635, 0.025033630430698395, -0.022148581221699715, 0.024298928678035736, -0.02270408719778061, 0.016916068270802498, -0.010482944548130035, -0.01605592854321003, 0.011531239375472069, 0.007714372128248215, -0.0451573021709919, 0.04229016974568367, -0.010008076205849648, -0.011531239375472069, 0.029907751828432083, 0.0011602917220443487, 0.020894210785627365, 0.054403796792030334, -0.030660374090075493, 0.01708630472421646, -0.06884696334600449, 0.026574712246656418, -0.019371047616004944, 0.029585199430584908, -0.00016505598614457995, 0.03741604834794998, -0.007163345813751221, 0.00711854686960578, -0.04490642622113228, -0.017794126644730568, 0.02209482155740261, -0.0024527402129024267, -0.008162361569702625, 0.05221761018037796, 0.0005919056129641831, 0.031430914998054504, -0.00044658913975581527, 0.02786492183804512, 0.02799035795032978, 0.0006742235855199397, -0.009542168118059635, 0.01542874425649643, 0.0106621403247118, 0.027022702619433403, -0.028778819367289543, -0.02374342270195484, -0.016638314351439476, 0.04881289228796959, -0.01429981179535389, -0.006115050986409187, 0.038957130163908005, -0.03026614338159561, 0.012973763979971409, -0.06633822619915009, -0.011074290610849857, -0.07633734494447708, -0.03748772665858269, 0.059313755482435226, -0.02560705691576004, 0.037953637540340424, -0.005667062010616064, 0.006195689085870981, 0.01831379346549511, -0.004842761904001236, 0.053507816046476364, -0.024549802765250206, 0.04565905034542084, 0.0045627690851688385, 0.01792852394282818, -0.05970798805356026, 0.05920623987913132, -0.03453100100159645, -0.0577009953558445, -0.012319699861109257, -0.008372915908694267, -0.015643779188394547, 0.008108602836728096, 0.02560705691576004, -0.013600949198007584, 0.02033870480954647, 0.019030576571822166, -0.017588051036000252, -0.02349254861474037, -0.004150618799030781, 0.009362972341477871, 0.01243617758154869, 0.005846257787197828, -0.02270408719778061, -0.00009722763206809759, -0.024263089522719383, 0.030588695779442787, 0.013206718489527702, 0.054547153413295746, -0.02121676318347454, -0.00984680000692606, 0.008229559287428856, 0.006070252042263746, -0.018618427217006683, 0.010456065647304058, -0.0389212928712368, 0.02861754409968853, 0.017238620668649673, 0.0023228235077112913, -0.02270408719778061, 0.011844831518828869, 0.029818154871463776, 0.010070795193314552, 0.002625216031447053, -0.010581502690911293, 0.031305477023124695, -0.02999735064804554, 0.003279280150309205, 0.022632408887147903, 0.02985399402678013, 0.032559849321842194, 0.04168090596795082, 0.030965005978941917, 0.03730853274464607, 0.03175346553325653, 0.002273544669151306, 0.03802531585097313, -0.005577464122325182, -0.003798947436735034, -0.02284744381904602, 0.004363413900136948, 0.011800033040344715, -0.02596544846892357, 0.00022959441412240267, -0.007261903025209904, 0.017874764278531075, 0.01248993631452322, -0.04469139128923416, 0.002097708871588111, 0.051285792142152786, -0.013842863030731678, 0.03677094355225563, -0.009004580788314342, 0.007400779984891415, -0.01944272592663765, -0.036072082817554474, -0.022381534799933434, 0.041860099881887436, -0.020231187343597412, 0.03974559158086777, -0.0294956024736166, 0.03526570275425911, -0.0015746817225590348, 0.005263871978968382, -0.05960046872496605, -0.02044622227549553, -0.021001728251576424, 0.023671744391322136, -0.010760698467493057, 0.009264414198696613, -0.06013805791735649, -0.005622263066470623, 0.011522279120981693, -0.04307863116264343, 0.03988894820213318, 0.04175258427858353, 0.005644662771373987, 0.009909518994390965, 0.0489204078912735, -0.024406446143984795, -0.008731307461857796, 0.0036936700344085693, 0.05046149343252182, -0.006697436794638634, 0.0034898349549621344, -0.04985222592949867, -0.008059323765337467, -0.008247478865087032, 0.006034413352608681, -0.03162803128361702, -0.004345494322478771, 0.003845986444503069, 0.00034747153404168785, -0.009192735888063908, 0.02876090072095394, -0.04415380582213402, 0.02358214557170868, 0.044117964804172516, 0.026413436979055405, 0.030158625915646553, 0.00018045560864266008, 0.013385914266109467, -0.0041035800240933895, -0.04780939593911171, -0.040964122861623764, 0.021664753556251526, -0.01969360001385212, 0.0288863368332386, 0.02721981704235077, 0.03311535343527794, -0.02575041353702545, 0.019854877144098282, 0.0003925504570361227, -0.05458299070596695, 0.02257865108549595, -0.020051991567015648, -0.022148581221699715, 0.02684350684285164, -0.03476395457983017, -0.009972237050533295, 0.02999735064804554, -0.059564631432294846, 0.007745731621980667, 0.015643779188394547, -0.028922175988554955, -0.02596544846892357 ]
High dimensional parameter space optimization is crucial in many applications. The parameters affecting this performance can be both numerical and categorical in their type. The existing techniques of black-box optimization and visual analytics are good in dealing with numerical parameters but analyzing categorical variables in context of the numerical variables are not well studied. Hence, we propose a novel approach, to create an auto-tuning framework for storage systems optimization combining both direct optimization techniques and visual analytics research. While the optimization algorithm will be the core of the system, visual analytics will provide a guideline with the help of an external agent (expert) to provide crucial hints to narrow down the large search space for the optimization engine. As part of the initial step towards creating an auto-tuning engine for storage systems optimization, we created an Interactive Configuration Explorer \textit{ICE}, which directly addresses the need of analysts to learn how the dependent numerical variable is affected by the parameter settings given multiple optimization objectives. No information is lost as ICE shows the complete distribution and statistics of the dependent variable in context with each categorical variable. Analysts can interactively filter the variables to optimize for certain goals such as achieving a system with maximum performance, low variance, etc. Our system was developed in tight collaboration with a group of systems performance researchers and its final effectiveness was evaluated with expert interviews, a comparative user study, and two case studies. We also discuss our research plan for creating an efficient auto-tuning framework combining black-box optimization and visual analytics for storage systems performance optimization.
[ -0.01839606463909149, 0.012104159221053123, -0.03500519320368767, -0.056655365973711014, 0.02614573761820793, 0.05804729834198952, -0.08953504264354706, 0.03731880709528923, -0.017446165904402733, 0.005360816605389118, 0.02892959862947464, -0.06952132284641266, 0.003366969060152769, -0.023173775523900986, -0.010025667026638985, 0.03515566885471344, -0.009151007980108261, 0.028083154931664467, 0.02996414341032505, -0.04804043844342232, 0.05789681896567345, 0.0040935007855296135, -0.03957599401473999, 0.05684346333146095, 0.03306777402758598, 0.03521209955215454, 0.03573877736926079, -0.004561396315693855, -0.0524795725941658, 0.03927503526210785, 0.03701784834265709, 0.03765738382935524, -0.010307815857231617, 0.026409074664115906, -0.053721025586128235, -0.04040362685918808, -0.00831396784633398, 0.037243567407131195, 0.024039030075073242, 0.10074573010206223, 0.0033646177034825087, -0.03957599401473999, -0.01708877831697464, 0.0437517873942852, 0.004596665035933256, 0.0001873640576377511, -0.06666222214698792, -0.018546544015407562, 0.03634069487452507, -0.021706605330109596, -0.004756548907607794, -0.048868075013160706, 0.03583282604813576, 0.0051680151373147964, -0.05138859897851944, -0.012856555171310902, 0.011257714591920376, 0.06252405047416687, 0.07501380890607834, 0.09675803780555725, 0.040478866547346115, -0.03536257892847061, -0.022778768092393875, 0.006766855251044035, 0.002574602607637644, -0.03442208468914032, 0.03005819208920002, 0.025130003690719604, -0.05526343360543251, 0.01669377088546753, -0.01690067909657955, -0.008539686910808086, 0.002140799770131707, 0.013392636552453041, 0.007453416008502245, -0.009099280461668968, 0.06782843917608261, -0.032973725348711014, -0.031450122594833374, -0.0004969923757016659, 0.027575287967920303, 0.0037290591280907393, 0.008751298300921917, -0.016853654757142067, 0.04585849493741989, -0.014709328301250935, -0.005252659786492586, -0.08818072825670242, 0.024546897038817406, -0.02776338718831539, -0.0622607097029686, -0.01956227794289589, 0.03304896503686905, -0.014953856356441975, -0.003961831331253052, 0.05812253803014755, 0.002170190215110779, 0.012527382001280785, -0.010702823288738728, 0.02328663505613804, -0.021499695256352425, 0.017370926216244698, -0.0014401316875591874, -0.018236180767416954, -0.008168191649019718, -0.027105040848255157, -0.020672060549259186, -0.010552343912422657, -0.009376726113259792, 0.0887826457619667, -0.027142660692334175, 0.0015823813155293465, -0.03711189702153206, -0.001253208378329873, -0.07742147892713547, -0.018386660143733025, -0.005713501945137978, -0.05575249344110489, -0.046272311359643936, -0.017653074115514755, 0.0218758936971426, 0.055978208780288696, 0.018894527107477188, -0.03824049234390259, -0.052103374153375626, 0.026841701939702034, 0.00800830777734518, -0.01245214231312275, 0.03197680041193962, -0.031055117025971413, 0.02706742100417614, 0.0020831944420933723, -0.012960009276866913, -0.029399845749139786, 0.0348547138273716, 0.0071007306687533855, 0.054511040449142456, -0.011530457995831966, -0.0026380859781056643, 0.025619059801101685, -0.024640945717692375, -0.026220975443720818, -0.0324658565223217, -0.020559201017022133, 0.0012050081277266145, -0.016044829040765762, 0.0076180025935173035, 0.07486332952976227, -0.056768227368593216, 0.0325222872197628, -0.048078060150146484, 0.04393988475203514, -0.02776338718831539, 0.05541391298174858, 0.044504180550575256, 0.014502419158816338, -0.011041400954127312, 0.0009881065925583243, 0.036265455186367035, -0.0374128557741642, 0.05041048675775528, -0.027086229994893074, 0.011370574124157429, 0.03931265324354172, 0.08803024888038635, -0.017079373821616173, -0.05458628013730049, -0.022440189495682716, -0.0598154254257679, 0.030829397961497307, 0.0324094258248806, -0.013797048479318619, -0.002073789481073618, 0.03314301371574402, -0.04931951314210892, 0.011850225739181042, -0.0008435056661255658, 0.051651936024427414, -0.016881870105862617, -0.03412112593650818, -0.07486332952976227, -0.028308873996138573, 0.015123145654797554, 0.018527735024690628, 0.04472989961504936, 0.013750024139881134, 0.06827987730503082, -0.011944275349378586, 0.040779825299978256, -0.014521229080855846, 0.028967218473553658, 0.035625915974378586, 0.05917588993906975, 0.059401609003543854, 0.009165115654468536, -0.0473632849752903, -0.008295157924294472, 0.010016262531280518, -0.008238728158175945, -0.01613887958228588, -0.0811082124710083, -0.05834825709462166, -0.023380683735013008, -0.006320120766758919, -0.05105002224445343, 0.03549424931406975, 0.03325587138533592, -0.01556517742574215, 0.0143425352871418, -0.03859787806868553, -0.006080294493585825, 0.020822539925575256, -0.053570546209812164, -0.010486509650945663, -0.011774986051023006, -0.002024413552135229, 0.009950428269803524, 0.02898602932691574, -0.010354840196669102, -0.019505849108099937, 0.008643141016364098, 0.038033582270145416, 0.07091325521469116, 0.036509983241558075, -0.021273978054523468, -0.014032172039151192, 0.022985676303505898, 0.001997374463826418, 0.037488095462322235, 0.023512354120612144, 0.0012020691065117717, -0.009386131539940834, 0.0021219898480921984, -0.030867017805576324, 0.012489762157201767, -0.02465975657105446, 0.01159629225730896, -0.03353802114725113, -0.04021552950143814, -0.021537315100431442, 0.009969238191843033, -0.004453239496797323, -0.01049591414630413, -0.016120068728923798, 0.07960342615842819, -0.0054360562935471535, -0.009428453631699085, 0.004472049418836832, 0.0676027163863182, 0.049056172370910645, -0.007241804618388414, 0.03334992006421089, -0.01611066423356533, 0.005849873647093773, -0.04954523220658302, 0.029531516134738922, 0.040290769189596176, -0.027010992169380188, -0.0034304524306207895, -0.03216489776968956, 0.014831592328846455, 0.03035915084183216, 0.02255304902791977, 0.04717518389225006, -0.020916588604450226, -0.03045319952070713, 0.06722652167081833, 0.02339949458837509, -0.018875716254115105, 0.010176146402955055, 0.019882045686244965, -0.022891627624630928, 0.0025887100491672754, -0.057144422084093094, -0.0004805337230209261, -0.024847855791449547, -0.039651233702898026, -0.0022454296704381704, -0.006705723237246275, -0.006531731691211462, -0.025374531745910645, -0.019994905218482018, 0.05300625041127205, 0.011709151789546013, -0.0059627327136695385, -0.042397476732730865, -0.0036538196727633476, -0.028609830886125565, -0.01638340763747692, -0.04442894086241722, -0.01571565680205822, -0.04431608319282532, 0.01708877831697464, 0.01782236434519291, 0.01843368448317051, 0.0015682739904150367, -0.055338673293590546, -0.03084820695221424, 0.02402021922171116, -0.02447165735065937, -0.0026615983806550503, 0.012198208831250668, -0.010749847628176212, 0.05883731320500374, -0.048228539526462555, 0.006376550067216158, -0.044993240386247635, 0.03904931619763374, -0.019430609419941902, -0.04570801556110382, 0.008135274052619934, 0.007683836854994297, -0.018659403547644615, -0.051802415400743484, 0.012470952235162258, 0.04405274614691734, 0.08524638414382935, -0.008596116676926613, -0.023474734276533127, -0.023267824202775955, 0.042736053466796875, 0.029042458161711693, -0.11052686721086502, -0.018057487905025482, -0.032785624265670776, -0.013439660891890526, -0.060191623866558075, 0.0013166917487978935, 0.011455218307673931, 0.02364402264356613, -0.05172717571258545, 0.06030448526144028, -0.04732566326856613, 0.005859278608113527, -0.01397574320435524, -0.019599897786974907, -0.051952894777059555, 0.05278053134679794, -0.026860512793064117, 0.0306036788970232, -0.012517976574599743, -0.026766462251544, -0.026710033416748047, 0.0017363872611895204, 0.0021525558549910784, -0.00559123745188117, -0.037394046783447266, -0.008257538080215454, 0.003451613476499915, -0.008337480016052723, 0.0011138977715745568, -0.02706742100417614, 0.01691008359193802, -0.013195132836699486, 0.014681112952530384, 0.04044124856591225, 0.014192056842148304, -0.031807512044906616, 0.005732311867177486, 0.02353116311132908, 0.050485726445913315, -0.06530791521072388, -0.028703881427645683, 0.016091855242848396, -0.03039677068591118, 0.08231204748153687, 0.05281814932823181, -0.004008856136351824, 0.009611849673092365, -0.022101612761616707, -0.02202637307345867, -0.003635009750723839, -0.006682210601866245, 0.0306036788970232, -0.00355506781488657, 0.0014424828113988042, -0.00808824971318245, -0.02642788551747799, -0.028421731665730476, 0.044015124440193176, -0.0075051430612802505, -0.008497364819049835, -0.042924150824546814, 0.019430609419941902, -0.029305797070264816, 0.0649317130446434, 0.024603325873613358, -0.03461018577218056, -0.0015765032730996609, 0.0018116268329322338, 0.024358797818422318, -0.03656641021370888, -0.02044634148478508, -0.05895017087459564, 0.03276681527495384, -0.004937594290822744, 0.04939475283026695, -0.031995609402656555, 0.025035953149199486, -0.015819111838936806, -0.01231106836348772, -0.014662303030490875, -0.024753805249929428, 0.01693829894065857, 0.004380351398140192, -0.0048576523549854755, -0.0028308872133493423, 0.01147402822971344, -0.017653074115514755, 0.035287339240312576, -0.036660462617874146, -0.03308658301830292, -0.023173775523900986, 0.0013942825607955456, 0.028647450730204582, 0.016806630417704582, -0.03167584165930748, -0.010166741907596588, -0.005069263279438019, -0.026597173884510994, -0.01556517742574215, 0.031450122594833374, -0.032089658081531525, 0.01574387215077877, 0.03152536228299141, 0.0036232536658644676, -0.05379626527428627, -0.008473851718008518, 0.034102316945791245, -0.011238904669880867, 0.043074630200862885, 0.0007811979157850146, -0.01772831380367279, -0.07298234105110168, 0.050824303179979324, 0.0025393341202288866, -0.006122616585344076, 0.03667927160859108, -0.007312342058867216, -0.054511040449142456, -0.06233594939112663, -0.04909379407763481, 0.03094225749373436, -0.018377255648374557, -0.019487038254737854, -0.003693790640681982, -0.014351940713822842, -0.03647236153483391, -0.036209024488925934, 0.021499695256352425, -0.07802339643239975, -0.020521581172943115, -0.040629345923662186, -0.032541096210479736, -0.0009710601880215108, -0.036942608654499054, 0.0006953778211027384, -0.0049328915774822235, 0.025242863222956657, -0.03605854511260986, -0.020070144906640053, 0.057257283478975296, 0.03530614823102951, 0.0004890569252893329, 0.016026020050048828, 0.03722475841641426, -0.047250423580408096, -0.05496247857809067, 0.027631716802716255, -0.007086623460054398, 0.002308913040906191, 0.002861453453078866, 0.05191527679562569, 0.048868075013160706, 0.008812430314719677, 0.0038536747451871634, 0.01971275731921196, 0.015104335732758045, 0.058235395699739456, -0.03769500553607941, 0.03421517461538315, -0.029343416914343834, -0.026164546608924866, 0.01629876345396042, 0.005934517830610275, 0.031751081347465515, 0.010975566692650318, 0.022684717550873756, 0.024283558130264282, -0.02648431435227394, -0.01475635264068842, 0.0020761408377438784, 0.0049187843687832355, 0.024302368983626366, -0.034102316945791245, 0.03137488290667534, -0.018254991620779037, 0.04416560381650925, 0.026014067232608795, 0.012141779065132141, -0.008384505286812782, 0.011088426224887371, -0.03897407650947571, -0.03662284091114998, -0.01377823855727911, 0.03383897989988327, 0.04345082864165306, 0.012122969143092632, -0.024603325873613358, -0.008431529626250267, -0.0006442384910769761, -0.010881517082452774, 0.03167584165930748, -0.036810941994190216, 0.040140289813280106, 0.020314672961831093, -0.015480533242225647, -0.003200031351298094, 0.029155317693948746, 0.006348335184156895, 0.00804122444242239, -0.008125869557261467, 0.016120068728923798, 0.017643669620156288, 0.006503516808152199, 0.027876246720552444, 0.04860473796725273, -0.026898132637143135, 0.04393988475203514, -0.020239433273673058, -0.0074581182561814785, 0.054360561072826385, 0.0002587828494142741, -0.0813339352607727, 0.007697944529354572, -0.027481239289045334, 0.051275741308927536, 0.03094225749373436, -0.010232576169073582, -0.03916217386722565, -0.0523667111992836, 0.023756882175803185, 0.02294805645942688, -0.02825244329869747, -0.017709504812955856, 0.007180672604590654, 0.036848559975624084, -0.0038630797062069178, 0.023042107000947, -0.028967218473553658, 0.020070144906640053, -0.03820287063717842, 0.053721025586128235, 0.00379489385522902, 0.03193918243050575, -0.008506769314408302, -0.01797284372150898, -0.004718929063528776, -0.022665908560156822, -0.046272311359643936, 0.02923055738210678, 0.006103806663304567, 0.002880263375118375, 0.010778062976896763, -0.0143425352871418, -0.014643494039773941, 0.00848325714468956, 0.04946999251842499, -0.017220446839928627, 0.034008268266916275, -0.03957599401473999, 0.0018668808043003082, -0.06124497577548027, -0.014624684117734432, -0.02657836489379406, 0.012640241533517838, 0.03432803601026535, -0.054548658430576324, -0.015772085636854172, -0.01341144647449255, 0.021217547357082367, -0.015922565013170242, 0.039350274950265884, -0.01449301466345787, 0.037883102893829346, 0.02065325155854225, -0.04454180225729942, -0.006404764950275421, -0.007636812515556812, -0.0362466424703598, -0.010796872898936272, 0.04634755104780197, -0.004220467526465654, 0.011530457995831966, -0.020371103659272194, -0.00704900361597538, 0.017897604033350945, 0.0062448810786008835, -0.003686737036332488, -0.002482904586941004, 0.022082801908254623, 0.03461018577218056, -0.0031953288707882166, 0.04860473796725273, 0.036359503865242004, 0.04826615750789642, -0.03946313261985779, -0.006550541613250971, 0.03413993865251541, 0.0400274284183979, -0.020615631714463234, -0.024584516882896423, 0.06959656625986099, -0.006150831468403339, 0.03242823854088783, -0.006875012069940567, 0.03558829799294472, 0.015781491994857788, -0.002224268624559045, -0.0065881614573299885, 0.03329349309206009, 0.006705723237246275, 0.021556125953793526, -0.009028743952512741, 0.03793953359127045, 0.02932460606098175, 0.006809177342802286, -0.03555067628622055, -0.014775162562727928, -0.020615631714463234, 0.011427003890275955, -0.03222132846713066, -0.019675137475132942, -0.0010316044790670276, 0.04551991447806358, -0.008934694342315197, -0.015311243943870068, 0.06824225187301636, 0.002894370583817363, 0.010063286870718002, -0.0500342883169651, -0.00648470688611269, 0.03301134333014488, 0.0783243477344513, 0.0019268373725935817, 0.023756882175803185, 0.01965632662177086, -0.05138859897851944, 0.03244704753160477, 0.04706232622265816, 0.04946999251842499, 0.0027180281467735767, 0.006912631914019585, 0.04311225190758705, -0.005346708931028843, -0.021292787045240402, 0.01608244888484478, 0.027782196179032326, -0.013007033616304398, 0.002171365777030587, 0.020709680393338203, 0.014022767543792725, 0.03540020063519478, 0.022252090275287628, -0.005158610176295042, 0.031356073915958405, -0.00582165876403451, 0.03908693417906761, -0.019900856539607048, 0.059853047132492065, -0.007721456699073315, -0.0009328526211902499, -0.04465465992689133, 0.04728804528713226, 0.029117697849869728, 0.0051539079286158085, -0.0059157079085707664, 0.046272311359643936, -0.0008893547346815467, -0.015574582852423191, 0.02221447043120861, 0.0268228929489851, 0.021292787045240402, 0.015678036957979202, -0.022665908560156822, -0.017775338143110275, -0.041946038603782654, 0.06858082860708237, 0.015800300985574722, -0.03856026008725166, -0.05974018573760986, 0.0040629347786307335, 0.027349568903446198, 0.011267120018601418, -0.02755647711455822, 0.0021725413389503956, -0.01628935895860195, -0.02392617054283619, 0.03365087881684303, -0.007665026932954788, -0.06767795979976654, 0.03244704753160477, 0.009941022843122482, 0.05684346333146095, 0.015461723320186138, 0.006052079610526562, -0.012649646028876305, 0.01118247490376234, -0.03045319952070713, -0.043037012219429016, -0.015997804701328278, -0.003157709026709199, -0.0008922938141040504, 0.016007209196686745, 0.018894527107477188, 0.02996414341032505, 0.009950428269803524, -0.01941179856657982, 0.008398612961173058, 0.03282324597239494, 0.0044508883729577065, -0.0023547622840851545, 0.04198365658521652, -0.09743519127368927, -0.03457256406545639, 0.04431608319282532, 0.041118402034044266, -0.01952465809881687, -0.02447165735065937, 0.0026122224517166615, 0.01681603491306305, -0.02883554995059967, -0.004914081655442715, 0.0020150085911154747, 0.003813703777268529, 0.00630131084471941, 0.004686011932790279, 0.05612868815660477, -0.012066539376974106, 0.013166917487978935, 0.006169641390442848, -0.015753276646137238, 0.00047406781231984496, 0.015160765498876572, -0.005774633958935738, 0.04093030467629433, -0.011511648073792458, 0.016975918784737587, -0.013467876240611076, 0.050184767693281174, 0.05255481228232384, -0.017464976757764816, -0.0036185511853545904, -0.0017646021442487836, -0.0774967148900032, 0.01916727051138878, -0.01699472963809967, -0.012668455950915813, 0.03299253433942795, 0.015903756022453308, 0.026841701939702034, 0.03109273500740528, 0.020672060549259186, 0.012122969143092632, 0.09209318459033966, -0.016063639894127846, 0.030171051621437073, 0.0013014087453484535, 0.031562983989715576, -0.01919548586010933, 0.005483080632984638, 0.03212727978825569, 0.05605344846844673, -0.07012324035167694, 0.02627740614116192, -0.04397750645875931, -0.013129297643899918, 0.027876246720552444, -0.04913141205906868, 0.03344397246837616, -0.020916588604450226, -0.0015894350362941623, -0.0510876402258873, 0.000015402427379740402, -0.02599525824189186, -0.00164233788382262, 0.007387581281363964, 0.03158179298043251, 0.0011650370433926582, 0.007768481504172087, -0.0026169249322265387, 0.028873169794678688, 0.02279757708311081, 0.03255990520119667, 0.0387483574450016, 0.004914081655442715, -0.0028849656227976084, -0.02608930692076683, -0.01296941377222538, -0.01790700852870941, 0.020878968760371208, 0.0012626133393496275, -0.006451789755374193, 0.0012485058978199959, -0.014822187833487988, -0.058235395699739456, -0.026559554040431976, -0.03348159044981003, -0.003980641253292561, -0.012922389432787895, 0.04551991447806358, -0.021349215880036354, -0.009103982709348202, 0.03438446670770645, 0.04642279073596001, -0.04883045330643654, -0.02648431435227394, 0.03793953359127045, -0.010712227784097195, 0.02138683572411537, -0.049018554389476776, -0.02202637307345867, -0.013025843538343906, 0.013514900580048561, -0.02813958376646042, 0.037883102893829346, -0.02736837975680828, 0.0058404686860740185, 0.03816525265574455, -0.014502419158816338, -0.007500440813601017, 0.026992181316018105, -0.0042768968269228935, 0.017098182812333107, -0.01162450760602951, 0.06617316603660583, 0.00908047053962946, -0.011859631165862083, -0.006207261234521866, 0.02264709770679474, -0.023211395367980003, 0.01910143531858921, 0.02148088626563549, 0.006550541613250971, 0.03581401705741882, 0.008953504264354706, -0.04220937564969063, 0.020766111090779305, 0.0037619764916598797, -0.006597566418349743, 0.023455923423171043, 0.020277053117752075, 0.056166309863328934, -0.016712579876184464, -0.015264219604432583, 0.02462213672697544, 0.011295334435999393, 0.020145384594798088, -0.019487038254737854, -0.024546897038817406, 0.013176322914659977, -0.015621607191860676, -0.009028743952512741, 0.013317396864295006, 0.031224405393004417, -0.008276348002254963, 0.0024593921843916178, -0.020483961328864098, -0.006089699454605579, -0.007420498877763748, -0.04909379407763481, 0.02364402264356613, 0.021951133385300636, -0.009249759837985039, 0.00021675450261682272, 0.020314672961831093, 0.005718204192817211, -0.0036914395168423653, 0.009950428269803524, 0.014558848924934864, 0.02971961535513401, 0.0041687400080263615, 0.03035915084183216, -0.030095811933279037, 0.012461546808481216, -0.025073572993278503, -0.055338673293590546, -0.008962908759713173, 0.003350510261952877, -0.05056096613407135, 0.04220937564969063, 0.01843368448317051, -0.02608930692076683, -0.01231106836348772, -0.01821737177670002, 0.03494876250624657, -0.04138174280524254, -0.020183004438877106, -0.005581832490861416, 0.01150224357843399, -0.0205403920263052, -0.029700804501771927, 0.007312342058867216, -0.04149460047483444, -0.005859278608113527, 0.03319944441318512, -0.014455394819378853, -0.006235476117581129, 0.0077261594124138355, -0.0362466424703598, -0.027575287967920303, -0.0006648118142038584, -0.0009781138505786657, 0.003362266579642892, 0.008083547465503216, -0.00035444871173240244, -0.07437427341938019, -0.030472010374069214, 0.022910436615347862, 0.01952465809881687, -0.016975918784737587, 0.04205889627337456, 0.0018798126839101315, 0.05594059079885483, 0.019750377163290977, 0.022421380504965782, -0.02398259937763214, 0.014361345209181309, 0.03786429390311241, 0.03583282604813576, -0.02603287808597088, 0.025920018553733826, 0.05782157927751541, -0.0031365479808300734, 0.04179555922746658, 0.007429903838783503, -0.02456570602953434, -0.028327682986855507, 0.007914258167147636, -0.023230204358696938, -0.019750377163290977, -0.0043591903522610664, 0.016468051820993423, 0.0348547138273716, 0.04604659229516983, -0.01919548586010933, 0.014963261783123016, 0.025957638397812843, -0.01473754271864891, 0.007373474072664976, -0.04781472310423851, 0.006465896964073181, 0.021067067980766296, -0.026164546608924866, -0.019261319190263748, -0.008473851718008518, -0.015141955576837063, 0.006432979833334684, 0.03942551463842392, 0.010430079884827137, -0.012320472858846188, -0.04860473796725273, -0.022665908560156822, -0.018292611464858055, 0.03225895017385483, 0.04051648825407028, -0.023305444046854973, 0.012922389432787895, 0.006611673627048731, 0.028233634307980537, 0.018649999052286148, -0.015762681141495705, 0.017653074115514755, 0.03188275173306465, 0.004674255847930908, -0.016439836472272873, -0.01778474450111389, 0.0015882594743743539, 0.0062919058836996555, 0.0007200658437795937, 0.055188193917274475, -0.015254815109074116, 0.015273625031113625, 0.014333130791783333, -0.012753100134432316, -0.03976409137248993, 0.019599897786974907, -0.0037337616086006165, -0.04454180225729942, 0.011784391477704048, -0.0292681772261858, -0.024095458909869194, 0.04198365658521652, -0.022289710119366646, -0.038522638380527496, 0.01815153658390045, -0.0040159099735319614, -0.022684717550873756, 0.03314301371574402, -0.0423598550260067, 0.024396417662501335, -0.05740776285529137, -0.010740443132817745, 0.0883312076330185, 0.025825968012213707, 0.017446165904402733, 0.03541900962591171, 0.026409074664115906, -0.006108509376645088, 0.008826537057757378, -0.01760604977607727, -0.028158394619822502, -0.01324215717613697, 0.027086229994893074, 0.005266766995191574, 0.02951270528137684, -0.033707309514284134, -0.008868860080838203, 0.03649117052555084, -0.07268138974905014, 0.03233418986201286, -0.033707309514284134, -0.03075415827333927, -0.006832689978182316 ]
Student assessment is one of the most fundamental tasks in the field of AI Education (AIEd). One of the most common approach to student assessment is Knowledge Tracing (KT), which evaluates a student's knowledge state by predicting whether the student will answer a given question correctly or not. However, in the context of multiple choice (polytomous) questions, conventional KT approaches are limited in that they only consider the binary (dichotomous) correctness label (i.e., correct or incorrect), and disregard the specific option chosen by the student. Meanwhile, Option Tracing (OT) attempts to model a student by predicting which option they will choose for a given question, but overlooks the correctness information. In this paper, we propose Dichotomous-Polytomous Multi-Task Learning (DP-MTL), a multi-task learning framework that combines KT and OT for more precise student assessment. In particular, we show that the KT objective acts as a regularization term for OT in the DP-MTL framework, and propose an appropriate architecture for applying our method on top of existing deep learning-based KT models. We experimentally confirm that DP-MTL significantly improves both KT and OT performances, and also benefits downstream tasks such as Score Prediction (SP).
[ 0.006764197256416082, -0.006595434155315161, -0.041816696524620056, -0.02089010365307331, 0.041050419211387634, 0.03293155878782272, -0.05148635059595108, 0.015307245776057243, -0.02202126942574978, 0.04283839464187622, 0.06385620683431625, -0.07443809509277344, 0.02280578948557377, -0.03911649063229561, -0.07367181777954102, -0.005377605091780424, 0.018089551478624344, 0.031216563656926155, -0.009852101095020771, -0.06060866639018059, -0.0006260189111344516, -0.03977329656481743, 0.0037378687411546707, 0.0421815887093544, 0.018162529915571213, 0.026564182713627815, 0.01539846882224083, 0.004041185602545738, -0.02442956157028675, 0.0498078428208828, 0.010244360193610191, 0.06064515560865402, 0.01182252075523138, -0.02116377279162407, -0.017533089965581894, -0.06301695853471756, 0.06812545657157898, 0.013738207519054413, -0.010134892538189888, 0.03464655578136444, -0.021711111068725586, -0.009386862628161907, 0.0061347573064267635, -0.019156862050294876, 0.00904021505266428, -0.05207017809152603, -0.023754509165883064, -0.00263634929433465, 0.00042618319275788963, -0.006800686474889517, -0.00622598035261035, -0.014887618832290173, 0.04853072017431259, 0.0016488585388287902, 0.01846356689929962, 0.05528123304247856, 0.048640187829732895, 0.022240204736590385, 0.07319746166467667, 0.01602790877223015, -0.011931988410651684, 0.05378517135977745, 0.0031905299983918667, -0.02377275377511978, 0.03694537654519081, -0.11450330913066864, -0.005240770522505045, 0.014586582779884338, 0.02902720868587494, 0.003119831904768944, -0.0332782082259655, -0.010919411666691303, -0.021473931148648262, -0.030249599367380142, 0.0024310972075909376, 0.010992390103638172, 0.061156004667282104, 0.03780287504196167, -0.003001241944730282, 0.010016302578151226, 0.010855555534362793, 0.05013624578714371, -0.042619459331035614, -0.05013624578714371, 0.03300453722476959, -0.04002872109413147, -0.0012497572461143136, -0.055974528193473816, 0.03127129748463631, -0.008086932823061943, -0.0433492437005043, -0.021528664976358414, -0.020944837480783463, 0.049296993762254715, -0.0044973017647862434, -0.010171381756663322, -0.0110744908452034, -0.002937385579571128, -0.0019077042816206813, -0.013838552869856358, 0.018919682130217552, -0.017414500936865807, 0.007325219456106424, 0.03700011223554611, 0.04152477905154228, -0.0565948449075222, -0.03601490333676338, 0.02103606052696705, 0.029829971492290497, 0.10618375241756439, -0.03904351219534874, 0.0619952566921711, -0.03366134315729141, 0.01189549919217825, -0.020543454214930534, 0.015352857299149036, -0.04776444286108017, -0.06294398009777069, 0.020616432651877403, -0.0796925500035286, -0.025195835158228874, 0.051851242780685425, -0.02751290425658226, -0.040722016245126724, -0.11377351731061935, 0.01635631173849106, -0.0243748277425766, 0.05024571344256401, 0.013482782058417797, -0.020196806639432907, 0.01881021447479725, 0.01395714282989502, -0.015124799683690071, -0.034683044999837875, -0.0321105495095253, 0.04356817901134491, 0.027239235118031502, -0.0266554057598114, -0.051194436848163605, 0.01182252075523138, -0.01011664792895317, -0.02344435080885887, -0.026035089045763016, 0.01568126119673252, 0.04528317600488663, -0.018518300727009773, 0.03813127800822258, 0.08728231489658356, 0.03294980525970459, 0.06849034875631332, 0.010773454792797565, 0.03732851520180702, -0.05477038398385048, 0.02961103618144989, 0.012570550665259361, -0.0182537529617548, -0.023736264556646347, 0.00956018641591072, -0.04656029865145683, -0.01756957918405533, 0.02377275377511978, 0.009108631871640682, 0.029100187122821808, 0.05812739580869675, 0.043604668229818344, 0.006267030723392963, 0.008880574256181717, 0.000987490639090538, -0.056448888033628464, 0.026254024356603622, -0.04276541620492935, 0.00949633028358221, 0.021236751228570938, 0.040065210312604904, -0.013665229082107544, 0.0001909984857775271, 0.002825637347996235, 0.001767448615282774, -0.05601101741194725, -0.004253279883414507, -0.05455144867300987, 0.009478085674345493, 0.04174371808767319, -0.02455727383494377, 0.09917781502008438, -0.04035712406039238, 0.06787002831697464, 0.008556731976568699, -0.0022247047163546085, -0.03358836472034454, -0.029902949929237366, 0.018089551478624344, 0.054989319294691086, 0.02103606052696705, 0.04586700350046158, -0.04371413588523865, -0.04203563183546066, 0.029428590089082718, 0.004971662070602179, -0.008118861354887486, -0.02313419245183468, -0.051778264343738556, -0.020215051248669624, 0.011275182478129864, 0.013272969052195549, 0.018417954444885254, -0.015763361006975174, 0.03610612452030182, 0.017186442390084267, -0.03506617993116379, 0.02247738651931286, 0.01830848678946495, -0.043239776045084, -0.009915957227349281, 0.0033684149384498596, -0.0066957795061171055, 0.02764061652123928, 0.001299929921515286, 0.014194322749972343, -0.005924943834543228, 0.04371413588523865, 0.05812739580869675, -0.012169169262051582, 0.022386163473129272, -0.009815611876547337, -0.02089010365307331, 0.03355187550187111, -0.012597917579114437, -0.03280384838581085, -0.03658048436045647, 0.03780287504196167, 0.015480569563806057, -0.019412288442254066, -0.025505995377898216, -0.0009150822879746556, -0.0006545261712744832, -0.005774425808340311, -0.016848916187882423, 0.04094095155596733, -0.006937521044164896, -0.024411316961050034, -0.061411429196596146, -0.027804818004369736, -0.02680136263370514, 0.02508636750280857, 0.033114004880189896, 0.018226386979222298, 0.04013818874955177, 0.023827487602829933, 0.0476914644241333, 0.03601490333676338, -0.07140948623418808, 0.03231124207377434, 0.015918441116809845, -0.009523697197437286, 0.03537634015083313, 0.04564806818962097, -0.07133650779724121, 0.011658319272100925, -0.12282285839319229, 0.0510849691927433, 0.03479251265525818, -0.016274211928248405, 0.0332782082259655, 0.0009800788247957826, 0.011448506265878677, 0.0808602049946785, -0.03260315582156181, -0.008556731976568699, 0.021838823333382607, -0.006153001915663481, -0.0521431565284729, -0.03158145770430565, -0.0014036963693797588, 0.04276541620492935, -0.08793912082910538, 0.029665770009160042, -0.02745817042887211, -0.018646012991666794, 0.02764061652123928, 0.008593221195042133, -0.028771784156560898, 0.01041768491268158, -0.035722989588975906, -0.016520513221621513, -0.06495089083909988, -0.015225145034492016, 0.039590850472450256, -0.02103606052696705, 0.00023390186834149063, -0.009961568750441074, -0.042874883860349655, 0.004825705196708441, -0.04400604963302612, 0.040722016245126724, 0.027877796441316605, -0.061812810599803925, -0.02063467726111412, 0.0034641993697732687, -0.03827723488211632, -0.03915297985076904, -0.0076216948218643665, 0.010837310925126076, 0.0188649483025074, -0.03747447207570076, 0.015161288902163506, 0.03163618966937065, 0.03260315582156181, -0.018901437520980835, -0.02619929052889347, 0.01901090517640114, -0.012150924652814865, -0.02908194251358509, 0.00815535057336092, -0.018773725256323814, -0.026874341070652008, 0.07837893813848495, 0.010591008700430393, -0.05232560262084007, -0.018271997570991516, 0.050866033881902695, -0.0035827895626425743, -0.044845305383205414, -0.009478085674345493, 0.022185470908880234, 0.008246573619544506, 0.011293427087366581, 0.02718450129032135, 0.0024333777837455273, -0.031015872955322266, -0.014194322749972343, -0.004885000176727772, -0.05301889777183533, -0.025195835158228874, -0.017742903903126717, 0.005952310748398304, 0.033770810812711716, -0.03643452748656273, -0.03130778670310974, 0.01792534999549389, -0.0017035924829542637, 0.0008084652363322675, 0.008310429751873016, 0.0322200171649456, 0.004743603989481926, -0.007986587472259998, -0.029337367042899132, 0.031107096001505852, -0.030760448426008224, 0.021893557161092758, 0.000941879115998745, 0.04002872109413147, -0.04539264366030693, 0.034427620470523834, 0.02043398655951023, -0.010426807217299938, -0.010153137147426605, -0.0037264658603817225, 0.00011039427045034245, 0.012789486907422543, -0.010828188620507717, -0.05936802923679352, -0.03097938373684883, 0.0021312010940164328, -0.05768952518701553, -0.0016066678799688816, 0.01149411778897047, 0.0036671708803623915, 0.004994467832148075, -0.03329645097255707, 0.023006480187177658, 0.027421681210398674, 0.07294203341007233, 0.01519777812063694, -0.03616086021065712, 0.023572063073515892, -0.018217263743281364, -0.0017320996848866343, -0.015991419553756714, 0.04670625552535057, 0.004743603989481926, -0.018290242180228233, -0.01163095235824585, 0.03922595828771591, -0.03690888732671738, 0.037237294018268585, 0.05907611548900604, -0.0133277028799057, -0.09078528732061386, 0.030888160690665245, 0.036379795521497726, 0.007493982091546059, 0.005400410853326321, -0.018071306869387627, 0.0454656220972538, 0.01421256735920906, -0.01633806712925434, 0.01182252075523138, 0.018883192911744118, -0.030687469989061356, 0.015307245776057243, 0.0011813398450613022, -0.02202126942574978, -0.014458870515227318, 0.02915492095053196, -0.042291056364774704, 0.014093977399170399, 0.0028142344672232866, 0.03962733969092369, 0.04236403480172157, -0.003099306719377637, 0.04396956041455269, -0.006613678764551878, -0.011649196967482567, 0.034610066562891006, 0.018828459084033966, -0.013856797479093075, 0.03597841411828995, -0.04801987111568451, -0.014659561216831207, 0.003377537475898862, 0.0532013438642025, 0.007493982091546059, -0.048895612359046936, 0.04630487412214279, 0.03758393973112106, -0.004679747857153416, -0.010919411666691303, 0.03178214654326439, -0.027038544416427612, 0.07224874198436737, -0.0355040542781353, 0.07560575008392334, 0.010764332488179207, -0.013291213661432266, -0.0332782082259655, -0.017432745546102524, 0.07002289593219757, 0.008228329010307789, 0.01879196986556053, -0.008159911260008812, -0.05903962627053261, 0.001254318398423493, -0.03570474311709404, -0.002006909344345331, -0.03780287504196167, -0.038605641573667526, -0.0282974224537611, -0.00861146580427885, -0.0072385575622320175, -0.03218352794647217, 0.055792082101106644, -0.04867667704820633, -0.04973486438393593, 0.01725029945373535, -0.002782306168228388, 0.04455338791012764, -0.03765691816806793, 0.04283839464187622, -0.050355181097984314, -0.04272892698645592, 0.042145099490880966, 0.015945807099342346, -0.014066610485315323, 0.002344435080885887, -0.0023603991139680147, -0.050866033881902695, 0.015124799683690071, 0.0029898390639573336, 0.012160046957433224, 0.04400604963302612, -0.05221613496541977, 0.01812604069709778, 0.046341363340616226, 0.0243748277425766, -0.0015564950881525874, 0.0023809242993593216, -0.07655446976423264, -0.014750784263014793, 0.018956171348690987, 0.036653462797403336, -0.02167462185025215, 0.03099762834608555, -0.002622665837407112, 0.018919682130217552, -0.017542213201522827, 0.02731221355497837, -0.01011664792895317, 0.03970031812787056, -0.02457551844418049, -0.0048120212741196156, -0.0697309821844101, 0.01635631173849106, -0.010901167057454586, -0.0016967507544904947, -0.01595493033528328, 0.0038176891393959522, -0.06250610947608948, 0.01893792673945427, -0.04531966522336006, 0.003222458064556122, -0.03271262347698212, -0.05115794762969017, 0.05181475356221199, 0.03289506956934929, 0.020853614434599876, -0.014896741136908531, 0.019704202190041542, -0.023499084636569023, 0.014942352660000324, 0.0333876758813858, -0.013829430565237999, 0.04586700350046158, 0.005888454616069794, 0.008397091180086136, 0.04115988686680794, 0.04659678786993027, -0.0048667555674910545, 0.04126935452222824, 0.008004832081496716, 0.003528055502101779, 0.014933230355381966, -0.039919253438711166, 0.006362815387547016, -0.057288143783807755, 0.02738519199192524, 0.0366169735789299, -0.02743992581963539, 0.06721322238445282, -0.02089010365307331, -0.039335425943136215, 0.028790028765797615, 0.02442956157028675, -0.022130737081170082, -0.025433016940951347, -0.018199019134044647, 0.004875877872109413, 0.015252511948347092, 0.001662541995756328, -0.022678077220916748, -0.03136252239346504, 0.0029647524934262037, 0.026235779747366905, -0.004171178676187992, -0.0007890802808105946, 0.013938898220658302, 0.021437441930174828, -0.04243701323866844, 0.02521407976746559, 0.024155892431735992, -0.01643841341137886, -0.024028180167078972, -0.012543183751404285, 0.026126312091946602, -0.021327974274754524, -0.05550016835331917, -0.07126352936029434, -0.02515934593975544, 0.028461623936891556, -0.016301577910780907, -0.0021266399417072535, 0.004168898332864046, 0.0144406259059906, 0.0004481337673496455, -0.01101063471287489, -0.017159076407551765, 0.007174701429903507, 0.0576530359685421, 0.043860092759132385, 0.006057217717170715, -0.015717750415205956, -0.03882457688450813, -0.023572063073515892, -0.018016573041677475, -0.0009367477614432573, 0.021327974274754524, -0.007685550954192877, -0.03293155878782272, -0.02868056111037731, -0.041962653398513794, 0.059003137052059174, -0.03513915836811066, -0.0030422923155128956, 0.017460111528635025, 0.017916228622198105, -0.017104342579841614, -0.010043669492006302, -0.006066340021789074, 0.02627226896584034, -0.01464131660759449, 0.018773725256323814, 0.053237833082675934, 0.0019852439872920513, -0.032329484820365906, -0.017305033281445503, -0.006964887958019972, 0.025524239987134933, -0.03382554650306702, 0.014540971256792545, -0.034628309309482574, 0.023553818464279175, 0.005163230467587709, 0.021565154194831848, 0.06925661861896515, -0.03970031812787056, -0.025141101330518723, 0.007968342863023281, 0.019029149785637856, -0.01422168966382742, 0.023079458624124527, 0.021254995837807655, -0.01957648992538452, 0.01048154104501009, -0.032785601913928986, 0.024849187582731247, -0.014559215866029263, 0.03271262347698212, 0.028863007202744484, 0.0006032131495885551, -0.011521484702825546, 0.03696362301707268, 0.0025565288960933685, 0.056120485067367554, -0.026181045919656754, -0.024684986099600792, 0.004469934850931168, 0.028461623936891556, -0.019248085096478462, -0.0188649483025074, -0.0577625036239624, -0.019795425236225128, 0.025834398344159126, 0.013227357529103756, -0.02187531255185604, 0.014723417349159718, -0.02627226896584034, 0.026618916541337967, 0.033515386283397675, -0.009742633439600468, 0.0030491340439766645, -0.07166491448879242, -0.035011447966098785, -0.009222661145031452, 0.0676146000623703, 0.001683067181147635, 0.03948138281702995, 0.022714566439390182, -0.011977600865066051, 0.07352586090564728, 0.029246143996715546, -0.01853654533624649, 0.006527016870677471, 0.027877796441316605, 0.06637396663427353, -0.031161829829216003, 0.0041483729146420956, -0.01293544378131628, -0.03273086994886398, 0.031344275921583176, -0.005806353874504566, 0.0399557426571846, -0.015316368080675602, 0.03039555624127388, -0.004638697486370802, 0.002084449166432023, -0.011147469282150269, -0.0019932258874177933, 0.041305843740701675, -0.04035712406039238, 0.02948332391679287, 0.01484200730919838, -0.05615697428584099, -0.04506424069404602, 0.03882457688450813, -0.0028872129041701555, -0.03355187550187111, -0.009487207978963852, 0.041816696524620056, -0.04528317600488663, -0.038605641573667526, -0.01689452864229679, -0.007411881349980831, 0.00892618577927351, 0.021528664976358414, -0.013665229082107544, 0.006394743453711271, 0.0320558175444603, 0.03369783237576485, -0.0656076967716217, 0.006554383784532547, -0.003461918793618679, -0.04371413588523865, 0.0008666199864819646, -0.025177590548992157, -0.010326460935175419, -0.002239528577774763, -0.04061254858970642, -0.028078487142920494, 0.012132680043578148, -0.025852642953395844, -0.01538934651762247, 0.007320658303797245, -0.04721710458397865, -0.030888160690665245, 0.06487791240215302, 0.009715266525745392, 0.014486237429082394, 0.004875877872109413, -0.024484295397996902, -0.002579334657639265, 0.016328945755958557, 0.013920653611421585, 0.04677923396229744, 0.01175866462290287, -0.036653462797403336, -0.0009629744454286993, 0.004472215194255114, -0.02207600325345993, -0.004711675923317671, 0.03247544541954994, -0.018554789945483208, 0.01546232495456934, 0.0333876758813858, -0.02731221355497837, -0.04028414562344551, 0.05079305171966553, -0.019047394394874573, -0.022112492471933365, -0.0015713188331574202, 0.007065233308821917, 0.02202126942574978, -0.026053333654999733, -0.026965564116835594, -0.002222424140200019, -0.013865919783711433, -0.003993293736129999, 0.006244224961847067, 0.03769340738654137, -0.012880709953606129, -0.027366947382688522, 0.020817125216126442, -0.032913316041231155, -0.02521407976746559, 0.007653622888028622, 0.0030103642493486404, 0.049224015325307846, 0.03747447207570076, 0.025925621390342712, -0.00591126037761569, -0.010955900885164738, 0.051267415285110474, -0.048238806426525116, -0.008246573619544506, 0.011950233951210976, -0.055792082101106644, 0.021054305136203766, -0.01437676977366209, -0.0002979006094392389, 0.013683473691344261, -0.04911454766988754, -0.02811497636139393, 0.01704048551619053, -0.0178067609667778, -0.012680018320679665, -0.005500756204128265, 0.021857067942619324, -0.011831643059849739, 0.02057994343340397, 0.012953688390552998, -0.03201932832598686, 0.023863976821303368, 0.013154379092156887, 0.06403865665197372, -0.05385814979672432, 0.001325016375631094, 0.012105313129723072, 0.006832614541053772, -0.03289506956934929, -0.07297852635383606, 0.03658048436045647, 0.0007503104861825705, 0.0044311648234725, 0.0019841035827994347, 0.02528705820441246, 0.002033136086538434, -0.00047407535021193326, 0.038167767226696014, 0.01476902887225151, -0.0011904621496796608, -0.01319999061524868, 0.0067413910292088985, -0.011831643059849739, -0.019758936017751694, -0.00496253976598382, 0.04900508001446724, -0.0188649483025074, 0.022185470908880234, 0.03026784397661686, -0.025505995377898216, 0.007010499481111765, 0.03196459263563156, -0.021437441930174828, -0.0018871790962293744, 0.03499320149421692, -0.01569950580596924, -0.01402099896222353, 0.020196806639432907, 0.005997922737151384, 0.00036147175705991685, 0.012561428360641003, 0.0033022782299667597, -0.037310272455215454, -0.0062533472664654255, -0.03499320149421692, 0.035084426403045654, -0.021802334114909172, -0.03163618966937065, 0.012096190825104713, -0.054004110395908356, -0.007211190648376942, 0.002403730060905218, -0.030869916081428528, -0.0008204382611438632, 0.006394743453711271, -0.027148012071847916, -0.018883192911744118, 0.04561157897114754, -0.0024903921876102686, 0.03127129748463631, -0.027932530269026756, 0.03802181035280228, 0.004392394796013832, -0.011320794001221657, -0.018700746819376945, -0.002540564863011241, 0.011904621496796608, -0.015708627179265022, -0.001688768737949431, -0.03375256806612015, 0.07801404595375061, -0.03769340738654137, -0.023863976821303368, -0.0020103303249925375, 0.004246437922120094, -0.012981055304408073, -0.026783118024468422, 0.04152477905154228, -0.005519000813364983, 0.015644771978259087, 0.03046853467822075, 0.026837851852178574, 0.04656029865145683, 0.04637785255908966, 0.06816194206476212, 0.0320558175444603, 0.021784089505672455, -0.0026135435327887535, 0.05181475356221199, 0.0008489455212838948, -0.021200262010097504, -0.0045429132878780365, 0.003959084860980511, -0.026637161150574684, -0.027750084176659584, 0.010353827849030495, 0.021473931148648262, 0.02351732924580574, -0.03293155878782272, -0.015599159523844719, -0.02390046790242195, -0.023499084636569023, -0.016985751688480377, -0.030961139127612114, 0.021583398804068565, 0.0042076678946614265, 0.011941110715270042, -0.021711111068725586, -0.011713053099811077, 0.023152437061071396, -0.042801905423402786, 0.054077088832855225, 0.0005561761790886521, 0.024539029225707054, -0.04940646141767502, 0.03519389405846596, 0.04703465849161148, -0.006422110367566347, -0.001351243001408875, 0.03388027846813202, -0.049224015325307846, 0.01612825319170952, -0.011859009973704815, 0.009551064111292362, -0.03446410968899727, 0.022969990968704224, 0.05378517135977745, -0.03904351219534874, -0.038751598447561264, -0.019612979143857956, 0.02587088756263256, 0.005920382682234049, -0.04619540646672249, -0.0007041287608444691, 0.00023019593209028244, 0.03714606910943985, -0.011667441576719284, 0.02174760028719902, 0.02844337932765484, 0.03260315582156181, -0.021802334114909172, 0.003918034490197897, 0.007557838689535856, 0.04145180061459541, -0.0020228733774274588, 0.030286088585853577, 0.00396364601328969, 0.002188215497881174, -0.0376204289495945, -0.009208977222442627, 0.005582856945693493, 0.027166256681084633, 0.015444080345332623, 0.020871859043836594, 0.06553471833467484, -0.0051039354875683784, -0.04178020730614662, 0.031873371452093124, -0.011658319272100925, 0.028005508705973625, -0.00906302034854889, -0.035741232335567474, 0.032986294478178024, -0.03019486553966999, 0.022130737081170082, 0.029957683756947517, 0.01964946836233139, -0.0029601913411170244, 0.03594192489981651, -0.029702259227633476, -0.001955596497282386, -0.010764332488179207, -0.01595493033528328, 0.01820814236998558, 0.011129224672913551, 0.03663522005081177, -0.02811497636139393, 0.028406890109181404, 0.01868250221014023, -0.0024333777837455273, 0.010144014842808247, -0.017213810235261917, -0.03929893672466278, -0.006581750698387623, 0.0039864517748355865, 0.01893792673945427, 0.04400604963302612, -0.006454038433730602, 0.02430184930562973, 0.01437676977366209, 0.03420868515968323, 0.026892585679888725, 0.020032605156302452, -0.03014013171195984, 0.003071939805522561, -0.0343363955616951, 0.03734676167368889, -0.0232619047164917, -0.04141531139612198, -0.02961103618144989, -0.028060242533683777, 0.01850917935371399, -0.020817125216126442, -0.024867432191967964, 0.02245914191007614, 0.004536071326583624, 0.0013010703260079026, 0.0024402195122092962, -0.007293291389942169, -0.016018785536289215, -0.03570474311709404, 0.09786420315504074, -0.026764873415231705, 0.025250568985939026, 0.012962810695171356, -0.004237315617501736, -0.007384514436125755, 0.05874771252274513, -0.013948020525276661, -0.012096190825104713, -0.0016956104664132, 0.0072522410191595554, -0.011457628570497036, 0.007243118714541197, 0.0015177252935245633, -0.03313225135207176, -0.009687899611890316, -0.04265594854950905, -0.018618647009134293, -0.004976223222911358, 0.007316097151488066, -0.055062297731637955, 0.012889832258224487, -0.02240440808236599, 0.04276541620492935, -0.00006121928890934214, 0.01679418236017227, 0.0478009358048439, -0.034555330872535706, -0.024612007662653923, 0.014951474964618683, -0.002910018665716052, -0.0019761216826736927, 0.007503104396164417, 0.006308081094175577, 0.0052726985886693, 0.015243389643728733, -0.017742903903126717, 0.025250568985939026, -0.014814640395343304, -0.03970031812787056, 0.017916228622198105, -0.007726601324975491, 0.017715536057949066, -0.01582721807062626 ]
Topology impacts important network performance metrics, including link utilization, throughput and latency, and is of central importance to network operators. However, due to the combinatorial nature of network topology, it is extremely difficult to obtain an optimal solution, especially since topology planning in networks also often comes with management-specific constraints. As a result, local optimization with hand-tuned heuristic methods from human experts are often adopted in practice. Yet, heuristic methods cannot cover the global topology design space while taking into account constraints, and cannot guarantee to find good solutions. In this paper, we propose a novel deep reinforcement learning (DRL) algorithm, called Advantage Actor Critic-Graph Searching (A2C-GS), for network topology optimization. A2C-GS consists of three novel components, including a verifier to validate the correctness of a generated network topology, a graph neural network (GNN) to efficiently approximate topology rating, and a DRL actor layer to conduct a topology search. A2C-GS can efficiently search over large topology space and output topology with satisfying performance. We conduct a case study based on a real network scenario, and our experimental results demonstrate the superior performance of A2C-GS in terms of both efficiency and performance.
[ 0.013931791298091412, 0.0015039024874567986, -0.02741638943552971, -0.02215326763689518, 0.005387819372117519, 0.03465748205780983, -0.012340814806520939, 0.0269003976136446, -0.08097638934850693, -0.0051599228754639626, 0.004175237379968166, -0.0026767097879201174, 0.00876326858997345, -0.022944455966353416, -0.043480947613716125, 0.06064629182219505, 0.03718584403395653, 0.0061188084073364735, -0.004375184420496225, -0.08675549924373627, 0.01614195853471756, -0.02542121894657612, 0.03587866201996803, 0.009150262922048569, 0.002913206350058317, 0.012530012056231499, 0.02351204678416252, 0.019745303317904472, -0.07733003795146942, 0.06415504217147827, 0.06683819741010666, 0.03725464269518852, 0.049122463911771774, 0.002773458370938897, -0.03352229669690132, -0.04403134062886238, 0.027450788766145706, 0.04530411958694458, 0.00016541314835194498, 0.06229746714234352, 0.057240743190050125, 0.023236852139234543, -0.0021166433580219746, 0.006707899272441864, 0.046611301600933075, -0.004342935048043728, -0.028757968917489052, 0.01182482298463583, -0.0100016500800848, -0.012280615977942944, 0.008475173264741898, -0.03164752572774887, 0.020295696333050728, -0.037873830646276474, -0.06800778210163116, 0.012667610310018063, 0.05806633085012436, 0.007499087601900101, 0.04939765855669975, 0.0022682161070406437, 0.05390399321913719, 0.004192437045276165, -0.04946645721793175, 0.01740613952279091, 0.014378984458744526, -0.05008564889431, -0.00969205517321825, 0.018076928332448006, 0.03656665235757828, -0.01864452101290226, -0.11957260966300964, 0.018076928332448006, -0.024595631286501884, -0.05270000919699669, 0.0007164767594076693, -0.013536197133362293, 0.03742663934826851, -0.005921011324971914, 0.025042824447155, 0.005409318953752518, 0.011885021813213825, 0.04578571394085884, -0.02516322210431099, 0.00370654440484941, 0.06917736679315567, -0.029996350407600403, 0.008535372093319893, -0.075128473341465, 0.037082646042108536, 0.013346999883651733, -0.045751314610242844, 0.01181622315198183, -0.030477942898869514, 0.014396184124052525, 0.02129328064620495, 0.008556871674954891, 0.021568477153778076, -0.013862992636859417, -0.022084468975663185, 0.08544831722974777, -0.029497558251023293, 0.0033109504729509354, -0.04805608093738556, 0.06140308082103729, 0.02179207280278206, -0.009812452830374241, -0.03852742165327072, 0.041588976979255676, -0.021465279161930084, 0.11964140832424164, 0.047230493277311325, -0.015935560688376427, -0.012650410644710064, 0.023443248122930527, -0.07918761670589447, -0.01087883673608303, -0.041588976979255676, -0.04606090858578682, 0.019693704321980476, -0.003910791594535112, -0.012770808301866055, 0.03390069305896759, -0.03104553557932377, -0.04712729528546333, -0.05421358719468117, 0.022359665483236313, -0.0538007952272892, 0.014344585128128529, 0.007959180511534214, 0.007838782854378223, -0.035465870052576065, 0.004996525123715401, 0.00672939931973815, -0.017113743349909782, 0.06054309383034706, 0.020244097337126732, 0.012633210979402065, -0.029600756242871284, -0.0350186750292778, -0.0488128699362278, 0.01876491867005825, -0.048847269266843796, 0.0038226426113396883, -0.04609530791640282, 0.01038864441215992, 0.04468493163585663, -0.0027326089330017567, 0.058616720139980316, -0.03742663934826851, 0.005443718284368515, -0.08042599260807037, 0.05583036318421364, -0.020553691312670708, 0.022445663809776306, -0.020347295328974724, -0.011661425232887268, 0.00931366067379713, -0.010724038816988468, -0.01650315336883068, 0.02426883578300476, 0.06845497339963913, -0.0638110414147377, -0.0008992240182124078, 0.034468282014131546, 0.0012351564364507794, 0.04303375631570816, 0.029377160593867302, 0.02614360861480236, -0.054385583847761154, 0.03591306135058403, 0.013132003135979176, -0.012074219062924385, -0.03488107770681381, 0.05452318117022514, 0.001167432521469891, 0.03039194457232952, 0.02528362162411213, -0.046370506286621094, -0.013561996631324291, 0.009795253165066242, -0.03445108234882355, -0.01952170766890049, 0.01713094301521778, 0.039731405675411224, 0.03216351941227913, 0.03066714107990265, 0.04540732130408287, 0.000033442076528444886, -0.011111033149063587, -0.007120693102478981, -0.01864452101290226, 0.021671675145626068, 0.03869941830635071, -0.07020934671163559, -0.008505272679030895, -0.06360464543104172, 0.010104849003255367, 0.0065015023574233055, 0.02464723028242588, -0.02141367830336094, -0.03027154691517353, 0.031183132901787758, 0.00528462091460824, -0.009416858665645123, -0.02027849666774273, -0.03144112974405289, 0.03402109071612358, -0.007292690686881542, -0.016451552510261536, -0.0293943602591753, -0.03866501897573471, 0.032490313053131104, -0.03904341533780098, 0.0025090123526751995, -0.035706665366888046, 0.007843082770705223, -0.007425988558679819, 0.004949226044118404, -0.009494258090853691, -0.0009868352208286524, -0.003573246533051133, 0.08709949254989624, 0.04420333728194237, -0.02626400627195835, -0.038114629685878754, -0.005736113991588354, 0.043343350291252136, -0.04588891193270683, 0.01891971565783024, 0.005594216287136078, -0.03269670903682709, -0.015952760353684425, -0.01076703891158104, 0.006845497526228428, 0.029566356912255287, 0.0035366970114409924, -0.013527597300708294, 0.02640160359442234, -0.024956826120615005, -0.0064757028594613075, -0.030615540221333504, 0.01489497721195221, -0.024681629613041878, 0.005435118451714516, 0.06439583748579025, 0.00375599367544055, 0.012349414639174938, 0.03457148000597954, 0.05596796050667763, 0.008281676098704338, -0.023374449461698532, -0.02652200311422348, 0.04829687625169754, 0.011687224730849266, -0.04138258099555969, -0.03725464269518852, 0.019934501498937607, -0.05669035017490387, -0.02051929198205471, -0.0074087888933718204, 0.036119457334280014, 0.014998175203800201, -0.019057314842939377, 0.03914661332964897, -0.01900571584701538, -0.00759798614308238, 0.03214631974697113, 0.037977032363414764, -0.04465053230524063, 0.008969665504992008, -0.041726574301719666, -0.08826907724142075, -0.01637415401637554, 0.005370619706809521, 0.014095189049839973, -0.03711704537272453, 0.040866587311029434, -0.009649055078625679, 0.024819228798151016, 0.013063204474747181, 0.0005321170319803059, -0.052493613213300705, -0.009580256417393684, 0.003403398906812072, -0.036601051688194275, -0.03577546402812004, -0.03532826900482178, -0.014559581875801086, -0.04544172063469887, -0.013966190628707409, -0.06941816210746765, 0.04970725625753403, -0.019590506330132484, 0.01444778311997652, 0.023563647642731667, -0.009674854576587677, -0.009408258832991123, -0.028757968917489052, 0.029979150742292404, -0.030976735055446625, -0.006935796234756708, -0.008621370419859886, 0.011291630566120148, 0.052768807858228683, -0.057481538504362106, -0.018730519339442253, -0.04213936999440193, 0.06938376277685165, 0.015978559851646423, -0.038493022322654724, 0.005151322577148676, -0.007425988558679819, -0.0001207341265399009, -0.07100053876638412, -0.005886611994355917, -0.022875657305121422, 0.0625726655125618, -0.059855103492736816, -0.030305946245789528, -0.04568251594901085, 0.027485188096761703, -0.015488367527723312, -0.08365954458713531, 0.077605240046978, -0.007623785641044378, 0.05720634385943413, 0.04368734359741211, -0.013475998304784298, -0.020811688154935837, 0.004927725996822119, -0.040350593626499176, 0.03894021734595299, -0.09583696722984314, 0.006617601029574871, -0.014817577786743641, -0.009855451993644238, -0.0027820582035928965, 0.0300307497382164, -0.014525182545185089, 0.008414973504841328, 0.0194013100117445, -0.0018812217749655247, -0.03666985034942627, 0.03028874658048153, 0.00043966842349618673, -0.06023349612951279, -0.04169217497110367, -0.0437905453145504, -0.007993579842150211, 0.03400389105081558, 0.0008529997430741787, 0.014095189049839973, 0.01728574000298977, 0.0018951966194435954, 0.08434753865003586, -0.019435709342360497, -0.015290570445358753, 0.002902456559240818, 0.0011620576260611415, -0.0175351370126009, 0.04733369126915932, -0.07602286338806152, -0.033075105398893356, 0.06766378879547119, -0.06800778210163116, 0.03852742165327072, -0.023546447977423668, -0.021344879642128944, -0.00606720894575119, 0.02590281143784523, -0.016924547031521797, 0.03166472539305687, 0.010741239413619041, -0.030254347249865532, -0.006669200025498867, -0.0002160717558581382, -0.0034119989722967148, -0.0016823498299345374, -0.05345679819583893, 0.025318020954728127, -0.006183307152241468, 0.003994639962911606, 0.02628120593726635, 0.01521317195147276, -0.03481227904558182, 0.04939765855669975, 0.04327455163002014, -0.017732935026288033, -0.018988516181707382, 0.07051894068717957, 0.016236556693911552, -0.06553101539611816, -0.04392814263701439, -0.003861342091113329, -0.001699549495242536, -0.03137233108282089, 0.0034764979500323534, -0.04520092159509659, 0.021688874810934067, -0.06415504217147827, -0.06016469746828079, -0.02377004362642765, -0.001594201079569757, 0.03529386967420578, -0.04213936999440193, 0.015127173624932766, -0.058375924825668335, -0.04289615526795387, -0.0047600287944078445, -0.008427873253822327, 0.0337458960711956, -0.02813877910375595, -0.028947165235877037, -0.03451988101005554, -0.010853037238121033, 0.014361784793436527, -0.036119457334280014, -0.025060024112462997, 0.04726489260792732, -0.020209698006510735, 0.006961595732718706, 0.020467692986130714, 0.04846887290477753, -0.019590506330132484, -0.0017833983292803168, 0.04967285692691803, 0.008045179769396782, 0.002878806786611676, -0.015832362696528435, -0.02303045429289341, 0.051117632538080215, 0.0064370036125183105, 0.018076928332448006, -0.02303045429289341, -0.05545197054743767, -0.018076928332448006, 0.016546152532100677, 0.00013289488560985774, -0.05070484057068825, 0.010173647664487362, 0.012349414639174938, -0.06291665881872177, -0.03040914423763752, -0.015686165541410446, -0.014869176782667637, -0.036601051688194275, -0.035603467375040054, -0.05782553181052208, -0.03367709368467331, -0.005065324250608683, -0.04478812962770462, 0.03169912472367287, -0.04946645721793175, -0.02153407782316208, 0.027106793597340584, 0.0056114159524440765, 0.004686929751187563, -0.02879236824810505, 0.07822442799806595, -0.01627955585718155, 0.01838652417063713, 0.025593215599656105, -0.011128232814371586, -0.09280981123447418, -0.006338105071336031, 0.011575426906347275, -0.018610121682286263, -0.00819137692451477, 0.018472522497177124, -0.01519597228616476, 0.0400753989815712, -0.04389374330639839, 0.018059728667140007, 0.03691064566373825, 0.0016436503501608968, 0.00807957910001278, 0.009201861917972565, -0.08207716792821884, 0.0031540028285235167, 0.004091388545930386, 0.037736233323812485, 0.04299935698509216, 0.017939331009984016, 0.027485188096761703, 0.023821642622351646, 0.03489827737212181, 0.0487784706056118, 0.022325266152620316, 0.017440538853406906, -0.02741638943552971, 0.045854512602090836, 0.004992225207388401, -0.029755553230643272, 0.009287861175835133, 0.006368204485625029, 0.012977205216884613, 0.02266925945878029, -0.029875952750444412, 0.022187666967511177, 0.007292690686881542, -0.005142722744494677, -0.009081464260816574, 0.008475173264741898, 0.012650410644710064, 0.01826612651348114, -0.012968605384230614, 0.02053649164736271, 0.08076998591423035, -0.012994404882192612, -0.0038527422584593296, -0.008178477175533772, 0.015488367527723312, -0.004876127000898123, -0.005916711408644915, 0.00118248222861439, 0.05706874653697014, -0.03317830339074135, 0.0011749573750421405, 0.03618825599551201, 0.02815597876906395, -0.005890911910682917, -0.05620875582098961, -0.030477942898869514, 0.02652200311422348, -0.06277906149625778, 0.06484302878379822, 0.05015444755554199, 0.0007471137796528637, 0.03670424968004227, 0.005142722744494677, -0.03402109071612358, 0.044994525611400604, 0.007456088438630104, -0.014869176782667637, -0.014172587543725967, -0.018558522686362267, 0.024182837456464767, 0.020450493320822716, -0.027725985273718834, -0.029428759589791298, -0.021241681650280952, 0.026590801775455475, -0.02327125146985054, 0.00858267117291689, 0.014869176782667637, 0.018936915323138237, 0.056002359837293625, -0.005245921202003956, -0.016468754038214684, -0.000537760672159493, 0.002715409267693758, -0.03739224001765251, -0.008040879853069782, -0.03350509703159332, -0.03292030841112137, -0.016477353870868683, -0.0362914577126503, -0.04867526888847351, -0.025455618277192116, -0.023477647453546524, -0.02989315241575241, 0.0012899807188659906, -0.026745598763227463, -0.044375333935022354, 0.015032574534416199, 0.008040879853069782, 0.05345679819583893, 0.028568772599101067, 0.010268245823681355, 0.03326430171728134, -0.04169217497110367, -0.014482183381915092, -0.035225071012973785, -0.017586736008524895, 0.005688814911991358, -0.002775608329102397, -0.021344879642128944, -0.011394829489290714, 0.00807527918368578, -0.024372035637497902, 0.023873241618275642, -0.026350004598498344, 0.02303045429289341, 0.013673795387148857, 0.003816192736849189, -0.043102554976940155, -0.06209107115864754, -0.005056724417954683, 0.020347295328974724, -0.043618544936180115, -0.017801733687520027, 0.04403134062886238, 0.006965895649045706, -0.023374449461698532, -0.026676800101995468, -0.02777758426964283, -0.0018844467122107744, 0.007636685390025377, 0.037873830646276474, -0.06394863873720169, 0.03904341533780098, 0.018747719004750252, -0.011145433411002159, -0.0175007376819849, -0.006415504030883312, -0.021362079307436943, 0.0488128699362278, 0.029377160593867302, 0.01976250298321247, 0.004566531628370285, -0.04155457764863968, 0.022961655631661415, 0.06766378879547119, -0.04454733058810234, -0.02291005663573742, 0.010354245081543922, -0.018317725509405136, 0.022583261132240295, -0.029325559735298157, -0.04520092159509659, 0.0437561459839344, -0.049122463911771774, 0.04083218798041344, -0.0077699837274849415, -0.01574636436998844, 0.039249811321496964, -0.0015737763606011868, -0.05328480154275894, -0.017586736008524895, -0.023838842287659645, -0.009236261248588562, -0.023494847118854523, -0.018988516181707382, -0.012125818058848381, 0.01824892684817314, -0.01677834801375866, -0.0337458960711956, 0.04265535995364189, 0.009098663926124573, 0.0125128123909235, -0.04977605491876602, 0.02153407782316208, 0.016718149185180664, 0.05909831449389458, 0.0012437563855201006, 0.017449138686060905, -0.014757378958165646, 0.0006068284274078906, 0.0275195874273777, 0.05947670713067055, 0.02076008915901184, 0.039249811321496964, 0.01888531632721424, 0.05479837954044342, -0.0007261516293510795, -0.03887141868472099, 0.018558522686362267, 0.0020671940874308348, -0.009545857086777687, 0.015926960855722427, -0.01900571584701538, -0.029119163751602173, -0.023322850465774536, 0.010337045416235924, 0.013742594048380852, -0.03914661332964897, 0.01558296661823988, 0.004274135921150446, 0.027605585753917694, 0.04217376932501793, -0.054626382887363434, 0.010784238576889038, -0.030477942898869514, 0.017320141196250916, 0.028069978579878807, -0.0269175972789526, 0.0034850977826863527, 0.06670060008764267, -0.037082646042108536, -0.014576781541109085, -0.029996350407600403, -0.03300630673766136, -0.0550735741853714, -0.00723249139264226, -0.024836428463459015, -0.00537491962313652, 0.007537786848843098, 0.02614360861480236, 0.0034549981355667114, 0.01891971565783024, -0.028551572933793068, -0.00231336522847414, 0.010122048668563366, -0.015135773457586765, 0.03866501897573471, 0.045235320925712585, 0.031613126397132874, -0.03039194457232952, 0.03290310502052307, -0.04268975928425789, -0.0034119989722967148, 0.000028033564376528375, 0.04244896396994591, 0.009872651658952236, -0.009477058425545692, 0.017414739355444908, 0.019332509487867355, 0.029566356912255287, -0.026332804933190346, -0.029050365090370178, 0.007980680093169212, 0.029927551746368408, -0.009649055078625679, 0.026745598763227463, 0.04943205788731575, 0.029325559735298157, -0.013708194717764854, -0.004293485544621944, 0.012246216647326946, 0.005903811659663916, -0.03400389105081558, 0.0002464400604367256, 0.02151687815785408, -0.06907416135072708, -0.0325419120490551, 0.017345940694212914, 0.03156152740120888, 0.032851506024599075, -0.026934796944260597, -0.004545032046735287, -0.027622785419225693, -0.014241386204957962, -0.033229902386665344, -0.01182482298463583, -0.01824892684817314, 0.029841553419828415, -0.008290275931358337, 0.026229606941342354, 0.0011556076351553202, -0.022875657305121422, 0.0032615012023597956, -0.001286755665205419, 0.020244097337126732, 0.03894021734595299, 0.029824353754520416, 0.018455322831869125, -0.009975850582122803, 0.02125888131558895, 0.009545857086777687, -0.03605065867304802, 0.04320575296878815, -0.046129707247018814, 0.04729929193854332, -0.022239265963435173, -0.09225941449403763, 0.027880782261490822, 0.023340050131082535, -0.0243892353028059, 0.019796904176473618, 0.005942510906606913, -0.037082646042108536, 0.03701384365558624, 0.014267186634242535, 0.04207056760787964, 0.03090793639421463, -0.002575661288574338, 0.0011900071986019611, -0.012684809975326061, 0.017818933352828026, -0.011773223988711834, 0.016675150021910667, 0.01878211833536625, 0.03150992840528488, -0.018868116661906242, 0.01727714017033577, 0.005405019037425518, 0.033728692680597305, -0.01126583106815815, -0.009270661510527134, -0.002065044129267335, -0.020192496478557587, -0.0034076988231390715, -0.03439948335289955, 0.049604058265686035, -0.013742594048380852, -0.026074809953570366, -0.007615185808390379, -0.019091714173555374, -0.009967250749468803, 0.04093538597226143, 0.004622430540621281, -0.0024853628128767014, 0.019831303507089615, 0.03732344135642052, 0.024114038795232773, -0.008539672009646893, 0.029944751411676407, 0.029101964086294174, 0.0036549451760947704, -0.022858457639813423, 0.0243892353028059, 0.017973730340600014, -0.010681039653718472, 0.04468493163585663, -0.01864452101290226, -0.03028874658048153, -0.03407268971204758, -0.02203286997973919, -0.03605065867304802, 0.009012664668262005, 0.01069823931902647, 0.004001089837402105, -0.047471288591623306, -0.015531367622315884, 0.013020205311477184, -0.03150992840528488, -0.0005334607558324933, 0.013467398472130299, -0.043102554976940155, -0.03345349803566933, -0.02416563779115677, -0.009029864333570004, -0.0362570583820343, -0.008427873253822327, -0.03770183399319649, -0.005985510069876909, 0.02889556623995304, -0.02289285697042942, 0.04857207089662552, 0.026969196274876595, 0.0038505923002958298, 0.035104673355817795, -0.02165447548031807, 0.030563941225409508, -0.06398303806781769, 0.03704824298620224, 0.003173352451995015, 0.025472817942500114, -0.026350004598498344, 0.018059728667140007, 0.007709784433245659, 0.021465279161930084, -0.004588031210005283, -0.03202591836452484, -0.036738649010658264, -0.0007643135613761842, -0.0029325559735298157, -0.005589916370809078, 0.0019338959828019142, 0.009520057588815689, 0.0218780729919672, 0.01700194552540779, 0.008909466676414013, 0.006230606697499752, 0.04496012628078461, 0.011592626571655273, 0.006376804318279028, 0.013561996631324291, -0.0200204998254776, -0.02763998508453369, 0.013699594885110855, 0.020605290308594704, 0.005921011324971914, -0.022961655631661415, 0.006742299068719149, 0.0012598810717463493, -0.015918361023068428, -0.022927256301045418, -0.010319845750927925, -0.036360256373882294, -0.028104377910494804, 0.019057314842939377, -0.00597261032089591, 0.05190882086753845, 0.032352715730667114, -0.003117453306913376, 0.0269003976136446, -0.03783943131566048, 0.0028852566611021757, -0.007056194357573986, -0.0032851507421582937, 0.009115863591432571, 0.032077521085739136, 0.015256171114742756, 0.02789798192679882, -0.026934796944260597, -0.02076008915901184, -0.008303175680339336, -0.015995759516954422, -0.055727165192365646, -0.013493197970092297, 0.018300525844097137, -0.06573741137981415, -0.0028895565774291754, 0.004777228459715843, 0.056621551513671875, 0.0011609826469793916, 0.011480827815830708, 0.02602320909500122, 0.058375924825668335, 0.008849266916513443, -0.03732344135642052, 0.026246806606650352, -0.03728904202580452, 0.0350530743598938, -0.01308040414005518, 0.010620840825140476, 0.005779113154858351, 0.02915356308221817, -0.026384403929114342, 0.027209991589188576, -0.034829478710889816, -0.0029368558898568153, -0.01988290250301361, 0.04977605491876602, 0.036360256373882294, -0.008238676935434341, -0.049122463911771774, 0.01057784166187048, -0.02149967849254608, 0.03725464269518852, 0.020966485142707825, -0.01271060947328806, 0.008548271842300892, -0.02741638943552971, 0.023064853623509407, -0.03814902901649475, 0.006656300276517868, 0.011902221478521824, -0.0077527835965156555, -0.04403134062886238, 0.02416563779115677, 0.01289120689034462, -0.004080638755112886, 0.005916711408644915, 0.027089593932032585, -0.022118868306279182, 0.006342404987663031, 0.006828297860920429, -0.006871297024190426, -0.015161572955548763, -0.002079018857330084, 0.000036918976547895, 0.021362079307436943, 0.021086884662508965, -0.03718584403395653, 0.040247395634651184, 0.021998470649123192, 0.01728574000298977, 0.01952170766890049, -0.03188832104206085, -0.028689170256257057, 0.004351534880697727, -0.02401084080338478, -0.026865996420383453, -0.04121058061718941, -0.005761913489550352, -0.02789798192679882, 0.021826472133398056, 0.027467988431453705, -0.004949226044118404, 0.03302350640296936, -0.004699829500168562, -0.020932085812091827, 0.005826412700116634, 0.048503272235393524, -0.015333570539951324, 0.01270200964063406, -0.014439183287322521, 0.03066714107990265, 0.023701244965195656, -0.0031454027630388737, 0.0375642366707325, 0.01713954284787178, -0.0077140843495726585, 0.03976580500602722, -0.01538516953587532, -0.021344879642128944, -0.02401084080338478, -0.001169582479633391, 0.045716915279626846, 0.041864171624183655, -0.02303045429289341, -0.02239406481385231, 0.004106438253074884, -0.04654250293970108, 0.02352924644947052, 0.000005055783731222618, -0.012727809138596058, -0.004250486381351948, -0.03666985034942627, 0.023099252954125404, 0.007189492229372263, 0.005056724417954683, -0.026625201106071472, -0.011343229562044144, -0.0150067750364542, -0.025455618277192116, 0.0425865612924099, 0.014972375705838203, -0.021430877968668938, 0.01615055836737156, -0.016073159873485565, 0.0613342821598053, 0.0031690525356680155, -0.018730519339442253, 0.011489427648484707, 0.017543736845254898, 0.03694504499435425, 0.048503272235393524, 0.0047471290454268456, -0.020209698006510735, -0.045613717287778854, -0.015436768531799316, 0.020244097337126732, 0.021086884662508965, -0.015264770947396755, 0.056759148836135864, -0.017578136175870895, -0.03680744767189026, 0.009571656584739685, 0.007335689850151539, 0.0007137893117032945, -0.006793898064643145 ]
Automated decision systems (ADS) are increasingly used for consequential decision-making. These systems often rely on sophisticated yet opaque machine learning models, which do not allow for understanding how a given decision was arrived at. This is not only problematic from a legal perspective, but non-transparent systems are also prone to yield unfair outcomes because their sanity is challenging to assess and calibrate in the first place -- which is particularly worrisome for human decision-subjects. Based on this observation and building upon existing work, I aim to make the following three main contributions through my doctoral thesis: (a) understand how (potential) decision-subjects perceive algorithmic decisions (with varying degrees of transparency of the underlying ADS), as compared to similar decisions made by humans; (b) evaluate different tools for transparent decision-making with respect to their effectiveness in enabling people to appropriately assess the quality and fairness of ADS; and (c) develop human-understandable technical artifacts for fair automated decision-making. Over the course of the first half of my PhD program, I have already addressed substantial pieces of (a) and (c), whereas (b) will be the major focus of the second half.
[ 0.016794702038168907, -0.018226733431220055, -0.03734970465302467, -0.00460782740265131, 0.0018143929773941636, -0.015031454153358936, -0.059307511895895004, 0.03604431450366974, -0.022405926138162613, -0.0024244673550128937, 0.018918395042419434, -0.07742708921432495, 0.026146741583943367, -0.002073765965178609, -0.008114841766655445, 0.011709531769156456, 0.03210866451263428, 0.031660549342632294, 0.003735944628715515, -0.08650635927915573, -0.0063905599527060986, -0.03425184264779091, -0.035693615674972534, 0.046097759157419205, -0.011875140480697155, 0.022815078496932983, -0.011388055048882961, -0.002392806811258197, -0.07107549160718918, -0.01600562408566475, 0.020964153110980988, 0.038849927484989166, -0.016697285696864128, -0.01095942035317421, -0.026010356843471527, -0.025425855070352554, 0.026887111365795135, -0.03444667533040047, 0.011582889594137669, 0.08619462698698044, -0.01467101089656353, 0.036745719611644745, -0.0386161282658577, 0.00866524875164032, 0.01944444701075554, -0.028095083311200142, -0.017398688942193985, -0.027179362252354622, 0.017632490023970604, -0.0048854658380150795, -0.03259574994444847, -0.00631749676540494, 0.03242040053009987, -0.0006362552521750331, -0.02443220093846321, 0.008051521144807339, 0.053657323122024536, -0.010930195450782776, -0.003253730246797204, 0.020145850256085396, 0.033862173557281494, 0.03380372375249863, 0.008655507117509842, -0.02517257072031498, -0.022405926138162613, -0.04940993711352348, -0.020944669842720032, 0.0511634461581707, -0.026575377210974693, -0.0009577315649949014, -0.006960449740290642, 0.01006318349391222, -0.014700235798954964, 0.03631708398461342, 0.003745686262845993, 0.014778169803321362, 0.02260076068341732, -0.03259574994444847, -0.050462041050195694, -0.014135217294096947, 0.009829382412135601, 0.016307616606354713, 0.01742791384458542, -0.01201152428984642, 0.05607326701283455, 0.007632627617567778, -0.02195780724287033, -0.09920954704284668, -0.0403306670486927, -0.049487870186567307, -0.022347476333379745, -0.017213596031069756, 0.024743935093283653, -0.012673960998654366, -0.004386203363537788, 0.0034388224594295025, 0.02283456176519394, -0.005562514532357454, -0.013628647662699223, 0.003127087838947773, -0.005255650728940964, 0.014768428169190884, -0.015508797951042652, 0.010735360905528069, 0.025055671110749245, -0.006609748117625713, -0.01737920567393303, 0.01231351774185896, 0.034777894616127014, 0.14752840995788574, -0.007033512461930513, 0.04773436486721039, -0.05630706623196602, -0.011563406325876713, -0.07290693372488022, 0.02086673676967621, -0.08042753487825394, -0.06893231719732285, 0.034544091671705246, -0.0065951356664299965, -0.032245051115751266, 0.030335675925016403, 0.03787575662136078, -0.022308509796857834, -0.027354713529348373, 0.02503618784248829, -0.012693444266915321, -0.01736946403980255, 0.030062908306717873, 0.025562239810824394, -0.011709531769156456, 0.022503342479467392, -0.031017595902085304, -0.021607106551527977, 0.026516927406191826, 0.047149863094091415, 0.05529392883181572, 0.038265425711870193, 0.010326209478080273, 0.04333111271262169, 0.0020895961206406355, 0.00909875426441431, -0.04730572924017906, 0.0027690802235156298, 0.00658052321523428, 0.01567440666258335, -0.007467018440365791, 0.010141116566956043, -0.04387664794921875, 0.030686376616358757, -0.024081500247120857, 0.004921997431665659, -0.03781730681657791, 0.02178245596587658, 0.07010132074356079, -0.0017084518913179636, 0.025912940502166748, -0.0010654991492629051, 0.027724897488951683, -0.006882516201585531, -0.004666277673095465, -0.00825122557580471, -0.005294617731124163, 0.09632600098848343, 0.010930195450782776, 0.030920177698135376, -0.024003565311431885, -0.047149863094091415, -0.03631708398461342, 0.05221555009484291, 0.0078079779632389545, 0.011251671239733696, -0.03107604570686817, 0.025757072493433952, 0.02425684966146946, 0.04874750226736069, 0.05482632666826248, 0.03631708398461342, -0.02860165201127529, -0.03062792681157589, -0.06254176050424576, 0.03565464913845062, 0.019006069749593735, -0.010774328373372555, 0.04161657392978668, 0.023535965010523796, 0.0948452576994896, -0.04072033613920212, 0.06721777468919754, 0.030335675925016403, 0.04021376743912697, 0.009736835956573486, 0.03107604570686817, 0.010423626750707626, 0.038168009370565414, -0.02653641067445278, 0.0011872705072164536, -0.036375533789396286, -0.00797845795750618, 0.007656981702893972, -0.047929197549819946, -0.10419730097055435, 0.02774438075721264, 0.016804443672299385, -0.002448821673169732, -0.00809048768132925, 0.04905923828482628, -0.005129008553922176, -0.015343188308179379, -0.08970163762569427, 0.0023721056059002876, -0.0007519380305893719, 0.0011263848282396793, -0.04383768141269684, -0.0369405522942543, -0.03838232532143593, -0.021938323974609375, -0.016288133338093758, -0.020321201533079147, -0.03577154874801636, -0.0029517372604459524, 0.014407984912395477, 0.027296263724565506, 0.0474226288497448, 0.024373751133680344, -0.013190271332859993, 0.02768593095242977, 0.007559564430266619, -0.01875278539955616, 0.003828490851446986, -0.03756402060389519, 0.018762527033686638, -0.012566802091896534, 0.0016828798688948154, -0.00002385957122896798, 0.0008554436499252915, -0.004393510054796934, -0.019863341003656387, 0.05163104832172394, -0.010530785657465458, -0.0015416251262649894, -0.03343353793025017, -0.001490481197834015, -0.04847473278641701, 0.042941443622112274, 0.020243266597390175, 0.039824098348617554, 0.07559564709663391, 0.05295591801404953, 0.05003340542316437, 0.012333001010119915, 0.060086850076913834, -0.04570809006690979, -0.022542310878634453, -0.03255678340792656, 0.030549993738532066, -0.0116900485008955, -0.000888930750079453, 0.03279058635234833, -0.06897128373384476, 0.05583946406841278, -0.0008499639225192368, 0.018684593960642815, 0.05065687745809555, -0.005781703162938356, -0.004907384980469942, 0.07618014514446259, 0.03210866451263428, 0.009142591618001461, -0.02994600683450699, -0.013414330780506134, -0.02754954807460308, 0.01746688038110733, -0.033355604857206345, -0.002856755629181862, -0.04566912353038788, 0.041187938302755356, -0.011310121975839138, 0.010092408396303654, 0.01421315036714077, 0.010969161987304688, -0.06339903175830841, 0.036200184375047684, 0.007043254096060991, -0.05357939004898071, -0.052566252648830414, -0.01265447773039341, -0.04761746525764465, -0.055410828441381454, -0.009415360167622566, -0.010296984575688839, -0.06421732902526855, -0.015596472658216953, -0.024471167474985123, 0.05357939004898071, -0.006176242139190435, -0.007038383278995752, -0.07294590026140213, 0.0226981770247221, -0.054397691041231155, 0.015752339735627174, -0.041421737521886826, -0.007150413002818823, 0.05120241269469261, 0.04044756665825844, 0.07695948332548141, -0.008183034136891365, 0.06760744750499725, 0.011465989053249359, 0.013112337328493595, 0.04769539833068848, 0.03824594244360924, -0.008475285023450851, -0.021470721811056137, 0.030978627502918243, 0.05287798494100571, -0.01737920567393303, 0.01494377851486206, 0.030199291184544563, -0.033121805638074875, 0.005679415073245764, -0.030238257721066475, -0.08635049313306808, 0.0188014954328537, 0.007695948705077171, 0.03281006962060928, -0.015440605580806732, 0.00042376425699330866, 0.012936986982822418, -0.023535965010523796, -0.04547428712248802, 0.03627811744809151, -0.0005525374435819685, -0.0061665005050599575, 0.014417726546525955, -0.07056892663240433, -0.010550268925726414, 0.0671008750796318, 0.03382320702075958, -0.03588844835758209, -0.034310292452573776, -0.008543477393686771, -0.05053997412323952, -0.06417836248874664, -0.012225842103362083, -0.02049655094742775, 0.03214763477444649, -0.00014148307673167437, 0.016375809907913208, -0.002839707536622882, 0.0010374918347224593, -0.05954131484031677, 0.021607106551527977, 0.011329605244100094, 0.011125029064714909, -0.046643294394016266, 0.013141563162207603, -0.057008467614650726, 0.008519122377038002, -0.019093746319413185, 0.07193276286125183, -0.07267313450574875, 0.013638390228152275, 0.044539082795381546, -0.004792919848114252, -0.028367850929498672, -0.02158762328326702, 0.05685260146856308, 0.004086646251380444, 0.0065951356664299965, -0.04594188928604126, 0.06756848096847534, 0.042473841458559036, -0.03460254147648811, -0.030978627502918243, 0.019084004685282707, -0.045318420976400375, -0.0025547626428306103, -0.09102650731801987, 0.03807058930397034, -0.054163891822099686, 0.005051075015217066, -0.00045664250501431525, 0.0589568093419075, -0.06148965284228325, -0.018635885789990425, 0.03651191666722298, -0.005825540982186794, 0.012050491757690907, 0.04149967059493065, 0.022113675251603127, 0.009074400179088116, 0.03653139993548393, -0.07890782505273819, -0.018859945237636566, -0.0037651697639375925, 0.044032514095306396, -0.046331558376550674, 0.03888889402151108, -0.03364785760641098, -0.0048854658380150795, -0.018499501049518585, -0.02209419198334217, 0.046877093613147736, 0.026692276820540428, -0.020613452419638634, 0.009741706773638725, -0.026984527707099915, 0.010706136003136635, 0.014865844510495663, 0.0007744657341390848, -0.0199023075401783, 0.023419063538312912, -0.004510410130023956, 0.008392480202019215, 0.05315075442194939, -0.05712537094950676, -0.009658902883529663, 0.01212842483073473, -0.01724282093346119, -0.017018761485815048, 0.04652639105916023, 0.08338901400566101, 0.032303500920534134, -0.008894178085029125, -0.002759338589385152, -0.022152641788125038, -0.034641511738300323, -0.029400471597909927, -0.055215995758771896, 0.03873302787542343, -0.013579939492046833, 0.001352879568003118, -0.0038796348962932825, 0.012050491757690907, 0.009858607314527035, -0.02764696441590786, -0.014125474728643894, -0.044305283576250076, 0.014973003417253494, -0.04122690483927727, -0.05377422273159027, -0.00685329083353281, 0.0343882255256176, -0.04983857274055481, 0.005596610717475414, -0.02484135329723358, -0.026205191388726234, -0.015440605580806732, -0.0008517904789187014, -0.06363283097743988, -0.013492263853549957, -0.07197172939777374, -0.03356992080807686, 0.0013236544327810407, -0.05089067667722702, 0.01180694904178381, -0.03731073811650276, 0.02737419679760933, -0.04262971132993698, 0.012323259375989437, 0.08479181677103043, 0.02375028096139431, 0.00519232964143157, -0.0007726391195319593, 0.07368627190589905, -0.053891122341156006, -0.05447562411427498, 0.021353822201490402, 0.03240091726183891, 0.05003340542316437, 0.0099949911236763, -0.04048653319478035, 0.02104208804666996, 0.015070420689880848, -0.03127088025212288, 0.0033535826951265335, 0.03910321369767189, -0.02378924936056137, 0.001857012859545648, 0.03929804638028145, 0.0153334466740489, -0.02723781205713749, -0.00003582741192076355, 0.0026107775047421455, 0.025971390306949615, 0.05782677233219147, 0.041655540466308594, -0.03314128890633583, -0.06277555972337723, -0.04044756665825844, -0.004795355256646872, -0.018450792878866196, 0.0045250230468809605, -0.03304386883974075, -0.0008109970949590206, -0.022405926138162613, 0.007189380005002022, 0.0271014291793108, -0.005333584733307362, -0.001162307453341782, 0.03053051047027111, -0.027062462642788887, -0.03304386883974075, 0.004076904151588678, 0.020691385492682457, -0.03279058635234833, -0.003480224870145321, -0.0067753572948277, 0.03318025544285774, -0.000523921160493046, -0.015187321230769157, -0.011066579259932041, -0.03177744895219803, 0.034407708793878555, -0.03205021470785141, 0.03598586469888687, -0.025659656152129173, 0.02384769916534424, 0.0016305182361975312, -0.021431755274534225, -0.045863956212997437, 0.01091071218252182, 0.014563851989805698, -0.01573285646736622, 0.03851870819926262, 0.05131931230425835, -0.017067471519112587, -0.010667169466614723, -0.031835898756980896, -0.019736697897315025, 0.02741316333413124, -0.015781564638018608, -0.025503788143396378, 0.0474226288497448, 0.016171233728528023, 0.035927414894104004, -0.013735806569457054, 0.018275441601872444, -0.024198399856686592, -0.031153978779911995, 0.015382155776023865, 0.021665556356310844, 0.02131485566496849, 0.005080300383269787, 0.04987753927707672, 0.03300490230321884, -0.013696840032935143, 0.02145123854279518, 0.021295372396707535, -0.02063293568789959, -0.0017632489325478673, -0.008689602836966515, 0.0006709600565955043, 0.05315075442194939, -0.016025107353925705, -0.012216100469231606, -0.0036774943582713604, -0.01324872113764286, 0.014242375269532204, -0.04111000522971153, -0.0069848038256168365, -0.003940520342439413, -0.0038577159866690636, -0.015693889930844307, 0.026711760088801384, 0.0014028057921677828, 0.07259520143270493, -0.008679861202836037, 0.014359275810420513, -0.025971390306949615, -0.0306668933480978, -0.03978513181209564, -0.02819249965250492, -0.04391561448574066, 0.03916166350245476, 0.026692276820540428, -0.04060343652963638, -0.045591190457344055, -0.030277226120233536, 0.02595190703868866, -0.019366513937711716, -0.006034987512975931, -0.013833223842084408, -0.016950570046901703, 0.01499248668551445, -0.020827770233154297, -0.00029362112400121987, 0.015576989389955997, -0.019278837367892265, -0.026341576129198074, 0.0037115903105586767, -0.004771001171320677, 0.03434925898909569, -0.03279058635234833, 0.0003388287441339344, 0.03588844835758209, 0.01604459062218666, -0.005786573980003595, -0.03618070110678673, -0.00948842242360115, -0.0024780468083918095, 0.013726064935326576, 0.024685485288500786, 0.011816690675914288, -0.045045651495456696, 0.0027958699502050877, 0.0009577315649949014, -0.03415442630648613, -0.01141728088259697, 0.02113950438797474, -0.0074183098040521145, 0.019863341003656387, -0.011056837625801563, 0.026692276820540428, -0.026205191388726234, 0.041694507002830505, -0.00022055832960177213, 0.010374917648732662, 0.03158261254429817, -0.001176311168819666, 0.004870853386819363, 0.04126587137579918, 0.033901140093803406, -0.006892257835716009, 0.023029394447803497, 0.02036016806960106, 0.018635885789990425, 0.03039412572979927, 0.031933315098285675, -0.0024086369667202234, -0.01944444701075554, -0.010199567303061485, 0.023438546806573868, -0.002184577751904726, -0.0030856856610625982, -0.014758686535060406, 0.06807504594326019, 0.014193667098879814, -0.03964874893426895, -0.0271014291793108, -0.037934206426143646, -0.00642952648922801, 0.08245380967855453, -0.016619352623820305, 0.0029200767166912556, 0.022074708715081215, -0.03602483123540878, -0.010170342400670052, 0.022269541397690773, 0.007910266518592834, -0.008465543389320374, 0.010637943632900715, 0.04075930267572403, -0.018499501049518585, -0.028445784002542496, 0.011017871089279652, 0.027939215302467346, 0.0016816621646285057, 0.018908653408288956, 0.011378313414752483, -0.019356772303581238, 0.03653139993548393, 0.03127088025212288, -0.001458820654079318, 0.02632209286093712, 0.009917058050632477, 0.00905491691082716, -0.00464192358776927, 0.08377867937088013, 0.01316104643046856, -0.04126587137579918, -0.05350145325064659, 0.04157760366797447, 0.0015757210785523057, 0.004196240101009607, -0.03731073811650276, 0.0009017167612910271, 0.008572702296078205, -0.006707165390253067, 0.026010356843471527, 0.012050491757690907, 0.01545034721493721, 0.0477733314037323, -0.05381318926811218, 0.005659931804984808, -0.010647686198353767, 0.05537186190485954, 0.0025620688684284687, 0.008787020109593868, -0.05244934931397438, 0.004213288426399231, -0.04874750226736069, 0.0153334466740489, -0.017437655478715897, 0.019746439531445503, -0.041655540466308594, -0.03978513181209564, -0.02567913942039013, -0.0019775666296482086, -0.003767605172470212, -0.015538022853434086, 0.02466600202023983, 0.03380372375249863, -0.006288271863013506, 0.04122690483927727, 0.023087846115231514, 0.003231811337172985, -0.011261412873864174, 0.010852261446416378, -0.005713511258363724, -0.003382807830348611, 0.005055945832282305, 0.009595581330358982, 0.012401193380355835, 0.04356491193175316, 0.06043754890561104, -0.05369628965854645, -0.053618356585502625, 0.006483105942606926, 0.016482967883348465, -0.03785627335309982, -0.032069697976112366, -0.05007237568497658, -0.002618083730340004, 0.014476176351308823, -0.018898911774158478, 0.011095804162323475, -0.011066579259932041, -0.007574177347123623, 0.030413608998060226, 0.015976399183273315, 0.01309285406023264, 0.016853153705596924, 0.016473226249217987, -0.03559619560837746, 0.029497887939214706, -0.007189380005002022, 0.014369017444550991, -0.0024244673550128937, -0.00008797978807706386, -0.014456693083047867, 0.03510911390185356, -0.029049770906567574, -0.013190271332859993, 0.03425184264779091, -0.002649744274094701, 0.020340684801340103, 0.01659986935555935, 0.05841127410531044, 0.05498219281435013, -0.02595190703868866, 0.024373751133680344, -0.005698898807168007, 0.0024025484453886747, 0.009420230984687805, 0.04699399322271347, -0.0053481971845030785, -0.008002812042832375, 0.024139950051903725, -0.02178245596587658, 0.044539082795381546, 0.017408430576324463, 0.02392563223838806, 0.025328438729047775, -0.02150968834757805, -0.005255650728940964, 0.011222446337342262, 0.003850409761071205, -0.01788577437400818, 0.02534792199730873, 0.005085171200335026, 0.022542310878634453, -0.03762247413396835, 0.011943332850933075, 0.002135869348421693, 0.011943332850933075, -0.03021877445280552, -0.03062792681157589, 0.016171233728528023, -0.008236613124608994, 0.002998010255396366, -0.024139950051903725, -0.035284463316202164, 0.003222069703042507, 0.00565019017085433, 0.029322538524866104, -0.06238589063286781, -0.04340904578566551, -0.00008341336797457188, -0.003967310301959515, 0.0034120329655706882, -0.0014308132231235504, -0.0018557951552793384, 0.06125585362315178, -0.03508962690830231, 0.013209754601120949, 0.004551812540739775, 0.002666792366653681, -0.0021456109825521708, 0.07641395181417465, -0.029868073761463165, 0.06332109868526459, -0.00491712661460042, -0.014651527628302574, -0.04465598613023758, -0.008075875230133533, 0.002082289895042777, 0.003850409761071205, 0.006979933008551598, 0.029731689020991325, 0.013979349285364151, -0.009415360167622566, 0.05225451663136482, 0.029556339606642723, -0.013833223842084408, -0.03762247413396835, 0.014271601103246212, -0.007296538446098566, -0.009235138073563576, -0.06176242232322693, -0.04251280799508095, -0.006770486477762461, -0.0001718497951515019, -0.030842244625091553, 0.015206804499030113, -0.009921928867697716, -0.011865398846566677, 0.03886941075325012, 0.0015318833757191896, 0.039492879062891006, 0.042980410158634186, -0.0133851058781147, -0.018635885789990425, -0.02063293568789959, 0.037388671189546585, -0.0010113109601661563, -0.03432977572083473, -0.0030637667514383793, 0.030413608998060226, 0.04286351054906845, -0.0026156483218073845, 0.01499248668551445, -0.010862003080546856, 0.026302609592676163, -0.022113675251603127, -0.03460254147648811, -0.04383768141269684, 0.048201967030763626, 0.00037688229349441826, -0.0004225465527269989, 0.030959144234657288, -0.018996328115463257, 0.004281480330973864, -0.023672347888350487, 0.0153334466740489, 0.01847027614712715, 0.0226981770247221, 0.00019072435679845512, -0.04808506742119789, -0.025016702711582184, -0.016288133338093758, -0.04496771842241287, -0.04570809006690979, 0.012751894071698189, -0.019093746319413185, -0.009201042354106903, -0.03758350387215614, -0.008918533101677895, -0.03144622966647148, -0.012430418282747269, -0.004856240935623646, -0.01416444219648838, -0.00623469240963459, 0.03002394177019596, 0.06394456326961517, 0.027120912447571754, -0.014398243278265, -0.016434259712696075, 0.017593523487448692, 0.01902555301785469, -0.004374026320874691, 0.04029170051217079, -0.03238143399357796, 0.02300991117954254, -0.04079826921224594, 0.0005945485318079591, 0.027530064806342125, 0.02747161313891411, -0.03943442925810814, 0.007715431973338127, 0.035050660371780396, 0.013443555682897568, -0.0027836926747113466, 0.032985419034957886, -0.00994628295302391, 0.01348252221941948, 0.026263641193509102, -0.031056562438607216, -0.05486529320478439, -0.012761636637151241, 0.004157273564487696, 0.0067948405630886555, 0.004785613622516394, -0.011047095991671085, 0.011884882114827633, 0.012498609721660614, 0.013833223842084408, 0.04925407096743584, -0.02425684966146946, -0.014690494164824486, -0.04442218318581581, -0.035459812730550766, 0.006185983773320913, 0.0032878261990845203, -0.041694507002830505, -0.05303385481238365, -0.00377734680660069, 0.03750557079911232, -0.02297094464302063, 0.020321201533079147, 0.007135800551623106, -0.01966850645840168, 0.025796040892601013, -0.014680752530694008, -0.006687681656330824, -0.025016702711582184, 0.037388671189546585, 0.0015331011964008212, -0.029829107224941254, -0.006181112956255674, 0.031426746398210526, -0.01336562167853117, -0.030413608998060226, 0.021256403997540474, 0.027062462642788887, -0.018421567976474762, 0.025776557624340057, -0.05817747488617897, 0.008295063860714436, -0.0487864688038826, 0.005172846373170614, 0.026166224852204323, 0.033589404076337814, 0.04769539833068848, -0.012323259375989437, -0.0003662272938527167, 0.002082289895042777, -0.009293588809669018, 0.03238143399357796, -0.04333111271262169, -0.014836619608104229, -0.006151888053864241, -0.030335675925016403, -0.053384553641080856, -0.0029736561700701714, -0.025250503793358803, 0.012050491757690907, 0.021353822201490402, 0.038401808589696884, 0.017311014235019684, -0.003024799982085824, -0.012498609721660614, -0.024646518751978874, -0.016336843371391296, -0.00024567366926930845, -0.016609610989689827, -0.019230129197239876, -0.06386663019657135, 0.019541863352060318, -0.025873973965644836, -0.04668226093053818, 0.028893902897834778, 0.01326820533722639, -0.01802215725183487, -0.01756429858505726, 0.0023367919493466616, 0.002318526152521372, 0.0004505539545789361, -0.0009674732573330402, 0.021860390901565552, -0.07762192189693451, 0.04535738751292229, -0.005830411799252033, -0.02947840467095375, -0.03238143399357796, 0.03479737788438797, 0.01958083175122738, -0.002462216420099139, 0.01765197329223156, -0.018216991797089577, -0.027159878984093666, 0.013209754601120949, -0.011982299387454987, -0.01984385773539543, 0.025386888533830643, 0.031835898756980896, 0.00831941794604063, 0.0020408877171576023, 0.020593969151377678, -0.059346478432416916, -0.002096902346238494, 0.011670565232634544, 0.024198399856686592, 0.004403251688927412, 0.02334113046526909, 0.026010356843471527, -0.019590573385357857, -0.029536856338381767, 0.019561348482966423, -0.005465097725391388, -0.021626589819788933, -0.01985359936952591, 0.018460534512996674, -0.051514144986867905, -0.010608718730509281, -0.04329214617609978, -0.011719273403286934, 0.029049770906567574, -0.05509909614920616, 0.04882543534040451, -0.0127031859010458, 0.013297430239617825, 0.011047095991671085 ]
Prior research on exposure fairness in the context of recommender systems has focused mostly on disparities in the exposure of individual or groups of items to individual users of the system. The problem of how individual or groups of items may be systemically under or over exposed to groups of users, or even all users, has received relatively less attention. However, such systemic disparities in information exposure can result in observable social harms, such as withholding economic opportunities from historically marginalized groups (allocative harm) or amplifying gendered and racialized stereotypes (representational harm). Previously, Diaz et al. developed the expected exposure metric -- that incorporates existing user browsing models that have previously been developed for information retrieval -- to study fairness of content exposure to individual users. We extend their proposed framework to formalize a family of exposure fairness metrics that model the problem jointly from the perspective of both the consumers and producers. Specifically, we consider group attributes for both types of stakeholders to identify and mitigate fairness concerns that go beyond individual users and items towards more systemic biases in recommendation. Furthermore, we study and discuss the relationships between the different exposure fairness dimensions proposed in this paper, as well as demonstrate how stochastic ranking policies can be optimized towards said fairness goals.
[ -0.046331554651260376, -0.015276644378900528, -0.04093228653073311, 0.008828531950712204, 0.006999894976615906, -0.0030006065499037504, -0.05899064615368843, 0.000014571239262295421, -0.042975250631570816, 0.015915071591734886, -0.04706118255853653, -0.010251312516629696, 0.0009074782719835639, -0.022563831880688667, 0.001069365069270134, 0.03356301411986351, 0.04242802783846855, 0.007519756909459829, 0.02956828661262989, -0.021378181874752045, 0.03327116370201111, -0.025172261521220207, -0.03983784094452858, 0.03826913237571716, -0.004728919360786676, 0.04873933643102646, -0.018277250230312347, -0.02820022962987423, -0.025810688734054565, 0.006096977274864912, 0.034420330077409744, 0.005458550062030554, -0.06132546439766884, -0.023092813789844513, -0.09353866428136826, -0.018559983000159264, 0.015322245657444, 0.023475870490074158, 0.02544587291777134, 0.04578433185815811, -0.02484392747282982, 0.016745025292038918, -0.045711368322372437, 0.007305427920073271, -0.026303188875317574, -0.03294282779097557, -0.002339378697797656, -0.028710970655083656, 0.006480033043771982, -0.006803806871175766, 0.020010123029351234, -0.06424398720264435, -0.03338060900568962, -0.028528563678264618, -0.05917305499315262, 0.04377784579992294, 0.01703687757253647, -0.019882438704371452, 0.04151599109172821, 0.03589783236384392, 0.03907172754406929, -0.01928049325942993, -0.018769752234220505, -0.008983578532934189, 0.02867448888719082, 0.02407781593501568, -0.018623825162649155, 0.015459051355719566, -0.025172261521220207, 0.03188486397266388, -0.057385459542274475, 0.03965543210506439, 0.04126061871647835, 0.029951343312859535, -0.004076811950653791, 0.003664114512503147, 0.0667247325181961, -0.0024032213259488344, -0.012276037596166134, 0.03310699760913849, 0.0007410312537103891, 0.025537077337503433, -0.008030498400330544, 0.04151599109172821, 0.07139436900615692, -0.051694341003894806, 0.02115929126739502, -0.0780704915523529, -0.0013201757101342082, -0.06625047326087952, -0.034237924963235855, -0.009749691002070904, 0.008796610869467258, -0.03910820931196213, -0.02130521833896637, 0.02453383430838585, 0.002245894633233547, 0.0036549940705299377, -0.04049450904130936, 0.0010585346026346087, 0.030863381922245026, -0.017775628715753555, 0.028528563678264618, -0.02787189558148384, 0.003917205147445202, -0.021542347967624664, -0.02790837734937668, 0.007195983547717333, -0.010643488727509975, 0.18255361914634705, -0.00048338036867789924, 0.04549247771501541, -0.06792862713336945, -0.0030644491780549288, -0.032541532069444656, 0.07019048184156418, -0.07537085562944412, -0.0366092249751091, 0.05242396891117096, -0.0005788594135083258, -0.02053910680115223, -0.0003804910520557314, 0.027215227484703064, 0.020885679870843887, 0.0011520185507833958, 0.07062825560569763, -0.030535047873854637, -0.05424804612994194, 0.0502350777387619, 0.030918102711439133, -0.007031816523522139, 0.017009517177939415, -0.025099297985434532, -0.02362179569900036, -0.009868255816400051, -0.013434326276183128, 0.03950950503349304, 0.030735695734620094, -0.0095034409314394, -0.04224562272429466, -0.0013395565329119563, -0.041588954627513885, -0.05625453218817711, 0.0004785351629834622, -0.029951343312859535, -0.0038921241648495197, -0.019882438704371452, 0.020028363913297653, -0.007382951211184263, -0.03199430927634239, -0.006808367092162371, 0.028911618515849113, -0.03137412294745445, 0.0024397028610110283, 0.04946896433830261, 0.0036618344020098448, -0.02115929126739502, -0.020739754661917686, -0.02331170253455639, 0.03294282779097557, 0.024406148120760918, -0.014975671656429768, -0.004966049455106258, 0.08164568245410919, 0.029933102428913116, 0.018787991255521774, 0.013087751343846321, -0.03168421611189842, -0.05001618713140488, 0.042063213884830475, -0.020156050100922585, -0.03186662495136261, -0.08018641918897629, 0.027981339022517204, -0.010205710306763649, 0.051110636442899704, 0.05027155950665474, -0.00009882791346171871, -0.0745682641863823, -0.029148748144507408, -0.051402486860752106, 0.027160504832863808, -0.006525635253638029, -0.012011546641588211, 0.0043960255570709705, 0.04979730024933815, 0.07201455533504486, 0.015805626288056374, 0.001567566068843007, 0.012467565946280956, 0.03551477566361427, 0.029933102428913116, 0.022782720625400543, 0.029367638751864433, 0.011254554614424706, -0.04720710963010788, -0.0290940273553133, -0.10112681984901428, 0.043449513614177704, -0.0428658090531826, 0.008071539923548698, -0.0024716241750866175, 0.0419902503490448, -0.05001618713140488, 0.03726588934659958, 0.013853863812983036, 0.035605981945991516, 0.025628279894590378, -0.052351005375385284, -0.016261644661426544, -0.017985397949814796, -0.04290228709578514, 0.0018696788465604186, 0.011856500059366226, -0.025464113801717758, 0.003208095207810402, 0.0037895196583122015, 0.02329346165060997, -0.006676121614873409, -0.020301975309848785, -0.01817692629992962, -0.028309673070907593, 0.0680745467543602, -0.003794079879298806, 0.04997970536351204, 0.0072552659548819065, 0.0046308753080666065, 0.013124233111739159, -0.043303586542606354, -0.027543561533093452, -0.027051061391830444, 0.005526952911168337, 0.02070327289402485, -0.016653822734951973, 0.04939600080251694, -0.0029185230378061533, -0.029294675216078758, -0.018733270466327667, 0.016434932127594948, -0.013771780766546726, -0.05286175012588501, -0.012139231897890568, 0.0419902503490448, 0.023475870490074158, 0.03834209591150284, 0.005107415374368429, -0.009512561373412609, 0.03051680698990822, 0.013178955763578415, 0.013899466022849083, -0.0056455181911587715, -0.02621198445558548, 0.003550109686329961, 0.012285158038139343, -0.02805430255830288, 0.051110636442899704, 0.031209954991936684, -0.0090793427079916, 0.013142473995685577, -0.0363173708319664, 0.04968785494565964, 0.0037211168091744184, -0.003951406572014093, 0.01423692051321268, -0.02650383673608303, 0.020958643406629562, 0.0769030824303627, -0.021852441132068634, 0.0008396453922614455, 0.0349128320813179, 0.0033563014585524797, -0.02927643433213234, 0.0033813826739788055, -0.02849208191037178, 0.029166989028453827, 0.00987737625837326, 0.018477899953722954, -0.03845154121518135, 0.06300361454486847, 0.0012415123637765646, 0.0022800960578024387, 0.008450035937130451, 0.01917104795575142, -0.012294278480112553, -0.00898813921958208, -0.027780691161751747, 0.03188486397266388, -0.028893377631902695, -0.04002024605870247, 0.022454386577010155, -0.023548832163214684, -0.040676914155483246, -0.04348599165678024, 0.0014581214636564255, 0.06511954218149185, 0.04334006831049919, -0.0031054909341037273, -0.030462084338068962, 0.00247390428557992, -0.05300767347216606, -0.014729420654475689, 0.026759207248687744, -0.0018411775818094611, 0.022563831880688667, -0.036700427532196045, 0.0013452566927298903, -0.04399673640727997, 0.10368052870035172, -0.008340591564774513, -0.021560588851571083, 0.0698256641626358, 0.012923585250973701, 0.013552891090512276, -0.06406158208847046, 0.0090793427079916, 0.02449735254049301, 0.004760840907692909, -0.017520258203148842, 0.025993095710873604, -0.05366434156894684, -0.01109950803220272, -0.019517622888088226, -0.08142679184675217, 0.0181586854159832, -0.07923790067434311, -0.019189288839697838, -0.05213211849331856, 0.05720305070281029, 0.009252630174160004, -0.017337851226329803, -0.06770973652601242, 0.031976066529750824, 0.02300160937011242, -0.04363191872835159, -0.012139231897890568, 0.0029709653463214636, -0.009667607955634594, 0.023165777325630188, 0.0214329045265913, -0.03540533408522606, -0.014209559187293053, 0.021250495687127113, -0.041443027555942535, 0.02070327289402485, 0.03341708704829216, -0.04089580476284027, -0.02592013217508793, 0.023019850254058838, 0.037648946046829224, -0.0037712790071964264, 0.001151448581367731, 0.019973641261458397, -0.027689486742019653, 0.05902712792158127, 0.08638828247785568, -0.008842213079333305, 0.024479111656546593, -0.0011246574576944113, 0.02714226394891739, -0.0003770708863157779, 0.02086743898689747, -0.032687459141016006, -0.005376466549932957, 0.011053905822336674, -0.04658692330121994, 0.012431084178388119, -0.029294675216078758, 0.05592619627714157, 0.00826306827366352, 0.015340486541390419, -0.0845642015337944, 0.029495323076844215, -0.021068088710308075, 0.021268736571073532, -0.016498776152729988, -0.004993410315364599, -0.01503039337694645, -0.0008214046247303486, -0.0618726871907711, 0.04793674126267433, -0.06190916895866394, 0.022892165929079056, 0.011354878544807434, 0.005080054048448801, -0.0581880547106266, 0.0016336889239028096, 0.027215227484703064, 0.04505470022559166, 0.02207132987678051, -0.01832285337150097, -0.007496956270188093, -0.018933918327093124, -0.005403827875852585, -0.033927831798791885, -0.001983683556318283, 0.0032992991618812084, -0.02021077275276184, -0.004297981038689613, 0.036408573389053345, -0.002294916659593582, -0.004051730968058109, -0.05428452789783478, -0.029641250148415565, 0.09667607396841049, 0.02407781593501568, -0.018012760207057, 0.015276644378900528, -0.03310699760913849, 0.0780704915523529, -0.025482354685664177, 0.010670850053429604, 0.0052259801886975765, -0.00686308927834034, 0.024096056818962097, -0.006931492127478123, 0.027032820507884026, -0.09288199245929718, 0.026558559387922287, 0.05260637775063515, -0.04731655493378639, -0.022326700389385223, 0.08303198218345642, 0.08288605511188507, -0.034566257148981094, 0.009767931886017323, 0.0023781403433531523, 0.007825289852917194, -0.0607052780687809, 0.03673690930008888, -0.05552490055561066, 0.02986013889312744, 0.03458449989557266, -0.032121993601322174, -0.05658286437392235, 0.02836439572274685, 0.023202259093523026, -0.0007889132830314338, -0.005321744363754988, 0.003340340917930007, -0.015440811403095722, -0.026284947991371155, 0.0010687950998544693, -0.0004651396011468023, 0.08106197416782379, -0.029604768380522728, -0.032249677926301956, 0.011236313730478287, -0.002861520741134882, -0.022855684161186218, -0.011135989800095558, -0.07150381803512573, -0.02449735254049301, -0.04892174154520035, -0.0357336662709713, 0.07197807729244232, -0.04425210505723953, 0.029385879635810852, -0.06530195474624634, 0.013470808044075966, -0.023877166211605072, -0.015422570519149303, 0.06694362312555313, 0.04235506430268288, 0.008372512646019459, -0.0027269949205219746, 0.027397634461522102, -0.05070933699607849, -0.011263675056397915, 0.004108733031898737, -0.035642463713884354, -0.023785963654518127, 0.018331972882151604, -0.0056318375281989574, -0.03721116855740547, -0.005230540409684181, 0.005016211420297623, 0.01271381601691246, -0.064098060131073, 0.013981549069285393, -0.01685447059571743, 0.03483986854553223, 0.05143896862864494, -0.020575586706399918, -0.008130822330713272, -0.015048634260892868, -0.0009616305469535291, -0.010990063659846783, 0.011254554614424706, -0.058625832200050354, -0.045565441250801086, 0.013388724066317081, 0.030261436477303505, -0.0450911819934845, 0.023202259093523026, -0.008605082519352436, -0.023019850254058838, -0.02159707061946392, -0.04166191816329956, 0.03370894119143486, 0.01884271390736103, -0.021378181874752045, 0.07336436957120895, -0.013279279693961143, -0.002902562264353037, 0.07522492855787277, -0.0015516054118052125, -0.02053910680115223, -0.010251312516629696, -0.02805430255830288, -0.0036914756055921316, 0.030079027637839317, 0.007729525677859783, 0.020739754661917686, -0.02252735011279583, -0.010461080819368362, 0.012750297784805298, 0.04319414123892784, -0.013197196647524834, 0.03595255687832832, 0.012969186529517174, -0.019389936700463295, -0.015413450077176094, 0.0065894778817892075, 0.07208751887083054, -0.04961489140987396, 0.01929873414337635, -0.005704800598323345, 0.0035660704597830772, 0.009238949976861477, 0.02500809356570244, 0.033015791326761246, 0.04779081419110298, -0.012084509246051311, -0.03980135917663574, 0.04180784150958061, -0.004530550912022591, 0.022946886718273163, 0.0022800960578024387, -0.011619369499385357, -0.0542115643620491, -0.022892165929079056, 0.07015399634838104, 0.01993716135621071, 0.012394602410495281, -0.027634765952825546, 0.03294282779097557, 0.014483170583844185, -0.054941195994615555, 0.018879195675253868, 0.004692438058555126, 0.0366092249751091, -0.02863800711929798, -0.013215437531471252, -0.03691931813955307, -0.01693655364215374, -0.015614097937941551, -0.02942235954105854, 0.052168600261211395, -0.006498273927718401, -0.008039618842303753, -0.002834159415215254, -0.01931697502732277, -0.007287187036126852, -0.030133750289678574, -0.01280501950532198, 0.0114187216386199, 0.01393594779074192, 0.08558569103479385, -0.023366425186395645, -0.0246797613799572, -0.017337851226329803, -0.033946070820093155, -0.03137412294745445, -0.01424604095518589, -0.03339884802699089, 0.02528170496225357, 0.01249492634087801, -0.06289417296648026, -0.027835413813591003, -0.005016211420297623, -0.013461687602102757, -0.0019688629545271397, 0.027361152693629265, 0.024169018492102623, -0.000668638211209327, 0.011281915940344334, 0.006247463170439005, -0.034730423241853714, 0.008495638146996498, -0.006922371685504913, 0.008336031809449196, 0.0490676686167717, 0.010461080819368362, 0.040202654898166656, -0.062128059566020966, 0.010670850053429604, -0.004829243756830692, 0.018952159211039543, 0.02177947759628296, -0.0490676686167717, 0.04753544554114342, 0.008536679670214653, 0.011546406894922256, -0.018268130719661713, -0.01855086162686348, 0.020283734425902367, 0.02927643433213234, -0.013698817230761051, 0.0029071224853396416, 0.009749691002070904, -0.017155442386865616, -0.027470597997307777, 0.05665582790970802, -0.028565043583512306, 0.03768542781472206, -0.011847379617393017, 0.06008509173989296, 0.00036453036591410637, -0.01431900355964899, 0.006096977274864912, 0.04458044096827507, -0.004133814480155706, 0.06588565558195114, 0.03797728195786476, 0.018824473023414612, 0.05059989169239998, -0.01263173297047615, -0.019499382004141808, -0.013607613742351532, 0.005312623921781778, -0.031155234202742577, 0.012759418226778507, -0.018021879717707634, -0.0074923960492014885, -0.002836439525708556, -0.011464322917163372, 0.027963098138570786, 0.0567287914454937, 0.038670431822538376, -0.027817172929644585, -0.018231648951768875, 0.033471811562776566, -0.00920246820896864, 0.06260231882333755, -0.003452065633609891, 0.031501807272434235, 0.040093209594488144, -0.027014579623937607, 0.013981549069285393, 0.02511753886938095, -0.02602957747876644, 0.034237924963235855, 0.002236774191260338, 0.028875136747956276, 0.001548185246065259, -0.007259826175868511, 0.0026791130658239126, -0.0040198094211518764, 0.010205710306763649, 0.005563434679061174, -0.001072215149179101, 0.003791799768805504, 0.011646730825304985, -0.006511954590678215, -0.008837652392685413, 0.025062816217541695, -0.009111263789236546, 0.04687877744436264, 0.05045396834611893, 0.008924296125769615, -0.006575797218829393, -0.003718836698681116, -0.03943654149770737, 0.008554920554161072, 0.029312916100025177, -0.0053399852477014065, -0.02300160937011242, 0.0447993278503418, -0.02311105467379093, 0.015486412681639194, -0.027780691161751747, 0.004099613055586815, -0.027342913672327995, 0.0349128320813179, 0.017438175156712532, -0.013689696788787842, 0.023877166211605072, 0.02374948188662529, 0.015440811403095722, 0.0019141406519338489, -0.005335425026714802, -0.05888120085000992, 0.013698817230761051, 0.02115929126739502, 0.012276037596166134, -0.027160504832863808, 0.014410207979381084, 0.031793661415576935, 0.019718270748853683, -0.014574374072253704, 0.0013623574050143361, 0.017319610342383385, 0.0004389185050968081, 0.027069300413131714, -0.003969647455960512, 0.00685396883636713, -0.010141867212951183, -0.005723041482269764, -0.048629891127347946, 0.015896830707788467, -0.01018746942281723, 0.03139236196875572, -0.0450911819934845, 0.06318602710962296, 0.05807860940694809, -0.011765295639634132, 0.03834209591150284, -0.03079041838645935, -0.01088973879814148, 0.008035059086978436, 0.023986611515283585, -0.0076018404215574265, 0.011464322917163372, -0.04647747799754143, -0.004097332712262869, 0.01654437743127346, -0.015003032982349396, -0.007478715386241674, 0.024333186447620392, 0.011756175197660923, 0.022144293412566185, -0.0036595542915165424, -0.00835427176207304, 0.006511954590678215, 0.02528170496225357, 0.0456748865544796, -0.022308461368083954, 0.026576800271868706, 0.03710172325372696, -0.016900071874260902, 0.01886095479130745, -0.029495323076844215, 0.027835413813591003, -0.028291432186961174, 0.0025240664836019278, 0.015386088751256466, 0.044033218175172806, -0.013197196647524834, 0.00398104777559638, -0.0066442000679671764, -0.00002476041845511645, -0.030316157266497612, 0.038378577679395676, -0.00413153413683176, -0.004523710813373327, 0.006808367092162371, -0.01502127293497324, -0.012248676270246506, -0.01633460819721222, -0.017027758061885834, 0.015422570519149303, 0.02128697745501995, 0.02772596850991249, 0.01822252757847309, 0.04155247285962105, 0.009539921768009663, -0.05567082762718201, 0.023804202675819397, -0.003937725909054279, -0.029021063819527626, 0.01824076846241951, -0.04242802783846855, -0.010917100124061108, -0.02728819102048874, 0.0036276329774409533, 0.01948114112019539, 0.024880409240722656, 0.0012711535673588514, -0.021396422758698463, 0.04786377772688866, 0.003632193198427558, -0.011592009104788303, -0.012166593223810196, -0.00605593528598547, -0.02604781836271286, -0.026996338739991188, 0.026321429759263992, 0.008577721193432808, -0.0030826900620013475, 0.030224954709410667, -0.03367245942354202, -0.012221314944326878, -0.01979123428463936, 0.014775022864341736, 0.016863590106368065, -0.012011546641588211, -0.0026038698852062225, 0.0032924588304013014, 0.00045573420356959105, -0.03338060900568962, 0.018085721880197525, -0.03214023634791374, 0.02741587534546852, 0.03679163008928299, -0.03356301411986351, -0.04505470022559166, -0.0031146113760769367, -0.0006144858780317008, 0.00616081990301609, 0.01732872985303402, -0.005727601703256369, 0.07252530008554459, -0.011519045569002628, -0.007191423326730728, -0.011446082964539528, -0.023348184302449226, -0.013516410253942013, 0.026485595852136612, -0.019535863772034645, -0.02515402063727379, -0.005727601703256369, -0.040676914155483246, -0.041005250066518784, -0.0380137637257576, -0.024296704679727554, -0.017730027437210083, -0.01088061835616827, -0.0019563224632292986, 0.03571542724967003, -0.026704486459493637, 0.010789414867758751, 0.010461080819368362, -0.027087541297078133, -0.013142473995685577, 0.005969291552901268, 0.009904737584292889, -0.0006053654942661524, -0.013680576346814632, 0.004295701161026955, 0.053700823336839676, 0.04888525977730751, -0.02066679112613201, 0.003116891486570239, 0.006739964243024588, -0.02039317972958088, 0.030899861827492714, -0.010743812657892704, 0.03536885231733322, 0.026850411668419838, -0.023329943418502808, 0.0167541466653347, 0.03511347994208336, -0.005704800598323345, -0.019408177584409714, -0.007588159758597612, -0.023804202675819397, 0.009722329676151276, -0.004446187522262335, -0.03434736654162407, 0.006315866485238075, 0.00505269318819046, -0.02635791152715683, -0.044981736689805984, -0.00819010566920042, 0.02973245270550251, 0.014528772793710232, 0.009421356953680515, -0.02405957505106926, -0.027361152693629265, -0.04410617798566818, 0.0003015427209902555, 0.07194159179925919, -0.021214013919234276, 0.01393594779074192, 0.04797322303056717, -0.004824683535844088, 0.05158489570021629, 0.009207027964293957, -0.004715238697826862, -0.010816776193678379, 0.019827716052532196, 0.011820018291473389, -0.017730027437210083, -0.01441932749003172, 0.019079843536019325, -0.05220508202910423, -0.018578223884105682, -0.0057139210402965546, -0.00987737625837326, -0.06125250086188316, 0.029823657125234604, -0.015386088751256466, 0.008541240356862545, -0.055853236466646194, 0.024789204820990562, -0.016507895663380623, 0.02495337277650833, 0.05855286866426468, -0.0071640620008111, -0.004792761988937855, 0.011318396776914597, -0.0015276643680408597, -0.006557556334882975, -0.03483986854553223, 0.04658692330121994, 0.018313731998205185, 0.01741081476211548, 0.0023667397908866405, 0.0609971322119236, -0.007861771620810032, 0.02053910680115223, -0.06460880488157272, -0.000342014420311898, -0.026941616088151932, 0.01701863668859005, -0.026284947991371155, 0.01533136609941721, -0.006343227345496416, 0.005317184142768383, -0.04184432327747345, 0.011044785380363464, -0.013215437531471252, -0.0007359010051004589, 0.029477082192897797, -0.0030690093990415335, -0.009375755675137043, 0.029513563960790634, 0.03474866598844528, -0.004026649985462427, -0.024424389004707336, -0.026868652552366257, 0.0025719483382999897, 0.011564647778868675, -0.016361970454454422, -0.017365211620926857, 0.022910406813025475, -0.06986214220523834, -0.005627277307212353, -0.022180775180459023, -0.010169228538870811, 0.026868652552366257, 0.00731454836204648, 0.003985607996582985, 0.02480744570493698, -0.0015162639319896698, -0.00057315913727507, 0.0014159396523609757, 0.008463717065751553, -0.024023093283176422, 0.07008103281259537, -0.07814345508813858, -0.008632443845272064, -0.014610855840146542, 0.00927543081343174, -0.007328229025006294, 0.02529994584619999, -0.02296512760221958, 0.0285103227943182, 0.030845141038298607, 0.002749796025454998, -0.00907022226601839, -0.022600313648581505, -0.030151991173624992, -0.016133960336446762, -0.032723940908908844, -0.0019369416404515505, -0.00635690800845623, -0.045419514179229736, -0.031629495322704315, 0.024716241285204887, -0.03662746399641037, -0.009986820630729198, 0.008413555100560188, -0.0004762550815939903, 0.020119568333029747, 0.0017294528661295772, 0.03511347994208336, -0.018003638833761215, -0.010762053541839123, 0.006530195474624634, 0.02174299582839012, 0.035934314131736755, 0.03834209591150284, 0.01211187057197094, 0.006379709113389254, 0.01569618098437786, -0.004446187522262335, 0.011537286452949047, -0.013981549069285393, -0.010907979682087898, -0.02022901363670826, -0.015978913754224777, -0.012385481968522072, -0.018933918327093124, 0.010698211379349232, 0.00490220682695508, -0.013352243229746819, -0.021688275039196014, -0.018003638833761215, 0.01991892047226429, -0.04476284608244896, 0.002574228448793292, 0.018195167183876038, 0.053080637007951736, 0.002070327289402485, -0.01424604095518589, 0.06034046411514282, -0.011026544496417046, -0.04173487797379494, 0.031337641179561615, 0.027835413813591003, -0.0007638321840204298, -0.0015801065601408482, 0.024314945563673973, -0.0105705251917243, -0.006876769941300154, -0.045601923018693924, 0.004879405722022057, 0.03958246856927872, -0.07168622314929962, 0.041297100484371185, 0.002469344064593315, 0.030151991173624992, -0.030425602570176125 ]
Identification of unknown physical processes and parameters of groundwater contaminant sources is a challenging task due to their ill-posed and non-unique nature. Numerous works have focused on determining nonlinear physical processes through model selection methods. However, identifying corresponding nonlinear systems for different physical phenomena using numerical methods can be computationally prohibitive. With the advent of machine learning (ML) algorithms, more efficient surrogate models based on neural networks (NNs) have been developed in various disciplines. In this work, a theory-guided U-net (TgU-net) framework is proposed for surrogate modeling of three-dimensional (3D) groundwater contaminant problems in order to efficiently elucidate their involved processes and unknown parameters. In TgU-net, the underlying governing equations are embedded into the loss function of U-net as soft constraints. For the considered groundwater contaminant problem, sorption is considered to be a potential process of an uncertain type, and three equilibrium sorption isotherm types (i.e., linear, Freundlich, and Langmuir) are considered. Different from traditional approaches in which one model corresponds to one equation, these three sorption types are modeled through only one TgU-net surrogate. The three mentioned sorption terms are integrated into one equation by assigning indicators. Accurate predictions illustrate the satisfactory generalizability and extrapolability of the constructed TgU-net. Furthermore, based on the constructed TgU-net surrogate, a data assimilation method is employed to identify the physical process and parameters simultaneously. This work shows the possibility of governing equation discovery of physical problems that contain multiple and even uncertain processes by using deep learning and data assimilation methods.
[ 0.015188639052212238, 0.008892904967069626, -0.03553314134478569, -0.06525631994009018, 0.04024652764201164, 0.031897105276584625, -0.01855534128844738, 0.017516473308205605, -0.06794968247413635, 0.020623458549380302, 0.008926572278141975, -0.042324263602495193, 0.03516761586070061, -0.016063982620835304, -0.011052404530346394, 0.05625279247760773, -0.012023938819766045, -0.0293384101241827, -0.00399435218423605, -0.019661543890833855, 0.07341335713863373, -0.03974632918834686, 0.018132099881768227, 0.040477387607097626, 0.032031770795583725, 0.0388806089758873, 0.02391320839524269, -0.014332534745335579, -0.07606824487447739, 0.06040826812386513, 0.07545261830091476, 0.014438345097005367, 0.04574868083000183, 0.040862154215574265, 0.0032584872096776962, -0.02676047757267952, -0.019719259813427925, 0.0575609989464283, -0.020104024559259415, 0.010927354916930199, 0.05883072689175606, -0.045979540795087814, 0.02064269781112671, 0.04236273840069771, 0.008315755985677242, -0.04978872463107109, 0.04024652764201164, -0.04267055168747902, 0.020931271836161613, -0.028318779543042183, -0.009378671646118164, -0.033474646508693695, -0.008753427304327488, 0.016650749370455742, -0.005290532950311899, 0.02687590755522251, 0.08157040178775787, 0.08672626316547394, 0.05956178158521652, 0.03218567743897438, 0.05271294713020325, -0.003580728778615594, 0.003135843202471733, -0.00713260006159544, 0.024201782420277596, -0.06387116014957428, 0.023297583684325218, -0.004304570145905018, 0.02272043377161026, -0.02039260044693947, -0.017006658017635345, 0.038264982402324677, 0.008748617954552174, -0.03143538534641266, -0.013611098751425743, 0.041054535657167435, -0.003171914955601096, -0.008883285336196423, 0.03295521065592766, 0.0011488873278722167, 0.028665069490671158, 0.07375964522361755, 0.04286293685436249, -0.02935764752328396, 0.02720295824110508, 0.011312121525406837, 0.012552991509437561, -0.06675690412521362, 0.010128965601325035, -0.009898106567561626, 0.009926963597536087, 0.030877474695444107, -0.013861196115612984, -0.03468665853142738, 0.010619542561471462, -0.013082045130431652, 0.010273252613842487, 0.007998323999345303, -0.0755680501461029, 0.04848051816225052, 0.0026404568925499916, -0.027972489595413208, -0.027530008926987648, 0.04821118339896202, -0.0071662673726677895, -0.05040435120463371, 0.0006811561179347336, 0.0434400849044323, 0.02789553813636303, 0.18391816318035126, -0.0027751249726861715, 0.006122589576989412, -0.009176669642329216, 0.009744199924170971, -0.013995864428579807, -0.015419499017298222, -0.0636403039097786, -0.07010436803102493, -0.0037538735195994377, -0.03116604872047901, 0.031396906822919846, 0.07352878898382187, 0.012918519787490368, -0.014169009402394295, -0.015063590370118618, 0.046287354081869125, -0.028357256203889847, -0.021104415878653526, 0.036572013050317764, 0.04363246634602547, -0.004357475321739912, -0.0009823557920753956, -0.020238693803548813, -0.02429797500371933, -0.011446789838373661, 0.015121305361390114, 0.04782641679048538, 0.007161457557231188, 0.009013144299387932, -0.031339194625616074, -0.004355070646852255, -0.03824574500322342, -0.04609496891498566, -0.07452917844057083, 0.006839216221123934, 0.04116996377706528, -0.015092447400093079, 0.055752597749233246, 0.0008813546737655997, -0.025067506358027458, -0.03299368545413017, 0.03728382661938667, 0.03768783435225487, 0.02487512305378914, 0.0008332589641213417, -0.018132099881768227, 0.0006114172865636647, -0.0028568878769874573, 0.020296407863497734, -0.02127756178379059, 0.03509066253900528, -0.05263599380850792, 0.02599094621837139, 0.05402114987373352, 0.015448356047272682, 0.023951685056090355, 0.051481693983078, 0.010465635918080807, -0.03728382661938667, 0.029434600844979286, 0.0030540802981704473, -0.024644264951348305, 0.05448286980390549, 0.012995473109185696, -0.06818053871393204, 0.0016833513509482145, 0.0011759412009269, 0.02449035830795765, 0.0014031935716047883, 0.03774554654955864, -0.01817057654261589, -0.023489966988563538, 0.038592033088207245, 0.02397092431783676, 0.008243612013757229, 0.05567564442753792, 0.0702967569231987, -0.023701587691903114, 0.025279128924012184, -0.005579107441008091, 0.006415973417460918, -0.03368626534938812, 0.04128539562225342, -0.02000783383846283, 0.016015885397791862, -0.021796995773911476, -0.02316291444003582, 0.03131995350122452, -0.02997327409684658, 0.02216252312064171, -0.04459438472986221, -0.04532543942332268, 0.02978089079260826, 0.026087136939167976, 0.0172952339053154, 0.009614340960979462, -0.005891730077564716, 0.011716125532984734, -0.002015212085098028, -0.02978089079260826, -0.016487224027514458, 0.007122981362044811, -0.023740064352750778, -0.04394027963280678, -0.02106594108045101, -0.011889270506799221, 0.013755385763943195, -0.026645047590136528, -0.02826106548309326, -0.02277814969420433, -0.030184894800186157, 0.04574868083000183, 0.04309379681944847, -0.02670276165008545, 0.06275533884763718, -0.02460578829050064, 0.05448286980390549, -0.004126615822315216, -0.02108517847955227, -0.008166658692061901, -0.006930598057806492, 0.053290095180273056, 0.04517153277993202, -0.028068682178854942, -0.06837292015552521, 0.0006348639726638794, -0.0018685200484469533, 0.002246071817353368, 0.004708574153482914, -0.018901631236076355, 0.019151728600263596, -0.012774231843650341, -0.03616800531744957, -0.023951685056090355, 0.003097366541624069, -0.027433818206191063, -0.01435177307575941, 0.038842130452394485, 0.0614471361041069, 0.027472294867038727, -0.003373917192220688, -0.010648399591445923, 0.025856276974081993, -0.01315899845212698, -0.034301891922950745, -0.01037906389683485, 0.01760304532945156, -0.035186853259801865, 0.04390180483460426, -0.020469551905989647, 0.03780326247215271, 0.032801304012537, 0.002291762735694647, 0.006021588575094938, -0.004547453485429287, -0.015881218016147614, 0.042901411652565, -0.0011957807000726461, 0.007632796186953783, 0.025798562914133072, 0.004665288142859936, 0.017381805926561356, -0.041939496994018555, -0.04636430740356445, 0.0017867572605609894, -0.0666799545288086, -0.003152676625177264, 0.0038765177596360445, -0.003943851683288813, -0.007344221696257591, 0.01467882376164198, 0.025259889662265778, 0.008666855283081532, 0.016775798052549362, -0.047557082027196884, -0.027049051597714424, 0.00615144707262516, 0.01357262209057808, -0.06691081076860428, -0.04517153277993202, -0.010648399591445923, 0.025548463687300682, -0.04971177130937576, -0.004215592984110117, 0.04671059548854828, 0.04051586240530014, -0.01848800852894783, -0.04998110607266426, 0.021681565791368484, -0.006449640728533268, 0.007969466038048267, -0.010427159257233143, 0.03091595135629177, 0.030704328790307045, 0.02197013981640339, 0.031339194625616074, 0.06964264810085297, 0.0231052003800869, -0.022681957110762596, -0.006194733083248138, 0.06756491214036942, 0.042824458330869675, -0.040669769048690796, -0.020988987758755684, -0.004992339294403791, 0.024182545021176338, 0.005160674452781677, 0.005588726606220007, -0.013659194111824036, -0.0023158106487244368, -0.0013286451576277614, 0.02839573286473751, -0.014871207065880299, 0.004381523001939058, 0.06814206391572952, 0.01590045541524887, -0.02518293634057045, 0.06444831192493439, 0.05290532857179642, -0.009869248606264591, -0.03218567743897438, 0.004299760330468416, -0.021316038444638252, 0.02247033640742302, -0.005487725604325533, -0.050135012716054916, 0.009773056954145432, 0.03509066253900528, -0.008820760995149612, -0.023297583684325218, -0.04355551302433014, -0.03963090106844902, -0.06737253069877625, -0.012235559523105621, 0.03353235870599747, -0.0606006495654583, 0.0035927528515458107, -0.03060813806951046, -0.04305531829595566, 0.049942631274461746, 0.0010406718356534839, 0.011504503898322582, -0.018353339284658432, 0.054559823125600815, -0.021046701818704605, -0.007541414350271225, 0.037591639906167984, -0.004900957457721233, -0.0019286397146061063, 0.009003524668514729, 0.031839389353990555, -0.06456373631954193, -0.010658019222319126, 0.0749908983707428, -0.07545261830091476, -0.009210336953401566, -0.018920868635177612, -0.04601801559329033, 0.059292446821928024, -0.00084828888066113, 0.0357062891125679, 0.058484435081481934, 0.04563325271010399, 0.007084504701197147, 0.016496842727065086, 0.03260892257094383, -0.0025562893133610487, 0.02581780031323433, -0.06240905076265335, 0.04463285952806473, -0.02127756178379059, -0.004715788643807173, 0.03943851962685585, 0.03495599329471588, 0.011831555515527725, 0.02980012819170952, 0.0038813273422420025, -0.003361893119290471, 0.032416537404060364, 0.011052404530346394, 0.003434036858379841, -0.014082436449825764, -0.01486158836632967, -0.031281478703022, 0.02399016171693802, 0.005660870112478733, -0.018757343292236328, -0.009205527603626251, 0.04809575527906418, 0.020854318514466286, -0.024086354300379753, -0.04767251014709473, -0.031012142077088356, 0.00009401216811966151, 0.00039709056727588177, 0.03357083722949028, -0.02776086889207363, -0.040669769048690796, -0.026221804320812225, -0.027376102283596992, 0.03870746120810509, 0.007214363198727369, -0.020931271836161613, -0.033994078636169434, 0.059100061655044556, -0.015679216012358665, -0.043517038226127625, 0.04309379681944847, 0.0023001793306320906, -0.04444047808647156, 0.007406746037304401, 0.06810358911752701, 0.01793009787797928, -0.029896320775151253, -0.0172952339053154, 0.05155864730477333, 0.03451351448893547, -0.007411555852741003, -0.002577932318672538, -0.0012324537383392453, 0.09896182268857956, 0.013457192108035088, 0.02233566716313362, -0.022066332399845123, 0.01862267591059208, -0.009768247604370117, -0.009008334949612617, -0.016939325258135796, -0.04524848610162735, -0.011312121525406837, 0.012860804796218872, -0.01692008599638939, 0.0028328399639576674, 0.017006658017635345, -0.004771098960191011, -0.04336313158273697, -0.03757240250706673, -0.014707681722939014, 0.01028287224471569, -0.021566135808825493, -0.02302824705839157, -0.02479817159473896, -0.02291281707584858, 0.016102459281682968, 0.03628343716263771, -0.013957387767732143, 0.007950227707624435, -0.032974448055028915, 0.03990023583173752, 0.011052404530346394, -0.00013842558837495744, 0.0636403039097786, 0.004934624303132296, -0.032666634768247604, 0.01435177307575941, 0.001646077143959701, -0.03857279568910599, -0.022758910432457924, -0.002224428579211235, 0.022124046459794044, 0.09365205466747284, -0.0035374427679926157, -0.015698453411459923, 0.0015643143560737371, 0.01372652780264616, -0.006670881062746048, -0.044209618121385574, -0.09065087884664536, 0.041439302265644073, -0.018824677914381027, 0.034301891922950745, 0.0003366702876519412, -0.0013743361923843622, 0.004381523001939058, -0.015150162391364574, -0.02095051109790802, 0.047172315418720245, 0.0029121979605406523, 0.05205884575843811, 0.017901239916682243, -0.012764613144099712, -0.0318201519548893, -0.011273644864559174, -0.015102067030966282, 0.03561009466648102, -0.03359007462859154, 0.020219454541802406, -0.028818976134061813, 0.08041609823703766, 0.030935188755393028, 0.017497235909104347, -0.04547934606671333, -0.025798562914133072, -0.036379627883434296, 0.012985853478312492, 0.02183547243475914, 0.03245501592755318, 0.020681174471974373, 0.005050054285675287, -0.02089279517531395, 0.007517366204410791, 0.0016665179282426834, -0.0009979868773370981, -0.044709812849760056, 0.04644126072525978, 0.02972317673265934, 0.008291708305478096, 0.033974841237068176, -0.0037081826012581587, 0.03028108738362789, 0.01696818135678768, -0.0058243959210813046, -0.01811286062002182, 0.04848051816225052, -0.08387899398803711, 0.029453840106725693, -0.02429797500371933, -0.028491925448179245, 0.058599866926670074, -0.00662759505212307, -0.027299148961901665, 0.028818976134061813, -0.02883821353316307, -0.02947307750582695, -0.030069464817643166, -0.03589867055416107, -0.0319548174738884, 0.01060030423104763, -0.016006266698241234, -0.03645658120512962, -0.050635211169719696, 0.04724926874041557, 0.023624634370207787, -0.01970002055168152, 0.013591860421001911, 0.007300935219973326, 0.01029249094426632, -0.006872883066534996, 0.036648962646722794, 0.004109782166779041, -0.04236273840069771, -0.0018637104658409953, 0.011793078854680061, -0.002416811650618911, 0.007676082197576761, 0.02468274161219597, 0.005405962932854891, -0.006319782231003046, -0.004217997658997774, -0.024451881647109985, 0.03636039048433304, 0.045094579458236694, -0.04609496891498566, -0.05186646059155464, -0.007565462030470371, 0.02106594108045101, 0.010927354916930199, 0.02631799690425396, -0.002318215323612094, -0.006161066237837076, 0.0172278992831707, -0.030838998034596443, -0.05825357884168625, 0.04328617826104164, 0.02701057493686676, 0.025837039574980736, 0.025144459679722786, 0.013957387767732143, 0.041939496994018555, 0.010234775952994823, -0.010013535618782043, -0.04501762613654137, 0.034321129322052, 0.0730670690536499, 0.014438345097005367, -0.0215853750705719, -0.044709812849760056, -0.006771882064640522, -0.028511162847280502, -0.04767251014709473, 0.012803089804947376, 0.0019106038380414248, 0.03772630915045738, -0.0027438628021627665, -0.007945418357849121, -0.018728487193584442, -0.0046316212974488735, -0.028126396238803864, 0.01955573260784149, -0.06521784514188766, -0.0009685282711870968, 0.005218389444053173, 0.03970785439014435, 0.008512948639690876, -0.0001143025656347163, 0.020546505227684975, 0.013967006467282772, -0.021181369200348854, 0.01015782356262207, -0.012341370806097984, -0.0329359732568264, 0.004958672448992729, 0.08395595103502274, -0.0448252409696579, 0.03339769318699837, 0.01126402523368597, 0.024259498342871666, 0.01970002055168152, 0.023778541013598442, -0.01919020526111126, 0.0050644828006625175, -0.03185862675309181, 0.05017349123954773, -0.01949801854789257, -0.0029073883779346943, 0.013976626098155975, 0.0025707180611789227, -0.05282837525010109, -0.018584199249744415, -0.010321348905563354, -0.051096927374601364, 0.00924881361424923, -0.03539847582578659, -0.031031379476189613, 0.09080478549003601, 0.0035326331853866577, -0.036379627883434296, 0.016054362058639526, 0.027414578944444656, 0.038207266479730606, -0.022374143823981285, 0.04551782086491585, -0.0572916604578495, 0.007233601529151201, -0.005338628776371479, 0.03337845206260681, -0.01006163191050291, -0.012956996448338032, 0.03176243603229523, 0.032281868159770966, -0.03270511329174042, 0.00985001027584076, 0.04116996377706528, 0.0445559062063694, -0.003412393620237708, -0.010032773949205875, -0.0012685254914686084, 0.015987029299139977, -0.007526985369622707, 0.002171523170545697, -0.007050837390124798, 0.02783782221376896, 0.06302467733621597, -0.006271686404943466, -0.012735755182802677, -0.02424025908112526, 0.02833801880478859, 0.008609140291810036, -0.030646614730358124, 0.027414578944444656, -0.018795819953083992, -0.021873949095606804, -0.004407975822687149, 0.027780108153820038, 0.02006554789841175, -0.03185862675309181, -0.019170967862010002, 0.016641130670905113, 0.021739279851317406, -0.08534110337495804, -0.04636430740356445, -0.028818976134061813, -0.0026332426350563765, 0.0030492707155644894, -0.03857279568910599, -0.008349423296749592, 0.009522959589958191, 0.022239476442337036, -0.026722000911831856, -0.009263242594897747, -0.00011813519813586026, -0.017006658017635345, 0.040669769048690796, -0.03468665853142738, 0.03974632918834686, -0.009239193983376026, -0.02468274161219597, -0.009619150310754776, 0.009946201927959919, -0.02039260044693947, -0.02258576638996601, 0.04147777706384659, 0.001163917244412005, 0.01963268592953682, 0.03526380658149719, 0.004836027976125479, 0.025779323652386665, 0.005896539427340031, -0.009301719255745411, 0.006343829911202192, 0.0005083120195195079, -0.002513003069907427, 0.007551033515483141, 0.026587333530187607, -0.007637605536729097, -0.025471510365605354, 0.033359214663505554, -0.05571412295103073, 0.018132099881768227, 0.01239908579736948, 0.00002791808219626546, -0.003097366541624069, -0.013274428434669971, -0.07695320248603821, -0.013293666765093803, 0.04840356484055519, 0.03497523069381714, -0.000003306583039375255, 0.011648791842162609, 0.002142665907740593, 0.0237977784126997, -0.0280879195779562, -0.0072480300441384315, 0.00643521174788475, -0.015352164395153522, -0.023432251065969467, 0.022451097145676613, 0.01728561334311962, -0.0172952339053154, -0.024528834968805313, -0.0028689117170870304, -0.021989379078149796, 0.04101605713367462, -0.024567311629652977, -0.013139760121703148, -0.0006799537222832441, -0.006305353250354528, 0.036379627883434296, -0.044902194291353226, 0.018920868635177612, 0.07410594075918198, -0.04867290332913399, 0.04167016223073006, -0.033917125314474106, 0.003943851683288813, 0.01414015144109726, -0.01562150102108717, -0.006050445605069399, -0.0004247456381563097, -0.019036298617720604, 0.015063590370118618, 0.034321129322052, -0.03882289305329323, 0.010629161261022091, 0.05875377357006073, 0.013303285464644432, -0.030569661408662796, -0.018449531868100166, 0.013765004463493824, -0.02252805046737194, -0.014082436449825764, 0.03905375301837921, 0.03849584236741066, -0.034936755895614624, 0.03230110928416252, -0.0028929596301168203, 0.05236665531992912, 0.005997540429234505, -0.05482915788888931, 0.01810324192047119, -0.02152765914797783, 0.01007125061005354, -0.016362175345420837, 0.004958672448992729, -0.002173928078263998, 0.038784414529800415, 0.019411446526646614, -0.05255904048681259, -0.027029814198613167, 0.03362854942679405, -0.021316038444638252, 0.00023446680279448628, 0.0014031935716047883, 0.013678432442247868, 0.026914384216070175, 0.021123655140399933, -0.012148987501859665, -0.004850456956773996, -0.005030815955251455, 0.003443656023591757, -0.015188639052212238, 0.025105983018875122, -0.009017953649163246, 0.015025113709270954, -0.02020021714270115, -0.03160852938890457, -0.034494273364543915, -0.018247529864311218, 0.017266375944018364, -0.012697279453277588, 0.02360539510846138, -0.014736538752913475, 0.03774554654955864, -0.019392207264900208, 0.04936548322439194, -0.012245179153978825, -0.007618367206305265, 0.011908508837223053, -0.008113753981888294, -0.02006554789841175, -0.036514297127723694, -0.04682602733373642, -0.007050837390124798, -0.027472294867038727, -0.04671059548854828, 0.00871014129370451, 0.014120913110673428, -0.011744983494281769, 0.035244569182395935, 0.019132491201162338, -0.004109782166779041, -0.005670489277690649, -0.02114289253950119, 0.008258040994405746, -0.013553383760154247, 0.056714512407779694, 0.01476539671421051, 0.047749463468790054, -0.006819977890700102, 0.0019262349233031273, -0.03468665853142738, -0.011735363863408566, 0.008070467039942741, -0.04563325271010399, -0.012485657818615437, 0.03193558007478714, -0.007974276319146156, -0.0017098040552809834, -0.027722392231225967, 0.0500965379178524, 0.01072535291314125, 0.007603938691318035, -0.0010791484965011477, 0.03314759209752083, -0.01423634309321642, -0.014101674780249596, 0.022200999781489372, 0.05117388069629669, 0.0003574115689843893, 0.0018108051735907793, 0.052789900451898575, 0.027472294867038727, 0.05794576555490494, -0.01476539671421051, 0.04798032343387604, -0.0333399772644043, -0.008027181029319763, -0.05748404562473297, 0.046287354081869125, -0.04374789819121361, -0.0011993878288194537, -0.030973665416240692, -0.0028689117170870304, 0.04671059548854828, -0.001670125056989491, -0.030492708086967468, -0.016939325258135796, -0.05055825784802437, -0.021989379078149796, -0.022258715704083443, 0.01542911771684885, 0.02045031450688839, 0.06498698145151138, -0.024278735741972923, 0.01486158836632967, -0.0057137757539749146, 0.014515298418700695, -0.008532186970114708, -0.003563895355910063, -0.04867290332913399, -0.007310554385185242, 0.010869639925658703, -0.05005805939435959, -0.04390180483460426, 0.0159774087369442, 0.008787094615399837, -0.033609312027692795, 0.0008975869859568775, -0.005324199795722961, 0.015217496082186699, -0.013033948838710785, -0.04190102219581604, 0.0037129921838641167, -0.03813031315803528, 0.011408313177525997, -0.018035907298326492, 0.02845344878733158, -0.017641521990299225, 0.011321740224957466, 0.03982328251004219, -0.030954428017139435, -0.012245179153978825, -0.047864895313978195, 0.013322523795068264, -0.020854318514466286, 0.03741849586367607, -0.016987420618534088, 0.018757343292236328, 0.016439128667116165, 0.03210872411727905, 0.02397092431783676, -0.022874340415000916, -0.008219564333558083, 0.01555416639894247, -0.034109510481357574, 0.018459150567650795, 0.02404787763953209, 0.03282054141163826, 0.023124437779188156, 0.016689226031303406, -0.011725745163857937, -0.000031976160244084895, 0.05598345771431923, 0.036129530519247055, 0.05263599380850792, 0.003263296792283654, 0.034109510481357574, -0.0051943412981927395, 0.025913992896676064, -0.008320565335452557, -0.04878833144903183, 0.01501549407839775, -0.03993871435523033, 0.035879433155059814, -0.00817146897315979, -0.007531795185059309, 0.014563394710421562, -0.0020212240051478148, -0.01454415637999773, 0.00711817154660821, 0.038957562297582626, -0.0014981827698647976, 0.023336060345172882, 0.0002451380423735827, -0.03357083722949028, 0.03780326247215271, -0.010119346901774406, 0.009210336953401566, -0.0278185848146677, -0.0015558976447209716, 0.019132491201162338, 0.015919694676995277, -0.04201645031571388, 0.00700755137950182, -0.02000783383846283, 0.05290532857179642, -0.050135012716054916, 0.02291281707584858, -0.042439691722393036, 0.003965494688600302, -0.01401510275900364, -0.035186853259801865, -0.00610335124656558, 0.015381022356450558, 0.05490611121058464, 0.021296799182891846, -0.0007130195735953748, -0.0024564906489104033, -0.005588726606220007, 0.007017170544713736, 0.01565035805106163, -0.01379386242479086, 0.052289701998233795, 0.000057451881730230525, -0.01608322001993656, 0.03384017199277878, -0.030396515503525734, -0.015611881390213966, -0.017304852604866028, -0.006550641730427742, 0.0258755162358284, 0.006877692881971598, 0.02726067416369915, 0.00460757315158844, -0.005805157590657473, 0.06294772028923035, 0.021431468427181244, -0.003446060698479414, 0.0010851604165509343, 0.0592154935002327, -0.014197866432368755, -0.0031983675435185432, 0.010263633914291859, 0.06768034398555756, 0.034609705209732056, -0.009032382629811764, 0.04213188216090202, -0.00451138149946928, 0.014592251740396023, 0.03249349072575569, -0.03780326247215271, -0.04663364216685295, -0.029954034835100174, -0.027279911562800407, -0.04478676617145538, 0.0063774967566132545, -0.016131315380334854, -0.014274819754064083, 0.004114591516554356, -0.049634817987680435, 0.008873666636645794, -0.05844596028327942, 0.019930880516767502, -0.012456799857318401 ]
One of the most promising applications of quantum computing is the processing of graphical data like images. Here, we investigate the possibility of realizing a quantum pattern recognition protocol based on swap test, and use the IBMQ noisy intermediate-scale quantum (NISQ) devices to verify the idea. We find that with a two-qubit protocol, swap test can efficiently detect the similarity between two patterns with good fidelity, though for three or more qubits the noise in the real devices becomes detrimental. To mitigate this noise effect, we resort to destructive swap test, which shows an improved performance for three-qubit states. Due to limited cloud access to larger IBMQ processors, we take a segment-wise approach to apply the destructive swap test on higher dimensional images. In this case, we define an average overlap measure which shows faithfulness to distinguish between two very different or very similar patterns when simulated on real IBMQ processors. As test images, we use binary images with simple patterns, greyscale MNIST numbers and MNIST fashion images, as well as binary images of human blood vessel obtained from magnetic resonance imaging (MRI). We also present an experimental set up for applying destructive swap test using the nitrogen vacancy centre (NVs) in diamond. Our experimental data show high fidelity for single qubit states. Lastly, we propose a protocol inspired from quantum associative memory, which works in an analogous way to supervised learning for performing quantum pattern recognition using destructive swap test.
[ -0.024634817615151405, -0.029664870351552963, -0.02118665538728237, 0.06039618328213692, 0.026874346658587456, 0.013730444945394993, 0.054246366024017334, 0.021097784861922264, -0.01076218020170927, 0.04152015596628189, -0.024066049605607986, -0.018520548939704895, 0.01810285821557045, -0.020422371104359627, -0.021684328094124794, 0.07234033942222595, -0.014708016999065876, 0.0021784305572509766, -0.05229122191667557, -0.032402072101831436, -0.005327768158167601, -0.043688587844371796, -0.09349144250154495, -0.07059848308563232, -0.014725791290402412, 0.027354246005415916, 0.02939826063811779, -0.008291589096188545, -0.09349144250154495, 0.036614518612623215, -0.009038099087774754, 0.022306419909000397, -0.017596298828721046, -0.004181342665106058, -0.016760919243097305, -0.03878295421600342, -0.030144769698381424, 0.014068151824176311, 0.008838141337037086, -0.012548471800982952, 0.062138039618730545, -0.044932771474123, 0.014299214817583561, 0.007122945971786976, 0.011313175782561302, -0.03233097866177559, -0.041342414915561676, -0.04912744462490082, -0.016840901225805283, -0.013828202150762081, 0.00834046769887209, -0.033077485859394073, 0.03206436708569527, -0.007154050748795271, 0.015907764434814453, -0.024883653968572617, -0.008891463279724121, 0.027958562597632408, 0.09185623377561569, 0.0038947362918406725, 0.020493466407060623, -0.005372203420847654, -0.03949391469359398, -0.026270030066370964, 0.000221620051888749, -0.002883837791159749, 0.040382616221904755, -0.05364204943180084, 0.01234406977891922, -0.007198486011475325, -0.0432264618575573, -0.03233097866177559, 0.0046212500892579556, -0.003972497768700123, -0.01635211519896984, 0.004519049543887377, 0.030642442405223846, 0.035334788262844086, -0.0145125025883317, 0.01516125537455082, 0.007722820155322552, 0.04692346230149269, 0.022146452218294144, 0.02820740081369877, 0.06775463372468948, -0.020653434097766876, 0.009340257383883, -0.07649946212768555, 0.021968713030219078, -0.0034126155078411102, -0.08936786651611328, 0.008873688988387585, 0.0176407340914011, -0.0049545131623744965, 0.02129329927265644, 0.00558549165725708, 0.04578592628240585, -0.02035127393901348, 0.011437593959271908, 0.015418979339301586, 0.03140672668814659, -0.016494307667016983, 0.022395288571715355, -0.017249705269932747, 0.018253937363624573, -0.06768354028463364, -0.054388560354709625, 0.020013567060232162, -0.0035770253743976355, 0.10671532899141312, -0.02986038476228714, -0.017694056034088135, -0.030126996338367462, -0.016663162037730217, -0.038747403770685196, -0.021542135626077652, -0.043937426060438156, -0.011286514811217785, -0.050727106630802155, -0.02267967350780964, 0.04653243348002434, 0.06540846079587936, -0.0012086346978321671, 0.0211511068046093, -0.026021193712949753, 0.054033078253269196, 0.0007942773518152535, 0.013081693090498447, -0.012681776657700539, -0.0051366970874369144, -0.012255200184881687, -0.040631454437971115, 0.024670366197824478, -0.07777919620275497, 0.027087636291980743, -0.06153372302651405, -0.0007198485545814037, 0.04329755902290344, -0.011206531897187233, -0.038747403770685196, -0.012050798162817955, -0.08666621148586273, 0.013117240741848946, 0.028527332469820976, 0.0399915874004364, 0.03115789033472538, -0.034179478883743286, 0.018165068700909615, -0.010904372669756413, 0.08737717568874359, -0.0926382914185524, 0.04315536841750145, 0.019107092171907425, -0.026021193712949753, 0.05211348086595535, 0.07230479270219803, 0.06352441757917404, 0.0046923463232815266, 0.009669077582657337, -0.07344233244657516, -0.00022342523152474314, -0.03796534612774849, 0.04727894440293312, 0.05570383742451668, -0.009429127909243107, 0.0011186535703018308, 0.028011886402964592, 0.023372860625386238, -0.010086767375469208, 0.03778760880231857, 0.02728315070271492, 0.04795435816049576, 0.030749088153243065, -0.006696369033306837, -0.015427866019308567, 0.0018951569218188524, 0.0477055199444294, -0.0002035682846326381, 0.01611216552555561, -0.04823874309659004, -0.06594168394804001, 0.019729183986783028, 0.03704109787940979, 0.06629716604948044, 0.019711408764123917, 0.012068572454154491, 0.04194673150777817, -0.027585308998823166, 0.03153114393353462, 0.006798570044338703, 0.0056743621826171875, -0.024883653968572617, 0.05271780118346214, -0.0036947783082723618, 0.04429290443658829, -0.025363553315401077, -0.039920490235090256, -0.013250546529889107, 0.02291073650121689, -0.023586150258779526, -0.02518581412732601, -0.024012727662920952, 0.07600179314613342, -0.014121473766863346, 0.014956854283809662, -0.012975048273801804, -0.035690270364284515, -0.04464838653802872, 0.010531118139624596, -0.028278496116399765, -0.01753409020602703, -0.0039458367973566055, 0.007029632572084665, -0.05794336646795273, -0.01716972142457962, -0.027318697422742844, -0.029220519587397575, -0.03208214044570923, -0.014325875788927078, -0.006954092998057604, -0.020297951996326447, -0.020831173285841942, 0.05442410707473755, -0.030269188806414604, -0.042160019278526306, -0.0033948414493352175, -0.02950490452349186, -0.0012775090290233493, -0.057801175862550735, 0.019586991518735886, 0.028545105829834938, -0.04219556972384453, -0.001440808060579002, 0.023017380386590958, -0.03489043936133385, -0.07507754117250443, -0.017320800572633743, -0.026323352009058, -0.013037257827818394, -0.013561591506004333, 0.02127552404999733, 0.04198228195309639, 0.00508337514474988, -0.0022628572769463062, -0.018173955380916595, 0.014832435175776482, -0.04432845488190651, 0.06220913678407669, 0.066865935921669, 0.03800089657306671, -0.02539910189807415, -0.04219556972384453, -0.03009144775569439, 0.052504509687423706, -0.01541009172797203, -0.03483711555600166, -0.03465937450528145, -0.020084664225578308, -0.036276813596487045, -0.018253937363624573, 0.033575158566236496, 0.04013378173112869, -0.027212053537368774, 0.07514863461256027, -0.0025594616308808327, -0.00717182457447052, 0.003185996552929282, -0.03606352582573891, 0.003654786851257086, -0.044044069945812225, 0.021933164447546005, -0.029913708567619324, -0.06914101541042328, -0.014068151824176311, 0.013259433209896088, -0.017702942714095116, -0.019551442936062813, -0.038747403770685196, -0.01498351525515318, -0.01282396912574768, 0.012566245160996914, -0.012806194834411144, 0.0070962850004434586, -0.023426182568073273, -0.017960665747523308, -0.04976730793714523, -0.036170169711112976, 0.054246366024017334, -0.0782768651843071, -0.008331581018865108, 0.00881592370569706, -0.018502775579690933, -0.02635890059173107, -0.007527305744588375, 0.013010596856474876, -0.025594616308808327, -0.055455002933740616, -0.01458359882235527, 0.007371782790869474, 0.01916041411459446, -0.050727106630802155, -0.02962932363152504, -0.019675862044095993, 0.03800089657306671, -0.03984939679503441, -0.015836669132113457, 0.041555702686309814, 0.03631236031651497, 0.02234196662902832, -0.030855732038617134, 0.062351327389478683, 0.011250967159867287, 0.007656167261302471, -0.0058432151563465595, -0.003819196717813611, -0.007354008499532938, 0.027691952884197235, 0.02646554447710514, 0.0005393309984356165, -0.028722846880555153, 0.005376646760851145, -0.030144769698381424, -0.07856125384569168, 0.02847401052713394, 0.04553708806633949, -0.005558830685913563, 0.0009231391595676541, 0.05364204943180084, -0.0853864848613739, 0.017320800572633743, 0.05346430838108063, -0.025843452662229538, -0.04269324243068695, 0.03871185705065727, 0.06384434551000595, 0.01716083474457264, -0.013508269563317299, 0.05019388720393181, -0.006927431561052799, 0.00947356317192316, 0.008598191663622856, 0.0009459121502004564, 0.008251597173511982, 0.007402887102216482, 0.01181973610073328, -0.0463191457092762, -0.01333941612392664, 0.0057321274653077126, -0.0022050917614251375, 0.010442247614264488, 0.0009320261888206005, -0.013952620327472687, -0.05058491602540016, 0.012859517708420753, -0.02150658704340458, -0.025594616308808327, -0.014041490852832794, -0.04660353064537048, 0.03672116622328758, -0.026554415002465248, 0.0057321274653077126, -0.04809654876589775, -0.004212447442114353, 0.003277088515460491, -0.067790187895298, -0.03778760880231857, -0.03197549656033516, -0.004136907402426004, -0.023141799494624138, 0.005678805522620678, -0.0034170590806752443, 0.06995861977338791, -0.06448421627283096, 0.05630815401673317, -0.09050540626049042, -0.04880751296877861, -0.012806194834411144, -0.04336865618824959, -0.005629926919937134, 0.03409060835838318, -0.060858309268951416, -0.00023967180459294468, -0.018182842060923576, -0.011091000400483608, -0.012281861156225204, 0.03739657998085022, 0.01846722699701786, -0.021382169798016548, -0.07330013811588287, 0.028509559109807014, -0.04311981797218323, 0.01540120504796505, -0.014485841616988182, 0.011144322343170643, 0.05282444506883621, -0.014681356027722359, -0.01064664963632822, -0.031584467738866806, 0.06220913678407669, -0.012548471800982952, -0.021222202107310295, -0.039813846349716187, -0.06395099312067032, -0.0007420661277137697, 0.03229542821645737, -0.007629506289958954, -0.033681802451610565, 0.007354008499532938, -0.0076428367756307125, 0.011677543632686138, -0.028527332469820976, -0.021382169798016548, -0.010842164047062397, 0.012610680423676968, 0.011464254930615425, 0.014281440526247025, -0.042515501379966736, 0.028029659762978554, 0.002037349157035351, 0.013135015033185482, -0.027443116530776024, 0.017951779067516327, 0.01133983675390482, 0.03442831337451935, -0.019729183986783028, 0.04695901274681091, 0.05524171516299248, -0.006332001183182001, 0.020173534750938416, -0.033575158566236496, -0.0018562761833891273, -0.021080009639263153, -0.026554415002465248, -0.016547629609704018, -0.06455530971288681, 0.039565011858940125, 0.043795231729745865, 0.009740173816680908, -0.003363736905157566, -0.04464838653802872, 0.04311981797218323, 0.04212447255849838, -0.030162544921040535, -0.03585023805499077, -0.007984987460076809, 0.00006460446456912905, -0.027318697422742844, -0.004527936223894358, -0.038178637623786926, 0.026856573298573494, -0.07013636082410812, 0.0764283686876297, -0.12129004299640656, -0.007953882217407227, 0.034143928438425064, -0.033895093947649, -0.03864075988531113, -0.04671017453074455, 0.08211605995893478, 0.0038414141163229942, 0.008913680911064148, 0.04372413456439972, -0.014619147405028343, -0.04120022431015968, 0.021559908986091614, 0.017800699919462204, -0.02810075506567955, -0.07507754117250443, -0.008531538769602776, 0.01457471214234829, -0.008851471357047558, -0.015667814761400223, -0.020066890865564346, 0.03800089657306671, 0.018431678414344788, -0.02502584643661976, 0.030375832691788673, 0.0017540755216032267, -0.002752754371613264, -0.022750770673155785, 0.046496886759996414, -0.026607736945152283, -0.04998059943318367, -0.033912867307662964, 0.037929799407720566, 0.02680325135588646, 0.0670081302523613, 0.005452186334878206, -0.04247995465993881, 0.015507848933339119, -0.023603923618793488, -0.05584603175520897, -0.040631454437971115, 0.02433265931904316, -0.00958909373730421, 0.013330529443919659, -0.029718194156885147, -0.03714774176478386, 0.06611942499876022, 0.04795435816049576, 0.04912744462490082, -0.08197386562824249, -0.0204579196870327, 0.0348193421959877, -0.07394000142812729, 0.00482120830565691, 0.031815528869628906, -0.003699221881106496, 0.003474824596196413, -0.03225988149642944, -0.02152436040341854, 0.012068572454154491, -0.010291168466210365, -0.02493697591125965, -0.031211212277412415, -0.010291168466210365, -0.028633976355195045, -0.042515501379966736, 0.01940925046801567, 0.03256203979253769, 0.021080009639263153, -0.0110021298751235, 0.005363316275179386, 0.03465937450528145, -0.028136303648352623, 0.03206436708569527, 0.03693445399403572, -0.03864075988531113, -0.05182909965515137, -0.04105802997946739, -0.021666552871465683, 0.016734257340431213, -0.015196803025901318, -0.060253992676734924, -0.006465306505560875, 0.01082438975572586, -0.01075329352170229, -0.004816764499992132, -0.03220655769109726, -0.023248443379998207, 0.016263246536254883, 0.07145163416862488, 0.019782505929470062, -0.010948807932436466, -0.012708437629044056, 0.02118665538728237, -0.017711829394102097, -0.0345882810652256, -0.023781664669513702, -0.03565472364425659, -0.02774527482688427, -0.01585444249212742, 0.00792722124606371, 0.014876870438456535, 0.0031215655617415905, -0.0206889808177948, 0.037680961191654205, -0.031460050493478775, 0.009042542427778244, 0.021684328094124794, 0.00864262692630291, 0.012983935885131359, -0.023906081914901733, 0.018502775579690933, 0.012877291068434715, -0.03480156883597374, -0.00019801390590146184, 0.07600179314613342, 0.015330108813941479, -0.027603082358837128, -0.0023461731616407633, -0.0018118411535397172, -0.029256068170070648, -0.03019809164106846, 0.011633108370006084, 0.0030726869590580463, 0.013792654499411583, -0.030766861513257027, 0.011242079548537731, -0.0068430048413574696, -0.008153839968144894, -0.02468813955783844, -0.01703641563653946, 0.04258659854531288, 0.007687272038310766, -0.02657218836247921, -0.014103700406849384, -0.041093576699495316, 0.0036458997055888176, 0.008807036094367504, -0.007042963057756424, 0.05890316516160965, -0.020084664225578308, 0.05140252038836479, -0.018067311495542526, 0.0023972734343260527, 0.054246366024017334, 0.0035103727132081985, 0.056379251182079315, -0.028829490765929222, -0.006918544881045818, 0.03069576621055603, 0.027674179524183273, 0.011037678457796574, 0.04407961666584015, 0.008847028017044067, 0.007518418598920107, 0.048843059688806534, 0.022715222090482712, 0.008567086420953274, 0.00225063762627542, -0.020493466407060623, 0.020529014989733696, -0.02269744873046875, 0.025559067726135254, 0.019693635404109955, 0.008069413714110851, -0.0004304650065023452, -0.029327165335416794, -0.015801120549440384, 0.043795231729745865, -0.049340732395648956, 0.019800279289484024, 0.004014710895717144, 0.01358825247734785, 0.02906055375933647, -0.06739915907382965, 0.00458125863224268, 0.002946046879515052, -0.014716904610395432, -0.029718194156885147, -0.028847265988588333, -0.014130361378192902, -0.019782505929470062, -0.02843846194446087, 0.004830094985663891, 0.010655536316335201, 0.0041035814210772514, 0.0035303684417158365, -0.007482870481908321, 0.014032604172825813, -0.004607919603586197, 0.011268740519881248, 0.020653434097766876, -0.005434412509202957, 0.01836058311164379, 0.012850630097091198, 0.014592486433684826, 0.0321887843310833, 0.057552337646484375, 0.02573680877685547, 0.02515026554465294, 0.02518581412732601, 0.027798596769571304, -0.017329687252640724, -0.013534930534660816, 0.03595688194036484, 0.040738098323345184, 0.004901191219687462, 0.02340840920805931, 0.030749088153243065, 0.041449058800935745, -0.005705466493964195, 0.00617203488945961, 0.024670366197824478, 0.04041816666722298, -0.030180318281054497, 0.011553125455975533, 0.020635658875107765, 0.034499410539865494, 0.006069834344089031, -0.05581048130989075, -0.029451582580804825, 0.02445707842707634, 0.02939826063811779, -0.0548151358962059, 0.014761339873075485, 0.0041280207224190235, 0.028385140001773834, -0.012797308154404163, -0.004208003636449575, -0.03728993237018585, 0.0005932085332460701, 0.0010436694137752056, -0.01164199598133564, -0.012317408807575703, 0.0001181695843115449, -0.01726747862994671, -0.02529245801270008, -0.022306419909000397, -0.005972077138721943, -0.04695901274681091, 0.019942471757531166, 0.009775721468031406, 0.0075850710272789, 0.013730444945394993, -0.03140672668814659, 0.005038939882069826, 0.020315727218985558, -0.051082588732242584, -0.06796792894601822, -0.017907343804836273, -0.02609228901565075, 0.003343741176649928, -0.00766949774697423, 0.009153629653155804, 0.013019483536481857, 0.009606868028640747, -0.016858676448464394, 0.008460442535579205, 0.013570479117333889, -0.002903833519667387, 0.029895933344960213, 0.05773007869720459, 0.030518025159835815, 0.011828622780740261, -0.024048274382948875, -0.029807062819600105, 0.015063498169183731, 0.0012275195913389325, 0.0023461731616407633, 0.046248048543930054, 0.010246733203530312, -0.031104568392038345, 0.024314885959029198, 0.0068963272497057915, 0.0036481216084212065, -0.03346851468086243, 0.013241658918559551, 0.012299635447561741, 0.027140958234667778, -0.015285673551261425, 0.027656404301524162, 0.01105545274913311, -0.03199326992034912, 0.014103700406849384, 0.026163386180996895, 0.020955592393875122, 0.02856288105249405, -0.01575668528676033, 0.018396129831671715, -0.008718166500329971, -0.055312808603048325, -0.00403248518705368, -0.0030482476577162743, 0.005190019495785236, 0.005900980904698372, -0.022715222090482712, 0.019569216296076775, 0.011153209954500198, 0.0503360778093338, 0.030837958678603172, 0.04329755902290344, -0.03974275290966034, -0.05012279003858566, -0.02609228901565075, -0.008940341882407665, -0.005963189993053675, 0.0025150266010314226, 0.0049545131623744965, 0.020760077983140945, 0.01857387088239193, -0.010531118139624596, 0.049909502267837524, 0.02808298170566559, -0.022128678858280182, -0.019338155165314674, -0.010895485989749432, 0.00799831748008728, -0.011562012135982513, 0.00236839079298079, 0.055917125195264816, 0.011224305257201195, -0.01076218020170927, 0.012352957390248775, -0.02502584643661976, 0.01621881127357483, 0.012370730750262737, -0.025221360847353935, 0.0341261550784111, 0.006380880251526833, 0.030393606051802635, 0.02388830855488777, 0.012370730750262737, 0.04116467386484146, -0.017960665747523308, -0.010184524580836296, -0.014316988177597523, -0.007771698758006096, -0.02843846194446087, -0.016298793256282806, -0.010842164047062397, 0.0031948834657669067, -0.04265769198536873, 0.06398653984069824, -0.007247364614158869, -0.044008519500494, 0.01164199598133564, -0.024243788793683052, -0.035441432148218155, 0.030375832691788673, -0.04347530007362366, 0.0004190785111859441, 0.03021586686372757, -0.04265769198536873, -0.03375289961695671, -0.026501093059778214, 0.0009964570635929704, -0.0472433939576149, -0.008864802308380604, -0.02186206728219986, -0.05499287694692612, 0.01364157535135746, 0.04365304112434387, 0.03268645703792572, 0.013792654499411583, -0.07785028964281082, 0.011286514811217785, 0.02420824207365513, -0.006914101075381041, 0.010602214373648167, -0.002903833519667387, 0.024190466850996017, -0.037680961191654205, -0.04383078217506409, 0.016307679936289787, 0.012681776657700539, -0.0045323800295591354, -0.01892935112118721, -0.003179331310093403, 0.016849789768457413, -0.0025305787567049265, -0.010611101053655148, 0.015730025246739388, 0.017071964219212532, 0.020155759528279305, -0.020724529400467873, 0.04596366360783577, -0.0020351274870336056, 0.013765993528068066, 0.015712250024080276, -0.006038729567080736, -0.006332001183182001, -0.01610327884554863, -0.002777193672955036, 0.006989640649408102, -0.02634112536907196, 0.04130686819553375, -0.005487734451889992, 0.027212053537368774, 0.038143087178468704, 0.013294980861246586, 0.02353282831609249, 0.010744406841695309, -0.02929161675274372, 0.008118292316794395, -0.0022217549849301577, 0.011544238775968552, -0.03526369482278824, 0.004790103528648615, 0.03128230944275856, 0.02317734621465206, -0.006949649192392826, 0.005745457950979471, 0.030749088153243065, -0.02363947220146656, 0.015347883105278015, 0.002517248271033168, 0.004474614281207323, 0.009144742973148823, -0.010504457168281078, -0.010184524580836296, -0.038178637623786926, 0.03231320157647133, -0.028314044699072838, -0.0006065390771254897, -0.002041792729869485, -0.03442831337451935, 0.028171852231025696, 0.028633976355195045, -0.02102668769657612, -0.0013630465837195516, -0.0024617044255137444, 0.005616596434265375, 0.03503262996673584, -0.0418400876224041, -0.002110667061060667, -0.03636568412184715, 0.0217731986194849, -0.0037614309694617987, -0.03490821272134781, -0.002752754371613264, 0.015072384849190712, 0.0404537133872509, 0.024243788793683052, -0.05058491602540016, -0.013721558265388012, -0.01859164424240589, 0.046745721250772476, -0.027105409651994705, 0.007002971600741148, -0.01985360123217106, -0.027691952884197235, -0.0032393187284469604, -0.005869876593351364, -0.038178637623786926, -0.0067852395586669445, -0.020653434097766876, 0.00009872922964859754, 0.016503194347023964, 0.00892701093107462, 0.012486262246966362, -0.007282912731170654, -0.0037592092994600534, -0.010602214373648167, 0.022786317393183708, -0.037076644599437714, 0.015356769785284996, 0.02870507352054119, -0.04219556972384453, 0.014441406354308128, 0.012077459134161472, -0.035583626478910446, 0.003796979086473584, 0.003988049924373627, -0.04880751296877861, -0.035317014902830124, 0.030126996338367462, -0.015107933431863785, -0.032526493072509766, 0.0015407870523631573, 0.05488623306155205, 0.0432264618575573, -0.007114059291779995, 0.02257302962243557, -0.0035725818015635014, -0.038178637623786926, 0.00834046769887209, -0.011828622780740261, -0.05165135860443115, 0.0138193154707551, -0.00840712059289217, 0.010877711698412895, 0.030642442405223846, -0.005541056860238314, -0.008598191663622856, 0.02797633782029152, 0.013206111267209053, 0.001566337188705802, -0.011855283752083778, -0.037218838930130005, -0.005781006067991257, 0.015081272460520267, -0.013366077095270157, -0.0199957937002182, -0.018893804401159286, -0.012006363831460476, -0.021790971979498863, -0.054850686341524124, 0.018876029178500175, 0.01216632965952158, -0.024723688140511513, -0.03846301883459091, 0.00541219487786293, 0.0019929141271859407, -0.015498962253332138, -0.011357611045241356, -0.050833750516176224, 0.001408592564985156, 0.01030005607753992, -0.033095259219408035, 0.011153209954500198, 0.04461283981800079, 0.02822517417371273, -0.014290327206254005, -0.04247995465993881, -0.014761339873075485, -0.01706307753920555, -0.05346430838108063, 0.014245891943573952, -0.003405950265005231, -0.04948292300105095, -0.0035303684417158365, -0.00012240480282343924, 0.0038214183878153563, 0.003185996552929282, 0.033681802451610565, -0.0013652683701366186, -0.06750579923391342, 0.012655115686357021, 0.037929799407720566, -0.05829884856939316, 0.05741014704108238, 0.02221754938364029, -0.00006359773396980017, -0.01423700526356697, -0.0158633291721344, -0.001655207364819944, 0.0035970211029052734, -0.005701023153960705, 0.0028038546442985535, -0.013419399037957191, -0.020991140976548195, 0.024030501022934914, 0.07070513069629669, 0.001531900023110211, 0.04699455946683884, 0.004772329702973366, -0.03201104328036308, 0.025825679302215576, -0.007953882217407227, -0.01800510101020336, 0.010540004819631577, -0.01575668528676033, 0.012379618361592293, 0.022164227440953255, -0.046283598989248276, 0.0010397812584415078, 0.06544401496648788, 0.005754345096647739, -0.00446350546553731, -0.034161701798439026, 0.006287566386163235, -0.02843846194446087 ]
In social robotics, endowing humanoid robots with the ability to generate bodily expressions of affect can improve human-robot interaction and collaboration, since humans attribute, and perhaps subconsciously anticipate, such traces to perceive an agent as engaging, trustworthy, and socially present. Robotic emotional body language needs to be believable, nuanced and relevant to the context. We implemented a deep learning data-driven framework that learns from a few hand-designed robotic bodily expressions and can generate numerous new ones of similar believability and lifelikeness. The framework uses the Conditional Variational Autoencoder model and a sampling approach based on the geometric properties of the model's latent space to condition the generative process on targeted levels of valence and arousal. The evaluation study found that the anthropomorphism and animacy of the generated expressions are not perceived differently from the hand-designed ones, and the emotional conditioning was adequately differentiable between most levels except the pairs of neutral-positive valence and low-medium arousal. Furthermore, an exploratory analysis of the results reveals a possible impact of the conditioning on the perceived dominance of the robot, as well as on the participants' attention.
[ 0.0009746655123308301, -0.0007753405370749533, -0.022612690925598145, -0.05812632665038109, 0.025711800903081894, 0.03538750857114792, -0.026937030255794525, -0.014306355267763138, -0.07005429267883301, 0.03873887285590172, 0.004842359106987715, -0.025459546595811844, 0.005171189084649086, 0.029837939888238907, 0.008000027388334274, 0.018288351595401764, -0.04836052656173706, -0.005950470920652151, 0.018090153113007545, -0.06281102448701859, -0.023369450122117996, 0.006837861612439156, -0.027153246104717255, -0.004936954006552696, 0.07401826977729797, 0.02318926900625229, 0.04000013694167137, -0.03834247589111328, -0.07899126410484314, 0.06129750981926918, 0.04554970562458038, 0.008801831863820553, -0.008328857831656933, -0.012495538219809532, -0.0034752371720969677, -0.010927965864539146, 0.015018070116639137, 0.0469190813601017, -0.03019830211997032, 0.03214425593614578, 0.017099158838391304, -0.008671200834214687, -0.010324359871447086, -0.06749572604894638, 0.007486512418836355, -0.047964129596948624, 0.009432464838027954, 0.031747858971357346, -0.012189230881631374, -0.010973011143505573, 0.046306464821100235, -0.04922539368271828, 0.03349561244249344, -0.005162179935723543, -0.04994611814618111, 0.06565788388252258, 0.034144263714551926, -0.024522606283426285, 0.07935162633657455, 0.03277488797903061, 0.03572985157370567, 0.04735151305794716, -0.06014434993267059, -0.014306355267763138, -0.04854070767760277, -0.036054179072380066, 0.07733359932899475, -0.012450492940843105, -0.03726138919591904, 0.0006255652406252921, -0.014504554681479931, -0.030252356082201004, -0.045153308659791946, -0.015234286896884441, 0.022846926003694534, 0.029855959117412567, 0.09340573102235794, 0.09837871789932251, 0.016909968107938766, -0.023081161081790924, 0.027405500411987305, 0.07250475138425827, -0.06648671627044678, -0.0067612845450639725, 0.06054075062274933, -0.008274802938103676, 0.03945959731936455, -0.054198384284973145, -0.004900917876511812, 0.003930193837732077, -0.07495521008968353, 0.023531612008810043, -0.002684694016352296, -0.01719825714826584, 0.0009318725788034499, 0.014387437142431736, 0.0046103764325380325, -0.022684762254357338, -0.019279345870018005, -0.005684704519808292, 0.02324332296848297, 0.01696402207016945, -0.0060090296901762486, -0.00555407302454114, -0.014450500719249249, -0.01724330335855484, -0.055423613637685776, -0.00789191946387291, -0.012630674056708813, 0.12223465740680695, -0.05823443457484245, -0.03063073568046093, -0.014180229045450687, -0.0033851468469947577, -0.010828866623342037, 0.032414525747299194, -0.006022543180733919, -0.0672074407339096, 0.015855910256505013, -0.04349564388394356, 0.050847023725509644, 0.026198288425803185, -0.029297398403286934, -0.07646872848272324, 0.02414422668516636, 0.017810871824622154, -0.041225366294384, -0.0038175806403160095, 0.08547776937484741, 0.027928024530410767, -0.043928079307079315, -0.013261307030916214, -0.02104511670768261, 0.04763980209827423, 0.018738802522420883, 0.004560826346278191, -0.013117162510752678, 0.006418941076844931, 0.014396445825695992, 0.028558656573295593, -0.041297439485788345, -0.034558676183223724, -0.020198266953229904, 0.002254512393847108, -0.01863069459795952, -0.02607216127216816, -0.05189207196235657, 0.04472087323665619, 0.0006756780203431845, -0.03848661854863167, -0.015270322561264038, 0.022378455847501755, 0.00555407302454114, 0.042018163949251175, 0.053765952587127686, -0.015927983447909355, -0.01494599785655737, -0.03154965862631798, 0.012828873470425606, -0.07099123299121857, 0.0364505760371685, -0.004639655817300081, 0.014333383180201054, 0.05149567127227783, 0.03848661854863167, -0.000939192424993962, -0.015045097097754478, 0.03733346238732338, -0.045874033123254776, 0.04165780171751976, -0.02414422668516636, 0.007513539399951696, 0.02708117477595806, 0.032216329127550125, -0.03381993621587753, 0.07156781107187271, 0.016810867935419083, -0.034828949719667435, -0.03877490758895874, -0.01771177351474762, -0.0531173013150692, 0.020270340144634247, 0.02565774694085121, 0.03135145828127861, 0.06681104004383087, 0.05297315493226051, 0.08158586919307709, -0.04908125102519989, 0.04093707725405693, -0.03084695339202881, 0.02944154292345047, 0.014927979558706284, 0.05643262714147568, 0.02924334444105625, -0.002049556700512767, -0.027369463816285133, -0.050126299262046814, -0.010351386852562428, -0.05578397586941719, 0.04259474202990532, -0.05787407234311104, -0.04767584055662155, -0.027964061126112938, -0.05455874651670456, -0.027405500411987305, -0.004729745909571648, 0.029855959117412567, 0.011306345462799072, -0.0016982040833681822, -0.03953166678547859, 0.027964061126112938, 0.009306338615715504, -0.008315344341099262, -0.0068333568051457405, -0.026198288425803185, -0.03715328127145767, 0.02872082032263279, -0.01769375428557396, 0.01674780622124672, -0.01870276778936386, -0.024937022477388382, 0.04281095787882805, 0.033873990178108215, -0.0010180214885622263, -0.006612635217607021, -0.026720812544226646, 0.03428840637207031, -0.026216305792331696, -0.022630708292126656, 0.038919053971767426, -0.0026711802929639816, 0.020144212990999222, 0.05978399142622948, -0.06843266636133194, 0.04637853801250458, -0.010612648911774158, 0.024504588916897774, -0.024594679474830627, -0.018756821751594543, -0.006117138080298901, -0.02153160609304905, 0.000876692240126431, 0.024991076439619064, -0.017594655975699425, 0.039819955825805664, 0.011549589224159718, 0.004173437599092722, 0.037657786160707474, -0.008198226802051067, -0.03273885324597359, -0.021621696650981903, 0.02133340761065483, 0.009991025552153587, 0.0035743366461247206, -0.0036621748004108667, 0.016819877550005913, 0.020054122433066368, -0.022846926003694534, 0.01318022608757019, -0.015027078799903393, 0.013009053654968739, 0.08072099834680557, 0.019567634910345078, 0.008581110276281834, -0.010198233649134636, -0.017378438264131546, 0.05989209935069084, 0.046774934977293015, 0.060000207275152206, -0.02801811508834362, 0.027117211371660233, -0.02055862918496132, 0.009792826138436794, -0.016846904531121254, 0.013891940005123615, 0.030342446640133858, 0.0184324961155653, 0.029279381036758423, 0.08000027388334274, 0.018576640635728836, 0.04191005602478981, 0.0001266896288143471, 0.04133347421884537, -0.009846881031990051, -0.008274802938103676, -0.041045185178518295, -0.05243261158466339, -0.03967581316828728, -0.08237866312265396, -0.015927983447909355, -0.014423472806811333, 0.012819863855838776, -0.04097311571240425, 0.009567600674927235, 0.02917127124965191, -0.01985592395067215, -0.049693863838911057, -0.014117165468633175, 0.05837858095765114, -0.020684756338596344, -0.0058018215931952, -0.019333399832248688, 0.04998215287923813, -0.03427038714289665, 0.00760362995788455, -0.023783866316080093, 0.029621724039316177, 0.042955104261636734, -0.010018052533268929, -0.006527049466967583, 0.002907667774707079, 0.018099160864949226, -0.015630684792995453, -0.023873956874012947, 0.0075901164673268795, 0.021891966462135315, 0.06479301303625107, -0.014126175083220005, -0.026919011026620865, 0.00004233545041643083, -0.02942352555692196, 0.04349564388394356, -0.10133368521928787, 0.028324421495199203, 0.03659472241997719, 0.015234286896884441, 0.045153308659791946, -0.05091909319162369, 0.0335136279463768, -0.02126133441925049, -0.033135250210762024, 0.014855907298624516, 0.003819833043962717, 0.021495569497346878, -0.0203604307025671, 0.0013592388713732362, -0.003060821443796158, -0.0008659939630888402, 0.001163292326964438, -0.04998215287923813, 0.005909930448979139, -0.03729742765426636, -0.02443251758813858, -0.04572988674044609, 0.005346865393221378, -0.058522723615169525, -0.03634246811270714, 0.04756773263216019, -0.013459505513310432, -0.03978392109274864, 0.0010084494715556502, -0.030756862834095955, -0.0430632121860981, -0.013810858130455017, 0.013324370607733727, -0.018360422924160957, 0.0014898700173944235, 0.005657677073031664, -0.040288425981998444, 0.030360465869307518, 0.003981995861977339, -0.0017939250683411956, 0.0062387604266405106, 0.002121628960594535, -0.07935162633657455, -0.07906333357095718, -0.049874044954776764, -0.01363968662917614, 0.04911728575825691, 0.0037297424860298634, -0.02798207849264145, 0.010099133476614952, -0.015882937237620354, -0.026216305792331696, 0.044865019619464874, -0.006567590404301882, -0.011387426406145096, -0.0284865852445364, -0.05268486589193344, 0.07704531401395798, -0.051819998770952225, 0.00705407839268446, -0.05455874651670456, 0.0037117244210094213, 0.0013502298388630152, 0.06875699758529663, 0.015477530658245087, -0.0005166121409274638, 0.04962179437279701, 0.06587409973144531, -0.0008935841615311801, -0.04140554741024971, -0.03688301146030426, -0.025315402075648308, 0.02700910158455372, 0.004099113401025534, 0.01893700286746025, 0.01819826103746891, 0.02992803044617176, 0.037189316004514694, -0.04263077676296234, -0.024252336472272873, 0.029099199920892715, -0.02585594542324543, 0.03499111160635948, -0.04958575591444969, -0.025747835636138916, 0.02180187776684761, 0.03801814839243889, 0.01064868550747633, -0.03232443705201149, -0.013549596071243286, -0.009297329001128674, -0.04554970562458038, 0.009261293336749077, -0.03848661854863167, 0.009121652692556381, -0.010864902287721634, 0.02803613245487213, -0.01820727065205574, 0.031693801283836365, 0.01750456541776657, 0.009991025552153587, 0.021477552130818367, -0.016333390027284622, 0.05131549388170242, -0.03614426776766777, 0.00527479313313961, -0.025909999385476112, -0.051567744463682175, 0.01846853271126747, -0.0034009127411991358, 0.03176587447524071, -0.06980204582214355, 0.05268486589193344, -0.00790543295443058, -0.01447752770036459, -0.008689219132065773, -0.050847023725509644, -0.004788304679095745, -0.03693706542253494, 0.0487569235265255, -0.0004591795150190592, -0.03214425593614578, -0.026270361617207527, -0.026937030255794525, 0.04544159770011902, -0.016585642471909523, -0.030000103637576103, -0.005504523403942585, -0.08122550696134567, 0.03895508870482445, -0.03154965862631798, -0.05700920522212982, -0.026504596695303917, -0.035315435379743576, 0.05718938633799553, -0.028324421495199203, -0.040828969329595566, -0.06893717497587204, -0.0006700473604723811, 0.020702773705124855, 0.011675716377794743, 0.009846881031990051, 0.025801891461014748, -0.0017376185860484838, -0.01031535118818283, -0.04443258419632912, -0.01846853271126747, 0.01629735343158245, -0.005157675594091415, 0.00394145492464304, -0.02778388001024723, -0.02538747526705265, 0.020973045378923416, 0.026216305792331696, -0.02679288573563099, -0.0661984235048294, 0.021621696650981903, 0.0242162998765707, 0.029567670077085495, -0.0799282044172287, 0.04980197176337242, -0.019477544352412224, 0.018261324614286423, -0.001870501902885735, 0.03374786302447319, -0.03403615206480026, -0.011342381127178669, -0.024108191952109337, -0.023279359564185143, -0.005540559533983469, -0.00043356005335226655, 0.017387447878718376, 0.01676582358777523, -0.0011599139543250203, 0.016576632857322693, -0.023765847086906433, 0.08843273669481277, 0.005765785463154316, -0.0032860473729670048, -0.04684700816869736, -0.019964033737778664, 0.00887390412390232, -0.0025833421386778355, 0.00803155917674303, -0.012243285775184631, -0.00017103098798543215, 0.01745951920747757, -0.002648657886311412, 0.02827036753296852, -0.010891929268836975, 0.005581100471317768, -0.013864913024008274, -0.04436051473021507, 0.021891966462135315, -0.0018975291168317199, 0.006027047988027334, 0.050666842609643936, -0.0032635247334837914, 0.004358123056590557, 0.0008186965133063495, -0.00007157964137149975, 0.0294055063277483, -0.03657670319080353, 0.04594610258936882, 0.018955020233988762, -0.003310822183266282, -0.01888294890522957, 0.016153208911418915, -0.02318926900625229, 0.02081088349223137, 0.0010591252939775586, -0.036072198301553726, 0.006454977206885815, -0.04760376736521721, 0.039603739976882935, 0.0065720947459340096, -0.0177207812666893, -0.02724333666265011, -0.005351369734853506, 0.0004681885475292802, -0.028360458090901375, -0.0006148669635877013, 0.0007927955011837184, -0.00945048313587904, 0.05664884299039841, 0.006076597608625889, -0.03275686874985695, -0.019225291907787323, 0.02153160609304905, -0.005549568682909012, 0.02825235016644001, 0.015288340859115124, -0.039387524127960205, -0.0025991080328822136, -0.019801869988441467, 0.011576616205275059, -0.0378740057349205, -0.04410826042294502, -0.015261313877999783, -0.015450503677129745, -0.029117217287421227, 0.02106313593685627, 0.014918969944119453, -0.015387440100312233, 0.01673879660665989, 0.07329755276441574, 0.03228839859366417, 0.010720757767558098, -0.044180333614349365, -0.028882982209324837, -0.03445056825876236, 0.007864891551434994, 0.04663079231977463, 0.031063171103596687, 0.07124348729848862, -0.03297308832406998, -0.011369409039616585, 0.03347759321331978, 0.0076621887274086475, 0.007144168950617313, -0.004527042619884014, 0.02682892046868801, 0.015351404435932636, 0.010144178755581379, 0.008234262466430664, -0.036973100155591965, 0.019063128158450127, 0.008405433967709541, 0.015603657811880112, 0.0310811884701252, 0.02942352555692196, -0.004195960238575935, -0.013612659648060799, -0.02702712081372738, 0.010171206668019295, 0.02445053495466709, -0.006576599087566137, -0.054702892899513245, -0.04133347421884537, 0.020720792934298515, 0.03225236386060715, 0.023621702566742897, -0.02634243294596672, -0.011594634503126144, 0.023549631237983704, -0.005824344232678413, 0.03610823303461075, 0.029063163325190544, 0.0017105914885178208, -0.027693789452314377, 0.02324332296848297, -0.014351400546729565, 0.0016925734234973788, -0.033369485288858414, 0.042270414531230927, -0.013459505513310432, 0.0063558779656887054, -0.0033513628877699375, 0.007018042262643576, 0.0031734344083815813, 0.021585660055279732, 0.008216244168579578, -0.018973037600517273, 0.02081088349223137, -0.00031447180663235486, -0.04165780171751976, 0.0031824433244764805, 0.03873887285590172, -0.009693726897239685, 0.01699104905128479, -0.048036202788352966, 0.013711758889257908, 0.0367748998105526, -0.003443705616518855, -0.0378740057349205, 0.04565781354904175, 0.02443251758813858, -0.021495569497346878, -0.0073243496008217335, 0.01891898363828659, -0.029495596885681152, -0.005166684277355671, -0.0181802436709404, 0.019225291907787323, -0.02798207849264145, 0.04165780171751976, 0.02178385853767395, 0.03356768190860748, 0.01915321871638298, 0.036270394921302795, -0.025513602420687675, 0.01628834381699562, 0.007936964742839336, -0.027225319296121597, 0.044648803770542145, 0.0076216477900743484, -0.045405562967061996, -0.027819916605949402, -0.0020000068470835686, -0.012522566132247448, -0.013450496830046177, -0.0378740057349205, 0.022144220769405365, 0.016648706048727036, 0.019297363236546516, 0.014018066227436066, 0.0016328885685652494, 0.020198266953229904, -0.003612625179812312, -0.014441491104662418, -0.029261361807584763, 0.009112644009292126, -0.006175696849822998, 0.0004436952294781804, 0.05023440718650818, 0.013252298347651958, 0.002729739062488079, -0.024000082165002823, -0.03371182829141617, -0.028666766360402107, -0.01054057665169239, 0.006117138080298901, -0.02992803044617176, -0.030288392677903175, 0.0469190813601017, 0.006360382307320833, -0.041081223636865616, -0.03855869174003601, -0.0588110126554966, -0.025765854865312576, -0.01281085517257452, 0.009702736511826515, 0.0037004631012678146, 0.01864871382713318, -0.02632441557943821, -0.004927944857627153, 0.023351432755589485, -0.013666713610291481, -0.031261369585990906, -0.041081223636865616, -0.04118933156132698, 0.023351432755589485, 0.003997761756181717, -0.014882934279739857, 0.012720764614641666, -0.0011289453832432628, -0.014819870702922344, 0.004824340809136629, 0.0125676104798913, 0.05344162508845329, 0.005612631794065237, 0.08418046683073044, 0.028576675802469254, -0.018756821751594543, -0.001727483468130231, 0.005013530608266592, -0.03156767785549164, 0.055892083793878555, 0.03205416351556778, -0.009702736511826515, 0.0023941523395478725, -0.02581990882754326, -0.01936943642795086, 0.020540611818432808, 0.03902716189622879, -0.01601807400584221, 0.007617143448442221, -0.008049577474594116, 0.034360479563474655, 0.00610362458974123, -0.049189358949661255, 0.026882976293563843, 0.022864943370223045, -0.02850460261106491, 0.03545958176255226, 0.01797303557395935, 0.025909999385476112, -0.018099160864949226, 0.026937030255794525, -0.04652268439531326, 0.04756773263216019, -0.013207253068685532, -0.0011255668941885233, -0.011531570926308632, -0.0064279502257704735, 0.02322530560195446, 0.003569832071661949, 0.04518934339284897, 0.055135324597358704, -0.002862622495740652, 0.0593155212700367, -0.024342427030205727, -0.028342440724372864, -0.007873901166021824, 0.04385600611567497, -0.011405444703996181, 0.02634243294596672, -0.0005433577462099493, 0.028648747131228447, 0.05340559035539627, 0.002741000382229686, 0.028901001438498497, 0.06064885854721069, 0.005459478124976158, 0.006319841835647821, -0.0019369436195120215, 0.025495583191514015, -0.03473885729908943, 0.017657717689871788, 0.008013540878891945, 0.06428851187229156, -0.029783885926008224, -0.006153174210339785, 0.0024572156835347414, -0.0003048997023142874, -0.027639735490083694, 0.00040512526175007224, 0.016477534547448158, -0.033639755100011826, -0.03463074937462807, -0.00803155917674303, 0.010486522689461708, -0.004527042619884014, -0.001942574279382825, -0.02753162570297718, -0.013729777187108994, 0.005378396715968847, 0.005648667924106121, -0.0026869461871683598, -0.030216321349143982, -0.007031555753201246, 0.030324429273605347, 0.05455874651670456, -0.03255867213010788, -0.02009015902876854, 0.04904521256685257, -0.03563976287841797, -0.037477605044841766, 0.020882954820990562, -0.01963970810174942, -0.014324373565614223, 0.018846912309527397, -0.03632444888353348, 0.05023440718650818, -0.042955104261636734, -0.009045076556503773, 0.013342387974262238, 0.020774846896529198, -0.013126171194016933, -0.006360382307320833, -0.014522572979331017, -0.015459512360394001, -0.017531592398881912, -0.031946055591106415, -0.007986513897776604, 0.034558676183223724, 0.008148676715791225, -0.04140554741024971, -0.059243448078632355, -0.01965772546827793, 0.011810851283371449, 0.03374786302447319, -0.06807230412960052, -0.018828893080353737, -0.012045086361467838, 0.02007214166224003, -0.003686949610710144, -0.016081135720014572, 0.08173000812530518, 0.01161265280097723, -0.015648702159523964, -0.013675723224878311, -0.021711787208914757, 0.012964008376002312, -0.010594631545245647, -0.0076937200501561165, -0.009198229759931564, 0.07095520198345184, -0.04219834506511688, 0.0008997778641059995, -0.0358559787273407, -0.0077297561801970005, -0.010945983231067657, -0.014351400546729565, 0.03852265700697899, 0.0320001095533371, -0.02944154292345047, -0.022126201540231705, -0.004085599444806576, 0.003241002094000578, 0.013720768503844738, -0.002666675951331854, -0.013603650964796543, -0.04400015249848366, 0.045117273926734924, 0.029261361807584763, 0.020036105066537857, -0.02326134219765663, -0.02776586078107357, -0.019459526985883713, -0.022792872041463852, -0.024486571550369263, 0.027873970568180084, -0.022558636963367462, -0.020306376740336418, -0.02989199571311474, -0.06172994151711464, -0.06147769093513489, -0.039855994284152985, 0.07145970314741135, -0.007319845259189606, 0.020000068470835686, 0.011180218309164047, 0.04277492314577103, -0.0025450538378208876, -0.01745051145553589, -0.0008327731629833579, -0.013864913024008274, -0.016909968107938766, 0.0294055063277483, 0.02682892046868801, -0.017585646361112595, 0.05574794113636017, -0.024360444396734238, -0.017342401668429375, -0.010964001528918743, 0.019459526985883713, -0.015153205022215843, -0.005896416958421469, -0.01507212407886982, -0.020396467298269272, -0.00665317615494132, 0.013081125915050507, -0.01679285056889057, 0.002623882843181491, -0.011090128682553768, -0.0000533504098712001, 0.0002134016394848004, -0.006549572106450796, -0.03545958176255226, 0.003855869174003601, -0.03518931195139885, -0.00010853078129002824, 0.004887404385954142, 0.01629735343158245, -0.045333489775657654, 0.042450595647096634, 0.0030923529993742704, -0.019027093425393105, -0.021711787208914757, 0.020648719742894173, 0.0070630875416100025, 0.014693744480609894, -0.00957660935819149, 0.03043253719806671, -0.0037297424860298634, 0.033369485288858414, -0.009378410875797272, -0.008792823180556297, 0.004198212642222643, -0.034090206027030945, -0.027567662298679352, -0.036486610770225525, 0.0172162763774395, -0.03418029844760895, 0.011288327164947987, -0.01293698139488697, 0.00990994367748499, -0.005085603334009647, 0.019261328503489494, -0.015846900641918182, 0.04627043008804321, 0.024252336472272873, -0.0021621696650981903, -0.015982037410140038, 0.02437846176326275, -0.010891929268836975, -0.007644170429557562, 0.000011956333764828742, -0.007491016760468483, 0.03848661854863167, -0.015252305194735527, 0.007828855887055397, -0.013783831149339676, 0.009954988956451416, 0.0059009213000535965, 0.0023491072934120893, 0.009621654637157917, 0.0055675869807600975, -0.01958565227687359, -0.025297384709119797, 0.026702795177698135, -0.0056756953708827496, 0.01888294890522957, -0.019063128158450127, -0.010495531372725964, -0.017369428649544716, 0.014955006539821625, -0.02942352555692196, 0.01051354967057705, -0.018288351595401764, -0.006360382307320833, -0.06547770649194717, 0.02369377575814724, 0.004015779588371515, 0.014360410161316395, 0.006049570627510548, 0.015189241617918015, -0.009459491819143295, 0.01423428300768137, -0.042738884687423706, 0.02872082032263279, 0.012964008376002312, -0.022432509809732437, -0.034846965223550797, -0.0056711905635893345, -0.05264883115887642, 0.0007804080960340798, 0.009207239374518394, -0.023333413526415825, 0.025297384709119797, 0.027819916605949402, 0.025441529229283333, -0.05243261158466339, 0.015396449714899063, -0.018063126131892204, -0.05679298937320709, 0.005491009913384914, -0.05535154044628143, -0.010270305909216404, 0.005288306623697281, 0.009013544768095016, -0.006072092801332474, -0.03619832172989845, 0.029261361807584763, -0.01888294890522957, 0.03495507687330246, 0.002382891019806266, -0.0373694971203804, -0.06108129024505615, -0.004099113401025534, 0.05816236138343811, 0.012531574815511703, 0.025693781673908234, 0.058774977922439575, -0.015036087483167648, -0.04745962470769882, 0.021423498168587685, -0.012738782912492752, 0.00706759188324213, 0.014747798442840576, -0.018144207075238228, 0.0010366026544943452, -0.00848651584237814, -0.04086500406265259, 0.0051081255078315735, -0.02509918622672558, -0.029729831963777542, 0.06940564513206482, -0.061874087899923325, 0.027910005301237106, -0.045153308659791946 ]
Previous electroencephalogram (EEG) emotion recognition relies on single-task learning, which may lead to overfitting and learned emotion features lacking generalization. In this paper, a graph-based multi-task self-supervised learning model (GMSS) for EEG emotion recognition is proposed. GMSS has the ability to learn more general representations by integrating multiple self-supervised tasks, including spatial and frequency jigsaw puzzle tasks, and contrastive learning tasks. By learning from multiple tasks simultaneously, GMSS can find a representation that captures all of the tasks thereby decreasing the chance of overfitting on the original task, i.e., emotion recognition task. In particular, the spatial jigsaw puzzle task aims to capture the intrinsic spatial relationships of different brain regions. Considering the importance of frequency information in EEG emotional signals, the goal of the frequency jigsaw puzzle task is to explore the crucial frequency bands for EEG emotion recognition. To further regularize the learned features and encourage the network to learn inherent representations, contrastive learning task is adopted in this work by mapping the transformed data into a common feature space. The performance of the proposed GMSS is compared with several popular unsupervised and supervised methods. Experiments on SEED, SEED-IV, and MPED datasets show that the proposed model has remarkable advantages in learning more discriminative and general features for EEG emotional signals.
[ 0.05203908681869507, 0.01260513998568058, -0.029714001342654228, -0.027690844610333443, 0.032124195247888565, 0.02447138912975788, 0.041800156235694885, 0.025438984856009483, -0.015938948839902878, -0.025139909237623215, -0.004890759009867907, -0.053763166069984436, 0.002691676840186119, -0.009148182347416878, 0.008879894390702248, 0.018929701298475266, 0.012807455845177174, 0.0008235563291236758, -0.05196871608495712, -0.0479927733540535, 0.011971804313361645, -0.05330575630068779, 0.02193804644048214, -0.08057437837123871, 0.03147326782345772, 0.00942966528236866, 0.07564843446016312, 0.0025641301181167364, -0.09528183937072754, 0.052250199019908905, -0.002348619978874922, -0.018788959830999374, -0.026248246431350708, -0.050842784345149994, -0.06924470514059067, -0.03122697025537491, 0.034464020282030106, 0.05897059291601181, -0.0007982669048942626, 0.002449777675792575, 0.041905712336301804, 0.039900150150060654, -0.0077803535386919975, -0.03303901478648186, 0.0006470800144597888, -0.06270023435354233, -0.045318689197301865, -0.0539390929043293, 0.015807004645466805, -0.00773197365924716, 0.019017664715647697, 0.01583339273929596, 0.04183534160256386, 0.006790766492486, -0.046339064836502075, 0.018384328112006187, 0.06111689656972885, -0.016062097623944283, 0.04032237455248833, 0.032212160527706146, -0.03968903794884682, 0.03947792574763298, -0.0855003222823143, -0.034569576382637024, 0.017267195507884026, -0.057774290442466736, 0.04285571724176407, -0.02598435804247856, 0.034464020282030106, 0.0011165840551257133, -0.04215200990438461, -0.0038066115230321884, 0.014689870178699493, -0.022659344598650932, 0.03532605990767479, 0.011734304018318653, 0.009658370167016983, 0.021427858620882034, 0.00117211090400815, -0.046444620937108994, 0.015375983901321888, 0.044192761182785034, 0.004347586072981358, 0.021586192771792412, 0.038527924567461014, -0.02506953850388527, 0.011013004928827286, -0.05534650385379791, 0.0007669299957342446, 0.016572285443544388, -0.025720467790961266, 0.04401683434844017, 0.0012886623153463006, 0.06551506370306015, 0.019211184233427048, -0.048837222158908844, 0.059040963649749756, -0.016238024458289146, -0.05320020020008087, -0.002291443757712841, 0.01125930156558752, -0.012411621399223804, -0.04236312210559845, -0.04968166723847389, -0.006896322127431631, -0.018736181780695915, -0.031877897679805756, -0.01651950739324093, 0.04753536358475685, 0.10872263461351395, -0.04563535749912262, 0.04246867820620537, -0.013467180542647839, 0.0008471964974887669, -0.03018900379538536, 0.0008790831780061126, 0.02017877995967865, -0.021234339103102684, 0.044579796493053436, -0.027233436703681946, 0.020952856168150902, 0.06755580753087997, -0.07096878439188004, -0.03838718309998512, -0.048977963626384735, 0.08901885151863098, -0.01929914765059948, 0.0006553265266120434, 0.009922259487211704, 0.04887240752577782, 0.0033601978793740273, 0.051757603883743286, 0.0014338017208501697, 0.00974633265286684, 0.008488457649946213, 0.03543161600828171, -0.034323278814554214, 0.058759480714797974, 0.0062761809676885605, -0.029573259875178337, -0.053235385566949844, 0.03166678547859192, -0.0069139148108661175, -0.01617644913494587, 0.037894587963819504, -0.007221786305308342, 0.025579726323485374, 0.07951881736516953, -0.002566329203546047, 0.023292681202292442, -0.036522358655929565, 0.0759299173951149, -0.0030237382743507624, 0.012948197312653065, 0.003463554661720991, 0.003140289569273591, 0.001864821882918477, -0.028165847063064575, -0.025579726323485374, -0.02438342571258545, 0.10196705162525177, -0.035308465361595154, 0.03230012208223343, 0.041166823357343674, 0.006236597429960966, 0.0005349267739802599, -0.018085254356265068, 0.027761215344071388, -0.05436131730675697, 0.0575631819665432, -0.04957611486315727, 0.03895014524459839, 0.03219456598162651, 0.02795473486185074, -0.020055631175637245, 0.026353802531957626, 0.06421320885419846, -0.039935335516929626, -0.0503150038421154, 0.00816299393773079, -0.0439816489815712, 0.0017537681851536036, 0.0726928636431694, 0.011804673820734024, 0.01563107781112194, -0.0024893612135201693, 0.049470558762550354, -0.006337755359709263, 0.024172313511371613, -0.02482324279844761, 0.01666904427111149, 0.03590661659836769, 0.11857452243566513, -0.035889025777578354, 0.05024463310837746, -0.03386586904525757, -0.03810570016503334, 0.039161257445812225, 0.0024255879689007998, -0.04208163917064667, -0.025579726323485374, -0.007709982804954052, 0.04577609896659851, -0.012833844870328903, 0.01880655251443386, 0.006003494840115309, 0.03186030685901642, 0.006315764505416155, -0.013731070794165134, -0.02619546838104725, -0.007512065581977367, -0.0015569502720609307, -0.046585362404584885, -0.045811284333467484, 0.013317642733454704, -0.025051945820450783, 0.07698547840118408, 0.026951953768730164, 0.02550935558974743, 0.008418086916208267, 0.015516725368797779, 0.049365002661943436, 0.037894587963819504, -0.029379740357398987, 0.013159308582544327, 0.011408839374780655, 0.006606043316423893, -0.0006162928184494376, -0.014065330848097801, 0.006900720298290253, 0.0035383235663175583, 0.02399638667702675, 0.037542734295129776, -0.04918907582759857, -0.0026872786693274975, -0.014804222621023655, 0.027726029977202415, -0.00670720124617219, -0.0031688776798546314, -0.014012552797794342, -0.025861209258437157, -0.03944274038076401, -0.04855573922395706, -0.023767681792378426, 0.036522358655929565, 0.02267693728208542, 0.010335687547922134, 0.043805722147226334, 0.053763166069984436, 0.00948244333267212, -0.024119535461068153, -0.02740936353802681, -0.06294653564691544, 0.001670203055255115, -0.005695623345673084, 0.0050666858442127705, 0.03567791357636452, -0.044931650161743164, 0.04299645870923996, -0.06678173691034317, 0.06579654663801193, 0.0010978918289765716, -0.05608539655804634, 0.012930604629218578, 0.011444024741649628, 0.03708532452583313, 0.04651499167084694, -0.004728027153760195, 0.05130019411444664, -0.0491538904607296, 0.0004675798991229385, -0.045705728232860565, -0.03708532452583313, -0.013431995175778866, 0.011426432058215141, -0.046198323369026184, 0.062172457575798035, -0.026740841567516327, 0.04327794164419174, -0.0055328914895653725, 0.023433422669768333, 0.009297720156610012, 0.029872335493564606, 0.005084278527647257, 0.0012996577424928546, -0.008250957354903221, -0.013502365909516811, 0.010652354918420315, -0.059920597821474075, 0.0024035971146076918, 0.010731521993875504, -0.08127808570861816, 0.0007015072624199092, 0.024858426302671432, 0.04704276844859123, 0.020213965326547623, -0.02271212264895439, -0.02922140620648861, 0.0050666858442127705, -0.05868910998106003, -0.01299217902123928, 0.011690322309732437, -0.010133371688425541, 0.02135748788714409, -0.07033544778823853, -0.01209495309740305, 0.010186149738729, 0.06094096973538399, -0.046092767268419266, -0.05499465391039848, 0.002096825046464801, 0.01759265922009945, -0.052003901451826096, -0.006258588284254074, -0.019475072622299194, -0.0057396050542593, 0.03831681236624718, 0.03771866112947464, -0.011400043033063412, -0.007965076714754105, -0.03340845927596092, -0.0006300371023826301, -0.055240947753190994, 0.04141312092542648, 0.011787081137299538, 0.038914963603019714, 0.0020352506544440985, -0.0037186483386904, -0.029256591573357582, -0.004477331880480051, -0.004145270213484764, -0.013291253708302975, -0.007727575488388538, 0.05094834044575691, 0.01861303299665451, 0.009719944559037685, -0.00993985217064619, 0.03430568426847458, -0.046198323369026184, -0.007995863445103168, -0.0031688776798546314, 0.0006437813863158226, -0.06400209665298462, -0.03687421232461929, -0.007819936610758305, 0.04232793673872948, -0.006416922435164452, -0.006337755359709263, -0.0015184663934633136, -0.0463038794696331, 0.000966496707405895, -0.03106863610446453, -0.017671825364232063, 0.011628747917711735, -0.0057264105416834354, -0.05749281123280525, 0.019580628722906113, 0.00847966130822897, -0.011866248212754726, 0.034903835505247116, -0.0032942253164947033, -0.05006870627403259, -0.03018900379538536, -0.0004664803564082831, -0.08170031011104584, -0.030505670234560966, -0.025298243388533592, -0.04401683434844017, 0.005779188591986895, -0.014531536027789116, -0.03270475193858147, 0.047711290419101715, 0.003949551843106747, -0.00031501855119131505, 0.005123862065374851, 0.010168557055294514, 0.036170508712530136, 0.011857451871037483, -0.033883459866046906, 0.052355751395225525, -0.018243586644530296, 0.005634048953652382, -0.04447424039244652, 0.01748710311949253, 0.006135439965873957, 0.04686684533953667, 0.017328768968582153, -0.012455602176487446, 0.0012721691746264696, 0.04806314408779144, -0.007261369843035936, -0.055029839277267456, -0.07867436856031418, -0.04563535749912262, 0.03972422331571579, 0.01573663391172886, 0.012640325352549553, 0.029696408659219742, 0.02345101535320282, 0.023855645209550858, -0.018190808594226837, -0.0044729337096214294, -0.03613532334566116, -0.005554881878197193, -0.049365002661943436, -0.023046383634209633, -0.05006870627403259, -0.02056581899523735, 0.03944274038076401, 0.005290992092341185, 0.044685352593660355, -0.0199852604418993, -0.007507667411118746, -0.01812043972313404, 0.011919026263058186, 0.029256591573357582, -0.03303901478648186, 0.0651983916759491, 0.02672324888408184, 0.00974633265286684, -0.03474550321698189, 0.022501010447740555, 0.0743817612528801, 0.030892709270119667, 0.03140289708971977, 0.00417825672775507, -0.015314409509301186, 0.00479839788749814, -0.04158904775977135, -0.04964648559689522, -0.005911133252084255, -0.046972401440143585, 0.020847300067543983, 0.0007251474307850003, -0.016739415004849434, -0.012816252186894417, 0.026987139135599136, 0.03439364954829216, -0.06199653074145317, -0.06709840148687363, -0.008901885710656643, -0.00805743783712387, -0.021814897656440735, -0.03384827449917793, -0.01987970434129238, -0.0002654017589520663, 0.0023948007728904486, -0.025738060474395752, 0.003419573185965419, -0.03268716111779213, -0.0679076611995697, -0.011232912540435791, -0.07402990758419037, -0.03465753793716431, 0.023169532418251038, 0.004701638128608465, 0.0157806146889925, -0.021515822038054466, 0.02174452692270279, -0.03592421114444733, 0.022448232397437096, 0.009878277778625488, 0.012473194859921932, -0.028711220249533653, -0.016484322026371956, 0.028060290962457657, -0.004925944376736879, 0.007687991950660944, -0.0009098703158088028, 0.025720467790961266, -0.042679790407419205, -0.042046453803777695, 0.022888049483299255, 0.03933718428015709, 0.017856549471616745, 0.017619047313928604, -0.03203623369336128, -0.06189097464084625, 0.0267760269343853, 0.0317547507584095, 0.014082923531532288, -0.030206594616174698, 0.0022463626228272915, 0.01783895678818226, -0.004165062215179205, -0.002992951078340411, 0.03666310012340546, -0.03873903676867485, 0.017944512888789177, -0.03367234766483307, 0.010538002476096153, 0.008857904002070427, 0.014452368952333927, 0.007740770000964403, 0.02853529341518879, -0.007441694848239422, -0.004991916939616203, 0.010687540285289288, 0.11153745651245117, 0.02149822935461998, 0.0491538904607296, -0.006711599417030811, 0.011224116198718548, 0.02320471778512001, 0.018771367147564888, 0.013300050050020218, 0.0029907519929111004, -0.007679195608943701, -0.0032568410970270634, 0.0066324323415756226, 0.02798992022871971, 0.03323253244161606, 0.02051304094493389, -0.03347883000969887, -0.022852864116430283, 0.03054085560142994, -0.013660700060427189, -0.006346551701426506, 0.0039627463556826115, 0.03442883491516113, -0.014804222621023655, 0.013370420783758163, 0.006962294690310955, 0.052003901451826096, -0.048731666058301926, 0.0066324323415756226, 0.033302903175354004, 0.018700996413826942, 0.013176901265978813, -0.0069139148108661175, -0.0759299173951149, 0.0022848465014249086, -0.003843995975330472, 0.0024431804195046425, 0.0068303500302135944, -0.015226446092128754, 0.0006564260693266988, 0.006773173809051514, 0.013150512240827084, -0.04637425020337105, -0.011936618946492672, -0.0007015072624199092, -0.007481278385967016, 0.005502104293555021, 0.011584766209125519, -0.01563107781112194, 0.003195266705006361, -0.06963174790143967, 0.03599458187818527, 0.028887145221233368, 0.012455602176487446, -0.018489884212613106, -0.013009771704673767, 0.0011402241652831435, -0.01841951347887516, -0.049963150173425674, 0.009491239674389362, -0.008712764829397202, -0.011241708882153034, 0.011065782979130745, 0.026301024481654167, 0.00036944582825526595, -0.0036240876652300358, 0.027321400120854378, 0.025878801941871643, -0.009667166508734226, -0.005414140876382589, 0.07072249054908752, 0.0004060055944137275, -0.013185697607696056, -0.03548439219594002, -0.02163897082209587, -0.033443644642829895, 0.0042508263140916824, -0.03379549831151962, 0.03573068976402283, 0.03743717819452286, -0.025227872654795647, 0.013431995175778866, 0.018982479348778725, 0.047464992851018906, 0.02339823730289936, 0.021480636671185493, 0.06709840148687363, 0.013739867135882378, -0.011030597612261772, -0.01397736743092537, -0.05590946972370148, 0.014575517736375332, -0.022166749462485313, 0.03335568308830261, 0.03321494162082672, 0.005752799566835165, -0.00962318480014801, -0.012174120172858238, -0.024594537913799286, -0.008897487074136734, -0.02443620376288891, 0.0611872673034668, -0.04014644771814346, 0.0207593385130167, 0.037789031863212585, 0.007762760855257511, 0.046092767268419266, -0.025245465338230133, -0.011206523515284061, 0.04574091359972954, 0.007212990429252386, 0.031737156212329865, -0.005018305964767933, 0.04260941967368126, 0.02427786961197853, 0.04486127942800522, -0.02105841226875782, 0.033989015966653824, 0.022149156779050827, 0.03286308795213699, -0.02364453300833702, -0.014716259203851223, -0.046726103872060776, 0.04943537339568138, -0.004662054590880871, 0.005889142397791147, -0.005946318618953228, 0.02667047083377838, 0.007683593779802322, 0.03486865013837814, -0.03909088671207428, 0.006227801088243723, -0.020090816542506218, -0.04187052696943283, 0.0547131709754467, -0.03534365072846413, -0.007498871069401503, 0.007283360697329044, 0.012781066820025444, -0.00084884581156075, 0.0022298695985227823, -0.008325725793838501, 0.04095571115612984, -0.05900577828288078, 0.015789411962032318, -0.03870385140180588, 0.0055328914895653725, -0.006953498348593712, -0.007116230670362711, -0.020196372643113136, 0.00517664011567831, 0.02031952142715454, 0.008778736926615238, 0.007859520614147186, 0.030892709270119667, 0.01861303299665451, 0.023732496425509453, -0.05295390263199806, -0.011039393953979015, 0.027338992804288864, -0.016924137249588966, 0.0093768872320652, 0.005462520755827427, -0.007644010242074728, 0.0030413309577852488, 0.011602358892560005, -0.04830944165587425, 0.03736680746078491, -0.008514846675097942, -0.029678815975785255, 0.04250386357307434, 0.0040067280642688274, 0.04925944656133652, -0.003518531797453761, -0.04486127942800522, -0.04373535141348839, 0.020636189728975296, 0.021867675706744194, -0.05232056975364685, 0.004991916939616203, 0.008765541948378086, -0.0020088618621230125, -0.03062881901860237, -0.02999548427760601, -0.041905712336301804, 0.007287758868187666, -0.03370753303170204, 0.014645888470113277, -0.007419703993946314, 0.020372299477458, 0.01598293147981167, -0.01360792201012373, -0.0070986379869282246, 0.016915341839194298, -0.016589878126978874, -0.003329410683363676, 0.011435228399932384, 0.008145401254296303, 0.053235385566949844, -0.042574234306812286, 0.022835271432995796, 0.012270879931747913, 0.01979174092411995, -0.03877422213554382, 0.012666714377701283, -0.022043602541089058, 0.025421392172574997, 0.03536124527454376, 0.033056605607271194, 0.01651071012020111, 0.02155100740492344, -0.023327866569161415, -0.018595440313220024, 0.017108861356973648, 0.006667617708444595, -0.0012886623153463006, 0.04440386965870857, 0.04880203679203987, 0.0022980410140007734, 0.005132658407092094, -0.04560017213225365, -0.013731070794165134, 0.04588165506720543, 0.0109954122453928, 0.026424173265695572, -0.023380644619464874, -0.05133537948131561, -0.01861303299665451, 0.030892709270119667, 0.03307420015335083, 0.009412072598934174, -0.0026850795838981867, -0.005295390263199806, 0.03743717819452286, 0.01847229152917862, -0.05232056975364685, 0.01973896287381649, 0.029203813523054123, -0.02999548427760601, -0.010494020767509937, 0.022536195814609528, -0.003182072192430496, -0.05288353189826012, 0.017707010731101036, -0.016440339386463165, -0.012913011945784092, 0.020988041535019875, -0.00847966130822897, 0.027286214753985405, 0.0023398236371576786, 0.04187052696943283, -0.03624087944626808, 0.010177353397011757, 0.019967667758464813, -0.0051106675527989864, 0.06009652465581894, -0.035150133073329926, -0.030224187299609184, 0.012930604629218578, 0.0035911016166210175, -0.05003352090716362, -0.009561610408127308, -0.01541116926819086, 0.025104723870754242, -0.022923234850168228, -0.008972256444394588, 0.019826926290988922, 0.03178993612527847, 0.07677436619997025, -0.0375075489282608, 0.008550032041966915, -0.013704681769013405, -0.012921808287501335, 0.02818343974649906, 0.00011139726848341525, 0.06435395032167435, -0.018006086349487305, 0.04845018312335014, 0.005229417700320482, 0.02320471778512001, -0.018138030543923378, -0.02848251536488533, 0.048344627022743225, -0.0027224640361964703, 0.013801440596580505, 0.011743100360035896, 0.05985022708773613, -0.030013076961040497, -0.010608373209834099, -0.02047785557806492, -0.04021681845188141, -0.033003829419612885, -0.00721738813444972, 0.0018076456617563963, -0.008347717113792896, -0.03474550321698189, 0.04605758190155029, 0.03122697025537491, 0.0009142684866674244, -0.030664004385471344, 0.03683902695775032, -0.03166678547859192, -0.0074460930190980434, 0.008664384484291077, -0.011470413766801357, 0.0074021113105118275, 0.016299597918987274, -0.02790195681154728, -0.033742718398571014, -0.021762119606137276, 0.044579796493053436, 0.005229417700320482, 0.0012941600289195776, -0.012596343643963337, 0.016484322026371956, 0.019263962283730507, -0.009693555533885956, 0.035889025777578354, -0.009148182347416878, -0.030171411111950874, -0.010757911019027233, -0.029238998889923096, -0.04415757581591606, -0.013106530532240868, -0.03516772389411926, -0.02550935558974743, -0.012209305539727211, -0.0594983734190464, -0.025280650705099106, 0.023855645209550858, 0.0031798731070011854, 0.041307564824819565, -0.022641751915216446, 0.022254712879657745, 0.007881511002779007, -0.021515822038054466, 0.029731594026088715, -0.07082804292440414, 0.0363464318215847, 0.021410265937447548, 0.005321779288351536, 0.017962105572223663, 0.022659344598650932, -0.01131207961589098, 0.005097473040223122, -0.042679790407419205, -0.01671302691102028, -0.01563107781112194, -0.056015025824308395, -0.015516725368797779, 0.004732425324618816, 0.04989277943968773, -0.01492737140506506, -0.004908351693302393, 0.017284788191318512, 0.03404179587960243, 0.0071426196955144405, 0.006847942713648081, -0.005647243466228247, 0.022852864116430283, 0.022835271432995796, 0.017029693350195885, 0.001602031523361802, 0.02740936353802681, -0.010977819561958313, -0.00429920619353652, -0.004776407033205032, 0.023468608036637306, -0.014751444570720196, 0.013651903718709946, -0.022307490929961205, -0.005884744226932526, -0.046479806303977966, -0.019088035449385643, 0.004868768155574799, -0.0032788317184895277, 0.026881583034992218, -0.0025311438366770744, 0.06410764902830124, -0.02755010314285755, -0.023239903151988983, -0.02202600985765457, -0.01243800949305296, 0.01282504852861166, -0.008061835542321205, 0.04510757699608803, -0.03219456598162651, 0.029133442789316177, 0.0301362257450819, -0.016158856451511383, -0.061679862439632416, -0.010362076573073864, 0.010230131447315216, -0.04563535749912262, -0.017029693350195885, -0.011663933284580708, -0.005225019529461861, 0.0483798123896122, 0.011751895770430565, 0.004666452761739492, -0.03898533061146736, 0.029397333040833473, 0.019527850672602654, -0.01905285008251667, -0.06910396367311478, -0.007586834020912647, -0.016941729933023453, -0.0063201626762747765, -0.028324181213974953, 0.028271403163671494, -0.023679718375205994, 0.011303283274173737, 0.00032738837762735784, 0.0032678365241736174, 0.011303283274173737, 0.004675249103456736, -0.030224187299609184, 0.013326439075171947, -0.011074578389525414, 0.039301998913288116, -0.012684307061135769, 0.03895014524459839, 0.029326962307095528, 0.014206072315573692, 0.027004731819033623, -0.012385232374072075, 0.03523809462785721, -0.018841737881302834, 0.000584406137932092, -0.03856310993432999, -0.0007498870836570859, 0.02202600985765457, 0.004692841786891222, -0.040814969688653946, 0.028060290962457657, 0.0487668514251709, 0.023046383634209633, 0.07480398565530777, -0.0571761429309845, -0.007472482044249773, 0.03729643672704697, -0.03599458187818527, 0.03166678547859192, 0.023363051936030388, 0.002671885071322322, -0.027004731819033623, 0.02941492572426796, -0.004371775779873133, -0.011452821083366871, -0.01167272962629795, -0.011954211629927158, 0.02130470983684063, -0.010889856144785881, -0.02755010314285755, -0.048837222158908844, -0.026019543409347534, 0.016677841544151306, -0.042820531874895096, -0.022113973274827003, -0.02559731900691986, -0.00942966528236866, -0.005880346056073904, 0.03631124645471573, -0.01987970434129238, 0.009544017724692822, -0.04208163917064667, 0.004244228824973106, -0.04264460504055023, 0.038668666034936905, -0.009420868940651417, -0.0022848465014249086, -0.03273993730545044, 0.01783015951514244, 0.03743717819452286, -0.03807051479816437, -0.0038066115230321884, 0.018243586644530296, -0.027286214753985405, -0.04968166723847389, -0.014294035732746124, 0.008092623203992844, -0.02927418425679207, 0.013678292743861675, -0.0029313769191503525, -0.004679647274315357, 0.0466909185051918, -0.015173668041825294, -0.006887525785714388, -0.04327794164419174, 0.00816299393773079, -0.001900007133372128, -0.05527613312005997, 0.03697976842522621, 0.00576599407941103, -0.022747308015823364, 0.013229679316282272, -0.01856025494635105, -0.05995578318834305, 0.009843092411756516, -0.0020880287047475576, -0.002904987893998623, 0.029643630608916283, 0.0327223464846611, 0.015173668041825294, -0.07297434657812119, 0.008813922293484211, 0.006161828991025686, -0.018454698845744133, 0.00479839788749814, 0.028517700731754303, 0.03177234157919884, -0.023486200720071793, 0.023926015943288803, 0.03312697634100914, -0.052109457552433014, 0.00026114104548469186, -0.000644880929030478, -0.011329672299325466, -0.01506811287254095, -0.02842973731458187, 0.02623065374791622, 0.032370492815971375, 0.002206779085099697, -0.0009192164288833737, -0.029520481824874878, -0.017372751608490944, -0.045318689197301865 ]
Machine Learning (ML) decision-making algorithms are now widely used in predictive decision-making, for example, to determine who to admit and give a loan. Their wide usage and consequential effects on individuals led the ML community to question and raise concerns on how the algorithms differently affect different people and communities. In this paper, we study fairness issues that arise when decision-makers use models (proxy models) that deviate from the models that depict the physical and social environment in which the decisions are situated (intended models). We also highlight the effect of obstacles on individual access and utilization of the models. To this end, we formulate an Equity Framework that considers equal access to the model, equal outcomes from the model, and equal utilization of the model, and consequentially achieves equity and higher social welfare than current fairness notions that aim for equality. We show how the three main aspects of the framework are connected and provide an equity scoring algorithm and questions to guide decision-makers towards equitable decision-making. We show how failure to consider access, outcome, and utilization would exacerbate proxy gaps leading to an infinite inequity loop that reinforces structural inequities through inaccurate and incomplete ground truth curation. We, therefore, recommend a more critical look at the model design and its effect on equity and a shift towards equity achieving predictive decision-making models.
[ -0.027514100074768066, -0.003624917706474662, -0.03003901056945324, -0.011686994694173336, -0.022519974038004875, 0.02925925888121128, -0.019419532269239426, 0.0038500246591866016, -0.06494218856096268, 0.0208490788936615, -0.022334320470690727, -0.050089769065380096, -0.005021973047405481, 0.002569003729149699, -0.05521385371685028, 0.004142431542277336, 0.022668499499559402, 0.013357890769839287, 0.03395633399486542, -0.049569934606552124, -0.06720717996358871, -0.04975559189915657, 0.0002625280467327684, 0.005458262749016285, 0.004901296924799681, 0.023578209802508354, -0.00554644875228405, -0.017070995643734932, -0.06668734550476074, 0.04990411549806595, 0.08243090659379959, 0.01574356108903885, -0.03603567183017731, -0.03746521845459938, -0.04229225218296051, -0.008595835417509079, 0.01912248507142067, -0.021498871967196465, -0.014267601072788239, 0.05231763422489166, -0.03345506638288498, -0.02584320306777954, 0.013218649663031101, 0.00033069829805754125, 0.010257449001073837, -0.023893823847174644, -0.054879676550626755, 0.024710705503821373, -0.0011295957956463099, 0.033789243549108505, 0.006697510834783316, -0.034141991287469864, 0.016068456694483757, -0.03596141189336777, -0.024395091459155083, 0.03828210011124611, 0.052169110625982285, -0.007013124879449606, 0.02630734071135521, 0.010749435983598232, -0.02630734071135521, -0.01001609768718481, -0.026678651571273804, -0.017052428796887398, -0.015734277665615082, -0.04496568813920021, -0.0306331068277359, 0.03263818100094795, 0.023708168417215347, -0.0028822969179600477, -0.03564579784870148, 0.01570642925798893, -0.008902166038751602, -0.006544345524162054, -0.026957133784890175, 0.020329244434833527, 0.042069464921951294, 0.005657841917127371, 0.0017323950305581093, -0.019382402300834656, -0.0011568638728931546, 0.04440872371196747, -0.01936383731663227, 0.04793617129325867, 0.06898947060108185, -0.016560442745685577, 0.01539081521332264, -0.07519035041332245, -0.017665091902017593, -0.03596141189336777, -0.06616751104593277, 0.022557105869054794, -0.0346432588994503, -0.003977662418037653, -0.016773946583271027, -0.0736679807305336, -0.007630428299307823, -0.014852415770292282, -0.06635316461324692, 0.005704255774617195, -0.011195007711648941, 0.0035506554413586855, 0.0061219800263643265, 0.031951259821653366, 0.006966711021959782, -0.05525098368525505, -0.05866704136133194, 0.004646021407097578, 0.010888677090406418, 0.16501033306121826, -0.002299803774803877, 0.04154963046312332, -0.010953656397759914, -0.027124224230647087, -0.0376880057156086, 0.04979272186756134, -0.06824684888124466, -0.09416431188583374, 0.050795260816812515, 0.02560185082256794, -0.01810138113796711, 0.052057716995477676, 0.03596141189336777, 0.017897160723805428, -0.005063745193183422, 0.03070736862719059, -0.0395074263215065, -0.016291243955492973, -0.008243090473115444, 0.0395074263215065, 0.03746521845459938, 0.020477768033742905, -0.02599172666668892, -0.017934290692210197, 0.04247790947556496, 0.026715781539678574, 0.06850676238536835, 0.03594284504652023, 0.025416195392608643, -0.02968626469373703, 0.0032234382815659046, -0.03235970064997673, -0.07567305862903595, -0.006005945615470409, 0.02324403077363968, -0.002307926071807742, 0.02690143696963787, 0.04002726078033447, -0.031635645776987076, -0.02034780941903591, -0.05369148030877113, 0.05435984209179878, 0.020477768033742905, 0.02120182290673256, 0.09527824819087982, -0.046747978776693344, -0.012986580841243267, 0.027272747829556465, -0.016643987968564034, 0.028052499517798424, 0.032341133803129196, -0.04648806154727936, 0.008219883777201176, 0.048790182918310165, 0.05881556496024132, 0.017767202109098434, -0.008363766595721245, -0.0012357673840597272, -0.06999200582504272, 0.0621202290058136, -0.04374036192893982, -0.004952352028340101, -0.062380146235227585, -0.0034624694380909204, -0.03909898176789284, 0.04314626753330231, 0.01669040136039257, 0.000008099751539702993, -0.04793617129325867, -0.002282398520037532, -0.05280033499002457, 0.021146126091480255, -0.016773946583271027, -0.010860828682780266, 0.023968085646629333, 0.030187534168362617, 0.05870417132973671, 0.029240692034363747, 0.021981574594974518, 0.01718238741159439, 0.01743302308022976, -0.00039335692417807877, 0.0261959470808506, -0.009370945394039154, 0.017312346026301384, -0.07983173429965973, -0.011816953308880329, -0.05807294324040413, -0.013469284400343895, -0.02658582292497158, 0.012689532712101936, -0.03165420889854431, 0.03776226565241814, 0.016783230006694794, 0.004123866092413664, -0.02725418284535408, 0.05060960352420807, -0.0018867208855226636, -0.017897160723805428, -0.05072099715471268, -0.028757989406585693, -0.041326846927404404, 0.006660379935055971, -0.02081194706261158, -0.040584225207567215, -0.026437299326062202, 0.01211400143802166, -0.0049987658858299255, -0.01739589124917984, 0.005527883302420378, 0.003720065811648965, 0.018574802204966545, 0.036889687180519104, 0.005003407597541809, 0.01644904911518097, -0.004933786578476429, 0.036611203104257584, 0.02940778248012066, -0.011269270442426205, -0.04318339750170708, -0.0013703673612326384, 0.013460000976920128, 0.009886139072477818, 0.040584225207567215, 0.009027483873069286, -0.011872649192810059, -0.026530126109719276, -0.01947522908449173, 0.020979037508368492, -0.0023496984504163265, -0.028108196333050728, -0.013617807999253273, 0.007997097447514534, -0.02823815494775772, 0.03869054093956947, -0.02250140905380249, -0.031320031732320786, 0.04173528775572777, -0.05064673721790314, 0.02823815494775772, -0.01947522908449173, -0.007351945620030165, -0.018259188160300255, 0.01262455340474844, 0.018992526456713676, 0.02344825118780136, 0.04006439074873924, -0.026363037526607513, 0.0007774311234243214, -0.09297612309455872, 0.08584696054458618, 0.00013750087236985564, -0.010573063045740128, 0.024023782461881638, 0.005732104182243347, -0.0421808585524559, 0.030967285856604576, -0.011668428778648376, -0.008609759621322155, 0.03559010103344917, 0.015892084687948227, -0.01932670548558235, -0.014416125603020191, -0.011547752656042576, 0.03943316265940666, -0.01849125698208809, -0.008201317861676216, -0.014973090961575508, 0.02634447254240513, 0.02799680270254612, 0.028999341651797295, -0.03183986619114876, 0.0554366409778595, -0.0001417796447640285, 0.0004684892774093896, -0.05643917992711067, -0.0064375936053693295, -0.04032430797815323, -0.07797518372535706, -0.005207628011703491, -0.02799680270254612, -0.01831488497555256, -0.0328795351088047, -0.027384141460061073, 0.0750046968460083, 0.003982303664088249, -0.044705770909786224, -0.014286166988313198, 0.014072663150727749, 0.000540140550583601, 0.00011915292270714417, -0.008688663132488728, 0.052094846963882446, 0.007208062801510096, -0.0017904122360050678, 0.026400167495012283, -0.03468038886785507, 0.03533018380403519, -0.04912436380982399, -0.0013657259987667203, 0.04893871024250984, 0.0008017983636818826, -0.011529187671840191, -0.042069464921951294, 0.035200223326683044, 0.07392789423465729, 0.007398359477519989, -0.01072158757597208, -0.03839349374175072, -0.02116469107568264, 0.013422870077192783, -0.0018565519712865353, -0.13768188655376434, 0.007625787053257227, -0.027866844087839127, -0.024562181904911995, -0.020941905677318573, 0.04778764769434929, -0.05302312225103378, -0.004499817732721567, -0.0634569451212883, 0.03113437630236149, -0.01070302166044712, -0.028201023116707802, -0.010972222313284874, -0.037483781576156616, -0.030094707384705544, 0.02109042927622795, 0.0072637596167624, -0.011009353213012218, -0.023708168417215347, -0.04893871024250984, -0.06687299907207489, -0.016142718493938446, -0.0029565589502453804, -0.0711059421300888, -0.01382202934473753, -0.014731739647686481, -0.002536514075472951, -0.0030029728077352047, 0.0011748492252081633, -0.0003260569355916232, -0.0020248019136488438, 0.024005215615034103, 0.03770656883716583, -0.011529187671840191, -0.011046484112739563, -0.002534193452447653, -0.005416490137577057, 0.012262525036931038, 0.06561054289340973, -0.02701283060014248, -0.036184195429086685, -0.001706867478787899, -0.05729319155216217, -0.0012601346243172884, -0.04719354957342148, 0.03126433491706848, 0.03362215682864189, -0.017832180485129356, -0.06594472378492355, 0.024747837334871292, 0.024729272350668907, -0.003752555465325713, 0.006038435269147158, 0.010155338793992996, -0.015260856598615646, -0.013849877752363682, -0.03559010103344917, 0.0368339903652668, -0.049421411007642746, 0.044631507247686386, 0.02151743695139885, 0.04693363234400749, -0.030447451397776604, -0.03187699615955353, 0.02123895473778248, 0.002703603822737932, 0.012401767075061798, 0.039841603487730026, 0.012216111645102501, -0.04102979600429535, 0.017869312316179276, -0.04385175555944443, 0.023633906617760658, -0.013107256963849068, 0.023782430216670036, -0.01746087148785591, 0.0063772560097277164, -0.021703092381358147, -0.008405539207160473, -0.044668640941381454, -0.023002678528428078, 0.0448542945086956, 0.031505685299634933, -0.0023206898476928473, 0.011148594319820404, -0.03352932631969452, 0.034661825746297836, -0.016931753605604172, 0.0022429467644542456, 0.014945242553949356, 0.027384141460061073, 0.02925925888121128, -0.0064515178091824055, 0.014230470173060894, -0.07162577658891678, 0.013515697792172432, 0.04244077578186989, -0.06048646196722984, -0.020477768033742905, 0.0027593004051595926, 0.07088315486907959, 0.02500775456428528, 0.034531865268945694, 0.01644904911518097, -0.02493349276483059, -0.039841603487730026, -0.038467757403850555, -0.07619289308786392, 0.04348044469952583, 0.03534874692559242, 0.006358690559864044, -0.00730553176254034, 0.0303917545825243, 0.04154963046312332, 0.005439697299152613, -0.014239753596484661, -0.04251503944396973, -0.004082093480974436, 0.03763230890035629, -0.01947522908449173, 0.015539339743554592, 0.02257567085325718, -0.0718485563993454, -0.023058375343680382, -0.005917759146541357, -0.06824684888124466, -0.018212774768471718, -0.05023829638957977, -0.07010339945554733, 0.02289128489792347, -0.05384000390768051, -0.023745298385620117, 0.05447123199701309, -0.03221117705106735, 0.03031749278306961, -0.049458544701337814, 0.08139123767614365, -0.04529986530542374, -0.04782477766275406, 0.07797518372535706, 0.056216392666101456, -0.005411848891526461, -0.003390528028830886, 0.02599172666668892, -0.061711784452199936, -0.023076940327882767, -0.0012554932618513703, -0.010972222313284874, 0.021387478336691856, 0.008182752877473831, -0.011612731963396072, -0.032731011509895325, 0.001453912234865129, 0.013738484121859074, 0.02729131281375885, -0.04418593645095825, 0.034030597656965256, 0.004242221359163523, 0.005671766120940447, 0.03310232236981392, -0.02116469107568264, 0.005769235081970692, -0.000057328292314196005, 0.03553440421819687, 0.026010291650891304, 0.008140980266034603, -0.03334367275238037, -0.031635645776987076, -0.014555366709828377, -0.007918193936347961, 0.004390745423734188, -0.033120885491371155, 0.00265022786334157, 0.009969683364033699, -0.018249904736876488, -0.016634704545140266, 0.027142789214849472, -0.022482844069600105, 0.02933352068066597, 0.02736557461321354, -0.056921880692243576, 0.01480600144714117, 0.02175878919661045, 0.0204220712184906, 0.027198486030101776, 0.0019725863821804523, -0.00505446270108223, 0.009148159995675087, 0.05202058330178261, 0.02701283060014248, 0.00989542156457901, -0.03590571507811546, -0.009533394128084183, 0.032693877816200256, 0.07834649085998535, -0.02669721655547619, 0.05038681998848915, 0.007398359477519989, 0.005189062561839819, 0.002750017447397113, -0.013209367170929909, 0.08859466016292572, -0.048753052949905396, 0.06754136085510254, 0.04099266603589058, -0.008632966317236423, 0.019976498559117317, -0.0408441424369812, 0.011501339264214039, 0.06085777282714844, -0.029519176110625267, -0.016328373923897743, 0.01747015304863453, -0.059743840247392654, 0.039358898997306824, 0.015465077944099903, -0.002562041627243161, -0.05744171515107155, -0.0355529710650444, 0.03221117705106735, 0.021294649690389633, 0.013970552943646908, -0.00037856254493817687, 0.03820784017443657, 0.043257661163806915, -0.03895045816898346, 0.0019899916369467974, 0.0087675666436553, -0.0016546519473195076, -0.01292160153388977, -0.0031932692509144545, -0.03278670832514763, 0.007115235086530447, -0.02784827910363674, 0.01001609768718481, 0.009073897264897823, -0.004179562442004681, -0.012420332059264183, 0.013645656406879425, -0.005110159050673246, -0.002215098589658737, -0.0032071934547275305, -0.0034578279592096806, -0.020477768033742905, 0.023002678528428078, 0.0630856305360794, -0.04374036192893982, 0.021350346505641937, -0.014258318580687046, -0.028925077989697456, -0.007811442017555237, -0.0013610846363008022, -0.0028590899892151356, 0.05384000390768051, 0.01936383731663227, -0.04567117616534233, -0.00387787283398211, -0.029352085664868355, -0.005569655913859606, 0.046710845082998276, 0.024914925917983055, 0.03427194803953171, 0.010340994223952293, -0.00560678681358695, -0.019308140501379967, -0.02799680270254612, -0.014406843110918999, -0.013524980284273624, -0.01177982147783041, 0.05443410202860832, -0.02753266505897045, -0.004274711012840271, -0.03144998848438263, 0.004711000714451075, 0.024599313735961914, -0.026920001953840256, 0.007885703817009926, -0.019568057730793953, 0.027978237718343735, -0.007964607328176498, 0.03776226565241814, -0.00850300770252943, -0.007876421324908733, -0.007857856340706348, 0.013367174193263054, 0.005885269492864609, 0.00681354571133852, -0.007932118140161037, -0.0505724735558033, 0.007444773335009813, 0.03633272275328636, -0.023578209802508354, 0.05090665444731712, -0.0031236486975103617, 0.0004119224613532424, 0.0008545940509065986, 0.007788235321640968, 0.00485024182125926, -0.011259987019002438, -0.01179838739335537, 0.05655056983232498, 0.04511421173810959, -0.0005076508969068527, 0.042700693011283875, 0.00952411163598299, -0.039247509092092514, -0.018054967746138573, 0.002773224376142025, -0.06653881818056107, 0.005374717991799116, -0.0159849114716053, 0.007876421324908733, 0.009059973061084747, 0.03876480460166931, -0.020830512046813965, 0.044557247310876846, -0.026363037526607513, -0.015130897983908653, 0.028609465807676315, 0.05584508180618286, -0.008776849135756493, 0.08176254481077194, 0.00505446270108223, 0.049347151070833206, -0.018092097714543343, -0.013571394607424736, 0.04856739938259125, 0.012141849845647812, -0.03655550628900528, 0.03035462461411953, 0.004727245308458805, 0.04615388065576553, -0.013961270451545715, 0.003638841677457094, -0.011974760331213474, 0.004615852143615484, -0.010730870068073273, -0.003295379690825939, -0.023392554372549057, 0.039136115461587906, 0.014323297888040543, -0.00654898677021265, 0.013088691048324108, -0.000961925950832665, 0.02380099520087242, 0.024562181904911995, -0.00891144946217537, -0.0003608672705013305, -0.03364071995019913, 0.02756979689002037, -0.03326940909028053, 0.0328238382935524, 0.029352085664868355, -0.037446651607751846, 0.0268643070012331, 0.025063451379537582, 0.015047353692352772, -0.008939297869801521, -0.027941105887293816, -0.02348538115620613, -0.0013564432738348842, 0.01380346342921257, -0.019698016345500946, 0.014100511558353901, -0.016152001917362213, 0.00847051851451397, -0.012420332059264183, 0.00019334247917868197, -0.05736745521426201, -0.03636985272169113, -0.007226628251373768, 0.014174774289131165, 0.00134019844699651, -0.023336857557296753, 0.02383812703192234, -0.014648194424808025, 0.01577140763401985, -0.012773077003657818, -0.012401767075061798, 0.011519904248416424, -0.017163822427392006, 0.03200695663690567, -0.02415374107658863, 0.0470450259745121, 0.021016167476773262, 0.042069464921951294, 0.011055766604840755, -0.010573063045740128, 0.001024004421196878, -0.00915744248777628, -0.03172847256064415, 0.041363976895809174, 0.037409521639347076, 0.009551960043609142, 0.015567188151180744, -0.028479507192969322, 0.01986510492861271, -0.01061947736889124, -0.0004197547968942672, -0.0005647978978231549, -0.008507649414241314, -0.0430348739027977, -0.020979037508368492, 0.0599294975399971, 0.017934290692210197, 0.011120745912194252, 0.0059084766544401646, 0.005305096972733736, 0.02123895473778248, -0.019233878701925278, -0.0025829279329627752, -0.0032907382119446993, 0.02289128489792347, -0.024599313735961914, 0.037558045238256454, 0.01010892540216446, 0.021665960550308228, -0.017275216057896614, -0.015762126073241234, -0.05049821361899376, 0.0074215661734342575, -0.019066788256168365, -0.0005755310994572937, 0.020013630390167236, 0.01680179499089718, 0.0002631082315929234, 0.017061712220311165, -0.0017811295110732317, 0.05172353610396385, -0.04507708176970482, 0.06356833875179291, -0.039915867149829865, -0.007973890751600266, -0.013135104440152645, -0.008493725210428238, 0.04166102409362793, -0.0042979177087545395, -0.04529986530542374, -0.004704038612544537, 0.025304801762104034, 0.0039753420278429985, 0.006920297164469957, 0.03973020985722542, -0.011167160235345364, -0.04782477766275406, 0.03499600291252136, 0.001694103586487472, -0.02764405868947506, 0.01771150529384613, -0.016328373923897743, 0.022371450439095497, -0.043926019221544266, -0.009250270202755928, 0.02309550531208515, 0.02190731279551983, -0.009542676620185375, -0.011789104901254177, 0.02376386523246765, -0.01380346342921257, 0.033362239599227905, 0.011139311827719212, -0.01052664965391159, -0.04162389412522316, -0.00020683149341493845, 0.022687064483761787, -0.044594377279281616, -0.024209437891840935, 0.001330915605649352, -0.03427194803953171, 0.012903035618364811, -0.024060912430286407, -0.03341793641448021, 0.04916149377822876, -0.027439838275313377, -0.005379359237849712, -0.008874318562448025, -0.0065072146244347095, -0.033436499536037445, 0.01038740761578083, -0.019141050055623055, 0.04982985183596611, -0.0028614106122404337, -0.08116845041513443, 0.0035924280527979136, -0.04581969976425171, -0.026641519740223885, 0.020923340693116188, -0.0006144026410765946, 0.027514100074768066, 0.07775239646434784, 0.01919674687087536, -0.010656608268618584, 0.03274957463145256, 0.002787148579955101, -0.01746087148785591, 0.03341793641448021, -0.02387525700032711, -0.04567117616534233, -0.00009152220445685089, -0.06820971518754959, -0.007045614533126354, -0.011000069789588451, -0.03757661208510399, -0.0016697363462299109, 0.022352885454893112, 0.01626339554786682, 0.07470764964818954, -0.04819608852267265, 0.03503313288092613, 0.0019702657591551542, -0.044631507247686386, -0.0037131039425730705, -0.031672775745391846, 0.029519176110625267, 0.005973455961793661, 0.005342228338122368, -0.021313216537237167, 0.02690143696963787, -0.02775545045733452, -0.004715641960501671, -0.00957980751991272, -0.01669040136039257, -0.014239753596484661, 0.016987450420856476, 0.039952997118234634, 0.008359124884009361, 0.00852157361805439, 0.020719120278954506, 0.010851546190679073, 0.013070125132799149, -0.005388641729950905, -0.002281238092109561, -0.010860828682780266, 0.005681049078702927, 0.06839537620544434, 0.007022407837212086, -0.02446935512125492, -0.007885703817009926, -0.017720788717269897, 0.0006103414343670011, 0.004525345284491777, 0.007843932136893272, 0.05736745521426201, -0.023541077971458435, 0.014536801725625992, -0.033083755522966385, -0.01767437346279621, -0.06687299907207489, 0.008103849366307259, 0.012986580841243267, -0.004947710782289505, 0.042032334953546524, 0.020366374403238297, 0.013478566892445087, 0.0224271472543478, 0.014397559687495232, -0.027272747829556465, -0.021888747811317444, 0.0319698229432106, 0.039990127086639404, 0.0319141261279583, -0.023392554372549057, 0.028572333976626396, -0.024525050073862076, -0.010006815195083618, -0.0029867279808968306, -0.030614541843533516, -0.06286285072565079, -0.023021243512630463, 0.02615881711244583, 0.013589960522949696, -0.016003478318452835, 0.030911589041352272, -0.0023299725726246834, -0.012197545729577541, -0.0021628830581903458, -0.005110159050673246, 0.0012845018645748496, 0.01242961548268795, -0.026530126109719276, -0.003395169274881482, -0.012550290673971176, 0.028683727607131004, 0.0017846105620265007, 0.030206099152565002, 0.01771150529384613, 0.01630052551627159, 0.02348538115620613, -0.012104718945920467, 0.005945607554167509, 0.0004072810697834939, 0.00026774959405884147, 0.03338080272078514, -0.01623554714024067, 0.021665960550308228, -0.005950248800218105, -0.0221857950091362, -0.009162083268165588, 0.005685690324753523, 0.019308140501379967, 0.015622884035110474, 0.03675972670316696, -0.014230470173060894, 0.02792254090309143, -0.003044745186343789, 0.05796154960989952, -0.026437299326062202, -0.01623554714024067, -0.010173904709517956, 0.03958168625831604, 0.01768365688621998, -0.004084414336830378, 0.010183187201619148, -0.0007490026764571667, -0.009496263228356838, 0.001322793192230165, -0.02073768526315689, 0.012661684304475784, -0.0022429467644542456, 0.01901109144091606, -0.001330915605649352, 0.04162389412522316, -0.003543693572282791, -0.003636521054431796, 0.054285578429698944, 0.02556472085416317, -0.03393777087330818, 0.08517859876155853, -0.014592498540878296, -0.008999635465443134, 0.03490317612886429, -0.04091840609908104, 0.007110593840479851, 0.0381707064807415, -0.02933352068066597, -0.002756979549303651, -0.016087021678686142, 0.009570525027811527, -0.00915744248777628, -0.035163093358278275, -0.03243396058678627, -0.01796213909983635, -0.028887948021292686, -0.04110405966639519, -0.011631297878921032, -0.04244077578186989, -0.027384141460061073, 0.01795285753905773, 0.03126433491706848, 0.01438827719539404, -0.014815283939242363, 0.015604319050908089, 0.023503948003053665, -0.020719120278954506, 0.00908318068832159, -0.0077789523638784885, -0.014620346017181873, 0.04645092785358429, 0.030558845028281212, -0.01919674687087536, 0.031672775745391846, 0.02627020888030529, -0.01767437346279621, -0.013107256963849068, -0.002884617540985346, -0.015065918676555157, -0.01845412701368332, 0.00833127647638321, -0.013524980284273624, 0.00022162588720675558, 0.01158488355576992, -0.012281090952455997, -0.026492996141314507, 0.01605917327105999, 0.022390015423297882, -0.03572005778551102, -0.003397490130737424, 0.018658347427845, -0.03883906453847885, 0.02704996056854725, 0.034884609282016754, 0.0457083098590374, -0.014638911932706833, -0.009951118379831314, 0.024042347446084023, -0.018918264657258987, -0.04292348027229309, 0.0029635210521519184, -0.019530925899744034, -0.05510246008634567, -0.046673715114593506, 0.04050996154546738, -0.054991066455841064, -0.004743490368127823, -0.052094846963882446, -0.025267671793699265, 0.02250140905380249, -0.06082063913345337, 0.037483781576156616, -0.041401106864213943, 0.010164622217416763, -0.02623307891190052 ]
The incredible feats of athleticism demonstrated by humans are made possible in part by a vast repertoire of general-purpose motor skills, acquired through years of practice and experience. These skills not only enable humans to perform complex tasks, but also provide powerful priors for guiding their behaviors when learning new tasks. This is in stark contrast to what is common practice in physics-based character animation, where control policies are most typically trained from scratch for each task. In this work, we present a large-scale data-driven framework for learning versatile and reusable skill embeddings for physically simulated characters. Our approach combines techniques from adversarial imitation learning and unsupervised reinforcement learning to develop skill embeddings that produce life-like behaviors, while also providing an easy to control representation for use on new downstream tasks. Our models can be trained using large datasets of unstructured motion clips, without requiring any task-specific annotation or segmentation of the motion data. By leveraging a massively parallel GPU-based simulator, we are able to train skill embeddings using over a decade of simulated experiences, enabling our model to learn a rich and versatile repertoire of skills. We show that a single pre-trained model can be effectively applied to perform a diverse set of new tasks. Our system also allows users to specify tasks through simple reward functions, and the skill embedding then enables the character to automatically synthesize complex and naturalistic strategies in order to achieve the task objectives.
[ 0.0522584430873394, -0.010604631155729294, -0.023862723261117935, -0.06132443621754646, -0.005657031666487455, 0.03158355876803398, -0.0012749051675200462, 0.01038350909948349, -0.0711275041103363, 0.0050950138829648495, 0.019163886085152626, 0.01140619721263647, 0.06655765324831009, -0.032541751861572266, 0.022941382601857185, 0.05981343612074852, -0.016335370019078255, 0.029961999505758286, -0.030238401144742966, -0.046656690537929535, 0.01025452185422182, -0.005993321072310209, -0.062245775014162064, -0.0035817117895931005, 0.05325349047780037, 0.018518947064876556, -0.003957158420234919, 0.008738916367292404, -0.09124957770109177, 0.036521945148706436, 0.025152601301670074, 0.0035126113798469305, 0.016215596348047256, 0.01975354366004467, -0.0015282738022506237, -0.01931130141019821, 0.04146033152937889, 0.031049180775880814, -0.04275020584464073, 0.01772659458220005, 0.0015167570672929287, -0.026737306267023087, -0.007126570213586092, -0.06058736518025398, 0.005638604983687401, -0.023144077509641647, -0.015275828540325165, -0.00544512365013361, -0.0051180473528802395, 0.002510653343051672, 0.05789704993367195, -0.03803294524550438, 0.04967869073152542, -0.04024416208267212, -0.012954049743711948, 0.06825292110443115, 0.08026719838380814, -0.037996090948581696, 0.04964183643460274, 0.01712772250175476, -0.046582985669374466, 0.01786479540169239, -0.03877001628279686, -0.021909480914473534, -0.002678798045963049, -0.09780952334403992, 0.05815502256155014, -0.0032891861628741026, 0.0015040886355563998, 0.02224116399884224, -0.02528158761560917, -0.01283427607268095, -0.03442128747701645, -0.02898537740111351, 0.003215478966012597, -0.00459288340061903, 0.05380629748106003, 0.0237153097987175, 0.03326039761304855, -0.021633079275488853, 0.001927905366756022, 0.017136937007308006, -0.03773811459541321, 0.009775424376130104, 0.1233859434723854, -0.012861915864050388, 0.046103887259960175, -0.06007141247391701, 0.018316252157092094, -0.02684786729514599, -0.04514569416642189, -0.006523091811686754, -0.005532650742679834, -0.006292756646871567, -0.05185305327177048, 0.04142347723245621, -0.0077300481498241425, -0.03296557068824768, -0.019606130197644234, -0.015008639544248581, 0.005472763441503048, -0.0048370384611189365, 0.012299898080527782, -0.06832662224769592, -0.04046528413891792, -0.03432915359735489, -0.0025935741141438484, 0.03491881117224693, -0.02684786729514599, 0.098546601831913, -0.0030219973996281624, -0.05833929032087326, -0.006053208373486996, 0.046103887259960175, -0.039285965263843536, -0.001793159288354218, -0.010005760006606579, -0.07953012734651566, 0.09744098782539368, -0.07466544955968857, 0.06626281887292862, 0.052000466734170914, 0.006421744357794523, -0.011092942208051682, -0.03880687057971954, 0.020453762263059616, -0.049973517656326294, -0.011673386208713055, 0.04802027717232704, 0.02620292827486992, 0.0048600719310343266, 0.00607163505628705, -0.003169412026181817, 0.04525625333189964, 0.03302085027098656, 0.028137745335698128, -0.012115630321204662, 0.009158126078546047, -0.013737189583480358, -0.008190718479454517, -0.03145457059144974, -0.011968215927481651, -0.06681562960147858, -0.017210643738508224, 0.030975474044680595, -0.0338500551879406, -0.008577682077884674, 0.042602792382240295, 0.011599679477512836, -0.01874006912112236, -0.024710357189178467, 0.05096856504678726, -0.03563745692372322, 0.04687781259417534, 0.01025452185422182, -0.01752389967441559, -0.03436600789427757, 0.015533803962171078, 0.02050904370844364, 0.037240590900182724, 0.07938271015882492, 0.0024139126762747765, -0.028506280854344368, 0.07392837852239609, 0.06504665315151215, -0.019495569169521332, 0.02085915394127369, 0.000874121964443475, -0.03784867376089096, 0.03427387401461601, -0.06500979512929916, -0.007559600286185741, 0.0034987912513315678, 0.0045997933484613895, 0.03501094505190849, 0.06349880248308182, 0.06066107004880905, -0.012493379414081573, -0.03394218906760216, -0.01600368693470955, -0.05609121918678284, 0.026147648692131042, 0.01632615737617016, 0.03865945339202881, 0.07835081219673157, 0.0494944229722023, 0.06036624312400818, 0.010733619332313538, 0.02426811307668686, -0.03685362637042999, 0.020969713106751442, -0.03381320461630821, 0.03473454341292381, 0.014004378579556942, 0.009296327829360962, -0.03869630768895149, -0.026718879118561745, -0.006219049450010061, -0.00814004521816969, 0.04809398204088211, -0.043745256960392, -0.06114016845822334, -0.0035033980384469032, -0.019790397956967354, 0.0165749192237854, 0.019587703049182892, -0.0169250275939703, -0.015985261648893356, 0.01892433688044548, -0.0651572123169899, 0.031178168952465057, 0.016842108219861984, -0.06195094808936119, -0.054137978702783585, -0.043745256960392, -0.0513371042907238, -0.018270185217261314, 0.02483934536576271, -0.017256710678339005, -0.03388690948486328, -0.029833011329174042, -0.0046113100834190845, 0.01223540399223566, -0.03038581646978855, 0.007158817257732153, 0.054506514221429825, 0.016169529408216476, -0.01910860650241375, -0.0032431192230433226, 0.02896695025265217, -0.00300126732327044, -0.04160774499177933, 0.06773696839809418, -0.030127840116620064, 0.038917429745197296, -0.01881377585232258, 0.00821835920214653, -0.007191063836216927, -0.01743176579475403, 0.009176553227007389, 0.037074748426675797, -0.023015091195702553, 0.004705747589468956, 0.01200506929308176, 0.06707359850406647, 0.005730738863348961, -0.007080503273755312, 0.07783485949039459, 0.0052977087907493114, -0.050452616065740585, 0.0019578489009290934, 0.009581943042576313, 0.011618105694651604, 0.029796157032251358, -0.00600253464654088, 0.06685248017311096, 0.058007609099149704, -0.0011217322899028659, 0.01016238797456026, -0.008734310045838356, 0.0046435571275651455, 0.012309111654758453, 0.021762067452073097, 0.029980426654219627, -0.016040541231632233, 0.0031786253675818443, 0.004182886797934771, 0.003664632560685277, 0.014207073487341404, -0.011157435365021229, -0.007683981209993362, 0.026276636868715286, -0.011922148056328297, -0.01809513010084629, 0.011986642144620419, -0.06803179532289505, 0.029575036838650703, -0.025631697848439217, 0.050452616065740585, -0.005555684212595224, 0.004233560524880886, -0.030054133385419846, 0.02511574700474739, 0.046840962022542953, -0.03674306720495224, -0.05583324655890465, -0.045735351741313934, -0.008738916367292404, 0.00510422745719552, 0.026553038507699966, -0.019974665716290474, 0.015091560781002045, -0.026626745238900185, 0.04109179601073265, 0.0224438589066267, -0.009738571010529995, -0.041939426213502884, 0.007089716382324696, 0.055980660021305084, -0.010143960826098919, -0.0068271346390247345, 0.025263162329792976, 0.02530001476407051, 0.0034158704802393913, -0.01499942597001791, -0.002386272419244051, -0.020343203097581863, 0.031159741804003716, -0.0043164812959730625, -0.04669354483485222, 0.025060467422008514, 0.03372107073664665, -0.03628239780664444, -0.02408384531736374, 0.008674422279000282, 0.023236211389303207, 0.0492733009159565, 0.05292180925607681, -0.04783600941300392, -0.03372107073664665, -0.021835774183273315, 0.0412023551762104, -0.06766325980424881, 0.03191523998975754, 0.0872693881392479, 0.007260164711624384, 0.0009144306532107294, 0.022185884416103363, -0.03556375205516815, -0.008881724439561367, -0.0409812331199646, -0.04064955189824104, -0.03574801981449127, 0.022922955453395844, 0.04072325676679611, -0.01195900235325098, -0.03092019259929657, 0.012576300650835037, -0.05612807348370552, -0.047946568578481674, -0.03349994868040085, 0.006490845233201981, 0.0003869630745612085, -0.021927908062934875, 0.015515376813709736, -0.03784867376089096, -0.016749974340200424, 0.03858574852347374, -0.05052632465958595, -0.016335370019078255, 0.0009795003570616245, -0.01569964550435543, -0.007241737563163042, -0.04308189079165459, 0.005366809666156769, -0.026184502989053726, -0.013903031125664711, 0.02104342170059681, -0.00418979674577713, 0.0014246230712160468, 0.014161006547510624, -0.04134976863861084, 0.003994011785835028, 0.036890480667352676, -0.04367154836654663, -0.02389957755804062, -0.01490729209035635, -0.06670506298542023, 0.08048832416534424, 0.0419025756418705, -0.04547737538814545, -0.015708858147263527, 0.02463665045797825, -0.027474379166960716, -0.04123920947313309, 0.010586204007267952, -0.005279282107949257, -0.028506280854344368, -0.04245537891983986, 0.05896580219268799, -0.002127145417034626, 0.023881150409579277, 0.013239665888249874, 0.03473454341292381, 0.004129909444600344, 0.05531729385256767, 0.020969713106751442, 0.0007935046451166272, -0.021743640303611755, 0.036319248378276825, 0.06276172399520874, -0.04636186361312866, -0.06475182622671127, -0.014704597182571888, 0.019421862438321114, -0.008398020640015602, 0.026387197896838188, -0.02594495378434658, 0.012014282867312431, 0.03294714167714119, -0.04271335527300835, -0.00687780836597085, -0.011461477726697922, 0.0026488543953746557, 0.005970287602394819, -0.0014372915029525757, 0.024489235132932663, -0.007992630824446678, 0.0428239144384861, -0.015091560781002045, -0.030330535024404526, -0.02299666404724121, -0.04709893465042114, 0.005947254132479429, 0.005067373625934124, 0.0014407464768737555, 0.005481977015733719, 0.040207307785749435, 0.021006567403674126, -0.04053898900747299, -0.014207073487341404, 0.019458714872598648, 0.03445814177393913, 0.0338500551879406, -0.044445473700761795, 0.0042612007819116116, 0.009019925259053707, 0.023475760594010353, -0.019034897908568382, -0.05030520260334015, -0.006721180398017168, 0.006509271916002035, 0.04470345005393028, -0.031122887507081032, 0.017302777618169785, -0.006085455417633057, 0.034034326672554016, 0.01565357856452465, -0.056828293949365616, -0.05454336851835251, -0.04337671771645546, -0.03506622463464737, -0.005786019377410412, -0.03685362637042999, 0.04728320240974426, -0.02907751128077507, 0.018472880125045776, -0.042418524622917175, 0.008066337555646896, -0.05107912793755531, -0.10120005905628204, -0.01190372183918953, -0.05446965992450714, -0.03082805871963501, 0.005965680815279484, 0.02032477594912052, 0.030035706236958504, -0.003551768371835351, -0.015063920058310032, -0.04433491453528404, -0.003114131512120366, -0.009941265918314457, -0.008245998993515968, -0.03895428404211998, 0.01966140978038311, -0.0022826215717941523, -0.0458090603351593, -0.016261663287878036, -0.005818266421556473, 0.04459289088845253, 0.038548894226551056, -0.028911670669913292, -0.037885528057813644, 0.01671312004327774, 0.027732353657484055, 0.020103653892874718, -0.027455952018499374, -0.058302439749240875, 0.05089486017823219, -0.00022371303930412978, -0.004636647179722786, 0.01920074038207531, 0.03762755170464516, -0.036779921501874924, -0.030883340165019035, 0.02732696384191513, 0.04142347723245621, 0.0038028336130082607, 0.0012956353602930903, -0.01881377585232258, 0.037885528057813644, -0.029575036838650703, -0.019440287724137306, 0.021301396191120148, -0.024618223309516907, -0.021909480914473534, -0.025705404579639435, -0.0071542104706168175, 0.06545203924179077, 0.014594036154448986, 0.0009950479725375772, 0.02463665045797825, 0.010282161645591259, -0.017201431095600128, -0.0014096512459218502, 0.015506163239479065, 0.0354531891644001, 0.041312918066978455, 0.008384199813008308, -0.04964183643460274, -0.0011119430419057608, 0.033278826624155045, 0.00421974016353488, -0.02410227246582508, -0.007974203675985336, 0.014400554820895195, 0.024784063920378685, 0.0046435571275651455, 0.06213521584868431, 0.015054706484079361, 0.00009832432260736823, 0.04146033152937889, 0.015174481086432934, 0.0184176005423069, -0.04230796545743942, 0.0633145347237587, 0.028782682493329048, -0.03924911469221115, -0.01768052764236927, 0.028303585946559906, -0.019182313233613968, 0.009959693066775799, -0.02207532338798046, -0.04577220603823662, -0.023586321622133255, -0.011102154850959778, 0.02520788088440895, 0.014068872667849064, 0.012345965020358562, -0.006702753249555826, -0.031141314655542374, 0.017330417409539223, -0.005200968123972416, 0.01747783273458481, 0.016473570838570595, 0.008365773595869541, 0.026239782571792603, -0.06257745623588562, 0.012207764200866222, 0.01194978877902031, 0.014363701455295086, 0.008679029531776905, 0.0073016248643398285, -0.006329610478132963, -0.03379477560520172, -0.040059894323349, -0.028229879215359688, -0.04485086351633072, 0.01136013027280569, -0.002992053981870413, -0.012567087076604366, -0.019532421603798866, -0.01370954979211092, 0.02023264206945896, 0.007969597354531288, -0.003438904182985425, 0.03552689775824547, 0.07562364637851715, -0.00044541063834913075, -0.016915814951062202, -0.011010020971298218, -0.006790280807763338, -0.029796157032251358, 0.01136013027280569, 0.024341821670532227, 0.02546585723757744, 0.01213405653834343, -0.038254063576459885, -0.03279972821474075, 0.01697109453380108, -0.01380168367177248, -0.0047449045814573765, 0.010448003187775612, 0.04905217885971069, -0.021762067452073097, 0.032633885741233826, -0.004535299725830555, -0.008706669323146343, 0.04134976863861084, -0.0007860187906771898, 0.002363238949328661, 0.019053325057029724, 0.0016111945733428001, 0.019034897908568382, -0.030606936663389206, -0.013479214161634445, -0.030017279088497162, 0.020656459033489227, 0.017376486212015152, -0.03602442145347595, 0.004567546304315329, 0.008503974415361881, 0.0021870324853807688, 0.01629851758480072, -0.0005398480570875108, 0.005689278710633516, 0.05749166011810303, 0.0053437757305800915, -0.03738800436258316, 0.015257401391863823, 0.013423933647572994, 0.04905217885971069, 0.021448811516165733, -0.03784867376089096, 0.041312918066978455, 0.0044754124246537685, 0.058302439749240875, 0.029519755393266678, 0.006781067233532667, 0.03436600789427757, 0.007895889692008495, 0.043524134904146194, 0.053585175424814224, -0.0013048487016931176, 0.0051733278669416904, 0.014151792973279953, 0.009563515894114971, -0.03121502324938774, 0.0025037433952093124, 0.023328345268964767, 0.008918577805161476, 0.021264543756842613, -0.030588511377573013, -0.0038512039463967085, 0.012456526048481464, 0.008863297291100025, 0.003947944846004248, 0.06961650401353836, 0.02907751128077507, 0.042049989104270935, -0.009296327829360962, -0.00041057245107367635, -0.02225959114730358, 0.033370960503816605, -0.00703904265537858, 0.04171830788254738, -0.0022054591681808233, -0.00004124439146835357, 0.013608202338218689, 0.010798112489283085, -0.0008937004604376853, -0.00351952132768929, 0.0294644758105278, 0.0455879382789135, 0.026184502989053726, 0.024894624948501587, 0.038364626467227936, -0.006076241843402386, -0.034200165420770645, -0.005555684212595224, 0.030422668904066086, -0.020472189411520958, 0.01117586251348257, -0.01136013027280569, 0.021393530070781708, 0.030017279088497162, 0.05037890747189522, 0.01931130141019821, -0.027216404676437378, 0.06449384987354279, 0.012392031960189342, -0.025502709671854973, -0.023973284289240837, 0.02769550122320652, 0.02196476235985756, 0.008628355339169502, 0.011876081116497517, 0.02806403674185276, 0.008080157451331615, -0.039175406098365784, -0.03766440600156784, -0.02362317591905594, -0.021633079275488853, -0.03692733496427536, -0.0018634115112945437, -0.03759070113301277, -0.0042588971555233, 0.04418749734759331, -0.05163193121552467, -0.010079466737806797, -0.00418979674577713, -0.01756996661424637, -0.0037567666731774807, 0.013092251494526863, 0.038991138339042664, 0.047430619597435, -0.038180358707904816, -0.020988140255212784, 0.03436600789427757, 0.014400554820895195, 0.005698492284864187, -0.012843488715589046, -0.04385581612586975, 0.034476567059755325, 0.06766325980424881, -0.031233448535203934, 0.016584131866693497, 0.004072325769811869, -0.009499022737145424, -0.015146841295063496, -0.001423471374437213, 0.011774733662605286, -0.004014742095023394, 0.0163445845246315, 0.031067607924342155, 0.04031786695122719, 0.030717497691512108, -0.0021110218949615955, -0.017072442919015884, 0.02399171143770218, 0.00174824392888695, -0.026479331776499748, -0.003862720914185047, -0.05970287695527077, -0.03703789412975311, 0.026350343599915504, 0.017717381939291954, -0.019974665716290474, -0.02058275043964386, -0.010576991364359856, 0.04510883986949921, -0.06272487342357635, -0.0014418981736525893, 0.01223540399223566, 0.021762067452073097, 0.0050397333689033985, -0.02021421492099762, 0.028358865529298782, -0.0035126113798469305, -0.05251641944050789, 0.00018901879957411438, -0.056644026190042496, 0.05833929032087326, 0.006477024871855974, 0.014068872667849064, -0.0017977659590542316, 0.013193598948419094, 0.051558226346969604, -0.03320511803030968, -0.02318093180656433, 0.08483704924583435, 0.009517448954284191, 0.03543476387858391, -0.010226881131529808, -0.05896580219268799, -0.004696534015238285, 0.042049989104270935, -0.01855580136179924, 0.00046671665040776134, 0.005431303288787603, 0.03939652815461159, 0.06176668033003807, -0.01786479540169239, 0.030514802783727646, 0.03877001628279686, 0.03092019259929657, -0.030588511377573013, -0.017330417409539223, -0.009839918464422226, -0.012640793807804585, 0.008434874005615711, -0.042418524622917175, 0.05089486017823219, 0.009042958728969097, -0.014114939607679844, 0.03379477560520172, -0.037240590900182724, 0.006283543538302183, -0.026829440146684647, 0.008047910407185555, -0.03009098581969738, -0.003093401435762644, -0.019606130197644234, 0.05030520260334015, -0.011203502304852009, 0.008342740125954151, -0.027640219777822495, -0.0069192685186862946, -0.01648278534412384, -0.0052977087907493114, 0.03464240953326225, 0.011470691300928593, 0.020269494503736496, 0.033352531492710114, 0.04459289088845253, -0.01743176579475403, -0.02760336734354496, -0.008536221459507942, -0.010263735428452492, -0.04514569416642189, -0.005915007088333368, 0.00026517335209064186, -0.005841299891471863, 0.03259703516960144, 0.014741450548171997, 0.009268687106668949, 0.009941265918314457, 0.047320056706666946, 0.006039388012140989, 0.012760568410158157, -0.015211334452033043, 0.016197169199585915, -0.0072325244545936584, -0.004390188492834568, -0.003957158420234919, -0.01592998020350933, 0.01204192265868187, 0.017698954790830612, 0.025539563968777657, -0.025318441912531853, -0.004919959232211113, -0.03736957907676697, 0.02955660969018936, 0.015036280266940594, -0.04510883986949921, -0.013562134467065334, -0.008900150656700134, 0.02141195721924305, 0.010899459943175316, 0.0004583669942803681, 0.0458090603351593, 0.0029068298172205687, -0.011756307445466518, 0.02999885194003582, 0.008927791379392147, -0.0019221469992771745, 0.026700453832745552, 0.021559372544288635, -0.022222736850380898, 0.055169880390167236, 0.008950824849307537, -0.019587703049182892, -0.03149142488837242, -0.044924572110176086, -0.021467238664627075, -0.042418524622917175, -0.008890938013792038, 0.021375102922320366, 0.008817230351269245, 0.0121432701125741, -0.004079235717654228, 0.006735000293701887, 0.019735116511583328, 0.005680065136402845, -0.0465092770755291, 0.02557641826570034, 0.05159507691860199, 0.04197628051042557, -0.028027184307575226, -0.0163445845246315, 0.01786479540169239, -0.0077530816197395325, 0.03560060262680054, -0.000184987933607772, 0.042787060141563416, -0.01011632103472948, 0.025889672338962555, -0.05693885311484337, -0.04415064677596092, -0.08476334065198898, -0.013995165005326271, 0.03847518563270569, -0.025557991117239, 0.029059085994958878, -0.042529087513685226, 0.02205689623951912, -0.030404241755604744, -0.042049989104270935, -0.035858578979969025, -0.03047795034945011, -0.004786364734172821, -0.011157435365021229, 0.031344011425971985, -0.006182196084409952, 0.055354148149490356, 0.010097893886268139, -0.015285042114555836, -0.006587585899978876, -0.00604860158637166, -0.034108031541109085, -0.0030749745201319456, -0.013046183623373508, -0.027474379166960716, 0.012843488715589046, 0.059960853308439255, -0.00038034096360206604, -0.02675573341548443, 0.017984570935368538, 0.004703443963080645, 0.006656686309725046, 0.0011896811192855239, 0.019458714872598648, -0.041128646582365036, -0.012935623526573181, -0.018297826871275902, -0.016814466565847397, -0.002630427712574601, 0.00032650009961798787, 0.0513371042907238, -0.0017378788907080889, -0.012659220956265926, -0.002688011387363076, 0.07289647310972214, -0.0046343435533344746, 0.023217786103487015, 0.01860186830163002, 0.01641829125583172, -0.0409812331199646, 0.04890476167201996, -0.03513993322849274, -0.0012956353602930903, 0.02491305209696293, -0.010881033726036549, 0.024986758828163147, -0.03427387401461601, 0.019071752205491066, 0.014483475126326084, -0.019053325057029724, 0.01402280479669571, 0.03197052329778671, -0.06504665315151215, 0.012207764200866222, 0.01555223111063242, 0.025908099487423897, 0.01472302433103323, -0.03810665011405945, -0.04053898900747299, 0.010715192183852196, -0.00473108422011137, 0.015220548026263714, -0.031509850174188614, -0.03322354331612587, 0.01278820913285017, 0.038917429745197296, 0.0032914895564317703, 0.007564207073301077, 0.013313372619450092, 0.04322930425405502, -0.010512497276067734, -0.0014718417078256607, -0.04024416208267212, -0.001468386733904481, 0.0034826677292585373, 0.011544398963451385, -0.030330535024404526, 0.023199358955025673, -0.009305540472269058, -0.009747784584760666, -0.00163768301717937, 0.045182548463344574, 0.023144077509641647, 0.020158933475613594, -0.017874009907245636, -0.000929402420297265, -0.014750664122402668, 0.03950708732008934, 0.0031233448535203934, -0.06486238539218903, -0.019919386133551598, 0.00002882788612623699, -0.03580329939723015, 0.006301970221102238, 0.028745830059051514, 0.004175976850092411, 0.030699072405695915, 0.012815848924219608, -0.028487853705883026, -0.017026375979185104, -0.014391341246664524, -0.0011528275208547711, 0.019145458936691284, -0.03204422816634178, 0.06504665315151215, 0.020380055531859398, -0.016703907400369644, -0.018887484446167946, 0.0014200162841007113, -0.019642982631921768, -0.0356927365064621, 0.007670161314308643, -0.018998045474290848, -0.007531960029155016, 0.011056087911128998, -0.06862145662307739, -0.04160774499177933, -0.0050627668388187885, 0.00933778751641512, -0.00033225849620066583, 0.029188072308897972, -0.018703216686844826, -0.04031786695122719, -0.013387080281972885, -0.027677074074745178, 0.05104227364063263, 0.03274444863200188, 0.03460555523633957, 0.07901417464017868, 0.00038034096360206604, -0.03639295697212219, 0.004809398204088211, 0.010530924424529076, 0.010217668488621712, 0.003058850998058915, -0.01892433688044548, -0.007720835041254759, 0.00257514719851315, 0.006007141433656216, -0.014299207367002964, -0.034384433180093765, -0.022664980962872505, 0.0204906165599823, -0.019808825105428696, 0.03639295697212219, -0.05575953796505928 ]
Phase equilibrium calculations are an essential part of numerical simulations of multi-component multi-phase flow in porous media, accounting for the largest share of the computational time. In this work, we introduce a GPUenabled, fast, and parallel framework, PTFlash, that vectorizes algorithms required for isothermal two-phase flash calculations using PyTorch, and can facilitate a wide range of downstream applications. In addition, to further accelerate PTFlash, we design two task-specific neural networks, one for predicting the stability of given mixtures and the other for providing estimates of the distribution coefficients, which are trained offline and help shorten computation time by sidestepping stability analysis and reducing the number of iterations to reach convergence. The evaluation of PTFlash was conducted on three case studies involving hydrocarbons, CO 2 and N 2 , for which the phase equilibrium was tested over a large range of temperature, pressure and composition conditions, using the Soave-Redlich-Kwong (SRK) equation of state. We compare PTFlash with an in-house thermodynamic library, Carnot, written in C++ and performing flash calculations one by one on CPU. Results show speed-ups on large scale calculations up to two order of magnitudes, while maintaining perfect precision with the reference solution provided by Carnot.
[ -0.053337257355451584, -0.018953491002321243, -0.032158054411411285, -0.0224966648966074, 0.015799565240740776, 0.013264449313282967, -0.044673945754766464, 0.0617610327899456, -0.05249887332320213, 0.09996743500232697, 0.06527426838874817, 0.005948541685938835, 0.007919744588434696, -0.0658331885933876, -0.03830621391534805, 0.047548409551382065, -0.013733545318245888, -0.011707448400557041, -0.006866772659122944, -0.024712398648262024, 0.04124056175351143, -0.029862476512789726, -0.026129668578505516, -0.0560121051967144, 0.030740786343812943, 0.01658804714679718, 0.01225639134645462, -0.004531271755695343, -0.0011465414427220821, 0.06259942054748535, 0.06998518854379654, -0.003580602817237377, -0.02295578084886074, 0.02018112689256668, -0.029024092480540276, -0.03752771392464638, 0.020939664915204048, 0.016049085184931755, -0.023973820731043816, 0.014352354221045971, 0.010070601478219032, 0.002629934111610055, -0.006372724659740925, 0.01875387504696846, -0.0065523786470294, -0.017017221078276634, 0.004820714239031076, -0.03736801818013191, 0.02163831889629364, -0.03423405811190605, 0.017985355108976364, -0.03766744211316109, 0.03183867037296295, 0.061721108853816986, 0.046470485627651215, 0.0077001675963401794, 0.06371726095676422, 0.10803190618753433, 0.004094612784683704, -0.03585094213485718, -0.012216468341648579, 0.032756902277469635, -0.033495478332042694, -0.01419266127049923, 0.008992677554488182, -0.01347404532134533, -0.0164582971483469, 0.024013742804527283, -0.02293582074344158, -0.019212990999221802, -0.04655033349990845, 0.014921258203685284, 0.03932425007224083, 0.025510860607028008, -0.020600318908691406, -0.026109706610441208, 0.04535263776779175, -0.007550456095486879, 0.031479362398386, 0.023414896801114082, 0.021837934851646423, 0.06387695670127869, -0.006771955639123917, 0.021817972883582115, 0.031419478356838226, 0.027007976546883583, -0.05888656899333, -0.05772880092263222, 0.006747003644704819, 0.007266003638505936, -0.018015297129750252, 0.009836053475737572, -0.00374279054813087, -0.030141938477754593, 0.058726876974105835, 0.0562516450881958, 0.0015008589252829552, 0.009521658532321453, -0.015480181202292442, 0.03668932616710663, -0.0070015131495893, 0.012156583368778229, -0.0008346422691829503, 0.0017229311633855104, -0.01262567937374115, -0.026528898626565933, -0.011158506385982037, 0.03569125011563301, 0.03261717036366463, 0.11937006562948227, -0.02415347471833229, 0.014691700227558613, -0.020899740979075432, -0.0057090031914412975, 0.008693254552781582, 0.006482513155788183, -0.016049085184931755, -0.0163385272026062, -0.010809178464114666, -0.017606087028980255, 0.008433754555881023, 0.006307849660515785, 0.0005558044067583978, 0.0012775391805917025, -0.02259647287428379, 0.01693737506866455, -0.019552337005734444, -0.02044062688946724, 0.03433386608958244, 0.03427397832274437, -0.010599582456052303, -0.030621016398072243, -0.01508095022290945, -0.006771955639123917, 0.03207821026444435, 0.010709371417760849, 0.009990755468606949, 0.0576888769865036, 0.0032911603339016438, -0.01680762507021427, -0.0033560353331267834, -0.024492820724844933, -0.007101321127265692, -0.0675099566578865, 0.020380740985274315, 0.021738126873970032, -0.020999548956751823, 0.041160713881254196, 0.04866625741124153, 0.03736801818013191, -0.05389618128538132, -0.00405968027189374, 0.0066122631542384624, 0.04195917770266533, -0.005190002731978893, -0.051860105246305466, 0.029503170400857925, 0.03862559795379639, 0.012076737359166145, -0.05517372116446495, 0.014342373237013817, -0.08140319585800171, 0.041160713881254196, -0.051261257380247116, -0.009726264514029026, -0.014571931213140488, 0.06766965240240097, 0.01716693304479122, -0.04710925742983818, 0.043196793645620346, 0.07277980446815491, 0.0524190291762352, 0.04822710156440735, -0.026848282665014267, -0.0897471234202385, 0.024672474712133408, -0.00457368977367878, 0.027127744629979134, -0.010290178470313549, 0.008997668512165546, -0.01901337504386902, 0.023235242813825607, 0.0540957972407341, -0.020380740985274315, -0.0005327238468453288, -0.015360412187874317, 0.028704708442091942, 0.000023139022232498974, 0.05213956534862518, 0.0009207264520227909, 0.007595369592308998, 0.029443284496665, 0.06044356897473335, 0.011717429384589195, 0.029762670397758484, -0.002896919846534729, -0.04531271755695343, -0.031080132350325584, 0.003333578584715724, 0.005953532177954912, -0.07769034802913666, -0.04543248564004898, 0.019622202962636948, -0.0040921177715063095, -0.0350724421441555, 0.019861740991473198, 0.001354890177026391, -0.005723974201828241, 0.07130265235900879, -0.05948541685938835, 0.011777314357459545, 0.0126855643466115, -0.07377788424491882, -0.04603133350610733, -0.03952386602759361, -0.0028445208445191383, 0.043955329805612564, 0.0147216422483325, -0.011976929381489754, -0.007216100115329027, -0.03357532620429993, 0.01982181891798973, 0.01731664314866066, -0.01900339499115944, 0.04818717762827873, -0.0259699746966362, 0.010829140432178974, 0.01016541849821806, -0.029483208432793617, 0.005913608707487583, 0.028345400467514992, -0.03040143847465515, 0.0131047572940588, -0.03954382985830307, 0.01716693304479122, -0.061960648745298386, 0.004990387242287397, -0.0416397899389267, 0.01694735512137413, 0.019302817061543465, 0.022995704784989357, -0.047428641468286514, 0.0016118950443342328, 0.006931648124009371, -0.030241746455430984, 0.03473309427499771, -0.0708635002374649, 0.07892796397209167, 0.010190370492637157, 0.015360412187874317, -0.04171963781118393, -0.050063565373420715, 0.04203902184963226, 0.0001593025226611644, -0.04064171388745308, 0.013264449313282967, 0.04128048196434975, -0.025750398635864258, 0.01886366307735443, -0.019522394984960556, 0.0409211739897728, -0.017047163099050522, -0.004950464237481356, 0.05605202913284302, -0.02860490046441555, 0.043955329805612564, 0.048746101558208466, 0.0240536667406559, -0.021837934851646423, 0.034932710230350494, 0.03403444215655327, -0.004049699287861586, -0.016368471086025238, -0.05058256536722183, 0.02357458882033825, -0.07501550018787384, -0.03678913414478302, 0.02307555079460144, 0.026728514581918716, -0.0015220681671053171, 0.036829058080911636, -0.01876385696232319, 0.07333873212337494, -0.05205972120165825, -0.01911318302154541, -0.09006650745868683, -0.01754620112478733, 0.005818791687488556, -0.071103036403656, -0.04894571751356125, -0.0134041802957654, -0.03469317406415939, -0.021298972889780998, 0.014372315257787704, 0.0631982609629631, 0.003610545303672552, -0.07593373209238052, -0.05900634080171585, 0.014302450232207775, -0.0044464352540671825, -0.0490654893219471, 0.04279756173491478, 0.0696658045053482, -0.024912012740969658, -0.01971202902495861, -0.01886366307735443, 0.06263934075832367, 0.0259699746966362, 0.04144017770886421, -0.04411502182483673, 0.018813759088516235, -0.02343485876917839, 0.001850186032243073, -0.01068940944969654, 0.027706630527973175, -0.032736942172050476, 0.006846811156719923, -0.04148009791970253, -0.052219413220882416, -0.05058256536722183, 0.03231774643063545, 0.013154661282896996, -0.09246189892292023, 0.046230949461460114, 0.055732645094394684, -0.025770360603928566, -0.031159978359937668, 0.013693622313439846, 0.019552337005734444, -0.019682087004184723, 0.01597921922802925, -0.04998371750116348, -0.03137955442070961, 0.018923548981547356, -0.010005726478993893, 0.0008652083924971521, -0.04674994945526123, -0.01707710511982441, -0.021239088848233223, -0.024313166737556458, -0.0459514856338501, 0.015719719231128693, 0.012246410362422466, 0.03211813420057297, -0.0030316603370010853, -0.09342005103826523, 0.012236429378390312, 0.021418742835521698, -0.0317189022898674, 0.04271771386265755, 0.0010323863243684173, -0.013873276300728321, -0.00002376282100158278, 0.018364625051617622, 0.04120063781738281, -0.017246779054403305, 0.009746226482093334, -0.013334314338862896, 0.040082789957523346, 0.011946987360715866, 0.009626457467675209, -0.026269398629665375, 0.022816050797700882, -0.02139878086745739, -0.018115105107426643, 0.04014267399907112, -0.024373050779104233, 0.0002814890176523477, 0.015011085197329521, 0.014332392252981663, 0.03934421390295029, 0.04243825376033783, -0.017855605110526085, 0.009107456542551517, 0.030002208426594734, -0.016318567097187042, 0.018344663083553314, 0.023255204781889915, -0.08264081180095673, 0.043835561722517014, -0.05421556904911995, 0.015330469235777855, 0.100526362657547, 0.004556223750114441, 0.05485433712601662, -0.004461406264454126, 0.0012862723087891936, -0.017596105113625526, -0.013034891337156296, -0.03822636604309082, 0.008244119584560394, -0.03295651823282242, -0.007780013605952263, -0.01803525909781456, -0.022995704784989357, -0.011647563427686691, 0.026748476549983025, -0.03716840595006943, 0.018713952973484993, 0.042118869721889496, -0.009915899485349655, -0.005888657178729773, -0.010489794425666332, 0.035771094262599945, -0.023534666746854782, 0.01610896922647953, -0.0021196668967604637, -0.01353393029421568, -0.015001104213297367, 0.037328097969293594, -0.03822636604309082, -0.03297647833824158, -0.0172966830432415, -0.015669815242290497, 0.039503905922174454, -0.0056840511970222, -0.05010348930954933, 0.021917780861258507, -0.0030266698449850082, 0.012795353308320045, -0.002592506119981408, 0.07485581189393997, 0.009421851485967636, -0.0032187998294830322, 0.019751952961087227, 0.030740786343812943, 0.04870618134737015, 0.0287246685475111, 0.0012513395631685853, -0.026409128680825233, 0.09397897124290466, -0.0593656487762928, 0.0028669775929301977, -0.05253879725933075, -0.03734805807471275, -0.03489278629422188, 0.04275763779878616, 0.005514377728104591, -0.030221784487366676, -0.0093070724979043, -0.05736949294805527, -0.013034891337156296, 0.045751869678497314, -0.018005317077040672, 0.030102016404271126, 0.015460220165550709, -0.016398413106799126, 0.006078291684389114, -0.008179244585335255, -0.054295413196086884, -0.005908618681132793, -0.00045007053995504975, -0.0540957972407341, -0.020700126886367798, -0.017965395003557205, -0.02018112689256668, -0.056451261043548584, -0.001296253059990704, 0.05876680091023445, -0.0593656487762928, 0.012735468335449696, 0.019432568922638893, 0.03485286608338356, -0.01949245296418667, -0.02595001459121704, -0.007270994130522013, -0.03231774643063545, 0.0019262895220890641, 0.02644905261695385, 0.046710025519132614, 0.021718164905905724, -0.009706303477287292, 0.04171963781118393, 0.016797643154859543, 0.08623389154672623, -0.017705893144011497, 0.009791139513254166, -0.034074366092681885, 0.02355462871491909, -0.055453184992074966, 0.024233320727944374, -0.0440351776778698, 0.02127901092171669, -0.01720685511827469, 0.00478328624740243, 0.05421556904911995, -0.018085163086652756, -0.009821082465350628, 0.043915409594774246, 0.021957704797387123, -0.013983065262436867, -0.031060170382261276, -0.023235242813825607, -0.03247744217514992, -0.0058736857026815414, -0.011447948403656483, -0.061002492904663086, -0.019682087004184723, 0.06699095666408539, -0.035411786288022995, -0.010908986441791058, -0.019771914929151535, -0.02403370477259159, -0.02018112689256668, -0.00648750364780426, 0.027566898614168167, 0.008378860540688038, 0.0025825253687798977, -0.04327663779258728, -0.008204196579754353, -0.003425900824368, 0.025890128687024117, -0.010180390439927578, -0.01081915944814682, 0.0069615901447832584, 0.04064171388745308, 0.007954677566885948, -0.014412238262593746, 0.030481286346912384, 0.04651040956377983, -0.00011563662701519206, 0.012765410356223583, 0.0075005521066486835, 0.03640986606478691, -0.047907717525959015, 0.03658951818943024, 0.013603795319795609, -0.04423479363322258, 0.06699095666408539, 0.002921871840953827, -0.04303710162639618, 0.09254173934459686, -0.03253732621669769, -0.026109706610441208, -0.008608417585492134, 0.015709739178419113, -0.0011228371877223253, 0.04042213782668114, -0.04191925376653671, -0.05034302547574043, -0.04722902551293373, 0.039982981979846954, 0.003413424827158451, 0.03806667402386665, -0.050782181322574615, 0.0301619004458189, 0.03571121022105217, -0.0464305616915226, 0.02511162869632244, 0.004384055268019438, -0.04120063781738281, 0.0232152808457613, 0.0252513587474823, 0.017117029055953026, 0.010978852398693562, 0.004139526281505823, -0.00163809466175735, -0.06327810883522034, 0.030201824381947517, -0.017695913091301918, -0.014681719243526459, 0.019811837002635002, -0.00507771922275424, -0.0409211739897728, -0.03187859430909157, -0.013613776303827763, 0.015560027211904526, 0.05138102546334267, -0.004533766768872738, -0.030840592458844185, 0.037427905946969986, -0.024852128699421883, -0.03413425013422966, 0.01910320296883583, -0.018065201118588448, 0.048267025500535965, -0.01497116219252348, -0.005943551193922758, -0.008204196579754353, -0.007839898578822613, 0.03870544210076332, -0.03145940229296684, 0.007565427105873823, 0.02441297471523285, -0.0064425901509821415, 0.02211739681661129, -0.020859818905591965, -0.014322411268949509, -0.0350724421441555, -0.03221793845295906, -0.019552337005734444, 0.018374605104327202, 0.016059067100286484, 0.02307555079460144, -0.000033802076359279454, -0.008084427565336227, 0.00871321652084589, -0.008488648571074009, 0.054774489253759384, -0.04311694577336311, 0.003543175058439374, 0.016997259110212326, -0.004880598746240139, 0.009451793506741524, 0.0015058493008837104, 0.0300421305000782, 0.0164582971483469, 0.017506279051303864, 0.028185706585645676, -0.0281258225440979, 0.012096698395907879, -0.028684746474027634, 0.04966433346271515, 0.008109379559755325, 0.04515302553772926, 0.010070601478219032, 0.05565279722213745, 0.01741645112633705, -0.005429541226476431, -0.04531271755695343, 0.032776862382888794, -0.01720685511827469, 0.0178955290466547, -0.003618030808866024, 0.006771955639123917, 0.011777314357459545, 0.006367734167724848, -0.03433386608958244, -0.019163087010383606, -0.053297337144613266, -0.020999548956751823, -0.0001331029925495386, -0.03447359427809715, -0.025630628690123558, 0.04203902184963226, 0.007560436613857746, 0.013613776303827763, 0.012176545336842537, 0.004044708795845509, 0.0505027174949646, -0.021698202937841415, -0.001185840810649097, -0.0027871313504874706, 0.03806667402386665, 0.01491127721965313, 0.005988464690744877, 0.0037951895501464605, 0.01825483702123165, 0.0631982609629631, -0.019642164930701256, -0.010719351470470428, -0.016617989167571068, 0.052698489278554916, 0.055093877017498016, 0.012755430303514004, -0.0008321470813825727, 0.013254468329250813, 0.010799198411405087, -0.017336605116724968, -0.006502474658191204, 0.00806446559727192, 0.046710025519132614, 0.040581829845905304, -0.01130821742117405, 0.003084059339016676, 0.015779605135321617, 0.031479362398386, 0.002391643123701215, -0.01912316307425499, 0.03487282618880272, -0.019522394984960556, -0.0123861413449049, -0.027926206588745117, 0.017626047134399414, 0.03808663412928581, -0.022197242826223373, 0.014601873233914375, 0.054774489253759384, 0.06435603648424149, -0.010185380466282368, -0.020999548956751823, -0.03593079000711441, 0.010370024479925632, -0.024672474712133408, -0.06926657259464264, -0.009786149486899376, -0.024792244657874107, -0.017735837027430534, -0.007161205634474754, -0.02257651276886463, 0.027946168556809425, -0.056091953068971634, 0.013903219252824783, -0.027926206588745117, 0.005893647205084562, 0.03090047836303711, -0.016887471079826355, 0.004995377734303474, -0.013004949316382408, -0.017286701127886772, -0.010110524483025074, -0.0021733136381953955, -0.016418373212218285, 0.006003435701131821, 0.01792547106742859, 0.00907751452177763, -0.000916983641218394, -0.0009662637603469193, -0.005629156716167927, -0.024951936677098274, -0.008443735539913177, -0.020131222903728485, -0.0224966648966074, 0.05689041316509247, 0.014112815260887146, 0.009342004545032978, -0.00878308154642582, -0.029882438480854034, 0.027926206588745117, 0.038505829870700836, -0.03896494209766388, 0.042518097907304764, -0.03519221022725105, -0.03437378630042076, -0.042877405881881714, 0.0509817972779274, -0.008199206553399563, -0.030361516401171684, -0.03932425007224083, -0.004538757260888815, 0.042158789932727814, -0.029303554445505142, 0.014581911265850067, 0.0012257638154551387, 0.028345400467514992, -0.0469096414744854, -0.0008446230203844607, 0.05677064508199692, -0.004486358258873224, -0.025151552632451057, 0.03303636237978935, 0.022636396810412407, -0.000079690245911479, 0.013973084278404713, -0.001687998534180224, 0.0056740702129900455, 0.011867141351103783, 0.04411502182483673, 0.007345850113779306, 0.0030017178505659103, 0.035052478313446045, -0.0031688958406448364, 0.010180390439927578, -0.033096250146627426, -0.06351765245199203, -0.017346587032079697, 0.002946823602542281, -0.016927393153309822, -0.02056039497256279, 0.007610340602695942, 0.02259647287428379, 0.036489710211753845, -0.010175399482250214, -0.010130486451089382, 0.035411786288022995, 0.012266372330486774, 0.003780218306928873, 0.016737759113311768, 0.004860637243837118, -0.009032600559294224, 0.009426841512322426, 0.030461324378848076, 0.049464717507362366, -0.01261569932103157, -0.0102302934974432, 0.021738126873970032, 0.012266372330486774, 0.03351544216275215, 0.008244119584560394, 0.05245894938707352, -0.03656955808401108, -0.025091666728258133, 0.002076001139357686, -0.013543911278247833, -0.011148525401949883, -0.00822415854781866, 0.035172250121831894, -0.006118214689195156, 0.023634474724531174, 0.02874463051557541, 0.02391393668949604, 0.0246525127440691, 0.004161982797086239, 0.011707448400557041, 0.0454724095761776, -0.00835390854626894, -0.03918452188372612, -0.02778647653758526, -0.06731034070253372, -0.026369206607341766, 0.025271320715546608, -0.017017221078276634, 0.0051750317215919495, -0.021778050810098648, 0.03341563418507576, -0.017745817080140114, -0.014891315251588821, -0.02379416674375534, 0.010839121416211128, -0.011078659445047379, 0.007660244591534138, -0.02008131891489029, 0.004229353275150061, 0.013673661276698112, 0.0010461099445819855, -0.009177322499454021, -0.010370024479925632, -0.012056775391101837, -0.00026277508004568517, -0.04255802184343338, -0.025450974702835083, -0.00403223279863596, 0.013144680298864841, -0.02898416854441166, -0.0028195688501000404, -0.042837485671043396, 0.033475518226623535, -0.020979588851332664, 0.01195696834474802, 0.030700862407684326, 0.012286333367228508, 0.0409211739897728, -0.036110442131757736, 0.011418006382882595, -0.05541326105594635, 0.0012132879346609116, 0.028165746480226517, 0.05557295307517052, -0.033595286309719086, 0.03894498199224472, 0.006302859168499708, -0.009177322499454021, -0.03764748200774193, -0.005913608707487583, 0.0009818586986511946, -0.009127418510615826, 0.009721274487674236, -0.004132040776312351, -0.0186141449958086, 0.02762678451836109, 0.02850509248673916, 0.025930052623152733, 0.012406102381646633, -0.008348917588591576, -0.026628706604242325, -0.0081692636013031, 0.002457765629515052, 0.017815683037042618, -0.012316275388002396, -0.03477301821112633, -0.007750071585178375, -0.025331206619739532, 0.03199836239218712, 0.025291282683610916, 0.02694809064269066, -0.016627971082925797, -0.022436780855059624, -0.011437967419624329, -0.020520472899079323, -0.04255802184343338, -0.0014409743016585708, -0.0013823373010382056, 0.017985355108976364, 0.007944696582853794, 0.019282856956124306, -0.010759275406599045, -0.050422873347997665, -0.08028534799814224, 0.01694735512137413, -0.005973493680357933, 0.010599582456052303, -0.03249740228056908, 0.001273172558285296, 0.026728514581918716, 0.01948247104883194, 0.0037328095640987158, 0.012635660357773304, 0.00048562706797383726, -0.04351617768406868, -0.0430770218372345, -0.004895569756627083, 0.027207590639591217, -0.021199164912104607, -0.003922444302588701, 0.008902850560843945, 0.0046460507437586784, -0.026868244633078575, -0.017865587025880814, -0.001613142667338252, -0.03976340591907501, 0.0008009571465663612, -0.04030236601829529, -0.0071512251161038876, -0.013124718330800533, 0.030102016404271126, -0.004374074283987284, -0.0026324293576180935, -0.014581911265850067, 0.021239088848233223, 0.0241734366863966, -0.013224526308476925, 0.020121240988373756, -0.018314721062779427, -0.030121978372335434, -0.023973820731043816, 0.03343559429049492, 0.0024365566205233335, 0.023854050785303116, 0.015789585188031197, -0.00198367889970541, -0.020121240988373756, 0.005773878190666437, 0.03523213416337967, 0.026988014578819275, -0.049943797290325165, 0.03437378630042076, -0.030740786343812943, 0.0186141449958086, 0.026668628677725792, 0.02091970294713974, -0.008099398575723171, 0.04167971387505531, 0.013264449313282967, 0.01947249099612236, 0.020011452957987785, 0.01672777719795704, -0.012575776316225529, -0.03519221022725105, -0.02199762687087059, -0.018055221065878868, -0.004538757260888815, -0.04399525374174118, 0.022037550806999207, 0.00642761867493391, -0.020700126886367798, -0.0612819567322731, 0.008139321580529213, 0.020101279020309448, -0.03040143847465515, 0.029902400448918343, -0.0025475926231592894, -0.00748558109626174, 0.03283674642443657, -0.034593366086483, -0.02848513051867485, 0.01972201094031334, -0.03595075011253357, -0.015110892243683338, 0.01731664314866066, 0.02293582074344158, -0.0038376078009605408, 0.001912565901875496, -0.024552704766392708, -0.02295578084886074, -0.011418006382882595, 0.004316684789955616, -0.04439448565244675, -0.05209964141249657, -0.06303857266902924, -0.003051621839404106, -0.022915858775377274, -0.017506279051303864, 0.05976487696170807, 0.02343485876917839, 0.05273841321468353, 0.03513232618570328, 0.0037477808073163033, -0.02920374646782875, -0.008194215595722198, -0.003847588552162051, 0.038905058056116104, 0.035751134157180786, 0.015470200218260288, -0.008209186606109142, 0.012336237356066704, -0.016298605129122734, -0.01045985147356987, -0.033715058118104935, -0.019622202962636948, 0.026768436655402184, 0.004164478275924921, 0.01550014317035675, 0.04507317766547203, -0.027946168556809425, -0.025271320715546608, 0.005199983716011047, 0.024452896788716316, -0.012565795332193375, 0.030461324378848076, -0.024792244657874107, 0.021977664902806282, 0.014571931213140488, -0.008882889524102211, 0.08639358729124069, 0.051261257380247116, 0.02788628451526165, 0.04004286602139473, 0.034453634172677994, -0.046710025519132614, 0.0060583301819860935, -0.009057552553713322, -0.04024248197674751, 0.013024910353124142, -0.03774728998541832, 0.010015707463026047, -0.019203010946512222, -0.0281258225440979, -0.005384627729654312, 0.04124056175351143, 0.018314721062779427, 0.003825131803750992, -0.021318934857845306, 0.04890579357743263, 0.010240274481475353 ]
The advent of Artificial Intelligence (AI) has impacted all aspects of human life. One of the concrete examples of AI impact is visible in radio positioning. In this article, for the first time we utilize the power of AI by training a Convolutional Neural Network (CNN) using 5G New Radio (NR) fingerprints consisting of beamformed Channel State Information (CSI). By observing CSI, it is possible to characterize the multipath channel between the transmitter and the receiver, and thus provide a good source of spatiotemporal data to find the position of a User Equipment (UE). We collect ray-tracing-based 5G NR CSI from an urban area. The CSI data of the signals from one Base Station (BS) is collected at the reference points with known positions to train a CNN. We evaluate our work by testing: a) the robustness of the trained network for estimating the positions for the new measurements on the same reference points and b) the accuracy of the CNN-based position estimation while the UE is on points other than the reference points. The results prove that our trained network for a specific urban environment can estimate the UE position with a minimum mean error of 0.98 m.
[ 0.005344586446881294, -0.02046545036137104, -0.02074761874973774, -0.04421732574701309, 0.012307487428188324, 0.025909624993801117, -0.0070541901513934135, 0.060251083225011826, -0.033196188509464264, -0.004983577877283096, -0.04049935191869736, -0.055670008063316345, 0.05022583529353142, -0.033528152853250504, -0.02282238006591797, -0.015261948108673096, 0.05819291993975639, -0.007510637864470482, -0.007440095767378807, -0.04561156406998634, 0.028880685567855835, -0.022241447120904922, -0.022772585973143578, -0.023237332701683044, -0.028532125055789948, 0.022108662873506546, -0.0042947567999362946, 0.011402891017496586, -0.09062559902667999, 0.03797644004225731, 0.003937897738069296, 0.01624123565852642, -0.02164391614496708, -0.05862446874380112, -0.04099729284644127, -0.004622569307684898, 0.06217646226286888, 0.03694735839962959, -0.0408313125371933, 0.03429166227579117, 0.07834300398826599, -0.011295003816485405, 0.06390266120433807, 0.0458439365029335, 0.035752296447753906, -0.05978633835911751, -0.03741210699081421, -0.05766177922487259, 0.0007427647360600531, -0.003881879383698106, -0.002645321423187852, -0.06191089376807213, -0.0003693076141644269, -0.012548159807920456, 0.01157717127352953, 0.025295495986938477, 0.059255197644233704, 0.05513887107372284, 0.015253649093210697, -0.0015384359285235405, 0.028000986203551292, 0.015071069821715355, -0.055172067135572433, -0.014083483256399632, 0.0004574849735945463, -0.0159341711550951, -0.013245279900729656, -0.029826777055859566, 0.016788972541689873, -0.002458592876791954, -0.04461567848920822, 0.017693569883704185, -0.01163526438176632, -0.010888350196182728, -0.03429166227579117, -0.014465239830315113, 0.001464781817048788, 0.07396110892295837, 0.04010099545121193, 0.03595147281885147, 0.08458389341831207, 0.027818406000733376, -0.03259865939617157, 0.015137461945414543, 0.09248458594083786, 0.00936962477862835, -0.0009979604510590434, -0.08438471704721451, 0.010000351816415787, 0.03002595342695713, -0.07900693267583847, 0.07196933776140213, -0.0525827631354332, 0.009054260328412056, 0.000023389697162201628, 0.013859408907592297, 0.02365228533744812, -0.008987868204712868, -0.04315504804253578, 0.050192639231681824, 0.001562295714393258, 0.0047304569743573666, 0.0732307955622673, -0.004983577877283096, 0.019419770687818527, -0.03195133060216904, -0.041462041437625885, 0.023735275492072105, 0.01006674487143755, 0.10151394456624985, 0.027702219784259796, -0.047736119478940964, -0.004527130164206028, 0.031619369983673096, -0.026590147987008095, -0.008597812615334988, -0.04747055098414421, -0.0592883937060833, 0.008361290208995342, 0.03714653477072716, -0.012747337110340595, 0.013618736527860165, -0.006452509202063084, 0.026922110468149185, -0.04909716546535492, 0.05513887107372284, 0.024465590715408325, -0.03455723449587822, 0.02209206484258175, -0.029544608667492867, -0.01917080022394657, -0.005236698780208826, 0.014133277349174023, 0.03641622141003609, 0.035154763609170914, 0.03344516083598137, -0.014797201380133629, 0.0019928086549043655, 0.04076492041349411, -0.03694735839962959, 0.05055779591202736, -0.05726342648267746, 0.010863453149795532, -0.003064423333853483, 0.018324296921491623, 0.05188564583659172, -0.0021349298767745495, -0.0029938812367618084, -0.05171966180205345, -0.024200022220611572, -0.11957267671823502, 0.04680662602186203, -0.005327988415956497, 0.01761057786643505, 0.04949551820755005, 0.0027781061362475157, -0.006352920550853014, -0.0329970121383667, -0.04126286506652832, 0.017295215278863907, 0.024863945320248604, -0.0838535726070404, -0.02952801063656807, 0.012622850947082043, 0.008564616553485394, 0.013917502015829086, 0.04743735492229462, 0.022175054997205734, -0.052250802516937256, 0.03551992401480675, 0.02337011694908142, -0.038673561066389084, -0.01569349877536297, 0.01188423577696085, 0.028150368481874466, 0.048234064131975174, 0.009668390266597271, -0.029179450124502182, 0.01194232888519764, 0.011851039715111256, -0.03674818202853203, -0.0099256606772542, 0.015876077115535736, -0.010705770924687386, -0.0057097445242106915, 0.036150649189949036, 0.029345432296395302, -0.0031328904442489147, 0.012788832187652588, -0.03070647455751896, 0.001585118006914854, -0.0016504729865118861, 0.05752899497747421, -0.07296522706747055, 0.02891388162970543, -0.07794465124607086, 0.007531385403126478, 0.02700510062277317, -0.01867285743355751, -0.022440623492002487, -0.004052009899169207, 0.0113199008628726, 0.024117032065987587, -0.006825966294854879, 0.006606041919440031, 0.014963182620704174, 0.02773541584610939, 0.018822239711880684, -0.03837479650974274, -0.0187392495572567, -0.030274923890829086, 0.025245701894164085, -0.008788690902292728, 0.0073114605620503426, -0.005149558652192354, 0.03054049424827099, 0.03684777021408081, -0.036150649189949036, -0.048400044441223145, 0.007406899705529213, 0.026706334203481674, 0.051354505121707916, 0.07203572988510132, -0.0017085663275793195, -0.01621633768081665, -0.05025903135538101, 0.03555312007665634, 0.008755494840443134, -0.031569577753543854, -0.03824200853705406, -0.023901255801320076, -0.013095896691083908, 0.002935787895694375, 0.04053254798054695, 0.06436741352081299, -0.012365580536425114, 0.030225129798054695, -0.027386857196688652, -0.06128016486763954, 0.023502901196479797, -0.04674023389816284, 0.013743222691118717, -0.034026093780994415, 0.009942258708178997, 0.08345521986484528, -0.052317194640636444, -0.05693146586418152, 0.030855858698487282, -0.013344868086278439, -0.004022963345050812, -0.007070788182318211, -0.004489784594625235, 0.007282414007931948, 0.017544185742735863, -0.00042325141839683056, 0.008323944173753262, -0.0006924517801962793, -0.03608425706624985, 0.03824200853705406, 0.05162007361650467, 0.016631290316581726, 0.037113338708877563, -0.01278053317219019, 0.0064027151092886925, -0.0006898583378642797, 0.0009870679350569844, 0.01124520879238844, 0.03717973083257675, -0.03390990570187569, 0.016324225813150406, -0.01459802407771349, -0.020814010873436928, 0.021942680701613426, -0.018324296921491623, 0.011693357490003109, -0.03608425706624985, -0.04524640738964081, 0.006456658709794283, 0.015834582969546318, 0.0014295108849182725, 0.048001691699028015, -0.0006711854366585612, 0.042026374489068985, -0.037046946585178375, -0.03953666239976883, -0.00561845488846302, -0.057794567197561264, 0.02931223437190056, -0.020332666113972664, -0.006942152976989746, -0.024366002529859543, -0.029826777055859566, -0.06569525599479675, 0.02554446831345558, 0.013170587830245495, -0.015286845155060291, -0.03668178990483284, -0.10184591263532639, 0.049395930022001266, -0.014622921124100685, 0.012664346024394035, 0.01795913837850094, 0.01946956478059292, 0.05500608682632446, 0.015734992921352386, 0.018473679199814796, 0.03115462325513363, 0.034192074090242386, -0.012431972660124302, 0.011344797909259796, 0.035088371485471725, 0.009228540584445, -0.030739670619368553, -0.027669023722410202, -0.012348982505500317, 0.023901255801320076, 0.016490207985043526, -0.0010747265769168735, -0.005734641570597887, -0.01423286646604538, 0.0117431515827775, -0.013046102598309517, -0.04338742047548294, 0.04484805092215538, -0.03439125046133995, 0.03611745312809944, 0.02839934080839157, 0.015618806704878807, 0.01560220867395401, -0.04368618503212929, 0.008987868204712868, -0.014938285574316978, -0.03512156754732132, -0.006004360970109701, -0.016598094254732132, 0.031221015378832817, -0.00936132576316595, 0.041462041437625885, -0.000033585205528652295, -0.0070375921204686165, -0.024017443880438805, -0.011427788063883781, -0.07522256672382355, -0.019436368718743324, -0.062442030757665634, -0.030955446884036064, -0.00470970943570137, 0.02006709575653076, -0.011958926916122437, 0.011892534792423248, 0.0008983718580566347, -0.010747266001999378, -0.023453107103705406, -0.009377923794090748, 0.04883159324526787, -0.01082195807248354, -0.0810650959610939, -0.03342856094241142, -0.03306340426206589, -0.015411331318318844, -0.008191159926354885, -0.004921335261315107, -0.015967367216944695, 0.030225129798054695, -0.03824200853705406, 0.012290889397263527, -0.004435840994119644, 0.006485705729573965, -0.00248141516931355, 0.01812511868774891, 0.052649155259132385, 0.022125260904431343, 0.016705982387065887, -0.027685621753335, -0.06167852133512497, 0.00005780156789114699, 0.013021205551922321, -0.01484699547290802, -0.0007578067597933114, 0.04468207061290741, 0.02393445186316967, 0.05171966180205345, 0.010772163048386574, -0.0074566942639648914, 0.002012518933042884, 0.0839199647307396, 0.040565744042396545, -0.0022262195125222206, -0.0198513213545084, 0.06864971667528152, -0.019917713478207588, -0.04989387094974518, -0.037777263671159744, -0.05626754090189934, 0.05009305104613304, -0.022224849089980125, 0.016954952850937843, 0.0076890671625733376, 0.004958680830895901, -0.05962035804986954, -0.030623484402894974, 0.028598517179489136, 0.02471456304192543, 0.04099729284644127, -0.03741210699081421, 0.03030812181532383, -0.012199599295854568, -0.042856279760599136, -0.019834723323583603, -0.03108823113143444, 0.031619369983673096, -0.016863664612174034, -0.023735275492072105, -0.0743594616651535, 0.04109688103199005, 0.02929563634097576, -0.027818406000733376, -0.009203643538057804, 0.023403313010931015, -0.05520526319742203, 0.008672504685819149, 0.030623484402894974, 0.04992707073688507, -0.06997756659984589, -0.004290607292205095, 0.05288153141736984, 0.006946302484720945, 0.009527306072413921, 0.016208039596676826, -0.03221690282225609, -0.03943707421422005, -0.024448992684483528, 0.033793721348047256, 0.017245421186089516, -0.020548440515995026, 0.00162868807092309, 0.042922671884298325, -0.007991982623934746, -0.05148728936910629, -0.0032407778780907393, -0.022971762344241142, 0.011452685110270977, -0.030557092279195786, -0.02410043403506279, -0.04491444304585457, 0.0313040055334568, 0.03439125046133995, -0.012714140117168427, -0.023668883368372917, -0.03535393998026848, -0.03309660032391548, 0.05825931206345558, -0.031685762107372284, -0.015660302713513374, 0.030042551457881927, -0.01597566530108452, -0.0248805433511734, -0.025793438777327538, -0.013236980885267258, -0.056167952716350555, -0.012340683490037918, 0.046275489032268524, -0.028283152729272842, -0.062276050448417664, 0.022905370220541954, -0.00823680404573679, -0.05042501166462898, -0.06662475317716599, 0.02298836037516594, -0.0038466083351522684, 0.0519852340221405, -0.04707219824194908, 0.0290798619389534, 0.009353026747703552, -0.011295003816485405, -0.011602068319916725, -0.030955446884036064, -0.0030955446418374777, -0.015834582969546318, 0.006531350314617157, 0.03137039765715599, 0.022108662873506546, 0.041628021746873856, -0.03070647455751896, 0.0014948658645153046, -0.020814010873436928, -0.005298941861838102, -0.04757013916969299, -0.04089770466089249, -0.03873995319008827, 0.034192074090242386, 0.012680944055318832, -0.023585893213748932, -0.03910510987043381, -0.03502197936177254, -0.04992707073688507, 0.007012695074081421, -0.021328551694750786, -0.004825896117836237, 0.06045025959610939, -0.04786890372633934, -0.04883159324526787, -0.03644941747188568, 0.03956985846161842, -0.02947821654379368, -0.005182755179703236, 0.10337293148040771, 0.031171221286058426, -0.04020058363676071, 0.04713859036564827, 0.041462041437625885, 0.015710096806287766, 0.011062630452215672, 0.008286599069833755, 0.0031494884751737118, 0.025361888110637665, 0.013851109892129898, -0.011344797909259796, -0.009328128769993782, 0.026922110468149185, 0.01673917844891548, -0.019535956904292107, -0.023453107103705406, 0.0548069104552269, -0.004004290327429771, 0.03181854635477066, 0.04053254798054695, -0.010971340350806713, -0.030772866681218147, 0.004888138733804226, -0.02220825105905533, -0.014066885225474834, -0.014307557605206966, -0.05693146586418152, -0.031685762107372284, -0.010456799529492855, -0.004585223738104105, 0.022224849089980125, -0.025710448622703552, -0.0059836129657924175, -0.03332897275686264, 0.026374371722340584, 0.008228505030274391, 0.0048341951332986355, -0.0012500439770519733, 0.028532125055789948, -0.01414987538009882, -0.030225129798054695, 0.005576959811151028, 0.015369835309684277, 0.016249535605311394, -0.030789466574788094, -0.004205542150884867, -0.00575953908264637, -0.013618736527860165, 0.017096037045121193, 0.0068550133146345615, -0.023619089275598526, -0.03518795967102051, 0.02851552702486515, 0.006203537806868553, -0.06805218756198883, -0.01829110085964203, 0.022440623492002487, 0.004664064384996891, -0.02756943553686142, -0.005626753903925419, 0.042358338832855225, -0.02884748950600624, 0.015610507689416409, 0.0032947217114269733, -0.011228610761463642, -0.013153989799320698, -0.014515033923089504, 0.055769599974155426, -0.011427788063883781, 0.03188493847846985, -0.04332102835178375, -0.004444140009582043, 0.020432254299521446, -0.008278300054371357, -0.0043362523429095745, -0.005178605671972036, 0.02745324932038784, 0.040798116475343704, -0.04259071126580238, -0.014921687543392181, -0.02381826564669609, -0.01633252575993538, -0.019984105601906776, -0.00858121458441019, 0.021328551694750786, -0.04992707073688507, -0.004485635086894035, -0.02298836037516594, -0.05005985498428345, 0.020116891711950302, 0.04020058363676071, 0.03956985846161842, -0.07761269062757492, 0.011909132823348045, 0.08624369651079178, 0.014473538845777512, 0.014066885225474834, -0.028830889612436295, -0.01795913837850094, 0.021328551694750786, 0.04126286506652832, -0.002437845105305314, 0.006020959001034498, -0.018822239711880684, -0.014266062527894974, 0.026540353894233704, -0.022672997787594795, 0.00711643323302269, -0.02740345522761345, 0.04883159324526787, -0.00039446409209631383, -0.0017801456851884723, -0.005099764559417963, 0.011668460443615913, -0.03814242035150528, 0.025179309770464897, 0.031669165939092636, -0.04388536140322685, 0.043420616537332535, -0.017411401495337486, 0.012647747993469238, 0.02856532111763954, -0.01794254034757614, -0.0048341951332986355, -0.03830840438604355, -0.0486656129360199, -0.021262159571051598, -0.014946584589779377, -0.003070647595450282, -0.045711152255535126, 0.043984949588775635, 0.02074761874973774, -0.002547807525843382, -0.02185969054698944, 0.019984105601906776, -0.06526371091604233, 0.04454928636550903, -0.0032117313239723444, 0.0106227807700634, -0.03791004791855812, 0.02332032285630703, 0.018938425928354263, 0.052416782826185226, 0.01569349877536297, 0.027934594079852104, -0.026888912543654442, 0.009311530739068985, 0.014515033923089504, -0.031901538372039795, 0.02672293223440647, -0.0005928631871938705, 0.03203432261943817, -0.0173284113407135, 0.024067237973213196, 0.03075626865029335, -0.007983683608472347, 0.006929704453796148, -0.005850828252732754, -0.004101803991943598, 0.02046545036137104, -0.013660231605172157, -0.023751873522996902, 0.0170628409832716, -0.02773541584610939, -0.04298906400799751, -0.003251151880249381, 0.00368477706797421, 0.0436197929084301, -0.030125541612505913, 0.017361607402563095, 0.019054612144827843, -0.03354474902153015, -0.020482048392295837, -0.0031142174266278744, 0.015303443185985088, 0.018656257539987564, -0.01711263507604599, 0.008037627674639225, -0.026241587474942207, 0.03781045973300934, 0.006045856047421694, 0.014448641799390316, -0.018540071323513985, -0.041130077093839645, -0.007693216670304537, 0.033577945083379745, -0.022274643182754517, 0.005477371159940958, 0.018689455464482307, -0.024747759103775024, 0.00841523427516222, 0.035320743918418884, -0.04494763910770416, -0.03478960692882538, 0.01822470873594284, -0.00666828453540802, -0.022623203694820404, -0.013660231605172157, 0.06124696880578995, 0.01727861724793911, 0.012340683490037918, -0.040632136166095734, -0.011137321591377258, 0.02426641434431076, -0.027386857196688652, 0.00008902025001589209, 0.06367029249668121, 0.028366144746541977, 0.0009922548197209835, -0.021942680701613426, 0.001409800723195076, -0.008539719507098198, 0.05195203796029091, 0.016722580417990685, 0.023668883368372917, -0.039901819080114365, -0.06134655699133873, 0.005199353210628033, 0.010307417251169682, 0.017660371959209442, 0.0043196543119847775, -0.028714703395962715, 0.009751380421221256, -0.0039773182943463326, -0.01579308696091175, -0.011477582156658173, 0.01761057786643505, -0.003966944757848978, -0.0059213703498244286, 0.012797131203114986, -0.022009072825312614, 0.008270001038908958, 0.02589302696287632, 0.005601856857538223, -0.05092295631766319, 0.03555312007665634, 0.003176460275426507, -0.009709885343909264, 0.054375357925891876, -0.028731301426887512, -0.010755565017461777, 0.002711713779717684, -0.026092205196619034, 0.06572845578193665, -0.012564757838845253, 0.05842529237270355, -0.0637366846203804, 0.005402680020779371, 0.0075936284847557545, 0.018091922625899315, 0.033196188509464264, -0.01554411556571722, -0.0026141998823732138, 0.023004958406090736, 0.014863593503832817, 0.02599261701107025, 0.0413624532520771, 0.020399058237671852, -0.00300632999278605, -0.02946161851286888, -0.011353096924722195, 0.010639378800988197, -0.01772676594555378, 0.05450814217329025, 0.0003825342282652855, 0.037113338708877563, -0.058358900249004364, 0.0042781587690114975, 0.01478890236467123, 0.010730667971074581, -0.010813659057021141, -0.011452685110270977, -0.061479341238737106, 0.00656869588419795, 0.0034524037037044764, -0.019552554935216904, 0.04288947582244873, -0.03897232562303543, -0.03321278840303421, -0.05082336440682411, -0.011087527498602867, -0.009162148460745811, 0.0159341711550951, 0.012606252916157246, -0.0357854925096035, -0.000005802849500469165, -0.010465098544955254, 0.007103984709829092, 0.019701939076185226, -0.003464852226898074, 0.0036204594653099775, -0.0033922356087714434, -0.02147793397307396, 0.009792875498533249, 0.005552062764763832, -0.017826354131102562, 0.01612504944205284, -0.011253507807850838, 0.017544185742735863, -0.02931223437190056, -0.004937933292239904, 0.0021847242023795843, -0.01917080022394657, 0.023054754361510277, -0.002564405556768179, -0.01302950456738472, 0.030125541612505913, 0.01923719234764576, -0.0017853325698524714, -0.034922391176223755, 0.027752013877034187, 0.0034959737677127123, -0.041694413870573044, -0.011253507807850838, -0.03231649100780487, -0.011502479203045368, 0.02197587676346302, -0.025179309770464897, 0.013693428598344326, 0.05819291993975639, 0.004402644466608763, 0.04508042708039284, 0.0120170209556818, 0.021942680701613426, 0.019884517416357994, 0.001568519975990057, 0.027752013877034187, 0.0010778388241305947, -0.023619089275598526, -0.03236628323793411, 0.02735365927219391, 0.002510461723431945, -0.04036656767129898, -0.006535499822348356, 0.04176080599427223, -0.008938074111938477, 0.005946267396211624, -0.061977285891771317, -0.03415887802839279, -0.03887273743748665, -0.003742870409041643, 0.0049088867381215096, -0.01124520879238844, -0.012564757838845253, 0.03445764631032944, 0.02086380496621132, 0.006274079903960228, 0.009187045507133007, -0.0019201920367777348, 0.014133277349174023, -0.010357211343944073, 0.017925942316651344, -0.06101459637284279, 0.011062630452215672, -0.0006478443974629045, 0.013485952280461788, -0.039005521684885025, 0.03485599905252457, -0.030839260667562485, -0.034524038434028625, -0.04737096279859543, -0.031071633100509644, -0.018473679199814796, 0.001563333091326058, -0.02343650907278061, -0.018091922625899315, 0.06559567153453827, -0.004688961897045374, -0.011419489048421383, 0.015112564899027348, 0.020000703632831573, 0.032183706760406494, -0.022507015615701675, 0.014871892519295216, 0.0464082732796669, -0.01574329286813736, 0.021776700392365456, 0.0503254234790802, -0.014996378682553768, -0.0029108908493071795, -0.03196793049573898, -0.015585610643029213, -0.05865766853094101, 0.004564476199448109, 0.053711432963609695, 0.010855154134333134, 0.008149664849042892, 0.014780603349208832, 0.002759433351457119, -0.02723747305572033, 0.021826494485139847, 0.04215915873646736, 0.03160277381539345, 0.009527306072413921, -0.002535359002649784, -0.009950557723641396, -0.04265710338950157, -0.0007733674719929695, 0.0023590042255818844, -0.022009072825312614, -0.01675577647984028, -0.008763793855905533, 0.021909484639763832, 0.01029081828892231, -0.022075466811656952, -0.009709885343909264, 0.003998065833002329, 0.017411401495337486, -0.006269930396229029, -0.023104548454284668, -0.011212012730538845, 0.0743594616651535, -0.013809614814817905, 0.0934140756726265, -0.0023258079309016466, -0.012855224311351776, -0.026075607165694237, -0.011253507807850838, -0.01043190248310566, 0.019270388409495354, -0.011502479203045368, -0.020930197089910507, 0.018440483137965202, -0.0020239301957190037, 0.028864087536931038, 0.033528152853250504, 0.01907121017575264, 0.06386946886777878, 0.039735838770866394, -0.022324437275528908, -0.04089770466089249, 0.002968984190374613, 0.019253790378570557, -0.04561156406998634, 0.008730597794055939, -0.011286704801023006, -0.010191230103373528, 0.022888772189617157, -0.03052389621734619, 0.02834954485297203, -0.025810036808252335, 0.015054471790790558, 0.0721685141324997, -0.01397559605538845, -0.03309660032391548, -0.0006592556019313633, -0.027984388172626495, -0.031171221286058426, 0.00561845488846302, 0.0018133418634533882, -0.0654296875, 0.01668938435614109, 0.018241306766867638, -0.02478095516562462, 0.01900481805205345, -0.0212455615401268, 0.012963111512362957, 0.0009834370575845242, 0.04278988763689995, 0.0078094033524394035, -0.020897001028060913, -0.0304741021245718, 0.05450814217329025, -0.008045926690101624, -0.04869880899786949, -0.01805872656404972, 0.0011608292115852237, -0.0068550133146345615, 0.030739670619368553, 0.036316629499197006, -0.04461567848920822, 0.0009829184273257852, 0.015635404735803604, 0.008888280019164085, 0.03387670964002609, 0.05965355411171913, 0.0016494356095790863, 0.0374784991145134, -0.017743363976478577, 0.04205957055091858, -0.06745465844869614, -0.047503747045993805, 0.033129796385765076, -0.00872229877859354, 0.005162007641047239, -0.024648170918226242, -0.010589584708213806, -0.017975736409425735, -0.00823680404573679, 0.03125421330332756, -0.01509596686810255, -0.023386714980006218, 0.03372732922434807, -0.02700510062277317, -0.048167672008275986, -0.00998375378549099, 0.04435010999441147, -0.030955446884036064, 0.012307487428188324, 0.02549467422068119, -0.018141716718673706, -0.0029752084519714117, 0.007606077007949352, 0.019419770687818527, -0.017378205433487892, -0.018490277230739594, -0.003645356511697173, -0.013461055234074593, 0.02863171324133873, -0.041130077093839645, 0.04388536140322685, 0.03132060542702675, -0.034524038434028625, -0.0015373985515907407, -0.01789274625480175, 0.02554446831345558, -0.006137145683169365 ]
Ontology Matching (OM) plays an important role in many domains such as bioinformatics and the Semantic Web, and its research is becoming increasingly popular, especially with the application of machine learning (ML) techniques. Although the Ontology Alignment Evaluation Initiative (OAEI) represents an impressive effort for the systematic evaluation of OM systems, it still suffers from several limitations including limited evaluation of subsumption mappings, suboptimal reference mappings, and limited support for the evaluation of ML-based systems. To tackle these limitations, we introduce five new biomedical OM tasks involving ontologies extracted from Mondo and UMLS. Each task includes both equivalence and subsumption matching; the quality of reference mappings is ensured by human curation, ontology pruning, etc.; and a comprehensive evaluation framework is proposed to measure OM performance from various perspectives for both ML-based and non-ML-based OM systems. We report evaluation results for OM systems of different types to demonstrate the usage of these resources, all of which are publicly available as part of the new BioML track at OAEI 2022.
[ -0.013928084634244442, 0.008962854743003845, -0.04284726083278656, 0.004540483001619577, 0.008299612440168858, 0.012874165549874306, -0.002587098628282547, 0.008635776117444038, -0.005215081851929426, 0.02491246536374092, 0.04535485804080963, -0.05796554684638977, 0.03526994585990906, -0.0006848202319815755, -0.0380137674510479, -0.02978229708969593, 0.004013523459434509, 0.0026120836846530437, -0.01960652880370617, -0.025166859850287437, -0.04164797067642212, -0.023458784446120262, -0.005564874038100243, 0.02794702537357807, -0.03312576562166214, -0.010121257044374943, 0.02424013800919056, 0.0009948632214218378, -0.027529090642929077, 0.04375581070780754, 0.022622916847467422, 0.004965230356901884, 0.058910440653562546, 0.023349758237600327, -0.04604535922408104, -0.01071181520819664, 0.05287766084074974, 0.023840375244617462, -0.008517664857208729, 0.03290771320462227, 0.031017927452921867, 0.008776601403951645, -0.024639898911118507, 0.02493063546717167, 0.005805640015751123, -0.04800782725214958, -0.035742390900850296, -0.043283361941576004, -0.010984379798173904, -0.015972323715686798, 0.013882657513022423, -0.01196561474353075, 0.01541810855269432, -0.0516783744096756, -0.03198099136352539, -0.009648810140788555, 0.04757172241806984, 0.045245833694934845, 0.05582136660814285, -0.02325890213251114, 0.013128560036420822, -0.003279868746176362, 0.017743999138474464, 0.004481427371501923, 0.0034547646064311266, -0.04386483505368233, -0.008953768759965897, 0.023131705820560455, 0.03319844976067543, 0.013691862113773823, -0.03975818678736687, -0.0005871509783901274, 0.0069140722043812275, 0.029218995943665504, -0.019333962351083755, -0.032035503536462784, 0.05462208017706871, 0.007954362779855728, -0.02111472189426422, -0.008022503927350044, 0.05324108153581619, 0.006882272660732269, 0.016608310863375664, 0.00904462393373251, 0.06101827695965767, -0.01609952189028263, 0.0051242271438241005, -0.06803228706121445, -0.03314393758773804, -0.08155152946710587, -0.032635148614645004, -0.02042422443628311, -0.027111157774925232, 0.020878499373793602, -0.012210924178361893, 0.01693538762629032, 0.024658070877194405, 0.009171821177005768, -0.045100465416908264, 0.029800469055771828, 0.004924345761537552, -0.02963692881166935, 0.015127371996641159, 0.0163266584277153, 0.028782891109585762, 0.007536429446190596, 0.031635742634534836, 0.008226928301155567, -0.03259880468249321, 0.10546458512544632, -0.0014480029931291938, 0.03670545667409897, -0.04415557160973549, -0.01815284602344036, -0.021841563284397125, -0.010248454287648201, -0.10771778970956802, -0.03834084793925285, -0.04604535922408104, -0.00934898853302002, -0.006464339327067137, 0.07246601581573486, -0.03314393758773804, -0.02825593203306198, -0.07660900801420212, 0.04110284149646759, -0.07493727654218674, 0.005951008293777704, -0.011456826701760292, 0.013491980731487274, -0.007277492433786392, -0.0043701296672225, -0.009930460713803768, -0.033925291150808334, 0.034161511808633804, 0.037650346755981445, 0.03957647457718849, 0.051787398755550385, -0.021296432241797447, -0.016281232237815857, -0.042592864483594894, -0.05120592564344406, -0.025421254336833954, 0.02135094627737999, 0.01610860787332058, -0.041139185428619385, 0.03032742813229561, 0.11520425230264664, -0.021678023040294647, -0.02135094627737999, -0.008167872205376625, -0.03381626307964325, 0.004363315645605326, -0.014064367860555649, 0.02841947227716446, -0.018025649711489677, 0.03906768932938576, 0.015018345788121223, 0.008585806004703045, 0.018171017989516258, 0.025166859850287437, -0.022986337542533875, 0.06363490223884583, 0.09536150097846985, 0.03928574174642563, -0.010648216120898724, 0.011738477274775505, -0.0011055928189307451, -0.039249397814273834, 0.04746269807219505, -0.01756228879094124, -0.015672503039240837, -0.006046405993402004, -0.011138834059238434, -0.028437642380595207, -0.00014068341988604516, 0.03844987228512764, 0.002959604375064373, -0.03312576562166214, 0.01063913106918335, -0.05970996245741844, 0.010384736582636833, 0.023822203278541565, 0.05796554684638977, 0.03245343640446663, -0.01807107776403427, 0.0995044931769371, 0.010230283252894878, 0.010094000026583672, 0.018489010632038116, 0.01588146947324276, -0.00034411365049891174, 0.06632421165704727, 0.0319083072245121, 0.022768285125494003, -0.013455638661980629, -0.06654226779937744, 0.05593039095401764, 0.022150469943881035, -0.03675996884703636, -0.0023554181680083275, -0.049279797822237015, -0.007150295190513134, 0.03641472011804581, 0.02627529203891754, -0.010502847842872143, -0.0002691581903491169, -0.05211447924375534, 0.011347800493240356, -0.04135723412036896, -0.05022469162940979, 0.0029323480557650328, -0.0979781299829483, -0.03230806812644005, 0.02507600374519825, -0.00725932139903307, 0.007318377494812012, -0.02992766536772251, -0.04869832843542099, -0.002691582078114152, 0.006841388065367937, -0.0009863455779850483, 0.04004892334342003, -0.031726595014333725, 0.025185029953718185, 0.010666387155652046, 0.00008105977030936629, -0.039249397814273834, 0.03739595413208008, 0.04324702173471451, 0.03465212881565094, 0.03637837618589401, -0.009866862557828426, -0.06497956067323685, -0.02020617201924324, 0.01454589981585741, 0.04059405252337456, -0.03685082495212555, 0.005305937025696039, 0.0014093895442783833, -0.02674773707985878, -0.020878499373793602, -0.012101897969841957, -0.02880106307566166, 0.05007932335138321, 0.011720306240022182, -0.01830730028450489, 0.024258308112621307, 0.027928853407502174, 0.057238705456256866, 0.08198763430118561, -0.05411329120397568, 0.011729392223060131, 0.01564524695277214, -0.027020303532481194, 0.0030118462163954973, 0.06425271928310394, -0.03739595413208008, -0.04477338865399361, -0.06476150453090668, 0.03943110629916191, 0.0005848795990459621, -0.013410210609436035, 0.06261732429265976, 0.028746549040079117, 0.011765734292566776, 0.049497850239276886, 0.03099975548684597, -0.051314953714609146, 0.037105217576026917, -0.010230283252894878, 0.007904392667114735, -0.026784079149365425, 0.044482652097940445, 0.046227067708969116, -0.06817765533924103, 0.037504978477954865, -0.0266023688018322, 0.03519726172089577, 0.010702729225158691, 0.01515462901443243, -0.004031694494187832, -0.017144355922937393, 0.03303490951657295, 0.0015842856373637915, -0.043646782636642456, 0.05160569027066231, -0.025512108579277992, -0.015854213386774063, -0.01332844141870737, 0.011929272674024105, 0.01869797706604004, -0.06487052887678146, 0.012601600959897041, -0.0018386798910796642, -0.02187790535390377, 0.015145543031394482, 0.0021498585119843483, 0.006259915418922901, -0.022368522360920906, -0.03661460056900978, 0.015572561882436275, 0.027383724227547646, -0.004186148289591074, 0.009012824855744839, -0.0038477128837257624, 0.01732606440782547, 0.05970996245741844, -0.0577474944293499, -0.04095747321844101, -0.017117097973823547, -0.020860327407717705, -0.0307817030698061, -0.017080755904316902, 0.03706887736916542, 0.04193870723247528, 0.010929866693913937, -0.026729566976428032, -0.004283817484974861, -0.00019022784545086324, -0.05127860978245735, -0.020769473165273666, -0.11215151846408844, 0.06668763607740402, -0.00006310169555945322, -0.014863892458379269, -0.011574937961995602, 0.03663277253508568, -0.03964915871620178, 0.037105217576026917, -0.043719466775655746, 0.000058736393839353696, -0.0235496386885643, -0.011574937961995602, 0.018734319135546684, -0.020696789026260376, 0.02780165709555149, 0.006655135191977024, -0.011493168771266937, -0.02111472189426422, -0.02469441294670105, 0.02006080374121666, 0.0010982109233736992, 0.05022469162940979, -0.0058692386373877525, -0.016826361417770386, 0.011157005093991756, -0.03830450400710106, -0.01778942532837391, 0.030182059854269028, 0.0011277387384325266, -0.015436279587447643, -0.024894293397665024, 0.0037182443775236607, -0.03775937482714653, -0.0031163294333964586, -0.052986688911914825, -0.019733725115656853, 0.024494532495737076, 0.03296222537755966, -0.0015161442570388317, -0.09107314050197601, 0.016808191314339638, -0.026711395010352135, -0.09623371064662933, -0.007295663468539715, -0.008494950830936432, 0.0608002245426178, 0.02013348788022995, -0.02027885615825653, -0.008958311751484871, 0.019588356837630272, 0.051642030477523804, 0.02453087456524372, -0.03683265298604965, 0.022241326048970222, 0.04237481206655502, 0.02369500696659088, -0.011593108996748924, 0.046844884753227234, -0.06552468985319138, -0.010648216120898724, -0.031726595014333725, 0.006100919097661972, -0.045936331152915955, 0.049279797822237015, 0.05498550087213516, -0.03321662172675133, -0.08758430182933807, 0.04146626219153404, 0.012774225324392319, 0.029455220326781273, -0.021605340763926506, -0.028237761929631233, 0.02285913936793804, 0.011947443708777428, 0.005601216107606888, 0.05153300613164902, -0.01625397428870201, -0.012274522334337234, 0.021678023040294647, -0.0018307300051674247, -0.007531886920332909, -0.00010540609946474433, 0.04662683233618736, -0.010003144852817059, 0.014173394069075584, 0.0005811886512674391, 0.03319844976067543, 0.009666981175541878, 0.008376838639378548, 0.010112171061336994, 0.007168466225266457, -0.00808610301464796, -0.005596673581749201, 0.051387637853622437, -0.024131111800670624, 0.025203201919794083, -0.03968550264835358, 0.031181465834379196, -0.04848027601838112, -0.01725338026881218, 0.020387882366776466, -0.03997623920440674, -0.030636334791779518, 0.00866757519543171, 0.00934898853302002, 0.00032764615025371313, -0.03147220239043236, -0.0020306112710386515, 0.062253907322883606, 0.032707832753658295, 0.05920117348432541, -0.01694447360932827, 0.01158402394503355, 0.04542754217982292, -0.006446168292313814, -0.00042701890924945474, -0.020151657983660698, -0.02978229708969593, -0.0034593073651194572, 0.022731943055987358, 0.01189293060451746, -0.006346228066831827, -0.07573679834604263, -0.06272635608911514, -0.010012230835855007, 0.01033930853009224, -0.04321068152785301, -0.0012855995446443558, 0.006396198179572821, 0.0395037904381752, -0.07842611521482468, -0.02309536375105381, 0.032635148614645004, 0.032925885170698166, 0.03327113389968872, -0.014409616589546204, 0.023386100307106972, -0.05007932335138321, -0.0326714888215065, 0.03819547966122627, 0.041211869567632675, -0.030654506757855415, -0.016426600515842438, 0.04230212792754173, -0.056330155581235886, -0.032944053411483765, -0.00592375174164772, 0.0163448303937912, -0.021060209721326828, 0.019279450178146362, -0.037032533437013626, 0.004192962311208248, 0.0011811160948127508, 0.011947443708777428, 0.019860921427607536, -0.014836635440587997, 0.0005334897432476282, 0.06301708519458771, 0.007295663468539715, 0.05364084243774414, -0.03209001570940018, 0.0014888877049088478, -0.012846909463405609, 0.01212006900459528, -0.0023486039135605097, 0.046227067708969116, 0.02712932974100113, -0.014527728781104088, -0.054440367966890335, -0.008849285542964935, 0.009403501637279987, 0.007886221632361412, 0.002171436557546258, -0.011075234971940517, -0.016308488324284554, -0.04884369671344757, 0.006714190822094679, -0.015109200961887836, -0.0300003495067358, -0.004647237714380026, 0.005492189899086952, 0.05302302911877632, 0.005069714039564133, 0.0020169829949736595, -0.0014911590842530131, 0.04004892334342003, 0.011792990379035473, -0.004113464150577784, 0.012737883254885674, -0.00448596989735961, 0.03254429250955582, -0.0021226019598543644, 0.012092811986804008, 0.024785267189145088, 0.03525177389383316, -0.05669357627630234, 0.034161511808633804, 0.025257714092731476, -0.021241920068860054, -0.03501554951071739, 0.01641751453280449, 0.03516091778874397, -0.0653793215751648, 0.014164308086037636, 0.017344236373901367, -0.000058381490816827863, 0.05084250867366791, -0.04237481206655502, -0.041975051164627075, 0.02607540972530842, -0.0027074816171079874, -0.003838627366349101, -0.051242269575595856, -0.034016143530607224, -0.0010817433940246701, 0.03174476698040962, -0.01633574441075325, -0.05004298314452171, -0.029346194118261337, 0.0372505858540535, -0.0032117273658514023, -0.010584617964923382, -0.007531886920332909, 0.05574868246912956, 0.074501171708107, -0.02438550628721714, 0.025330398231744766, 0.04702659323811531, 0.002120330696925521, 0.04048502817749977, 0.011956529691815376, -0.015327253378927708, -0.007981619797647, -0.04415557160973549, -0.0015343152917921543, -0.03539714217185974, -0.020024461671710014, 0.0193703044205904, -0.010348394513130188, 0.013092217966914177, 0.03834084793925285, 0.04306531324982643, 0.004313345067203045, -0.06276269257068634, -0.015563476830720901, 0.034452248364686966, -0.012419890612363815, 0.004008980933576822, -0.02667505294084549, 0.01352832280099392, -0.011547681875526905, -0.055966734886169434, -0.017108013853430748, 0.05658454820513725, 0.023277074098587036, -0.028001537546515465, -0.0296187587082386, 0.015554390847682953, 0.000327930087223649, -0.027456408366560936, -0.013546493835747242, -0.0349246971309185, 0.005183282773941755, -0.055058181285858154, -0.04833490774035454, -0.04840759187936783, 0.009367159567773342, 0.0387406088411808, 0.04491875693202019, -0.017580458894371986, -0.027383724227547646, -0.0284921545535326, 0.036669112741947174, 0.02400391362607479, -0.032180871814489365, 0.024058427661657333, 0.028601180762052536, -0.018752489238977432, 0.009358073584735394, 0.015690673142671585, -0.01299227774143219, 0.051242269575595856, 0.012220009230077267, 0.00994863174855709, -0.004470070358365774, -0.0075591434724628925, 0.009403501637279987, 0.0178621094673872, -0.043283361941576004, -0.053822554647922516, 0.02636614628136158, -0.019352134317159653, 0.004626795183867216, -0.004644966218620539, 0.014482300728559494, -0.04063039645552635, 0.016808191314339638, -0.014236992225050926, 0.028673864901065826, -0.05567599833011627, -0.016290316358208656, 0.0017376035684719682, 0.015454450622200966, 0.06178145855665207, 0.036342035979032516, -0.05963727831840515, 0.0021691652946174145, -0.00994863174855709, -0.049497850239276886, 0.020605934783816338, 0.005882867146283388, -0.017734913155436516, 0.028146905824542046, 0.02035154029726982, -0.031726595014333725, 0.006346228066831827, 0.009249048307538033, 0.020496908575296402, 0.0006036185077391565, 0.011275116354227066, -0.011157005093991756, 0.05149666219949722, -0.007327463012188673, 0.06599713861942291, -0.020460566505789757, 0.0010476727038621902, 0.01393717061728239, 0.025439424440264702, 0.004828948061913252, -0.02438550628721714, -0.0005945329903624952, 0.04473704472184181, -0.014945661649107933, 0.0019136352930217981, -0.021369116380810738, -0.01832547038793564, 0.025094175711274147, -0.0008375703473575413, 0.019115909934043884, 0.0216598529368639, 0.01946116052567959, -0.002412202535197139, 0.022005101665854454, 0.02629346214234829, 0.025657476857304573, 0.04491875693202019, -0.002664325525984168, -0.04695390909910202, 0.04731732979416847, -0.04222944378852844, -0.03561519458889961, 0.020260684192180634, -0.015554390847682953, -0.017126183956861496, -0.02743823640048504, 0.04430093988776207, -0.016826361417770386, -0.019933605566620827, -0.03819547966122627, -0.01718069799244404, 0.03997623920440674, -0.018134675920009613, 0.0007120767259038985, -0.010684558190405369, -0.006169060245156288, 0.026693224906921387, 0.013846315443515778, 0.008454065769910812, 0.03546982631087303, -0.006141803693026304, 0.011856588535010815, -0.007227522321045399, 0.03432505205273628, 0.011456826701760292, -0.028601180762052536, -0.03336199000477791, 0.030727190896868706, -0.026620540767908096, -0.032562464475631714, 0.013628263026475906, -0.04749903827905655, 0.020533250644803047, 0.003943110816180706, -0.024403676390647888, 0.021696195006370544, -0.0212782621383667, 0.016980815678834915, 0.0022872767876833677, 0.012510745786130428, 0.030818045139312744, 0.009185449220240116, -0.004224761389195919, 0.009730580262839794, -0.033779922872781754, -0.0016308488557115197, 0.037214245647192, 0.004304259549826384, 0.031581226736307144, -0.03997623920440674, 0.008017961867153645, 0.02712932974100113, -0.02947339043021202, -0.011220603249967098, 0.016808191314339638, 0.021314604207873344, -0.03837718814611435, 0.031181465834379196, -0.014700353145599365, -0.0025643848348408937, -0.015299996361136436, 0.0014888877049088478, 0.030872559174895287, 0.01846175454556942, -0.021459972485899925, 0.017289722338318825, 0.030981585383415222, -0.01041199266910553, 0.0015377223026007414, -0.01264702808111906, 0.002503057708963752, 0.0012946849456056952, -0.00789984967559576, 0.014200650155544281, 0.02825593203306198, 0.03964915871620178, 0.0054104202426970005, -0.048589300364255905, 0.01657196879386902, 0.04339239001274109, -0.03470664471387863, 0.02082398533821106, -0.014863892458379269, 0.007595485541969538, -0.0008012282778508961, 0.02643883042037487, -0.00839046761393547, 0.002282734028995037, -0.028146905824542046, -0.03125414997339249, 0.000329633621731773, 0.03481566905975342, 0.001136256381869316, 0.0052196248434484005, 0.018861515447497368, -0.05563965439796448, 0.021859733387827873, -0.00877205841243267, -0.002952790353447199, 0.013691862113773823, -0.010057657957077026, 0.05135129392147064, -0.06745081394910812, -0.005764755420386791, -0.017807597294449806, -0.03844987228512764, -0.006736904848366976, -0.031726595014333725, 0.045027781277894974, -0.03881329298019409, 0.030981585383415222, 0.02400391362607479, -0.003066359320655465, -0.04193870723247528, -0.016808191314339638, 0.04499144107103348, -0.01708984188735485, 0.018570780754089355, 0.006023692432790995, -0.014037110842764378, -0.019733725115656853, -0.0011595380492508411, -0.0002847739087883383, 0.006468882318586111, -0.00037562899524345994, 0.029800469055771828, -0.003014117479324341, 0.01929762028157711, 0.03819547966122627, 0.04201139137148857, 0.004304259549826384, -0.016844533383846283, 0.04982493072748184, -0.0592738576233387, -0.01846175454556942, -0.03823181986808777, 0.01303770486265421, -0.02409476973116398, 0.018861515447497368, 0.018661634996533394, 0.047135621309280396, 0.007718139793723822, -0.0059918928891420364, 0.05494915693998337, 0.010729986242949963, -0.0023327043745666742, 0.00846769381314516, 0.01770765706896782, 0.02453087456524372, -0.004118006676435471, -0.04895272105932236, 0.0010533512104302645, -0.016126777976751328, 0.020842157304286957, 0.012683370150625706, -0.0038704266771674156, 0.03261697664856911, 0.01447321567684412, -0.03632386401295662, 0.006164517719298601, -0.02096935361623764, -0.04317433759570122, 0.002877834951505065, -0.02044239453971386, 0.07192088663578033, 0.03661460056900978, 0.008067931979894638, 0.04611804336309433, 0.057238705456256866, -0.00789984967559576, -0.024966977536678314, -0.016680995002388954, -0.010457420721650124, 0.013210330158472061, 0.043283361941576004, 0.006187231279909611, 0.0028823777101933956, -0.0071957227773964405, 0.06603347510099411, 0.023585980758070946, -0.008040674962103367, 0.014727610163390636, 0.040157947689294815, -0.011084320954978466, 0.0016524269012734294, 0.04382849484682083, 0.05338644981384277, 0.0034229655284434557, 0.04317433759570122, 0.013582835905253887, 0.018970541656017303, 0.016090435907244682, -0.036887165158987045, 0.00043610442662611604, 0.025730160996317863, 0.0020135759841650724, -0.03209001570940018, 0.0012026942567899823, -0.011293287388980389, -0.013473809696733952, 0.012483488768339157, -0.03986721113324165, 0.07130306959152222, -0.04277457669377327, 0.021696195006370544, -0.016517454758286476, 0.028056051582098007, 0.04488241299986839, 0.013819058425724506, -0.04095747321844101, 0.00024942561867646873, -0.0015774714993312955, -0.01723521016538143, 0.05462208017706871, -0.0016138134524226189, -0.03705070540308952, -0.05069714039564133, -0.030254743993282318, -0.04128454998135567, -0.024785267189145088, -0.001795523683540523, -0.005860153120011091, 0.009548869915306568, 0.03943110629916191, 0.052078135311603546, -0.030418284237384796, 0.018952371552586555, -0.0284921545535326, 0.04993395507335663, 0.006123633123934269, -0.06868644803762436, -0.061272669583559036, -0.03439773619174957, 0.005669357255101204, -0.012774225324392319, 0.00797253381460905, -0.014773037284612656, 0.025312228128314018, 0.012301778420805931, -0.03625117987394333, -0.01733515039086342, 0.014482300728559494, -0.0004207726160530001, -0.0004866425588261336, 0.0027915225364267826, -0.005623930133879185, -0.03705070540308952, -0.011320543475449085, 0.014564070850610733, 0.0193703044205904, -0.016399342566728592, -0.01929762028157711, 0.01398259773850441, -0.035360801964998245, 0.015699759125709534, -0.026020897552371025, -0.01906139776110649, 0.02454904466867447, -0.010248454287648201, 0.020169829949736595, 0.02796519547700882, -0.030363770201802254, 0.0033843519631773233, 0.03281685709953308, -0.007627284619957209, 0.04248384013772011, 0.016844533383846283, -0.024948807433247566, 0.023386100307106972, -0.020478736609220505, 0.005723870359361172, 0.04604535922408104, 0.026111751794815063, -0.020078973844647408, 0.03487018123269081, 0.017416920512914658, 0.03928574174642563, -0.029764126986265182, -0.0033116680569946766, 0.012183667160570621, 0.00706852599978447, 0.038704268634319305, 0.02118740603327751, 0.01695355959236622, 0.040085263550281525, -0.01332844141870737, 0.04066673666238785, -0.044628020375967026, 0.003879512194544077, -0.021478142589330673, 0.0456092543900013, -0.037105217576026917, 0.003252612194046378, -0.04611804336309433, -0.03485201299190521, 0.02743823640048504, -0.023876717314124107, -0.032108187675476074, 0.030636334791779518, 0.027601774781942368, 0.0440465472638607, 0.012538001872599125, 0.03928574174642563, -0.004288360010832548, -0.013228501193225384, 0.007895306684076786, -0.004404200240969658, -0.007595485541969538, 0.04953419417142868, 0.042738232761621475, -0.021078379824757576, -0.004738092888146639, 0.00816332921385765, -0.04066673666238785, -0.02620260789990425, 0.010739071294665337, -0.0003324728459119797, -0.00956704095005989, 0.015708845108747482, 0.03895866125822067, -0.015445364639163017, 0.02491246536374092, -0.004783520475029945, -0.065342977643013, -0.013292099349200726, 0.026184435933828354, -0.037504978477954865, 0.019388476386666298, -0.02013348788022995, -0.027256526052951813, -0.09150924533605576, -0.02736555226147175, 0.02651151455938816, -0.00448596989735961, 0.018598036840558052, 0.03699619323015213, -0.017589544877409935, -0.010312052443623543, 0.018970541656017303, 0.036269351840019226, -0.017644058912992477, 0.003182199550792575, 0.05658454820513725, -0.008399552665650845, 0.03639654815196991, -0.00016510073328390718, 0.05476744845509529, 0.006591536570340395, -0.05309571325778961, -0.005710242316126823, -0.06243561580777168, -0.020551420748233795, -0.03599678725004196 ]
The progression of innovation and technology and ease of inter-connectivity among networks has allowed us to evolve towards one of the promising areas, the Internet of Vehicles. Nowadays, modern vehicles are connected to a range of networks, including intra-vehicle networks and external networks. However, a primary challenge in the automotive industry is to make the vehicle safe and reliable; particularly with the loopholes in the existing traditional protocols, cyber-attacks on the vehicle network are rising drastically. Practically every vehicle uses the universal Controller Area Network (CAN) bus protocol for the communication between electronic control units to transmit key vehicle functionality and messages related to driver safety. The CAN bus system, although its critical significance, lacks the key feature of any protocol authentication and authorization. Resulting in compromises of CAN bus security leads to serious issues to both car and driver safety. This paper discusses the security issues of the CAN bus protocol and proposes an Intrusion Detection System (IDS) that detects known attacks on in-vehicle networks. Multiple Artificial Intelligence (AI) algorithms are employed to provide recognition of known potential cyber-attacks based on messages, timestamps, and data packets traveling through the CAN. The main objective of this paper is to accurately detect cyberattacks by considering time-series features and attack frequency. The majority of the evaluated AI algorithms, when considering attack frequency, correctly identify known attacks with remarkable accuracy of more than 99%. However, these models achieve approximately 92% to 97% accuracy when timestamps are not taken into account. Long Short Term Memory (LSTM), Xgboost, and SVC have proved to the well-performing classifiers.
[ -0.02898750640451908, 0.007548830006271601, -0.013458484783768654, -0.04808245226740837, 0.0418708436191082, 0.013631029985845089, -0.004558055195957422, -0.007563208695501089, -0.04198587313294411, 0.03295603394508362, 0.021012108772993088, -0.07162521779537201, 0.037863973528146744, -0.04175581410527229, -0.03723130747675896, 0.035505861043930054, -0.007759717758744955, -0.04950115084648132, -0.0009298241348005831, -0.05724649131298065, 0.027492118999361992, 0.007783682085573673, -0.03318609297275543, 0.0023521194234490395, 0.006494390312582254, 0.04118066281080246, 0.01166593749076128, 0.024501344189047813, -0.06667893379926682, 0.060390640050172806, 0.000775851949583739, 0.005439950153231621, -0.005046932026743889, -0.027300402522087097, 0.012327359057962894, -0.051264941692352295, 0.008646405301988125, 0.048312511295080185, -0.018174706026911736, 0.019919324666261673, 0.05042139068245888, -0.03416384756565094, 0.004706635605543852, 0.0015564968343824148, 0.004469386767596006, -0.0020381840877234936, -0.07848865538835526, -0.028143955394625664, -0.009432442486286163, 0.03293686360120773, -0.021433884277939796, -0.05218518152832985, 0.021299682557582855, 0.0003229221620131284, -0.005535808391869068, 0.058665189892053604, 0.009039424359798431, 0.021222995594143867, 0.057553235441446304, -0.03034869208931923, 0.005986341740936041, 0.00694492319598794, 0.0024395901709795, 0.006791550200432539, -0.016468431800603867, 0.017446184530854225, 0.015327719040215015, -0.01738866977393627, 0.014196593314409256, -0.028776617720723152, -0.05398731306195259, 0.016679318621754646, -0.013813160359859467, -0.023274360224604607, 0.029466796666383743, -0.023044301196932793, -0.013017538003623486, 0.09363424777984619, 0.015778252854943275, -0.0033095027320086956, 0.012682033702731133, 0.04068220034241676, -0.02152974158525467, -0.025805015116930008, 0.005612494889646769, -0.001174861565232277, -0.018692340701818466, -0.0875760093331337, 0.07016816735267639, -0.06272957473993301, -0.01956464909017086, 0.014666297473013401, -0.012404045090079308, -0.01738866977393627, -0.010113035328686237, -0.01053481176495552, 0.001380357425659895, -0.024367142468690872, -0.026916969567537308, 0.0024383917916566133, 0.02302512899041176, -0.011819310486316681, 0.03493071347475052, 0.027108686044812202, 0.0607740692794323, -0.03193993866443634, -0.05624956637620926, 0.030252834782004356, -0.0011952313361689448, 0.11840399354696274, -0.00860326923429966, 0.016324644908308983, 0.016918964684009552, -0.001967488555237651, -0.04049048572778702, 0.0287191029638052, 0.004744978621602058, -0.0681743174791336, -0.01498262956738472, 0.05260695517063141, -0.020053526386618614, 0.020954592153429985, 0.02521069534122944, -0.00461317365989089, -0.05578944832086563, 0.05176340416073799, 0.037653084844350815, -0.004608381073921919, -0.04628031700849533, -0.004033232107758522, -0.019372932612895966, 0.008171907626092434, 0.02958182618021965, 0.06035229563713074, 0.07074332237243652, 0.02166394330561161, 0.008473861031234264, 0.004567641299217939, 0.0458201989531517, -0.008071256801486015, -0.008814157918095589, -0.02162560075521469, -0.051188256591558456, 0.06514520198106766, 0.0231593307107687, 0.04528339207172394, -0.008890843950212002, 0.03462396562099457, -0.05943205580115318, 0.03090466931462288, -0.02256500907242298, 0.0006644168170168996, 0.0030818397644907236, 0.03197827935218811, 0.03303271904587746, 0.031959109008312225, 0.02448217384517193, -0.03874586522579193, 0.01905660144984722, -0.016257543116807938, 0.03711627796292305, -0.06794425845146179, -0.007088710553944111, 0.00976315326988697, 0.05663299933075905, 0.00669089937582612, -0.004018853418529034, -0.01164676621556282, -0.06771419942378998, 0.049769554287195206, -0.002059752121567726, -0.04156409576535225, 0.0011550907511264086, 0.020302757620811462, 0.014378723688423634, 0.030789639800786972, 0.03669450059533119, 0.004680274520069361, 0.011253747157752514, 0.04773736000061035, -0.0647234246134758, -0.019631750881671906, 0.002540241228416562, 0.016238370910286903, 0.050191331654787064, 0.029025848954916, 0.06733077019453049, 0.020705360919237137, 0.04562848061323166, -0.013429727405309677, -0.019334590062499046, 0.009796703234314919, 0.03500739857554436, -0.022890927270054817, -0.043903034180402756, -0.009111317805945873, -0.00685865106061101, 0.0314989909529686, -0.018203463405370712, -0.017187368124723434, 0.010630669072270393, 0.010410196147859097, 0.005583737511187792, 0.0050133815966546535, 0.023561934009194374, -0.011819310486316681, 0.02131885476410389, 0.014541681855916977, 0.019449619576334953, 0.003244798630475998, -0.07082000374794006, 0.008929187431931496, -0.018730683252215385, 0.027089515700936317, -0.004054800141602755, -0.01196309830993414, 0.026150105521082878, -0.03291768953204155, 0.0023760839831084013, 0.0036809532903134823, 0.05759157985448837, 0.019919324666261673, -0.02114630863070488, -0.02131885476410389, -0.03316692262887955, -0.06641053408384323, -0.007678238209336996, 0.056019507348537445, -0.0518784336745739, -0.03176739439368248, -0.004641931038349867, -0.019957667216658592, 0.02962017059326172, 0.016717663034796715, -0.022334950044751167, -0.0585501603782177, 0.023868680000305176, -0.02260335348546505, -0.0245780311524868, -0.03360787034034729, -0.029811887070536613, -0.009571436792612076, -0.059317026287317276, -0.06491514295339584, -0.001641570939682424, -0.0007093503372743726, -0.011934340000152588, 0.0552142970263958, 0.021759800612926483, 0.02846987172961235, 0.01789671741425991, -0.0011329235276207328, -0.013947362080216408, 0.003654592204838991, -0.017187368124723434, -0.02375365048646927, 0.052683643996715546, -0.04697049781680107, -0.0061349221505224705, 0.015787838026881218, 0.0029524313285946846, -0.0038415156304836273, -0.03117307275533676, 0.049769554287195206, -0.08627234399318695, 0.028565730899572372, 0.05007630214095116, 0.05007630214095116, 0.024347972124814987, -0.039531905204057693, -0.008641612716019154, -0.02291009947657585, -0.04443984106183052, -0.02375365048646927, -0.005737110506743193, 0.019938496872782707, 0.012912093661725521, 0.005344092380255461, -0.030540408566594124, 0.04102729260921478, -0.0066525558941066265, -0.07519114017486572, 0.06947799026966095, -0.035678405314683914, -0.014829256571829319, -0.04900268837809563, -0.0865790843963623, 0.035850949585437775, -0.02277589775621891, -0.0008765030070208013, -0.016458844766020775, -0.010774456895887852, -0.061157502233982086, -0.04225427657365799, 0.021855659782886505, 0.019497549161314964, 0.010055520571768284, -0.021203823387622833, -0.0536038801074028, 0.0007980191730894148, -0.048005763441324234, 0.01806926168501377, 0.028028924018144608, 0.044976647943258286, -0.02162560075521469, -0.048312511295080185, -0.0016859052702784538, 0.0276071485131979, -0.0198234673589468, -0.03780645504593849, -0.04294445365667343, -0.02739626169204712, -0.04183249920606613, -0.03583177924156189, 0.020302757620811462, 0.0011119545670226216, 0.014666297473013401, -0.017522871494293213, -0.002247873693704605, -0.008493032306432724, 0.01831849291920662, 0.006580662447959185, -0.04221593216061592, 0.05475417897105217, -0.032169997692108154, -0.01802133396267891, 0.03385709971189499, -0.01789671741425991, -0.054140686988830566, -0.010410196147859097, -0.010228064842522144, 0.003709710668772459, -0.04091225937008858, 0.00009825461165746674, 0.012567004188895226, -0.025095665827393532, -0.04815913736820221, 0.07085835188627243, -0.03368455544114113, -0.005928826984018087, 0.016803935170173645, -0.018634825944900513, -0.05103488266468048, -0.03907178342342377, -0.04888765886425972, -0.011416706256568432, 0.039493560791015625, 0.03209330886602402, -0.031153900548815727, -0.07515279203653336, 0.0012329755118116736, -0.049807898700237274, -0.03562089055776596, -0.03391461446881294, -0.022411637008190155, 0.00937492772936821, -0.01618085615336895, -0.053105417639017105, -0.01481008529663086, 0.0034532900899648666, 0.0351991131901741, -0.024002881720662117, 0.00780285382643342, 0.0012024207971990108, -0.044631559401750565, 0.0026888211723417044, 0.0040452140383422375, -0.018979914486408234, -0.027645492926239967, 0.011445463635027409, -0.027472946792840958, 0.032687630504369736, 0.011407120153307915, -0.02281424030661583, -0.05253027006983757, -0.025114836171269417, 0.0033957751002162695, -0.03249591588973999, -0.006973681040108204, 0.047929078340530396, -0.00952830072492361, -0.015529021620750427, -0.044669900089502335, 0.03922515735030174, -0.04160244017839432, 0.027108686044812202, 0.02753046341240406, -0.04079722985625267, 0.03364621102809906, 0.07519114017486572, -0.008871672675013542, 0.003251987975090742, -0.01609458401799202, -0.0435962900519371, 0.02384950965642929, -0.037269651889801025, -0.018011746928095818, -0.049807898700237274, 0.029869401827454567, -0.06813597679138184, -0.026265135034918785, 0.06924793124198914, -0.021683115512132645, -0.0007728564087301493, -0.05739986523985863, 0.020782047882676125, -0.04516836255788803, 0.005392021499574184, -0.01892239972949028, -0.01631505787372589, -0.004383114166557789, -0.027894724160432816, 0.01380357425659895, -0.023178502917289734, 0.03652195632457733, 0.02475057542324066, 0.005602909252047539, 0.012768306769430637, 0.020149383693933487, -0.017407841980457306, -0.02375365048646927, 0.02551744133234024, 0.033665385097265244, -0.024903949350118637, -0.002083716681227088, 0.03673284500837326, -0.017235295847058296, -0.007730960380285978, -0.01534689124673605, 0.025325724855065346, 0.0017290414543822408, -0.02590087428689003, -0.000998722156509757, 0.00008058076491579413, -0.013324283994734287, -0.018002161756157875, -0.013985704630613327, -0.028067268431186676, -0.012749134562909603, -0.0070551601238548756, -0.04374966397881508, 0.004522108472883701, -0.028220640495419502, 0.05245358496904373, -0.07450095564126968, -0.03995367884635925, 0.028546558693051338, -0.04440149664878845, -0.02799058146774769, -0.04750730097293854, -0.07791350781917572, 0.021031279116868973, -0.010870315134525299, -0.046855468302965164, 0.017331155017018318, -0.036196038126945496, -0.0157494954764843, -0.05425571650266647, -0.0063937390223145485, 0.019880982115864754, 0.0435962900519371, 0.12047453224658966, -0.038784209638834, 0.017436599358916283, 0.03052123636007309, 0.06863444298505783, -0.06065903976559639, -0.05954708531498909, -0.00241922028362751, -0.0003822344006039202, 0.0932508111000061, -0.038803379982709885, 0.04823582246899605, 0.020839562639594078, -0.0021088793873786926, -0.025709157809615135, 0.00636977469548583, 0.036713674664497375, -0.01823222078382969, 0.0143595514819026, -0.0027750935405492783, 0.047545645385980606, 0.018030919134616852, -0.022852584719657898, -0.009585815481841564, 0.02927508018910885, 0.052338551729917526, -0.019459206610918045, -0.08021410554647446, -0.03527580201625824, 0.01440748106688261, -0.0231593307107687, -0.029600998386740685, -0.03884172439575195, -0.02329353243112564, -0.01496345829218626, -0.025114836171269417, 0.01896074414253235, 0.04405640810728073, 0.10268325358629227, -0.0060342708602547646, -0.015826182439923286, 0.02676359750330448, 0.047545645385980606, -0.036157697439193726, 0.002576187951490283, 0.025824187323451042, -0.03573592007160187, -0.0002702001656871289, 0.003443704219534993, -0.034700650721788406, 0.022929271683096886, -0.005852140486240387, 0.014742984436452389, 0.0025162766687572002, 0.005406400188803673, -0.0032903312239795923, 0.0022071341518312693, 0.0014402688248082995, 0.045014988631010056, 0.00867037009447813, -0.024328799918293953, -0.011531735770404339, 0.014234935864806175, -0.025287382304668427, 0.058051697909832, 0.030847154557704926, -0.009379720315337181, -0.000019190352759324014, -0.02718537300825119, -0.033799584954977036, 0.007635102141648531, -0.027837209403514862, -0.03617686778306961, 0.008708713576197624, 0.008310901932418346, 0.007313977461308241, 0.053143762052059174, -0.039014268666505814, 0.00006122190825408325, -0.04674043878912926, 0.014388308860361576, -0.016200028359889984, -0.015490678139030933, 0.007529658265411854, 0.007903505116701126, 0.020149383693933487, -0.0017566006863489747, 0.026514366269111633, -0.036406926810741425, 0.011474221013486385, 0.0298310574144125, 0.0007578785298392177, 0.007697409950196743, -0.03684787452220917, 0.006408117711544037, 0.018213050439953804, -0.013353041373193264, 0.02551744133234024, -0.014330794103443623, -0.05107322707772255, -0.027453776448965073, 0.03287934884428978, 0.016468431800603867, 0.01845269463956356, 0.0016619408270344138, -0.004181812051683664, 0.04305948317050934, -0.020782047882676125, 0.015145588666200638, -0.025325724855065346, -0.01230818685144186, -0.06184768304228783, -0.05264529958367348, 0.014464995823800564, 0.003963734954595566, 0.044976647943258286, -0.04072054475545883, -0.0001406418887199834, 0.005430364515632391, -0.04397972300648689, 0.012011026963591576, -0.009902147576212883, 0.040260426700115204, -0.007807646878063679, 0.018030919134616852, -0.0326109454035759, -0.024635545909404755, -0.015308547765016556, 0.000409494066843763, -0.013669373467564583, -0.018606068566441536, -0.024252112954854965, -0.0038846516981720924, -0.01909494400024414, -0.0030746504198759794, 0.03861166536808014, -0.001337221241556108, -0.008066464215517044, -0.006341016851365566, 0.012423217296600342, 0.09509129077196121, 0.028412356972694397, 0.05218518152832985, 0.020571161061525345, 0.024367142468690872, -0.015289375558495522, 0.006609419826418161, 0.006532733328640461, -0.007889126427471638, 0.013602272607386112, -0.0507664792239666, 0.04789073392748833, -0.01277789194136858, 0.05624956637620926, 0.013458484783768654, 0.05732317641377449, 0.010429367423057556, 0.00819587241858244, 0.016717663034796715, 0.014091148972511292, 0.010525225661695004, 0.013055880554020405, 0.017311982810497284, 0.023101815953850746, 0.005607702303677797, -0.01338179875165224, 0.02787555195391178, -0.009509129449725151, -0.03677118942141533, -0.0028637624345719814, -0.022526666522026062, -0.00817670114338398, -0.028872476890683174, -0.03976196423172951, -0.01777210272848606, -0.02302512899041176, -0.01196309830993414, -0.024424659088253975, 0.038170717656612396, 0.012892922386527061, 0.011426292359828949, -0.03422136232256889, 0.05828176066279411, -0.011253747157752514, 0.018098019063472748, -0.04808245226740837, -0.036886218935251236, 0.02718537300825119, 0.08228464424610138, 0.03293686360120773, 0.024520516395568848, 0.01215481385588646, 0.019593406468629837, 0.0049319020472466946, -0.019152458757162094, 0.022162405773997307, 0.006326638162136078, 0.02530655264854431, 0.005449536256492138, 0.012058955617249012, 0.0067340354435145855, -0.00504213897511363, 0.0030267213005572557, 0.005564565770328045, 0.01393777597695589, 0.044669900089502335, -0.021644771099090576, 0.00693533755838871, 0.02444382943212986, -0.034489765763282776, 0.0036809532903134823, -0.02705117128789425, 0.01810760609805584, 0.018481452018022537, -0.019880982115864754, 0.0030267213005572557, 0.07239207625389099, 0.023657793179154396, -0.049079377204179764, -0.00504213897511363, 0.005483086686581373, -0.05448577553033829, 0.04559013992547989, -0.037518881261348724, -0.004203380085527897, 0.002830212004482746, 0.007764510810375214, -0.022124063223600388, -0.02302512899041176, 0.0025618092622607946, -0.009298240765929222, 0.027070343494415283, 0.011905582621693611, 0.015203103423118591, -0.0003172305878251791, -0.028795789927244186, 0.011742624454200268, 0.001971083227545023, 0.005248234141618013, 0.01395694725215435, -0.024156255647540092, -0.03874586522579193, -0.020532816648483276, -0.0458201989531517, -0.008071256801486015, 0.020015183836221695, -0.02611176110804081, -0.008814157918095589, -0.03274514526128769, -0.028834134340286255, 0.04121900722384453, -0.00935575645416975, 0.018653996288776398, 0.08052085340023041, 0.027204545214772224, 0.05651796981692314, 0.012940851040184498, -0.057514894753694534, 0.007534451317042112, 0.052338551729917526, -0.024980636313557625, 0.02513400837779045, -0.0209354218095541, -0.017484527081251144, -0.0023401372600346804, -0.022967614233493805, -0.01918121799826622, -0.05364222452044487, 0.003549148328602314, 0.05954708531498909, -0.039033442735672, -0.015040144324302673, 0.020283585414290428, 0.022104891017079353, 0.003529976587742567, 0.06970804929733276, 0.012451974675059319, 0.0008135961252264678, 0.0007279228884726763, 0.018596481531858444, -0.04593522846698761, 0.00865119881927967, 0.02221992053091526, -0.0061349221505224705, 0.001242561382241547, -0.00717019010335207, 0.01643967442214489, -0.02714703045785427, 0.011991855688393116, 0.02337021939456463, -0.007059953175485134, 0.028354842215776443, -0.046088602393865585, -0.03912929818034172, 0.004016456659883261, 0.055252641439437866, -0.018117191269993782, -0.009015459567308426, 0.00798019114881754, -0.01164676621556282, 0.031115557998418808, -0.0447082445025444, 0.0017134645022451878, 0.06713905185461044, -0.048274166882038116, 0.013841917738318443, -0.009489957243204117, 0.034566450864076614, 0.059355370700359344, 0.003213644726201892, 0.04666374996304512, 0.027089515700936317, 0.00346287596039474, -0.01055398304015398, -0.030559580773115158, 0.07898712158203125, -0.019765952602028847, 0.022584181278944016, -0.033454496413469315, -0.04524505138397217, -0.0035994737409055233, -0.009686466306447983, 0.024942291900515556, -0.029505141079425812, -0.018903227522969246, -0.0306937824934721, -0.032265856862068176, 0.007328356150537729, 0.04194752871990204, 0.00717019010335207, 0.005626873578876257, 0.05398731306195259, -0.004407078959047794, 0.03169070556759834, -0.0054878792725503445, -0.030214490368962288, 0.012384873814880848, 0.015174346044659615, 0.006791550200432539, 0.05325879156589508, -0.019420862197875977, -0.016468431800603867, -0.01814594864845276, 0.04478492960333824, -0.040260426700115204, -0.03318609297275543, -0.02423294261097908, -0.04635700583457947, -0.01267244853079319, 0.01781044527888298, -0.011292090639472008, -0.016257543116807938, 0.048312511295080185, -0.0024683475494384766, 0.01944003440439701, -0.012461560778319836, 0.0016451656119897962, -0.0028206261340528727, -0.022239092737436295, -0.005622080992907286, -0.0027774900663644075, -0.02705117128789425, -0.015490678139030933, -0.03374207019805908, -0.025881702080368996, 0.05889525264501572, 0.0558277890086174, 0.031192244961857796, 0.0026169277261942625, 0.02753046341240406, 0.02200903184711933, 0.022411637008190155, 0.027798864990472794, -0.04344291612505913, 0.03312857821583748, -0.009921318851411343, -0.0018644410884007812, 0.028968334197998047, -0.012432802468538284, 0.029907744377851486, 0.0016044258372858167, 0.037902314215898514, 0.014973044395446777, -0.021683115512132645, -0.008775814436376095, -0.040528830140829086, -0.04493830353021622, 0.038765039294958115, -0.016621803864836693, -0.004423853941261768, 0.003944563213735819, -0.00999800581485033, 0.005377642344683409, -0.03238088637590408, 0.07285220175981522, 0.015298961661756039, 0.02256500907242298, 0.006561490707099438, -0.030962184071540833, -0.0007518873899243772, 0.016343815252184868, -0.009595401585102081, 0.01905660144984722, 0.01093741599470377, 0.03794065862894058, -0.0061349221505224705, -0.02697448432445526, -0.02333187498152256, -0.06437833607196808, -0.011100374162197113, -0.004534090869128704, -0.0167368333786726, 0.03832409158349037, -0.020609503611922264, -0.04923274740576744, 0.016257543116807938, 0.06219277158379555, -0.02478891983628273, -0.01513600256294012, -0.030329519882798195, -0.03301354870200157, -0.0013072656001895666, 0.006355395540595055, 0.04440149664878845, -0.0326109454035759, -0.004759357310831547, 0.0021256546024233103, -0.014081562869250774, -0.02628430724143982, -0.0023868680000305176, 0.021012108772993088, -0.022699210792779922, -0.003510805079713464, 0.04290610924363136, -0.008032913319766521, -0.046126943081617355, 0.009456407278776169, -0.041334036737680435, 0.0002442885306663811, 0.00959060899913311, -0.03514159843325615, -0.03330112248659134, 0.023216845467686653, -0.0070120240561664104, -0.009892561472952366, 0.028699932619929314, -0.010352680459618568, -0.005411192774772644, -0.02020689845085144, -0.04973120987415314, -0.019449619576334953, -0.03740385174751282, -0.036023493856191635, 0.06625715643167496, 0.008406760171055794, -0.017407841980457306, -0.047200556844472885, 0.03617686778306961, -0.019497549161314964, 0.05072813481092453, 0.018356837332248688, -0.043174512684345245, 0.0099117336794734, -0.025153180584311485, -0.004114711191505194, -0.011407120153307915, -0.03539083153009415, -0.003975716885179281, -0.009743981994688511, -0.017014821991324425, 0.023868680000305176, 0.014436238445341587, 0.021989861503243446, 0.024693060666322708, -0.004402285907417536, -0.030789639800786972, -0.005037345923483372, -0.058588504791259766, -0.018165120854973793, -0.05130328610539436, -0.03882255405187607, 0.023178502917289734, 0.022526666522026062, -0.014110320247709751, -0.006729242391884327, 0.040528830140829086, -0.015308547765016556, 0.022795069962739944, 0.019842637702822685, -0.04332788661122322, -0.009499543346464634, 0.016640976071357727, -0.029524311423301697, -0.01534689124673605, -0.02037944458425045, -0.039148472249507904, -0.04654872044920921, -0.013276354409754276, 0.052376896142959595, 0.018941571936011314, 0.01751328445971012, -0.00452690152451396, -0.01609458401799202, -0.044248126447200775, 0.031096385791897774, 0.010007591918110847, -0.018184293061494827, -0.02388785220682621, 0.011330434121191502, -0.02478891983628273, -0.03429804742336273, -0.01810760609805584, -0.0029883780516684055, -0.010045934468507767, -0.007539243903011084, 0.014129492454230785, -0.03723130747675896, -0.017158610746264458, -0.01652594655752182, 0.0424843356013298, -0.02731957472860813, -0.03447059169411659, -0.03822823241353035, -0.04148741066455841, -0.000682390236761421, 0.02187483198940754, 0.022296607494354248, -0.02555578388273716, 0.04079722985625267, -0.02705117128789425, 0.021012108772993088, 0.005703560076653957, 0.03241922706365585, -0.030425379052758217, 0.006168472580611706, 0.010323923081159592, 0.0012713187607005239, 0.009370135143399239, -0.00024563653278164566, -0.019152458757162094, 0.02927508018910885, 0.0036378169897943735, 0.04049048572778702, -0.018385594710707664, 0.009758360683918, 0.023983711376786232, -0.025785844773054123, -0.01725446805357933, 0.011368777602910995, -0.0182801503688097, -0.06541360914707184, 0.0005284181097522378, 0.008675162680447102, 0.003331070998683572, -0.005904862657189369, -0.011800139211118221, 0.0268019400537014, 0.005425571464002132, -0.01553860679268837, 0.01156049408018589, 0.025996731594204903, -0.02701282873749733, 0.01914287358522415 ]
Personalized recommendation models (RecSys) are one of the most popular machine learning workload serviced by hyperscalers. A critical challenge of training RecSys is its high memory capacity requirements, reaching hundreds of GBs to TBs of model size. In RecSys, the so-called embedding layers account for the majority of memory usage so current systems employ a hybrid CPU-GPU design to have the large CPU memory store the memory hungry embedding layers. Unfortunately, training embeddings involve several memory bandwidth intensive operations which is at odds with the slow CPU memory, causing performance overheads. Prior work proposed to cache frequently accessed embeddings inside GPU memory as means to filter down the embedding layer traffic to CPU memory, but this paper observes several limitations with such cache design. In this work, we present a fundamentally different approach in designing embedding caches for RecSys. Our proposed ScratchPipe architecture utilizes unique properties of RecSys training to develop an embedding cache that not only sees the past but also the "future" cache accesses. ScratchPipe exploits such property to guarantee that the active working set of embedding layers can "always" be captured inside our proposed cache design, enabling embedding layer training to be conducted at GPU memory speed.
[ -0.021274391561746597, -0.002058240585029125, -0.03227056935429573, -0.002805725671350956, 0.02401398867368698, 0.005120213143527508, -0.013868031091988087, 0.019914038479328156, -0.04099949076771736, -0.00653724605217576, 0.010712770745158195, 0.021123241633176804, -0.001752397627569735, -0.037598613649606705, 0.05116434395313263, 0.04787682741880417, 0.024391863495111465, -0.011959759518504143, -0.023220449686050415, -0.03557698056101799, 0.039487991482019424, -0.03956356644630432, 0.015625152736902237, -0.04969063028693199, 0.050786469131708145, 0.03587928041815758, -0.031949374824762344, -0.007127676624804735, -0.052486907690763474, -0.010778899304568768, 0.03708847984671593, 0.037334099411964417, -0.009583867155015469, -0.02592225931584835, -0.060724593698978424, -0.045836299657821655, 0.0732322707772255, 0.06083795800805092, 0.00043721377733163536, -0.012809979729354382, 0.004584102425724268, 0.01606915518641472, -0.03319636359810829, 0.030305616557598114, 0.025582171976566315, 0.006527799181640148, 0.00846913456916809, -0.015606258064508438, -0.007354401983320713, -0.01907326653599739, 0.02618677355349064, -0.048179127275943756, 0.037579718977212906, -0.051504433155059814, -0.0635208711028099, 0.018978796899318695, 0.003034812631085515, 0.02849181368947029, 0.044664885848760605, 0.00956025067716837, -0.06552360951900482, 0.026507966220378876, -0.026262348517775536, -0.048897091299295425, -0.01764678582549095, -0.01748618856072426, -0.01048604492098093, 0.022219080477952957, -0.0029663227032870054, -0.01601247489452362, -0.06711068749427795, -0.04995514079928398, 0.07644421607255936, -0.02144443430006504, -0.02902083843946457, 0.026696905493736267, 0.09144587069749832, 0.031193623319268227, 0.04035710543394089, -0.02943650260567665, 0.02450522594153881, 0.04859479144215584, 0.020688684657216072, 0.05207124352455139, 0.065863698720932, -0.05626566335558891, 0.01250767894089222, -0.06004441902041435, 0.021860098466277122, -0.010911155492067337, -0.04780125245451927, 0.009739740751683712, 0.03204384446144104, -0.027282612398266792, -0.06408768892288208, 0.05770159140229225, -0.03440556675195694, -0.015275617130100727, -0.03374428302049637, 0.05872185528278351, -0.03960135206580162, -0.030003314837813377, 0.008577774278819561, -0.003134005004540086, 0.01790185272693634, -0.040168166160583496, 0.011147327721118927, 0.01929999142885208, 0.016645416617393494, 0.07980730384588242, -0.010996176861226559, -0.04814133793115616, 0.01888432912528515, -0.010760004632174969, -0.015606258064508438, 0.02025412768125534, -0.04432479664683342, -0.024845315143465996, 0.001460724975913763, -0.03990365192294121, 0.06767750531435013, -0.0007734639220871031, -0.017788490280508995, 0.006527799181640148, -0.025808896869421005, 0.08094093203544617, 0.00026908869040198624, -0.01766568049788475, 0.018922116607427597, 0.015086679719388485, 0.04825470224022865, 0.01237542275339365, -0.030513446778059006, -0.015152808278799057, 0.019385013729333878, 0.03610600531101227, 0.02735818736255169, 0.05158000811934471, -0.018071895465254784, -0.03933684155344963, -0.03472675755620003, -0.0007764160982333124, -0.05226018279790878, -0.05369611084461212, 0.0200651902705431, 0.014774932526051998, -0.010042041540145874, 0.033800963312387466, -0.039714716374874115, 0.03701290488243103, -0.0635586604475975, 0.04980399087071419, 0.02242691069841385, 0.07678430527448654, -0.0018338770605623722, -0.01835530251264572, -0.025865579023957253, -0.0014784379163756967, 0.002897832775488496, 0.020650897175073624, 0.019989613443613052, -0.053393810987472534, 0.010656089521944523, 0.04549621045589447, 0.0059279222041368484, 0.021085454151034355, 0.040168166160583496, -0.006131030153483152, -0.06042229384183884, 0.01865760236978531, -0.00677341828122735, 0.0401303805410862, -0.0013509049313142896, 0.03706958889961243, 0.0016213221242651343, 0.01812857761979103, 0.06518352776765823, -0.03200605511665344, -0.0566057525575161, 0.003828351153060794, -0.007699213456362486, 0.03892117738723755, 0.038316577672958374, -0.012876108288764954, 0.01955505833029747, 0.04901045188307762, 0.02288036234676838, 0.015492895618081093, 0.01271551102399826, -0.021387754008173943, 0.051995668560266495, -0.0001710772339720279, 0.02473195269703865, -0.005120213143527508, -0.006400266196578741, -0.03633273020386696, -0.0377497635781765, -0.021047666668891907, 0.0271125677973032, 0.01179916225373745, -0.05369611084461212, -0.07958058267831802, 0.010665535926818848, -0.02943650260567665, 0.03425441309809685, 0.002118464559316635, 0.04768788814544678, 0.01677767187356949, 0.02431628853082657, -0.06964245438575745, 0.0028576834592968225, 0.013594071380794048, -0.0400548055768013, -0.05158000811934471, 0.02875632606446743, -0.022313548251986504, -0.024146245792508125, 0.0016354924300685525, -0.05547212436795235, -0.022729212418198586, -0.019403906539082527, 0.00169453548733145, 0.06790422648191452, -0.02072647213935852, 0.02779274433851242, -0.04307780787348747, -0.002886024070903659, 0.036691710352897644, -0.008209344930946827, -0.009139863774180412, 0.02401398867368698, 0.021085454151034355, -0.003920458257198334, -0.049350541085004807, 0.01345236785709858, -0.04746116325259209, -0.0329885333776474, -0.045118335634469986, -0.03085353597998619, -0.001349724130704999, 0.007193805184215307, 0.030116677284240723, -0.018818199634552002, -0.005687026306986809, 0.02495867758989334, -0.0006984792416915298, -0.005039914511144161, 0.042586568742990494, 0.023995094001293182, -0.029342032968997955, -0.008549433201551437, 0.0008756084134802222, 0.007930662482976913, -0.00861083809286356, -0.00767087284475565, 0.07349678874015808, 0.05721035227179527, -0.07995845377445221, 0.007812576368451118, -0.02735818736255169, 0.01167635340243578, -0.028624068945646286, -0.02072647213935852, 0.011950313113629818, -0.039261266589164734, -0.0007699213456362486, 0.05320487171411514, 0.006480564828962088, 0.025808896869421005, 0.007047377992421389, 0.02526097744703293, -0.032686229795217514, 0.001757121062837541, -0.0728921890258789, 0.016635969281196594, -0.04077276587486267, -0.02544991485774517, -0.009645272046327591, 0.046327538788318634, -0.005559493321925402, 0.010797793045639992, -0.018676497042179108, -0.011015070602297783, 0.021028771996498108, -0.04462709650397301, -0.03979029133915901, -0.010504938662052155, -0.011166221462190151, 0.002805725671350956, 0.017079973593354225, -0.025997834280133247, -0.0306079164147377, -0.014897742308676243, 0.03888338804244995, 0.04156630486249924, -0.01463322900235653, -0.012564360164105892, 0.018780412152409554, -0.011289030313491821, -0.07602855563163757, -0.02733929269015789, 0.030475659295916557, 0.006853716913610697, -0.0035614767111837864, -0.03567144647240639, 0.00482499785721302, -0.05210903286933899, 0.06329414993524551, -0.03043787181377411, -0.0353124663233757, 0.07274103164672852, 0.03204384446144104, -0.0016862694174051285, -0.02265363745391369, 0.028340663760900497, 0.038297683000564575, 0.024089563637971878, 0.03937462717294693, -0.02526097744703293, -0.043040018528699875, -0.007585851009935141, -0.019233863800764084, -0.10860142111778259, 0.01907326653599739, 0.04077276587486267, -0.0027655763551592827, 0.002836428117007017, 0.07466819882392883, -0.004624251741915941, 0.009475228376686573, -0.014113650657236576, -0.033630918711423874, -0.04810355231165886, 0.0111945616081357, 0.010042041540145874, -0.02331491932272911, -0.01860092207789421, 0.050295230001211166, -0.03510463610291481, -0.0018421431304886937, -0.015662940219044685, 0.0006825376185588539, 0.015700727701187134, 0.03606821596622467, 0.016106942668557167, -0.015152808278799057, -0.020594215020537376, 0.014812720008194447, -0.012252612970769405, -0.03370649367570877, 0.0012611595448106527, -0.0013638944365084171, 0.005384725984185934, 0.04455152153968811, 0.06408768892288208, 0.017287803813815117, 0.008284920826554298, 0.02218129299581051, 0.013433474116027355, -0.00771810719743371, 0.030041102319955826, -0.016815459355711937, -0.030456766486167908, 0.06881113350391388, -0.002682916121557355, 0.03812763839960098, -0.015247276984155178, -0.01717444136738777, 0.04024374112486839, 0.012904448434710503, -0.0112040089443326, 0.010410469956696033, -0.014756038784980774, -0.03040008433163166, -0.022766999900341034, -0.002287327777594328, 0.020443065091967583, -0.028113937005400658, -0.014784378930926323, 0.04885930195450783, -0.00653724605217576, -0.009673613123595715, -0.001530395820736885, 0.008341602049767971, 0.006584480870515108, 0.012753298506140709, 0.024184033274650574, 0.021992353722453117, 0.0002631843963172287, 0.02048085257411003, 0.021992353722453117, -0.07183413207530975, 0.0017594827804714441, -0.06635493785142899, -0.009191821329295635, -0.002914364915341139, 0.0659392774105072, -0.0005054085049778223, 0.003592178924009204, 0.0003194228920619935, -0.04761231318116188, 0.011459074914455414, -0.0708894431591034, 0.061858221888542175, -0.019762888550758362, 0.0020641449373215437, 0.031477030366659164, -0.0659770667552948, 0.025563277304172516, -0.012545466423034668, 0.02331491932272911, -0.0352935716509819, 0.01837419718503952, 0.017760148271918297, 0.028435131534934044, 0.031703755259513855, -0.02450522594153881, -0.02259695529937744, 0.040659405291080475, -0.014434844255447388, -0.035463616251945496, 0.004461292643100023, 0.028680751100182533, 0.021104346960783005, 0.016173072159290314, 0.019271651282906532, 0.0013083938974887133, 0.017146101221442223, -0.014519866555929184, -0.05233575776219368, -0.012177038006484509, 0.005285533610731363, 0.016352562233805656, -0.045874085277318954, -0.020405277609825134, 0.017533423379063606, -0.01095838937908411, 0.02973880246281624, -0.04557178542017937, -0.037825338542461395, -0.013631858862936497, -0.05441407486796379, -0.006149923894554377, 0.004744699224829674, -0.004817912820726633, 0.016626521944999695, -0.00430541904643178, -0.042095333337783813, 0.030948003754019737, -0.06155591830611229, -0.08215013891458511, 0.02357943169772625, -0.09303294867277145, -0.023296024650335312, 0.019876250997185707, -0.032157205045223236, -0.006612821482121944, -0.003722073743119836, -0.004022012464702129, -0.03512352705001831, -0.013471261598169804, 0.016116390004754066, 0.0018693029414862394, -0.02737708017230034, -0.007477211765944958, 0.05018186569213867, -0.05732371285557747, -0.052184607833623886, 0.009541356936097145, -0.0024278501514345407, -0.016333669424057007, 0.00677341828122735, 0.027754956856369972, 0.036880649626255035, 0.02971990779042244, -0.02169005386531353, 0.04311559721827507, -0.03903454169631004, 0.0011306743836030364, 0.017155548557639122, 0.00814794097095728, 0.03516131639480591, -0.0008460868848487735, 0.027301505208015442, -0.019706208258867264, 0.02425960823893547, -0.015644045546650887, 0.013046151958405972, 0.03353645280003548, -0.04126400500535965, -0.010684429667890072, 0.023995094001293182, -0.010325448587536812, -0.020102977752685547, -0.044664885848760605, -0.018213599920272827, -0.017542870715260506, -0.03211941942572594, 0.031458135694265366, 0.039941441267728806, 0.010419917292892933, 0.019479481503367424, -0.025997834280133247, -0.0188937745988369, -0.02169005386531353, 0.02289925515651703, 0.0063766492530703545, 0.010164851322770119, -0.04746116325259209, -0.005498088430613279, 0.015993580222129822, 0.035236891359090805, -0.008672242984175682, -0.006556140258908272, -0.009106799960136414, 0.00006406170723494142, -0.009125693701207638, -0.05773937702178955, 0.017760148271918297, 0.035350251942873, -0.02660243585705757, 0.0424732081592083, -0.06537245959043503, 0.052184607833623886, -0.09000994265079498, 0.04062161594629288, 0.01435926929116249, -0.022937042638659477, 0.08547543734312057, -0.01670209690928459, -0.01238487008959055, 0.035520296543836594, 0.012706063687801361, -0.035747021436691284, 0.0033512834925204515, -0.01143073383718729, 0.059250880032777786, 0.012432103976607323, -0.013055598363280296, -0.03251618891954422, -0.008676966652274132, 0.02758491225540638, 0.01885598711669445, 0.03659724444150925, -0.047498952597379684, 0.029776589944958687, 0.047536738216876984, -0.06253839284181595, -0.010816686786711216, 0.009054841473698616, -0.026810267940163612, -0.023466069251298904, 0.0200462955981493, -0.01086392067372799, 0.007387466263025999, -0.027188142761588097, -0.02499646507203579, -0.03155260533094406, -0.007467764895409346, 0.002841151552274823, -0.028831901028752327, 0.013348452746868134, -0.002417222363874316, -0.02076425962150097, -0.007241039536893368, -0.04024374112486839, 0.0706249326467514, 0.03179822489619255, 0.014066415838897228, 0.029606545343995094, -0.014123097062110901, -0.012413210235536098, -0.01486940123140812, 0.01701384410262108, -0.024920890107750893, -0.007401636335998774, -0.0007858629687689245, -0.03837325796484947, 0.021066559478640556, 0.05989326909184456, 0.03113694116473198, -0.012092016637325287, 0.012488785199820995, 0.017816830426454544, 0.01839308999478817, 0.035728130489587784, -0.024939782917499542, -0.06155591830611229, -0.022313548251986504, -0.030570128932595253, -0.014009734615683556, 0.06034671887755394, -0.04156630486249924, 0.00811015348881483, -0.06737520545721054, -0.023012617602944374, 0.013934159651398659, -0.027150355279445648, 0.02261584997177124, -0.020386382937431335, 0.016654862090945244, 0.043531257659196854, 0.020575322210788727, -0.00918709859251976, -0.02148222178220749, -0.00725048640742898, 0.08940534293651581, -0.01167635340243578, -0.014094755984842777, 0.0471588633954525, -0.019895145669579506, 0.015927452594041824, 0.04999293014407158, -0.026696905493736267, 0.04995514079928398, -0.02665911614894867, 0.04526948556303978, 0.003962969407439232, 0.011572437360882759, 0.008695860393345356, 0.026772480458021164, -0.015644045546650887, 0.07255209982395172, 0.00258844718337059, -0.00941382348537445, 0.030343404039740562, 0.02331491932272911, -0.04194417968392372, 0.012639936059713364, -0.02214350551366806, -0.020820939913392067, -0.004865147173404694, -0.05698362737894058, -0.02660243585705757, -0.001203887746669352, 0.013886924833059311, 0.010060935281217098, 0.02452412061393261, 0.04288886860013008, 0.012942235916852951, -0.0082329623401165, -0.009928679093718529, 0.0020960283000022173, 0.036408305168151855, -0.004442398902028799, 0.033593133091926575, 0.02805725671350956, -0.01675877906382084, 0.03208163008093834, 0.049652840942144394, 0.014047522097826004, 0.007401636335998774, 0.010552173480391502, 0.033101893961429596, -0.019989613443613052, -0.00813849363476038, 0.08366163820028305, 0.02852960117161274, 0.04413585737347603, 0.040205955505371094, -0.011185115203261375, 0.05796610191464424, -0.00921543873846531, -0.0039464375004172325, 0.021312179043889046, -0.005965709686279297, -0.013433474116027355, 0.011487415060400963, -0.007132400292903185, 0.043266747146844864, -0.04149072989821434, -0.022011248394846916, -0.045647360384464264, 0.03134477511048317, 0.035236891359090805, -0.022993724793195724, 0.042095333337783813, 0.014992211014032364, 0.012498232536017895, 0.005465024616569281, -0.00242076488211751, -0.018279727548360825, -0.025884471833705902, -0.023050405085086823, -0.014378163032233715, -0.024335183203220367, -0.02569553442299366, 0.03183601051568985, -0.04058383032679558, 0.019498376175761223, -0.005767324939370155, 0.003174154320731759, 0.0353313609957695, 0.010457704775035381, 0.020159658044576645, 0.047234438359737396, -0.0011637384304776788, 0.007170187775045633, 0.03408437222242355, 0.016560394316911697, -0.039752501994371414, 0.05403619632124901, -0.027660487219691277, 0.009947572834789753, 0.007892875000834465, 0.03255397453904152, 0.015266170725226402, -0.003849606728181243, -0.016919376328587532, 0.006721460726112127, 0.011638565920293331, -0.012195931747555733, -0.025601064786314964, 0.03519910201430321, 0.03945020213723183, -0.01840253733098507, 0.012441551312804222, -0.02048085257411003, -0.01401918102055788, 0.03754193335771561, -0.025393234565854073, 0.019611738622188568, 0.027962787076830864, -0.06658166646957397, -0.0306645967066288, 0.035482510924339294, 0.025884471833705902, 0.0007752352394163609, -0.032875169068574905, 0.000028967995604034513, 0.03132588043808937, -0.007378019392490387, -0.03629494085907936, -0.008294367231428623, 0.011685799807310104, 0.009026501327753067, -0.0014855230692774057, 0.010514385998249054, -0.01472769770771265, -0.024127351120114326, 0.005328044760972261, -0.028680751100182533, -0.019649526104331017, 0.003254452720284462, 0.0057862186804413795, -0.01959284581243992, 0.03519910201430321, 0.02121770940721035, -0.020820939913392067, 0.013575177639722824, 0.001035024644806981, 0.007165464106947184, 0.05547212436795235, -0.019044926390051842, -0.09121914952993393, -0.01106230542063713, -0.0006494735134765506, -0.013773562386631966, 0.007118229754269123, -0.06888670474290848, 0.03400879725813866, 0.06650608777999878, -0.01506778597831726, 0.02289925515651703, 0.05467858538031578, -0.0005243022460490465, -0.027641592547297478, -0.0048887645825743675, -0.02452412061393261, -0.014302588067948818, 0.01143073383718729, 0.01788295805454254, 0.07274103164672852, -0.0047494228929281235, 0.007207975257188082, -0.014604887925088406, 0.02849181368947029, 0.01951727084815502, -0.06178264692425728, 0.010741110891103745, 0.008105429820716381, 0.017637338489294052, -0.02121770940721035, 0.02497757039964199, -0.024580800905823708, 0.03888338804244995, 0.0330641083419323, -0.025865579023957253, -0.011052859015762806, 0.030570128932595253, 0.01002314779907465, 0.04311559721827507, 0.022993724793195724, -0.007113506551831961, 0.04980399087071419, 0.004799019079655409, 0.0015410236082971096, -0.04360683262348175, 0.017098866403102875, -0.030589021742343903, 0.04217090830206871, -0.0200651902705431, 0.01603136770427227, 0.03963914141058922, -0.055774424225091934, -0.018449772149324417, 0.029096413403749466, -0.015275617130100727, -0.019044926390051842, 0.007623638492077589, 0.001333191990852356, 0.01129847764968872, -0.0518067330121994, -0.020235233008861542, 0.026035621762275696, -0.039487991482019424, -0.03674839437007904, 0.013886924833059311, -0.009536633267998695, -0.04058383032679558, -0.0036748393904417753, 0.010571067221462727, 0.013716881163418293, -0.021878991276025772, -0.012441551312804222, -0.026281241327524185, 0.01368854008615017, 0.03487790748476982, 0.07277882099151611, -0.003157622180879116, 0.029096413403749466, -0.004447122570127249, 0.0017063440755009651, 0.03603043034672737, -0.009352418594062328, 0.038089852780103683, 0.007179634645581245, 0.04273771867156029, 0.020159658044576645, 0.024939782917499542, 0.017032738775014877, -0.020178552716970444, -0.0448538213968277, -0.02784942463040352, 0.0002671697875484824, -0.009621654637157917, -0.04062161594629288, 0.0007728735217824578, 0.02996552735567093, 0.007590574212372303, 0.03211941942572594, 0.03945020213723183, 0.001791366026736796, -0.03232724964618683, -0.05014408007264137, -0.025582171976566315, 0.028416238725185394, -0.004123566672205925, -0.02499646507203579, -0.012942235916852951, 0.0330074243247509, 0.010429363697767258, -0.027433762326836586, -0.0021775076165795326, 0.000020148439944023266, -0.013868031091988087, 0.004333759658038616, 0.012885554693639278, -0.04579851031303406, -0.03842993825674057, 0.009777529165148735, 0.03742856904864311, -0.033819857984781265, -0.008436070755124092, 0.003259176155552268, 0.005493365228176117, 0.021860098466277122, -0.004680932965129614, -0.024146245792508125, -0.0069198450073599815, 0.03937462717294693, 0.005172171164304018, 0.0028458749875426292, 0.024694165214896202, 0.07119174301624298, -0.052713632583618164, 0.007566956803202629, 0.0032520911190658808, -0.024146245792508125, -0.022351335734128952, -0.01720278337597847, 0.01906381919980049, -0.0106277484446764, -0.019611738622188568, 0.02049974538385868, -0.007122953422367573, -0.008738371543586254, 0.015077232383191586, -0.000256984872976318, 0.014047522097826004, -0.00507770199328661, -0.042284268885850906, -0.0637475997209549, -0.033857643604278564, -0.004558123182505369, 0.0018433239310979843, 0.01720278337597847, -0.017977427691221237, 0.03818431869149208, -0.037598613649606705, 0.0005443769041448832, 0.01936611905694008, 0.00018997100414708257, -0.018903221935033798, 0.029398715123534203, 0.02051864005625248, 0.00424165278673172, -0.007633085362613201, 0.00894620269536972, -0.038770027458667755, 0.020688684657216072, 0.03244061395525932, -0.0041377367451786995, 0.02097208984196186, -0.00931935478001833, 0.0329696387052536, 0.010608854703605175, -0.010410469956696033, -0.009975912980735302, -0.02544991485774517, -0.06918900460004807, 0.02781163714826107, 0.010240426287055016, -0.010741110891103745, 0.05849512666463852, 0.025506597012281418, -0.04458931088447571, -0.004246375989168882, -0.023749476298689842, 0.0032355589792132378, -0.055056460201740265, -0.016900481656193733, 0.0029828548431396484, 0.058343976736068726, -0.028227301314473152, -0.015927452594041824, 0.011562990956008434, 0.03162818029522896, -0.0034693696070462465, 0.006924568675458431, -0.08343490958213806, -0.0016473010182380676, 0.001516225514933467, -0.009262673556804657, -0.007595297880470753, 0.005049361381679773, -0.01765623316168785, 0.011402393691241741, 0.004850976634770632, 0.009701953269541264, -0.03722073882818222, -0.02216239832341671, 0.009376036003232002, -0.026300135999917984, 0.003266261424869299, 0.005394172854721546, -0.08207456022500992, -0.01284776721149683, -0.004487271420657635, 0.0164753720164299, -0.045609574764966965, -0.01700439862906933, 0.027207037433981895, 0.04859479144215584, 0.023201556876301765, 0.006485288497060537, 0.016428137198090553, -0.004884040914475918, 0.022483592852950096, 0.05728592723608017, 0.030286721885204315, -0.026035621762275696, 0.009815316647291183, 0.023749476298689842, 0.018808754161000252, -0.02756601758301258, 0.0494261160492897, -0.00827074982225895, -0.06922679394483566, 0.01697605662047863, -0.02478863298892975, -0.031420350074768066, 0.06450334936380386, -0.05297814682126045, -0.06151813268661499, 0.012734404765069485, -0.025034252554178238, -0.01936611905694008, -0.00280100223608315, -0.01930943876504898, -0.02524208463728428, -0.015464555472135544, 0.018941009417176247, 0.04356904700398445, -0.004279440268874168, 0.016598181799054146, 0.06794201582670212, -0.003509518690407276, -0.0020157296676188707, 0.033158574253320694, 0.006924568675458431, -0.030966898426413536, -0.01026876736432314, -0.02070757746696472, 0.017495635896921158, 0.004218035377562046, -0.04757452756166458, 0.010202638804912567, -0.013943606056272984, 0.0235983245074749, 0.01153464987874031, -0.009116246365010738, 0.03408437222242355, -0.0023298386950045824 ]
Graph neural networks (GNNs) can extract features by learning both the representation of each objects (i.e., graph nodes) and the relationship across different objects (i.e., the edges that connect nodes), achieving state-of-the-art performance in various graph-based tasks. Despite its strengths, utilizing these algorithms in a production environment faces several challenges as the number of graph nodes and edges amount to several billions to hundreds of billions scale, requiring substantial storage space for training. Unfortunately, state-of-the-art ML frameworks employ an in-memory processing model which significantly hampers the productivity of ML practitioners as it mandates the overall working set to fit within DRAM capacity. In this work, we first conduct a detailed characterization on a state-of-the-art, large-scale GNN training algorithm, GraphSAGE. Based on the characterization, we then explore the feasibility of utilizing capacity-optimized NVM SSDs for storing memory-hungry GNN data, which enables large-scale GNN training beyond the limits of main memory size. Given the large performance gap between DRAM and SSD, however, blindly utilizing SSDs as a direct substitute for DRAM leads to significant performance loss. We therefore develop SmartSAGE, our software/hardware co-design based on an in-storage processing (ISP) architecture. Our work demonstrates that an ISP based large-scale GNN training system can achieve both high capacity storage and high performance, opening up opportunities for ML practitioners to train large GNN datasets without being hampered by the physical limitations of main memory size.
[ -0.028597218915820122, 0.04387175291776657, -0.03373648226261139, 0.003276951378211379, 0.06693575531244278, 0.015525228343904018, 0.007964066229760647, 0.023619119077920914, -0.026484211906790733, -0.0037626742850989103, -0.013125712051987648, 0.008657955564558506, 0.009463763795793056, -0.022687964141368866, -0.03087138757109642, 0.040720149874687195, 0.0018679070053622127, -0.03253672271966934, -0.0045393831096589565, -0.04809776693582535, 0.07886171340942383, -0.04190199822187424, -0.017199518159031868, -0.03490042686462402, 0.0280062947422266, 0.018820086494088173, 0.018372414633631706, 0.03454228863120079, -0.04852753132581711, 0.056370723992586136, -0.007717846892774105, 0.000388914137147367, 0.019607987254858017, -0.015561041422188282, -0.038714583963155746, -0.009222021326422691, 0.08595281839370728, 0.0417945571243763, -0.04297640919685364, -0.01680556684732437, 0.032411377876996994, -0.007968543097376823, -0.040182944387197495, 0.023404236882925034, 0.03835644572973251, 0.013510708697140217, -0.038678769022226334, -0.05329074710607529, 0.0005279718898236752, -0.014468724839389324, -0.0011163793969899416, -0.012158743105828762, 0.016742892563343048, -0.015364066697657108, -0.04627126827836037, 0.02304610051214695, 0.06267393380403519, 0.021398670971393585, 0.041257355362176895, 0.002062643878161907, -0.047739628702402115, 0.004465517587959766, -0.06869062781333923, -0.003841016674414277, 0.015364066697657108, -0.0353660024702549, 0.0006155475275591016, 0.02250889502465725, 0.02272377721965313, -0.019661707803606987, -0.04175874590873718, 0.013474895618855953, 0.04584150388836861, -0.013618149794638157, -0.006312160287052393, -0.01784416288137436, 0.02023472636938095, 0.013027224689722061, 0.0326978862285614, -0.036888085305690765, 0.034022990614175797, 0.011451422236859798, -0.03903690725564957, 0.01706521585583687, 0.07642637938261032, -0.04111409932374954, 0.006500182207673788, -0.06048929691314697, 0.043800123035907745, -0.003393345745280385, -0.016259407624602318, -0.007064247503876686, 0.015793830156326294, -0.012257230468094349, 0.0066568669863045216, 0.00460205739364028, -0.027021417394280434, -0.04809776693582535, -0.010645614936947823, 0.021291229873895645, -0.018533576279878616, 0.011675258167088032, 0.030047673732042313, -0.017557654529809952, -0.009213067591190338, -0.0071493047289550304, -0.014343377202749252, 0.015525228343904018, 0.05522468686103821, 0.10185409337282181, 0.05397120863199234, 0.0023413191083818674, -0.03928760066628456, 0.019625894725322723, -0.029403027147054672, 0.005600363481789827, -0.000799092638771981, -0.02476515620946884, 0.009920388460159302, 0.005658560898154974, 0.03239347040653229, 0.018444042652845383, -0.05662142112851143, -0.00008841501403367147, -0.06306788325309753, 0.06500182300806046, -0.02186424843966961, -0.07685614377260208, -0.015211858786642551, 0.015023836866021156, 0.0029053844045847654, 0.027021417394280434, 0.016492197290062904, -0.04064851999282837, 0.04068433493375778, -0.018802179023623466, 0.05608421564102173, 0.05289679765701294, -0.02229401282966137, 0.0032635212410241365, -0.021685181185603142, 0.00043759835534729064, -0.010269571095705032, -0.05697955563664436, 0.00491095008328557, 0.02395934797823429, -0.023726560175418854, 0.0726301297545433, -0.05450841411948204, 0.03574204817414284, -0.0704813152551651, 0.06775947660207748, 0.028615126386284828, 0.018605204299092293, -0.00014927027223166078, 0.01803218573331833, -0.03810574859380722, -0.03685227036476135, -0.01610719971358776, -0.003232184099033475, 0.04254664480686188, -0.018641017377376556, -0.017539747059345245, 0.015337206423282623, -0.036458320915699005, 0.06439299136400223, 0.057624202221632004, 0.012158743105828762, -0.03971736505627632, 0.0345781035721302, 0.08752862364053726, 0.0511777400970459, 0.0064598917961120605, -0.0037671509198844433, 0.014226982370018959, 0.011684211902320385, 0.04727404937148094, -0.038069937378168106, -0.03713878244161606, 0.0032568061724305153, -0.015722203999757767, 0.0022943136282265186, 0.037425290793180466, 0.04215269535779953, -0.005734664853662252, 0.047202423214912415, 0.024245858192443848, 0.03531228378415108, 0.03746110573410988, 0.0042058685794472694, 0.01959007978439331, -0.0016261646524071693, 0.022168664261698723, -0.06038185581564903, 0.0163489431142807, -0.015086510218679905, -0.01068142894655466, 0.016098247841000557, 0.01953635923564434, -0.003910405561327934, -0.07635475695133209, -0.025982821360230446, 0.06066836416721344, -0.03903690725564957, 0.02449655346572399, -0.00019557624182198197, -0.0083759231492877, -0.018444042652845383, 0.002753176260739565, -0.03357531875371933, -0.015337206423282623, 0.02542771026492119, -0.02952837571501732, -0.08638258278369904, 0.012660134583711624, 0.01090526394546032, 0.01476418785750866, -0.029671629890799522, -0.00389921385794878, -0.018444042652845383, -0.0014504538848996162, 0.008505747653543949, 0.05683630332350731, -0.012812342494726181, -0.0011639444855973125, -0.049781009554862976, -0.027666063979268074, 0.034828800708055496, -0.02417423017323017, 0.022902844473719597, 0.023941442370414734, -0.0056182704865932465, 0.03477507829666138, -0.018014278262853622, 0.03674482926726341, -0.02985069900751114, -0.00960701797157526, -0.024317486211657524, -0.032572537660598755, 0.010753056034445763, -0.02979697845876217, 0.02789885364472866, -0.0217030867934227, -0.02352958545088768, 0.0017179371789097786, -0.00019781460287049413, -0.044552210718393326, 0.023135634139180183, 0.047632187604904175, 0.052323780953884125, -0.02336842380464077, -0.03174882382154465, 0.005085541866719723, -0.020915186032652855, -0.035759955644607544, 0.00301506370306015, 0.0006938899750821292, -0.037855055183172226, -0.003999939654022455, -0.022043317556381226, 0.02481887675821781, -0.03303811699151993, -0.06707901507616043, 0.05748094990849495, -0.04025457054376602, 0.02564259059727192, 0.017208470031619072, 0.017244284972548485, 0.026000728830695152, -0.032518815249204636, -0.009750273078680038, -0.06535995751619339, -0.0241205096244812, -0.008635572157800198, -0.057301878929138184, -0.07549522817134857, -0.02471143566071987, -0.01003678236156702, 0.033969271928071976, 0.007896915078163147, 0.026108169928193092, -0.017083123326301575, -0.024192137643694878, 0.023225167766213417, -0.046342894434928894, -0.05271773040294647, -0.0035343619529157877, 0.007234362419694662, -0.019572174176573753, 0.04705917090177536, -0.04294059798121452, -0.007990926504135132, -0.009759226813912392, 0.012454205192625523, 0.05769583210349083, -0.03223230689764023, -0.035061586648225784, -0.014074774459004402, 0.03636878728866577, -0.005067634861916304, -0.010296431370079517, -0.006213672459125519, 0.009624925442039967, 0.04122154042124748, -0.023941442370414734, -0.01122758723795414, -0.0450177900493145, 0.06450042873620987, 0.009320508688688278, -0.0426182746887207, 0.06306788325309753, 0.016232548281550407, 0.0028225653804838657, -0.03432740643620491, 0.0018869329942390323, 0.0594865158200264, 0.006813551764935255, 0.025266548618674278, -0.04534011334180832, -0.0111201461404562, 0.020431701093912125, -0.03735366463661194, -0.0870988592505455, 0.021774714812636375, 0.012695947661995888, 0.010565034113824368, -0.03033418208360672, 0.057337693870067596, -0.04702335596084595, -0.00042472779750823975, -0.03681645914912224, -0.026000728830695152, -0.04419407621026039, 0.021613553166389465, 0.00352764711715281, -0.017468120902776718, -0.050604723393917084, 0.051894016563892365, -0.032572537660598755, 0.0031762253493070602, 0.023977255448698997, -0.021506112068891525, -0.043800123035907745, 0.021183788776397705, 0.018658924847841263, 0.03892946615815163, -0.05203726887702942, 0.03287695348262787, 0.0021241987124085426, -0.046128012239933014, 0.0009250000584870577, -0.000506427779328078, 0.00992934126406908, -0.0012165458174422383, 0.03946667164564133, -0.007234362419694662, 0.015659529715776443, 0.0035656990949064493, -0.022867031395435333, -0.008456503972411156, 0.018014278262853622, -0.06088324636220932, -0.03266207128763199, 0.05533212795853615, -0.05142843723297119, 0.0023681793827563524, 0.0002946234308183193, -0.009669692255556583, 0.008823594078421593, 0.034828800708055496, 0.016205688938498497, 0.024747248739004135, -0.020789839327335358, -0.027272114530205727, -0.007592499256134033, -0.007843194529414177, 0.05218052491545677, -0.003894737223163247, 0.008017786778509617, 0.04268990084528923, 0.03971736505627632, 0.04605638608336449, 0.0004163339617662132, 0.0012008772464469075, 0.0335036925971508, 0.04996007680892944, 0.03717459365725517, 0.0073194196447730064, 0.01637580245733261, 0.04888566583395004, 0.04140060767531395, -0.074492447078228, -0.056693047285079956, -0.011075379326939583, 0.03835644572973251, 0.008071507327258587, 0.03233974799513817, -0.024908410385251045, 0.02066449075937271, -0.0017783727962523699, -0.05164331942796707, -0.034739263355731964, -0.011308168061077595, 0.004767695441842079, -0.03060278482735157, -0.033378344029188156, 0.036673203110694885, -0.06897713989019394, -0.0064330315217375755, -0.0361718125641346, 0.00366418669000268, -0.049781009554862976, -0.000005683322342520114, 0.017853116616606712, 0.021631460636854172, 0.022544708102941513, -0.04953031241893768, -0.013636057265102863, 0.005336237605661154, -0.04129316657781601, -0.05099867284297943, 0.019231943413615227, 0.034613918513059616, 0.02963581681251526, -0.03275160491466522, 0.003057592548429966, -0.028471872210502625, 0.006164428777992725, 0.0030464008450508118, -0.00389921385794878, 0.021506112068891525, -0.028615126386284828, -0.0019630370661616325, -0.02181052789092064, -0.062029287219047546, 0.01559685543179512, -0.0007733515230938792, 0.001433666213415563, -0.0538637675344944, -0.004669208079576492, -0.02623351663351059, -0.03097882866859436, -0.04713079705834389, -0.009562251158058643, -0.03028046153485775, -0.01613406091928482, -0.04132898151874542, -0.028561405837535858, 0.016169873997569084, -0.07298827171325684, -0.09583739191293716, -0.0001508091518189758, -0.05268191546201706, -0.05271773040294647, 0.002869570627808571, -0.03914434835314751, -0.043692681938409805, -0.03545553982257843, 0.013940473087131977, -0.026860255748033524, 0.03260835260152817, 0.04616382718086243, -0.034399036318063736, -0.027558622881770134, -0.031104177236557007, 0.06553902477025986, -0.02925977297127247, -0.03728203475475311, 0.004355838056653738, 0.013448035344481468, 0.032035332173109055, -0.002151058753952384, 0.007444767747074366, 0.025051666423678398, -0.03271579369902611, 0.003670901758596301, 0.00700157368555665, -0.05372051149606705, 0.02283121831715107, 0.0023234121035784483, 0.01760242134332657, 0.022473081946372986, -0.004946764092892408, 0.02186424843966961, -0.028668846935033798, 0.02283121831715107, 0.0061823357827961445, -0.02023472636938095, 0.02816745638847351, -0.06783109903335571, -0.031927891075611115, 0.0471666119992733, -0.022705869749188423, -0.028507685288786888, -0.0111201461404562, 0.000553992809727788, -0.015292439609766006, -0.00779842771589756, 0.029223958030343056, 0.0892476812005043, 0.006173382047563791, -0.02487259730696678, 0.0033418636303395033, 0.017029402777552605, 0.0217030867934227, -0.004772172309458256, 0.03746110573410988, 0.04652196541428566, -0.01964380033314228, 0.034184154123067856, -0.025982821360230446, -0.024836784228682518, -0.04910054802894592, -0.0313548743724823, -0.01567743718624115, -0.0037380524445325136, -0.034309498965740204, -0.040505267679691315, 0.02816745638847351, 0.025893287733197212, 0.006164428777992725, 0.02130913734436035, -0.05758839100599289, 0.05683630332350731, -0.05314749479293823, 0.05543956905603409, 0.022258199751377106, -0.02374446578323841, 0.027612343430519104, -0.026305144652724266, 0.008425166830420494, 0.03148021921515465, -0.039323415607213974, -0.0009938294533640146, -0.013698730617761612, 0.018820086494088173, 0.022311920300126076, -0.010806776583194733, -0.02503375895321369, -0.03334253281354904, -0.036888085305690765, 0.005846582353115082, -0.01030538510531187, 0.025391895323991776, 0.02293865941464901, -0.00966073852032423, 0.01014422345906496, -0.06482275575399399, -0.015041743405163288, 0.0013284635497257113, -0.03001186065375805, -0.037317849695682526, 0.041042473167181015, -0.02888372913002968, 0.0071403514593839645, -0.03925178945064545, -0.011308168061077595, -0.04054107889533043, -0.02542771026492119, -0.00014045675925444812, 0.03151603415608406, 0.045304298400878906, -0.028865821659564972, -0.036888085305690765, 0.0015153661370277405, -0.05694374442100525, 0.04820520803332329, 0.04089921712875366, -0.00848336424678564, -0.01101270504295826, -0.008832547813653946, -0.020628677681088448, -0.0661836713552475, -0.039968062192201614, 0.014101634733378887, 0.01832764782011509, 0.006777738220989704, -0.023135634139180183, 0.03507949411869049, -0.0009272384340874851, 0.021989597007632256, 0.0006653509335592389, 0.025087479501962662, 0.020037751644849777, -0.032250214368104935, 0.018873807042837143, -0.03464972972869873, -0.05454422906041145, 0.006903085857629776, -0.020055657252669334, -0.0006955687422305346, 0.024299578741192818, -0.018211252987384796, -0.0006278585060499609, -0.06428554654121399, -0.02007356472313404, -0.009427949786186218, 0.004611010663211346, 0.03344997391104698, -0.008760920725762844, 0.017879977822303772, 0.03133696690201759, 0.019572174176573753, 0.03210695832967758, 0.024908410385251045, -0.014325469732284546, 0.038499701768159866, 0.009078766219317913, -0.00982190016657114, -0.014468724839389324, -0.01362710352987051, 0.020001936703920364, 0.06611204147338867, -0.05354144424200058, 0.01851567067205906, 0.01677870750427246, 0.026090262457728386, 0.010699335485696793, -0.017906837165355682, -0.03903690725564957, 0.05346981808543205, -0.019303571432828903, 0.056478165090084076, 0.012946643866598606, 0.017315911129117012, 0.004928857088088989, 0.01718161068856716, -0.03477507829666138, 0.02082565240561962, -0.003285904647782445, -0.02320726215839386, -0.014021053910255432, -0.04516104608774185, 0.006356927566230297, -0.034846704453229904, -0.04387175291776657, -0.012991410680115223, 0.006652390118688345, -0.01637580245733261, -0.01702044904232025, -0.029671629890799522, 0.005157169420272112, 0.012194556184113026, 0.047094982117414474, -0.011773745529353619, 0.0020380220375955105, 0.007574592251330614, -0.001262432080693543, 0.011791652999818325, 0.028847916051745415, 0.05415027588605881, 0.01797846518456936, 0.012409438379108906, 0.031713008880615234, 0.017145797610282898, -0.011514096520841122, 0.06661343574523926, 0.01144246943295002, 0.045519180595874786, 0.04974519461393356, -0.002529340796172619, 0.024962130934000015, 0.017826257273554802, 0.013349547050893307, 0.050819605588912964, -0.0033463402651250362, -0.027540715411305428, 0.04415826126933098, -0.002125317696481943, 0.084162138402462, -0.04168711602687836, -0.040075503289699554, -0.03221439942717552, -0.008863884955644608, 0.02417423017323017, -0.05884186923503876, -0.01200653426349163, 0.0005993194645270705, 0.004669208079576492, -0.014450818300247192, -0.003073260886594653, -0.038392260670661926, -0.002151058753952384, -0.013833031989634037, -0.024210045114159584, -0.004102904349565506, -0.02768397144973278, 0.010493407025933266, -0.013600243255496025, 0.0027464611921459436, -0.004611010663211346, -0.010672475211322308, 0.014164308086037636, 0.04200943931937218, 0.06629111617803574, -0.006052511278539896, -0.005582456476986408, 0.01548941433429718, 0.050497282296419144, -0.00361046614125371, -0.031874172389507294, 0.03713878244161606, 0.004179008305072784, 0.012051302008330822, 0.008071507327258587, 0.07151991128921509, 0.00949957687407732, 0.038499701768159866, -0.021667273715138435, 0.01856939122080803, -0.013653963804244995, -0.002988203428685665, -0.010439686477184296, 0.07273757457733154, 0.030352089554071426, 0.019679615274071693, 0.002136509632691741, -0.02095099911093712, -0.01651010476052761, 0.05569026619195938, -0.014907442033290863, -0.00992934126406908, -0.024138417094945908, -0.05884186923503876, -0.030352089554071426, -0.0194289181381464, 0.0012019964633509517, 0.02229401282966137, -0.0335036925971508, -0.016823474317789078, 0.045411739498376846, -0.03330671787261963, 0.023941442370414734, -0.011075379326939583, 0.038714583963155746, -0.0012109498493373394, 0.01680556684732437, 0.035545073449611664, -0.009866667911410332, -0.041472237557172775, -0.008178948424756527, 0.004416273906826973, -0.028131641447544098, -0.009615971706807613, 0.011728978715837002, -0.008837024681270123, 0.015077557414770126, 0.02503375895321369, -0.05361307039856911, 0.01368082407861948, 0.02218657173216343, -0.004915426950901747, 0.0029747732914984226, -0.03771179914474487, -0.06310369819402695, -0.019017061218619347, 0.011182820424437523, -0.014504538848996162, 0.02138076350092888, -0.021076347678899765, 0.0029680582229048014, 0.020628677681088448, 0.02018100582063198, 0.025839567184448242, 0.06740133464336395, 0.01851567067205906, -0.03631506487727165, -0.044122446328401566, -0.028239082545042038, 0.010941077955067158, 0.005680944304913282, 0.010609800927340984, 0.054759107530117035, -0.025606777518987656, 0.02883000858128071, 0.04014712944626808, 0.021165881305933, -0.002956866519525647, -0.037532731890678406, 0.005918209906667471, -0.025338174775242805, 0.001167302019894123, -0.033217184245586395, 0.07083944976329803, -0.000027699639758793637, 0.008169994689524174, 0.006321113556623459, -0.020592862740159035, 0.004897519946098328, 0.008129703812301159, -0.003165033645927906, 0.013206292875111103, 0.015578948892652988, 0.04734567925333977, 0.0723436251282692, -0.0038119179662317038, -0.012615366838872433, -0.006585239432752132, -0.022490987554192543, -0.031981613487005234, 0.04254664480686188, -0.06639855355024338, 0.04132898151874542, 0.06707901507616043, -0.021935876458883286, -0.033270902931690216, -0.04111409932374954, -0.002562916139140725, -0.010645614936947823, -0.03264416381716728, 0.024908410385251045, 0.01570429652929306, -0.05579770728945732, 0.028561405837535858, 0.04845590144395828, -0.025714218616485596, -0.043907564133405685, 0.030155114829540253, 0.01476418785750866, -0.038607142865657806, 0.010081549175083637, -0.038392260670661926, -0.010332245379686356, -0.029761163517832756, -0.026161890476942062, -0.014343377202749252, 0.05003170296549797, -0.01384198572486639, 0.0881732702255249, 0.0033284334931522608, 0.011532003059983253, 0.04899310693144798, -0.005783908534795046, 0.029671629890799522, -0.07198549062013626, 0.03626134619116783, 0.02095099911093712, 0.03368275985121727, 0.003995463252067566, 0.00534071447327733, 0.007686510216444731, 0.032948579639196396, -0.02336842380464077, -0.005210889503359795, -0.00022089762205723673, -0.00960701797157526, -0.020915186032652855, -0.011684211902320385, 0.025087479501962662, 0.023565398529171944, -0.012749668210744858, 0.026358865201473236, -0.001459407270886004, 0.016680218279361725, -0.019876589998602867, 0.023225167766213417, 0.03468554466962814, 0.00619128905236721, -0.025051666423678398, -0.021685181185603142, 0.06525251269340515, -0.039753179997205734, 0.00007351596286753193, -0.002748699625954032, -0.005278040189296007, -0.01144246943295002, -0.0017716577276587486, -0.008308772929012775, 0.0011091047199442983, -0.013797217980027199, 0.011576770804822445, 0.018479855731129646, -0.03081766702234745, -0.00027685650275088847, 0.010081549175083637, 0.01618778146803379, 0.030208835378289223, 0.015632668510079384, -0.025606777518987656, 0.010493407025933266, -0.015238719061017036, 0.01042177900671959, -0.019625894725322723, -0.023511677980422974, 0.030513251200318336, -0.030369997024536133, -0.02768397144973278, -0.068081796169281, -0.028507685288786888, -0.012203509919345379, -0.02438911236822605, -0.0008114035590551794, -0.022365640848875046, -0.002636781893670559, 0.005295947194099426, 0.020646583288908005, 0.009965155273675919, -0.0026770723052322865, 0.010547127574682236, 0.00872062984853983, 0.011925953440368176, -0.025409802794456482, -0.0345601961016655, -0.024102604016661644, 0.0025203872937709093, 0.01969752088189125, -0.003997701685875654, -0.026251424103975296, 0.01779044233262539, -0.027880946174263954, -0.016957774758338928, 0.0035701757296919823, -0.0014896250795572996, -0.06876225769519806, 0.018981248140335083, 0.015077557414770126, 0.006343497429043055, -0.026788629591464996, 0.05372051149606705, 0.014585119672119617, 0.008416214026510715, 0.029456747695803642, -0.02612607553601265, 0.04183037206530571, -0.01160363107919693, 0.004718451760709286, -0.002051452174782753, -0.0017828495474532247, 0.0008516939706169069, 0.03361113369464874, -0.006621052976697683, 0.032518815249204636, 0.04297640919685364, -0.013761404901742935, 0.06997992098331451, -0.04036201164126396, -0.010162129998207092, -0.006562856025993824, -0.038714583963155746, 0.019303571432828903, -0.06131301075220108, -0.014531399123370647, -0.00561379361897707, 0.035974837839603424, -0.030101394280791283, -0.012391531839966774, 0.02164936624467373, -0.005170599557459354, 0.0015041743172332644, 0.03982480615377426, -0.019446825608611107, 0.023028193041682243, 0.040827590972185135, -0.0034873567055910826, -0.03799830749630928, -0.015847550705075264, -0.006880702450871468, -0.009938294999301434, -0.00758354552090168, 0.016769753769040108, -0.004875136539340019, 0.01953635923564434, -0.014773140661418438, 0.0016742893494665623, 0.02164936624467373, 0.0332350917160511, -0.05855535715818405, -0.03028046153485775, -0.002954628085717559, 0.0067464010789990425, 0.014737327583134174, -0.020360074937343597, 0.06059673801064491, 0.04118572548031807, -0.03130115196108818, 0.020807744935154915, -0.001123654074035585, -0.01707416959106922, -0.0013083183439448476, 0.0064957053400576115, 0.018587296828627586, 0.014370237477123737, 0.03081766702234745, 0.03156975284218788, 0.025767939165234566, -0.04054107889533043, 0.010985844768583775, -0.02267005667090416, -0.08050914108753204, -0.008541561663150787, -0.03593902289867401, 0.02433539181947708, 0.021792620420455933, -0.029403027147054672, -0.04630708321928978, 0.048921480774879456, 0.0015399879775941372, -0.010976891033351421, -0.01683242805302143, 0.004785602446645498, 0.02130913734436035, -0.07216455787420273, 0.002274168422445655, 0.0025203872937709093, 0.01894543506205082, -0.008756443858146667, 0.01073514949530363, 0.024353299289941788, -0.03968155384063721, 0.06578972190618515, -0.00230102869682014, -0.014316516928374767, 0.004552813246846199, -0.013501755893230438, -0.01787102408707142, 0.014307563193142414, -0.016017666086554527, 0.04329873248934746, -0.031175803393125534, 0.0031068362295627594, -0.016223594546318054, -0.033217184245586395, -0.0337722972035408, -0.03556298092007637 ]
Preventing poaching through ranger patrols protects endangered wildlife, directly contributing to the UN Sustainable Development Goal 15 of life on land. Combinatorial bandits have been used to allocate limited patrol resources, but existing approaches overlook the fact that each location is home to multiple species in varying proportions, so a patrol benefits each species to differing degrees. When some species are more vulnerable, we ought to offer more protection to these animals; unfortunately, existing combinatorial bandit approaches do not offer a way to prioritize important species. To bridge this gap, (1) We propose a novel combinatorial bandit objective that trades off between reward maximization and also accounts for prioritization over species, which we call ranked prioritization. We show this objective can be expressed as a weighted linear sum of Lipschitz-continuous reward functions. (2) We provide RankedCUCB, an algorithm to select combinatorial actions that optimize our prioritization-based objective, and prove that it achieves asymptotic no-regret. (3) We demonstrate empirically that RankedCUCB leads to up to 38% improvement in outcomes for endangered species using real-world wildlife conservation data. Along with adapting to other challenges such as preventing illegal logging and overfishing, our no-regret algorithm addresses the general combinatorial bandit problem with a weighted linear objective.
[ 0.02803771011531353, 0.015343395061790943, -0.03213701769709587, -0.009909880347549915, 0.009092919528484344, 0.01418321393430233, -0.07692001014947891, 0.010973379947245121, -0.04161183163523674, 0.06531819701194763, -0.012094887904822826, -0.023300305008888245, 0.030648117884993553, -0.021772732958197594, -0.05383240431547165, 0.027225583791732788, 0.0294105913490057, 0.02627810277044773, 0.04400953650474548, -0.039117440581321716, -0.031904980540275574, -0.023629022762179375, 0.012259247712790966, 0.028057046234607697, 0.0360429622232914, 0.042385283857584, -0.03323918953537941, 0.025427302345633507, -0.04911433532834053, 0.052865587174892426, 0.005670385435223579, 0.023068267852067947, -0.036545705050230026, 0.023841721937060356, 0.004234661348164082, -0.007033598143607378, 0.04814751818776131, 0.007173786871135235, 0.002403750317171216, 0.025640003383159637, -0.05452851206064224, -0.03629433363676071, -0.0342833511531353, -0.0172576941549778, 0.04149581119418144, -0.012771660462021828, -0.04594317451119423, 0.029661964625120163, -0.016223199665546417, -0.0032581754494458437, -0.004486033692955971, -0.04400953650474548, 0.010760679841041565, -0.05978799983859062, 0.006468009669333696, 0.017122339457273483, -0.006719382479786873, 0.017866790294647217, 0.0972231775522232, 0.01927834376692772, -0.006008771248161793, 0.027225583791732788, -0.0228942409157753, -0.016841962933540344, 0.08121267706155777, -0.047219373285770416, 0.0005501796258613467, 0.04447361081838608, 0.02026449702680111, 0.002348158275708556, -0.07227928191423416, 0.004283002112060785, -0.0014284730423241854, 0.015208041295409203, 0.030184045433998108, 0.01811816170811653, 0.044550955295562744, -0.008309797383844852, 0.0003169348929077387, 0.04122510179877281, 0.022584859281778336, 0.013535446487367153, -0.024383140727877617, 0.01122475229203701, 0.07564380764961243, -0.025311285629868507, 0.0021560033783316612, -0.07966577261686325, 0.05162806063890457, -0.02266220562160015, -0.040335629135370255, 0.006424502935260534, -0.022681541740894318, 0.02322295866906643, 0.024499157443642616, 0.029642628505825996, -0.04807016998529434, -0.003202583407983184, 0.010412625968456268, -0.01999378763139248, -0.019191330298781395, -0.029043201357126236, -0.03250440955162048, -0.008991403505206108, 0.04099306836724281, -0.05433515086770058, -0.01533372700214386, 0.052053458988666534, -0.04188253730535507, 0.11802909523248672, -0.026316775009036064, 0.0886378362774849, -0.02475053071975708, 0.03695176914334297, -0.0749090313911438, 0.005902421660721302, -0.042965374886989594, -0.04354546591639519, -0.04145713895559311, 0.055882059037685394, 0.0033500229474157095, -0.0006906703347340226, 0.07951108366250992, -0.0088947219774127, -0.035018134862184525, 0.029874663800001144, 0.0049476888962090015, 0.05019716918468475, 0.044937681406736374, -0.01086703035980463, 0.008280793204903603, -0.011282761581242085, -0.022198133170604706, -0.009242776781320572, -0.004896931350231171, 0.022159459069371223, 0.05781569331884384, -0.03302649036049843, -0.06133490800857544, -0.018147166818380356, 0.00019442097982391715, -0.04671662673354149, -0.054451167583465576, 0.04269466549158096, -0.03625566139817238, -0.016880635172128677, 0.0008139395504258573, 0.01610718108713627, -0.000539605098310858, 0.06899210810661316, 0.010809021070599556, 0.07475433498620987, -0.013042369857430458, 0.020709233358502388, 0.022198133170604706, 0.01987777091562748, -0.02562066726386547, -0.002375954296439886, 0.013690137304365635, -0.006197300739586353, 0.04814751818776131, 0.013342083431780338, -0.03459273278713226, 0.05924658477306366, 0.08662685751914978, 0.08229551464319229, -0.022314149886369705, -0.023667695000767708, -0.06709714233875275, 0.03979421406984329, 0.016667935997247696, -0.06377129256725311, -0.0652795284986496, 0.02759297378361225, 0.017277030274271965, 0.013110047206282616, 0.011543801985681057, 0.052478861063718796, -0.013139051385223866, 0.036932431161403656, -0.023938404396176338, 0.018756261095404625, 0.0050322855822741985, 0.008343636058270931, 0.01333241444081068, -0.0028376097325235605, 0.0685667023062706, -0.016271540895104408, -0.017702430486679077, 0.050467878580093384, -0.010383620858192444, -0.0163198821246624, 0.042385283857584, -0.061412256211042404, 0.022855568677186966, -0.004403854254633188, 0.0058927531354129314, -0.003040641313418746, -0.004418356344103813, 0.03490211442112923, 0.00804875697940588, -0.05042920634150505, -0.00737681845203042, 0.016658267006278038, 0.007512172684073448, -0.016078175976872444, 0.02009047009050846, 0.01801181212067604, 0.00812610238790512, -0.01185318361967802, -0.05843445658683777, -0.05263355001807213, -0.07166051864624023, 0.0420372299849987, -0.047722116112709045, 0.011872520670294762, 0.05472187697887421, 0.03509547933936119, 0.05448983982205391, -0.016087844967842102, -0.00766686350107193, 0.041147757321596146, 0.04690999165177345, 0.0076910341158509254, -0.028173064813017845, 0.009784194640815258, -0.016464903950691223, 0.028347091749310493, 0.004263665527105331, -0.00257415184751153, 0.02212078683078289, -0.0064535075798630714, -0.010480303317308426, 0.027090229094028473, 0.0022986088879406452, -0.009049412794411182, -0.04795415326952934, -0.04768344387412071, -0.04188253730535507, 0.010006561875343323, -0.040606338530778885, -0.013148719444870949, -0.008604676462709904, -0.02962329238653183, 0.026084739714860916, 0.038189295679330826, -0.009353959932923317, 0.061528272926807404, -0.014840650372207165, 0.03931080549955368, -0.017644422128796577, -0.05151204392313957, -0.01155347004532814, -0.03323918953537941, 0.014386245980858803, 0.01089603453874588, 0.0420372299849987, -0.04134112223982811, -0.026568148285150528, -0.032175689935684204, 0.07212459295988083, 0.03826664015650749, 0.026916202157735825, 0.03658437728881836, 0.009760024026036263, 0.01333241444081068, 0.004174234811216593, -0.013738478533923626, -0.0020182316657155752, 0.011630815453827381, -0.018417876213788986, -0.021656714379787445, -0.016416562721133232, -0.013757814653217793, 0.037377167493104935, 0.011099066585302353, 0.033045824617147446, 0.015246713533997536, 0.03650703281164169, 0.056268785148859024, -0.02442181296646595, 0.0013583787949755788, 0.006119955331087112, 0.007604020647704601, -0.04660061001777649, -0.026413457468152046, -0.051009297370910645, 0.017818449065089226, -0.012878010980784893, 0.009194435551762581, -0.017924798652529716, 0.004440109711140394, 0.038073278963565826, -0.03465074300765991, 0.06767722964286804, 0.009150928817689419, -0.06872139871120453, -0.029990682378411293, -0.05545665696263313, 0.007521841209381819, 0.004299921449273825, -0.003267843509092927, -0.0008109182817861438, 0.04072235897183418, 0.00039669734542258084, -0.014192882925271988, -0.032562416046857834, 0.009677844122052193, -0.05162806063890457, 0.029913336038589478, -0.0420372299849987, -0.00903491023927927, -0.0023771626874804497, -0.028327755630016327, 0.013284074142575264, 0.04172784835100174, 0.03979421406984329, 0.017170680686831474, 0.003265426494181156, -0.013032701797783375, -0.017044994980096817, -0.029584618285298347, -0.07374884933233261, 0.0012943270849063993, -0.0008260247996076941, -0.0003812887007370591, 0.02759297378361225, 0.019587725400924683, -0.03354857116937637, -0.00287386542186141, -0.06825732439756393, -0.012017542496323586, -0.04304271936416626, -0.00799558125436306, -0.005854080431163311, 0.007807052228599787, -0.0555340051651001, 0.021502023562788963, 0.02047719620168209, -0.009900212287902832, -0.036216989159584045, -0.06570492684841156, 0.025814030319452286, 0.061528272926807404, -0.028598465025424957, 0.023300305008888245, -0.026084739714860916, 0.0114181162789464, -0.014811646193265915, -0.0032291708048433065, 0.0012115433346480131, -0.004916267469525337, -0.014714963734149933, 0.0008296503801830113, 0.07529575377702713, 0.027148239314556122, 0.014840650372207165, 0.012945687398314476, -0.028888510540127754, -0.004754325374960899, 0.03033873625099659, -0.07684266567230225, -0.0877096951007843, 0.00677739130333066, -0.01410586852580309, 0.03842133283615112, 0.01953938417136669, 0.01588481292128563, -0.0007819137535989285, 0.004836505278944969, -0.06261111050844193, 0.02322295866906643, 0.07301406562328339, -0.035791587084531784, -0.055882059037685394, 0.018214844167232513, 0.030976835638284683, 0.014231555163860321, -0.04451228305697441, 0.011012052185833454, 0.006584027782082558, -0.029932674020528793, 0.03861469402909279, -0.03159559890627861, 0.029487937688827515, 0.0625724345445633, 0.034476716071367264, 0.010161252692341805, -0.04346812143921852, 0.004239495377987623, 0.02212078683078289, -0.0024339633528143167, -0.011688824743032455, 0.006018439773470163, 0.021714722737669945, -0.040761031210422516, 0.009102587588131428, -0.01872725784778595, -0.003758503356948495, -0.022700877860188484, 0.028521118685603142, -0.02304893173277378, 0.0180214811116457, 0.0722019374370575, 0.007197957020252943, 0.025910712778568268, -0.04265599325299263, -0.00818894524127245, -0.02041918784379959, 0.013061705976724625, 0.025930048897862434, 0.012442942708730698, -0.039349477738142014, 0.08515729755163193, 0.016832293942570686, 0.029874663800001144, -0.016174858435988426, -0.03952350467443466, -0.042733337730169296, -0.05885985493659973, -0.055766038596630096, -0.010402957908809185, 0.03832465037703514, 0.017605748027563095, -0.04911433532834053, -0.011089397594332695, 0.00039216538425534964, 0.00007734540849924088, -0.01621353067457676, -0.051280006766319275, -0.020786577835679054, 0.03598495200276375, -0.007304307073354721, -0.027032220736145973, -0.02359035052359104, 0.03832465037703514, -0.051550716161727905, -0.0009698389330878854, 0.029874663800001144, -0.042269267141819, 0.04451228305697441, -0.007952074520289898, -0.044164229184389114, -0.08670420199632645, 0.020380515605211258, -0.010083907283842564, -0.027941029518842697, 0.003548220731317997, 0.018601570278406143, -0.010248267091810703, -0.044550955295562744, -0.010103244334459305, -0.005506026092916727, 0.0027602643240243196, 0.02397707663476467, -0.037106458097696304, 0.0017028074944391847, -0.055108603090047836, 0.03130555525422096, 0.02331964112818241, 0.012143229134380817, 0.027070892974734306, 0.0014804394450038671, -0.05568869411945343, 0.009842202998697758, 0.016880635172128677, -0.03838266059756279, -0.03434136137366295, 0.0076765320263803005, -0.005578537471592426, -0.008754533715546131, -0.06984290480613708, 0.0029681301675736904, -0.014598946087062359, 0.000741428229957819, -0.007908567786216736, -0.03378060832619667, -0.044937681406736374, -0.0457884818315506, 0.003026139223948121, 0.011389111168682575, -0.0020822833757847548, -0.01966506987810135, -0.014289564453065395, 0.0021874248050153255, -0.0229522492736578, 0.005390007980167866, -0.008058425039052963, -0.01349677424877882, 0.0293525829911232, -0.01893995702266693, 0.016822626814246178, -0.0678705945611, 0.01905597560107708, 0.02738027460873127, 0.010712339542806149, -0.018765930086374283, -0.10642728209495544, 0.057080913335084915, -0.013912505470216274, 0.011060393415391445, -0.07997515052556992, 0.029217228293418884, 0.0037053285632282495, 0.04319741204380989, -0.038247305899858475, 0.04776078835129738, 0.03668105974793434, 0.005622044205665588, 0.022217469289898872, -0.009044578298926353, 0.08832845836877823, -0.01511135883629322, -0.008749699220061302, -0.015072686597704887, 0.04698733612895012, 0.025930048897862434, 0.000271766388323158, 0.03327786177396774, 0.0027820176910609007, 0.025485312566161156, -0.004067885223776102, -0.025485312566161156, 0.01676461659371853, -0.041534483432769775, 0.005075792316347361, 0.03180829808115959, -0.01577846333384514, 0.07254999130964279, -0.045208390802145004, 0.011737165972590446, 0.06686510890722275, -0.051821425557136536, -0.032175689935684204, -0.0026007394772022963, -0.007197957020252943, -0.008914058096706867, -0.0075073386542499065, -0.016890304163098335, 0.004239495377987623, -0.024731194600462914, 0.0749090313911438, 0.011998206377029419, -0.0033089332282543182, -0.03269777074456215, -0.005660716909915209, 0.03300715237855911, -0.05874383822083473, -0.010596320964396, -0.025369293987751007, -0.03712579607963562, -0.014434587210416794, 0.01823418028652668, -0.02299092337489128, -0.006468009669333696, -0.04795415326952934, 0.00361348083242774, -0.037918586283922195, -0.015459413640201092, -0.04749008268117905, 0.025775358080863953, -0.03248507156968117, 0.05336833372712135, -0.02179206907749176, -0.0038455170579254627, -0.028869174420833588, 0.03078347258269787, 0.03366458788514137, -0.0027336766943335533, -0.02310694009065628, 0.014666623435914516, -0.008972067385911942, 0.0023892479948699474, -0.03998757526278496, -0.02654881216585636, -0.04474432021379471, 0.023532340303063393, 0.0486115887761116, 0.017837785184383392, -0.007865061052143574, -0.015546427108347416, -0.07618522644042969, 0.011804843321442604, -0.015517422929406166, 0.03642968833446503, -0.03762854263186455, -0.03412866219878197, -0.025446640327572823, -0.001302786753512919, -0.04961707815527916, 0.005361003801226616, 0.04281068220734596, -0.01844687946140766, -0.014018855057656765, -0.0520147867500782, -0.03078347258269787, -0.0028158563654869795, -0.007840890437364578, -0.01587514579296112, -0.0420372299849987, 0.055224623531103134, 0.0013644213322550058, -0.00139946851413697, -0.0022889405954629183, -0.0325237438082695, 0.02359035052359104, 0.016329549252986908, -0.0025644837878644466, 0.021037951111793518, 0.014192882925271988, 0.051280006766319275, -0.014869654551148415, 0.04342944547533989, -0.04435759037733078, 0.03532751649618149, 0.008309797383844852, 0.0005151325021870434, 0.0003797780373133719, -0.0066033643670380116, -0.005883085075765848, 0.0057573989033699036, -0.029816655442118645, 0.0308221448212862, -0.02053520642220974, 0.008836712688207626, 0.061025526374578476, -0.05990402027964592, -0.03407065197825432, 0.0114181162789464, -0.0081599410623312, 0.025659339502453804, -0.022604195401072502, 0.023629022762179375, -0.029101209715008736, -0.015121027827262878, -0.022816896438598633, -0.02256552316248417, -0.009658508002758026, -0.029468601569533348, -0.0016919308109208941, -0.04698733612895012, -0.016087844967842102, 0.025369293987751007, 0.033645253628492355, -0.007961742579936981, -0.0018103659385815263, 0.014192882925271988, -0.03801526874303818, 0.07417424768209457, 0.0064535075798630714, -0.03389662504196167, 0.007386486511677504, 0.008783537894487381, 0.0616442896425724, 0.0029101211111992598, -0.023396985605359077, 0.007004593499004841, -0.027148239314556122, -0.014801977202296257, 0.0328717976808548, 0.01719001680612564, -0.022082114592194557, -0.018495220690965652, -0.011157074943184853, 0.01256862934678793, 0.006032941862940788, -0.0009535238496027887, -0.006646871101111174, -0.03231104463338852, 0.030841480940580368, -0.023725703358650208, -0.023725703358650208, -0.024054422974586487, -0.01292635127902031, 0.009242776781320572, -0.023242294788360596, -0.08446118980646133, 0.03221436217427254, -0.0005803927197121084, -0.023474331945180893, 0.008701358921825886, -0.0354628711938858, -0.021830741316080093, -0.0426173210144043, -0.029932674020528793, -0.01207555178552866, 0.016029836609959602, 0.03465074300765991, -0.03350989893078804, -0.017228689044713974, -0.033645253628492355, -0.013622459955513477, 0.021327996626496315, 0.019375024363398552, 0.03198232501745224, 0.029932674020528793, -0.00892856065183878, -0.009948553517460823, -0.012355929240584373, 0.010499639436602592, -0.042462628334760666, 0.019723080098628998, 0.003840683028101921, 0.025330621749162674, -0.026026729494333267, 0.0055495332926511765, -0.010722007602453232, 0.020631887018680573, -0.012520288117229939, -0.0039156111888587475, -0.011920860968530178, 0.056268785148859024, -0.04451228305697441, 0.03300715237855911, 0.06021340191364288, -0.025814030319452286, 0.028733819723129272, -0.03913677856326103, -0.0038261807058006525, -0.009112255647778511, 0.032330382615327835, 0.03223370015621185, 0.054953914135694504, -0.01894962601363659, -0.030918827280402184, -0.0008175651310011744, 0.041418466717004776, -0.021173305809497833, -0.006468009669333696, -0.00396878644824028, -0.02047719620168209, 0.019636064767837524, -0.0242477860301733, 0.0057573989033699036, -0.0007523049716837704, 0.04277200996875763, 0.019346021115779877, 0.009015574119985104, -0.029874663800001144, 0.013129383325576782, 0.020303169265389442, -0.03213701769709587, 0.014299232512712479, 0.004067885223776102, 0.030377408489584923, 0.015382068231701851, -0.00837747473269701, -0.007284970488399267, 0.004094472620636225, -0.00718828896060586, 0.0029898835346102715, -0.0019408863736316562, 0.0310541819781065, 0.010180589742958546, -0.04091572016477585, 0.027728328481316566, -0.016165191307663918, 0.014144541695713997, 0.0011493044439703226, -0.023300305008888245, -0.022275477647781372, 0.038750048726797104, -0.0025427304208278656, -0.014318568632006645, 0.038576021790504456, -0.020303169265389442, -0.02857912890613079, 0.01100238412618637, 0.05619144067168236, -0.0004021356871817261, 0.02206277847290039, -0.019800424575805664, 0.03963952139019966, -0.01894962601363659, -0.018968962132930756, -0.04172784835100174, -0.004345844965428114, 0.004860675428062677, -0.044048208743333817, 0.01900763437151909, -0.032717108726501465, 0.009189601056277752, 0.005162806250154972, 0.02660682052373886, 0.022797558456659317, -0.0324077270925045, -0.0030793140176683664, -0.006733884569257498, -0.006878907326608896, 0.007396154571324587, 0.009784194640815258, -0.029758645221590996, -0.005660716909915209, 0.023745041340589523, 0.028405101969838142, -0.04083837568759918, 0.006371328141540289, 0.04253997653722763, -0.021869413554668427, -0.06280447542667389, 0.00351921608671546, 0.016841962933540344, 0.0033065162133425474, 0.022526850923895836, 0.005752564873546362, -0.021772732958197594, -0.009890544228255749, 0.007729706820100546, -0.02863713726401329, 0.010199925862252712, 0.014308900572359562, 0.013893169350922108, -0.033374544233083725, 0.013313078321516514, -0.019259007647633553, -0.02502124011516571, -0.024789202958345413, -0.003925279714167118, -0.021057287231087685, 0.038305312395095825, -0.02968130074441433, -0.02020648866891861, -0.021444015204906464, 0.040490321815013885, -0.036062296479940414, 0.015971826389431953, 0.008682021871209145, -0.0028859504964202642, 0.00277960067614913, 0.012916683219373226, -0.028231075033545494, 0.03093816339969635, -0.02869514748454094, 0.0012411520583555102, 0.01659058965742588, 0.0389820858836174, -0.01779911294579506, -0.030706128105521202, -0.013670801185071468, 0.03246573358774185, 0.021327996626496315, -0.01953938417136669, -0.025175930932164192, -0.0008604676695540547, 0.04161183163523674, 0.030744800344109535, -0.040490321815013885, 0.0180214811116457, -0.009281449019908905, -0.01207555178552866, -0.020515870302915573, 0.015353064052760601, 0.030628781765699387, -0.006463175639510155, -0.01322606485337019, 0.0018732091411948204, 0.023184286430478096, 0.006327821407467127, -0.03859535977244377, 0.015266049653291702, 0.012810333631932735, -0.015121027827262878, -0.00963433738797903, 0.031846970319747925, 0.012452610768377781, 0.006139291916042566, 0.04308139160275459, -0.07169919461011887, 0.03575291484594345, -0.03505680710077286, 0.004631056450307369, 0.03832465037703514, -0.027844347059726715, 0.06373261660337448, 0.014231555163860321, -0.006584027782082558, -0.009059080854058266, -0.056268785148859024, 0.006144125945866108, -0.020902596414089203, -0.040219612419605255, -0.01806982047855854, 0.03602362424135208, -0.027457620948553085, 0.020728569477796555, -0.018437212333083153, 0.0006060737650841475, 0.016880635172128677, 0.010760679841041565, -0.052208151668310165, -0.024460485205054283, 0.028501782566308975, -0.019800424575805664, -0.0245958399027586, -0.013699805364012718, 0.007033598143607378, -0.014869654551148415, -0.03039674647152424, 0.012820001691579819, 0.003741584252566099, 0.005375505890697241, -0.05897587537765503, 0.010054903104901314, -0.026819519698619843, -0.008251788094639778, 0.08662685751914978, 0.03521149605512619, -0.0012846589088439941, 0.04807016998529434, -0.01824384741485119, 0.006999759469181299, -0.01894962601363659, 0.008024586364626884, -0.0021318327635526657, 0.022932913154363632, 0.017760438844561577, -0.029526609927415848, -0.013052037917077541, 0.0022563105449080467, -0.004321674816310406, 0.040335629135370255, -0.018427543342113495, -0.03138289973139763, 0.03525016829371452, 0.011969202198088169, 0.014318568632006645, 0.03443804383277893, -0.004575464408844709, -0.0037512523122131824, 0.0021995101124048233, -0.006540521048009396, 0.01100238412618637, 0.014260559342801571, 0.03163427114486694, 0.0020641556475311518, 0.025717347860336304, 0.08368773013353348, 0.012433274649083614, 0.0048050833866000175, 0.0026104075368493795, 0.013564450666308403, 0.023899732157588005, -0.014337904751300812, 0.031170200556516647, 0.026239430531859398, -0.07332345098257065, 0.002624909859150648, -0.017818449065089226, -0.06133490800857544, 0.03936881199479103, 0.0017342290375381708, 0.016774285584688187, -0.019094647839665413, -0.010006561875343323, -0.04045164957642555, 0.022642867639660835, -0.006994925439357758, -0.0006447464693337679, -0.05951729044318199, 0.042849358171224594, -0.024170439690351486, 0.05994269251823425, -0.046793971210718155, -0.0114761246368289, -0.02146335132420063, 0.0067242165096104145, -0.040606338530778885, 0.017161011695861816, -0.02370636723935604, 0.04366148263216019, 0.021946759894490242, -0.03728048875927925, -0.0009583579376339912, 0.034360699355602264, 0.023242294788360596, 0.02815372869372368, -0.0114761246368289, -0.02857912890613079, 0.01828252151608467, -0.029797319322824478, 0.028231075033545494, -0.01981976069509983, -0.02672283910214901, 0.0021004113368690014, 0.005916923750191927, -0.000895514793228358, 0.001710058655589819, 0.03248507156968117, 0.003374193562194705, 0.007662029471248388, -0.03223370015621185, 0.0002217637957073748, 0.008730363100767136, -0.03339387848973274, 0.011050725355744362, 0.038518015295267105, -0.011785506270825863, -0.027012884616851807, 0.027786338701844215, 0.01522737741470337, -0.007086772937327623, 0.015913818031549454, -0.032272372394800186, 0.040219612419605255, 0.05383240431547165, -0.012365597300231457, 0.006173130590468645, 0.017924798652529716, 0.014850318431854248, 0.01746072620153427, -0.031904980540275574, -0.033645253628492355, 0.011263425461947918, 0.003787508001551032, -0.020902596414089203, -0.020612550899386406, 0.02217879518866539, -0.012684646993875504, 0.03269777074456215, -0.02923656441271305, 0.027186911553144455, -0.004111391957849264, -0.008440317586064339, 0.005520528648048639 ]
Variational quantum machine learning is an extensively studied application of near-term quantum computers. The success of variational quantum learning models crucially depends on finding a suitable parametrization of the model that encodes an inductive bias relevant to the learning task. However, precious little is known about guiding principles for the construction of suitable parametrizations. In this work, we holistically explore when and how symmetries of the learning problem can be exploited to construct quantum learning models with outcomes invariant under the symmetry of the learning task. Building on tools from representation theory, we show how a standard gateset can be transformed into an equivariant gateset that respects the symmetries of the problem at hand through a process of gate symmetrization. We benchmark the proposed methods on two toy problems that feature a non-trivial symmetry and observe a substantial increase in generalization performance. As our tools can also be applied in a straightforward way to other variational problems with symmetric structure, we show how equivariant gatesets can be used in variational quantum eigensolvers.
[ -0.0017847794806584716, -0.014024626463651657, -0.036452192813158035, 0.038785405457019806, 0.04706999287009239, 0.0674264132976532, -0.013238435611128807, 0.01169986929744482, -0.015554739162325859, 0.017177842557430267, -0.045413076877593994, 0.01370338723063469, 0.002048956463113427, -0.011378630064427853, 0.007937989197671413, 0.08501002937555313, -0.012866474688053131, 0.0012511421227827668, -0.046461328864097595, 0.010321921668946743, -0.035133421421051025, -0.0662090852856636, -0.038785405457019806, -0.005718902684748173, 0.032495878636837006, 0.018648779019713402, 0.02549624629318714, -0.0030116173438727856, -0.09454575926065445, 0.016518456861376762, -0.02686573937535286, -0.018006300553679466, -0.005663954187184572, 0.004074665252119303, -0.041963979601860046, -0.03239443525671959, 0.011285639367997646, 0.015106694772839546, -0.05711294338107109, -0.0008231754181906581, -0.0046706488355994225, 0.013940089382231236, 0.011158835142850876, -0.006031688302755356, 0.009121501818299294, -0.03841344267129898, -0.03188721463084221, -0.03800766542553902, 0.018226096406579018, -0.0010614630300551653, 0.00460724625736475, -0.005887975916266441, 0.08054649829864502, 0.020440956577658653, -0.006627671420574188, -0.02186117134988308, 0.005228590220212936, 0.021387767046689987, 0.05112775042653084, 0.0010852389968931675, 0.01213100552558899, -0.03396681696176529, -0.1135495975613594, -0.03398372232913971, 0.001143357832916081, -0.001223667641170323, 0.033036913722753525, -0.027220793068408966, 0.041220057755708694, -0.016425466164946556, -0.05741727724671364, -0.03783859312534332, -0.0002747440303210169, -0.014168338850140572, 0.03533630818128586, -0.0224022064357996, 0.019122185185551643, 0.039901286363601685, -0.01761743240058422, 0.007582935504615307, 0.03712848573923111, 0.03178577125072479, 0.01053326390683651, 0.03560682758688927, 0.050924863666296005, -0.042234499007463455, -0.006183854304254055, -0.049606092274188995, -0.0027558940928429365, -0.009163769893348217, -0.04341801255941391, 0.03239443525671959, -0.02106652781367302, -0.006052822340279818, 0.025208821520209312, 0.002154627349227667, 0.00999222882091999, -0.010051405057311058, 0.004497348330914974, -0.006276844535022974, 0.03794003650546074, -0.02448180690407753, 0.01446421630680561, -0.037737149745225906, 0.020981989800930023, -0.03560682758688927, -0.06434927880764008, 0.027186978608369827, 0.019612496718764305, 0.07621822506189346, 0.004890443757176399, -0.04318130761384964, 0.024278918281197548, 0.017448360100388527, -0.04416193440556526, -0.0383458137512207, -0.06695301085710526, -0.06086637079715729, -0.03220845386385918, -0.01658608578145504, 0.0018196508754044771, 0.09495154023170471, 0.028793174773454666, -0.00945964828133583, -0.0588713064789772, 0.073715940117836, -0.03706085681915283, 0.031008034944534302, 0.027254607528448105, 0.024583250284194946, -0.004053531214594841, 0.023095406591892242, -0.007794276811182499, -0.06999632716178894, 0.014540299773216248, -0.03824437037110329, 0.01868259534239769, 0.025902021676301956, -0.01274812314659357, -0.07500089704990387, -0.032732583582401276, -0.018293725326657295, -0.024955211207270622, -0.036181677132844925, -0.012595957145094872, -0.029012970626354218, -0.012207088991999626, 0.04453389346599579, -0.005313126835972071, 0.00664880545809865, -0.04473678395152092, 0.09028511494398117, -0.04280934855341911, 0.007553347386419773, 0.025056656450033188, 0.03440640866756439, -0.029029877856373787, 0.041422948241233826, 0.057214390486478806, -0.012587503530085087, 0.02443108521401882, -0.044905856251716614, -0.011023576371371746, 0.08250774443149567, 0.020626936107873917, 0.05055290088057518, -0.0008517064852640033, -0.026155631989240646, -0.0094765555113554, 0.04412811994552612, 0.0276434775441885, 0.00029614235972985625, -0.024803046137094498, 0.0017351142596453428, -0.012951010838150978, 0.0005354866734705865, 0.00724478904157877, -0.02684883214533329, -0.036857970058918, -0.046156998723745346, -0.06137359142303467, 0.03203938156366348, 0.0414905771613121, 0.07621822506189346, 0.08230485767126083, 0.07148417085409164, 0.050654347985982895, 0.0032673405949026346, 0.00579075887799263, 0.01766815409064293, 0.006090864073485136, 0.0224022064357996, 0.06779837608337402, 0.015199685469269753, 0.003100380767136812, -0.0521421916782856, -0.008462116122245789, -0.04764484241604805, 0.004076778888702393, 0.031210921704769135, 0.0331045426428318, -0.032191548496484756, 0.03452475741505623, -0.03413588926196098, 0.00892706774175167, 0.004725597333163023, -0.0029270807281136513, -0.012393069453537464, -0.03472764790058136, 0.00014146676403470337, 0.0024346548598259687, -0.030855868011713028, -0.01841207779943943, -0.046968549489974976, -0.0060274614952504635, -0.023568810895085335, -0.0012564256321638823, -0.03077133186161518, -0.04953846335411072, -0.0010318751446902752, -0.060900185257196426, -0.022774167358875275, 0.09001459926366806, -0.026916461065411568, -0.019544867798686028, 0.009577999822795391, 0.004226831253618002, -0.03291856124997139, -0.023061592131853104, 0.02789708599448204, 0.01041491236537695, 0.031227828934788704, 0.006467051804065704, 0.010482541285455227, 0.052547965198755264, -0.008187372237443924, 0.000040815339161781594, -0.013382147997617722, -0.0016093660378828645, -0.07506852596998215, -0.021793542429804802, -0.012815752997994423, -0.009577999822795391, -0.02686573937535286, 0.0014498031232506037, -0.0033497638069093227, -0.012443791143596172, 0.06833940744400024, 0.055422212928533554, 0.0054357051849365234, -0.036181677132844925, 0.01680588163435459, -0.026392335072159767, -0.04341801255941391, -0.008626963011920452, -0.026764295995235443, 0.023619532585144043, 0.00106621824670583, -0.00884253066033125, -0.006758703384548426, 0.07067261636257172, 0.0599195621907711, 0.01763433963060379, 0.06401113420724869, 0.01604505255818367, -0.02290942519903183, 0.014058440923690796, 0.027677292004227638, -0.003368784673511982, 0.004653741139918566, -0.00401548994705081, -0.02025497518479824, -0.055117879062891006, -0.027474403381347656, 0.04348564147949219, -0.05129682645201683, -0.008707272820174694, 0.025428617373108864, -0.011708322912454605, -0.04521018639206886, 0.02025497518479824, -0.01605350524187088, 0.03668889403343201, -0.01793867163360119, 0.030095038935542107, -0.014058440923690796, -0.0016495209420099854, -0.012223996222019196, -0.10441964119672775, 0.011150380596518517, 0.038548700511455536, 0.04497348517179489, -0.019849199801683426, 0.007206747308373451, 0.01897001825273037, 0.02028878964483738, -0.0800054594874382, -0.03428805619478226, 0.00844520889222622, -0.0030242977663874626, 0.013145445846021175, -0.049335576593875885, 0.0026755842845886946, 0.03217463940382004, -0.046698033809661865, -0.036215491592884064, 0.05660572648048401, 0.03844725713133812, -0.012621317990124226, 0.01603659801185131, 0.041050985455513, -0.006107771303504705, 0.013897821307182312, -0.015859071165323257, 0.002897492842748761, -0.00959490705281496, 0.01630711555480957, 0.01924053579568863, -0.02181044965982437, -0.0033751248847693205, 0.03187030926346779, 0.013339879922568798, -0.08595684170722961, -0.010989760980010033, 0.0358097143471241, -0.010710790753364563, 0.0462922565639019, 0.02524263598024845, -0.04767865687608719, 0.028539564460515976, 0.003865437349304557, -0.015656182542443275, -0.030095038935542107, 0.030483907088637352, 0.04078046977519989, -0.005215909797698259, -0.0189531110227108, 0.028793174773454666, -0.027812549844384193, -0.07331015914678574, -0.03337505832314491, 0.02260509319603443, 0.021928800269961357, -0.009113048203289509, 0.027947809547185898, -0.015098241157829762, -0.02813378907740116, -0.0017351142596453428, 0.03347650542855263, 0.027491310611367226, 0.000706409162376076, 0.008242321200668812, -0.034355685114860535, 0.013314519077539444, 0.02451562136411667, -0.023095406591892242, 0.013889367692172527, -0.01079532690346241, 0.02444799244403839, 0.03888684883713722, -0.009053872898221016, -0.04720525071024895, -0.03261423110961914, 0.012984826229512691, -0.05684242770075798, -0.03743281960487366, -0.020643843337893486, -0.03665507957339287, 0.013306064531207085, -0.010482541285455227, -0.017465267330408096, 0.0019221515394747257, 0.008047887124121189, 0.01785413548350334, -0.008187372237443924, -0.020221160724759102, -0.017955578863620758, -0.03132927417755127, -0.045244000852108, 0.029317302629351616, -0.0483887642621994, 0.002447335282340646, -0.008166237734258175, -0.005397663451731205, 0.01868259534239769, -0.020643843337893486, -0.003394145518541336, -0.03405135124921799, -0.0358097143471241, 0.007020766846835613, -0.010769966058433056, 0.03002741001546383, -0.03712848573923111, -0.014624835923314095, -0.00584993464872241, 0.014210606925189495, -0.042505014687776566, -0.047780100256204605, 0.04974135011434555, 0.04767865687608719, 0.03841344267129898, -0.016121134161949158, -0.05166878551244736, -0.0017065831925719976, 0.007003859616816044, -0.027220793068408966, -0.04240357130765915, -0.023298293352127075, 0.05494880676269531, -0.04206542670726776, -0.0002697246673051268, -0.03807529807090759, 0.0001776590070221573, 0.010068312287330627, 0.022469835355877876, -0.010753058828413486, -0.06164410710334778, 0.040949542075395584, 0.030331742018461227, -0.029554003849625587, -0.005317353643476963, -0.034660015255212784, 0.01951105333864689, 0.006496639922261238, 0.002751667285338044, 0.0341527983546257, 0.017566710710525513, -0.037500448524951935, -0.007844998501241207, 0.00032546601141802967, 0.06313195079565048, 0.025394802913069725, 0.015411026775836945, -0.01552092470228672, -0.035403940826654434, 0.03821055591106415, -0.009620267897844315, -0.007430769503116608, 0.004573431331664324, -0.05058671906590462, -0.03127855062484741, 0.03706085681915283, -0.01580834947526455, -0.041050985455513, -0.025073563680052757, -0.0020965083967894316, -0.03584352880716324, -0.05035001412034035, -0.02471850998699665, -0.004611473064869642, -0.024853767827153206, -0.005004568491131067, -0.09731856733560562, -0.03151525557041168, 0.06881281733512878, -0.009670990519225597, 0.0094765555113554, -0.024126753211021423, 0.045683592557907104, -0.02128632180392742, 0.027778735384345055, 0.034372590482234955, 0.031464532017707825, -0.07263386994600296, 0.04446626454591751, 0.04744195565581322, -0.03760189190506935, -0.061204519122838974, -0.01632402278482914, -0.0020288790110498667, 0.013466684147715569, -0.04521018639206886, -0.041050985455513, 0.011496981605887413, -0.003434300422668457, 0.009552638977766037, -0.020643843337893486, -0.043823786079883575, -0.03837962821125984, -0.01817537471652031, 0.04372234269976616, -0.005858388263732195, 0.010685429908335209, -0.006691073998808861, -0.024583250284194946, 0.012959464453160763, 0.012266264297068119, -0.02478613890707493, -0.03315526619553566, 0.040137991309165955, -0.02181044965982437, -0.023822421208024025, 0.027778735384345055, 0.05508406460285187, 0.018581150099635124, -0.026645945385098457, 0.007815411314368248, -0.015377212315797806, 0.07500089704990387, 0.039055921137332916, -0.034829091280698776, -0.030365556478500366, -0.023856235668063164, 0.029570911079645157, -0.0638420581817627, 0.01488689985126257, 0.032225362956523895, 0.01185203529894352, 0.004953846335411072, -0.03868396207690239, -0.003848529886454344, 0.029351117089390755, -0.00611622491851449, 0.007126437500119209, 0.015055973082780838, -0.01579989492893219, -0.04101717099547386, -0.044601522386074066, 0.006336020305752754, 0.009299028664827347, 0.004150748252868652, -0.04230212792754173, 0.01918981410562992, 0.04054376482963562, -0.018479706719517708, 0.06617527455091476, 0.011742137372493744, -0.051702599972486496, -0.04392522946000099, -0.005959832109510899, -0.0205254927277565, 0.0041444082744419575, -0.05582798644900322, -0.06749404221773148, 0.009873878210783005, -0.024650881066918373, -0.0034575480967760086, -0.04571740701794624, -0.026916461065411568, -0.01577453501522541, -0.04453389346599579, 0.06759548932313919, -0.019612496718764305, 0.02715316414833069, 0.02952018938958645, 0.013787923380732536, 0.04389141499996185, -0.013331426307559013, 0.019578682258725166, -0.051702599972486496, -0.004759412258863449, -0.058533161878585815, 0.002612181706354022, -0.015960514545440674, -0.01380483154207468, -0.029418746009469032, -0.01198729407042265, 0.012756576761603355, -0.006877054460346699, 0.0034681151155382395, 0.012579049915075302, 0.009975321590900421, 0.0005336374742910266, 0.016628354787826538, -0.02417747490108013, -0.041997797787189484, 0.03269876539707184, 0.05596324801445007, 0.007443449925631285, -0.02946946769952774, -0.047239065170288086, -0.026747388765215874, -0.0045311632566154, 0.005317353643476963, -0.012528328225016594, -0.006669939961284399, 0.016459280624985695, 0.004114820156246424, 0.009831609204411507, -0.02267272397875786, -0.0205254927277565, -0.007933761924505234, 0.01871640980243683, 0.05971667170524597, 0.010896771214902401, -0.0416596494615078, -0.05548984184861183, 0.002662903629243374, -0.013136991299688816, -0.047475770115852356, -0.039089735597372055, 0.0642816498875618, -0.012891835533082485, 0.023636439815163612, -0.03077133186161518, 0.01792176440358162, 0.00035003447555936873, -0.026459963992238045, 0.06972581148147583, -0.022216225042939186, -0.012587503530085087, 0.012477605603635311, 0.022520557045936584, 0.024042217060923576, 0.012739669531583786, -0.019020741805434227, -0.019950643181800842, 0.02236839197576046, -0.039360255002975464, 0.0437561571598053, -0.002935534343123436, 0.033561039716005325, 0.013855553232133389, -0.019899921491742134, 0.042234499007463455, 0.001092635910026729, -0.017203204333782196, 0.014134524390101433, -0.025141192600131035, 0.005296219605952501, 0.04571740701794624, 0.010871410369873047, 0.027947809547185898, -0.04020562022924423, 0.01891929656267166, -0.0031194014009088278, -0.006543134804815054, 0.006991179194301367, 0.016535364091396332, -0.049639906734228134, -0.018581150099635124, -0.0009853800293058157, -0.09393709897994995, -0.00046046043280512094, -0.005871068686246872, -0.009654082357883453, -0.029418746009469032, 0.029063692316412926, 0.05596324801445007, 0.04679947718977928, -0.00984851736575365, -0.004641060717403889, -0.0056597269140183926, 0.01235080137848854, -0.0009372998611070216, 0.030314834788441658, 0.005093331914395094, -0.034372590482234955, -0.004535390064120293, 0.041050985455513, 0.04311367869377136, 0.025445524603128433, -0.010042951442301273, 0.04693473502993584, -0.016645262017846107, 0.046190813183784485, -0.023805513978004456, -0.029165135696530342, 0.01538566593080759, 0.010169756598770618, 0.02843812108039856, 0.033341243863105774, 0.0013705500168725848, -0.0165522713214159, 0.01951105333864689, -0.010212024673819542, 0.018209189176559448, 0.07094313949346542, 0.0062261223793029785, 0.051465898752212524, 0.013771016150712967, -0.032766398042440414, -0.024025309830904007, -0.00021966313943266869, 0.03139690309762955, -0.01947723887860775, -0.00949346274137497, 0.010474087670445442, 0.016205672174692154, -0.0036287347320467234, 0.00029878414352424443, -0.02580057829618454, 0.02050858549773693, -0.014709373004734516, -0.02865791693329811, -0.0033096089027822018, 0.004374770447611809, 0.008052113465964794, -0.03281711786985397, -0.015191231854259968, -0.0473405122756958, -0.04764484241604805, 0.004484667908400297, -0.029334209859371185, -0.02813378907740116, -0.014895353466272354, -0.008221186697483063, 0.023061592131853104, -0.04284316301345825, -0.04206542670726776, -0.03932643681764603, 0.0020151417702436447, 0.006957364268600941, 0.028269048780202866, 0.023856235668063164, -0.0004966526757925749, 0.031988658010959625, 0.02260509319603443, -0.001563927624374628, 0.0028890392277389765, -0.011158835142850876, 0.01118419598788023, 0.02581748552620411, 0.05630139261484146, 0.01871640980243683, 0.03946169838309288, 0.01632402278482914, 0.00533003406599164, -0.03400063142180443, -0.0008252888219431043, 0.022030245512723923, 0.04869309812784195, -0.010119033977389336, -0.07026684284210205, -0.007713967002928257, 0.04267409071326256, 0.03973221406340599, -0.005892202723771334, 0.018750224262475967, -0.015901340171694756, 0.027812549844384193, -0.059885747730731964, 0.041997797787189484, 0.008910160511732101, 0.02182735688984394, -0.027947809547185898, -0.007223654538393021, 0.004729824140667915, 0.00479745352640748, -0.06722352653741837, -0.0023501182440668344, 0.00735891330987215, -0.012325440533459187, -0.009442741051316261, 0.007029220461845398, 0.001725603942759335, 0.0006451201043091714, -0.013483592309057713, -0.019122185185551643, 0.0389544777572155, 0.02554696798324585, 0.010271199978888035, 0.027575846761465073, -0.012274717912077904, -0.033070728182792664, 0.022300761193037033, -0.01922362856566906, -0.005372302606701851, -0.01198729407042265, 0.018513521179556847, 0.036959413439035416, 0.02160756103694439, -0.009020058438181877, 0.023298293352127075, 0.041050985455513, 0.022047152742743492, -0.04521018639206886, 0.03400063142180443, 0.019527960568666458, 0.0002810842706821859, 0.03499816358089447, -0.01094749290496111, -0.018259910866618156, 0.019037649035453796, -0.033341243863105774, -0.017701970413327217, -0.034338776022195816, 0.009544185362756252, 0.010119033977389336, 0.049098871648311615, -0.018598057329654694, 0.013483592309057713, -0.014514938928186893, 0.002557232975959778, -0.00149524153675884, -0.02426201105117798, 0.004467760678380728, -0.0462922565639019, 0.023230664432048798, 0.009155316278338432, -0.007160252425819635, -0.02316303551197052, -0.00016920534835662693, -0.026493778452277184, 0.06789981573820114, -0.018530428409576416, -0.03254660218954086, 0.04023943468928337, -0.03587734326720238, -0.027491310611367226, 0.013069362379610538, -0.019832292571663857, 0.01538566593080759, 0.021235600113868713, -0.00161464954726398, -0.010347283445298672, -0.0273391455411911, -0.012283171527087688, 0.030450092628598213, 0.013762562535703182, 0.0015597007004544139, -0.03736519068479538, 0.028556471690535545, -0.01866568624973297, 0.052277449518442154, 0.016949594020843506, -0.027271514758467674, -0.00408945931121707, 0.04078046977519989, -0.005875295493751764, -0.007519532926380634, -0.0018883368466049433, -0.006395195610821247, -0.02028878964483738, -0.048016805201768875, -0.01868259534239769, -0.00220640585757792, -0.006961591076105833, -0.004266986157745123, -0.04920031502842903, 0.018614964559674263, -0.009299028664827347, -0.06590475142002106, 0.03976602852344513, 0.011327908374369144, 0.057214390486478806, -0.000521221139933914, 0.03050081431865692, -0.03946169838309288, 0.014438855461776257, -0.043079864233732224, -0.026950277388095856, -0.011370176449418068, -0.026392335072159767, -0.0192574430257082, 0.0573834627866745, -0.0005043137934990227, 0.005034156143665314, -0.025225728750228882, -0.010389551520347595, 0.010972853749990463, 0.00869881920516491, 0.03080514632165432, 0.0003888684732373804, -0.009011604823172092, -0.03295237571001053, -0.00513982679694891, 0.009307482279837132, -0.03403444588184357, -0.033070728182792664, 0.004269099794328213, 0.023264478892087936, 0.022030245512723923, -0.019899921491742134, 0.050924863666296005, -0.0028214098419994116, 0.05136445537209511, -0.028573378920555115, -0.035167235881090164, -0.020085902884602547, 0.003108834382146597, 0.035674456506967545, -0.005190548952668905, 0.0076590185053646564, -0.00909614097326994, 0.03584352880716324, -0.018817853182554245, -0.05816119909286499, -0.05339333415031433, 0.0010561795206740499, -0.01552092470228672, 0.02554696798324585, -0.002893266035243869, -0.003943633753806353, 0.008115516044199467, -0.004309254698455334, -0.018530428409576416, -0.04767865687608719, 0.018834760412573814, -0.02581748552620411, -0.047509584575891495, -0.048016805201768875, -0.010102126747369766, 0.02162446826696396, 0.04335038363933563, -0.017532896250486374, -0.03574208542704582, -0.025648413226008415, -0.017287740483880043, -0.009518824517726898, -0.007126437500119209, -0.026493778452277184, -0.06350391358137131, -0.024109845981001854, -0.002853111131116748, 0.0027791415341198444, 0.03132927417755127, 0.015884432941675186, 0.044601522386074066, -0.014996797777712345, 0.0071982936933636665, -0.006052822340279818, -0.018090838566422462, -0.0358097143471241, 0.0358097143471241, 0.009586453437805176, -0.032732583582401276, 0.005287765990942717, 0.04071284085512161, 0.03966458514332771, -0.0051820953376591206, 0.000982738332822919, 0.0022423339542001486, 0.03763570636510849, -0.05630139261484146, -0.0536300353705883, -0.02338283136487007, 0.03345959633588791, -0.006551588419824839, -0.028607195243239403, -0.049301762133836746, -0.013044001534581184, 0.0400027297437191, 0.0013642098056152463, 0.03543775528669357, 0.010059858672320843, -0.040374692529439926, -0.009265214204788208, -0.007722420617938042, -0.007519532926380634, -0.01897001825273037, -0.07797658443450928, 0.028556471690535545, 0.01976466365158558, -0.014421948231756687, 0.01629866100847721, 0.05308900028467178, 0.013956996612250805, -0.02267272397875786, 0.0038738909643143415, -0.040949542075395584, 0.01514051016420126, -0.013728748075664043, 0.04940320551395416, -0.0057611712254583836, 0.01142935175448656, -0.023619532585144043, -0.013678026385605335, -0.048557836562395096, 0.05248033627867699, 0.031937938183546066, 0.011268732137978077, -0.023906957358121872, -0.0074772643856704235, -0.04003654792904854, 0.003110947785899043, -0.0009748129523359239, -0.04084809869527817, -0.016171855852007866, 0.0022148597054183483, -0.016966501250863075, 0.016510002315044403, 0.023484274744987488, -0.001523772720247507, 0.022757260128855705, -0.06762930005788803, -0.013838646002113819, -0.01538566593080759, -0.0341527983546257, 0.01839517056941986, 0.036418378353118896, -0.018090838566422462, -0.0035484249237924814, 0.02338283136487007, -0.00481436075642705, 0.016915779560804367, -0.010846049524843693, -0.006103544495999813, -0.062016069889068604, 0.032766398042440414, 0.030416278168559074, -0.008195825852453709, 0.05139826983213425, -0.0321408249437809, 0.003878117771819234, 0.006073956377804279, -0.001331451814621687, 0.025716042146086693, 0.012908742763102055, -0.02683192491531372, -0.02945256046950817, -0.021100342273712158, -0.006374061573296785, 0.03973221406340599, 0.06110307201743126, -0.01606195978820324, 0.055895619094371796, -0.01978157088160515, -0.007616749964654446, -0.00896088220179081, -0.016510002315044403, -0.050451457500457764, 0.009180678054690361, -0.0045692045241594315, -0.028759360313415527, 0.04111861437559128, -0.020221160724759102, 0.018361356109380722, 0.06691919267177582, -0.03449094295501709, 0.012731215916574001, -0.03530249372124672, -0.037737149745225906, -0.04108479991555214 ]
Cloud service providers have launched Machine-Learning-as-a-Service (MLaaS) platforms to allow users to access large-scale cloudbased models via APIs. In addition to prediction outputs, these APIs can also provide other information in a more human-understandable way, such as counterfactual explanations (CF). However, such extra information inevitably causes the cloud models to be more vulnerable to extraction attacks which aim to steal the internal functionality of models in the cloud. Due to the black-box nature of cloud models, however, a vast number of queries are inevitably required by existing attack strategies before the substitute model achieves high fidelity. In this paper, we propose a novel simple yet efficient querying strategy to greatly enhance the querying efficiency to steal a classification model. This is motivated by our observation that current querying strategies suffer from decision boundary shift issue induced by taking far-distant queries and close-to-boundary CFs into substitute model training. We then propose DualCF strategy to circumvent the above issues, which is achieved by taking not only CF but also counterfactual explanation of CF (CCF) as pairs of training samples for the substitute model. Extensive and comprehensive experimental evaluations are conducted on both synthetic and real-world datasets. The experimental results favorably illustrate that DualCF can produce a high-fidelity model with fewer queries efficiently and effectively.
[ -0.04391782730817795, -0.03386295586824417, -0.02192038856446743, -0.03673302382230759, 0.0059616523794829845, 0.010353434830904007, -0.005012989044189453, 0.013262027874588966, -0.0785127505660057, 0.07466030865907669, -0.007276298012584448, -0.039718665182590485, -0.03216788172721863, -0.07535374909639359, -0.0356736034154892, -0.002000861568376422, -0.001692666206508875, -0.013079036958515644, 0.04784731566905975, -0.04264651983976364, -0.02390439622104168, -0.039641618728637695, -0.009125469252467155, 0.06776443868875504, 0.040758825838565826, 0.0990847796201706, 0.04280062019824982, -0.01508230622857809, -0.041953083127737045, 0.03135886788368225, 0.04349405691027641, 0.021207688376307487, -0.022344157099723816, -0.06067594513297081, -0.023596201092004776, -0.02020605280995369, 0.002248862525448203, 0.033111728727817535, -0.020572034642100334, 0.05458908900618553, 0.00369834341108799, -0.02818060666322708, -0.019974905997514725, 0.04673010855913162, 0.02556094527244568, -0.05670792981982231, -0.042415376752614975, -0.026196599006652832, -0.04260799661278725, -0.025426110252738, -0.02787240967154503, -0.03994981199502945, 0.02271013893187046, -0.017557499930262566, -0.027371592819690704, 0.06572264432907104, 0.012260393239557743, -0.01482226699590683, 0.03214861825108528, -0.004273801576346159, 0.03263017535209656, 0.012992356903851032, -0.015554230660200119, -0.0021730174776166677, -0.02297981083393097, -0.003551468951627612, 0.020957278087735176, 0.014369605109095573, 0.0037970622070133686, 0.023846609517931938, -0.06021365150809288, 0.01697000302374363, 0.014610382728278637, -0.04264651983976364, -0.013628009706735611, -0.00928919855505228, 0.02463635988533497, 0.04561290144920349, -0.007733775302767754, -0.006236138753592968, -0.034286726266145706, 0.03987276554107666, -0.027313806116580963, 0.022864237427711487, 0.09423070400953293, -0.01661365106701851, -0.048155512660741806, -0.07142425328493118, -0.01634398102760315, -0.03135886788368225, -0.014860791154205799, 0.002170609775930643, 0.014658537693321705, -0.033034682273864746, -0.03368959575891495, -0.003313099266961217, 0.038909655064344406, -0.04033505544066429, -0.08937662839889526, -0.0165077093988657, -0.056091539561748505, 0.052662868052721024, -0.009958559647202492, 0.0015518113505095243, 0.0501587800681591, -0.00980446208268404, -0.03320804238319397, 0.035808440297842026, 0.02877773344516754, 0.14739438891410828, -0.0211306381970644, 0.022228583693504333, -0.021804815158247948, -0.007647095248103142, 0.009987452998757362, -0.000552283541765064, -0.06487510353326797, -0.039603091776371, 0.0036188866943120956, -0.060059554874897, -0.017143363133072853, 0.049619439989328384, 0.059250541031360626, 0.019695604220032692, -0.04021948203444481, 0.07712586969137192, 0.02654331922531128, 0.014976364560425282, 0.03777318447828293, 0.03243755176663399, 0.018636183813214302, -0.018241308629512787, 0.007863795384764671, -0.02845027670264244, 0.026369959115982056, 0.017990900203585625, 0.07735701650381088, 0.04892599955201149, -0.02455931156873703, 0.0208031814545393, 0.044726841151714325, -0.03276501223444939, -0.03149370476603508, 0.013445018790662289, -0.018732493743300438, -0.046653058379888535, 0.04615224152803421, 0.05936611443758011, 0.02733306959271431, 0.018231676891446114, -0.02687077596783638, 0.0448809377849102, 0.027448641136288643, 0.011374332010746002, 0.03627073019742966, -0.0058364481665194035, 0.019955644384026527, -0.0326879620552063, 0.024790458381175995, 0.017605654895305634, 0.03837031126022339, -0.06529887765645981, 0.0326879620552063, 0.00853797234594822, 0.016604021191596985, -0.0031373316887766123, 0.04699977859854698, 0.006963287014514208, -0.03883260488510132, 0.05605301633477211, 0.0554366260766983, -0.007406317628920078, -0.010546057485044003, -0.02931707538664341, 0.021939652040600777, 0.051661234349012375, 0.04503503441810608, -0.053048111498355865, -0.04387930408120155, -0.01502451952546835, -0.041298165917396545, -0.0075989398173987865, -0.0039872764609754086, -0.006828451529145241, 0.04588257148861885, -0.00237286277115345, 0.03817769140005112, -0.011586216278374195, 0.039718665182590485, -0.02232489548623562, -0.003811508882790804, 0.02219006046652794, 0.04588257148861885, 0.019724497571587563, 0.03553876653313637, -0.028565850108861923, -0.015843164175748825, 0.03368959575891495, 0.004271394107490778, -0.007507444359362125, -0.04699977859854698, -0.04395635053515434, -0.033304352313280106, -0.022922024130821228, 0.023653987795114517, 0.003346808021888137, 0.019435564056038857, -0.010748310014605522, -0.04742354899644852, -0.00392226641997695, -0.007334084715694189, 0.057016126811504364, -0.04715387895703316, -0.017364878207445145, 0.028296178206801414, -0.002259697299450636, 0.021246211603283882, 0.00240055238828063, -0.031262557953596115, -0.0333428755402565, 0.027641264721751213, 0.04299324005842209, 0.0044808704406023026, -0.03800433129072189, -0.04114406928420067, -0.030819527804851532, -0.0069488403387367725, 0.013146454468369484, -0.0317055881023407, -0.012067771516740322, -0.020379412919282913, 0.008383874781429768, 0.02912445366382599, -0.019358515739440918, 0.017335984855890274, -0.07046114653348923, 0.004203976131975651, -0.03823547810316086, -0.010228230617940426, 0.004721648059785366, -0.013127192854881287, -0.06398904323577881, -0.016469184309244156, -0.03889039158821106, 0.06198577582836151, -0.0105653190985322, -0.056939076632261276, 0.03453713282942772, 0.0016059863846749067, 0.013984360732138157, -0.009717782028019428, -0.02521422691643238, -0.01827983185648918, 0.04260799661278725, -0.02719823271036148, -0.000029532871849369258, -0.0176538098603487, -0.0043243649415671825, 0.01128765195608139, -0.07019147276878357, 0.041105546057224274, -0.0389481782913208, -0.038601458072662354, 0.07600866258144379, -0.01968597248196602, -0.0076326485723257065, 0.06583821773529053, -0.03767687454819679, -0.022729402408003807, 0.03155149146914482, 0.018337618559598923, -0.013897680677473545, -0.06171610578894615, -0.0356736034154892, -0.03785023093223572, -0.03559655323624611, -0.00047192402416840196, 0.01950298249721527, 0.016305455937981606, -0.028431015089154243, 0.013888049870729446, -0.00317826378159225, 0.01043048407882452, 0.007011442445218563, -0.022536778822541237, -0.029894942417740822, -0.0455743782222271, 0.0037753921933472157, -0.031724851578474045, 0.012982726097106934, -0.058325957506895065, -0.05474318563938141, -0.03592401370406151, -0.0005170698277652264, 0.01808721013367176, 0.027949459850788116, 0.03293836861848831, 0.011297282762825489, 0.03289984539151192, -0.005894234869629145, -0.0956946313381195, -0.013618378899991512, 0.05520547926425934, 0.06984475255012512, -0.038062117993831635, 0.025599470362067223, 0.02910519205033779, 0.06695542484521866, -0.005605301819741726, 0.01644992269575596, 0.032187145203351974, -0.0429161936044693, -0.016758117824792862, -0.024713408201932907, -0.020417938008904457, 0.06198577582836151, -0.005566777195781469, -0.04476536437869072, -0.014697062782943249, -0.008306825533509254, 0.055552199482917786, 0.027313806116580963, -0.08922253549098969, -0.006014623679220676, -0.00023235034313984215, -0.000688623811583966, -0.041953083127737045, 0.029740843921899796, -0.014051778241991997, 0.0064432076178491116, -0.046845681965351105, -0.025830617174506187, -0.05493580922484398, -0.019647449254989624, -0.035943273454904556, -0.010295648127794266, -0.04927271977066994, 0.037542037665843964, -0.025734305381774902, -0.013791739009320736, -0.01879028044641018, 0.001814258866943419, -0.04303176701068878, 0.03266869857907295, -0.0211306381970644, -0.010603844188153744, -0.03209083154797554, -0.041953083127737045, -0.040373582392930984, 0.031262557953596115, 0.0011539264814928174, -0.009977822192013264, -0.07801192998886108, -0.0018082394963130355, 0.018299095332622528, -0.000400593678932637, -0.01680627465248108, 0.005330814979970455, -0.02687077596783638, 0.03952604532241821, 0.04372520372271538, 0.010651999153196812, -0.04661453515291214, 0.03062690608203411, -0.05042845383286476, -0.044534217566251755, 0.0037320521660149097, 0.005167086608707905, -0.0036309256684035063, 0.039448995143175125, -0.017769383266568184, 0.06553002446889877, 0.0013158493675291538, 0.05586039274930954, -0.046383388340473175, -0.014870421960949898, 0.003611663356423378, -0.0031638171058148146, -0.01585279405117035, 0.05624563992023468, -0.03565433993935585, 0.005956836976110935, 0.03315025568008423, -0.0003933703410439193, 0.019002165645360947, -0.0059712836518883705, -0.03288058191537857, -0.003977645188570023, -0.05597596615552902, 0.038851868361234665, 0.019859332591295242, 0.015207510441541672, -0.0026485531125217676, -0.05512842908501625, 0.01716262474656105, -0.02461709827184677, 0.01908884570002556, 0.007651911117136478, 0.013743583112955093, -0.051198940724134445, 0.0021055997349321842, 0.07516112178564072, -0.014803004451096058, 0.042685046792030334, 0.012289286591112614, 0.0006181963835842907, 0.05790218710899353, -0.02581135369837284, -0.02039867453277111, 0.012308549135923386, -0.006212061271071434, -0.06641608476638794, -0.0064769163727760315, -0.019955644384026527, 0.037195317447185516, 0.04303176701068878, 0.005475281737744808, -0.004781842231750488, -0.026504794135689735, -0.008171990513801575, -0.011749944649636745, 0.0069921803660690784, 0.05736284703016281, -0.009448111057281494, -0.00047884637024253607, 0.033766645938158035, 0.011990722268819809, 0.023519152775406837, 0.024135543033480644, -0.025194963440299034, 0.047038305550813675, -0.0058364481665194035, 0.023615462705492973, -0.032379765063524246, 0.0067802960984408855, 0.0026052133180201054, -0.004890192300081253, -0.03016461245715618, -0.03623220697045326, -0.020745394751429558, 0.007348531391471624, -0.01333907712250948, -0.03239902853965759, -0.013011619448661804, -0.03827400133013725, -0.06344970315694809, -0.004179898649454117, -0.0422612763941288, 0.012135189026594162, -0.006963287014514208, -0.08798975497484207, 0.01596836745738983, -0.08074716478586197, -0.041298165917396545, 0.04865632951259613, -0.029548222199082375, -0.03318877890706062, -0.04807846248149872, 0.010016346350312233, -0.05963578447699547, -0.0012857521651312709, 0.06988327950239182, -0.00007061554060783237, -0.008123834617435932, 0.007512259762734175, 0.04649896174669266, -0.05909644439816475, -0.04345553368330002, -0.01066162995994091, 0.02012900449335575, 0.017143363133072853, 0.031146984547376633, -0.004899823572486639, -0.015698697417974472, 0.005316368769854307, 0.02833470329642296, 0.010690523311495781, -0.05004320666193962, -0.000578167091589421, -0.03340066224336624, 0.05143008753657341, 0.018674707040190697, -0.0004391180700622499, -0.029355600476264954, 0.011066136881709099, -0.0030771372839808464, -0.02007121779024601, -0.03280353546142578, -0.0541267953813076, -0.041105546057224274, 0.03209083154797554, -0.06264068931341171, 0.0254068486392498, -0.052662868052721024, -0.023942921310663223, -0.05158418416976929, -0.026851514354348183, -0.012713055126369, 0.03744572773575783, -0.004931124392896891, 0.039911288768053055, -0.013493174687027931, 0.002222376875579357, 0.007141462527215481, 0.001277324976399541, -0.007314822170883417, -0.03669450059533119, 0.007536337710916996, 0.04041210561990738, 0.028026508167386055, -0.020456461235880852, 0.022941285744309425, 0.023942921310663223, -0.0356350801885128, -0.0037946542724967003, 0.013242766261100769, 0.01680627465248108, 0.0012701016385108232, 0.01881917379796505, 0.02818060666322708, 0.024848245084285736, -0.03419041261076927, 0.0011984703596681356, 0.0045025404542684555, 0.03247607871890068, 0.027082659304142, 0.05247024446725845, 0.00960220955312252, 0.006558780558407307, -0.016353612765669823, 0.009318091906607151, 0.040566202253103256, -0.02232489548623562, -0.01593947410583496, 0.017673073336482048, 0.004338811617344618, 0.016132095828652382, -0.024000708013772964, -0.047038305550813675, -0.029028141871094704, -0.046576011925935745, 0.09091760963201523, -0.015708327293395996, -0.01409993413835764, 0.02338431589305401, 0.027352331206202507, 0.019618555903434753, -0.020841706544160843, 0.02627364732325077, 0.0003461177402641624, 0.029875678941607475, -0.02733306959271431, -0.0023114646319299936, -0.01178846973925829, 0.01350280549377203, -0.024019969627261162, 0.01860729046165943, 0.02014826610684395, -0.002337950048968196, -0.04927271977066994, -0.01811610348522663, 0.02904740534722805, 0.013050143606960773, 0.03230271860957146, -0.005769030191004276, -0.016421029344201088, -0.0053452616557478905, 0.05578334629535675, 0.004266578238457441, 0.01438886672258377, -0.002949525136500597, -0.0369834341108799, -0.022151535376906395, 0.03347771242260933, 0.012558957561850548, -0.001977987587451935, -0.007772299461066723, -0.0091639943420887, 0.033997792750597, 0.00844647642225027, -0.04145226627588272, -0.01109503023326397, 0.0024101834278553724, 0.033439189195632935, 0.022267108783125877, 0.012973095290362835, 0.00279783527366817, -0.017740489915013313, -0.03249533846974373, -0.0051430086605250835, -0.0017552684294059873, 0.030819527804851532, -0.010324541479349136, -0.003551468951627612, 0.010892776772379875, 0.0495423898100853, 0.031397394835948944, -0.02694782428443432, 0.020032692700624466, 0.0051767174154520035, 0.01786569505929947, -0.007656726520508528, 0.03998833894729614, 0.020957278087735176, 0.004037839826196432, 0.003024166217073798, 0.01721077971160412, 0.01846282370388508, -0.033246565610170364, 0.011297282762825489, 0.03756130114197731, -0.019002165645360947, 0.03758056089282036, -0.042877666652202606, 0.006106119137257338, 0.031917475163936615, 0.03790801763534546, 0.01871323212981224, -0.0069825490936636925, -0.01211592648178339, 0.05042845383286476, -0.03282279893755913, 0.060059554874897, -0.0048685222864151, -0.01792348176240921, 0.013300552032887936, 0.006664722692221403, -0.013329445384442806, -0.015900950878858566, -0.006057963240891695, -0.028951093554496765, -0.016055047512054443, -0.010343804024159908, -0.010931300930678844, -0.03471049293875694, 0.01702778972685337, -0.0009492655517533422, 0.0020670753438025713, 0.03576991334557533, -0.001477170386351645, 0.0035490612499415874, -0.003681488800793886, -0.009501082822680473, 0.05131451413035393, 0.0018118511652573943, -0.021958913654088974, -0.055821869522333145, -0.0013977137859910727, 0.052662868052721024, 0.0660308375954628, 0.016112834215164185, 0.0035442456137388945, 0.008692069910466671, 0.021226949989795685, -0.01201961562037468, -0.017692334949970245, 0.04280062019824982, 0.034305986016988754, 0.029432648792862892, 0.02798798307776451, 0.009322906844317913, -0.05532105267047882, 0.013733952306210995, -0.032784271985292435, 0.00911102257668972, -0.03155149146914482, 0.020379412919282913, 0.03029944747686386, -0.026774464175105095, 0.03908301517367363, -0.018289463594555855, -0.0006416721735149622, -0.022941285744309425, 0.04310881346464157, 0.014966732822358608, -0.022344157099723816, 0.051661234349012375, 0.006573227234184742, -0.0089087700471282, 0.004594035912305117, -0.03049207106232643, 0.00939514022320509, -0.008793196640908718, 0.010998719371855259, -0.025272013619542122, -0.010950563475489616, -0.02964453399181366, 0.023191694170236588, -0.022170796990394592, -0.037002693861722946, -0.0035322068724781275, -0.00663582980632782, 0.0273908544331789, -0.02450152486562729, -0.017875326797366142, 0.02608102560043335, -0.02627364732325077, 0.004793881438672543, -0.008817274123430252, 0.002459542825818062, -0.018241308629512787, 0.0173263531178236, -0.024251116439700127, 0.010834990069270134, -0.010006715543568134, 0.02197817526757717, 0.01849171705543995, -0.024308903142809868, -0.016305455937981606, 0.01369542721658945, 0.013213872909545898, 0.042222753167152405, -0.002944709500297904, 0.004567550495266914, 0.03499942645430565, 0.0049840956926345825, 0.051661234349012375, 0.015313453041017056, 0.021997438743710518, 0.04403340071439743, 0.06872754544019699, 0.03696417063474655, 0.017095206305384636, -0.0435711070895195, -0.026447007432579994, 0.04214570298790932, 0.019464457407593727, -0.001312237698584795, -0.027044136077165604, 0.0024234261363744736, 0.04229980334639549, 0.00004973561590304598, -0.061831679195165634, 0.006606936454772949, 0.034768279641866684, -0.008629467338323593, 0.07046114653348923, 0.026254385709762573, 0.038659244775772095, -0.008017892949283123, 0.026986349374055862, 0.030530594289302826, -0.010180075652897358, -0.04723092541098595, -0.005870156921446323, 0.02496381662786007, -0.006631013937294483, -0.003043428296223283, 0.011335807852447033, 0.022883499041199684, 0.035423193126916885, -0.003009719541296363, 0.045728474855422974, -0.03910227492451668, -0.04303176701068878, -0.010372697375714779, 0.001974375918507576, 0.010093395598232746, 0.016006892547011375, -0.013791739009320736, 0.014658537693321705, 0.0554366260766983, -0.004504948388785124, -0.02093801647424698, 0.05289401486515999, 0.0018311133608222008, -0.03810064122080803, 0.035750653594732285, 0.029413387179374695, -0.04079734906554222, 0.016719594597816467, 0.026042500510811806, 0.043802253901958466, -0.046113718301057816, -0.03247607871890068, 0.0007042743382044137, 0.041221119463443756, -0.021958913654088974, -0.015987630933523178, 0.0025835433043539524, 0.009390325285494328, 0.018530240282416344, 0.02766052633523941, 0.025830617174506187, -0.050197307020425797, 0.030453545972704887, 0.023153170943260193, -0.008239408023655415, -0.021535145118832588, 0.044996511191129684, -0.023653987795114517, 0.030819527804851532, 0.005937574431300163, -0.037407200783491135, 0.04726945236325264, 0.013040512800216675, -0.02646626904606819, -0.02602323889732361, -0.017634548246860504, -0.07670210301876068, 0.08953072875738144, -0.018780650570988655, 0.018973272293806076, -0.024077756330370903, -0.01359911635518074, -0.010834990069270134, -0.005167086608707905, 0.021092114970088005, -0.0028050586115568876, 0.012693792581558228, 0.03180190175771713, -0.01340649463236332, 0.006818820722401142, 0.05948168784379959, 0.016228407621383667, 0.004309918265789747, -0.027699051424860954, 0.03769613429903984, -0.02977936901152134, -0.030530594289302826, -0.033304352313280106, -0.007555599790066481, 0.007223326712846756, -0.015034151263535023, -0.0667242780327797, 0.029894942417740822, 0.02925928868353367, -0.01629582606256008, 0.039448995143175125, -0.024848245084285736, 0.032976895570755005, 0.019782284274697304, -0.020051956176757812, 0.0415678396821022, -0.02534906193614006, 0.02613881230354309, -0.045728474855422974, 0.024540048092603683, -0.0086631765589118, -0.003269759239628911, 0.00604351656511426, 0.010680892504751682, -0.010690523311495781, -0.04830960929393768, -0.002499271184206009, 0.007647095248103142, -0.013579854741692543, -0.002439076779410243, -0.0468842051923275, 0.01588168740272522, -0.0006591285928152502, 0.02488676831126213, 0.036617450416088104, 0.004049878567457199, -0.038659244775772095, 0.01122023444622755, -0.02502160333096981, 0.04283914342522621, -0.00828274805098772, -0.015034151263535023, -0.017798276618123055, 0.0402965322136879, -0.0016168212750926614, 0.008624652400612831, 0.03804285451769829, -0.013801369816064835, 0.01514972373843193, -0.024713408201932907, -0.006428760942071676, -0.11102735251188278, -0.0012436161050572991, -0.025098653510212898, -0.0076085710898041725, 0.03016461245715618, 0.010180075652897358, -0.0020466092973947525, 0.009968191385269165, -0.0005429533775895834, 0.055629245936870575, -0.056553833186626434, 0.01561201736330986, 0.019406670704483986, 0.032726485282182693, 0.01664254441857338, 0.017750121653079987, -0.018722863867878914, -0.03328508883714676, -0.038909655064344406, -0.0042111994698643684, -0.009722597897052765, -0.04418749734759331, 0.03201378509402275, -0.013079036958515644, -0.012751579284667969, 0.005046697799116373, -0.020841706544160843, 0.006106119137257338, 0.031127722933888435, -0.01501488871872425, -0.00518153328448534, -0.011075767688453197, -0.015130462124943733, -0.03532688319683075, -0.01993638277053833, 0.022035961970686913, 0.030415020883083344, 0.03840883821249008, -0.05270139127969742, 0.029490435495972633, 0.000485166790895164, 0.04283914342522621, 0.018433930352330208, -0.03447934612631798, 0.00932772271335125, -0.00863428320735693, 0.008773934096097946, 0.008576496504247189, -0.017152993008494377, -0.0017456372734159231, -0.0007163132540881634, 0.03116624802350998, 0.024193329736590385, 0.00316140940412879, 0.011721051298081875, -0.00911102257668972, -0.0004872735880780965, -0.022864237427711487, 0.04834813252091408, 0.007815639488399029, 0.029028141871094704, -0.04041210561990738, -0.007189617957919836, 0.01327165961265564, 0.02925928868353367, 0.019897857680916786, -0.003048243932425976, -0.038601458072662354, -0.014119195751845837, -0.026832250878214836, 0.003763353219255805, 0.011701789684593678, 0.007131831254810095, 0.01999416947364807, -0.009920035488903522, 0.009948928840458393, -0.009371062740683556, 0.025772830471396446, 0.024867506697773933, -0.003551468951627612, 0.027101922780275345, -0.04503503441810608, -0.020841706544160843, 0.020321626216173172, -0.03619368374347687, -0.056091539561748505, 0.017307091504335403, -0.027679787948727608, 0.014176982454955578, -0.00338533241301775, 0.03234124183654785, 0.04237684980034828, 0.00031120498897507787, -0.008990634232759476, -0.0015325491549447179, -0.040643252432346344, -0.013127192854881287, -0.019300729036331177, -0.05755546689033508, -0.012684161774814129, 0.03282279893755913, 0.0208031814545393, -0.009679257869720459, -0.016709962859749794, 0.01879028044641018, 0.02646626904606819, -0.00006978787132538855, 0.0186554454267025, -0.016989264637231827, -0.00790231954306364, 0.029471173882484436, 0.02891257032752037, 0.023326529189944267, -0.008518709801137447, 0.0343252494931221, 0.004892600234597921, -0.024867506697773933, 0.024135543033480644, -0.0056679039262235165, -0.0461907684803009, 0.01122023444622755, -0.0024149988312274218, 0.009631102904677391, 0.016035785898566246, -0.03550024330615997, -0.03511499986052513, -0.0046373759396374226, -0.010748310014605522, -0.031320344656705856, -0.0183279886841774, 0.006091672461479902, -0.005441572982817888, 0.03511499986052513, 0.028816258534789085, 0.05574481934309006, 0.0008475370123051107, 0.018453191965818405, 0.030877314507961273, -0.018395405262708664, -0.029528960585594177, 0.03571212664246559, -0.032456815242767334, -0.02014826610684395, 0.0038524409756064415, 0.023422840982675552, -0.032052308320999146, 0.027968721464276314, -0.06329560279846191, -0.021573670208454132, -0.008956925012171268, -0.013878419063985348, 0.019377777352929115, -0.025233488529920578, -0.009785200469195843, -0.049889110028743744 ]
Upside-Down Reinforcement Learning (UDRL) is an approach for solving RL problems that does not require value functions and uses only supervised learning, where the targets for given inputs in a dataset do not change over time. Ghosh et al. proved that Goal-Conditional Supervised Learning (GCSL) -- which can be viewed as a simplified version of UDRL -- optimizes a lower bound on goal-reaching performance. This raises expectations that such algorithms may enjoy guaranteed convergence to the optimal policy in arbitrary environments, similar to certain well-known traditional RL algorithms. Here we show that for a specific episodic UDRL algorithm (eUDRL, including GCSL), this is not the case, and give the causes of this limitation. To do so, we first introduce a helpful rewrite of eUDRL as a recursive policy update. This formulation helps to disprove its convergence to the optimal policy for a wide class of stochastic environments. Finally, we provide a concrete example of a very simple environment where eUDRL diverges. Since the primary aim of this paper is to present a negative result, and the best counterexamples are the simplest ones, we restrict all discussions to finite (discrete) environments, ignoring issues of function approximation and limited sample size.
[ 0.02320907451212406, -0.012702505104243755, -0.03617044910788536, -0.03852706402540207, -0.0206025168299675, 0.005654980428516865, -0.005003341007977724, 0.007819673046469688, -0.08848012983798981, -0.059200990945100784, -0.023030543699860573, 0.014630643650889397, 0.0188707634806633, -0.03902694955468178, -0.045454081147909164, 0.01981697976589203, 0.00530238077044487, 0.052631039172410965, -0.05238109454512596, -0.02852930873632431, 0.03677745535969734, 0.000518856686539948, -0.031582195311784744, 0.0856950432062149, -0.02665472961962223, 0.04034808278083801, 0.017005110159516335, -0.02463732473552227, -0.07062699645757675, 0.04102650284767151, -0.015567933209240437, 0.029207726940512657, 0.006007579620927572, 0.005329160485416651, -0.0006639134371653199, 0.018138784915208817, 0.0013021630002185702, -0.03372456878423691, -0.06402134150266647, 0.04870335012674332, -0.033278241753578186, 0.011452785693109035, 0.026012016460299492, -0.010881485417485237, -0.040598027408123016, -0.04177633300423622, -0.0011749593541026115, 0.047310806810855865, -0.049060411751270294, 0.03909836336970329, -0.039812490344047546, -0.03745587542653084, 0.02403031848371029, 0.0020162882283329964, -0.01794240064918995, 0.00043740178807638586, 0.019709860906004906, -0.044347185641527176, 0.029904000461101532, 0.025387156754732132, -0.005329160485416651, -0.049667418003082275, -0.09383607655763626, 0.013371997512876987, 0.023976759985089302, -0.03274264931678772, 0.04691803827881813, -0.006538710556924343, 0.07898226380348206, -0.03351033106446266, -0.024280263110995293, 0.010274478234350681, -0.059165287762880325, 0.035795532166957855, 0.009212217293679714, 0.005793341901153326, -0.01411290280520916, 0.02620840072631836, 0.03368886560201645, -0.05095284432172775, 0.0033184513449668884, -0.008948883041739464, -0.014523524791002274, -0.012988154776394367, 0.053702227771282196, -0.017192568629980087, 0.01994195021688938, -0.057308562099933624, 0.0720195397734642, 0.010649394243955612, -0.04938177019357681, 0.02665472961962223, 0.007373344618827105, -0.059772294014692307, -0.038919832557439804, -0.017353245988488197, -0.042347632348537445, 0.01842443458735943, -0.045596905052661896, 0.022869864478707314, 0.0005528892506845295, 0.02992185205221176, -0.06030788645148277, 0.026422638446092606, 0.019567035138607025, -0.024994388222694397, -0.012836403213441372, 0.0358848012983799, 0.011640243232250214, 0.20081205666065216, 0.0035081407986581326, 0.031403664499521255, 0.005347013473510742, 0.035956211388111115, -0.07191242277622223, 0.008083006367087364, -0.01606782153248787, -0.08855154365301132, 0.052024032920598984, 0.004461051896214485, -0.009105098433792591, 0.08098181337118149, 0.034527961164712906, -0.01129210740327835, -0.02370896190404892, 0.06852032989263535, -0.023673254996538162, 0.03738446161150932, 0.03311756253242493, 0.020245453342795372, -0.008551651611924171, -0.021887943148612976, -0.019299237057566643, 0.007940181531012058, -0.015800023451447487, 0.005766562186181545, -0.016380250453948975, -0.04113361984491348, -0.035295646637678146, 0.03927689418196678, -0.005088143050670624, -0.0708412379026413, -0.003325146157294512, 0.008864081464707851, 0.006561026908457279, 0.01776386797428131, -0.005900460761040449, 0.028600720688700676, -0.004735543858259916, 0.023137662559747696, -0.021798675879836082, 0.05227397754788399, 0.010524422861635685, 0.028922077268362045, 0.06369998306035995, 0.03620615601539612, 0.002365540247410536, -0.04627532511949539, 0.004148622043430805, -0.026851113885641098, 0.08548080921173096, 0.06191466748714447, -0.006650292314589024, 0.04695374146103859, 0.009712104685604572, 0.04713227227330208, 0.011943746358156204, 0.009105098433792591, -0.039526838809251785, 0.04552549123764038, -0.03731305152177811, -0.02822580561041832, 0.024744443595409393, 0.05066719278693199, 0.05205973982810974, 0.01646951586008072, 0.03788435086607933, -0.0020229832734912634, 0.0022517265751957893, -0.02231641672551632, -0.03659892454743385, -0.05505906417965889, -0.009158657863736153, 0.016335617750883102, 0.02669043466448784, 0.01949562318623066, 0.038919832557439804, -0.04852481931447983, -0.002535145031288266, -0.030278915539383888, -0.02820795215666294, 0.038455650210380554, 0.04663238674402237, -0.032349880784749985, 0.02513721212744713, -0.016665900126099586, -0.055416129529476166, 0.04566831886768341, 0.00038523715920746326, -0.0014594937674701214, 0.013782619498670101, -0.03525993973016739, 0.02992185205221176, 0.018076298758387566, 0.007092157378792763, 0.03215349465608597, 0.03456366807222366, -0.002465964062139392, -0.004985487554222345, -0.06384281069040298, 0.0015164006035774946, -0.06709207594394684, -0.06777049601078033, -0.005070290062576532, -0.050774313509464264, -0.02913631498813629, -0.025458568707108498, 0.006342325825244188, -0.02326263301074505, -0.0754830539226532, -0.02542286366224289, -0.006520857103168964, 0.014389625750482082, -0.030743097886443138, -0.008694476447999477, 0.011434932239353657, -0.01671053282916546, 0.010158433578908443, -0.01627313159406185, -0.05063148960471153, 0.011274253949522972, 0.004909611772745848, -0.0008240337483584881, -0.04370447248220444, -0.030939482152462006, 0.033938806504011154, -0.049667418003082275, 0.014577084220945835, -0.01824590377509594, -0.026868967339396477, -0.023744668811559677, 0.004376249387860298, -0.018049519509077072, 0.02388749271631241, 0.0007833062554709613, 0.011488491669297218, 0.04566831886768341, -0.02310195565223694, 0.06466405093669891, -0.005150629207491875, -0.00866769626736641, -0.023441165685653687, -0.04506130889058113, -0.007319785188883543, -0.03538491204380989, 0.05848686769604683, 0.017897766083478928, -0.03224276006221771, 0.03513496741652489, -0.0451684296131134, 0.015791097655892372, 0.04538266733288765, 0.0023856251500546932, 0.020191894844174385, 0.029850440099835396, 0.038134295493364334, -0.00372684164904058, 0.024208849295973778, -0.008600747212767601, 0.009073855355381966, -0.0016324459575116634, -0.02228071168065071, -0.0564873181283474, 0.021013138815760612, -0.004438735544681549, -0.04470424726605415, 0.02715461701154709, 0.017513925209641457, 0.022816305980086327, 0.003345231059938669, 0.038134295493364334, -0.04698944836854935, 0.003650965867564082, -0.016415957361459732, 0.034385137259960175, -0.0027248344849795103, -0.00705645140260458, 0.030778802931308746, -0.012041939422488213, 0.01713900826871395, -0.008324023336172104, 0.0021803139243274927, -0.00965854525566101, 0.0011716119479387999, 0.05391646549105644, 0.02528003789484501, -0.0031131403520703316, -0.004704300779849291, -0.0032693552784621716, 0.0036911354400217533, 0.038919832557439804, -0.00019024746143259108, 0.004476673435419798, 0.04227622225880623, -0.0001705811155261472, 0.0020843534730374813, -0.03133225068449974, -0.02369110845029354, -0.022405683994293213, -0.03286762163043022, 0.02074534259736538, 0.004545854404568672, -0.009694252163171768, -0.04977453872561455, 0.01162239070981741, -0.013613014481961727, 0.07398338615894318, 0.015782169997692108, -0.033278241753578186, 0.014139682054519653, 0.024762297049164772, -0.026226254180073738, -0.061843257397413254, 0.0005986379110254347, 0.0870518833398819, 0.01472883578389883, 0.04459713026881218, 0.007065377663820982, -0.06334292143583298, 0.012640018947422504, -0.012889962643384933, -0.01667482778429985, -0.042811814695596695, 0.018817203119397163, 0.033438920974731445, -0.05380934476852417, -0.02510150708258152, -0.009810296818614006, -0.029118461534380913, -0.04116932675242424, -0.008908714167773724, -0.010577982291579247, -0.006092382129281759, -0.030118238180875778, 0.012970302253961563, -0.04866764321923256, 0.006561026908457279, -0.016317764297127724, -0.03506355360150337, 0.008645379915833473, 0.0010728618362918496, 0.0243159681558609, -0.025583541020751, 0.019763419404625893, 0.05955805629491806, -0.03259982168674469, -0.049524594098329544, 0.02854716219007969, -0.040776558220386505, -0.004568170756101608, -0.00046194985043257475, -0.04798922315239906, -0.08298137038946152, 0.026619022712111473, -0.059343818575143814, 0.0188707634806633, -0.003954469226300716, 0.015237649902701378, 0.005570177920162678, 0.017853133380413055, -0.01162239070981741, -0.007534022442996502, 0.04284752160310745, -0.0349564366042614, -0.011667023412883282, 0.011256401427090168, -0.0009456581901758909, 0.01504126563668251, -0.0546305887401104, 0.02586919069290161, -0.018317315727472305, -0.0018455677200108767, -0.025387156754732132, 0.016683753579854965, 0.021887943148612976, 0.0833384320139885, -0.014086122624576092, 0.010738660581409931, 0.040133845061063766, -0.04116932675242424, 0.009390748105943203, -0.06109342351555824, -0.01643381081521511, 0.038919832557439804, -0.005547861568629742, 0.02792230248451233, 0.007476000115275383, -0.018120931461453438, -0.040169551968574524, -0.0010466399835422635, 0.006989501882344484, -0.0036933671217411757, -0.004802492912858725, -0.0075250961817801, 0.0026266423519700766, 0.018656525760889053, -0.030332474038004875, -0.035956211388111115, -0.005284527782350779, -0.02294127643108368, 0.05430923402309418, -0.06262879818677902, -0.0001802050683181733, 0.010729733854532242, 0.020620370283722878, 0.016808725893497467, -0.02153087966144085, -0.01255075354129076, -0.03540276363492012, -0.03770582005381584, 0.020174041390419006, 0.037205930799245834, 0.08448103070259094, 0.06977004557847977, -0.030118238180875778, 0.023316193372011185, -0.038455650210380554, 0.011881261132657528, -0.016246352344751358, -0.041097912937402725, 0.019085001200437546, 0.028886370360851288, 0.06427128612995148, -0.0018890846986323595, -0.03525993973016739, -0.020638223737478256, -0.02231641672551632, 0.010872558690607548, 0.009854930453002453, -0.01717471517622471, 0.008127639070153236, -0.00038188969483599067, -0.02772591821849346, -0.02388749271631241, 0.020620370283722878, -0.041240740567445755, -0.00936396885663271, -0.008024984039366245, -0.0038763617631047964, 0.009056001901626587, -0.06512822955846786, 0.0022137886844575405, -0.011354593560099602, -0.02899348922073841, 0.07469751685857773, -0.011524197645485401, 0.009024759754538536, -0.061022013425827026, 0.016924770548939705, 0.009899563156068325, 0.0504886619746685, 0.036741748452186584, 0.005168482195585966, -0.035456325858831406, -0.00768131110817194, 0.008493628352880478, -0.000012369920113997068, -0.03543847054243088, -0.02510150708258152, -0.03742016851902008, 0.00047812925186008215, -0.09205076098442078, -0.02461947128176689, 0.020977431908249855, 0.021762970834970474, 0.021316641941666603, -0.01536262221634388, -0.05880822241306305, -0.010131653398275375, -0.01770138181746006, 0.0287078395485878, 0.031100159510970116, 0.024673031643033028, -0.052773863077163696, -0.02669043466448784, -0.003668819088488817, 0.10033461451530457, -0.025797778740525246, -0.04620391130447388, -0.023173367604613304, -0.04959600791335106, -0.005097069777548313, -0.06852032989263535, 0.025779925286769867, 0.020548956468701363, -0.028797104954719543, 0.019067147746682167, -0.026083428412675858, 0.06541388481855392, 0.0010455241426825523, -0.008395436219871044, -0.04470424726605415, -0.030653830617666245, -0.008743572048842907, -0.0014806942781433463, -0.02806512638926506, 0.007230519317090511, 0.009533573873341084, -0.03040388785302639, -0.009962048381567001, 0.008007130585610867, -0.01215798407793045, -0.007306395098567009, 0.027654504403471947, 0.03465293347835541, 0.005619273986667395, 0.012773917056620121, 0.03222490847110748, 0.009872782975435257, 0.008047300390899181, -0.00904261227697134, -0.007328711450099945, 0.005628200713545084, 0.01037267129868269, -0.051238495856523514, 0.04131215065717697, 0.032046373933553696, -0.0071189370937645435, 0.03629542142152786, -0.0001307602651650086, -0.022691333666443825, 0.05223827064037323, -0.02106669917702675, -0.006810970604419708, -0.03966966271400452, -0.005605883896350861, 0.019299237057566643, 0.05102425813674927, 0.0170765221118927, 0.02274489216506481, -0.03506355360150337, 0.09690681099891663, -0.0017183641903102398, 0.04366876557469368, 0.012122278101742268, -0.002238336717709899, -0.022120032459497452, -0.013023861683905125, 0.00960498582571745, 0.05052436888217926, 0.020781047642230988, -0.006650292314589024, -0.04449000954627991, -0.01701403595507145, -0.03604547679424286, -0.022262858226895332, -0.04252616688609123, 0.002055342076346278, 0.025065800175070763, -0.010220919735729694, 0.0330997109413147, 0.010167360305786133, -0.00974781159311533, 0.0023142124991863966, 0.0036799772642552853, -0.029082754626870155, 0.041704922914505005, 0.05088143050670624, 0.0026355688460171223, -0.0028765862807631493, -0.023958906531333923, 0.011497418396174908, -0.03622400760650635, -0.019584888592362404, 0.04802493005990982, 0.004405261017382145, -0.05430923402309418, 0.003325146157294512, -0.049167532473802567, -0.018674379214644432, 0.007841989398002625, -0.005061363335698843, -0.0025485348887741566, 0.010435156524181366, -0.04759645462036133, -0.04688233137130737, -0.044847071170806885, -0.027368854731321335, 0.019924096763134003, -0.02478015050292015, -0.050595782697200775, 0.027708064764738083, 0.03258197009563446, 0.018210196867585182, -0.04552549123764038, -0.0701628178358078, 0.0030796655919402838, 0.006663682404905558, -0.0003489729715511203, -0.03809858858585358, 0.03243914619088173, 0.001942644128575921, 0.009274703450500965, 0.012327589094638824, -0.026440491899847984, 0.030457446351647377, 0.012363295070827007, -0.007511706091463566, 0.023048395290970802, -0.04845340549945831, -0.011060016229748726, 0.040633734315633774, 0.015567933209240437, -0.03963395953178406, 0.0013166686985641718, -0.025476422160863876, 0.024601619690656662, 0.029350552707910538, 0.011274253949522972, -0.03318897634744644, -0.008373119868338108, -0.015300136059522629, 0.022530654445290565, 0.012488267384469509, -0.03277835249900818, 0.02586919069290161, 0.011559904552996159, -0.011774142272770405, -0.01497877947986126, -0.04473995417356491, -0.012916742824018002, -0.018174489960074425, -0.006690462119877338, -0.0023186758626252413, -0.036545366048812866, 0.030975187197327614, -0.03372456878423691, 0.03302829712629318, -0.026476198807358742, -0.005663906689733267, -0.061022013425827026, 0.07198383659124374, 0.011408152990043163, 0.034081634134054184, -0.022066473960876465, -0.03429587185382843, 0.018442288041114807, -0.010783293284475803, 0.03777723014354706, 0.015737537294626236, -0.03302829712629318, -0.007819673046469688, 0.0008223599870689213, 0.03777723014354706, -0.022334270179271698, -0.02902919612824917, 0.010756513103842735, 0.0028408800717443228, -0.01153312437236309, 0.017022963613271713, 0.0011972758220508695, -0.009488941170275211, 0.01347911637276411, -0.004931928124278784, 0.002651190385222435, -0.017737088724970818, 0.06980575621128082, -0.005342550575733185, -0.020959580317139626, 0.05723714828491211, -0.040133845061063766, 0.003813875839114189, 0.00046669208677485585, 0.00028327901964075863, 0.01160453725606203, -0.005311307497322559, -0.009533573873341084, 0.027797330170869827, -0.009274703450500965, -0.026458345353603363, -0.0349564366042614, 0.029404111206531525, 0.056987203657627106, -0.023137662559747696, -0.03293903172016144, -0.006061139050871134, 0.023816080763936043, 0.009006906300783157, -0.04166921600699425, 0.011327813379466534, -0.03809858858585358, -0.019709860906004906, -0.004972097929567099, -0.03899124637246132, 0.0061593311838805676, 0.0282436590641737, -0.06505682319402695, -0.05352369695901871, 0.021602291613817215, 0.028154391795396805, -0.030653830617666245, -0.03806288167834282, 0.006993965245783329, 0.00881052203476429, 0.05266674607992172, -0.0017540703993290663, 0.0120954979211092, 0.015425107441842556, -0.015567933209240437, 0.02417314425110817, 0.008386509492993355, 0.012104424647986889, 0.005623737350106239, 0.0010840200120583177, 0.013452336192131042, -0.021173816174268723, 0.025226479396224022, -0.01611245423555374, 0.020191894844174385, -0.013532675802707672, 0.042347632348537445, 0.01005131471902132, 0.045918259769678116, -0.030653830617666245, -0.010952897369861603, -0.016407029703259468, 0.02961834892630577, -0.016407029703259468, 0.008319560438394547, -0.0010031230049207807, 0.005396110005676746, -0.013148833066225052, -0.018460141494870186, -0.0029011343140155077, -0.02403031848371029, -0.0020252149552106857, 0.018210196867585182, -0.011211767792701721, 0.0033898637630045414, -0.01736217364668846, 0.023191221058368683, 0.008578430861234665, 0.06752055138349533, 0.018495846539735794, -0.013854032382369041, -0.05523759871721268, 0.003561700228601694, 0.019620593637228012, -0.0034300333354622126, -0.0005116038955748081, 0.05577319115400314, 0.016728386282920837, 0.05905816704034805, -0.009194363839924335, -0.042169101536273956, 0.03145722299814224, 0.01122069451957941, 0.0043740179389715195, -0.0034679712262004614, -0.0225842148065567, 0.020013364031910896, 0.03456366807222366, 0.015532226301729679, -0.022834159433841705, 0.020870313048362732, -0.011122502386569977, -0.0433117039501667, 0.004601645283401012, 0.029207726940512657, -0.0015275587793439627, 0.029975412413477898, 0.006422664970159531, 0.032671235501766205, -0.07769683748483658, -0.02228071168065071, 0.014478892087936401, 0.008712329901754856, -0.02774376980960369, -0.06348574161529541, 0.029600495472550392, -0.015862509608268738, 0.005387183278799057, 0.0038272656966000795, 0.01979912631213665, -0.0022294102236628532, 0.029832586646080017, 0.023191221058368683, -0.012738211080431938, 0.020459691062569618, 0.000038216865505091846, -0.043883003294467926, -0.006623512599617243, -0.033135417848825455, -0.008997979573905468, 0.04363305866718292, -0.008480238728225231, -0.07212666422128677, 0.009006906300783157, 0.0030506541952490807, -0.015407254919409752, -0.026619022712111473, -0.0067975809797644615, -0.03058241866528988, 0.010872558690607548, -0.004686447791755199, -0.030760949477553368, 0.01433606632053852, -0.0006717241485603154, 0.029207726940512657, 0.005797805264592171, 0.02977902814745903, 0.02138805389404297, -0.029386259615421295, 0.02153087966144085, -0.010881485417485237, -0.013452336192131042, 0.002048647031188011, 0.014880587346851826, 0.001658109831623733, -0.010720807127654552, -0.015059119090437889, -0.029047049582004547, -0.04149068519473076, 0.008533798158168793, -0.055130477994680405, -0.026565464213490486, -0.017665676772594452, 0.004628424998372793, -0.00034953089198097587, 0.0465252660214901, 0.0064628347754478455, 0.08898001909255981, -0.003970090765506029, -0.029207726940512657, -0.04034808278083801, 0.01903144083917141, -0.0012128972448408604, -0.012488267384469509, 0.010345891118049622, 0.0119258938357234, 0.00012566932127811015, -0.022084327414631844, 0.014505671337246895, -0.02836862951517105, 0.014880587346851826, -0.007261762395501137, 0.012131204828619957, 0.007194812875241041, -0.05205973982810974, 0.01535369548946619, 0.0430617593228817, -0.0037982542999088764, 0.04024096578359604, 0.0029011343140155077, -0.03179643303155899, 0.01029233168810606, 0.023030543699860573, 0.06187896430492401, -0.027511680498719215, 0.0001527279819129035, 0.038741301745176315, 0.017112229019403458, 0.022512802854180336, -0.012961375527083874, 0.02026330679655075, -0.055416129529476166, 0.050452958792448044, -0.041205033659935, 0.013148833066225052, -0.021602291613817215, 0.03211778774857521, 0.009712104685604572, -0.011488491669297218, 0.03511711582541466, -0.009109561331570148, 0.03192140534520149, 0.004704300779849291, 0.005958483554422855, -0.0016960477223619819, -0.06494969874620438, 0.007364417891949415, 0.012943522073328495, 0.02120952308177948, -0.046703800559043884, 0.03663463145494461, 0.007409050595015287, -0.014514598064124584, -0.017103303223848343, 0.007859841920435429, -0.027368854731321335, -0.02556568756699562, 0.022869864478707314, -0.06312867999076843, 0.015219796448946, 0.029064903035759926, 0.03413519263267517, -0.0112296212464571, -0.0037045252975076437, 0.0421333983540535, -0.004242350813001394, -0.021298788487911224, -0.0009835960809141397, 0.04541837424039841, -0.031118012964725494, 0.0025887044612318277, -0.048739057034254074, 0.0043717860244214535, 0.0008000435773283243, 0.0650925263762474, 0.005632663611322641, -0.017183640971779823, -0.024119583889842033, 0.021441614255309105, -0.03663463145494461, 0.025315744802355766, -0.04941747710108757, -0.04416865482926369, -0.0074313669465482235, 0.011640243232250214, -0.002423563040792942, 0.04252616688609123, -0.01675516553223133, 0.0192099716514349, 0.016817651689052582, 0.0007068725535646081, -0.010506569407880306, 0.005422889720648527, 0.0349564366042614, -0.002622178988531232, -0.007230519317090511, -0.017165789380669594, 0.007074304390698671, 0.01310420036315918, 0.02165585197508335, 0.041097912937402725, 0.020977431908249855, -0.008953346870839596, 0.025940604507923126, 0.011024310253560543, 0.010131653398275375, -0.04806063696742058, -0.01091719139367342, 0.00313768838532269, -0.005931703839451075, 0.016683753579854965, -0.027083205059170723, 0.018620818853378296, -0.00611916184425354, 0.007734870538115501, -0.06030788645148277, -0.003874130081385374, -0.017228273674845695, -0.01247041393071413, -0.043133173137903214, -0.023673254996538162, -0.03554559126496315, -0.02308410219848156, -0.05427352711558342, -0.03147507458925247, 0.07255513966083527, 0.013854032382369041, 0.024583766236901283, -0.05213114991784096, -0.005954020190984011, -0.01746036484837532, 0.03949113190174103, -0.028957784175872803, 0.0032224906608462334, -0.0257085133343935, 0.060879185795784, -0.005226504988968372, -0.01060476154088974, 0.047953519970178604, 0.0028721229173243046, 0.012800697237253189, 0.0180673711001873, -0.020548956468701363, -0.005306844133883715, -0.021566586568951607, -0.009310409426689148, 0.013023861683905125, 0.014273581095039845, 0.005704076495021582, -0.03279620781540871, -0.02727958932518959, -0.0017094375798478723, 0.003461276413872838, 0.04852481931447983, 0.020031215623021126, -0.022245004773139954, -0.007502779830247164, 0.0368131622672081, 0.029993265867233276, -0.00714125344529748, 0.005088143050670624, 0.024673031643033028, -0.00040225344127975404, 0.01433606632053852, 0.03902694955468178, 0.018442288041114807, 0.004307068418711424, 0.04520413652062416, -0.018960028886795044, 0.0007794008706696332, 0.03336750715970993, -0.030528860166668892, 0.04552549123764038, 0.02619054727256298, 0.012059791944921017, 0.017995959147810936, -0.0011972758220508695, -0.051524143666028976, -0.0034791294019669294, 0.011167135089635849, -0.046703800559043884, -0.020013364031910896, -0.022387830540537834, 0.0005503786378540099, -0.02181652933359146, 0.015853583812713623, -0.007859841920435429, -0.011577757075428963, 0.020459691062569618, -0.015201943926513195 ]
In this paper, we present DendroMap, a novel approach to interactively exploring large-scale image datasets for machine learning (ML). ML practitioners often explore image datasets by generating a grid of images or projecting high-dimensional representations of images into 2-D using dimensionality reduction techniques (e.g., t-SNE). However, neither approach effectively scales to large datasets because images are ineffectively organized and interactions are insufficiently supported. To address these challenges, we develop DendroMap by adapting Treemaps, a well-known visualization technique. DendroMap effectively organizes images by extracting hierarchical cluster structures from high-dimensional representations of images. It enables users to make sense of the overall distributions of datasets and interactively zoom into specific areas of interests at multiple levels of abstraction. Our case studies with widely-used image datasets for deep learning demonstrate that users can discover insights about datasets and trained models by examining the diversity of images, identifying underperforming subgroups, and analyzing classification errors. We conducted a user study that evaluates the effectiveness of DendroMap in grouping and searching tasks by comparing it with a gridified version of t-SNE and found that participants preferred DendroMap. DendroMap is available at https://div-lab.github.io/dendromap/.
[ 0.012502304278314114, 0.028610877692699432, -0.034832119941711426, 0.018732091411948204, 0.06378482282161713, -0.029841452836990356, -0.007554365787655115, 0.020697593688964844, 0.00895585399121046, 0.0116990115493536, -0.003454583929851651, -0.053837671875953674, 0.03385791555047035, -0.014288347214460373, -0.03172149881720543, 0.002849978394806385, 0.005482042673975229, 0.012211751192808151, -0.0025829265359789133, -0.057734496891498566, 0.0074731819331645966, -0.03076438419520855, -0.04122427478432655, 0.004507836885750294, 0.03613106161355972, -0.01745878905057907, 0.034268107265233994, -0.00028681379626505077, -0.07397125661373138, 0.07643240690231323, 0.014689994044601917, -0.002050959039479494, 0.007960284128785133, -0.0037130904383957386, -0.06740818172693253, -0.02220163121819496, -0.0056016817688941956, 0.04453999176621437, 0.007383452262729406, 0.03428519889712334, -0.0033669909462332726, -0.009972788393497467, 0.023927854374051094, 0.02748285047709942, -0.00837474875152111, -0.02401331067085266, -0.08942180871963501, -0.04218139126896858, -0.04252321645617485, 0.008669574744999409, -0.0016653359634801745, -0.03086693212389946, -0.06446848064661026, -0.03131130710244179, -0.05069287121295929, 0.00814401637762785, 0.026901746168732643, 0.04700114205479622, 0.06433174759149551, 0.0294654443860054, 0.05958035960793495, 0.0120835667476058, -0.021449612453579903, -0.009169495664536953, 0.055307526141405106, -0.04160028323531151, -0.003956641536206007, -0.025654079392552376, 0.049804121255874634, -0.02608136087656021, -0.0068365298211574554, -0.005520497914403677, -0.01997975818812847, 0.03869475796818733, 0.01892009750008583, 0.029191982001066208, 0.028696333989501, -0.052743829786777496, -0.05995636805891991, -0.042044658213853836, 0.058076322078704834, -0.033721182495355606, -0.04806080460548401, 0.039070770144462585, 0.09933478385210037, -0.006793801672756672, -0.029892727732658386, -0.0731508731842041, 0.03479793667793274, -0.005567498970776796, -0.04156610369682312, -0.02502170018851757, -0.006464793812483549, -0.007678277790546417, 0.02360311895608902, 0.012630488723516464, -0.009160949848592281, -0.02729484625160694, -0.029123617336153984, 0.020236128941178322, -0.015749655663967133, -0.01650167442858219, -0.02032158523797989, -0.04009624943137169, -0.045223645865917206, -0.05120560899376869, -0.014083251357078552, 0.01608293689787388, -0.029585083946585655, 0.050624504685401917, 0.02199653536081314, -0.0283032339066267, -0.0731508731842041, -0.009075493551790714, -0.05462387576699257, 0.0661776065826416, -0.022304179146885872, -0.041087545454502106, -0.0188688226044178, -0.07308250665664673, 0.017945891246199608, 0.015467649325728416, -0.05294892564415932, 0.040677353739738464, -0.044266533106565475, 0.03495175763964653, 0.004755661357194185, 0.01735624112188816, 0.01735624112188816, 0.031755682080984116, -0.03862639516592026, -0.019091010093688965, 0.0005359732895158231, 0.000017341686543659307, 0.027448667213320732, 0.03507139906287193, 0.04060898721218109, 0.04590729996562004, -0.005627318751066923, -0.009195133112370968, 0.015570197254419327, -0.0441981665790081, -0.02259473130106926, -0.0003773444041144103, -0.07820989936590195, -0.011784468777477741, -0.0460098460316658, 0.09632670879364014, -0.06405828893184662, 0.04474508762359619, -0.04060898721218109, 0.05482897162437439, 0.005417949985712767, 0.009588233195245266, 0.037498366087675095, 0.04669350013136864, -0.01288685854524374, 0.004304877482354641, -0.0215863436460495, -0.04669350013136864, 0.0783466324210167, -0.042899224907159805, 0.05301728844642639, 0.05294892564415932, 0.03112330287694931, 0.014749813824892044, -0.02103942073881626, -0.027311937883496284, -0.023022014647722244, 0.040130432695150375, 0.0423864871263504, -0.0020968918688595295, -0.0034439018927514553, 0.019911393523216248, -0.02647446282207966, -0.004700114484876394, 0.01069062389433384, 0.00290125235915184, -0.046830229461193085, -0.041292641311883926, -0.05158161744475365, -0.01588638685643673, 0.04074572026729584, 0.027756310999393463, 0.02329547517001629, 0.00509321503341198, 0.06163131818175316, 0.02098814770579338, 0.015800930559635162, -0.013878155499696732, 0.015467649325728416, 0.035481590777635574, 0.056162092834711075, -0.002907661721110344, 0.03650707006454468, -0.050863783806562424, -0.02905525267124176, 0.03279825299978256, 0.05322238430380821, -0.006716890726238489, -0.06624597311019897, -0.05664065107703209, 0.03900240361690521, 0.056093730032444, -0.0042044660076498985, 0.0011931881308555603, -0.035139765590429306, -0.037156540900468826, 0.005623045843094587, -0.07062135636806488, -0.006909167859703302, 0.006387882865965366, -0.07219375669956207, -0.022782735526561737, 0.024594416841864586, -0.0038070925511419773, 0.034165557473897934, -0.004373242612928152, 0.003815638367086649, 0.014493443071842194, 0.012040838599205017, 0.022150356322526932, 0.031191667541861534, 0.006558795925229788, -0.01830480806529522, -0.023415114730596542, 0.028063954785466194, 0.02326129376888275, 0.0245602335780859, 0.0064177922904491425, 0.020697593688964844, -0.04030134528875351, 0.007597093936055899, -0.037498366087675095, 0.033669911324977875, -0.09325026720762253, 0.019962666556239128, -0.03534486144781113, -0.041737016290426254, -0.0036468615289777517, 0.013305596075952053, -0.040574803948402405, -0.06737400591373444, 0.0033691274002194405, 0.07670586556196213, 0.0008930217009037733, 0.017877526581287384, -0.034780845046043396, 0.05930689722299576, 0.0018650908023118973, 0.007725278846919537, 0.022150356322526932, -0.03228551149368286, -0.0014890816528350115, -0.01987721025943756, -0.020184854045510292, 0.02486787736415863, -0.04358287900686264, -0.04573638364672661, -0.016860591247677803, -0.0027474304661154747, -0.019484110176563263, -0.05164998397231102, 0.02476532943546772, 0.005742684938013554, 0.01333977933973074, 0.01563856191933155, 0.015484740026295185, 0.00314694014377892, -0.0029867091216146946, -0.013408144004642963, -0.015980388969182968, -0.040335528552532196, -0.012057929299771786, -0.015578743070363998, -0.043001774698495865, -0.012211751192808151, 0.02900397777557373, -0.004759933799505234, -0.026559919118881226, 0.03613106161355972, -0.025534439831972122, -0.030029457062482834, 0.06128948926925659, -0.01850990578532219, -0.01333977933973074, 0.05783704295754433, -0.0027047020848840475, -0.016484582796692848, 0.009357500821352005, -0.05059032142162323, -0.0009304090053774416, -0.013963612727820873, -0.009793329052627087, 0.0345073863863945, -0.020595045760273933, -0.01001551654189825, 0.019142283126711845, -0.006229788064956665, -0.04081408306956291, -0.0731508731842041, -0.011887016706168652, 0.016834955662488937, 0.02794431708753109, 0.033567361533641815, 0.022116174921393394, -0.041531920433044434, 0.07123664021492004, -0.06392155587673187, -0.010639349929988384, -0.013057772070169449, 0.02471405640244484, -0.021295791491866112, -0.038660578429698944, -0.040232978761196136, 0.039310045540332794, 0.039412595331668854, 0.05547843873500824, 0.03279825299978256, -0.04071153700351715, 0.06580159813165665, -0.014339621178805828, -0.06911731511354446, 0.007541547063738108, 0.004832572303712368, -0.018988462164998055, -0.06381900608539581, 0.03233678638935089, -0.03185822814702988, 0.011211909353733063, -0.028918521478772163, -0.03630197420716286, -0.002294510370120406, 0.03883149102330208, 0.05353002995252609, 0.039412595331668854, -0.007169810589402914, 0.019706297665834427, 0.0010484459344297647, 0.05270964652299881, -0.02370566688477993, -0.051171425729990005, -0.052538733929395676, -0.04272831231355667, 0.012023746967315674, -0.05387185513973236, -0.04624912515282631, -0.007494546007364988, -0.021774347871541977, -0.007721005938947201, 0.0010078540071845055, -0.006101603154093027, -0.0343877449631691, 0.004200193099677563, 0.009767692536115646, 0.008028649725019932, -0.06963005661964417, -0.006404974032193422, -0.02633773162961006, 0.0016033799620345235, -0.0032516245264559984, -0.0361994244158268, -0.038352932780981064, -0.0148010877892375, -0.07458654046058655, 0.02657701075077057, 0.010254794731736183, 0.026594102382659912, 0.0030080731958150864, 0.0509321466088295, 0.030576379969716072, -0.004922301508486271, -0.08285874128341675, 0.04030134528875351, 0.0011194817489013076, -0.02396203763782978, 0.021500887349247932, -0.03211459890007973, -0.04635167494416237, -0.004324105102568865, 0.008101288229227066, 0.021415429189801216, -0.03409719467163086, -0.03126003220677376, -0.002111846813932061, 0.07718442380428314, -0.005986236501485109, -0.0064177922904491425, 0.011639192700386047, 0.03168731555342674, -0.002177007496356964, -0.0030465286690741777, -0.005033395253121853, -0.0449843667447567, 0.07691096514463425, -0.012946678325533867, 0.032815344631671906, -0.016937503591179848, 0.0006323790294118226, -0.014912180602550507, -0.033875007182359695, -0.006507521960884333, -0.013348325155675411, -0.0259788129478693, 0.001142982393503189, -0.026269366964697838, 0.03657543659210205, 0.03900240361690521, 0.012809948064386845, 0.04231812059879303, -0.02799559012055397, 0.006887803785502911, -0.0094344113022089, 0.03701981157064438, -0.007943193428218365, 0.0013373962137848139, -0.01956956647336483, 0.013835427351295948, -0.024320954456925392, -0.018441539257764816, -0.0014217846328392625, -0.02507297322154045, 0.008712302893400192, 0.03187531977891922, -0.07041625678539276, 0.0158351119607687, 0.0004235444066580385, -0.0165444016456604, -0.0032943529076874256, 0.012169023044407368, 0.06046910583972931, 0.0158351119607687, -0.03264443203806877, -0.010579530149698257, -0.007759461645036936, 0.00787055492401123, -0.020389949902892113, 0.034370653331279755, -0.008793486282229424, -0.009759146720170975, -0.02567116916179657, -0.001766815665178001, 0.04611239582300186, -0.015074548311531544, -0.07916701585054398, 0.011639192700386047, -0.01715114526450634, -0.008186744526028633, -0.028046865016222, -0.009366045705974102, -0.06142622232437134, 0.04351451247930527, -0.09748891741037369, -0.08121797442436218, 0.043001774698495865, -0.010844445787370205, -0.08935344964265823, -0.0005308992695063353, 0.00044570970931090415, -0.012271570973098278, 0.054897334426641464, 0.0418737456202507, 0.0030636200681328773, -0.012220297008752823, -0.05100051313638687, 0.010160792618989944, -0.039617691189050674, -0.03705399110913277, 0.014869452454149723, -0.007118536625057459, 0.0022646004799753428, -0.010656440630555153, 0.014818178489804268, 0.03975442051887512, 0.018526995554566383, 0.010562438517808914, 0.0018020665738731623, -0.04296759143471718, 0.02148379571735859, -0.03784019500017166, 0.04583893343806267, -0.005182944238185883, -0.03637034073472023, -0.003157622180879116, 0.006733981892466545, -0.0065673417411744595, 0.024902060627937317, 0.03999369964003563, 0.035037215799093246, -0.0367121659219265, 0.0004473120206966996, -0.014972000382840633, -0.055751901119947433, -0.03221714869141579, 0.013758516870439053, 0.009699326939880848, -0.10220612585544586, -0.04983830451965332, 0.031191667541861534, 0.04283085837960243, 0.005443586967885494, 0.033567361533641815, 0.0055632260628044605, -0.03091820701956749, 0.022765643894672394, 0.010972630232572556, 0.025636987760663033, -0.019791753962635994, 0.009357500821352005, -0.019279014319181442, 0.028610877692699432, 0.0034097193274646997, 0.033875007182359695, -0.056162092834711075, 0.01684350147843361, 0.024132950231432915, -0.007985921576619148, 0.01004115305840969, 0.006695526652038097, 0.007571456953883171, 0.010810263454914093, 0.02768794633448124, -0.015236916020512581, 0.014895089901983738, -0.047548066824674606, 0.05875997617840767, 0.010323160327970982, -0.02461150847375393, 0.025842083618044853, -0.05390603840351105, -0.019945576786994934, 0.07486000657081604, 0.005520497914403677, -0.029602175578475, -0.006272516213357449, -0.000363457715138793, 0.0200310330837965, -0.01364742312580347, -0.001826635329052806, -0.038216203451156616, -0.0006350495386868715, 0.012040838599205017, 0.007067262660712004, 0.0017807023832574487, -0.03353317826986313, -0.007178356405347586, 0.008126924745738506, -0.027346119284629822, -0.020800141617655754, -0.024132950231432915, 0.020612137392163277, -0.0017358376644551754, 0.013963612727820873, -0.005738412495702505, 0.003693862585350871, 0.007088627200573683, -0.019176466390490532, -0.012451030313968658, -0.03551577404141426, 0.036336157470941544, -0.020714685320854187, 0.05800795555114746, 0.04224975407123566, 0.014399440959095955, 0.010220612399280071, -0.022714370861649513, -0.018321899697184563, 0.08367912471294403, -0.00423651235178113, 0.04016461223363876, 0.03006364032626152, -0.024645689874887466, -0.05623045936226845, -0.00717408349737525, -0.008208109065890312, 0.0215863436460495, 0.07349269837141037, -0.03944677859544754, -0.04030134528875351, -0.011613555252552032, 0.01755279116332531, 0.023466389626264572, 0.03630197420716286, 0.026166819036006927, 0.040062066167593, -0.006575887091457844, -0.023363841697573662, -0.04122427478432655, 0.027756310999393463, 0.007550092879682779, 0.026816288009285927, 0.019432837143540382, 0.01649312861263752, 0.0015350145986303687, 0.014877998270094395, -0.007733824662864208, 0.022252904251217842, 0.024098768830299377, 0.043206870555877686, -0.031191667541861534, 0.027072658762335777, 0.03958350792527199, 0.032507698982954025, 0.018885914236307144, 0.029345804825425148, -0.00741336215287447, 0.05503406748175621, -0.02965344861149788, 0.05910180136561394, 0.010904265567660332, 0.0060417833738029, -0.03327681124210358, 0.015561651438474655, 0.005400858819484711, 0.014946363866329193, 0.036643799394369125, 0.03845548257231712, 0.006845075637102127, -0.03510558232665062, -0.04149773716926575, 0.04867609217762947, -0.02603008784353733, 0.0473087877035141, 0.03066183626651764, 0.017689520493149757, 0.06351136416196823, -0.024047493934631348, -0.04160028323531151, 0.004067735280841589, -0.05141070485115051, 0.008079923689365387, 0.022081991657614708, 0.010229158215224743, -0.038763124495744705, -0.02608136087656021, 0.027158115059137344, -0.006272516213357449, 0.006887803785502911, -0.009417319670319557, -0.0177066121250391, -0.03153349459171295, 0.01624530367553234, 0.015655653551220894, 0.039310045540332794, -0.004918028600513935, 0.00022806235938332975, -0.025346435606479645, -0.0022774189710617065, 0.03811365365982056, 0.03440483659505844, 0.00447792699560523, 0.015877841040492058, 0.008972945623099804, 0.034421928226947784, -0.01563001610338688, -0.010160792618989944, 0.0625542476773262, 0.025654079392552376, -0.0043326509185135365, 0.006336608901619911, 0.057973772287368774, 0.006315244361758232, 0.00004536545020528138, 0.01897137053310871, 0.042044658213853836, 0.008242291398346424, 0.013613239862024784, 0.017569882795214653, 0.0079474663361907, 0.05995636805891991, 0.027209389954805374, -0.016920411959290504, -0.05783704295754433, 0.03630197420716286, 0.02768794633448124, -0.022064900025725365, 0.006464793812483549, -0.002728202845901251, -0.0008679188322275877, 0.012818493880331516, 0.009690781123936176, -0.014066160656511784, 0.026867562904953957, 0.009972788393497467, -0.036746349185705185, 0.002561562228947878, 0.0029247528873384, 0.011083723977208138, -0.00207339134067297, 0.009383137337863445, -0.005682865623384714, -0.01912519335746765, 0.02319292724132538, -0.011622101068496704, 0.035584136843681335, -0.01663840562105179, -0.050316859036684036, -0.048197537660598755, 0.04026716202497482, -0.016322216019034386, -0.03989115357398987, 0.0028563877567648888, -0.02527806907892227, 0.04932556301355362, -0.0027581125032156706, 0.036336157470941544, -0.011912653222680092, 0.026953019201755524, -0.03208041563630104, 0.0029503898695111275, -0.0033712638542056084, 0.012715945951640606, 0.01079317182302475, -0.01786043494939804, 0.007216812111437321, 0.015373646281659603, -0.02773921936750412, -0.03262734040617943, 0.004725751467049122, 0.015775293111801147, 0.04621494188904762, 0.07089481502771378, 0.021774347871541977, -0.047787345945835114, -0.042147208005189896, -0.007703914772719145, -0.005456405691802502, -0.01992848515510559, -0.02350057102739811, -0.005806777626276016, -0.019501201808452606, -0.039104949682950974, -0.0259788129478693, -0.001142982393503189, -0.017219509929418564, 0.005264128092676401, -0.009084039367735386, 0.02739739418029785, -0.026816288009285927, -0.014493443071842194, 0.010297522880136967, -0.04054062440991402, 0.018783366307616234, -0.011690466664731503, 0.04515527933835983, 0.012425392866134644, -0.02481660433113575, 0.004670204594731331, -0.007041625678539276, -0.005084669217467308, 0.025158429518342018, -0.03096948005259037, 0.06105021387338638, -0.04361706227064133, -0.02859378606081009, -0.00952841341495514, 0.02849123813211918, -0.0109213562682271, 0.020065216347575188, 0.0059264167211949825, -0.025107156485319138, -0.0170571431517601, 0.018168078735470772, 0.06289607286453247, 0.011852833442389965, 0.02965344861149788, -0.015100185759365559, 0.016424763947725296, -0.007387725170701742, 0.013878155499696732, -0.012374118901789188, 0.020048124715685844, 0.059546176344156265, -0.037806011736392975, -0.0215863436460495, 0.012656126171350479, 0.013835427351295948, 0.017638247460126877, -0.02980727143585682, 0.0021460293792188168, -0.011134997941553593, 0.009084039367735386, -0.0028200685046613216, 0.029516717419028282, 0.011724648997187614, -0.009750600904226303, 0.027175206691026688, 0.017270782962441444, -0.010630804114043713, 0.014972000382840633, -0.04850517958402634, -0.057734496891498566, 0.011793014593422413, -0.024953333660960197, 0.04344614967703819, 0.002369284862652421, -0.016305124387145042, -0.019381562247872353, -0.026542827486991882, -0.035584136843681335, 0.027568306773900986, -0.003648997750133276, 0.037806011736392975, 0.020407041534781456, -0.01634785160422325, -0.031191667541861534, -0.004499291069805622, -0.017330603674054146, 0.025534439831972122, 0.020595045760273933, 0.042489033192396164, 0.020287401974201202, -0.039412595331668854, 0.032302603125572205, 0.044608358293771744, -0.04580475017428398, -0.017176780849695206, -0.011229000054299831, -0.009118221700191498, -0.030080731958150864, -0.022218722850084305, -0.033516086637973785, -0.0077124605886638165, -0.013698697090148926, -0.0473087877035141, 0.021654708310961723, 0.017980074509978294, -0.03143094480037689, 0.041531920433044434, -0.014578900299966335, -0.007819280959665775, 0.03613106161355972, -0.06662198156118393, 0.011989564634859562, -0.025944631546735764, 0.0454971082508564, -0.034575749188661575, 0.029533809050917625, -0.009451502934098244, 0.034028828144073486, 0.018954278901219368, 0.01614275574684143, 0.0066228886134922504, -0.01336541585624218, 0.023090379312634468, 0.0007156992214731872, -0.034216832369565964, 0.07041625678539276, 0.020663412287831306, 0.023380933329463005, 0.015202733688056469, 0.03510558232665062, -0.013655968941748142, 0.022458000108599663, 0.0023286929354071617, 0.01658713072538376, 0.059238530695438385, 0.03746418282389641, -0.009075493551790714, 0.018424447625875473, 0.04536037519574165, 0.029533809050917625, -0.030696019530296326, -0.003405446419492364, 0.030644744634628296, -0.0020872780587524176, 0.004270694684237242, 0.00750309182330966, -0.032251328229904175, 0.014818178489804268, -0.008024376817047596, -0.006135785486549139, 0.03189241141080856, 0.028269050642848015, 0.007990194484591484, 0.006362245883792639, -0.013510691933333874, 0.00952841341495514, 0.01633930578827858, -0.030901115387678146, 0.04197629541158676, -0.003040119307115674, 0.06911731511354446, 0.03221714869141579, -0.012972315773367882, -0.037806011736392975, -0.01791170798242092, -0.014510534703731537, 0.003881867276504636, -0.007832099683582783, -0.002602154156193137, -0.005922144278883934, 0.002009298885241151, -0.053188204765319824, 0.032764069736003876, 0.015296735800802708, -0.005161580163985491, 0.0035485862754285336, 0.0012444620952010155, -0.000243017275352031, 0.020543772727251053, -0.01472417637705803, 0.022936558350920677, -0.0013192365877330303, -0.017040051519870758, 0.040779899805784225, 0.018373174592852592, -0.019193558022379875, 0.002531652571633458, -0.028986886143684387, 0.005793959368020296, -0.01314322929829359, -0.03838711604475975, 0.0013480782508850098, 0.02375694178044796, -0.040130432695150375, -0.06498121470212936, -0.01018643006682396, 0.006665616761893034, -0.037600915879011154, -0.015185642056167126, 0.0031960776541382074, 0.014835270121693611, 0.017894616350531578, -0.003396900836378336, -0.0037750464398413897, -0.02114196866750717, 0.013211593963205814, -0.010365888476371765, 0.042591582983732224, -0.035891782492399216, 0.04918883368372917, 0.005187217146158218, 0.012365574017167091, 0.041292641311883926, -0.007960284128785133, -0.03156767785549164, -0.002491060644388199, 0.006033237557858229, -0.0009191927965730429, 0.040779899805784225, 0.00726381316781044, -0.004777025431394577, 0.06563068926334381, -0.024081677198410034, -0.026252275332808495, 0.02476532943546772, -0.005413677077740431, 0.0037365909665822983, 0.014715630561113358, -0.029978184029459953, 0.008447387255728245, 0.004589020740240812, 0.03091820701956749, -0.047342970967292786, 0.003471675328910351, -0.005537589080631733, 0.03691726177930832, 0.012032292783260345, 0.013057772070169449, -0.02199653536081314, 0.018048439174890518, -0.003446038346737623, -0.012827039696276188, -0.01579238474369049, 0.00804146844893694, -0.026713740080595016, -0.044813454151153564, -0.02204780839383602, -0.01871500164270401, 0.037498366087675095, -0.016048753634095192, 0.020663412287831306, 0.007310814224183559, 0.033020440489053726, 0.00991296861320734, -0.015758201479911804, 0.004264285787940025, -0.03937841206789017, -0.030439648777246475, -0.02763667143881321, 0.0028008408844470978, -0.0028328869957476854, 0.03334517404437065, -0.006169968284666538, 0.0008380090002901852, 0.0072937230579555035, -0.030337100848555565, -0.028183594346046448, 0.032405152916908264, -0.014040523208677769, -0.022406727075576782, 0.05486315116286278, -0.03314007818698883, -0.018544087186455727, -0.028166502714157104, -0.035584136843681335, -0.01786043494939804, 0.0021086421329528093, 0.04488182067871094, -0.010776080191135406, -0.034080103039741516, -0.005131670273840427, 0.02900397777557373, 0.012476666830480099, 0.01309195440262556, 0.05257291719317436, 0.015168550424277782, 0.03363572806119919, 0.022013626992702484, 0.016202576458454132, -0.025295160710811615, -0.021244516596198082, 0.03358445316553116, -0.01266467198729515, 0.04802662134170532, -0.046283308416604996, 0.036951445043087006, -0.004195920191705227, -0.001214552321471274, 0.018578270450234413, -0.023227110505104065, -0.06248588487505913, 0.012604852207005024 ]
In general, multiple domain cyberspace security assessments can be implemented by reasoning user's permissions. However, while existing methods include some information from the physical and social domains, they do not provide a comprehensive representation of cyberspace. Existing reasoning methods are also based on expert-given rules, resulting in inefficiency and a low degree of intelligence. To address this challenge, we create a Knowledge Graph (KG) of multiple domain cyberspace in order to provide a standard semantic description of the multiple domain cyberspace. Following that, we proposed a user's permissions reasoning method based on reinforcement learning. All permissions in cyberspace are represented as nodes, and an agent is trained to find all permissions that user can have according to user's initial permissions and cyberspace KG. We set 10 reward setting rules based on the features of cyberspace KG in the reinforcement learning of reward information setting, so that the agent can better locate user's all permissions and avoid blindly finding user's permissions. The results of the experiments showed that the proposed method can successfully reason about user's permissions and increase the intelligence level of the user's permissions reasoning method. At the same time, the F1 value of the proposed method is 6% greater than that of the Translating Embedding (TransE) method.
[ -0.008287801407277584, -0.009145320393145084, -0.029795296490192413, -0.03100045770406723, 0.08669745177030563, 0.0020661563612520695, -0.0160935390740633, 0.026995614171028137, -0.0434228889644146, -0.0171874538064003, 0.07479416579008102, -0.022267673164606094, 0.01848532073199749, -0.06504163146018982, 0.008774501271545887, 0.0397888645529747, 0.022545786574482918, -0.022193510085344315, 0.0030754790641367435, -0.05009762942790985, -0.008793042972683907, 0.0016999727813526988, 0.0156392864882946, 0.024362800642848015, 0.016835177317261696, 0.0031102432403713465, 0.0023002359084784985, 0.02955426461994648, -0.06463372707366943, 0.08069019019603729, 0.039343882352113724, 0.014860566705465317, 0.0060211713425815105, -0.042310431599617004, 0.00014050559548195451, -0.05013471096754074, 0.013126987963914871, -0.018429698422551155, -0.00954858586192131, 0.009539315477013588, 0.004732575733214617, -0.04004843905568123, -0.001676796586252749, 0.027774333953857422, 0.01340510230511427, -0.017715871334075928, -0.03773082047700882, -0.0687498152256012, -0.01181058119982481, -0.027737252414226532, -0.006266838870942593, -0.01260784175246954, 0.04453534632921219, -0.021785609424114227, -0.016149161383509636, 0.010735206305980682, 0.04579612985253334, -0.016557062044739723, 0.020598988980054855, -0.014610263518989086, 0.01152319647371769, 0.01481421384960413, -0.055363256484270096, 0.014183822087943554, -0.006359543651342392, -0.0625942274928093, 0.028423266485333443, -0.020673152059316635, 0.028330562636256218, -0.029832378029823303, -0.036952100694179535, 0.020339414477348328, -0.0057755038142204285, -0.10153020918369293, 0.020098382607102394, 0.014638074673712254, 0.0828409343957901, 0.024844864383339882, 0.045128658413887024, 0.037712279707193375, 0.013655404560267925, 0.039195556193590164, 0.011133836582303047, -0.015027434565126896, 0.026383763179183006, -0.043534137308597565, -0.004625965375453234, -0.06381792575120926, 0.05050553008913994, -0.018494591116905212, -0.03967761993408203, -0.007694491650909185, 0.003404580755159259, -0.04757606238126755, 0.01604718714952469, -0.04409036412835121, 0.0001229061745107174, -0.02004276029765606, -0.023027852177619934, 0.010225330479443073, -0.017029857262969017, -0.020858561620116234, -0.04308915138244629, -0.007916983217000961, 0.03875057399272919, -0.01510159857571125, -0.012218481861054897, 0.018438968807458878, 0.020024219527840614, 0.1374254673719406, -0.040456339716911316, 0.037860605865716934, -0.013720298185944557, 0.014758591540157795, -0.024677995592355728, -0.01806814968585968, -0.03748978674411774, -0.0546216182410717, 0.04720524325966835, -0.011829121969640255, 0.029684050008654594, 0.019505072385072708, 0.04468367248773575, -0.03270622342824936, -0.06648782640695572, 0.07201302796602249, -0.012682005763053894, 0.02688436768949032, -0.01642727665603161, 0.007411742117255926, -0.017057668417692184, 0.04735356941819191, -0.02940593659877777, -0.04676026105880737, 0.06793401390314102, 0.025586502626538277, 0.017400676384568214, 0.003705871058627963, 0.022193510085344315, -0.014137469232082367, 0.021099593490362167, 0.008320248685777187, -0.024084685370326042, 0.024640914052724838, 0.01571344956755638, 0.04627819359302521, -0.02126646228134632, 0.05729151517152786, -0.022008100524544716, 0.05506660416722298, 0.022471623495221138, 0.061370521783828735, -0.003094020066782832, -0.0008024752023629844, 0.06904647499322891, -0.02745913714170456, 0.0416058786213398, 0.004862362518906593, -0.005019960459321737, 0.03035152517259121, 0.06389208883047104, -0.015806155279278755, -0.0028970225248485804, 0.030796507373452187, 0.03407825529575348, 0.03867640718817711, 0.0030244914814829826, -0.013469995930790901, -0.035320498049259186, 0.03498676046729088, -0.023324506357312202, 0.01078155916184187, -0.007509082090109587, 0.03552444651722908, -0.0010087431874126196, 0.034245122224092484, 0.06789693236351013, -0.02640230394899845, -0.034449074417352676, -0.005692069884389639, -0.0444982647895813, 0.01567636802792549, -0.021952476352453232, 0.02582753449678421, 0.04394203796982765, -0.010966967791318893, 0.045573640614748, -0.06318753212690353, 0.00124571961350739, -0.0622234083712101, -0.02684728614985943, 0.011254352517426014, 0.07145679742097855, -0.016529250890016556, -0.016445817425847054, -0.030907753854990005, -0.02753330208361149, 0.05488119274377823, 0.019004467874765396, -0.05310126394033432, -0.007606422062963247, -0.026235435158014297, 0.016362382099032402, -0.024029063060879707, 0.017011316493153572, -0.0014056352665647864, 0.04616694897413254, 0.0017926774453371763, -0.024066144600510597, -0.020376497879624367, -0.05936810001730919, 0.0006385037559084594, -0.023250343278050423, -0.030481310561299324, -0.03750832751393318, -0.005812585819512606, 0.01685371808707714, 0.006966759450733662, -0.04727940633893013, -0.021915394812822342, 0.03509800508618355, 0.033559106290340424, 0.03952929005026817, 0.03849099949002266, -0.03773082047700882, -0.008459305390715599, 0.018012527376413345, 0.02122938074171543, -0.023417212069034576, -0.04405328258872032, -0.03129711374640465, 0.014804943464696407, 0.06845316290855408, -0.010744476690888405, 0.0473906509578228, -0.03161231055855751, 0.03639587387442589, -0.06352127343416214, -0.05599365010857582, -0.0002461020485498011, -0.002016327576711774, -0.008621538989245892, 0.0002616011188365519, -0.014499017968773842, 0.04913350194692612, -0.016232596710324287, -0.020747315138578415, 0.027792874723672867, 0.06311336904764175, 0.019987137988209724, -0.004574977792799473, 0.01993151381611824, 0.02810806967318058, -0.03663690388202667, 0.0206175297498703, -0.00588674983009696, 0.025623584166169167, -0.032465193420648575, -0.011606630869209766, -0.05332375317811966, 0.04868851974606514, 0.011124566197395325, -0.004139265511184931, -0.022453082725405693, -0.013775921426713467, -0.0028251763433218002, 0.060035575181245804, 0.028349103406071663, 0.019875891506671906, -0.04902225360274315, 0.0093168243765831, -0.05729151517152786, -0.09322386234998703, -0.03578402101993561, -0.022045182064175606, -0.025160061195492744, 0.0023431116715073586, 0.00678135035559535, 0.05150674283504486, -0.00043947831727564335, -0.039158474653959274, -0.015592933632433414, -0.022508705034852028, -0.07438626885414124, -0.05439912900328636, -0.046611931174993515, -0.056920696049928665, -0.017085479572415352, -0.022694114595651627, 0.014647345058619976, -0.013516347855329514, -0.051061756908893585, -0.0712343081831932, 0.003548273118212819, 0.007166074588894844, 0.033225372433662415, -0.008255355060100555, -0.010531255975365639, -0.027403514832258224, -0.015277737751603127, -0.05862646549940109, 0.03426366299390793, -0.03472718596458435, 0.019152794033288956, -0.04601862281560898, 0.025808993726968765, -0.01021606009453535, 0.03591380640864372, -0.015147950500249863, -0.042310431599617004, 0.030703803524374962, 0.015815425664186478, -0.02890533022582531, -0.01397987175732851, 0.002637449186295271, -0.007708397228270769, 0.026179812848567963, -0.0012005261378362775, 0.006169498898088932, -0.03146398067474365, 0.008287801407277584, 0.026977073401212692, -0.07371879369020462, 0.016955692321062088, -0.05436204746365547, 0.035283416509628296, -0.004276005085557699, 0.05959059298038483, -0.007045558653771877, -0.03975178301334381, -0.012070153839886189, 0.030740885064005852, -0.022694114595651627, -0.015166492201387882, -0.033948466181755066, -0.04323748126626015, -0.0015852507203817368, 0.05443621054291725, -0.029906542971730232, 0.013497807085514069, 0.036877937614917755, 0.023862194269895554, -0.027663087472319603, 0.02643938548862934, -0.021618740633130074, -0.00889965333044529, 0.03878765553236008, 0.027403514832258224, -0.0379718542098999, 0.028849707916378975, 0.0011576501419767737, -0.027143942192196846, -0.04783563315868378, -0.039047226309776306, 0.03131565451622009, -0.0018645236268639565, 0.01434141956269741, 0.008510293439030647, 0.012311186641454697, -0.031816259026527405, -0.012858144007623196, -0.05002346634864807, -0.07230968028306961, 0.03548736497759819, -0.09033147990703583, -0.01005846168845892, 0.038935981690883636, 0.018874680623412132, 0.02677312307059765, 0.006424436811357737, -0.015583663247525692, 0.03194604441523552, 0.04865143448114395, 0.01605645753443241, -0.021748526021838188, 0.023750949651002884, 0.012172129936516285, -0.006762809120118618, -0.013998412527143955, 0.040752995759248734, 0.025160061195492744, -0.00484845694154501, -0.0023755584843456745, -0.0017474839696660638, -0.020487742498517036, 0.012700546532869339, 0.05799607187509537, 0.05907144770026207, 0.043571218848228455, 0.03012903407216072, -0.06849024444818497, 0.048095207661390305, -0.0354502834379673, -0.06266839057207108, 0.02427009493112564, -0.03231686353683472, -0.05206296965479851, 0.007731573656201363, 0.04134630411863327, 0.013618323020637035, -0.009567126631736755, 0.002697707386687398, -0.00893673487007618, -0.025493796914815903, 0.025586502626538277, -0.027607465162873268, 0.017604626715183258, -0.07683367282152176, -0.0017532779602333903, 0.0024960744194686413, 0.02525276504456997, 0.019264040514826775, -0.02590169757604599, -0.011263622902333736, 0.03213145583868027, 0.06834191828966141, -0.023991981521248817, 0.03576548025012016, 0.0036131662782281637, 0.008524199016392231, -0.019801728427410126, -0.020747315138578415, 0.02065461128950119, -0.0066469283774495125, -0.0640033408999443, 0.030685260891914368, 0.01481421384960413, -0.047983963042497635, 0.014081846922636032, -0.0575140081346035, 0.0012294963235035539, -0.021544575691223145, 0.08929318189620972, -0.0359879732131958, -0.012997201643884182, 0.00819973275065422, 0.03700772300362587, 0.05150674283504486, 0.04134630411863327, -0.004276005085557699, -0.010772287845611572, -0.05343499779701233, -0.035172171890735626, -0.056920696049928665, -0.012580030597746372, 0.00996575690805912, -0.014230174012482166, -0.03335515782237053, 0.01978318765759468, -0.03200167044997215, -0.04179128631949425, -0.023102015256881714, 0.017298700287938118, 0.002693071961402893, 0.016798095777630806, -0.012181400321424007, -0.0032724766060709953, -0.050839267671108246, -0.03153814375400543, 0.0013268362963572145, -0.02445550449192524, 0.08343424648046494, -0.01684444770216942, -0.0271254014223814, 0.022842442616820335, 0.0528046078979969, -0.08291509747505188, -0.046426523476839066, 0.02163728140294552, 0.02167436294257641, 0.05221129581332207, -0.005260992795228958, 0.08269260823726654, -0.04171712324023247, -0.05139549449086189, 0.02860867604613304, 0.028423266485333443, -0.026495007798075676, -0.02669895812869072, 0.008602998219430447, -0.011068942956626415, 0.009455881081521511, 0.013942789286375046, -0.023250343278050423, 0.01615843176841736, -0.0004136947973165661, 0.0046213301829993725, 0.017771493643522263, -0.02857159450650215, -0.0488368459045887, -0.03240957111120224, -0.0492076650261879, -0.03643295541405678, -0.015324089676141739, -0.002595732221379876, -0.018781976774334908, -0.04249584302306175, -0.014026223681867123, 0.052433788776397705, 0.0041670771315693855, -0.013896437361836433, -0.01879124715924263, -0.0005217537400312722, 0.04409036412835121, 0.04624111205339432, 0.02380657196044922, -0.015908129513263702, 0.006976029835641384, -0.03205729275941849, 0.05291585251688957, -0.0030430324841290712, 0.02517860196530819, 0.011449032463133335, -0.02122938074171543, 0.0002721752680372447, 0.03656274080276489, -0.0011646030470728874, -0.02944301813840866, 0.045128658413887024, 0.05184047669172287, -0.011569548398256302, -0.004593518562614918, -0.01909717172384262, -0.015991562977433205, 0.014211633242666721, 0.04542531073093414, 0.0186336487531662, -0.016918610781431198, -0.034745726734399796, -0.0012526725186035037, -0.02145187184214592, -0.002419593045488, -0.01481421384960413, -0.050876349210739136, 0.015528040006756783, 0.005274898372590542, 0.01829991117119789, 0.04112381115555763, -0.011588090099394321, -0.019412368535995483, -0.04153171554207802, 0.09448464959859848, -0.018281370401382446, 0.009483692236244678, 0.012950848788022995, 0.036006513983011246, 0.06663615256547928, -0.03190896287560463, -0.0114861149340868, 0.019987137988209724, -0.016686849296092987, -0.01443412434309721, -0.000804792856797576, -0.05476994812488556, 0.024640914052724838, -0.03500530123710632, 0.04130922257900238, 0.016557062044739723, 0.022267673164606094, -0.008018958382308483, 0.025345470756292343, 0.0018795881187543273, -0.009386352263391018, -0.01076301746070385, 0.0003913877299055457, 0.0029572804924100637, 0.01575053110718727, 0.039047226309776306, 0.03750832751393318, 0.008575186133384705, -0.02336158975958824, -0.03504238277673721, -0.04008552059531212, -0.010920615866780281, -0.00394690316170454, 0.011421221308410168, 0.009798889048397541, -0.01650143973529339, -0.010772287845611572, 0.0023825112730264664, -0.00987305212765932, -0.009780347347259521, -0.015880318358540535, 0.029869459569454193, -0.004211111925542355, 0.003246982814744115, -0.0031612308230251074, -0.03628462553024292, -0.005325885955244303, -0.037563953548669815, -0.026995614171028137, 0.04446118324995041, -0.006313191261142492, -0.02517860196530819, 0.029461558908224106, -0.026216894388198853, 0.042162105441093445, -0.03159376606345177, 0.01772514171898365, -0.04872560128569603, -0.022508705034852028, 0.03658128157258034, 0.05365749076008797, 0.007736208848655224, -0.01791055127978325, -0.012876685708761215, 0.025549421086907387, -0.035431742668151855, -0.01372956857085228, -0.0000987884632195346, -0.007685221266001463, 0.0006709503941237926, 0.01779930666089058, -0.0698251947760582, 0.0015551216201856732, -0.012042342685163021, 0.04460950940847397, -0.014091117307543755, -0.028312020003795624, -0.03647003695368767, -0.018355533480644226, -0.029962165281176567, 0.045017410069704056, -0.050765104591846466, -0.017066938802599907, -0.07905858010053635, 0.03392992541193962, -0.019189877435564995, 0.017641708254814148, 0.01228337548673153, -0.03661836311221123, 0.03049985133111477, -0.031167326495051384, -0.008399047888815403, 0.04553655907511711, 0.00456338981166482, 0.020246710628271103, 0.06048055738210678, -0.005622541066259146, 0.04531406611204147, -0.04234751686453819, 0.014443394728004932, -0.030796507373452187, 0.09055396914482117, 0.012978660874068737, 0.01860583759844303, -0.014044764451682568, 0.029072199016809464, 0.020895643159747124, 0.053991228342056274, 0.036989182233810425, 0.024325717240571976, -0.0018842234276235104, 0.009798889048397541, 0.031130244955420494, -0.013136258348822594, -0.02007984183728695, -0.05009762942790985, -0.031667932868003845, 0.023862194269895554, -0.0018691589357331395, -0.010457091964781284, 0.0022017371375113726, -0.0020302333869040012, 0.0008754801820032299, 0.006521776784211397, 0.018466779962182045, 0.009669101797044277, -0.02955426461994648, 0.03446761518716812, -0.001530786626972258, -0.049430154263973236, -0.04316331818699837, 0.07720448821783066, 0.005766233429312706, -0.04431285709142685, 0.0021646551322191954, 0.006062888540327549, -0.052656278014183044, -0.024789242073893547, 0.007356119342148304, 0.01302501279860735, -0.03287309408187866, -0.02300931140780449, -0.03378159925341606, -0.0036595186684280634, -0.002767235739156604, 0.0349125973880291, -0.005937737412750721, 0.03077796660363674, -0.006730362307280302, 0.022508705034852028, 0.005483483895659447, 0.012394621036946774, 0.0139242485165596, -0.0023940992541611195, -0.029850918799638748, 0.00960420910269022, 0.006206580903381109, 0.03693355992436409, -0.01906009018421173, 0.01604718714952469, 0.002190148923546076, 0.05350916460156441, 0.021025430411100388, 0.028627216815948486, 0.02336158975958824, 0.04783563315868378, 0.01222775224596262, -0.01213504746556282, -0.029313232749700546, 0.03226124122738838, -0.005427861120551825, 0.01860583759844303, 0.0033999455627053976, -0.0028877519071102142, 0.04446118324995041, -0.017178183421492577, 0.0051960996352136135, 0.014999623410403728, 0.028664298355579376, -0.0024103226605802774, 0.01989443227648735, -0.04108672961592674, -0.07546164095401764, -0.006294650491327047, 0.011745687574148178, -0.023973440751433372, 0.014656616374850273, 0.0006338685052469373, 0.03773082047700882, -0.02959134615957737, 0.005112665239721537, 0.02236037887632847, -0.009136050008237362, 0.019912973046302795, 0.015203573741018772, -0.004034972749650478, -0.014424853958189487, 0.004700129386037588, 0.002748694969341159, -0.021006889641284943, 0.03354056552052498, -0.05035720393061638, 0.0119403675198555, -0.02962842769920826, -0.031742095947265625, -0.003817116841673851, -0.03641441464424133, 0.01586177758872509, 0.03274330496788025, -0.05202588811516762, 0.021210839971899986, -0.022416001185774803, -0.0023709230590611696, 0.013998412527143955, 0.05284168943762779, 0.00734221376478672, 0.014165281318128109, 0.03012903407216072, -0.023417212069034576, 0.06311336904764175, -0.03500530123710632, 0.05432496592402458, 0.049467235803604126, 0.004774292930960655, -0.014916189014911652, 0.007703762035816908, 0.02681020461022854, -0.02380657196044922, 0.014248714782297611, -0.04742773249745369, 0.03863932564854622, -0.03294725716114044, 0.02564212493598461, 0.035580072551965714, -0.005330521147698164, -0.019152794033288956, -0.02528984658420086, 0.02734789252281189, -0.005386143922805786, 0.0007561228703707457, -0.049726810306310654, 0.06978811323642731, -0.0018135360442101955, 0.004289910662919283, 0.022768279537558556, -0.018049608916044235, 0.014461936429142952, 0.018624378368258476, -0.024066144600510597, 0.04590737819671631, 0.022694114595651627, 0.01005846168845892, -0.012385350652039051, -0.0011333151487633586, -0.00584039743989706, 0.018689271062612534, -0.016547791659832, -0.029239067807793617, 0.03750832751393318, -0.021322084590792656, -0.0034022631589323282, 0.017984716221690178, -0.027904119342565536, -0.012181400321424007, -0.010503444820642471, 0.015453876927495003, -0.03669252619147301, 0.03519071266055107, 0.033911384642124176, -0.03826850652694702, 0.009622749872505665, 0.03643295541405678, -0.00578013900667429, -0.016371652483940125, -0.03378159925341606, 0.021822690963745117, -0.02376949042081833, -0.013840814121067524, 0.005200734827667475, -0.05921977385878563, -0.03493113815784454, -0.014183822087943554, -0.025920238345861435, -0.040493421256542206, 0.021247921511530876, 0.012765439227223396, 0.026216894388198853, -0.014554640278220177, 0.03628462553024292, 0.05732859671115875, -0.04264416918158531, 0.05035720393061638, -0.02556796185672283, 0.04687150567770004, 0.024029063060879707, -0.0022759009152650833, 0.03674814850091934, 0.05213713273406029, -0.011208000592887402, 0.028998035937547684, 0.002910928102210164, -0.0093168243765831, -0.01837407425045967, -0.0026722135953605175, -0.04138338565826416, -0.01340510230511427, 0.01002138014882803, 0.0070084766484797, 0.034523237496614456, 0.039343882352113724, -0.031130244955420494, 0.045276984572410583, -0.020191088318824768, 0.006118511315435171, 0.04234751686453819, 0.017623167484998703, 0.0114861149340868, -0.03422658145427704, 0.017484109848737717, -0.03628462553024292, -0.002876163925975561, -0.009780347347259521, 0.011449032463133335, -0.023194720968604088, 0.06062888726592064, -0.053842898458242416, -0.02499319240450859, -0.03500530123710632, -0.0179939866065979, -0.03009195066988468, -0.0260500255972147, 0.017029857262969017, -0.00964129064232111, -0.006164863705635071, -0.0009745583520270884, -0.014230174012482166, 0.011513926088809967, 0.0011512767523527145, -0.021210839971899986, 0.0003702394606079906, 0.017141101881861687, 0.016900070011615753, 0.006609846372157335, -0.022786820307374, 0.012311186641454697, -0.049504321068525314, 0.03302142024040222, -0.01893957331776619, -0.01597302220761776, 0.015908129513263702, -0.021322084590792656, -0.0071892510168254375, 0.030332984402775764, 0.034782811999320984, -0.020357955247163773, -0.005715245846658945, -0.01920841820538044, 0.013414372690021992, 0.007879900746047497, -0.03719313442707062, -0.03335515782237053, -0.006285380106419325, 0.01605645753443241, -0.025419633835554123, -0.00005511585186468437, -0.0444982647895813, 0.03431928530335426, 0.023639703169465065, 0.0019247817108407617, -0.03168647363781929, -0.03472718596458435, -0.0010116401826962829, -0.011625171639025211, -0.013210422359406948, -0.022879524156451225, -0.013052823953330517, -0.0025609678123146296, 0.009075791575014591, 0.028515972197055817, 0.03776790201663971, -0.026216894388198853, 0.03567277640104294, -0.016269678249955177, 0.0025401092134416103, -0.0280339065939188, -0.040419258177280426, -0.007629598490893841, 0.0025563326198607683, -0.039232637733221054, 0.016557062044739723, 0.012913767248392105, -0.005858938209712505, -0.018383346498012543, -0.024047603830695152, -0.025846075266599655, -0.029257608577609062, -0.019264040514826775, -0.008227543905377388, -0.009256565943360329, -0.0027463773731142282, 0.046426523476839066, -0.00550666032359004, 0.03081504814326763, 0.012774710543453693, 0.06385500729084015, 0.015945211052894592, 0.01306209433823824, 0.00992867536842823, -0.02084002085030079, -0.014091117307543755, 0.020858561620116234, -0.02643938548862934, -0.02651354856789112, -0.007995781488716602, -0.020228169858455658, -0.01882832869887352, 0.00875132530927658, 0.02069169282913208, 0.025493796914815903, 0.022193510085344315, -0.016788823530077934, -0.005349062383174896, -0.06993643939495087, -0.0075368937104940414, -0.024900486692786217, -0.017474839463829994, -0.05818147957324982, 0.026291057467460632, 0.0031102432403713465, -0.013423643074929714, 0.02734789252281189, -0.002001263201236725, 0.01306209433823824, -0.025512337684631348, 0.010577607899904251, -0.00039718177868053317, 0.012431702576577663, 0.0049179852940142155, 0.049281828105449677, 0.036043595522642136, -0.01034584641456604, 0.01982026919722557, -0.0037313648499548435, -0.027644546702504158, 0.04012260213494301, 0.006563493981957436, 0.0013963647652417421, -0.006345638073980808, 0.0012793251080438495, -0.028441807255148888, -0.04579612985253334, -0.013154799118638039, -0.018958114087581635, 0.020265251398086548, 0.006707186345010996, -0.015991562977433205, -0.0441274456679821, 0.0033929927740246058, 0.012682005763053894, -0.0191713348031044, -0.02156311832368374, 0.03324391320347786, -0.02202664129436016, 0.007787196431308985, 0.03572839871048927, 0.03179771825671196, 0.017335781827569008, 0.01639946550130844, -0.005515930708497763, 0.00681843189522624, 0.044832002371549606, 0.006526411976665258, -0.015509499236941338, -0.04316331818699837, -0.05803315341472626, -0.03378159925341606, 0.02590169757604599, -0.049652647227048874, -0.03656274080276489, 0.0056503526866436005, -0.008704973384737968, -0.01784565858542919 ]
In recent years cybersecurity has become a major concern in adaptation of smart applications. Specially, in smart homes where a large number of IoT devices are used having a secure and trusted mechanisms can provide peace of mind for users. Accurate detection of cyber attacks is crucial, however precise identification of the type of attacks plays a huge role if devising the countermeasure for protecting the system. Artificial Neural Networks (ANN) have provided promising results for detecting any security attacks for smart applications. However, due to complex nature of the model used for this technique it is not easy for normal users to trust ANN based security solutions. Also, selection of right hyperparameters for ANN architecture plays a crucial role in the accurate detection of security attacks, especially when it come to identifying the subcategories of attacks. In this paper, we propose a model that considers both the issues of explainability of ANN model and the hyperparameter selection for this approach to be easily trusted and adapted by users of smart home applications. Also, our approach considers a subset of the dataset for optimal selection of hyperparamters to reduce the overhead of the process of ANN architecture design. Distinctively this paper focuses on configuration, performance and evaluation of ANN architecture for identification of five categorical attacks and nine subcategorical attacks. Using a very recent IoT dataset our approach showed high performance for intrusion detection with 99.9%, 99.7%, and 97.7% accuracy for Binary, Category, and Subcategory level classification of attacks.
[ -0.036918189376592636, -0.0061437408439815044, -0.024686450138688087, -0.028142552822828293, 0.0876607894897461, 0.02374677173793316, -0.03073861263692379, 0.0047023706138134, -0.006856462452560663, 0.0672745555639267, -0.003370496677234769, -0.11371693760156631, 0.006860444322228432, -0.03016524948179722, -0.02217002399265766, -0.020290669053792953, 0.007302411366254091, -0.0774039626121521, -0.006820627022534609, -0.08046189695596695, 0.025657981634140015, 0.0021879361011087894, -0.022631900385022163, -0.009484374895691872, 0.026979900896549225, 0.033669132739305496, 0.01238304190337658, 0.017917584627866745, -0.055902864784002304, 0.0732630118727684, 0.032347213476896286, -0.004937290214002132, 0.005693810060620308, -0.017423855140805244, -0.03953017294406891, -0.03628112003207207, -0.01108501199632883, 0.06873981654644012, -0.025212032720446587, 0.04220586642622948, 0.03580331429839134, -0.0345928817987442, 0.002574159763753414, 0.0580689013004303, 0.014063313603401184, -0.0019281312124803662, -0.04526380077004433, -0.05736812576651573, -0.02043401077389717, 0.011013342067599297, 0.021692221984267235, -0.07307188957929611, -0.013808485120534897, 0.014501298777759075, -0.056093983352184296, 0.02013140171766281, 0.042046599090099335, -0.0026159672997891903, 0.061190541833639145, 0.036918189376592636, 0.03647223860025406, 0.05048777163028717, -0.002677683485671878, 0.010201077908277512, -0.03338244929909706, 0.00514433765783906, 0.028636282309889793, -0.031471241265535355, -0.02145332098007202, 0.0017867813585326076, -0.061827611178159714, 0.050806306302547455, -0.016739005222916603, -0.030260810628533363, 0.00653394591063261, -0.03274537995457649, 0.019287284463644028, 0.028413306921720505, 0.03806491196155548, 0.03580331429839134, 0.006155685987323523, 0.014708345755934715, 0.02404938079416752, -0.00453115813434124, 0.0478120781481266, 0.010686843656003475, -0.006091978866606951, -0.07606612145900726, 0.017153101041913033, -0.0239060390740633, -0.050169236958026886, 0.009771056473255157, -0.0012412904761731625, 0.013211232610046864, -0.006155685987323523, 0.013888118788599968, 0.0007072468870319426, -0.03024488314986229, -0.03194904327392578, -0.0193669181317091, -0.008759708143770695, 0.010471832938492298, 0.0061158686876297, 0.017471635714173317, 0.024893498048186302, -0.011793752200901508, -0.01438981108367443, 0.02575354091823101, -0.012319334782660007, 0.07077844440937042, -0.03258611261844635, 0.004336055368185043, -0.019988061860203743, 0.0026020314544439316, 0.0019281312124803662, -0.007135180290788412, -0.005992436781525612, -0.06064903363585472, -0.05297234281897545, -0.005661956965923309, -0.019701380282640457, 0.03401952236890793, 0.015138368122279644, 0.01650010421872139, -0.031741995364427567, 0.051570791751146317, 0.037587109953165054, -0.001534939743578434, 0.009396777488291264, 0.028381453827023506, 0.019701380282640457, 0.021134786307811737, 0.058100756257772446, -0.0022158080246299505, 0.01657973788678646, 0.006155685987323523, 0.04762095957994461, -0.004989051725715399, -0.013609400950372219, -0.030181175097823143, 0.023667138069868088, 0.015942668542265892, -0.013290866278111935, 0.019191723316907883, 0.02307784929871559, 0.015608207322657108, 0.025849102064967155, 0.03191719204187393, -0.033509865403175354, -0.02167629636824131, -0.009564008563756943, 0.06944059580564499, -0.017583122476935387, 0.009293253533542156, 0.033478010445833206, -0.017455710098147392, 0.02005176804959774, -0.000019379609511815943, -0.03151902183890343, 0.0025801321025937796, 0.030037835240364075, -0.010941672138869762, 0.01418276410549879, 0.04309776425361633, 0.028445161879062653, 0.05663549527525902, -0.019159870222210884, -0.009261400438845158, -0.054501309990882874, 0.055871009826660156, 0.004921363200992346, -0.04150509089231491, -0.006036235019564629, 0.043448153883218765, 0.006084015592932701, 0.04086802154779434, 0.007632891181856394, -0.009556044824421406, 0.0020844123791903257, 0.017153101041913033, -0.034943271428346634, -0.006119850557297468, -0.00042255636071786284, -0.010623136535286903, 0.03605814278125763, 0.03462473675608635, 0.06262394785881042, -0.02296636253595352, 0.09135579317808151, -0.008528769947588444, 0.006924150977283716, 0.017869804054498672, 0.030690832063555717, -0.017965365201234818, -0.013816448859870434, -0.0559665709733963, 0.023762699216604233, 0.008337649516761303, 0.013999606482684612, -0.03484771028161049, -0.007704561576247215, -0.029814861714839935, 0.002625921508297324, -0.056922174990177155, 0.04332073777914047, 0.017583122476935387, 0.040422070771455765, 0.018984677270054817, 0.008369502611458302, 0.005407128948718309, -0.0254509337246418, 0.02217002399265766, -0.00671312166377902, -0.032299432903528214, 0.015488756820559502, 0.00907824281603098, 0.04434004798531532, -0.016078045591711998, -0.03062712401151657, -0.020832179114222527, 0.05615769326686859, 0.05797334015369415, 0.04191918671131134, 0.01108501199632883, -0.011427436955273151, 0.0037487568333745003, -0.013927935622632504, 0.044499315321445465, -0.051029279828071594, -0.007043601479381323, -0.03707745671272278, -0.04166435822844505, 0.03148717060685158, 0.02729843556880951, 0.033095769584178925, -0.011300023645162582, -0.007397971581667662, -0.03293650224804878, -0.014620749279856682, -0.023460090160369873, -0.022679680958390236, -0.0065458910539746284, -0.04376668855547905, -0.05357756093144417, 0.030228955671191216, -0.03975314646959305, 0.030754538252949715, 0.08033448457717896, 0.012486565858125687, 0.017981290817260742, -0.03274537995457649, -0.027919579297304153, 0.02881147712469101, 0.009564008563756943, -0.026183564215898514, -0.035325512290000916, 0.015058734454214573, -0.02839738130569458, 0.04844914749264717, -0.011180573143064976, 0.03507068753242493, -0.006155685987323523, -0.0020824214443564415, 0.09294846653938293, -0.054055362939834595, 0.01680271327495575, 0.06982284039258957, 0.005200081039220095, 0.04293849691748619, -0.022711534053087234, 0.033669132739305496, -0.0038721892051398754, -0.06612782925367355, -0.019048383459448814, 0.0036930132191628218, -0.006087996996939182, 0.049181777983903885, -0.02619948983192444, 0.011100939474999905, 0.0487995371222496, -0.03484771028161049, -0.05418277531862259, 0.013450133614242077, 0.01823611930012703, 0.004869601223617792, -0.05271751433610916, -0.0691857635974884, 0.030085615813732147, -0.05010553076863289, -0.03284094110131264, -0.019701380282640457, -0.03209238499403, -0.04504082724452019, -0.022249657660722733, -0.005335458554327488, 0.01544097624719143, 0.03870198130607605, -0.043288882821798325, -0.02768067829310894, -0.03178977593779564, -0.0835198312997818, -0.0021262201480567455, -0.002932511270046234, 0.050392210483551025, -0.056316960602998734, 0.001736014848574996, 0.027250654995441437, 0.06176390498876572, -0.011220389977097511, -0.029575960710644722, -0.010710733942687511, -0.01914394460618496, -0.04363927245140076, -0.04507267847657204, -0.006251246202737093, 0.02748955599963665, -0.006979894824326038, -0.00740991672500968, 0.032156091183423996, -0.004035438410937786, 0.043862245976924896, 0.029846714809536934, -0.07976112514734268, 0.048958804458379745, -0.05918377265334129, -0.011045195162296295, 0.06071273982524872, -0.03151902183890343, -0.052430834621191025, -0.038351595401763916, -0.030690832063555717, 0.004774041008204222, -0.06256024539470673, -0.027855871245265007, -0.037555258721113205, -0.03984870761632919, -0.006342825014144182, 0.06048976629972458, -0.016866419464349747, 0.004563011694699526, -0.0016961980145424604, -0.052430834621191025, -0.05064703896641731, -0.005805297289043665, -0.030021907761693, -0.006064107175916433, -0.03140753507614136, -0.0068803527392446995, -0.04293849691748619, 0.008226161822676659, 0.0008286882657557726, -0.0387338362634182, 0.01589488796889782, -0.021437395364046097, -0.01718495413661003, 0.027059534564614296, 0.006056143436580896, -0.005478799343109131, 0.020784398540854454, -0.00917380303144455, 0.0427473746240139, -0.0016533948946744204, 0.00965160597115755, -0.01672307960689068, -0.06791162490844727, -0.01620545983314514, 0.0010203069541603327, -0.009747166186571121, 0.008337649516761303, 0.00478598615154624, -0.055871009826660156, 0.0589926540851593, -0.030802318826317787, -0.0249253511428833, -0.01333068311214447, 0.019000602886080742, 0.01608601026237011, -0.008751744404435158, -0.01185745932161808, 0.04211030527949333, -0.022743387147784233, 0.004264384973794222, -0.05720885843038559, 0.03567590191960335, -0.01575154811143875, 0.057336270809173584, 0.06944059580564499, 0.01672307960689068, 0.011244280263781548, 0.0815449208021164, 0.006864425726234913, -0.02209039032459259, -0.013872192241251469, -0.06090386211872101, 0.03949832171201706, -0.051411524415016174, -0.030754538252949715, -0.009826799854636192, 0.07154292613267899, -0.059980109333992004, -0.03602629154920578, 0.017089394852519035, 0.010065700858831406, -0.038574568927288055, 0.0008744776714593172, -0.014676492661237717, -0.01544097624719143, -0.04596457630395889, 0.006828590761870146, -0.0024089196231216192, -0.011475217528641224, 0.015138368122279644, 0.01455704215914011, -0.007258612662553787, 0.0027334270998835564, 0.04593272507190704, -0.02487757056951523, 0.00513637438416481, 0.01306789182126522, -0.030993439257144928, -0.004077245946973562, 0.03650409355759621, 0.03220387175679207, -0.006717103533446789, -0.0073860264383256435, 0.0019251449266448617, -0.069313183426857, -0.04778022691607475, 0.04819432273507118, 0.012295444495975971, 0.04271552339196205, -0.012072470039129257, 0.03803306072950363, -0.029352985322475433, -0.04402151331305504, -0.01895282231271267, -0.03148717060685158, 0.01925543136894703, -0.01626916602253914, -0.034752149134874344, -0.02537130005657673, 0.009277326986193657, -0.04376668855547905, 0.011451327241957188, -0.010591283440589905, -0.01571173034608364, -0.00024586907238699496, -0.015799328684806824, -0.023842332884669304, -0.03698189556598663, -0.031168634071946144, 0.0244634747505188, -0.014190726913511753, -0.039020515978336334, 0.03828788921236992, -0.005944656208157539, -0.018331680446863174, -0.015202075242996216, 0.008488953113555908, -0.03303206339478493, -0.0315030962228775, 0.10148520022630692, -0.036950040608644485, 0.0127254668623209, 0.024113086983561516, 0.0243997685611248, -0.039593879133462906, -0.0630698949098587, 0.011992836371064186, 0.01586303487420082, 0.03688633441925049, -0.024447549134492874, 0.029878567904233932, -0.004953216761350632, 0.0076846531592309475, 0.008990645408630371, -0.00008890357275959104, 0.010471832938492298, 0.053418293595314026, -0.014676492661237717, 0.00714712543413043, 0.004344018641859293, 0.024606816470623016, 0.023810479789972305, -0.0002906630397774279, -0.01627713069319725, -0.0034441580064594746, -0.023284897208213806, -0.06262394785881042, -0.06287878006696701, -0.019239503890275955, -0.011546888388693333, -0.028572574257850647, -0.010065700858831406, -0.047557249665260315, -0.028445161879062653, -0.01763090305030346, -0.001185546861961484, 0.08224569261074066, 0.02771253138780594, -0.014302214607596397, -0.05348199978470802, -0.0021302017848938704, -0.006482183933258057, -0.012606016360223293, 0.0023073868360370398, 0.012797136791050434, 0.04535936191678047, 0.04615569859743118, 0.013665144331753254, 0.006438385229557753, -0.01906431093811989, 0.007963370531797409, -0.017694611102342606, -0.0073939901776611805, 0.01994028128683567, -0.03844715654850006, -0.005813261028379202, 0.022552266716957092, 0.021501101553440094, 0.01809277944266796, -0.02330082282423973, 0.003266972955316305, -0.007190924137830734, -0.03765081614255905, 0.03650409355759621, 0.019319137558341026, -0.012964367866516113, -0.04109099507331848, -0.0055305613204836845, 0.017917584627866745, 0.016109898686408997, -0.06529964506626129, -0.04131396859884262, -0.001906231977045536, 0.02291858196258545, 0.012526382692158222, 0.043480005115270615, -0.047111302614212036, -0.041441380977630615, -0.06651007384061813, 0.06125424802303314, -0.02170814946293831, -0.03198089823126793, -0.022647827863693237, -0.008791561238467693, 0.03908422589302063, -0.03260204195976257, 0.021962977945804596, 0.016818638890981674, -0.008234125562012196, -0.031248267740011215, 0.020529570057988167, -0.007915590889751911, -0.012996221892535686, -0.02869998849928379, -0.012677686288952827, 0.014835759997367859, 0.022329291328787804, -0.02269560657441616, -0.009412704035639763, 0.00037452729884535074, -0.01759904995560646, -0.032649822533130646, -0.008258015848696232, -0.044308196753263474, 0.0031375682447105646, 0.029703373089432716, 0.04975514113903046, 0.021341834217309952, -0.030531564727425575, -0.03889310359954834, -0.03765081614255905, -0.023762699216604233, 0.01421461720019579, 0.016109898686408997, 0.004738205578178167, -0.011220389977097511, 0.012542309239506721, 0.01114075630903244, -0.0008719891193322837, 0.011029268614947796, 0.0058451141230762005, 0.014772052876651287, 0.02291858196258545, -0.015918778255581856, -0.0076090008951723576, 0.005100538954138756, -0.02019510790705681, -0.00549472589045763, 0.0031793757807463408, 0.028254039585590363, -0.027616970241069794, -0.006418476812541485, -0.00383237237110734, 0.01944655179977417, 0.01100537832826376, 0.00715508870780468, 0.04007168114185333, -0.014684456400573254, -0.01378459483385086, 0.008871194906532764, 0.04666535556316376, 0.06606412678956985, 0.03526180610060692, 0.03628112003207207, -0.0326179675757885, -0.0007002789643593132, -0.00021575758000835776, -0.03128012269735336, -0.01123631652444601, -0.015194111503660679, 0.013872192241251469, -0.03831974044442177, 0.018490947782993317, 0.03822417929768562, 0.021501101553440094, 0.002900657942518592, -0.007987260818481445, 0.02288672886788845, 0.012486565858125687, -0.04093172773718834, 0.03905237093567848, -0.015265782363712788, 0.017121247947216034, 0.008385430090129375, 0.021915197372436523, -0.0016902254428714514, 0.010917781852185726, 0.00513637438416481, -0.030037835240364075, -0.003340634051710367, -0.03379654511809349, -0.008393392898142338, -0.015942668542265892, -0.002005774062126875, -0.02979893423616886, 0.029050378128886223, -0.020179182291030884, 0.04561419039964676, 0.028445161879062653, -0.0025124435778707266, -0.049372900277376175, 0.09205656498670578, -0.012980294413864613, 0.027027681469917297, -0.02303006872534752, -0.03436990827322006, 0.051443375647068024, 0.03618555888533592, 0.022185951471328735, 0.004041410982608795, 0.005327495280653238, 0.02076847106218338, -0.013410316780209541, -0.0315030962228775, 0.025275738909840584, 0.04398966208100319, -0.010137371718883514, -0.04013539105653763, -0.009938286617398262, -0.003155485726892948, -0.007831975817680359, 0.010949634946882725, -0.010105517692863941, -0.000014674688827653881, 0.012717503122985363, -0.006187539082020521, 0.020609203726053238, 0.04341629892587662, -0.015050770714879036, -0.05230342224240303, -0.07460086047649384, 0.040804311633110046, 0.03946646675467491, -0.023284897208213806, 0.024973131716251373, 0.08523992449045181, 0.014644639566540718, -0.06322916597127914, -0.0006982880877330899, 0.01997213438153267, -0.05173005908727646, 0.028110699728131294, -0.015910815447568893, -0.02680470608174801, 0.0014423655811697245, 0.026374684646725655, -0.005677883513271809, 0.0034501305781304836, -0.028190333396196365, 0.012255627661943436, 0.0188094824552536, -0.027648823335766792, -0.011284097097814083, -0.02382640540599823, 0.0017051567556336522, -0.020943665876984596, 0.021947050467133522, 0.03605814278125763, -0.005287678446620703, 0.008345612324774265, -0.011284097097814083, 0.03538922220468521, 0.003073861123993993, -0.012016726657748222, 0.017200881615281105, -0.0007231736090034246, -0.023619357496500015, -0.0366952121257782, 0.0069161877036094666, 0.06259209662675858, 0.02817440591752529, 0.03659965470433235, 0.06701973080635071, 0.054246481508016586, 0.005243879742920399, 0.012948441319167614, -0.05494726076722145, 0.044117074459791183, 0.06549075990915298, -0.0004875076119787991, -0.007724469993263483, -0.0437985397875309, -0.01582321897149086, -0.008409319445490837, -0.015878962352871895, -0.03688633441925049, -0.030977513641119003, 0.009556044824421406, 0.05360941216349602, -0.017997218295931816, -0.007891700603067875, 0.018172413110733032, -0.035325512290000916, -0.010734624229371548, 0.06593671441078186, 0.016898272559046745, -0.0015010954812169075, 0.02291858196258545, 0.01053554005920887, -0.03886124864220619, -0.0020724672358483076, -0.005944656208157539, 0.00601234519854188, 0.004129007924348116, -0.06456701457500458, -0.002667729277163744, -0.016213422641158104, 0.0012671714648604393, 0.06144537031650543, 0.002466654172167182, 0.017455710098147392, -0.046123843640089035, -0.05478799343109131, 0.020322522148489952, 0.0028389417566359043, 0.016452323645353317, -0.038160473108291626, 0.03535736724734306, -0.027282508090138435, 0.04809876158833504, -0.03424249589443207, 0.0011049177264794707, 0.04800320044159889, -0.05055147781968117, -0.0032331286929547787, 0.004240495152771473, 0.02994227409362793, 0.006454312242567539, 0.033509865403175354, 0.062018733471632004, 0.07211628556251526, -0.04908622056245804, -0.032235726714134216, -0.02911408431828022, 0.04335259273648262, 0.00008398867794312537, -0.028413306921720505, 0.03554848954081535, -0.004387817345559597, -0.030021907761693, -0.00654987245798111, 0.04889509826898575, -0.03803306072950363, -0.021023299545049667, -0.024144940078258514, -0.04800320044159889, -0.02269560657441616, 0.05208044499158859, -0.025769468396902084, -0.004989051725715399, -0.006633487995713949, 0.009428631514310837, 0.010033847764134407, -0.01148318126797676, -0.03752340376377106, 0.029783006757497787, -0.010153298266232014, -0.030340444296598434, 0.04813061282038689, 0.0005634084809571505, 0.006486165802925825, -0.013545693829655647, 0.0028608411084860563, -0.03583516925573349, -0.04844914749264717, -0.004535140004009008, -0.016786785796284676, -0.030706757679581642, 0.02666136622428894, -0.026072077453136444, -0.03180570527911186, 0.029894495382905006, 0.032028678804636, 0.006299026310443878, -0.026932120323181152, 0.009723275899887085, 0.010304601863026619, -0.06676489859819412, -0.03440176323056221, -0.044499315321445465, -0.028556648641824722, -0.012653796933591366, -0.0733904242515564, 0.012677686288952827, 0.005602231714874506, 0.03752340376377106, 0.0045032864436507225, 0.0022854874841868877, -0.0254509337246418, 0.005984473507851362, -0.009850690141320229, 0.02103922702372074, -0.020529570057988167, 0.0014383838279172778, -0.02740992233157158, 0.035325512290000916, -0.00007297682896023616, -0.01696198061108589, 0.0005009457818232477, 0.04972328990697861, 0.016627518460154533, -0.03924349322915077, 0.0056420485489070415, -0.007692616432905197, -0.04516823962330818, -0.0049731251783668995, 0.061190541833639145, 0.010033847764134407, -0.004690425470471382, 0.051443375647068024, 0.014620749279856682, 0.019430624321103096, -0.021087005734443665, 0.028986670076847076, 0.021612588316202164, -0.00488154636695981, 0.0036870408803224564, -0.03300020843744278, -0.00026751949917525053, 0.02253633923828602, 0.006299026310443878, -0.0038980701938271523, 0.03882939741015434, 0.031327903270721436, 0.044913411140441895, -0.03542107343673706, -0.0020505681168287992, -0.03771452605724335, -0.017758317291736603, -0.04316147044301033, -0.006952022667974234, 0.0468883290886879, 0.009118059650063515, -0.01922357827425003, -0.0006967949448153377, -0.012430822476744652, -0.004244476556777954, 0.013657181523740292, 0.001222377410158515, 0.006605616305023432, 0.03930719941854477, -0.021501101553440094, 0.046729061752557755, 0.01429425086826086, 0.01815648563206196, -0.050360359251499176, -0.00836153980344534, -0.04924548789858818, -0.01342624332755804, 0.026597658172249794, -0.020147329196333885, 0.020529570057988167, 0.030483784154057503, -0.002948438050225377, -0.012486565858125687, 0.028763696551322937, -0.010017920285463333, 0.03612184897065163, 0.02054549753665924, -0.04086802154779434, -0.03618555888533592, 0.020529570057988167, -0.0001857705065049231, 0.034083228558301926, -0.0005385229596868157, 0.008823415264487267, -0.03357357159256935, -0.035134393721818924, -0.028986670076847076, -0.07683060318231583, -0.01309974491596222, 0.014270360581576824, 0.006959986407309771, 0.018570581451058388, -0.03344615921378136, 0.006963967811316252, 0.003963768016546965, -0.03284094110131264, 0.04596457630395889, 0.0642484799027443, -0.06029864400625229, 0.04376668855547905, 0.005916784517467022, 0.02076847106218338, -0.019350990653038025, -0.04214216023683548, 0.008162455633282661, 0.012263591401278973, -0.028301820158958435, 0.021134786307811737, 0.009333070367574692, -0.0037607019767165184, 0.019191723316907883, 0.00836153980344534, -0.02530759386718273, 0.014334067702293396, -0.04086802154779434, -0.033478010445833206, 0.007167033851146698, 0.00808282196521759, -0.007891700603067875, 0.03806491196155548, 0.012645833194255829, 0.004586901515722275, 0.041409529745578766, 0.018554653972387314, 0.010949634946882725, 0.011634484864771366, -0.0458371639251709, -0.0013438188470900059, 0.009030462242662907, -0.011984873563051224, -0.06574559211730957, -0.018379461020231247, -0.025546494871377945, -0.037969354540109634, 0.0132351228967309, 0.004829784389585257, 0.02435198798775673, -0.02080032415688038, -0.03975314646959305, -0.013028074987232685, -0.021309981122612953, 0.03844715654850006, 0.005180172622203827, 0.0027911614160984755, -0.0325542613863945, 0.029560033231973648, -0.010495723225176334, -0.01815648563206196, 0.0203543771058321, -0.000009168764336209279, -0.009643642231822014, -0.020497716963291168, 0.04051763191819191, -0.022377071902155876, 0.012518418952822685, 0.0089110117405653, 0.03742784261703491, 0.005363330245018005, 0.031025294214487076, -0.025275738909840584, 0.010941672138869762, -0.03081824630498886, 0.02280709519982338, -0.0316305086016655, -0.035134393721818924, -0.008982682600617409, -0.01861836202442646, -0.016285093501210213, 0.006510055623948574, 0.015608207322657108, -0.025705762207508087, -0.0019291265634819865, 0.012494528666138649, -0.005335458554327488, -0.005661956965923309, 0.008887122385203838, 0.023045996204018593, -0.03073861263692379, 0.01148318126797676, 0.06514037400484085, -0.0033625334035605192, 0.02854072116315365, 0.016221387311816216, -0.08377466350793839, 0.013378463685512543, -0.040230948477983475, 0.0007978302310220897, 0.005653993226587772, -0.005510652903467417, 0.02553056739270687, 0.030834171921014786, 0.02197890356183052, -0.032076459378004074, 0.0692494735121727, -0.02900259755551815, -0.062178000807762146, 0.042619962245225906, 0.026629513129591942, 0.01368903461843729, 0.007577147334814072 ]
Accurate ADMET (an abbreviation for "absorption, distribution, metabolism, excretion, and toxicity") predictions can efficiently screen out undesirable drug candidates in the early stage of drug discovery. In recent years, multiple comprehensive ADMET systems that adopt advanced machine learning models have been developed, providing services to estimate multiple endpoints. However, those ADMET systems usually suffer from weak extrapolation ability. First, due to the lack of labelled data for each endpoint, typical machine learning models perform frail for the molecules with unobserved scaffolds. Second, most systems only provide fixed built-in endpoints and cannot be customised to satisfy various research requirements. To this end, we develop a robust and endpoint extensible ADMET system, HelixADMET (H-ADMET). H-ADMET incorporates the concept of self-supervised learning to produce a robust pre-trained model. The model is then fine-tuned with a multi-task and multi-stage framework to transfer knowledge between ADMET endpoints, auxiliary tasks, and self-supervised tasks. Our results demonstrate that H-ADMET achieves an overall improvement of 4%, compared with existing ADMET systems on comparable endpoints. Additionally, the pre-trained model provided by H-ADMET can be fine-tuned to generate new and customised ADMET endpoints, meeting various demands of drug research and development requirements.
[ -0.040516406297683716, 0.014695581048727036, -0.026905734091997147, -0.03329683467745781, -0.026767656207084656, -0.052549030631780624, -0.06024201959371567, 0.006450274959206581, -0.06055762991309166, 0.0005714263534173369, 0.028168173506855965, -0.02801036834716797, 0.008817348629236221, -0.043948665261268616, -0.004889485891908407, 0.03864247351884842, -0.015218310058116913, -0.02386799082159996, -0.02150091715157032, -0.025663021951913834, -0.0028330909553915262, -0.05057647079229355, 0.0027788456063717604, 0.026530947536230087, 0.04671024903655052, 0.027241069823503494, 0.002825693925842643, -0.009719795547425747, -0.04513220116496086, -0.006682050880044699, -0.004901814740151167, -0.0017210596706718206, 0.052272871136665344, 0.021422015503048897, -0.019025353714823723, 0.007554909214377403, 0.01699361391365528, -0.0008919675019569695, 0.016638554632663727, -0.0007199848187156022, -0.004919074475765228, 0.018078522756695747, -0.028483783826231956, 0.028444333001971245, -0.02057381346821785, -0.060675982385873795, -0.018887273967266083, -0.044145919382572174, 0.010947714559733868, 0.017348675057291985, -0.055981285870075226, -0.010849086567759514, 0.004359360318630934, -0.02331567369401455, -0.02159954607486725, 0.08655598759651184, 0.052036166191101074, 0.04268622398376465, 0.01769387349486351, -0.000805667950771749, -0.012525763362646103, -0.037873174995183945, 0.04197610169649124, 0.01081949844956398, -0.010474300011992455, -0.07464171946048737, -0.0021377631928771734, -0.013946007937192917, -0.0000787098178989254, 0.06237238645553589, -0.03491433337330818, 0.011016754433512688, 0.003422393696382642, -0.003230069065466523, -0.061977874487638474, -0.0390961617231369, 0.010346083901822567, 0.017023203894495964, 0.005828918423503637, 0.02595890499651432, 0.018265916034579277, 0.04450098052620888, 0.03390832617878914, 0.039451222866773605, 0.045211102813482285, 0.0030130872037261724, 0.008462287485599518, -0.06844787299633026, -0.007840930484235287, -0.03590061515569687, -0.022901436313986778, 0.05479774996638298, 0.007579566445201635, -0.002616109326481819, -0.03233027830719948, 0.024814819917082787, -0.014458873309195042, 0.03915534168481827, -0.05053701996803284, -0.0301801860332489, 0.019163431599736214, -0.022763356566429138, 0.03783372417092323, -0.007199848536401987, -0.028819119557738304, -0.05243067815899849, -0.003930328413844109, 0.009054056368768215, -0.011894543655216694, 0.16474831104278564, 0.004615793004631996, -0.03467762470245361, -0.005163178779184818, -0.006016311701387167, -0.014833659864962101, -0.04998470097780228, -0.06335866451263428, -0.03834658861160278, 0.0431990921497345, -0.046749699860811234, 0.04022052139043808, 0.031127015128731728, -0.029982930049300194, -0.03741948679089546, -0.030160460621118546, 0.01625390350818634, 0.00040067650843411684, -0.025801099836826324, 0.010405260138213634, -0.012180565856397152, -0.052549030631780624, 0.010395397432148457, 0.017190871760249138, -0.01553391944617033, 0.011095657013356686, 0.028306253254413605, 0.01969602331519127, 0.050694823265075684, -0.005459063220769167, 0.0207513440400362, -0.03901726007461548, -0.022487197071313858, -0.07211683690547943, -0.03227110207080841, 0.03706442564725876, 0.01237782184034586, -0.006179048214107752, 0.0336124412715435, -0.01318657211959362, 0.01667800545692444, -0.06406878679990768, 0.006381235551089048, 0.00398210808634758, -0.01297945249825716, 0.018177151679992676, -0.0038662198930978775, 0.007328065112233162, 0.021816527470946312, -0.014133401215076447, -0.0074858698062598705, 0.06450275331735611, -0.028621863573789597, -0.007540115155279636, 0.06781665235757828, 0.06683037430047989, 0.02516988106071949, -0.022092685103416443, -0.03175823390483856, -0.08576696366071701, 0.052036166191101074, -0.010987166315317154, -0.03000265546143055, 0.00889625120908022, -0.028779668733477592, -0.0041892267763614655, 0.029331985861063004, 0.015238035470247269, 0.028582412749528885, -0.02307896688580513, -0.040476955473423004, -0.052312321960926056, 0.023256497457623482, 0.0565730556845665, -0.013472593389451504, 0.04726256802678108, -0.00793955847620964, 0.07736384868621826, 0.012584940530359745, 0.05850616469979286, 0.0221124105155468, 0.005037428345531225, -0.03102838806807995, 0.04087146744132042, 0.011914269998669624, -0.015573371201753616, -0.02122475951910019, -0.037636466324329376, -0.011302775703370571, 0.0003633827727753669, -0.04529000446200371, 0.006864512804895639, -0.04959018900990486, -0.008462287485599518, 0.03728140518069267, 0.02558411844074726, 0.002079819329082966, 0.026491496711969376, -0.0020268065854907036, 0.035545554012060165, -0.01949876733124256, 0.04221281036734581, -0.029746223241090775, -0.03956957906484604, -0.032251376658678055, 0.0387411005795002, -0.015326800756156445, -0.017111968249082565, -0.04002326726913452, -0.02317759394645691, -0.02205323427915573, -0.005459063220769167, -0.011825504712760448, 0.08071720600128174, -0.02599835768342018, 0.060715433210134506, 0.007199848536401987, 0.0003541363694239408, 0.016914712265133858, 0.013837517239153385, -0.019725611433386803, 0.03702497482299805, 0.010119238868355751, 0.011430991813540459, -0.005089208018034697, -0.03919479250907898, -0.005143453367054462, 0.013364101760089397, -0.021520642563700676, -0.000012598193279700354, 0.0179207194596529, 0.019577670842409134, 0.01648074947297573, 0.008299550972878933, -0.07231409102678299, 0.044974394142627716, 0.029509516432881355, 0.014557501301169395, 0.12734855711460114, 0.052036166191101074, 0.02921363152563572, 0.055152811110019684, -0.02544604055583477, -0.006376304198056459, 0.04911677539348602, 0.005513308569788933, -0.03728140518069267, 0.04197610169649124, -0.031324271112680435, -0.002225295640528202, -0.06209622696042061, 0.0344606451690197, -0.0431990921497345, 0.03864247351884842, 0.006198773626238108, -0.025564393028616905, -0.03359271585941315, 0.09996940195560455, -0.008605298586189747, 0.005611936561763287, 0.05984750762581825, 0.018088385462760925, -0.0037084149662405252, -0.0003772523195948452, 0.06477890908718109, 0.004716887138783932, -0.05586293339729309, 0.07752165198326111, -0.014902699738740921, 0.04091091826558113, 0.005158247426152229, -0.052588481456041336, -0.06600189954042435, 0.032527536153793335, 0.03377024829387665, -0.029982930049300194, -0.0171415563672781, -0.02637314423918724, -0.032251376658678055, -0.014784346334636211, -0.029272807762026787, -0.028030095621943474, -0.0289769247174263, -0.003848960157483816, -0.0024694001767784357, 0.020031359046697617, 0.008462287485599518, -0.02945033833384514, 0.015455016866326332, -0.0005772823933511972, -0.07554909586906433, -0.04091091826558113, -0.06576518714427948, 0.02011026069521904, 0.019942594692111015, 0.043120186775922775, 0.02945033833384514, -0.004608395975083113, 0.11101574450731277, -0.00882227998226881, -0.04832775145769119, 0.05460049584507942, 0.030160460621118546, 0.023197319358587265, -0.03953012824058533, 0.014291206374764442, 0.005266738589853048, 0.007170259952545166, -0.06324031203985214, -0.027102991938591003, -0.0421733595430851, -0.003602389944717288, -0.02252664975821972, -0.08781842142343521, -0.01736840233206749, -0.0023448821157217026, -0.004827843513339758, -0.024084972217679024, 0.003400202374905348, -0.04639463871717453, 0.037222228944301605, -0.052312321960926056, -0.029272807762026787, -0.028819119557738304, 0.020238477736711502, -0.0025125497486442327, -0.034756530076265335, -0.026116710156202316, 0.015524056740105152, -0.0029415818862617016, 0.015849528834223747, -0.010898401029407978, -0.0005837548524141312, -0.03367162123322487, -0.00801352970302105, 0.03181741386651993, -0.030673326924443245, -0.019252197816967964, 0.03913561627268791, 0.005626731086522341, -0.00006661246879957616, 0.0010349781950935721, -0.013452867045998573, -0.025248782709240913, 0.031008662655949593, 0.001455996767617762, 0.0018665360985323787, -0.006825061980634928, -0.0843467190861702, -0.030022380873560905, 0.021717898547649384, 0.03834658861160278, -0.053140800446271896, 0.018936587497591972, 0.03663046285510063, -0.0510893352329731, 0.04280457645654678, 0.004329771734774113, 0.028503509238362312, 0.01574103906750679, 0.024637289345264435, 0.01969602331519127, -0.04540836066007614, 0.04974799230694771, 0.05562622472643852, -0.03075222857296467, -0.0234932042658329, -0.006164253689348698, -0.008501739241182804, -0.02499235048890114, 0.05239122733473778, 0.013009041547775269, 0.02568274736404419, -0.0008013530168682337, 0.035683631896972656, 0.005271669942885637, 0.007845861837267876, 0.0320541188120842, -0.0313834473490715, -0.028306253254413605, 0.014784346334636211, 0.032350003719329834, -0.0018098249565809965, 0.042883481830358505, -0.014774483628571033, -0.002491591265425086, -0.022901436313986778, 0.0076732630841434, 0.047302018851041794, 0.09144793450832367, -0.011697287671267986, -0.008674337528645992, 0.035170767456293106, 0.013226022943854332, 0.027004363015294075, 0.011430991813540459, -0.014656130224466324, 0.042055003345012665, -0.08411000669002533, 0.03832686319947243, 0.023808814585208893, -0.011786052957177162, -0.01219042856246233, -0.000010055438906420022, -0.01625390350818634, 0.02187570370733738, 0.023789087310433388, -0.019094392657279968, -0.021579818800091743, -0.022408295422792435, -0.015208447352051735, -0.017723461613059044, 0.01337396539747715, 0.055981285870075226, -0.0008192293462343514, 0.005858507007360458, 0.04828829690814018, -0.01834481954574585, -0.041344884783029556, -0.03621622547507286, -0.026905734091997147, 0.00820092298090458, 0.005301258061081171, 0.02526850998401642, -0.034243661910295486, -0.02061326429247856, -0.03349408879876137, 0.019094392657279968, -0.0257221981883049, 0.012269331142306328, 0.02219131402671337, -0.015218310058116913, 0.011223873123526573, -0.03741948679089546, -0.0003553692367859185, -0.03367162123322487, -0.007589429151266813, -0.01774318888783455, 0.003954985179007053, -0.03136372193694115, -0.05341695621609688, -0.04169994220137596, 0.03377024829387665, -0.012890687212347984, -0.009345008991658688, 0.0802437886595726, 0.009645824320614338, 0.009118163958191872, 0.00018261601508129388, 0.06256964057683945, -0.06245128810405731, -0.00156695325858891, 0.024459758773446083, 0.027970917522907257, -0.04828829690814018, 0.022467471659183502, 0.03655155748128891, -0.08071720600128174, 0.002257349668070674, 0.04035860300064087, 0.0093844598159194, 0.03347436338663101, -0.011332363821566105, -0.00028432620456442237, -0.006775747984647751, 0.04033887758851051, -0.028681039810180664, 0.03079168125987053, -0.022447746247053146, 0.038800280541181564, 0.05538951978087425, 0.018078522756695747, -0.0016717456746846437, 0.017536068335175514, -0.00002904904613387771, -0.008812417276203632, 0.013156983070075512, 0.03960902988910675, 0.028503509238362312, 0.029785674065351486, 0.007643674500286579, -0.0322316512465477, -0.032527536153793335, -0.018187014386057854, -0.03732085973024368, 0.0003279382945038378, -0.012723020277917385, -0.019705886021256447, 0.011845230124890804, 0.05235177278518677, -0.000397286145016551, -0.005676045082509518, -0.052549030631780624, 0.0011163463350385427, 0.018916862085461617, -0.004837706219404936, 0.037636466324329376, 0.003257191739976406, -0.035920340567827225, 0.03834658861160278, -0.020869698375463486, 0.01342327892780304, -0.017111968249082565, -0.023848265409469604, -0.0016125687398016453, 0.011371815577149391, 0.048406653106212616, -0.015336663462221622, 0.051523298025131226, -0.024716192856431007, 0.019015489146113396, 0.010789909400045872, -0.00011134183296235278, -0.019449453800916672, -0.005533033981919289, -0.04410646855831146, -0.011717014014720917, 0.028503509238362312, -0.013650123961269855, 0.03116646781563759, -0.06576518714427948, -0.002135297516360879, -0.022467471659183502, -0.0019651642069220543, 0.008398178964853287, -0.04248896986246109, 0.021836252883076668, -0.03459872305393219, -0.011430991813540459, -0.012890687212347984, -0.0006478630821220577, -0.023710185661911964, 0.06529177725315094, 0.03065360151231289, -0.019242335110902786, 0.018325094133615494, 0.04536890611052513, 0.047617629170417786, -0.03728140518069267, -0.012328507378697395, 0.017624834552407265, 0.005873301066458225, -0.0006312195910140872, 0.024952899664640427, 0.0027443256694823503, 0.0017481823451817036, -0.05400872603058815, -0.030239364132285118, -0.05609964206814766, -0.0010565530974417925, 0.029844850301742554, -0.009571853093802929, 0.0038834798615425825, -0.0074908011592924595, -0.03272479027509689, -0.010858949273824692, -0.019094392657279968, 0.03949067369103432, -0.019429728388786316, 0.007480938453227282, 0.03300094977021217, 0.012989315204322338, -0.02047518454492092, -0.013955870643258095, 0.0017259910237044096, -0.02475564368069172, 0.01297945249825716, 0.023572105914354324, -0.03562445566058159, -0.005799329839646816, -0.02935171127319336, 0.0637926310300827, -0.05763823911547661, -0.0033632167614996433, -0.03702497482299805, -0.005533033981919289, -0.027379149571061134, -0.03501296043395996, -0.08868635445833206, -0.06426604092121124, -0.007199848536401987, -0.00008005824929568917, 0.01867029257118702, 0.004879623185843229, -0.0028922678902745247, -0.021303661167621613, -0.0009850477799773216, -0.00815160945057869, -0.0015398305840790272, 0.031186193227767944, -0.011391540989279747, 0.008625023998320103, 0.024814819917082787, 0.026767656207084656, 0.028779668733477592, 0.001489283749833703, 0.02043573372066021, 0.014103813096880913, 0.016549788415431976, 0.005547828506678343, -0.001472023781388998, 0.0212642103433609, 0.021106405183672905, 0.021343111991882324, 0.003022950142621994, 0.027438325807452202, -0.011667699553072453, 0.06032092124223709, 0.002899664919823408, 0.003885945538058877, 0.02019902691245079, -0.021619271486997604, -0.004472782369703054, 0.029687047004699707, 0.0029243219178169966, 0.010405260138213634, 0.005557691212743521, -0.00028201460372656584, -0.023000063374638557, -0.015721313655376434, -0.029470063745975494, -0.025663021951913834, -0.008057912811636925, -0.048367202281951904, -0.045763421803712845, 0.0716828778386116, -0.020909149199724197, -0.004790857899934053, 0.008644749410450459, 0.030337991192936897, -0.002916924888268113, -0.035959791392087936, 0.041542138904333115, 0.006090282928198576, 0.0324091799557209, -0.011144970543682575, 0.036334577947854996, 0.007900107651948929, 0.007988872937858105, 0.06568628549575806, 0.024735918268561363, -0.02232939377427101, 0.007441487163305283, 0.01592843234539032, 0.03586116433143616, -0.011243598535656929, -0.0630825087428093, 0.004623190499842167, 0.015307075344026089, 0.045526713132858276, 0.005976860411465168, -0.002993361558765173, -0.027655309066176414, 0.006435480900108814, 0.012762471102178097, 0.023808814585208893, 0.0068497187457978725, 0.002825693925842643, 0.021244484931230545, 0.00010879908222705126, 0.009803629480302334, 0.010582790710031986, -0.029272807762026787, -0.024814819917082787, 0.06884238868951797, 0.03779427334666252, 0.012693431228399277, 0.03743921220302582, 0.022368844598531723, -0.002314060926437378, -0.030476070940494537, -0.014695581048727036, -0.0504186637699604, -0.023572105914354324, 0.03315875306725502, -0.011786052957177162, -0.000628445646725595, -0.03193576633930206, 0.026826832443475723, 0.0035703356843441725, 0.006420686841011047, 0.017940444871783257, 0.0034322564024478197, 0.032488081604242325, 0.002073654904961586, -0.031146742403507233, 0.021678447723388672, -0.021007776260375977, -0.06264854222536087, 0.016382120549678802, -0.015671998262405396, 0.02791174128651619, 0.01681608520448208, -0.03349408879876137, -0.03014073520898819, -0.013916418887674809, -0.01304849237203598, 0.0044974396005272865, -0.04489549249410629, 0.005863438360393047, -0.02716216817498207, 0.0034988303668797016, 0.027458051219582558, -0.03560473024845123, 0.005370297934859991, 0.06596244871616364, 0.0012168237008154392, 0.037912625819444656, -0.02256610058248043, -0.005843712482601404, 0.013462730683386326, -0.0035826642997562885, 0.018611114472150803, 0.016638554632663727, -0.04568451642990112, 0.004043750464916229, 0.023374849930405617, 0.02341430075466633, -0.013798065483570099, -0.013965733349323273, -0.003474173368886113, 0.03803097829222679, -0.01853221282362938, -0.013078080490231514, 0.010730733163654804, -0.018167288973927498, -0.041265979409217834, 0.0062530189752578735, 0.02455838769674301, -0.01611582562327385, -0.0221124105155468, 0.013620534911751747, -0.009601442143321037, 0.03000265546143055, -0.02887829579412937, 0.014882974326610565, 0.034894607961177826, -0.007786685600876808, -0.001349971629679203, -0.003230069065466523, 0.007909970358014107, 0.020554088056087494, -0.029193906113505363, 0.030988937243819237, -0.056217994540929794, -0.025524942204356194, 0.026669027283787727, 0.00042348424904048443, -0.020041221752762794, -0.021520642563700676, 0.006958209443837404, -0.06418713927268982, 0.03231055289506912, -0.008625023998320103, 0.0032054120674729347, 0.05223342031240463, 0.02767503447830677, -0.06406878679990768, -0.011539483442902565, 0.006090282928198576, 0.0020107796881347895, 0.023572105914354324, 0.015810078009963036, 0.04296238347887993, -0.041344884783029556, 0.04272567480802536, -0.0016717456746846437, 0.01890699937939644, 0.005636593792587519, -0.039589304476976395, 0.05602073669433594, -0.02678738161921501, -0.019676297903060913, 0.005498514510691166, -0.03477625548839569, -0.008925839327275753, -0.005947271827608347, 0.047341469675302505, -0.02516988106071949, -0.019814377650618553, -0.005720427725464106, 0.0008266264339908957, -0.01843358390033245, 0.03887918218970299, 0.039826009422540665, 0.007934627123177052, -0.0033262313809245825, 0.03158070519566536, -0.012387684546411037, -0.032862868160009384, -0.025051526725292206, 0.07472062110900879, 0.028345704078674316, 0.01918315701186657, 0.06679092347621918, -0.03872137516736984, -0.04315963760018349, -0.006953278090804815, -0.004628121852874756, 0.032350003719329834, -0.0012180565390735865, 0.013985458761453629, 0.020080672577023506, 0.030121009796857834, 0.046749699860811234, 0.04611848294734955, -0.021895429119467735, -0.03637402877211571, -0.010084719397127628, -0.02911500260233879, 0.02372991107404232, -0.012160839512944221, 0.02870076522231102, -0.010523614473640919, 0.02637314423918724, -0.028030095621943474, -0.03246835619211197, 0.05219396948814392, 0.010277044028043747, 0.01927192322909832, -0.021422015503048897, 0.05329860374331474, -0.0212642103433609, 0.021954605355858803, -0.016076374799013138, -0.0365121066570282, 0.03089030832052231, -0.010217866860330105, 0.007145603187382221, -0.008477081544697285, 0.03236972913146019, -0.04828829690814018, 0.0002673745038919151, -0.05408762767910957, -0.03177795931696892, -0.024637289345264435, 0.02280280739068985, 0.01931137405335903, 0.0003032812965102494, -0.007027249317616224, 0.059334639459848404, -0.012969589792191982, -0.04998470097780228, 0.007628880441188812, 0.017753051593899727, -0.005419611930847168, 0.02907555177807808, 0.05720427632331848, 0.007974078878760338, 0.023098692297935486, -0.01390655618160963, 0.009280900470912457, 0.03678826615214348, -0.016451161354780197, -0.009833217598497868, 0.007914901711046696, -0.0006275210180319846, 0.015583233907818794, -0.008062844164669514, 0.010296769440174103, -0.04848555475473404, -0.0015965417260304093, -0.0011292912531644106, -0.013837517239153385, -0.03031826578080654, 0.034342288970947266, -0.008876525796949863, -0.024952899664640427, 0.012387684546411037, -0.0421733595430851, -0.0284640584141016, 0.025485491380095482, -0.001410381286405027, 0.013226022943854332, -0.0013857242884114385, 0.04008244350552559, -0.04430372640490532, -0.01625390350818634, 0.0005301258061081171, -0.02280280739068985, -0.059650249779224396, -0.01699361391365528, 0.003535815980285406, 0.019567808136343956, -0.011480306275188923, 0.04173939675092697, -0.0016162673709914088, 0.016983751207590103, -0.01030663214623928, -0.05089208111166954, 0.028385154902935028, 0.011628248728811741, -0.03659101203083992, -0.025465765967965126, -0.01374875195324421, -0.0010657995007932186, -0.05400872603058815, 0.03570335730910301, -0.025643296539783478, 0.037636466324329376, 0.003027881495654583, 0.008501739241182804, -0.009601442143321037, 0.024223051965236664, -0.013255611062049866, 0.02558411844074726, 0.012644117698073387, 0.038760825991630554, -0.018216602504253387, 0.030219636857509613, -0.06588354706764221, -0.017575521022081375, 0.009211860597133636, -0.05033976212143898, 0.035644181072711945, -0.015632547438144684, 0.018502624705433846, -0.01857166364789009, 0.01741771586239338, -0.000022480262487079017, -0.041305430233478546, -0.0322316512465477, 0.024400582537055016, 0.03655155748128891, -0.018098250031471252, -0.002236391184851527, -0.07767946273088455, -0.00800859834998846, -0.006400960963219404, -0.03751811385154724, 0.0070075239054858685, -0.015524056740105152, 0.040516406297683716, 0.002625972032546997, 0.0131175322458148, 0.00028910351102240384, -0.0620567761361599, -0.03363217040896416, 0.056809764355421066, -0.026432320475578308, -0.016608964651823044, -0.014182714745402336, -0.008516533300280571, 0.013472593389451504, -0.036807991564273834, -0.01621445268392563, 0.016283493489027023, 0.0038736171554774046, 0.03102838806807995, -0.005858507007360458, 0.002571726683527231, -0.00018831795023288578, 0.03203439339995384, 0.0007828602101653814, -0.009946639649569988, 0.006800404749810696, 0.01212138868868351, 0.003718277905136347, -0.02698463760316372, -0.044145919382572174, -0.01797003298997879, 0.020554088056087494, 0.007663400378078222, 0.008501739241182804, 0.07093330472707748, -0.02842460758984089, -0.011628248728811741, 0.0016902383649721742, -0.014399697072803974, -0.004864829126745462, -0.0165399257093668, 0.02311841771006584, -0.016135551035404205, 0.03256698697805405, -0.00919706653803587, -0.010434849187731743, -0.06900019198656082, 0.008117089048027992, -0.02842460758984089, -0.07333982735872269, 0.034243661910295486, 0.024676740169525146, -0.021994058042764664, 0.01616513915359974, -0.03274451568722725, -0.06339811533689499, -0.0006799171678721905, 0.023611558601260185, -0.014823797158896923, 0.007870519533753395, 0.015583233907818794, -0.01797003298997879, -0.027418600395321846, -0.002944047562777996, 0.04351469874382019, 0.021895429119467735, 0.029706772416830063, 0.042331162840127945, 0.05661250650882721, -0.03609786927700043, -0.017437441274523735, 0.04450098052620888, -0.014646266587078571, -0.033454637974500656, 0.03412530943751335, -0.00877789780497551, -0.02043573372066021, -0.014449010603129864, -0.04118707776069641, -0.03315875306725502, -0.02879939414560795, 0.02428222820162773, -0.03747866302728653, -0.012782196514308453, -0.012723020277917385 ]
Supervised learning techniques typically assume training data originates from the target population. Yet, in reality, dataset shift frequently arises, which, if not adequately taken into account, may decrease the performance of their predictors. In this work, we propose a novel and flexible framework called DetectShift that quantifies and tests for multiple dataset shifts, encompassing shifts in the distributions of $(X, Y)$, $X$, $Y$, $X|Y$, and $Y|X$. DetectShift equips practitioners with insights into data shifts, facilitating the adaptation or retraining of predictors using both source and target data. This proves extremely valuable when labeled samples in the target domain are limited. The framework utilizes test statistics with the same nature to quantify the magnitude of the various shifts, making results more interpretable. It is versatile, suitable for regression and classification tasks, and accommodates diverse data forms - tabular, text, or image. Experimental results demonstrate the effectiveness of DetectShift in detecting dataset shifts even in higher dimensions.
[ -0.04465820640325546, 0.009929019957780838, -0.02023407071828842, 0.03239241987466812, 0.0183718204498291, -0.016357365995645523, -0.0048481193371117115, 0.023743698373436928, -0.008375652134418488, 0.01448616199195385, 0.007422143593430519, -0.041614141315221786, 0.02651916816830635, -0.04286758229136467, -0.04612651839852333, -0.02240072749555111, -0.012937271036207676, 0.0005136857507750392, 0.0021722528617829084, -0.03588414192199707, 0.00041855877498164773, -0.062492839992046356, -0.03753151744604111, 0.052322085946798325, -0.01753917895257473, 0.06141846254467964, 0.02809491753578186, -0.04258108139038086, -0.032320793718099594, 0.037603139877319336, 0.021380072459578514, 0.030100418254733086, -0.026250572875142097, -0.05937714874744415, -0.03774639219045639, -0.0019226843724027276, -0.01491591241210699, 0.0532890222966671, -0.034809764474630356, 0.05368296056985855, -0.02483597956597805, 0.01578436605632305, -0.01966107077896595, -0.017709288746118546, -0.02286629192531109, -0.05407689884305, -0.07721178233623505, 0.03670782968401909, -0.015139740891754627, -0.002361387712880969, -0.014190709218382835, -0.043010830879211426, 0.003048540325835347, -0.007999620400369167, -0.049886833876371384, 0.06263609230518341, 0.05217883363366127, 0.0055777993984520435, 0.06883165240287781, -0.0004815104475710541, -0.032195452600717545, -0.0035342476330697536, 0.02832769975066185, -0.00651340140029788, 0.009373925626277924, -0.07098040729761124, 0.0015332233160734177, -0.03511417284607887, 0.0021017470862716436, 0.021917259320616722, -0.03572298586368561, 0.017915211617946625, -0.008075722493231297, 0.03577670454978943, 0.009338113479316235, -0.01829124242067337, 0.03756732866168022, -0.04247364401817322, -0.026340104639530182, -0.049886833876371384, 0.019678976386785507, 0.03463070094585419, -0.0015253893798217177, 0.027127981185913086, 0.04404939338564873, 0.012767162173986435, -0.004134107381105423, -0.0602724626660347, 0.029634855687618256, -0.03147920221090317, -0.047559019178152084, -0.018282288685441017, 0.01660805381834507, -0.003963997587561607, -0.08186741173267365, 0.038355205208063126, 0.023421384394168854, -0.008236878551542759, -0.06929721683263779, 0.001564559293910861, -0.015954475849866867, -0.018873196095228195, -0.03497092053294182, 0.014898006804287434, -0.04043233022093773, -0.045804206281900406, -0.0693330317735672, 0.044121019542217255, -0.02059219591319561, 0.1508423089981079, 0.04530283063650131, 0.018049508333206177, 0.013375974260270596, 0.0569060854613781, -0.030512262135744095, 0.027181699872016907, -0.06030827760696411, -0.11051741987466812, 0.01855088211596012, -0.07592253386974335, 0.036546673625707626, 0.0641760304570198, 0.018747851252555847, 0.041148580610752106, -0.02657288685441017, -0.000284121953882277, 0.0005478195962496102, 0.0040177167393267155, 0.0015309849986806512, 0.041435081511735916, 0.024853885173797607, 0.024119729176163673, 0.011361520737409592, 0.002641173079609871, 0.04218714311718941, 0.02315279096364975, 0.06510715186595917, 0.04687858372926712, -0.05078214779496193, 0.0019909520633518696, -0.03878495469689369, -0.03054807521402836, 0.01924922689795494, 0.07491978257894516, -0.045052144676446915, -0.007256511133164167, -0.004525806754827499, 0.041435081511735916, -0.006508924532681704, 0.01314319297671318, -0.03018995001912117, 0.05375458672642708, -0.009454503655433655, -0.0012814165093004704, 0.058374401181936264, 0.07309334725141525, 0.0017380261560902, 0.023976478725671768, -0.014960678294301033, -0.06281515210866928, 0.06682615727186203, -0.03094201348721981, 0.054828960448503494, 0.041793204843997955, 0.05031658336520195, -0.007493768818676472, -0.012015098705887794, -0.07921728491783142, -0.04240201786160469, 0.045410268008708954, 0.03296542167663574, -0.013823631219565868, -0.03018995001912117, 0.044407520443201065, -0.03257148340344429, 0.04182901605963707, 0.0025068761315196753, 0.016464803367853165, -0.005121189635246992, -0.011083973571658134, -0.08358640968799591, -0.0006205637473613024, -0.01308947429060936, 0.02890069968998432, 0.07413190603256226, -0.004646673798561096, 0.08831366151571274, 0.025462698191404343, 0.04222295433282852, -0.027127981185913086, 0.04308245703577995, 0.0019506629323586822, 0.040289077907800674, -0.0050809006206691265, -0.02925882488489151, 0.007099831011146307, -0.04544608294963837, 0.01908807083964348, -0.014253380708396435, -0.019911758601665497, -0.005327111575752497, -0.08000516146421432, -0.01632155478000641, -0.027432385832071304, -0.01829124242067337, -0.0004683605511672795, 0.03328773379325867, -0.027002636343240738, 0.01948200911283493, -0.08236878365278244, 0.005197291262447834, 0.0018958250293508172, -0.02281257137656212, 0.009678332135081291, -0.04985102266073227, -0.03914307802915573, 0.02152332104742527, 0.00992006715387106, 0.023349760100245476, 0.018130086362361908, -0.00261879013851285, -0.017395928502082825, 0.0218635406345129, -0.013760958798229694, -0.07248453050851822, 0.022543977946043015, 0.02188144624233246, 0.004713822156190872, -0.00020871982269454747, 0.001038562972098589, -0.01096758246421814, -0.03606320172548294, -0.013698287308216095, -0.006370150949805975, 0.003988618962466717, -0.00738633144646883, 0.008962081745266914, 0.04612651839852333, -0.03135385736823082, -0.0569060854613781, 0.020090820267796516, -0.012015098705887794, -0.029097668826580048, -0.05916227400302887, 0.04902733489871025, 0.04211551696062088, 0.020448945462703705, 0.0507105216383934, 0.07226965576410294, 0.02488969825208187, -0.03817614167928696, -0.04240201786160469, 0.002037955913692713, -0.0015108404913917184, -0.04960033297538757, 0.014880100265145302, -0.021129384636878967, -0.005094330292195082, 0.037209201604127884, -0.04780970886349678, 0.025874542072415352, 0.005926971323788166, -0.043548017740249634, 0.04089789092540741, 0.010349816642701626, 0.029939262196421623, 0.05078214779496193, 0.0029343878850340843, 0.0019148504361510277, -0.020753351971507072, -0.0010738158598542213, -0.007072971668094397, -0.02007291465997696, -0.0033171342220157385, 0.01704675704240799, -0.04032489284873009, 0.054828960448503494, -0.010305051691830158, 0.011289895512163639, 0.038534265011548996, -0.03008251264691353, -0.006195565219968557, 0.03745989128947258, -0.021308446303009987, 0.02589244768023491, -0.01271344255656004, 0.007923519238829613, -0.002979153534397483, -0.020395226776599884, -0.04344058036804199, 0.05239370837807655, -0.07749827951192856, -0.043368954211473465, 0.015864944085478783, 0.01448616199195385, -0.044873081147670746, -0.05966364964842796, 0.01445930264890194, 0.005604658741503954, -0.017172101885080338, -0.06288677453994751, -0.025444792583584785, 0.035329047590494156, 0.07649553567171097, 0.014960678294301033, -0.05554521083831787, 0.07792803645133972, 0.06714846938848495, -0.025158291682600975, -0.05060308426618576, 0.023761603981256485, -0.019643165171146393, -0.010358770377933979, -0.008787496015429497, -0.022060509771108627, 0.04250945523381233, -0.009082948789000511, -0.0331086702644825, 0.023170696571469307, -0.005564369726926088, -0.025910355150699615, -0.005130142904818058, -0.09970204532146454, -0.016187256202101707, 0.05730002373456955, -0.060630589723587036, 0.007516151759773493, 0.02809491753578186, -0.07065809518098831, 0.032320793718099594, -0.06729171425104141, -0.03464860841631889, -0.005828486755490303, 0.006101557519286871, 0.002641173079609871, 0.040289077907800674, -0.021666571497917175, 0.02315279096364975, -0.009293347597122192, 0.060809649527072906, -0.02000129036605358, -0.0014940534019842744, -0.033413078635931015, -0.020520571619272232, -0.021791916340589523, 0.007560917176306248, -0.014092224650084972, -0.040217455476522446, -0.057693962007761, 0.06206309050321579, 0.0008650960517115891, -0.05439921095967293, -0.05128352344036102, 0.025265729054808617, 0.032374512404203415, -0.027880042791366577, -0.03738826513290405, -0.05160583555698395, 0.017995789647102356, -0.019750602543354034, -0.025981979444622993, -0.054649896919727325, -0.07577928155660629, -0.013313302770256996, -0.060344088822603226, -0.005864299368113279, -0.01666177250444889, -0.02739657461643219, -0.025158291682600975, 0.01393106859177351, -0.013537131249904633, -0.0019943094812333584, 0.022597696632146835, 0.024997135624289513, -0.010815379209816456, -0.013707240112125874, -0.008680058643221855, 0.023546729236841202, 0.036958515644073486, 0.029061855748295784, -0.015399381518363953, 0.04619814455509186, -0.029992980882525444, -0.029419980943202972, -0.008603956550359726, 0.0024218212347477674, 0.0170736163854599, 0.0173332579433918, -0.010681082494556904, 0.02279466576874256, -0.008608433417975903, -0.010242379270493984, -0.03606320172548294, -0.03407560661435127, 0.03375329449772835, 0.0007017014431767166, 0.0015690358122810721, 0.011970332823693752, 0.04931383207440376, -0.040754642337560654, 0.0181121788918972, -0.01125408336520195, -0.03942957893013954, -0.004588478710502386, 0.012910411693155766, 0.014566740952432156, 0.010296097956597805, 0.00913219153881073, -0.0061866119503974915, 0.026375917717814445, -0.019464101642370224, 0.024979230016469955, 0.03753151744604111, 0.030619701370596886, 0.025140386074781418, 0.03094201348721981, -0.044586580246686935, 0.03738826513290405, -0.006562643218785524, -0.010045410133898258, 0.019696883857250214, -0.055760085582733154, 0.03792545199394226, 0.021720290184020996, -0.03735245391726494, 0.034469544887542725, 0.061311025172472, 0.007135643623769283, 0.020968228578567505, -0.049886833876371384, 0.023582540452480316, -0.0004666818422265351, -0.009038183838129044, -0.0294916070997715, -0.003532009432092309, 0.016106678172945976, 0.024531573057174683, -0.05980690196156502, -0.011540583334863186, -0.030172044411301613, -0.034756045788526535, -0.023403478786349297, 0.029509512707591057, -0.02628638595342636, -0.01855088211596012, -0.04003839194774628, 0.0057210493832826614, 0.02395857311785221, -0.028721638023853302, -0.02907976321876049, -0.06679034233093262, 0.07187572121620178, -0.05146258324384689, -0.02286629192531109, 0.03745989128947258, -0.012570193037390709, -0.054542459547519684, -0.03692270442843437, 0.040683016180992126, -0.007628065533936024, 0.020860789343714714, 0.05393364652991295, 0.042079705744981766, -0.04333314299583435, 0.03151501342654228, 0.03857007995247841, -0.07255615293979645, -0.03629598394036293, -0.018336007371544838, 0.007252034265547991, 0.045410268008708954, -0.039357952773571014, -0.006280619651079178, -0.0028985755052417517, -0.007865323685109615, -0.004420607350766659, 0.015873897820711136, -0.06671871244907379, 0.0367436408996582, -0.027611449360847473, 0.0726994052529335, -0.012525427155196667, 0.007986190728843212, -0.020681727677583694, 0.005094330292195082, 0.00697896396741271, 0.056154023855924606, 0.0040512909181416035, 0.008236878551542759, 0.012346364557743073, -0.00036344106774777174, 0.0038476071786135435, -0.0029612474609166384, 0.015309850685298443, 0.006401487160474062, -0.021147290244698524, -0.043297331780195236, -0.015578444115817547, 0.09755329042673111, -0.0012556762667372823, 0.006580549757927656, -0.007005823310464621, 0.006970010697841644, -0.023689979687333107, -0.036672014743089676, -0.020717540755867958, -0.023045353591442108, -0.001161668449640274, 0.03665411099791527, -0.04379870742559433, 0.020251978188753128, 0.01433395966887474, 0.011755458079278469, 0.002569548087194562, -0.01908807083964348, 0.02856048010289669, 0.032320793718099594, -0.012695536948740482, 0.02395857311785221, 0.028488855808973312, 0.04827526956796646, 0.030924107879400253, 0.007659401744604111, 0.012033005245029926, -0.014933818951249123, 0.054005272686481476, 0.03821195289492607, 0.00954403541982174, 0.04601908102631569, -0.03482767194509506, 0.009741004556417465, 0.028417231515049934, 0.011621161364018917, -0.007887706160545349, 0.02809491753578186, -0.04548189416527748, 0.02390485443174839, 0.009785769507288933, -0.011540583334863186, 0.019911758601665497, -0.04430008307099342, 0.01186289545148611, -0.005958307068794966, -0.0037200250662863255, -0.006311955861747265, 0.02379741705954075, 0.04555352032184601, 0.0027150362730026245, 0.027665168046951294, 0.00014828619896434247, -0.001377662643790245, -0.02465691603720188, 0.004395986441522837, 0.027772605419158936, 0.0038050797302275896, -0.040503956377506256, -0.02711007371544838, 0.006795424968004227, 0.02209632284939289, -0.017754053696990013, -0.0021129383239895105, 0.02734285593032837, 0.01710047572851181, 0.0066163623705506325, 0.019213413819670677, -0.048955708742141724, -0.02000129036605358, 0.05966364964842796, -0.029402075335383415, 0.06335233896970749, -0.011325707659125328, 0.010108082555234432, -0.008599480614066124, -0.03344888985157013, 0.03282216936349869, 0.011468958109617233, 0.020717540755867958, -0.029240919277071953, 0.005622564814984798, 0.004821259994059801, -0.0020871981978416443, -0.012086723931133747, 0.005439025815576315, 0.01186289545148611, -0.015542631968855858, 0.016822928562760353, 0.005904588382691145, -0.036492954939603806, 0.00994692649692297, -0.012928318232297897, -0.011128739453852177, 0.03692270442843437, -0.02209632284939289, 0.01055573858320713, -0.03221335634589195, 0.0018208426190540195, 0.02517619915306568, -0.013823631219565868, 0.032481949776411057, -0.002632219810038805, 0.04544608294963837, 0.03199848160147667, -0.0219888836145401, 0.010188660584390163, 0.010985489003360271, -0.003451431170105934, -0.027718886733055115, 0.005474838428199291, 0.005322635173797607, 0.001491815084591508, 0.015148693695664406, -0.03652876615524292, 0.05550939962267876, -0.013241677545011044, 0.015130788087844849, 0.046269770711660385, 0.042616892606019974, 0.028488855808973312, -0.015372522175312042, 0.020037101581692696, 0.019213413819670677, 0.0078116049990057945, 0.03432629629969597, 0.016984084621071815, 0.025391073897480965, 0.04186483100056648, 0.022723041474819183, -0.025050854310393333, -0.0036730212159454823, -0.012856693007051945, -0.044873081147670746, 0.023994386196136475, -0.04276014491915703, -0.0253552608191967, -0.01436977181583643, 0.04677114635705948, 0.024048104882240295, 0.0201803520321846, 0.019052257761359215, -0.06353139877319336, 0.00910533219575882, 0.0403607040643692, 0.016545381397008896, 0.04401358217000961, -0.01626783423125744, 0.0026098371017724276, 0.01619620993733406, -0.022902103140950203, 0.04472983255982399, 0.03164035826921463, -0.024764355272054672, 0.02582082338631153, 0.005994119681417942, 0.026626605540513992, -0.013680380769073963, 0.016697585582733154, 0.029115574434399605, 0.01896272599697113, 0.016769209876656532, -0.02356463484466076, 0.014360819011926651, 0.008442800492048264, -0.007963808253407478, 0.009091902524232864, 0.02605360560119152, -0.008107057772576809, 0.014593600295484066, 0.012113583274185658, 0.024209260940551758, 0.05078214779496193, 0.031443387269973755, -0.0437270812690258, -0.013734099455177784, 0.04351220652461052, 0.020610103383660316, -0.02279466576874256, 0.03745989128947258, -0.017494414001703262, 0.029043950140476227, -0.03198057785630226, 0.04046814143657684, -0.02216794714331627, 0.017610805109143257, 0.014593600295484066, -0.05629727244377136, 0.0005304728983901441, -0.0019170887535437942, 0.037316642701625824, -0.004071435425430536, -0.029563231393694878, -0.011263036169111729, -0.016876647248864174, 0.032195452600717545, 0.006262713577598333, -0.035346951335668564, -0.08172415941953659, -0.0027575637213885784, 0.014548834413290024, 0.055115461349487305, 0.0328579843044281, 0.013375974260270596, -0.019678976386785507, -0.01976850815117359, 0.03910726681351662, 0.01774510182440281, 0.048955708742141724, 0.011361520737409592, 0.010161801241338253, -0.008241355419158936, -0.03099573217332363, -0.02659079246222973, 0.019177602604031563, -0.018568789586424828, 0.02589244768023491, 0.01787939853966236, 0.026662416756153107, 0.007162502966821194, -0.013295396231114864, -0.046090707182884216, 0.02605360560119152, -0.032249171286821365, 0.025910355150699615, 0.012176254764199257, -0.015632163733243942, -0.04000258073210716, -0.010448301210999489, 0.016742350533604622, -0.03147920221090317, -0.03814033046364784, -0.0183718204498291, 0.05346808582544327, -0.002441965974867344, 0.010331911034882069, -0.0065850261598825455, 0.024979230016469955, -0.022382821887731552, -0.02822026237845421, 0.017324304208159447, -0.025229917839169502, -0.009705191478133202, 0.013635614886879921, -0.024925511330366135, 0.00962461344897747, 0.003314896021038294, 0.008908363059163094, 0.020251978188753128, 0.0021979932207614183, -0.023582540452480316, 0.02972438745200634, 0.019625257700681686, 0.022364916279911995, -0.028703730553388596, 0.021093571558594704, 0.0008455110946670175, -0.024979230016469955, 0.04791714623570442, -0.008362222462892532, 0.014495115727186203, 0.0031268801540136337, 0.016052959486842155, -0.028524668887257576, -0.0009904399048537016, 0.015488913282752037, -0.03753151744604111, 0.03425467014312744, -0.00968728493899107, -0.04186483100056648, 0.025158291682600975, 0.029760200530290604, -0.002730704378336668, 0.03753151744604111, -0.019499914720654488, 0.018873196095228195, -0.0016798308352008462, 0.039178892970085144, 0.04233039170503616, 0.03710176423192024, -0.03174779564142227, -0.0018488210625946522, 0.05944877490401268, 0.003793888259679079, -0.03328773379325867, -0.02245444618165493, -0.025605948641896248, 0.026143135502934456, 0.011639067903161049, 0.0219888836145401, 0.015390428714454174, 0.007990667596459389, 0.016518522053956985, -0.03942957893013954, 0.009356020018458366, 0.00959775410592556, -0.03849845379590988, 0.044479142874479294, 0.04147089272737503, -0.026680324226617813, 0.03500673547387123, 0.003874466521665454, -0.012462755665183067, 0.04555352032184601, 0.016446897760033607, -0.02320650964975357, 0.021075665950775146, 0.00847413670271635, -0.01407431811094284, 0.016366319730877876, -0.02413763478398323, 0.006943151354789734, 0.01448616199195385, 0.00455266609787941, -0.004237068351358175, 0.00017178815323859453, -0.01000064518302679, 0.030154138803482056, -0.027199605479836464, -0.014360819011926651, -0.03343098238110542, -0.005998596549034119, -0.009955879300832748, -0.025802917778491974, -0.07921728491783142, 0.0004795519635081291, -0.012668677605688572, -0.029652763158082962, -0.0296169500797987, 0.010134941898286343, -0.014906959608197212, 0.04376289248466492, -0.008697964251041412, -0.006320909131318331, 0.005174908321350813, -0.014128037728369236, 0.022436540573835373, -0.021559134125709534, 0.02157703973352909, -0.036331795156002045, 0.024674823507666588, 0.03549020364880562, -0.013778865337371826, 0.0219888836145401, -0.012838786467909813, -0.03128223121166229, -0.002887384034693241, -0.008465182967483997, -0.018273336812853813, 0.0059090652503073215, 0.03106735646724701, 0.026608698070049286, 0.017315350472927094, 0.025229917839169502, 0.0015914186369627714, 0.04218714311718941, 0.005931447725743055, -0.028632106259465218, 0.009526128880679607, 0.02843513712286949, 0.04741577059030533, 0.0018029363127425313, -0.013196911662817001, 0.021774008870124817, 0.006943151354789734, 0.008800925686955452, 0.01448616199195385, 0.019356664270162582, 0.008250308223068714, 0.013975834473967552, -0.06213471293449402, -0.012579145841300488, -0.03328773379325867, 0.02320650964975357, 0.003167169401422143, 0.00100107176695019, 0.015667974948883057, 0.02651916816830635, 0.0338965468108654, 0.03593786060810089, -0.021093571558594704, -0.03461279720067978, -0.03101363778114319, 0.018094273284077644, 0.03235660865902901, 0.043010830879211426, -0.03939376771450043, 0.020628008991479874, -0.023654166609048843, 0.0013575181365013123, -0.008478612639009953, -0.011352567002177238, -0.025838728994131088, -0.011961380019783974, 0.007305752951651812, -0.036278076469898224, -0.015068115666508675, 0.017422787845134735, -0.021093571558594704, 0.012982036918401718, -0.0052375802770257, 0.003883419558405876, -0.040503956377506256, 0.008577097207307816, -0.03497092053294182, 0.0351857952773571, 0.00271279807202518, 0.026483355090022087, 0.017888352274894714, 0.004158728290349245, 0.044873081147670746, 0.05160583555698395, 0.016420038416981697, 0.014987537637352943, -0.036331795156002045, 0.0367436408996582, -0.0315687321126461, 0.04544608294963837, -0.019589446485042572, -0.03421885892748833, -0.01599028892815113, 0.002157703973352909, -0.015497866086661816, 0.018094273284077644, 0.02292001061141491, 0.0259998869150877, 0.04122020676732063, -0.012149395421147346, 0.0382835790514946, 0.0024598720483481884, 0.024442041292786598, -0.014405583962798119, 0.050638895481824875, -0.018568789586424828, 0.041793204843997955, 0.0006686868146061897, -0.012668677605688572, 0.04852595925331116, -0.005465885158628225, -0.0014906959841027856, 0.017216866835951805, -0.03060179390013218, -0.02832769975066185, 0.04695020616054535, 0.021612852811813354, -0.03174779564142227, -0.017261631786823273, 0.025964073836803436, -0.01663491316139698, 0.03814033046364784, 0.012391130439937115, -0.0226335097104311, -0.01271344255656004, -0.043941956013441086, -0.027092168107628822, 0.009109808132052422, -0.0024083915632218122, -0.014638365246355534, 0.060523152351379395, -0.011737551540136337, 0.026322199031710625, -0.02646544948220253, -0.034057702869176865, 0.0023972003255039454, 0.042258769273757935, -0.0473441444337368, 0.006334338802844286, 0.007390807848423719, -0.00021543465845752507, -0.01445034984499216, -0.035167891532182693, -0.022311197593808174, -0.007901135832071304, -0.051211897283792496, -0.014620459638535976, -0.00222149514593184, 0.0033887592144310474, -0.024298790842294693, 0.026966823264956474, 0.0019439480965957046, -0.005031658336520195, -0.009669379331171513, -0.004105009604245424, -0.03203429654240608, -0.015488913282752037, 0.02915138751268387, 0.006101557519286871, 0.03228498250246048, -0.039823517203330994, 0.006173182278871536, -0.021594947203993797, -0.03867751732468605, -0.0318194180727005, 0.01221206784248352, -0.017109429463744164, 0.012033005245029926, 0.01003645732998848, -0.022239571437239647, 0.012409036979079247, -0.02134425938129425, -0.014898006804287434, -0.00962461344897747, 0.04745158180594444, -0.027002636343240738, 0.04727252200245857, -0.02093241550028324, 0.02832769975066185, 0.00703715905547142, 0.03147920221090317, 0.03921470418572426, -0.01585599035024643, -0.019625257700681686, -0.008568144403398037, 0.01102130115032196, -0.015793319791555405, 0.006723799742758274, -0.002115176757797599, -0.04974358528852463, -0.0034693374764174223, -0.04490889236330986, 0.0024979228619486094, 0.038355205208063126, -0.036027390509843826, -0.029652763158082962, -0.053360648453235626, -0.019643165171146393, 0.002777708228677511 ]
In human contact, emotion is very crucial. Attributes like words, voice intonation, facial expressions, and kinesics can all be used to portray one's feelings. However, brain-computer interface (BCI) devices have not yet reached the level required for emotion interpretation. With the rapid development of machine learning algorithms, dry electrode techniques, and different real-world applications of the brain-computer interface for normal individuals, emotion categorization from EEG data has recently gotten a lot of attention. Electroencephalogram (EEG) signals are a critical resource for these systems. The primary benefit of employing EEG signals is that they reflect true emotion and are easily resolved by computer systems. In this work, EEG signals associated with good, neutral, and negative emotions were identified using channel selection preprocessing. However, researchers had a limited grasp of the specifics of the link between various emotional states until now. To identify EEG signals, we used discrete wavelet transform and machine learning techniques such as recurrent neural network (RNN) and k-nearest neighbor (kNN) algorithm. Initially, the classifier methods were utilized for channel selection. As a result, final feature vectors were created by integrating the features of EEG segments from these channels. Using the RNN and kNN algorithms, the final feature vectors with connected positive, neutral, and negative emotions were categorized independently. The classification performance of both techniques is computed and compared. Using RNN and kNN, the average overall accuracies were 94.844 % and 93.438 %, respectively.
[ 0.009986602701246738, 0.0019347969209775329, -0.009470943361520767, -0.06297919899225235, -0.01683627814054489, 0.0265220794826746, 0.0007358888979069889, -0.007043047342449427, -0.010124112479388714, 0.02834407612681389, 0.010081140324473381, -0.0707484632730484, -0.017386315390467644, -0.03575238212943077, 0.01983569748699665, -0.008938095532357693, -0.004722580313682556, -0.012521928176283836, -0.018563736230134964, -0.013166502118110657, -0.02700336091220379, -0.006351204589009285, 0.032074011862277985, -0.07783018797636032, 0.027690907940268517, 0.02937539480626583, 0.07088597118854523, -0.02337655797600746, -0.07459872215986252, 0.020884204655885696, 0.014189226552844048, -0.014687697403132915, -0.058441393077373505, -0.06459493190050125, -0.0653856098651886, -0.018804378807544708, -0.0005395623156800866, 0.03726498410105705, 0.03953388333320618, -0.007171962410211563, 0.054969288408756256, 0.014438462443649769, -0.00011797050683526322, -0.044827986508607864, -0.005504663567990065, -0.03181618079543114, -0.02851596288383007, -0.07618007808923721, 0.024940723553299904, -0.0739799290895462, 0.006660600192844868, -0.062085386365652084, 0.040427692234516144, 0.02229367382824421, -0.04888450726866722, 0.037436868995428085, 0.011026515625417233, 0.005775384604930878, 0.06597001850605011, 0.015942469239234924, 0.043762292712926865, 0.06878896057605743, -0.07136725634336472, 0.0024085589684545994, -0.032778747379779816, -0.024614140391349792, 0.03253810480237007, -0.04307474568486214, -0.025164177641272545, 0.009771744720637798, -0.030733298510313034, 0.01320947427302599, -0.04056520387530327, 0.017231617122888565, -0.02153737284243107, 0.01007254607975483, 0.028705038130283356, 0.09962538629770279, 0.01993882842361927, 0.029787922278046608, 0.005513257812708616, 0.05964459851384163, -0.007902479730546474, 0.025662647560238838, 0.015366649255156517, 0.02798311412334442, 0.020007582381367683, -0.07370491325855255, 0.008160308934748173, 0.022156164050102234, -0.010863224044442177, 0.06119157746434212, -0.004722580313682556, 0.04249032959342003, 0.01999039389193058, -0.050362732261419296, 0.06143222004175186, -0.02745026722550392, -0.01466191466897726, 0.007064533419907093, 0.032606858760118484, 0.00015214637096505612, -0.012874295003712177, -0.03709309548139572, 0.0008981067221611738, -0.02738151140511036, -0.03846818953752518, 0.02148580737411976, 0.03296782076358795, 0.1211455687880516, -0.08408685028553009, 0.015486969612538815, 0.024717271327972412, -0.001897196751087904, 0.00849978532642126, -0.019010642543435097, 0.031919315457344055, -0.031695861369371414, -0.0031605621334165335, -0.01050226204097271, 0.02904880978167057, 0.06951088458299637, -0.02287808619439602, 0.03585551306605339, -0.025043856352567673, 0.06280730664730072, 0.01645812764763832, 0.03626804053783417, 0.01203205157071352, 0.06346047669649124, -0.01730896532535553, -0.0003647215780802071, 0.0147392638027668, -0.015787770971655846, 0.021417051553726196, 0.036371175199747086, 0.016105759888887405, 0.03953388333320618, 0.03678370267152786, -0.012375825084745884, -0.009367811493575573, -0.018340284004807472, -0.03881195932626724, 0.009178736247122288, 0.0029048810247331858, -0.037436868995428085, 0.03564925119280815, 0.020334167405962944, -0.023015595972537994, -0.018804378807544708, -0.0477156788110733, 0.03874320536851883, 0.016810495406389236, 0.00711609935387969, 0.03901822492480278, -0.02588609978556633, 0.022981218993663788, -0.04640934243798256, -0.05235661193728447, -0.049228280782699585, 0.004166097845882177, -0.02712368220090866, 0.031128637492656708, 0.042902857065200806, 0.009952225722372532, 0.06077904999256134, -0.03757437691092491, 0.02353125624358654, -0.07549253106117249, 0.05778822675347328, -0.04723439738154411, 0.027897171676158905, 0.0002873726771213114, 0.0267970971763134, -0.000680025783367455, 0.04352165013551712, 0.055072419345378876, -0.03049265593290329, -0.04572179540991783, 0.0011301534250378609, -0.030750486999750137, 0.0027673719450831413, 0.06971714645624161, 0.00929905753582716, 0.03661181405186653, 0.009161547757685184, 0.06373549997806549, -0.02196708880364895, 0.08394934237003326, -0.03152397647500038, 0.052700385451316833, 0.028258133679628372, 0.07349864393472672, 0.0023892216850072145, 0.06136346235871315, -0.02567983604967594, -0.006480119191110134, 0.03138646483421326, -0.0012805541045963764, 0.0023892216850072145, -0.08016784489154816, -0.07109224051237106, 0.016269052401185036, -0.01002098061144352, -0.0450342521071434, -0.006183614954352379, 0.04867824167013168, -0.02042010985314846, -0.03822754696011543, 0.011507797986268997, 0.015100224874913692, -0.004196178168058395, -0.033156897872686386, 0.002561108209192753, -0.0013697202084586024, -0.012857106514275074, 0.043865423649549484, 0.01492833811789751, 0.04200904816389084, 0.0035902783274650574, 0.021210787817835808, 0.08834964036941528, 0.06902959942817688, -0.02824094332754612, -0.028172189369797707, 0.004640934057533741, -0.020832637324929237, -0.018134020268917084, -0.018288718536496162, -0.011516392230987549, -0.010708525776863098, 0.04651247337460518, 0.052700385451316833, -0.035082023590803146, -0.04575617238879204, -0.014636131934821606, 0.031627107411623, -0.03836505487561226, -0.03540860861539841, 0.0008717866148799658, -0.02057480812072754, -0.019577866420149803, -0.03477263078093529, 0.005607795435935259, 0.0017768761608749628, -0.009900659322738647, -0.008370870724320412, 0.075011245906353, 0.023926593363285065, -0.0006977515877224505, -0.05771947279572487, -0.014679103158414364, 0.013467303477227688, 0.04004954174160957, 0.006226586643606424, 0.010768686421215534, 0.02995980903506279, -0.018684057518839836, 0.028911301866173744, -0.031919315457344055, 0.03332878276705742, 0.003276585601270199, 0.0049632214941084385, 0.002954298397526145, -0.026917418465018272, 0.03527110069990158, 0.05184095352888107, -0.037161849439144135, 0.0648699477314949, -0.08133666962385178, 0.01811683177947998, 0.012427390553057194, -0.028876924887299538, -0.03365536779165268, 0.02722681500017643, -0.02057480812072754, 0.07858648896217346, -0.05830388516187668, 0.030750486999750137, 0.019371602684259415, -0.040874600410461426, 0.03953388333320618, 0.0396713949739933, 0.02867066115140915, -0.013630595989525318, 0.016801901161670685, -0.00913576502352953, 0.019423170015215874, -0.08271176367998123, -0.01590809039771557, 0.020488865673542023, -0.077211394906044, -0.05170344561338425, -0.019320037215948105, 0.01816839724779129, -0.005427314899861813, -0.0227749552577734, -0.030802052468061447, -0.005491772200912237, -0.014696291647851467, 0.03348348289728165, -0.04675311595201492, 0.017566796392202377, 0.03097393922507763, -0.06511058658361435, -0.006871161051094532, 0.061019692569971085, 0.029237885028123856, -0.020437300205230713, -0.010596799664199352, 0.0002656182914506644, 0.04709688946604729, -0.004709688946604729, -0.037058718502521515, 0.007292282767593861, -0.0013299714773893356, 0.02497510239481926, 0.056722529232501984, 0.036302417516708374, -0.012521928176283836, -0.00022090095444582403, 0.02347968891263008, -0.05242536962032318, 0.08319304138422012, -0.046237457543611526, 0.011671090498566628, 0.03729936107993126, 0.04967518523335457, -0.021245164796710014, -0.030045751482248306, -0.03205682337284088, 0.012178155593574047, -0.000742871779948473, -0.013733727857470512, 0.000013470593330566771, -0.03520234674215317, -0.05586309731006622, -0.014558782801032066, 0.014808017760515213, 0.017755869776010513, 0.01639796793460846, -0.05111902952194214, -0.06404489278793335, -0.0423528216779232, -0.043762292712926865, -0.012453173287212849, -0.025972042232751846, -0.017996512353420258, 0.005758196115493774, -0.05723818764090538, 0.0010001643095165491, -0.00229683262296021, -0.006179317831993103, 0.015933874994516373, -0.032400596886873245, -0.04035893827676773, 0.0015512752579525113, 0.007902479730546474, 0.005242536775767803, 0.018254341557621956, -0.017669927328824997, 0.02593766525387764, -0.022603068500757217, -0.006003134418278933, -0.05070650205016136, -0.0761113241314888, -0.00795834232121706, -0.004060817416757345, 0.026281438767910004, 0.011567958630621433, 0.026006421074271202, 0.04149338975548744, -0.0105882054194808, -0.011026515625417233, -0.028687849640846252, 0.03822754696011543, 0.023892216384410858, -0.01882156729698181, -0.00008654751582071185, 0.03176461532711983, -0.018718434497714043, 0.007515734992921352, -0.03809003904461861, 0.010038169100880623, 0.007107504643499851, 0.031128637492656708, -0.016655797138810158, 0.026350192725658417, -0.0302863921970129, 0.07693637907505035, -0.02750183269381523, -0.04489674046635628, -0.026195496320724487, -0.04747503995895386, 0.01592528074979782, 0.0002238552551716566, -0.038674451410770416, 0.0327099934220314, 0.06050403043627739, 0.023514065891504288, -0.0610884465277195, 0.0033023685682564974, -0.009144359268248081, -0.03396476432681084, -0.043177876621484756, -0.04977831616997719, -0.052597254514694214, -0.00884355790913105, 0.050293974578380585, 0.021692071110010147, 0.0008669522940181196, 0.017498040571808815, 0.020488865673542023, -0.05263163149356842, -0.0353742316365242, -0.028103435412049294, -0.006922726985067129, 0.06902959942817688, 0.009909253567457199, -0.019062208011746407, -0.05510679632425308, 0.029770733788609505, 0.04465610161423683, 0.004004954360425472, -0.03736811503767967, 0.052390992641448975, -0.031541164964437485, -0.0015491266967728734, 0.03503045812249184, -0.03252091631293297, -0.07886150479316711, 0.0535941943526268, 0.024940723553299904, -0.0044647506438195705, 0.006153535097837448, -0.027089305222034454, 0.01864968053996563, 0.03221151977777481, -0.04438108205795288, -0.03011450730264187, -0.04090897738933563, 0.00459366524592042, -0.0283956415951252, -0.04651247337460518, -0.036577437072992325, 0.03527110069990158, 0.0230499729514122, -0.008211875334382057, -0.013020399026572704, -0.00747706089168787, -0.02899724431335926, -0.002419301774352789, -0.03843381255865097, -0.041940294206142426, 0.024957913905382156, 0.016415156424045563, -0.021743636578321457, -0.04334976524114609, 0.041183993220329285, -0.0332256518304348, -0.029014432802796364, 0.016922220587730408, 0.021021712571382523, 0.007219231221824884, 0.0007353517576120794, 0.0026771314442157745, -0.03329440578818321, -0.03774626553058624, -0.009213114157319069, 0.044449836015701294, -0.0024536792188882828, -0.055656831711530685, -0.013682161457836628, 0.019199715927243233, 0.021262355148792267, -0.017962133511900902, 0.002181883668527007, -0.02229367382824421, -0.004129571840167046, 0.0017779505578801036, 0.04163089767098427, -0.02181239053606987, -0.013587623834609985, -0.010914789512753487, -0.015658855438232422, -0.014644726179540157, 0.01698238216340542, 0.023067161440849304, 0.011662496253848076, -0.03826192393898964, 0.01342433225363493, 0.002649199916049838, 0.021296732127666473, -0.0033388943411409855, -0.006346907466650009, 0.01580495946109295, -0.0015308636939153075, 0.015057253651320934, 0.10216930508613586, 0.014610348269343376, 0.030991127714514732, 0.005341371521353722, 0.0025310281198471785, 0.00035639581619761884, -0.0281378123909235, 0.003667627228423953, 0.0036998558789491653, 0.002219483722001314, -0.00605470035225153, 0.016269052401185036, 0.025181366130709648, -0.027089305222034454, 0.0070473444648087025, -0.02631581574678421, 0.002147506456822157, 0.035821136087179184, -0.010081140324473381, 0.031214579939842224, -0.013957180082798004, 0.009874876588582993, 0.015151791274547577, 0.00956548098474741, 0.03558049723505974, 0.038674451410770416, -0.05166906863451004, -0.008435327559709549, 0.029598847031593323, 0.013587623834609985, -0.06452617794275284, -0.011662496253848076, -0.03726498410105705, -0.013450114987790585, 0.004830009303987026, -0.032985009253025055, -0.00020935232168994844, -0.017979323863983154, 0.023926593363285065, -0.0076231639832258224, -0.011017921380698681, -0.06397613883018494, -0.035133592784404755, 0.0680670365691185, 0.02105609141290188, -0.05916331708431244, 0.01683627814054489, -0.027158059179782867, 0.033036574721336365, -0.040118299424648285, 0.008478299714624882, 0.017119890078902245, -0.005805464927107096, 0.006613331381231546, -0.002842572284862399, -0.020918581634759903, 0.01784181408584118, -0.027106493711471558, 0.03420540317893028, -0.03243497386574745, -0.052287857979536057, -0.029495716094970703, -0.013579029589891434, 0.0013858345337212086, -0.011791410855948925, 0.02684866450726986, -0.0019799170549958944, 0.0043573216535151005, -0.019388791173696518, 0.07116099447011948, -0.0014717777958139777, -0.026917418465018272, -0.010708525776863098, -0.05658502131700516, -0.024837592616677284, -0.017455069348216057, -0.005930082406848669, 0.03420540317893028, 0.05655064433813095, -0.07026718556880951, 0.021296732127666473, 0.04902201518416405, 0.03408508375287056, 0.01763555034995079, 0.01650109887123108, 0.016535477712750435, 0.0278627946972847, -0.03585551306605339, 0.009195925667881966, -0.050293974578380585, 0.010974950157105923, 0.0015007836045697331, -0.003010161453858018, 0.042696595191955566, -0.0035387123934924603, -0.015779176726937294, -0.017076918855309486, 0.012453173287212849, 0.025576705113053322, 0.011069487780332565, 0.01784181408584118, -0.07308612018823624, -0.007631758693605661, 0.032297465950250626, 0.014060311950743198, 0.05826950818300247, 0.030097318813204765, 0.003852405119687319, 0.013286822475492954, 0.03977452591061592, 0.033741310238838196, 0.014275169931352139, 0.02282652072608471, -0.02165769226849079, 0.06906397640705109, 0.0364399291574955, -0.0016135841142386198, 0.0027437375392764807, 0.004417481832206249, -0.0013869088143110275, 0.004761254880577326, -0.0011613077949732542, 0.008426733314990997, -0.028361264616250992, 0.010106923058629036, 0.009788933210074902, 0.042902857065200806, 0.0407370887696743, -0.003985617309808731, -0.03185056149959564, 0.030733298510313034, 0.018580924719572067, -0.05098152160644531, 0.02031697891652584, -0.021984277293086052, -0.013389954343438148, 0.04764692485332489, 0.014808017760515213, -0.017704304307699203, -0.0029414070304483175, 0.015985440462827682, 0.03023482672870159, -0.00471828319132328, 0.002492353552952409, -0.05276913940906525, 0.032400596886873245, -0.006587548181414604, 0.008289224468171597, -0.03142084181308746, 0.01693940907716751, 0.0621541403234005, -0.010141300968825817, 0.06115720048546791, 0.013879830949008465, 0.010442102327942848, 0.012152371928095818, -0.008168904110789299, -0.051531556993722916, 0.01449862215667963, 0.01479082927107811, 0.013785293325781822, -0.03661181405186653, -0.019423170015215874, 0.0450342521071434, 0.022860897704958916, -0.024373499676585197, 0.02062637358903885, -0.007137584965676069, -0.019337225705385208, -0.022499937564134598, 0.051531556993722916, 0.044346705079078674, -0.04420919716358185, -0.06359798461198807, -0.0358898900449276, 0.007997017353773117, 0.007197745144367218, -0.04537802189588547, 0.046237457543611526, 0.026333004236221313, 0.05778822675347328, -0.035718005150556564, -0.07212355732917786, -0.02540481835603714, 0.0190278310328722, 0.008903718553483486, 0.018477793782949448, -0.008018502965569496, -0.027433078736066818, 0.014997093006968498, -0.042799726128578186, -0.01971537619829178, -0.00379224494099617, -0.02562827058136463, 0.01758398488163948, -0.020179469138383865, -0.010433508083224297, 0.007266500033438206, -0.06748262047767639, 0.012814135290682316, -0.010338970459997654, 0.014773640781641006, -0.03564925119280815, -0.037608757615089417, -0.02416723594069481, 0.022499937564134598, 0.015933874994516373, 0.05744445323944092, 0.02009352669119835, 0.007322363089770079, -0.03344910219311714, -0.04469047859311104, 0.0077391876839101315, 0.004885872360318899, 0.007601678371429443, 0.05177219957113266, 0.018580924719572067, -0.01219534408301115, -0.011619524098932743, 0.017223022878170013, -0.029169131070375443, 0.04187154024839401, 0.04524051398038864, 0.03778064250946045, -0.01095776166766882, -0.01334698311984539, -0.024562574923038483, 0.03678370267152786, 0.05610373988747597, 0.026659589260816574, -0.039946410804986954, -0.0037857990246266127, 0.024992290884256363, 0.040427692234516144, -0.06655443459749222, -0.0007342774188145995, -0.019440358504652977, -0.03393038734793663, 0.02985667623579502, 0.046168699860572815, 0.00927327387034893, -0.013484491966664791, -0.005384343210607767, -0.055931851267814636, -0.023771896958351135, 0.0050405701622366905, 0.02562827058136463, -0.005049164406955242, -0.05906018614768982, 0.04046206921339035, -0.033638179302215576, 0.0190278310328722, 0.01444705668836832, 0.0037557189352810383, 0.044449836015701294, -0.06136346235871315, -0.028550339862704277, 0.007025858853012323, 0.025972042232751846, -0.006729354616254568, 0.021021712571382523, 0.025439195334911346, -0.007868102751672268, -0.006153535097837448, -0.004421778954565525, -0.002021814463660121, 0.03252091631293297, 0.034171026200056076, -0.014309546910226345, 0.03654306009411812, 0.026143928989768028, -0.046925000846385956, 0.021743636578321457, 0.02416723594069481, 0.06253229081630707, -0.020918581634759903, 0.013897019438445568, 0.0029048810247331858, 0.005031975917518139, -0.02384065091609955, -0.009591263718903065, 0.017721492797136307, -0.022585880011320114, 0.01907939650118351, 0.04214655980467796, 0.03238340839743614, -0.003493592143058777, -0.008826369419693947, -0.012178155593574047, -0.005706630181521177, -0.007975531741976738, 0.009127170778810978, 0.015272111631929874, -0.012719597667455673, 0.01248755119740963, 0.018030889332294464, 0.021142033860087395, -0.003727787407115102, -0.021038901060819626, 0.05321604758501053, -0.05778822675347328, -0.016544071957468987, 0.01789337955415249, -0.011585147120058537, -0.0278627946972847, -0.013604812324047089, -0.0332256518304348, -0.032606858760118484, -0.04867824167013168, -0.013338388875126839, -0.009445160627365112, 0.011155431158840656, 0.008516973815858364, -0.009531104005873203, 0.0008024948765523732, 0.010003791190683842, 0.03185056149959564, -0.00918733049184084, -0.034755442291498184, 0.01763555034995079, 0.0012923713074997067, 0.0015340866521000862, -0.00024117817520163953, -0.026281438767910004, -0.008375167846679688, -0.020832637324929237, -0.05864765867590904, -0.020935770124197006, 0.04775005578994751, 0.02616111747920513, 0.00787669699639082, -0.02732994593679905, 0.02610955201089382, -0.0018327393336221576, 0.022035842761397362, 0.003184196539223194, -0.015572912991046906, 0.01859811507165432, -0.009204519912600517, 0.008590025827288628, 0.029891055077314377, 0.0171542689204216, 0.0024042618460953236, 0.0036805185955017805, 0.02165769226849079, 0.006768029183149338, -0.015392431989312172, -0.003882485209032893, -0.014352519065141678, -0.02009352669119835, 0.02047167718410492, 0.0015330122550949454, -0.01522054523229599, -0.01705113612115383, 0.014730668626725674, 0.006398473400622606, -0.01720583438873291, 0.010149895213544369, 0.02186395600438118, 0.019371602684259415, 0.006901240907609463, 0.005049164406955242, 0.006836783606559038, -0.018048077821731567, 0.005620686803013086, 0.00862869992852211, 0.019956016913056374, -0.060057125985622406, -0.008435327559709549, -0.005998837295919657, -0.03784939646720886, -0.02519855462014675, 0.002187255071476102, -0.009118576534092426, -0.0049632214941084385, 0.017119890078902245, -0.009032633155584335, 0.007825130596756935, -0.03564925119280815, 0.023118728771805763, 0.024029726162552834, 0.010923383757472038, 0.038983847945928574, 0.021726448088884354, -0.003888930892571807, -0.001199982245452702, 0.06191350147128105, 0.021588938310742378, -0.025095421820878983, -0.03595864772796631, 0.03478981927037239, -0.015684638172388077, 0.006896943785250187, -0.02727838046848774, 0.03712747246026993, -0.00036391583853401244, 0.01882156729698181, 0.006243775598704815, 0.006437147501856089, -0.03664619103074074, 0.010631177574396133, 0.006239478476345539, 0.007171962410211563, -0.031627107411623, 0.0017639846773818135, -0.006462930701673031, -0.02932382933795452, -0.03719623014330864, -0.007421197835355997, -0.004744065925478935, 0.004817117936909199, -0.005998837295919657, -0.04345289617776871, -0.0028060462791472673, 0.0026212683878839016, -0.03472106531262398, 0.05826950818300247, -0.005474583711475134, 0.010820251889526844, -0.02315310575067997, 0.026814287528395653, -0.015272111631929874, 0.011421854607760906, 0.020248224958777428, -0.0369899645447731, 0.01377669908106327, -0.019113773480057716, 0.008332195691764355, -0.035993024706840515, -0.026968983933329582, -0.008877934888005257, -0.0016436642035841942, -0.0028919896576553583, 0.04025580734014511, 0.031695861369371414, 0.0005041107651777565, 0.020609185099601746, -0.0385713204741478, 0.007588787004351616, 0.04589368402957916, -0.0071633681654930115, -0.007563003804534674, -0.008156011812388897, 0.004989004228264093, -0.00048289349069818854, -0.01870124600827694, -0.0047913347370922565, -0.047887567430734634, 0.012796946801245213, -0.04266221821308136, 0.018048077821731567, -0.0007455574814230204, -0.0034592149313539267, -0.03970577195286751, 0.017773060128092766, -0.014060311950743198, -0.02186395600438118, -0.011928919702768326, -0.028756603598594666, -0.03809003904461861, -0.020987335592508316, 0.018099643290042877, -0.038674451410770416, -0.026178305968642235, 0.012728191912174225, 0.00747706089168787, -0.020454488694667816, 0.015572912991046906, -0.04111523926258087, 0.007468466181308031, -0.025473572313785553, -0.0036246555391699076, 0.040805842727422714, -0.0024601249024271965, 0.0035150779876857996, 0.02770809642970562, -0.01945754699409008, -0.011963296681642532, -0.01117261964827776, -0.025662647560238838, -0.007949748076498508, -0.011791410855948925, -0.017506634816527367, 0.01356184110045433, -0.007468466181308031, -0.018254341557621956, 0.011267157271504402, -0.01801370084285736, 0.027673719450831413, -0.02315310575067997, -0.05472864583134651, 0.012745380401611328, 0.009582669474184513, -0.007868102751672268, -0.01864968053996563, 0.0391213558614254, -0.04524051398038864, 0.0055390410125255585, -0.017773060128092766, 0.013252445496618748, 0.016690174117684364, 0.030200449749827385, -0.001198907964862883, -0.0302863921970129, 0.024235989898443222, 0.05617249384522438, -0.006682085804641247, 0.018185587599873543, 0.035821136087179184, 0.003931902814656496, -0.010510856285691261, 0.02262025699019432, 0.019680999219417572, -0.0010066099930554628, 0.0385713204741478, 0.008787695318460464, 0.007932559587061405, 0.012367229908704758, -0.029083188623189926, 0.03006293997168541, 0.03183336928486824, -0.0056249843910336494, 0.018735622987151146, -0.0024794621858745813, -0.045206137001514435, -0.051428426057100296 ]
Constrained random test generation is one of the most widely adopted methods for generating stimuli for simulation-based verification. Randomness leads to test diversity, but tests tend to repeatedly exercise the same design logic. Constraints are written (typically manually) to bias random tests towards interesting, hard-to-reach, and yet-untested logic. However, as verification progresses, most constrained random tests yield little to no effect on functional coverage. If stimuli generation consumes significantly less resources than simulation, then a better approach involves randomly generating a large number of tests, selecting the most effective subset, and only simulating that subset. In this paper, we introduce a novel method for automatic constraint extraction and test selection. This method, which we call coverage-directed test selection, is based on supervised learning from coverage feedback. Our method biases selection towards tests that have a high probability of increasing functional coverage, and prioritises them for simulation. We show how coverage-directed test selection can reduce manual constraint writing, prioritise effective tests, reduce verification resource consumption, and accelerate coverage closure on a large, real-life industrial hardware design.
[ 0.027578148990869522, 0.003368394449353218, -0.020247483626008034, -0.018187474459409714, 0.032514750957489014, 0.038973160088062286, -0.030677443370223045, 0.035242870450019836, -0.06354480981826782, 0.0028093152213841677, 0.01055059116333723, -0.04751013591885567, 0.048066895455121994, -0.02119397558271885, 0.029786627739667892, 0.021769292652606964, 0.02399633079767227, -0.042944710701704025, 0.018846306949853897, -0.0631365180015564, 0.01685125194489956, 0.055527471005916595, -0.01508818008005619, 0.0652150884270668, 0.029935097321867943, 0.006388814188539982, -0.03125276044011116, -0.004725495353341103, -0.05025681480765343, 0.01822459138929844, -0.0017619115533307195, 0.05838550254702568, -0.07404900342226028, -0.04320453107357025, -0.06848140805959702, -0.010448518209159374, 0.031902313232421875, -0.00329647958278656, -0.036634769290685654, 0.0643242672085762, 0.015162414871156216, -0.08514707535505295, -0.02102694660425186, 0.016368726268410683, -0.004291687160730362, 0.007335305213928223, 0.025128407403826714, -0.02750391513109207, -0.028673110529780388, -0.03657909482717514, -0.026186250150203705, -0.02598210610449314, 0.01944946125149727, -0.02043307013809681, -0.01690692827105522, 0.05174150690436363, 0.004164096433669329, 0.03904739394783974, 0.06721942126750946, 0.00735850352793932, 0.03704306110739708, 0.005535116419196129, -0.01769566908478737, 0.0326075442135334, 0.033349890261888504, -0.02514696680009365, -0.016275933012366295, -0.008676167577505112, 0.03169816732406616, -0.007493053562939167, -0.03485313802957535, -0.05619558319449425, -0.0038114821072667837, 0.04869788885116577, 0.01776990480720997, 0.05411701649427414, 0.03431493788957596, -0.008189002983272076, -0.05181574076414108, 0.023124074563384056, 0.022159025073051453, 0.0855182483792305, -0.043018944561481476, 0.006008361931890249, -0.003233844181522727, -0.0567152239382267, 0.01506034191697836, -0.062245700508356094, 0.016192419454455376, -0.05159303918480873, -0.026891479268670082, -0.012981773354113102, 0.004871645011007786, 0.013093125075101852, -0.01761215552687645, 0.02247452177107334, -0.014420068822801113, -0.0008194802794605494, -0.03659765049815178, 0.04157136753201485, 0.0006315739592537284, -0.0324590727686882, 0.02882157824933529, -0.015978995710611343, 0.03706161677837372, -0.052186913788318634, -0.0508878119289875, 0.02752247266471386, 0.01875351369380951, 0.09991975873708725, -0.05159303918480873, 0.032588984817266464, 0.03628215566277504, -0.0077435956336557865, -0.03613368421792984, -0.04079190641641617, -0.05229826644062996, -0.11914651095867157, -0.006838861387223005, -0.06885258108377457, 0.005340250674635172, 0.04903194680809975, -0.022678665816783905, -0.03485313802957535, -0.07360359281301498, 0.012582763098180294, -0.01989486999809742, 0.0052057006396353245, 0.027151301503181458, 0.016721341758966446, -0.02965671755373478, -0.017500804737210274, 0.01459637563675642, 0.011181584559381008, 0.0689639300107956, 0.006978051271289587, 0.0249984972178936, -0.026575982570648193, -0.056678108870983124, -0.02021036669611931, -0.04962582141160965, -0.04914329573512077, 0.041125960648059845, 0.05036816745996475, 0.003141050925478339, -0.024868587031960487, -0.021249650046229362, 0.09219935536384583, -0.026743009686470032, 0.03180951997637749, 0.00413161888718605, 0.03650485724210739, -0.015134576708078384, 0.020061897113919258, 0.026538865640759468, 0.029860863462090492, 0.0029090680181980133, -0.02050730586051941, 0.013492136262357235, -0.036616209894418716, 0.06900104880332947, -0.031586818397045135, -0.01617386005818844, 0.049959879368543625, 0.008142606355249882, 0.018168915063142776, 0.0015032504452392459, 0.03500160947442055, -0.05838550254702568, 0.021769292652606964, 0.007377061992883682, 0.011840417049825191, -0.006416652351617813, 0.05426548421382904, 0.01557998452335596, 0.03002789057791233, 0.014206644147634506, 0.0008502179989591241, 0.02026604302227497, 0.004064343869686127, -0.051110513508319855, 0.014652051962912083, 0.03591098263859749, 0.03192087262868881, 0.05066510662436485, 0.0417940728366375, 0.08974961936473846, 0.008509139530360699, -0.008931349031627178, 0.006681113038212061, -0.02026604302227497, 0.019189640879631042, 0.019263874739408493, 0.06554914265871048, 0.031661052256822586, -0.030009333044290543, -0.0435757040977478, 0.005470161326229572, -0.012053840793669224, -0.0006663714302703738, -0.01517169363796711, -0.010160859674215317, 0.019931986927986145, -0.01639656536281109, 0.0214909128844738, -0.00034130513085983694, 0.03453764319419861, 0.08210345357656479, -0.015960436314344406, -0.03025059401988983, -0.04042073339223862, -0.003806842491030693, 0.00823539961129427, -0.024720117449760437, -0.02691003866493702, -0.00896382611244917, 0.021546589210629463, -0.017287379130721092, -0.020006220787763596, -0.015450073406100273, 0.04246218502521515, -0.016108905896544456, 0.05229826644062996, -0.0567152239382267, -0.04398399218916893, 0.04364993795752525, 0.01097743958234787, 0.0003326057631056756, 0.048438068479299545, 0.07764937728643417, 0.0028139548376202583, -0.03682035580277443, 0.0019103807862848043, 0.020618656650185585, 0.03687603026628494, -0.019338110461831093, 0.0025564536917954683, -0.01017941813915968, 0.03565116226673126, 0.010068066418170929, -0.0003320257819723338, -0.04773284122347832, -0.01776990480720997, -0.010838249698281288, 0.02987942099571228, 0.017732787877321243, -0.03344268351793289, 0.005484080407768488, 0.038008108735084534, 0.02416335791349411, -0.05114763230085373, -0.021064063534140587, -0.018697837367653847, 0.06395309418439865, -0.0010508834384381771, 0.007196115329861641, -0.009780406951904297, -0.0977669507265091, -0.0182802677154541, -0.019616490229964256, 0.0250727329403162, -0.007321386132389307, 0.00011715145956259221, -0.011079512536525726, -0.027039948850870132, -0.0057439012452960014, 0.015969716012477875, -0.0050154742784798145, -0.034871697425842285, 0.009808245114982128, 0.010717618279159069, -0.04725031554698944, 0.02600066363811493, -0.03923298045992851, 0.011571316048502922, -0.04869788885116577, 0.0035099040251225233, -0.01158987544476986, -0.04639661684632301, 0.056047115474939346, -0.036467742174863815, 0.004004028160125017, -0.04494904354214668, 0.000560529122594744, -0.0018547048093751073, -0.05961037427186966, -0.029248427599668503, 0.03490881621837616, -0.07271277904510498, -0.0567152239382267, -0.011181584559381008, -0.047213196754455566, 0.013529254123568535, 0.008351391181349754, 0.04643373563885689, 0.007646162528544664, -0.019468020647764206, -0.05085069313645363, -0.032514750957489014, 0.005122186616063118, -0.03882468864321709, -0.011218702420592308, 0.010225814767181873, 0.004690697882324457, -0.03262609988451004, -0.010476356372237206, -0.020841360092163086, 0.016860531643033028, -0.02021036669611931, -0.049737174063920975, -0.009478828869760036, -0.010346445254981518, 0.023680834099650383, -0.0014904913259670138, -0.038453515619039536, 0.016285212710499763, 0.01368700247257948, -0.00811476819217205, -0.03665332868695259, -0.039752621203660965, 0.017361614853143692, -0.06031560152769089, -0.11209423094987869, -0.026631658896803856, 0.0006860899738967419, 0.004945879336446524, 0.02227037586271763, 0.0634334534406662, -0.017547201365232468, 0.008871032856404781, -0.007567288354039192, 0.006398093421012163, -0.05396854504942894, -0.06588319689035416, -0.06677401065826416, -0.04884636029601097, -0.021509472280740738, 0.01874423399567604, -0.04936600103974342, -0.003929793369024992, -0.03886180743575096, 0.032199252396821976, -0.03904739394783974, -0.014559258706867695, -0.017417289316654205, -0.001971856225281954, -0.0017816300969570875, 0.003572539659217, 0.030139243230223656, -0.039975326508283615, 0.0010433439165353775, 0.003869477892294526, -0.0029021084774285555, -0.025573816150426865, 0.0986577644944191, 0.054302603006362915, -0.006277462467551231, -0.0020646494813263416, -0.00421281298622489, -0.025963546708226204, 0.056826576590538025, -0.012295103631913662, -0.0007127680582925677, -0.012749790214002132, -0.010912484489381313, 0.04751013591885567, 0.011005277745425701, -0.005725342780351639, 0.012712673284113407, 0.03726576268672943, 0.0028093152213841677, 0.05623270198702812, 0.03741423413157463, 0.02613057568669319, 0.029860863462090492, -0.030213477090001106, -0.0034194306936115026, 0.0009447511401958764, -0.03572539612650871, 0.028413288295269012, 0.0162295363843441, 0.019764959812164307, -0.006263543386012316, 0.025109849870204926, -0.025481022894382477, 0.04524598270654678, -0.020321719348430634, -0.017417289316654205, -0.033424124121665955, 0.03923298045992851, 0.026724452152848244, -0.049959879368543625, 0.0023615879472345114, -0.010337166488170624, 0.028153467923402786, -0.031902313232421875, 0.02408912405371666, -0.01745440810918808, 0.02865455113351345, -0.055156297981739044, -0.03893604129552841, 0.02111973986029625, -0.03329421207308769, 0.0001938508648891002, -0.011292936280369759, 0.02980518713593483, -0.038527749478816986, 0.006978051271289587, -0.049588706344366074, -0.022604431957006454, 0.05600999668240547, -0.060092899948358536, 0.0014939710963517427, -0.013018891215324402, 0.03535422310233116, 0.0034403090830892324, -0.00659295916557312, -0.02728121168911457, 0.03919586166739464, -0.03279313072562218, -0.022437404841184616, 0.07249007374048233, 0.059870194643735886, -0.025518139824271202, 0.02720697596669197, -0.010494914837181568, -0.007650802377611399, -0.022604431957006454, -0.026186250150203705, -0.027039948850870132, 0.019913427531719208, 0.019950546324253082, -0.04892059415578842, -0.023495247587561607, 0.0003734927740879357, -0.03034338727593422, -0.039604153484106064, 0.02644607238471508, -0.0417940728366375, 0.04468922317028046, -0.007590486668050289, -0.05226115137338638, -0.027169859036803246, -0.03683891519904137, -0.05266943946480751, -0.026241926476359367, -0.04847518727183342, -0.018011167645454407, -0.060798127204179764, -0.035409897565841675, -0.036857474595308304, 0.00577637879177928, -0.08084146678447723, -0.011163026094436646, 0.02026604302227497, -0.08470166474580765, 0.03986397385597229, -0.034036558121442795, 0.009780406951904297, -0.011571316048502922, 0.013937544077634811, 0.03574395552277565, -0.009219007566571236, -0.034945931285619736, 0.025276876986026764, 0.034574758261442184, -0.023588040843605995, -0.02355092391371727, 0.015273766592144966, 0.011645550839602947, -0.02095271274447441, -0.022771459072828293, -0.008133326657116413, -0.0007771433447487652, 0.016860531643033028, 0.018642161041498184, -0.02134244330227375, -0.059721726924180984, -0.021361002698540688, -0.060167133808135986, -0.007010528817772865, 0.018920540809631348, -0.0180575642734766, 0.03819369524717331, 0.023606598377227783, 0.038156576454639435, 0.05419125035405159, -0.027095625177025795, 0.02286425232887268, -0.03585530444979668, -0.026798686012625694, 0.00560471136122942, -0.008857114240527153, -0.01837306097149849, 0.02460876666009426, 0.003041298361495137, -0.04702761024236679, -0.07920830696821213, 0.0037952433340251446, -0.0033150382805615664, -0.013260153122246265, -0.019764959812164307, -0.002271114382892847, 0.01957937330007553, -0.0312713198363781, -0.019857753068208694, -0.004876284394413233, 0.03669044375419617, 0.0070151686668396, 0.009219007566571236, -0.018103960901498795, 0.011181584559381008, -0.05036816745996475, -0.032588984817266464, 0.024571647867560387, 0.03695026785135269, 0.014225202612578869, -0.0011709346435964108, 0.007534810807555914, -0.02460876666009426, 0.02087847702205181, -0.0024381421972066164, -0.008968465961515903, -0.011719785630702972, -0.01920820027589798, 0.010541311465203762, 0.022771459072828293, -0.03010212630033493, 0.02889581397175789, -0.011840417049825191, -0.0028696306981146336, 0.06061254069209099, -0.013696281239390373, -0.039901092648506165, 0.019226757809519768, -0.025184083729982376, 0.02134244330227375, 0.01532016322016716, 0.0010671222116798162, -0.009219007566571236, -0.020692890509963036, 0.02538822963833809, -0.04398399218916893, 0.032885923981666565, 0.01653575524687767, 0.011422847397625446, 0.0027837969828397036, -0.00491804163902998, 0.02713274210691452, 0.008351391181349754, -0.015227369964122772, 0.040977492928504944, -0.0312713198363781, -0.016452239826321602, -0.016981162130832672, -0.044392284005880356, 0.015180973336100578, -0.012285823933780193, -0.0013849390670657158, -0.04717608168721199, -0.05007122829556465, 0.051258984953165054, 0.05266943946480751, -0.02065577358007431, -0.006764627061784267, -0.04435516521334648, 0.03696882352232933, 0.03360971063375473, -0.00781319011002779, 0.019004054367542267, -0.026483189314603806, -0.010068066418170929, -0.017547201365232468, -0.0017213145038112998, -0.007632243447005749, 0.01959793083369732, -0.0027675582095980644, -0.00016949264681898057, -0.0021771611645817757, 0.021361002698540688, 0.007052286062389612, -0.06220858544111252, 0.028951488435268402, -0.03489025682210922, -0.0035075843334198, -0.012341500259935856, -0.05181574076414108, -0.019560813903808594, 0.01647079922258854, -0.009205088950693607, -0.0282833781093359, 0.005711423698812723, -0.023662274703383446, -0.01196104846894741, 0.033869531005620956, 0.04602544382214546, -0.029471131041646004, -0.020637216046452522, -0.005098988302052021, -0.015245928429067135, 0.03531710430979729, 0.01860504411160946, -0.020934153348207474, 0.009845362044870853, 0.016415122896432877, 0.013009611517190933, -0.05441395193338394, -0.03162393346428871, -0.002260675188153982, 0.021862085908651352, 0.014002499170601368, -0.017983328551054, 0.010494914837181568, -0.01482835877686739, 0.0004442476201802492, -0.0067228698171675205, 0.04261065274477005, 0.034407731145620346, -0.013000331819057465, 0.026093456894159317, 0.097915418446064, -0.01935666799545288, 0.04572850465774536, -0.0036003775894641876, 0.00960410013794899, 0.027002831920981407, -0.012211590074002743, -0.03271889314055443, -0.002693323651328683, -0.04765860736370087, -0.00933499913662672, -0.004982996731996536, -0.00785030797123909, -0.0009435912361368537, 0.002017092891037464, 0.04353858530521393, -0.0008345591486431658, 0.047287434339523315, 0.01471700705587864, -0.005623269826173782, -0.013297270983457565, 0.00926076527684927, -0.02316119149327278, 0.04056920111179352, -0.006560481619089842, 0.01957937330007553, 0.03531710430979729, 0.016795575618743896, 0.06187452748417854, 0.03047329932451248, 0.026019223034381866, 0.05478512495756149, 0.015301604755222797, 0.05389431118965149, -0.017426569014787674, -0.027652384713292122, 0.0426848866045475, 0.02440462075173855, -0.0005358809139579535, -0.0429818257689476, 0.013659164309501648, -0.012759069912135601, -0.007558009121567011, 0.017862698063254356, 0.023643717169761658, -0.002156282775104046, 0.023755067959427834, 0.01586764305830002, -0.03101149946451187, 0.06974339485168457, -0.019171081483364105, -0.02399633079767227, -0.023216867819428444, -0.00729818781837821, 0.02629760280251503, -0.020841360092163086, 0.0022409565281122923, 0.03409223631024361, -0.01974640041589737, 0.03214357793331146, -0.009432432241737843, 0.003240803722292185, 0.010532031767070293, 0.0018616642337292433, -0.020915595814585686, -0.023884978145360947, -0.011135187931358814, 0.039901092648506165, -0.021991996094584465, 0.013863309286534786, -0.06788752973079681, -0.019764959812164307, -0.006982691120356321, -0.030770236626267433, -0.011330054141581059, 0.058199916034936905, 0.008931349031627178, -0.0422394797205925, 0.04862365499138832, -0.033795297145843506, -0.0037395674735307693, 0.02536967024207115, -0.004674459341913462, -0.004138578195124865, 0.021231092512607574, 0.004964438267052174, -0.00579493772238493, -0.020711449906229973, 0.0005063030985184014, -0.017510082572698593, -0.036541976034641266, 0.05845973640680313, -0.013510694727301598, 0.004178015515208244, 0.03849063441157341, -0.03401799872517586, 0.027151301503181458, -0.019468020647764206, -0.04687914252281189, 0.042944710701704025, 0.03409223631024361, 0.058496855199337006, -0.004565427079796791, -0.08262309432029724, -0.010903204791247845, 0.04613679647445679, 0.020395953208208084, -0.00729818781837821, 0.020989829674363136, -0.014800520613789558, 0.004625742789357901, -0.029304103925824165, -0.002568052848801017, -0.011784740723669529, 0.012118796817958355, -0.024571647867560387, -0.02102694660425186, 0.026743009686470032, -0.0001591983891557902, -0.018382340669631958, 0.01950513757765293, 0.002851072233170271, 0.012972494587302208, -0.005539756268262863, -0.022455962374806404, -0.001578644965775311, -0.000207624863833189, 0.010680501349270344, 0.009511306881904602, 0.013519974425435066, 0.04305605962872505, -0.009761848486959934, 0.08165805041790009, -0.010392841883003712, -0.056975048035383224, 0.013807632960379124, 0.007836388424038887, 0.03078879602253437, 0.008021974936127663, -0.037841081619262695, -0.05426548421382904, -0.017742065712809563, 0.014475744217634201, 0.01215591374784708, 0.02034027688205242, -0.0023453489411622286, -0.012777628377079964, -0.016507916152477264, 0.05615846440196037, 0.011051674373447895, 0.031438346952199936, -0.0036467742174863815, 0.03180951997637749, -0.03680179640650749, 0.0249984972178936, 0.011534199118614197, 0.019764959812164307, -0.0011181584559381008, 0.026037782430648804, 0.03377673774957657, -0.0280606746673584, -0.016415122896432877, -0.029935097321867943, 0.0036050172057002783, -0.018799910321831703, -0.0034890256356447935, 0.013584929518401623, -0.014095292426645756, 0.016637826338410378, 0.028172025457024574, 0.007437377702444792, -0.004133938811719418, 0.004936600103974342, 0.028710227459669113, 0.00911229569464922, 0.01307456661015749, -0.0012515487615019083, 0.032588984817266464, -0.029693834483623505, -0.014429348520934582, 0.0252954363822937, 0.013705560937523842, -0.03871333599090576, 0.023513805121183395, 0.04290759190917015, -0.038082342594861984, -0.007418819237500429, -0.07234160602092743, 0.021323885768651962, 0.04918041452765465, 0.03561404347419739, -0.03787820041179657, -0.018159635365009308, -0.007418819237500429, 0.009348918683826923, -0.021546589210629463, 0.009441711939871311, -0.008889592252671719, -0.04324164614081383, -0.00035754393320530653, 0.006128993351012468, -0.00731674674898386, 0.021064063534140587, 0.012786908075213432, -0.029025724157691002, -0.011868255212903023, 0.0040365057066082954, -0.025035614147782326, 0.004978356882929802, -0.02796788141131401, -0.015533587895333767, 0.034333497285842896, -0.046693556010723114, -0.03333133086562157, -0.016721341758966446, 0.06766482442617416, -0.04810401424765587, -0.010624825023114681, 0.0058877309784293175, 0.007525531575083733, -0.012814746238291264, -0.018567927181720734, 0.01721314527094364, -0.0067414287477731705, -0.034036558121442795, -0.01112590916454792, -0.007437377702444792, 0.06632860749959946, -0.003055217210203409, 0.0011320774210616946, 0.01943090371787548, 0.03416647017002106, -0.007372422609478235, -0.018029725179076195, -0.03539133816957474, 0.002290833042934537, 0.01982063427567482, -0.0020089736208319664, -0.08091570436954498, -0.03583674877882004, 0.028840137645602226, 0.007655441761016846, -0.0021841207053512335, -0.015338721685111523, 0.016888368874788284, 0.018957657739520073, 0.003547021420672536, -0.034500524401664734, -0.015385118313133717, -0.07661009579896927, -0.034407731145620346, -0.010411401279270649, -0.03889892250299454, -0.01166410930454731, 0.02729976922273636, -0.0022131185978651047, 0.0212682094424963, -0.007590486668050289, -0.019171081483364105, -0.03318285942077637, 0.010318608023226261, 0.014846917241811752, 0.00043061861651949584, -0.01368700247257948, 0.05092492699623108, -0.01562638022005558, -0.025128407403826714, -0.02293848805129528, -0.011413567699491978, -0.046767789870500565, 0.0017920694081112742, 0.02874734438955784, -0.017435848712921143, -0.005651107989251614, 0.018883423879742622, -0.0063795349560678005, -0.009098377078771591, 0.0035331023391336203, 0.023606598377227783, -0.02431182749569416, -0.015004666522145271, -0.05497071146965027, -0.005678946152329445, -0.02041451260447502, -0.00007064609962981194, -0.002804675605148077, 0.00838386919349432, -0.029619600623846054, 0.04595120996236801, -0.026316162198781967, -0.02173217572271824, -0.027578148990869522, 0.04094037413597107, -0.016480078920722008, 0.004254569765180349, 0.04780707508325577, -0.03218069300055504, -0.017203865572810173, -0.039381448179483414, -0.045468684285879135, -0.027726618573069572, 0.024497414007782936, -0.0107825743034482, 0.002112206071615219, -0.046990495175123215, 0.0036908509209752083, 0.03923298045992851, -0.01170122716575861, 0.0007435057777911425, 0.008165804669260979, -0.032125018537044525, 0.018159635365009308, 0.04108884558081627, 0.008077651262283325, 0.033275652676820755, 0.024757234379649162, -0.012146634049713612, -0.03604089096188545, -0.02232605218887329, -0.0017793102888390422, -0.047287434339523315, -0.0010822011390700936, 0.02698427252471447, -0.03026915341615677, 0.047138962894678116, 0.015013945288956165, 0.019226757809519768, 0.018549367785453796, 0.015180973336100578, 0.04932888224720955, -0.026501748710870743, 0.008189002983272076, -0.03630071505904198, -0.027726618573069572, -0.01738017238676548, -0.0217136163264513, -0.02293848805129528, -0.016340889036655426, 0.05600999668240547, 0.03941856697201729, -0.049885641783475876, 0.024831470102071762, -0.016108905896544456, -0.009024142287671566, -0.012146634049713612, 0.04197965934872627, -0.02600066363811493, -0.0024335025809705257, -0.006365615874528885, -0.015765570104122162, -0.005757820326834917, -0.052112679928541183, 0.033201418817043304, 0.05868244171142578, 0.015412956476211548, -0.015914039686322212, 0.019560813903808594, -0.03049185685813427, 0.04918041452765465, -0.0082632377743721, 0.015821246430277824, -0.012100237421691418, -0.03604089096188545, -0.02110118232667446, -0.0027675582095980644, 0.02303128130733967, 0.008244679309427738, -0.03180951997637749, -0.038305047899484634, -0.04168272018432617, -0.001127437804825604, 0.012332220561802387, 0.03561404347419739, 0.016043949872255325, -0.052409619092941284, 0.007265710271894932, -0.0024381421972066164, -0.02026604302227497, -0.007423458620905876, 0.018465854227542877, -0.026891479268670082, 0.003609656821936369, 0.00869008619338274, 0.04810401424765587, -0.01950513757765293, 0.04550580307841301, 0.018781350925564766, 0.01599755324423313, -0.010188696905970573, 0.019041171297430992, 0.007223953492939472, -0.05356025695800781, 0.058274149894714355, 0.05214979872107506, 0.009854641743004322, 0.015589263290166855, -0.02514696680009365, 0.004512071143835783, 0.011404288932681084, -0.0428333580493927, -0.00044279772555455565, -0.042573537677526474, -0.01891126111149788, 0.02887725457549095 ]
Graphical structures estimated by causal learning algorithms from time series data can provide highly misleading causal information if the causal timescale of the generating process fails to match the measurement timescale of the data. Although this problem has been recently recognized, practitioners have limited resources to respond to it, and so must continue using models that they know are likely misleading. Existing methods either (a) require that the difference between causal and measurement timescales is known; or (b) can handle only very small number of random variables when the timescale difference is unknown; or (c) apply to only pairs of variables, though with fewer assumptions about prior knowledge; or (d) return impractically too many solutions. This paper addresses all four challenges. We combine constraint programming with both theoretical insights into the problem structure and prior information about admissible causal interactions. The resulting system provides a practical approach that scales to significantly larger sets (>100) of random variables, does not require precise knowledge of the timescale difference, supports edge misidentification and parametric connection strengths, and can provide the optimum choice among many possible solutions. The cumulative impact of these improvements is gain of multiple orders of magnitude in speed and informativeness.
[ 0.004403489641845226, -0.04275251924991608, -0.04047717526555061, 0.003510317299515009, 0.026525724679231644, 0.011935577727854252, -0.05237283557653427, 0.02844180352985859, -0.043910153210163116, 0.015847573056817055, 0.052811939269304276, 0.010024487972259521, 0.045466966927051544, 0.004291219636797905, 0.011596271768212318, 0.00761940935626626, 0.018562018871307373, 0.0022790865041315556, 0.03676477447152138, 0.026166459545493126, -0.01301337219774723, 0.0342499203979969, -0.003762301756069064, 0.05604531988501549, 0.04941888153553009, 0.02959943376481533, -0.0071054608561098576, -0.023751400411128998, -0.08310994505882263, 0.02784302830696106, 0.03704420104622841, 0.04766247421503067, -0.042832355946302414, -0.01744430512189865, -0.02630617283284664, -0.02073756791651249, -0.027763191610574722, 0.03902015835046768, -0.03165522962808609, 0.043710559606552124, -0.016476286575198174, 0.04538713023066521, -0.021196627989411354, -0.046345170587301254, 0.01319300476461649, -0.021715566515922546, -0.0455867201089859, -0.0078389598056674, -0.013761840760707855, -0.0023239946458488703, 0.014859594404697418, -0.04091627895832062, 0.03860101476311684, -0.002704466227442026, -0.01748422347009182, 0.0010260256240144372, 0.002572236815467477, 0.009959621354937553, 0.08941704034805298, 0.05652434006333351, 0.0013796769781038165, 0.0445089265704155, -0.07388880848884583, 0.009435692802071571, 0.026146499440073967, -0.058160994201898575, -0.04886002466082573, 0.022753441706299782, 0.02636605128645897, -0.04083644226193428, -0.01810295879840851, -0.009869804605841637, 0.004812652710825205, -0.004515760112553835, 0.052253082394599915, 0.0033256951719522476, 0.015188921242952347, -0.011596271768212318, -0.018292570486664772, -0.024190502241253853, 0.02165568806231022, 0.07476701587438583, -0.02842184342443943, 0.013572229072451591, 0.035068243741989136, -0.08550503849983215, 0.010957579128444195, -0.04231341928243637, 0.050736185163259506, -0.005179401952773333, -0.014699921011924744, -0.01898116059601307, 0.00010236866364721209, -0.00016746982873883098, -0.0455867201089859, -0.023531850427389145, 0.009091397747397423, 0.02101699635386467, -0.0543687529861927, -0.004193918313831091, 0.01652618497610092, -0.017883406952023506, -0.008602398447692394, -0.011546374298632145, -0.008337939158082008, -0.044868193566799164, -0.0627116784453392, 0.022873196750879288, 0.0402376651763916, 0.18346460163593292, 0.01392151415348053, 0.036525264382362366, 0.013312759809195995, -0.020518016070127487, -0.07592464238405228, -0.013901554979383945, -0.0384213849902153, -0.06830024719238281, 0.048381004482507706, -0.03438963368535042, 0.008532540872693062, 0.12119202315807343, 0.007454746402800083, -0.006561574060469866, -0.06574547290802002, 0.04021770879626274, -0.00211691833101213, -0.019589915871620178, 0.010119293816387653, -0.006057605147361755, -0.034509386867284775, 0.025867071002721786, -0.008951683528721333, -0.012454516254365444, 0.014809696935117245, -0.019909262657165527, 0.03668493777513504, 0.038880445063114166, 0.01572781801223755, -0.04227350279688835, 0.0007490921998396516, -0.040058035403490067, -0.016995225101709366, -0.06075568497180939, 0.013662044890224934, -0.01779359206557274, -0.029719188809394836, 0.07265134155750275, -0.03075706586241722, 0.027962783351540565, -0.04315170273184776, 0.004186433739960194, -0.00022485241061076522, 0.06047625467181206, 0.04359080642461777, -0.01156633347272873, -0.05021724849939346, 0.0072850934229791164, 0.03023812733590603, -0.025408010929822922, 0.04327145963907242, -0.021994994953274727, -0.00871716346591711, 0.011187109164893627, 0.020238587632775307, 0.014210921712219715, -0.022134708240628242, -0.03848126158118248, -0.02898070029914379, 0.03664501756429672, 0.05388973280787468, 0.01068812981247902, 0.0015605568187311292, 0.029799025505781174, 0.049019698053598404, 0.020198669284582138, 0.018142877146601677, 0.028621435165405273, -0.009979580529034138, 0.031495556235313416, -0.03971872851252556, -0.04379039630293846, 0.007090491708368063, 0.004034245386719704, 0.0639890655875206, -0.006057605147361755, 0.08207206428050995, 0.016226796433329582, 0.03546742722392082, 0.009271030314266682, 0.02516850084066391, 0.04029754549264908, 0.04057697206735611, 0.007464725989848375, -0.020238587632775307, -0.030038535594940186, -0.053131286054849625, 0.022094789892435074, -0.029659312218427658, 0.02778315171599388, -0.025986826047301292, -0.008023582398891449, -0.008876836858689785, -0.017354490235447884, 0.04610566049814224, 0.01078792568296194, 0.05656426027417183, -0.0037847557105123997, 0.016765695065259933, -0.038002241402864456, -0.03311224654316902, 0.04379039630293846, 0.007150369230657816, -0.057282790541648865, 0.0012936030980199575, -0.035108163952827454, 0.04051709547638893, 0.029399842023849487, -0.03554726392030716, -0.03580673411488533, 0.018462223932147026, 0.008732132613658905, 0.041515052318573, -0.041036032140254974, 0.02928008697926998, 0.057562217116355896, -0.019410282373428345, -0.009216141887009144, 0.03730367124080658, 0.021076872944831848, 0.014699921011924744, -0.009360846132040024, -0.018312528729438782, -0.008512581698596478, -0.01926058903336525, 0.018442263826727867, 0.024509849026799202, -0.02458968572318554, 0.019779527559876442, -0.06347013264894485, -0.00009854835661826655, -0.041515052318573, 0.0019821941386908293, -0.010837824083864689, 0.012494434602558613, -0.022134708240628242, 0.038640934973955154, 0.026405969634652138, 0.05887952074408531, 0.017344510182738304, -0.021096833050251007, -0.020877281203866005, 0.03672485426068306, 0.026865029707551003, -0.047542721033096313, 0.0408763587474823, -0.016166919842362404, -0.03618595749139786, -0.0074148280546069145, 0.014250840060412884, 0.006087543908506632, 0.004628030117601156, -0.022573810070753098, 0.016077103093266487, -0.03872077167034149, 0.002337716519832611, 0.019060997292399406, -0.02606666274368763, 0.028282130137085915, 0.01746426522731781, 0.00975503958761692, 0.007359940093010664, 0.03812199458479881, -0.000687967287376523, 0.004982305224984884, -0.05856017395853996, 0.03107641264796257, 0.03131592273712158, 0.02423042058944702, 0.035527303814888, -0.013242903165519238, 0.05121520534157753, -0.019639814272522926, 0.06135445833206177, 0.045466966927051544, 0.021955076605081558, 0.012195046991109848, -0.014829656109213829, -0.06426849216222763, -0.027902906760573387, -0.008327959105372429, 0.027144458144903183, -0.04255292937159538, 0.02961939387023449, -0.01393149420619011, -0.027483763173222542, -0.03275298327207565, -0.005037193186581135, 0.021176669746637344, -0.02365160547196865, -0.059119030833244324, -0.017633918672800064, 0.035906530916690826, 0.0207575261592865, -0.022434096783399582, 0.01836242713034153, 0.06706278026103973, 0.07508636265993118, 0.0233322586864233, -0.030697187408804893, -0.026445887982845306, -0.028880905359983444, 0.011496475897729397, -0.007599450182169676, -0.012474475428462029, 0.004558173008263111, 0.018172815442085266, -0.05600540339946747, -0.06554587930440903, -0.02045813947916031, 0.008727142587304115, -0.034529346972703934, -0.1144857406616211, -0.01152641512453556, 0.046065740287303925, 0.038361504673957825, -0.019190732389688492, -0.0064817373640835285, -0.001123326481319964, 0.009380805306136608, -0.03796232119202614, 0.040716685354709625, -0.04538713023066521, 0.04766247421503067, -0.0231127068400383, -0.02425037883222103, -0.005079606082290411, 0.008846897631883621, -0.06414873898029327, -0.0015667941188439727, -0.02073756791651249, 0.0207575261592865, 0.0010409948881715536, -0.025906989350914955, 0.017903367057442665, 0.0001776053395587951, -0.029699230566620827, -0.006262186449021101, 0.024749359115958214, -0.028042620047926903, 0.0011788378469645977, -0.04682419076561928, 0.03195461630821228, 0.02488907240331173, 0.08051525056362152, -0.023611687123775482, 0.0034703989513218403, 0.007993643172085285, 0.008722152560949326, -0.007998633198440075, 0.047223374247550964, -0.04977814480662346, -0.043910153210163116, 0.07780080288648605, -0.06530637294054031, 0.022913115099072456, -0.006711267400532961, -0.027144458144903183, -0.03203445300459862, 0.004889994394034147, 0.01713493838906288, 0.04351096972823143, 0.030298005789518356, 0.01360216736793518, -0.012264903634786606, 0.03730367124080658, 0.02251393347978592, 0.02604670450091362, -0.030557474121451378, 0.02221454493701458, -0.07760121673345566, 0.038640934973955154, 0.027064621448516846, 0.005408932454884052, 0.019400304183363914, 0.0037049190141260624, -0.007145379204303026, 0.01626671478152275, 0.025926949456334114, 0.055486466735601425, 0.013183025643229485, -0.06003715470433235, 0.0019435231806710362, -0.07177314162254333, 0.004014286212623119, -0.017823530361056328, 0.030078453943133354, -0.01951007917523384, 0.052851855754852295, 0.019350405782461166, -0.0024325225967913866, 0.0078389598056674, 0.005364024080336094, 0.0030836903024464846, 0.0030013585928827524, 0.05776181071996689, -0.009590376168489456, -0.013961432501673698, 0.017224755138158798, 0.044229499995708466, -0.0018936253618448973, 0.003328189952298999, 0.009096386842429638, -0.02187523990869522, 0.003278292017057538, 0.026266254484653473, -0.025527765974402428, -0.02369152382016182, 0.046943943947553635, -0.045466966927051544, -0.04590606689453125, -0.01752414181828499, 0.0522131621837616, -0.025527765974402428, -0.0015717839123681188, 0.043071866035461426, 0.017534121870994568, -0.01051847729831934, -0.027643436565995216, 0.014699921011924744, 0.07959713041782379, 0.06578539311885834, -0.028202293440699577, -0.01438057515770197, 0.009425713680684566, 0.013951453380286694, -0.01656610332429409, -0.008233153261244297, -0.017594000324606895, -0.04347104951739311, -0.027383968234062195, -0.05089585855603218, 0.01006440632045269, 0.03341163322329521, 0.024190502241253853, -0.03351143002510071, -0.04590606689453125, -0.009011561051011086, 0.008387836627662182, -0.04554680362343788, -0.07484684884548187, 0.053131286054849625, -0.0462254136800766, -0.01868177391588688, 0.03105645254254341, 0.012374679557979107, -0.00702562415972352, -0.054967526346445084, -0.02008889429271221, -0.02872123196721077, 0.016685858368873596, 0.04498794674873352, 0.010508498176932335, -0.07899835705757141, -0.0021643214859068394, 0.060196828097105026, -0.06498702615499496, 0.018512120470404625, 0.00989475380629301, 0.041355378925800323, 0.017274653539061546, -0.043111786246299744, -0.07568513602018356, -0.003879561787471175, -0.018232692033052444, 0.015807654708623886, 0.024050787091255188, -0.05648442357778549, 0.02698478475213051, -0.06123470142483711, 0.03602628409862518, 0.02778315171599388, 0.013672024942934513, 0.0048850043676793575, -0.051973652094602585, 0.03486865386366844, 0.008337939158082008, 0.03995823860168457, -0.009141295216977596, -0.011237007565796375, -0.027364008128643036, 0.0006284016999416053, 0.0078389598056674, 0.029439760372042656, 0.032673146575689316, 0.04179448261857033, -0.05025716498494148, -0.05097569525241852, 0.0010441135382279754, -0.002136877505108714, 0.021436138078570366, 0.016366511583328247, -0.0023052829783409834, 0.008956673555076122, 0.03820183128118515, -0.0425928458571434, 0.010368783958256245, -0.025847112759947777, 0.010728048160672188, -0.0620729885995388, -0.009779988788068295, 0.024410052224993706, -0.026645477861166, -0.014131085015833378, 0.02812245674431324, -0.012913576327264309, -0.03904011845588684, -0.0310364942997694, 0.005453840363770723, 0.03219412639737129, 0.02157585136592388, -0.03259330987930298, -0.026186417788267136, 0.0130532905459404, -0.06993689388036728, 0.06151413172483444, 0.016057144850492477, -0.014220901764929295, 0.05321112275123596, -0.03341163322329521, 0.016745734959840775, 0.03494849056005478, -0.0367048941552639, -0.05652434006333351, -0.02401086874306202, -0.055526383221149445, 0.05325103923678398, 0.0622725784778595, -0.04319162294268608, -0.004989790264517069, -0.010498518124222755, 0.05337079241871834, 0.013312759809195995, 0.05213332548737526, -0.0013547280104830861, 0.004917438142001629, 0.0006181102362461388, 0.028601476922631264, 0.021196627989411354, -0.019639814272522926, -0.0009549210662953556, 0.024070747196674347, -0.0060675847344100475, -0.025028787553310394, -0.005882962606847286, 0.005498748738318682, 0.009320927783846855, -0.0310364942997694, -0.01184576191008091, -0.003123608650639653, 0.048979777842760086, 0.04211382940411568, 0.030437719076871872, 0.00992968212813139, -0.012135169468820095, 0.008911765180528164, 0.024809235706925392, 0.03295257315039635, -0.010278967209160328, 0.023511890321969986, -0.03576681390404701, 0.0155182471498847, -0.025248337537050247, -0.006122472230345011, -0.005683370865881443, 0.011436598375439644, 0.013691984117031097, -0.040117911994457245, -0.05277201905846596, 0.01333271898329258, -0.005768197122961283, -0.02486911416053772, 0.026545682922005653, 0.018312528729438782, -0.010997497476637363, -0.011296885088086128, -0.039219748228788376, -0.058799684047698975, -0.022314341738820076, 0.01748422347009182, -0.05680377036333084, 0.02125650644302368, -0.004675433039665222, 0.0028890883550047874, -0.0007179060485213995, 0.013282821513712406, -0.012085271067917347, -0.028821026906371117, 0.004954861477017403, -0.017933305352926254, 0.04263276606798172, -0.0018237682525068521, -0.02159581147134304, 0.003807209897786379, -0.042153745889663696, -0.0014445441775023937, -0.009206162765622139, 0.006007707212120295, 0.003747332375496626, 0.029100455343723297, 0.004226352088153362, -0.03640550747513771, 0.014141065068542957, -0.0627116784453392, 0.03279289975762367, -0.0384213849902153, 0.011865721084177494, -0.008357898332178593, -0.019939200952649117, -0.01713493838906288, 0.05891944095492363, -0.01111725252121687, 0.04462868347764015, -0.026884987950325012, -0.0005735139711759984, 0.02245405502617359, -0.0021880229469388723, 0.004034245386719704, -0.0077042356133461, -0.05883960425853729, 0.008986611850559711, -0.004139030817896128, -0.01899114064872265, -0.03289269655942917, 0.01662597991526127, 0.006965747103095055, -0.018721692264080048, 0.06426849216222763, 0.009545468725264072, 0.03880060836672783, -0.024370133876800537, 0.008417775854468346, -0.02281332015991211, 0.0308169424533844, -0.0006115611176937819, 0.002019617473706603, 0.005718299187719822, 0.030697187408804893, 0.05365022271871567, 0.032772939652204514, 0.01125696673989296, 0.06382939219474792, 0.06015690788626671, 0.05919886752963066, 0.016516204923391342, -0.015019267797470093, 0.04522745683789253, -0.006192329339683056, -0.010957579128444195, 0.02369152382016182, -0.022354260087013245, 0.020288486033678055, 0.004667948465794325, 0.01953003741800785, 0.021555893123149872, -0.015318655408918858, 0.04239325597882271, 0.01748422347009182, 0.005339075345546007, 0.04446901008486748, -0.013312759809195995, -0.039179831743240356, -0.015318655408918858, 0.02283327840268612, 0.01571783795952797, -0.030118372291326523, -0.009939662180840969, 0.014141065068542957, -0.02630617283284664, 0.006736216600984335, -0.030577434226870537, -0.003510317299515009, 0.010728048160672188, -0.009156264364719391, -0.001326036755926907, 0.002316510071977973, -0.017354490235447884, -0.012474475428462029, 0.0038995209615677595, 0.00726014468818903, 0.027982741594314575, -0.006391921080648899, 0.030038535594940186, 0.012913576327264309, -0.011626210995018482, 0.006426849402487278, -0.035128120332956314, 0.012773862108588219, 0.05369013920426369, -0.006731226574629545, -0.006366971880197525, 0.05353046581149101, -0.004837601445615292, 0.03792240470647812, -0.0034229960292577744, -0.011366741731762886, 0.013432514853775501, 0.0010802895994856954, -0.020009057596325874, -0.0473032109439373, 0.0054837791249156, 0.06167380511760712, -0.011875700205564499, -0.006636420730501413, 0.025348132476210594, 0.010588334873318672, 0.04650484398007393, 0.01496937032788992, -0.01156633347272873, 0.014121105894446373, 0.02578723430633545, -0.024948950856924057, 0.04075660556554794, -0.03131592273712158, -0.01467996183782816, 0.004136535804718733, 0.06331045925617218, 0.014420493505895138, 0.004770239349454641, -0.014101146720349789, 0.004593101795762777, -0.03405032679438591, 0.03522791713476181, 0.013662044890224934, -0.0015144012868404388, -0.006681328639388084, -0.001287365797907114, 0.0296393521130085, -0.000818325555883348, -0.005154453217983246, 0.0121451485902071, -0.018472202122211456, 0.008497612550854683, -0.006047625560313463, -0.009251071140170097, 0.013103188946843147, -0.022114749997854233, 0.006696298252791166, 0.013971412554383278, 0.01721477508544922, 0.029559515416622162, -0.007973684929311275, 0.014400534331798553, 0.0017152403015643358, -0.03353139013051987, 0.0019060998456552625, 0.013033331371843815, 0.004588111769407988, -0.0033207053784281015, 0.012903597205877304, 0.021456096321344376, 0.029699230566620827, 0.02367156371474266, -0.015817634761333466, 0.06374955922365189, 0.008332949131727219, -0.06670351326465607, 0.011855741031467915, 0.042832355946302414, -0.04143521562218666, 0.011217048391699791, 0.027344049885869026, 0.033591266721487045, -0.03345155343413353, 0.007634378969669342, 0.013851657509803772, 0.0031959605403244495, 0.013073249720036983, -0.027723273262381554, 0.026705356314778328, 0.0002866010763682425, -0.031256046146154404, -0.03383077681064606, 0.06307094544172287, 0.041315462440252304, 0.027443844825029373, -0.04434925317764282, -0.013791779987514019, 0.026286214590072632, 0.020897241309285164, 0.005129504017531872, -0.04410974308848381, 0.03207436949014664, -0.059039194136857986, 0.016097063198685646, -0.031176207587122917, -0.06239233538508415, -0.023152625188231468, 0.0061873397789895535, 0.005179401952773333, 0.005503738299012184, -0.028481721878051758, -0.02608662284910679, 0.005718299187719822, 0.025667479261755943, -0.051095448434352875, -0.010728048160672188, -0.05009749159216881, 0.007549552246928215, -0.014460411854088306, 0.023192543536424637, 0.024749359115958214, 0.023032870143651962, -0.04061689227819443, 0.01804308034479618, -0.01983940601348877, -0.034489430487155914, 0.027603518217802048, -0.029379883781075478, -0.0017913345945999026, -0.017554081976413727, -0.06470759958028793, 0.023292340338230133, -0.050137411803007126, -0.024789277464151382, -0.0331721231341362, 0.017603978514671326, 0.017294611781835556, 0.05656426027417183, -0.013911535032093525, 0.008662275038659573, 0.056444503366947174, -0.04379039630293846, 0.03546742722392082, -0.015877511352300644, 0.024410052224993706, -0.02247401513159275, -0.02510862424969673, 0.03790244460105896, 0.02544792927801609, 0.007644358556717634, -0.0017713754205033183, -0.022613728418946266, 0.010757987387478352, 0.021196627989411354, 0.021975034847855568, -0.003467904170975089, 0.014570186845958233, -0.008642316795885563, -0.022414136677980423, 0.012374679557979107, -0.023731442168354988, -0.022713523358106613, 0.0030063483864068985, -0.020068936049938202, 0.010278967209160328, 0.05001765489578247, -0.0020819897763431072, 0.000992968212813139, -0.04650484398007393, 0.035367630422115326, -0.01509910449385643, 0.02137625962495804, -0.0391598716378212, 0.013252882286906242, 0.02313266694545746, 0.0028516650199890137, -0.05365022271871567, -0.0014782253419980407, -0.018881365656852722, -0.023731442168354988, 0.03516804054379463, -0.03259330987930298, 0.0212964229285717, 0.02337217703461647, 0.015398492105305195, 0.026765232905745506, -0.027982741594314575, -0.037443384528160095, -0.011087313294410706, 0.030996575951576233, -0.001196302124299109, 0.05333087593317032, 0.014630064368247986, 0.015069166198372841, -0.017663856968283653, -0.00489498395472765, -0.011406660079956055, -0.017933305352926254, -0.01627669483423233, -0.02043817937374115, 0.010987517423927784, -0.029479678720235825, 0.012394638732075691, -0.005738258361816406, 0.015009288676083088, -0.03854113817214966, -0.008936714380979538, 0.02816237509250641, -0.015358573757112026, -0.023831237107515335, -0.052851855754852295, 0.02187523990869522, 0.007629388943314552, 0.0013347688363865018, -0.047822147607803345, 0.026186417788267136, -0.005149463191628456, 0.02572735771536827, 0.002849170006811619, -0.003161031985655427, 0.021136751398444176, 0.0005407684948295355, -0.03249351307749748, 0.02157585136592388, -0.0174942035228014, -0.039239708334207535, -0.02490903250873089, -0.021096833050251007, -0.01079790573567152, -0.0012050343211740255, 0.023891115561127663, 0.03281285986304283, 0.030677229166030884, -0.02395099215209484, -0.002577226608991623, 0.02365160547196865, -0.0070356037467718124, 0.04239325597882271, 0.038660891354084015, -0.04095619544386864, 0.02191515825688839, 0.057562217116355896, -0.020258547738194466, 0.02367156371474266, -0.011885680258274078, -0.024150583893060684, -0.027044661343097687, 0.012065311893820763, 0.005224310327321291, -0.05748238041996956, -0.024749359115958214, 0.017234735190868378, -0.004001811612397432, -0.01007438637316227, 0.021396219730377197, 0.04646492376923561, 0.026465846225619316, -0.032154206186532974, -0.010757987387478352, 0.0015019268030300736, 0.024110665544867516, 0.041954156011343, -0.003046266734600067, -0.013801759108901024, -0.006611471995711327, -0.009385795332491398, 0.02542796917259693, -0.02812245674431324, 0.014560207724571228, 0.0110773341730237, 0.019100915640592575, 0.001964729744940996, -0.015009288676083088, -0.022553851827979088, 0.0373435877263546, 0.02015875093638897, -0.039798565208911896, -0.029120415449142456, 0.004029255360364914, 0.031535472720861435, -0.005947829689830542, -0.004568152595311403, 0.007918796502053738, 0.06522653251886368, 0.00351281207986176, 0.011356761679053307, 0.015318655408918858, -0.008073479868471622, -0.034150123596191406, -0.014220901764929295, -0.00013277519610710442, -0.008507591672241688, -0.019589915871620178, 0.02399091050028801, -0.009535488672554493, 0.0402376651763916, -0.011775904335081577, 0.02337217703461647, 0.006621451582759619, -0.002749374369159341, 0.01688545010983944, 0.0556461401283741, -0.025527765974402428, -0.02814241498708725, 0.02576727606356144, -0.022972993552684784, -0.004346107132732868, 0.041355378925800323, 0.007110450882464647, 0.0007877630996517837, -0.017883406952023506, -0.006356992293149233, 0.009869804605841637, 0.059079114347696304, -0.010678150691092014, 0.02874119020998478, 0.008103419095277786, -0.009191193617880344, 0.003974367864429951, -0.012983433902263641, -0.016117021441459656, -0.025587642565369606, 0.0012462000595405698, -0.038301628082990646, 0.029120415449142456, -0.0014470390742644668, 0.020797444507479668, 0.017234735190868378, -0.0732102021574974, 0.007444766815751791, -0.05840050429105759, -0.011726006865501404, -0.0492192879319191 ]
Graph embedding methods including traditional shallow models and deep Graph Neural Networks (GNNs) have led to promising applications in recommendation. Nevertheless, shallow models especially random-walk-based algorithms fail to adequately exploit neighbor proximity in sampled subgraphs or sequences due to their optimization paradigm. GNN-based algorithms suffer from the insufficient utilization of high-order information and easily cause over-smoothing problems when stacking too much layers, which may deteriorate the recommendations of low-degree (long-tail) items, limiting the expressiveness and scalability. In this paper, we propose a novel framework SAC, namely Spatial Autoregressive Coding, to solve the above problems in a unified way. To adequately leverage neighbor proximity and high-order information, we design a novel spatial autoregressive paradigm. Specifically, we first randomly mask multi-hop neighbors and embed the target node by integrating all other surrounding neighbors with an explicit multi-hop attention. Then we reinforce the model to learn a neighbor-predictive coding for the target node by contrasting the coding and the masked neighbors' embedding, equipped with a new hard negative sampling strategy. To learn the minimal sufficient representation for the target-to-neighbor prediction task and remove the redundancy of neighbors, we devise Neighbor Information Bottleneck by maximizing the mutual information between target predictive coding and the masked neighbors' embedding, and simultaneously constraining those between the coding and surrounding neighbors' embedding. Experimental results on both public recommendation datasets and a real scenario web-scale dataset Douyin-Friend-Recommendation demonstrate the superiority of SAC compared with state-of-the-art methods.
[ 0.02865845151245594, 0.0202863197773695, -0.03664078935980797, -0.026811160147190094, -0.009846576489508152, -0.01867629401385784, 0.008562793023884296, 0.0013526331167668104, -0.043419841676950455, -0.006156228482723236, -0.035928986966609955, -0.0006794942892156541, -0.004825839307159185, -0.03847113251686096, -0.02691284567117691, 0.02665862999856472, 0.029387200251221657, -0.0025802776217460632, -0.0005767492111772299, -0.05389348044991493, 0.01567656360566616, -0.05941841006278992, 0.01371063757687807, 0.029421094805002213, 0.08311120420694351, 0.01928640902042389, -0.002893808763474226, 0.008668715134263039, -0.06531618535518646, 0.060842011123895645, 0.012905624695122242, -0.003603491000831127, 0.012032820843160152, -0.0038047442212700844, 0.0010692898649722338, 0.02447238564491272, 0.062468983232975006, 0.052910517901182175, 0.01348184421658516, 0.006385021843016148, 0.02104896306991577, 0.03752206638455391, -0.015761300921440125, 0.021201491355895996, 0.02098117209970951, -0.03894566744565964, 0.0043385946191847324, -0.02359110862016678, -0.005330031272023916, -0.05941841006278992, 0.025302819907665253, 0.0029298225417733192, -0.01798144169151783, 0.0005677457666024566, -0.026692526414990425, 0.057350799441337585, 0.02154044434428215, -0.008609399199485779, 0.003957272972911596, 0.021709920838475227, -0.02598072588443756, 0.01772722601890564, -0.07246808707714081, 0.017557749524712563, 0.016210412606596947, -0.031505655497312546, 0.03965746611356735, 0.024014798924326897, 0.05575772002339363, -0.04138612747192383, -0.06104538217186928, 0.015481664799153805, 0.0177950169891119, -0.025387557223439217, 0.00494870962575078, 0.07341715693473816, 0.029641414061188698, 0.027760226279497147, 0.009431359358131886, 0.008668715134263039, 0.05833376199007034, 0.023574160411953926, -0.01909998431801796, 0.048605818301439285, 0.04131833463907242, -0.019388094544410706, 0.03470875695347786, -0.048232968896627426, 0.005825749598443508, 0.016261255368590355, -0.04758895933628082, 0.012117559090256691, -0.012312456965446472, -0.03364105522632599, -0.0045080711133778095, 0.022506460547447205, 0.014252961613237858, -0.01148202270269394, -0.06087590754032135, 0.06690926849842072, -0.027387378737330437, -0.028810979798436165, -0.026489153504371643, -0.023387737572193146, 0.008202655240893364, -0.04209792613983154, -0.02098117209970951, 0.050300583243370056, -0.029692256823182106, 0.10636336356401443, 0.021743817254900932, 0.011575235053896904, -0.01308357436209917, 0.006435864605009556, -0.05626615136861801, 0.005580008961260319, -0.06592629849910736, -0.0052071609534323215, -0.0019924063235521317, -0.061214860528707504, 0.013058152981102467, -0.003756019752472639, -0.03586119785904884, -0.05643562600016594, -0.02179466001689434, 0.05582551285624504, -0.025319768115878105, -0.014515649527311325, -0.027234850451350212, 0.04033537209033966, -0.002626883564516902, 0.01891356147825718, 0.013668267987668514, -0.05036837235093117, -0.004554676823318005, 0.005664747208356857, 0.023302998393774033, 0.017184901982545853, -0.02933635748922825, -0.03291230648756027, -0.01986262947320938, 0.008266209624707699, -0.028556765988469124, -0.014439385384321213, 0.02970920503139496, 0.03284451737999916, 0.003647978650406003, 0.06535008549690247, -0.08189097791910172, 0.038674503564834595, -0.051351334899663925, 0.017371326684951782, -0.013100522570312023, 0.05541876703500748, 0.0038725347258150578, 0.03775933012366295, -0.044809550046920776, -0.005982515402138233, 0.040233686566352844, -0.018439026549458504, 0.07545087486505508, -0.03514939546585083, -0.007613725028932095, 0.08446701616048813, -0.019777890294790268, 0.039182934910058975, 0.015964671969413757, -0.0029298225417733192, -0.06450270116329193, 0.03908124566078186, 0.01572740636765957, 0.038301657885313034, -0.039996419101953506, 0.043114785104990005, 0.013456422835588455, 0.005118186119943857, 0.06192665919661522, -0.08202655613422394, -0.04287751764059067, 0.052978307008743286, -0.05911335349082947, 0.0007403998170047998, 0.041420020163059235, 0.02203192561864853, 0.002626883564516902, 0.01793059892952442, 0.06650251895189285, 0.008829718455672264, 0.006817186251282692, 0.004563150927424431, 0.0355900339782238, 0.009236461482942104, 0.02360805682837963, -0.009668625891208649, -0.008812770247459412, -0.02909909002482891, -0.030370162799954414, -0.0048724450170993805, 0.008558555506169796, 0.01473596878349781, -0.06934972107410431, -0.024489333853125572, 0.05108017474412918, 0.017947545275092125, 0.03053963929414749, -0.005800328217446804, 0.01288867648690939, -0.02742127515375614, -0.005558824632316828, -0.025573981925845146, 0.008380605839192867, -0.039996419101953506, -0.09043258428573608, -0.01872713677585125, 0.009329672902822495, 0.00007063721568556502, 0.007300193887203932, 0.013490318320691586, 0.001211755909025669, 0.0033217365853488445, 0.008011994883418083, 0.028183918446302414, 0.08643294125795364, 0.017176428809762, 0.02035411074757576, -0.0048724450170993805, 0.012498880736529827, -0.026878949254751205, 0.008287393487989902, -0.01308357436209917, 0.006219782400876284, 0.01316831260919571, -0.004821602255105972, -0.007872176356613636, -0.029793942347168922, -0.010736326687037945, -0.010244845412671566, -0.03772543743252754, -0.019625362008810043, -0.009999104775488377, -0.05518149957060814, 0.05663899704813957, -0.018523765727877617, -0.03252251073718071, 0.05592719838023186, 0.015829091891646385, -0.012685305438935757, 0.050537850707769394, 0.05009721219539642, 0.04826686531305313, -0.03157344460487366, -0.03364105522632599, 0.007109533064067364, 0.02747211791574955, -0.030624376609921455, 0.0017032374162226915, 0.027743279933929443, -0.02059137634932995, 0.030743010342121124, -0.036064568907022476, 0.03694584593176842, 0.00016166456043720245, -0.016371415928006172, 0.01854071393609047, -0.01984568126499653, -0.004222079645842314, 0.06135043874382973, -0.03657299652695656, 0.052537668496370316, 0.026675578206777573, 0.02828560397028923, -0.05758806690573692, -0.04525018855929375, -0.052537668496370316, -0.015278293751180172, -0.0009172907448373735, 0.031437862664461136, -0.03609846532344818, 0.04592809081077576, -0.021370967850089073, 0.02565871924161911, -0.0349460244178772, -0.04125054553151131, 0.0029149933252483606, -0.03252251073718071, -0.03975915163755417, -0.03491212800145149, -0.024879129603505135, -0.03782712295651436, 0.007185797672718763, -0.03972525894641876, 0.019066089764237404, -0.06457049399614334, 0.012931046076118946, 0.04613146558403969, 0.02540450543165207, -0.0252858716994524, 0.0006440101424232125, 0.037047531455755234, -0.09077153354883194, -0.018439026549458504, -0.01473596878349781, -0.019455885514616966, 0.006918872240930796, -0.046165358275175095, -0.00032200507121160626, -0.018710190430283546, 0.09978767484426498, -0.034878235310316086, -0.004601282998919487, 0.048300761729478836, 0.004372490104287863, -0.019506728276610374, -0.0070798746310174465, 0.020404953509569168, 0.012066716328263283, 0.00043587200343608856, -0.035047709941864014, -0.024082589894533157, -0.057655856013298035, -0.014930866658687592, -0.0019267343450337648, -0.048978667706251144, -0.015134238637983799, -0.017218798398971558, 0.06948530673980713, 0.020710010081529617, 0.015041026286780834, -0.0056944056414067745, 0.011490496806800365, -0.0028260182589292526, -0.014913919381797314, 0.0024341042153537273, -0.04125054553151131, -0.009117827750742435, 0.010499060153961182, -0.02184550277888775, 0.05074122175574303, -0.02598072588443756, -0.05362232029438019, -0.012159928679466248, -0.01798144169151783, 0.015252872370183468, 0.05463917553424835, 0.0168544240295887, -0.015100343152880669, -0.03464096784591675, -0.008855139836668968, 0.04901256039738655, -0.0004146874707657844, 0.0008383783278986812, 0.020760852843523026, 0.03028542548418045, -0.013464896008372307, 0.09043258428573608, -0.054096851497888565, -0.01542234793305397, 0.0037284798454493284, -0.02054053358733654, 0.05785922706127167, 0.03267504274845123, -0.05324947088956833, -0.07267145812511444, 0.0165493655949831, -0.096126988530159, -0.009016142226755619, -0.01767638325691223, 0.031878501176834106, 0.02991257607936859, 0.022862359881401062, -0.07090890407562256, 0.005435954313725233, -0.06236729770898819, -0.014532597735524178, 0.009821155108511448, 0.0014617335982620716, 0.037115320563316345, -0.02235393039882183, 0.023709742352366447, 0.03813217952847481, 0.02047274447977543, 0.01404958963394165, 0.02815002202987671, -0.03438675403594971, -0.007486618123948574, 0.027522960677742958, 0.03009900078177452, 0.03775933012366295, -0.00958388764411211, 0.021896345540881157, -0.009668625891208649, -0.028573714196681976, -0.018811875954270363, -0.022709831595420837, 0.029675310477614403, -0.0067239743657410145, -0.008956825360655785, 0.018117021769285202, 0.03235303610563278, -0.04775843769311905, -0.039487991482019424, -0.029353303834795952, -0.014058063738048077, 0.02335384115576744, -0.01821870729327202, -0.000984551734291017, 0.007990810088813305, -0.07328157871961594, 0.0624350905418396, -0.01954062283039093, 0.0271501112729311, -0.056096673011779785, -0.04426722228527069, 0.010227898135781288, 0.02359110862016678, 0.02628578245639801, -0.051351334899663925, 0.015134238637983799, 0.041860658675432205, 0.0374542735517025, -0.005961330607533455, 0.017388274893164635, 0.05874050408601761, 0.03647131100296974, -0.03021763451397419, 0.04514849931001663, 0.002385379746556282, -0.001240355079062283, -0.02965836226940155, -0.05043616145849228, 0.00003972102058469318, -0.008033179678022861, 0.028997404500842094, -0.0029425332322716713, -0.08250109106302261, 0.01199045218527317, -0.03542055934667587, -0.014812233857810497, -0.018320394679903984, -0.004855497740209103, -0.01967620477080345, -0.02504860609769821, -0.031437862664461136, -0.005770669784396887, -0.0031183648388832808, 0.006469760090112686, 0.017134059220552444, -0.017184901982545853, -0.015718931332230568, -0.06535008549690247, -0.09666931629180908, 0.019489780068397522, -0.06101148948073387, -0.07138343900442123, 0.014176697470247746, -0.03952188417315483, -0.02933635748922825, -0.003088706638664007, 0.018201760947704315, -0.01239719521254301, -0.03664078935980797, -0.007681515999138355, -0.01935419999063015, -0.03484433889389038, -0.034556228667497635, 0.028607608750462532, -0.006550261285156012, -0.02142181061208248, 0.013414053246378899, -0.014930866658687592, 0.016405310481786728, 0.015176607295870781, 0.01529524102807045, -0.008054363541305065, -0.01586298644542694, 0.030878592282533646, 0.005897777155041695, -0.11565066128969193, 0.03301399573683739, 0.02072695828974247, -0.015286766923964024, 0.054469700902700424, 0.03321736678481102, -0.00364374159835279, 0.02023547701537609, -0.0009437714470550418, 0.009075459092855453, 0.022370878607034683, 0.0067027900367975235, -0.06155381351709366, 0.006194360554218292, 0.06663810461759567, -0.047487273812294006, -0.019150828942656517, -0.011651499196887016, -0.015473191626369953, -0.011227808892726898, -0.00993131473660469, 0.05450359731912613, 0.08568724244832993, 0.016388364136219025, 0.03172597289085388, 0.004690258298069239, 0.013846218585968018, 0.018930509686470032, 0.03164123371243477, 0.009499149397015572, 0.019337251782417297, -0.017328957095742226, -0.004499597009271383, -0.008613635785877705, 0.05480865389108658, -0.03260724991559982, -0.0143631212413311, -0.04908035323023796, -0.006452812347561121, -0.021930240094661713, -0.045419663190841675, 0.005940146278589964, -0.0024277488701045513, -0.017625540494918823, 0.007215455640107393, -0.005749485455453396, 0.0318615548312664, -0.05274104326963425, 0.014651230536401272, 0.0036140831653028727, 0.01542234793305397, 0.06402816623449326, 0.028370341286063194, -0.010355005040764809, -0.006829896941781044, -0.017659436911344528, -0.04765675216913223, 0.02516723796725273, -0.01220229733735323, 0.021574340760707855, 0.03460707142949104, -0.007829807698726654, -0.03908124566078186, -0.01516813412308693, 0.030488796532154083, -0.006033358164131641, 0.025319768115878105, 0.020455796271562576, -0.02167602628469467, 0.03282757103443146, -0.05267325043678284, -0.08568724244832993, 0.01967620477080345, -0.01716795563697815, 0.008626346476376057, 0.0027391614858061075, -0.0022243771236389875, -0.01672731712460518, -0.028743190690875053, -0.03145481273531914, 0.001621676841750741, -0.027455169707536697, -0.024065641686320305, 0.006160465534776449, 0.027980545535683632, -0.0046733105555176735, -0.035115499049425125, 0.01420211885124445, 0.010592272505164146, 0.03128533437848091, 0.05277493596076965, 0.0399625226855278, -0.01404958963394165, -0.020998120307922363, -0.002104684477671981, -0.030861644074320793, -0.008219603449106216, 0.0009988512611016631, -0.0015284648397937417, -0.0021523497998714447, 0.012964941561222076, 0.031675130128860474, -0.0038810085970908403, -0.021896345540881157, -0.020777801051735878, 0.007406116928905249, 0.010719379410147667, 0.023692794144153595, 0.01254972442984581, -0.019879575818777084, -0.05280883237719536, 0.008024705573916435, -0.035251080989837646, 0.022828465327620506, 0.06185887008905411, -0.0008330821874551475, -0.02970920503139496, -0.028200864791870117, -0.018405131995677948, 0.0005783380474895239, 0.027048425748944283, 0.019693152979016304, -0.06521449983119965, 0.008922929875552654, -0.0020750260446220636, 0.01492239348590374, -0.013583529740571976, -0.05175808072090149, -0.005245293024927378, 0.09334757924079895, 0.00933814700692892, 0.030573533847928047, 0.028641503304243088, -0.009744890034198761, 0.041792869567871094, 0.043114785104990005, -0.07443401217460632, 0.005156318191438913, 0.0030929434578865767, 0.016447680070996284, 0.008872087113559246, -0.044673968106508255, -0.015269819647073746, 0.0524359829723835, -0.010660062544047832, 0.08521271497011185, 0.0162273608148098, -0.030692167580127716, 0.0196592565625906, 0.0020178279373794794, 0.004203013610094786, -0.015498613007366657, 0.020557481795549393, -0.012803938239812851, 0.027455169707536697, -0.04209792613983154, -0.027997493743896484, -0.04189455509185791, -0.020506639033555984, 0.01760859414935112, 0.048538029193878174, 0.014142801985144615, -0.02914993278682232, -0.01542234793305397, -0.0004191891639493406, -0.026048514991998672, 0.015218976885080338, -0.004728390369564295, 0.03342073783278465, -0.01254972442984581, 0.004372490104287863, 0.02735348418354988, 0.007647620514035225, -0.008109443821012974, 0.0586727149784565, -0.03298009932041168, 0.02859066054224968, 0.0206083245575428, -0.01979483850300312, 0.05880829691886902, 0.010914277285337448, -0.02896350994706154, 0.007596777752041817, -0.022997941821813583, 0.0013971206499263644, -0.01236329972743988, -0.010321110486984253, -0.00388524541631341, -0.018761033192276955, -0.009507623501121998, -0.0209133829921484, -0.002616291167214513, 0.05548655986785889, -0.019405042752623558, -0.0012424734886735678, -0.05338505282998085, 0.04725000634789467, 0.043046995997428894, -0.025573981925845146, 0.02047274447977543, 0.013354736380279064, 0.017371326684951782, -0.017693331465125084, -0.015498613007366657, -0.02221835032105446, -0.04799570515751839, -0.017388274893164635, -0.020388005301356316, -0.010719379410147667, -0.0006810831255279481, -0.010363479144871235, -0.014981709420681, 0.03613235801458359, -0.06416374444961548, -0.008376369252800941, 0.01021095085889101, 0.0057028792798519135, 0.007935730740427971, 0.04077601060271263, -0.023675845935940742, -0.021625183522701263, 0.03221745416522026, 0.02335384115576744, -0.015379979275166988, 0.023269103839993477, 0.004533492494374514, -0.005003789439797401, 0.015473191626369953, 0.03267504274845123, 0.003173444652929902, 0.006520602852106094, -0.03742038086056709, -0.0037242427933961153, 0.029421094805002213, 0.019506728276610374, -0.019760942086577415, 0.028827928006649017, 0.0224725641310215, 0.013075101189315319, -0.0030293897725641727, -0.03159039095044136, -0.004255975130945444, 0.01654089242219925, -0.03352242335677147, -0.0028323736041784286, 0.0271501112729311, -0.06358753144741058, 0.0212353877723217, -0.031251441687345505, 0.009524570778012276, 0.030929435044527054, 0.008172997273504734, -0.0035399373155087233, 0.05575772002339363, -0.007177323568612337, -0.02391311340034008, -0.004935998935252428, -0.0060714902356266975, -0.0028472028207033873, -0.043928273022174835, 0.039555780589580536, 0.006338415667414665, -0.032810620963573456, 0.010838013142347336, -0.03728479892015457, -0.004296225495636463, 0.002499776193872094, 0.00011704460484907031, 0.0168459489941597, 0.006995136383920908, 0.05768975242972374, -0.003234880045056343, -0.011371863074600697, 0.001450082054361701, -0.013303893618285656, 0.040369268506765366, -0.04599588364362717, -0.08331457525491714, 0.024116484448313713, 0.001988169504329562, 0.0021036253310739994, -0.028014441952109337, -0.02791275642812252, 0.013600477948784828, 0.04514849931001663, -0.027675488963723183, 0.014405489899218082, 0.03775933012366295, -0.012049769051373005, -0.04450448974967003, -0.018761033192276955, -0.006707026623189449, -0.05426632985472679, 0.030692167580127716, 0.0019277934916317463, 0.026268834248185158, -0.015507086180150509, 0.018710190430283546, 0.029607519507408142, 0.024235118180513382, 0.01054990291595459, -0.01791365072131157, -0.010092317126691341, 0.0343359112739563, 0.03819996863603592, -0.01220229733735323, 0.06104538217186928, -0.024896075949072838, -0.005957094021141529, -0.03403085097670555, -0.037183113396167755, 0.01823565550148487, -0.007719648070633411, 0.015583351254463196, -0.04609756916761398, 0.020388005301356316, 0.016566313803195953, 0.0586727149784565, -0.03045490011572838, 0.010100791230797768, -0.028997404500842094, 0.021879397332668304, -0.029980367049574852, 0.033810533583164215, -0.028302552178502083, 0.02165907807648182, 0.02179466001689434, -0.016329046338796616, 0.003419185522943735, -0.005435954313725233, 0.025523139163851738, -0.006262151524424553, 0.02340468391776085, 0.025590930134058, 0.01508339587599039, -0.006198597606271505, -0.015100343152880669, -0.00046685439883731306, -0.012583618983626366, -0.011770132929086685, -0.016286678612232208, -0.02642136439681053, -0.041555602103471756, 0.015278293751180172, -0.005995226092636585, -0.02242172136902809, -0.00852042343467474, 0.012388721108436584, -0.026268834248185158, 0.025895986706018448, 0.00999063067138195, 0.03421727567911148, 0.0017975085647776723, 0.01715948060154915, 0.019811786711215973, -0.05267325043678284, 0.005995226092636585, -0.01804923266172409, 0.011134596541523933, 0.005308846943080425, 0.02203192561864853, 0.03643741458654404, 0.038064390420913696, 0.028980456292629242, 0.010405847802758217, 0.014210592024028301, -0.029573623090982437, -0.0337257944047451, 0.026065463200211525, 0.002362076658755541, 0.019998209550976753, 0.060028523206710815, 0.01299036294221878, -0.012490407563745975, 0.01704932190477848, 0.04043705761432648, -0.017269641160964966, -0.014973236247897148, 0.01239719521254301, 0.007850992493331432, -0.0011386692058295012, 0.04321647062897682, -0.03328515589237213, 0.04999552294611931, -0.012126033194363117, -0.043555423617362976, 0.0025845144409686327, 0.02547229640185833, 0.0012456511612981558, -0.006673131603747606, -0.02970920503139496, 0.00618164986371994, -0.027387378737330437, 0.008380605839192867, 0.0013081455836072564, -0.05019889771938324, 0.053724005818367004, 0.019574519246816635, 0.02765854075551033, 0.02733653597533703, -0.00605454295873642, 0.01916777528822422, -0.016337521374225616, -0.01847292296588421, -0.016134148463606834, 0.027133164927363396, 0.01385469175875187, 0.0805351659655571, -0.04538576677441597, 0.0034446069039404392, -0.03647131100296974, 0.0014045352581888437, -0.046538207679986954, 0.02298099361360073, 0.027692437171936035, 0.008846665732562542, -0.039860837161540985, 0.0343189612030983, -0.006122333463281393, -0.0324716679751873, 0.028692346066236496, -0.03160734102129936, 0.03701363503932953, 0.004181829281151295, -0.023438580334186554, 0.0104566914960742, -0.03708142787218094, 0.023930061608552933, 0.00889750849455595, 0.008461106568574905, -0.031692080199718475, -0.0009051096858456731, 0.0024150379467755556, 0.0038810085970908403, -0.011778607033193111, -0.005902014207094908, -0.06199445202946663, 0.015134238637983799, -0.010507534258067608, 0.0003241235390305519, -0.005304609891027212, 0.05382569134235382, 0.02059137634932995, 0.039115142077207565, 0.03938630595803261, -0.029810890555381775, 0.04413164407014847, -0.025184186175465584, 0.02772633172571659, 0.004974131006747484, 0.04277583211660385, -0.025590930134058, -0.01710016466677189, -0.05287662148475647, 0.02086254023015499, 0.01742216944694519, -0.0021354020573198795, 0.012287035584449768, 0.016066359356045723, -0.0337257944047451, -0.03819996863603592, 0.0006418916746042669, 0.021320125088095665, -0.03403085097670555, 0.021133702248334885, 0.0028895719442516565, 0.045860301703214645, -0.0005825749831274152, 0.008067074231803417, 0.045046813786029816, -0.009761838242411613, 0.016007041558623314, -0.0017667909851297736, -0.06575682759284973, 0.008753453381359577, -0.04165728762745857, 0.007346800062805414, 0.006499418057501316, -0.0024976576678454876, -0.02677726373076439, 0.0009930254891514778, -0.046300940215587616, -0.00023316239821724594, 0.012566671706736088, 0.012473459355533123, -0.0006371251656673849, -0.005965567659586668, -0.024997761473059654, 0.008550082333385944, -0.02460796758532524, -0.03796270489692688, -0.01079564355313778, 0.009253408759832382, -0.0012996718287467957, -0.044945128262043, 0.015591824427247047, 0.0070671639405190945, -0.0034742653369903564, 0.01295646745711565, 0.024675756692886353, -0.01566808857023716, -0.015405400656163692, 0.022947099059820175, -0.0055291661992669106, 0.06524839997291565, 0.02516723796725273, 0.0038831268902868032, 0.02072695828974247, -0.0020993882790207863, 0.0265399981290102, 0.010033000260591507, -0.00889750849455595, -0.01754080317914486, -0.03008205257356167, -0.02154044434428215, 0.021387916058301926, -0.05552045255899429, -0.05019889771938324, 0.02098117209970951, -0.0499277338385582, -0.0009432418155483902, -0.008287393487989902, 0.030048158019781113, -0.03164123371243477, -0.029997315257787704, -0.019489780068397522, 0.024014798924326897, -0.0271501112729311, -0.005787617526948452, 0.062401194125413895, -0.0038365209475159645, -0.03921682760119438, 0.05050395429134369, 0.00738493213430047, 0.013142891228199005, -0.0499616302549839, -0.010761748999357224, -0.009787259623408318, -0.008117916993796825, -0.03235303610563278, 0.029675310477614403, 0.006732448004186153, -0.006444338243454695, 0.032556407153606415, -0.03284451737999916, 0.03259030357003212, -0.03153954818844795 ]
IFTT-PIN is a self-calibrating version of the PIN-entry method introduced in Roth et al. (2004) [1]. In [1], digits are split into two sets and assigned a color respectively. To communicate their digit, users press the button with the same color that is assigned to their digit, which can thus be identified by elimination after a few iterations. IFTT-PIN uses the same principle but does not pre-assign colors to each button. Instead, users are free to choose which button to use for each color. The button-to-color mapping only exists in the user's mind and is never directly communicated to the interface. In other words, IFTT-PIN infers both the user's PIN and their preferred button-to-color mapping at the same time, a process called self-calibration. In this paper, we present online interactive demonstrations of IFTT-PIN with and without self-calibration and introduce the key concepts and assumptions making self-calibration possible. IFTT-PIN can be tested at https://jgrizou.github.io/IFTT-PIN/ with a video introduction available at https://youtu.be/5I1ibPJdLHM. We review related work in the field of brain-computer interface and further propose self-calibration as a novel approach to protect users against shoulder surfing attacks. Finally, we introduce a vault cracking challenge as a test of usability and security that was informally tested at our institute. With IFTT-PIN, we wish to demonstrate a new interactive experience where users can decide actively and on-the-fly how to use an interface. The self-calibration paradigm might lead to novel opportunities for interaction in other applications or domains. We hope this work will inspire the community to invent them.
[ -0.0645199790596962, -0.005729432683438063, -0.03342777490615845, -0.04195675626397133, 0.023397356271743774, 0.03588845580816269, 0.02502390928566456, 0.04833785444498062, -0.043875254690647125, 0.049797579646110535, 0.024815376847982407, -0.0434998981654644, 0.011698678135871887, -0.06101663410663605, -0.008299596607685089, 0.005169001407921314, 0.0004978715442121029, -0.013419072143733501, -0.009133727289736271, -0.05025635287165642, 0.015806769952178, -0.017902521416544914, -0.07778265327215195, -0.042707473039627075, 0.014326188713312149, 0.03830743581056595, 0.003075855551287532, -0.009566431865096092, -0.015577384270727634, 0.005917111877351999, 0.029507361352443695, 0.01975846290588379, -0.011552705429494381, -0.03463726118206978, -0.02542012184858322, -0.05913984030485153, -0.011688251048326492, 0.09625864028930664, 0.007939877919852734, 0.007319493684917688, -0.020801125094294548, 0.026900703087449074, 0.018277881667017937, 0.023272236809134483, -0.04654447361826897, -0.046419352293014526, -0.02531585469841957, -0.06168393790721893, 0.01980016939342022, -0.016547059640288353, 0.07148496806621552, 0.0011228176299482584, 0.043916963040828705, 0.04696153849363327, 0.04675300419330597, 0.05396823212504387, -0.011458865366876125, 0.03163439407944679, 0.10051270574331284, -0.05742987245321274, 0.004577290266752243, 0.019539503380656242, -0.0653541088104248, 0.006819015368819237, 0.0577218197286129, -0.022375546395778656, -0.025774627923965454, -0.02994527854025364, 0.040288496762514114, 0.007684425916522741, -0.06255977600812912, 0.03495006263256073, -0.008648889139294624, 0.013961256481707096, -0.017016258090734482, 0.013606751337647438, 0.1341281533241272, -0.017860814929008484, 0.020676005631685257, 0.028068486601114273, -0.03269790858030319, 0.059556905180215836, -0.011969770304858685, -0.0456269308924675, 0.009957430884242058, 0.016578340902924538, -0.02117648348212242, -0.07528026401996613, 0.05801376327872276, -0.028422990813851357, -0.0028777497354894876, -0.041518837213516235, -0.038891326636075974, -0.01935182325541973, -0.011156492866575718, 0.022187866270542145, 0.03211401775479317, -0.024606844410300255, -0.03238511085510254, -0.0068659354001283646, 0.009284913539886475, -0.008476849645376205, -0.09792689979076385, -0.010609094984829426, 0.04068470746278763, 0.03211401775479317, 0.002945522777736187, 0.03615954890847206, 0.032030604779720306, 0.09066996723413467, -0.04425061494112015, -0.02631681226193905, -0.03367801383137703, 0.00573464622721076, -0.008732302114367485, -0.008471636101603508, -0.005484406836330891, -0.0479624941945076, -0.00625597732141614, -0.0477539598941803, -0.016140421852469444, 0.010400562547147274, 0.011740384623408318, 0.0857485979795456, -0.016672179102897644, 0.023543328046798706, 0.015619090758264065, 0.02781824581325054, 0.005677299574017525, -0.015629516914486885, 0.01191763672977686, 0.008732302114367485, 0.05288386344909668, -0.009519512765109539, 0.04721177741885185, 0.04337477684020996, 0.0021087857894599438, -0.019132863730192184, 0.008784434758126736, 0.025524388998746872, 0.009284913539886475, 0.02754715457558632, -0.010614308528602123, 0.007997224107384682, -0.058180589228868484, -0.020811552181839943, -0.06848210096359253, 0.04554351791739464, -0.032072313129901886, 0.08103576302528381, -0.043708428740501404, 0.028047632426023483, -0.047378603368997574, -0.010895827785134315, 0.015024772845208645, -0.009149366989731789, -0.0019354430260136724, -0.0006842475268058479, -0.009816671721637249, -0.020821979269385338, 0.007700065616518259, -0.01914329081773758, 0.028047632426023483, 0.018726225942373276, 0.04804590716958046, -0.015827622264623642, 0.027901658788323402, -0.005682513117790222, 0.03816146403551102, 0.04210272803902626, 0.01801721565425396, 0.004699802957475185, 0.03974631056189537, -0.03920412436127663, 0.01576506346464157, 0.017089245840907097, -0.0011821191292256117, -0.01859067939221859, -0.0358676053583622, -0.04083067923784256, -0.052383385598659515, 0.04412549361586571, -0.017704416066408157, 0.013523338362574577, 0.04566863551735878, 0.01908073201775551, 0.06489533931016922, -0.002433314686641097, 0.031780365854501724, -0.02421063371002674, 0.011114786379039288, 0.07849166542291641, 0.02771398052573204, 0.07031718641519547, 0.06243465468287468, 0.001255757175385952, -0.006089151371270418, -0.016588766127824783, 0.0477539598941803, 0.04166480898857117, -0.03987142816185951, -0.04233211278915405, -0.02640022523701191, 0.002901209518313408, 0.010061697103083134, 0.01693284511566162, -0.04683641716837883, -0.015619090758264065, 0.0405387356877327, -0.004819709341973066, 0.003516380675137043, 0.0001037775436998345, -0.03342777490615845, 0.014566000550985336, -0.022354692220687866, -0.030612582340836525, 0.03021637164056301, 0.028214458376169205, -0.0027343835681676865, 0.048754919320344925, 0.011698678135871887, 0.08408033847808838, -0.016432367265224457, -0.046419352293014526, 0.0010543928947299719, -0.02054045908153057, 0.009451739490032196, 0.05421847105026245, 0.003917805850505829, -0.015733784064650536, -0.0003870885993819684, -0.011729957535862923, -0.014795387163758278, 0.005849339067935944, -0.006897215265780687, -0.03361545130610466, 0.01729777827858925, -0.015264584682881832, 0.008101491257548332, 0.055719904601573944, -0.011146066710352898, 0.0029611627105623484, -0.00019549929129425436, -0.007517599500715733, 0.02300114370882511, 0.014399174600839615, -0.009076381102204323, 0.02293858490884304, -0.012522381730377674, -0.012835180386900902, -0.06564605981111526, 0.03647235035896301, -0.013992535881698132, 0.019831448793411255, -0.024940496310591698, 0.08041016757488251, -0.01935182325541973, -0.0252532958984375, 0.039162419736385345, -0.03605528175830841, 0.051007069647312164, 0.043958667665719986, -0.0030289357528090477, 0.02416892722249031, 0.006454083602875471, 0.031842924654483795, 0.05630379915237427, -0.037869516760110855, 0.04550180956721306, -0.015076905488967896, 0.02117648348212242, -0.027192648500204086, 0.041352011263370514, -0.06168393790721893, 0.06235124170780182, 0.01074985507875681, -0.011344172060489655, -0.010489189065992832, -0.008831354789435863, 0.005567819811403751, 0.0062507642433047295, 0.023251382634043694, 0.015942316502332687, -0.02306370437145233, 0.004016858991235495, -0.02123904414474964, -0.05697110295295715, 0.05400994047522545, -0.0623929500579834, -0.0071891606785357, -0.0013697984395548701, -0.02646278403699398, -0.044000376015901566, -0.02037363313138485, 0.03874535486102104, 0.041602250188589096, -0.05563649162650108, -0.07949262112379074, -0.02648363821208477, -0.0422278493642807, -0.06285171955823898, -0.03866194188594818, -0.07736558467149734, 0.005468767136335373, -0.013846563175320625, 0.005906685255467892, 0.013325232081115246, 0.04320795089006424, -0.03928753733634949, -0.02172909490764141, 0.022167013958096504, -0.04700324311852455, -0.03603443130850792, -0.03376142680644989, -0.01933097094297409, -0.04345818981528282, 0.007220440544188023, 0.013002006337046623, -0.005677299574017525, -0.03957948461174965, 0.030925381928682327, 0.0019276230596005917, -0.07928408682346344, 0.006026591639965773, 0.014357468113303185, -0.006016165018081665, 0.020915817469358444, 0.0011580075370147824, 0.03405337035655975, -0.029382240027189255, -0.035429686307907104, -0.00778347859159112, -0.057012807577848434, -0.02285517193377018, -0.03476238250732422, 0.01992528885602951, -0.020571738481521606, 0.04954734072089195, -0.03505432605743408, 0.06393609195947647, 0.024314898997545242, 0.050006113946437836, 0.020404912531375885, -0.029173707589507103, -0.062017589807510376, -0.017099671065807343, 0.009550792165100574, -0.00787210464477539, -0.03638893738389015, -0.011865504086017609, 0.0015405344311147928, 0.005281087476760149, -0.0014923112466931343, -0.017183084040880203, 0.041539691388607025, -0.02421063371002674, 0.004830135963857174, -0.0382031686604023, -0.006136071402579546, -0.026129132136702538, 0.01994614116847515, -0.04099750518798828, 0.0017594937235116959, 0.018277881667017937, -0.05780523270368576, -0.04963075369596481, -0.01442002784460783, -0.01865324005484581, -0.024982202798128128, 0.03355289250612259, 0.002601444022729993, 0.023480769246816635, -0.05288386344909668, -0.011750810779631138, -0.03023722395300865, 0.04833785444498062, 0.0011371542932465672, -0.013033286668360233, -0.0008947351016104221, 0.05680427700281143, -0.04320795089006424, -0.05280045047402382, 0.0430828332901001, 0.009410033002495766, -0.002875142963603139, -0.006104791536927223, 0.06581288576126099, 0.045084744691848755, -0.00007942158845253289, 0.001255757175385952, -0.028110193088650703, -0.03105050139129162, -0.01143801212310791, -0.05250850319862366, 0.03741074725985527, 0.004785822704434395, 0.009227566421031952, -0.0012929020449519157, 0.045126449316740036, -0.04445914551615715, -0.024481724947690964, 0.012689207680523396, -0.09392307698726654, -0.002115302486345172, -0.00009392112406203523, -0.03711879998445511, -0.018382146954536438, -0.033219240605831146, -0.0067408159375190735, -0.029590774327516556, 0.03524200618267059, -0.03643064200878143, -0.0029689825605601072, -0.025816334411501884, 0.021040936931967735, -0.002098359167575836, -0.06439486145973206, 0.06527069956064224, 0.019685475155711174, 0.00787210464477539, 0.001844210084527731, 0.0657711774110794, -0.03144671395421028, -0.029674187302589417, 0.015858903527259827, -0.006469723302870989, -0.015076905488967896, 0.011093933135271072, 0.057054515928030014, -0.0014714580029249191, 0.04946392774581909, -0.04189419746398926, 0.007804331835359335, 0.0010530895087867975, 0.015170745551586151, -0.040330201387405396, -0.02631681226193905, 0.02886090986430645, 0.008257890120148659, -0.02154141664505005, -0.006010951939970255, 0.034387022256851196, -0.069608174264431, -0.022229572758078575, 0.0019067698158323765, 0.005453126970678568, -0.004147191531956196, -0.03515859320759773, -0.012282568961381912, 0.051132190972566605, -0.024669405072927475, -0.034303609281778336, -0.026900703087449074, -0.03876620903611183, 0.04093494638800621, -0.0021856820676475763, -0.04687812551856041, -0.07273616641759872, 0.012876886874437332, -0.03351118788123131, 0.03380313143134117, 0.03859937936067581, 0.016432367265224457, -0.056136973202228546, 0.05451041832566261, -0.030758555978536606, -0.06243465468287468, -0.01984187588095665, 0.009853164665400982, 0.0012798687675967813, 0.03153012692928314, 0.005849339067935944, 0.014440881088376045, 0.03582589700818062, 0.05059000477194786, -0.015024772845208645, -0.019727181643247604, 0.021228617057204247, 0.006459296680986881, -0.03818231448531151, 0.006172564346343279, -0.015994448214769363, -0.003860459430143237, -0.04166480898857117, 0.0369311198592186, 0.04908857122063637, -0.014430454932153225, -0.030591730028390884, -0.006229910999536514, 0.024523431435227394, -0.0481710284948349, -0.026754731312394142, 0.002604050561785698, 0.02109307050704956, 0.0008224003831855953, -0.043916963040828705, -0.05150754749774933, -0.0452098622918129, 0.013283525593578815, -0.05067341774702072, 0.010708148591220379, 0.02179165557026863, -0.025795480236411095, 0.054760657250881195, 0.011187773197889328, -0.005380140617489815, -0.004725869745016098, -0.0048405625857412815, 0.05776352435350418, 0.0479624941945076, -0.005374927539378405, 0.01852812059223652, -0.007152667734771967, 0.015316718257963657, 0.01680772565305233, -0.01142758596688509, 0.0069180685095489025, -0.005004781764000654, -0.010864547453820705, -0.0028777497354894876, 0.05400994047522545, 0.029403094202280045, -0.029674187302589417, 0.0005904078716412187, -0.013116699643433094, 0.04235296696424484, 0.026817290112376213, -0.029215414077043533, 0.02162482962012291, 0.008367369882762432, 0.010947960428893566, 0.03113391436636448, -0.018684519454836845, -0.036701735109090805, 0.02631681226193905, 0.01691199280321598, 0.015806769952178, -0.005406207405030727, -0.02088453806936741, -0.018684519454836845, -0.030800262466073036, -0.031655244529247284, 0.0358676053583622, -0.004983928520232439, 0.0028777497354894876, -0.02396039292216301, 0.003339128103107214, 0.016307247802615166, 0.02389783412218094, -0.016421940177679062, 0.0024450444616377354, 0.014618134126067162, -0.049714166671037674, 0.0028542897198349237, 0.025920599699020386, 0.01863238587975502, 0.014993492513895035, -0.0007591889589093626, 0.020915817469358444, -0.0227091982960701, -0.02031107433140278, 0.0036779935471713543, 0.03488750010728836, -0.027422035112977028, -0.02062387205660343, -0.014743253588676453, -0.004996961914002895, 0.0460439957678318, 0.003341734642162919, -0.013565044850111008, -0.002927276073023677, -0.0035268072970211506, -0.029319681227207184, 0.03273961693048477, -0.03223913908004761, 0.014576427638530731, 0.03388654440641403, -0.00906074047088623, -0.0039282324723899364, -0.0060213785618543625, 0.0017321237828582525, -0.026024866849184036, -0.008982541039586067, 0.03962118923664093, -0.052091438323259354, 0.03115476854145527, 0.0011397609487175941, 0.008205757476389408, -0.036576613783836365, -0.03932924568653107, 0.009144153445959091, 0.07553049921989441, 0.01668260619044304, 0.0337405726313591, -0.009410033002495766, -0.008591542020440102, -0.00143366155680269, 0.031884633004665375, 0.01990443468093872, -0.024877937510609627, -0.0024776277132332325, 0.03893303498625755, 0.047420307993888855, 0.06297683715820312, 0.005338434129953384, -0.006490576546639204, 0.0052054948173463345, -0.04226955398917198, 0.032989855855703354, -0.00752281304448843, 0.014784960076212883, 0.020123394206166267, 0.048838332295417786, 0.02152056246995926, 0.0674811452627182, -0.035367127507925034, 0.025670360773801804, -0.028402138501405716, 0.0022013220004737377, -0.026170838624238968, 0.013106272555887699, -0.03701453283429146, 0.027234354987740517, -0.006641762796789408, 0.06760626286268234, -0.007986797951161861, -0.0036102202720940113, -0.060808099806308746, -0.030550023540854454, -0.04316624626517296, 0.015160318464040756, -0.009237993508577347, 0.014294908381998539, 0.01259536761790514, 0.02170824259519577, 0.06485363095998764, -0.009816671721637249, 0.024731963872909546, 0.0023199249990284443, 0.020769845694303513, 0.02635851874947548, -0.03392825275659561, -0.015139465220272541, 0.0645199790596962, -0.013419072143733501, 0.009999137371778488, 0.04662788659334183, -0.0024046413600444794, 0.06622994691133499, 0.02166653610765934, 0.022479811683297157, -0.050506591796875, 0.027004970237612724, 0.010822840966284275, -0.003472067415714264, -0.028485551476478577, 0.04700324311852455, -0.022625785320997238, 0.003323487937450409, -0.019529076293110847, 0.010228523053228855, 0.041497983038425446, 0.03269790858030319, -0.006568776443600655, 0.025357561185956, 0.029173707589507103, -0.021458003669977188, -0.012929020449519157, 0.02881920337677002, -0.0067408159375190735, 0.0007898171315900981, -0.04199846088886261, -0.040351055562496185, 0.015358424745500088, 0.023126263171434402, -0.02642107754945755, 0.008596755564212799, 0.042790886014699936, 0.03472067415714264, -0.04950563609600067, 0.005630379542708397, -0.01318968553096056, 0.002825616393238306, -0.02277175895869732, 0.018788786605000496, -0.0066730426624417305, -0.03859937936067581, -0.00035906705306842923, -0.03595101833343506, -0.00009717944340081885, -0.0033026346936821938, 0.0008660618914291263, 0.022542372345924377, -0.0029298828449100256, -0.03273961693048477, -0.016244689002633095, -0.03200975060462952, 0.0022560618817806244, 0.03282302990555763, 0.023689301684498787, -0.06839868426322937, 0.018277881667017937, -0.014805813319981098, -0.016609620302915573, 0.0006099577876739204, 0.032051458954811096, -0.0050412751734256744, -0.024398311972618103, -0.003023722441866994, -0.024502579122781754, -0.01638023369014263, -0.008654101751744747, 0.010968813672661781, 0.008315236307680607, -0.0028542897198349237, 0.009378752671182156, 0.01552525069564581, -0.008909554220736027, -0.042624060064554214, 0.03219743072986603, -0.004830135963857174, 0.0360761359333992, -0.010327575728297234, -0.054718948900699615, -0.0019719363190233707, 0.03985057771205902, -0.013085419312119484, 0.006839868612587452, 0.017495883628726006, 0.0005627121427096426, 0.04600228741765022, -0.014774533919990063, 0.014399174600839615, -0.009138940833508968, 0.005257627926766872, 0.003438181011006236, 0.011667397804558277, 0.013252245262265205, 0.023439062759280205, -0.018382146954536438, 0.01797550916671753, -0.005239380989223719, -0.002047529211267829, -0.02295943722128868, -0.009477806277573109, -0.014899653382599354, -0.0369311198592186, 0.05501089617609978, 0.01381528377532959, 0.0011899390956386924, 0.023313943296670914, -0.007574946153908968, 0.0430828332901001, -0.05488577485084534, -0.03722306713461876, -0.030904529616236687, 0.021854214370250702, -0.03599272295832634, 0.004285344388335943, -0.049880992621183395, -0.0356590710580349, 0.01625511422753334, -0.017089245840907097, -0.023084556683897972, 0.014659840613603592, 0.013804856687784195, -0.05913984030485153, 0.02765141986310482, 0.02266749180853367, -0.016755593940615654, 0.033219240605831146, 0.022417252883315086, 0.041352011263370514, -0.03355289250612259, -0.012929020449519157, 0.032969001680612564, 0.015139465220272541, 0.023042850196361542, -0.014211495406925678, 0.02295943722128868, -0.03221828490495682, 0.0007239990518428385, 0.020217234268784523, 0.036889415234327316, -0.007022334728389978, -0.03342777490615845, 0.020780272781848907, 0.022417252883315086, 0.008732302114367485, -0.04108091816306114, 0.0649370476603508, 0.027067529037594795, 0.019831448793411255, 0.017944227904081345, 0.02990357205271721, 0.02111392468214035, -0.00812755711376667, 0.017412470653653145, -0.025566095486283302, -0.026900703087449074, 0.011698678135871887, -0.024377459660172462, -0.013585898093879223, 0.010098190046846867, 0.01555653102695942, 0.004061172250658274, -0.008727088570594788, -0.010676868259906769, -0.038870472460985184, 0.009926150552928448, -0.030299784615635872, -0.031926337629556656, 0.01132331881672144, 0.01446173433214426, -0.01560866367071867, 0.0061308578588068485, 0.009029461070895195, -0.018726225942373276, 0.01822574809193611, 0.030404049903154373, -0.03478323668241501, 0.013544191606342793, -0.010525682009756565, 0.029611626639962196, -0.012011476792395115, 0.015650371089577675, 0.03970460221171379, -0.0053592873737216, -0.0009318799711763859, -0.005771139170974493, 0.03338606655597687, -0.013606751337647438, 0.02763056755065918, -0.001870276639238, 0.015347997657954693, 0.026692170649766922, -0.028402138501405716, -0.000585846253670752, -0.02529500238597393, 0.030278930440545082, -0.016964126378297806, 0.001669564051553607, -0.041310302913188934, -0.04214443638920784, -0.003359981346875429, -0.03349033370614052, -0.01138587947934866, 0.04458426684141159, 0.0287566427141428, -0.018663665279746056, 0.062142711132764816, 0.035533953458070755, 0.024544285610318184, 0.03634722903370857, 0.000380246143322438, 0.022312985733151436, 0.012720488011837006, 0.01937267743051052, -0.02279261127114296, -0.042749181389808655, 0.01560866367071867, -0.012292996048927307, -0.026045719161629677, -0.00777826551347971, -0.0009990014368668199, -0.0027161368634551764, 0.01670346036553383, 0.008685382083058357, -0.04337477684020996, -0.03330265358090401, -0.012261715717613697, -0.026629609987139702, 0.03259364143013954, -0.0006783825810998678, 0.012856033630669117, -0.006110004615038633, -0.021895920857787132, 0.01570250280201435, 0.007397693581879139, 0.01695369929075241, 0.005932752043008804, 0.027192648500204086, -0.013429498299956322, 0.0007116174674592912, -0.029277974739670753, 0.02291773073375225, 0.0012596671003848314, -0.05292556807398796, 0.014357468113303185, 0.013512911275029182, 0.016484500840306282, 0.022312985733151436, -0.039266686886548996, 0.0028855695854872465, 0.019768888130784035, -0.027234354987740517, -0.022146159783005714, -0.006485363468527794, -0.009269272908568382, -0.011156492866575718, -0.005380140617489815, -0.003717093262821436, 0.022271279245615005, -0.04558522254228592, 0.009269272908568382, 0.011239905841648579, 0.0037744396831840277, 0.00009164029324892908, 0.04354160279035568, -0.010384922847151756, 0.016494927927851677, -0.0074602533131837845, -0.018955612555146217, -0.04103921353816986, -0.014023816213011742, 0.024919643998146057, -0.053509462624788284, 0.03743159770965576, 0.017621003091335297, 0.006813802290707827, 0.06564605981111526, 0.10718575119972229, -0.02277175895869732, 0.01992528885602951, 0.012355555780231953, -0.05617867782711983, 0.0033443414140492678, 0.008654101751744747, 0.017725270241498947, 0.028318725526332855, -0.021374590694904327, 0.015076905488967896, -0.0003678645007312298, 0.04679471254348755, -0.005252414382994175, 0.042707473039627075, -0.013533764518797398, -0.00514032831415534, -0.03015381097793579, -0.058180589228868484, 0.0458354614675045, -0.006407163571566343, 0.0023212283849716187, -0.0016135209007188678, 0.04245723411440849, -0.011281612329185009, 0.007256933953613043, -0.01901817135512829, 0.0012107923394069076, -0.015587810426950455, -0.010416202247142792, -0.10835353285074234, -0.0011514908401295543, -0.017047539353370667, -0.0549691878259182, -0.028172751888632774, -0.03355289250612259, -0.01442002784460783, 0.012282568961381912, 0.04558522254228592, 0.003294814843684435, -0.01852812059223652, -0.022438105195760727, -0.023293089121580124, -0.04195675626397133, 0.03726477175951004, -0.035700779408216476, -0.026984116062521935, 0.011490145698189735, 0.00301850913092494, -0.01327309850603342, 0.011146066710352898, -0.0073247067630290985, 0.0742793083190918, 0.04341648519039154, -0.027234354987740517, -0.01910158433020115, -0.0311964750289917, -0.009665485471487045, 0.029778452590107918, 0.03326094523072243, -0.002804763149470091, -0.009456953033804893, 0.031029649078845978, -0.005943178664892912, 0.010958387516438961, 0.011969770304858685, -0.009300553239881992, -0.03253108263015747, 0.00005347720434656367, -0.037911225110292435, -0.0011599624995142221, 0.025878893211483955, -0.054552122950553894, 0.007074467837810516, -0.01050482876598835, 0.01945609040558338, -0.03634722903370857, -0.0657711774110794, -0.010697721503674984, -0.00807542447000742, 0.010947960428893566, 0.019685475155711174, 0.0579303503036499, 0.0027109235525131226, 0.012678780592978, 0.01873665302991867, -0.006162137724459171, 0.009535152465105057, 0.0027552368119359016, 0.01322096586227417, 0.03699367865920067, 0.017026685178279877, -0.0012107923394069076, 0.012689207680523396, -0.01501434575766325, -0.04204016923904419, 0.002656183671206236, 0.004128945060074329, 0.056011851876974106, 0.04846297204494476, 0.07031718641519547, 0.0016630473546683788, -0.005453126970678568 ]
In a world increasingly dependent on road-based transportation, it is essential to understand vehicles. We introduce the AI mechanic, an acoustic vehicle characterization deep learning system, as an integrated approach using sound captured from mobile devices to enhance transparency and understanding of vehicles and their condition for non-expert users. We develop and implement novel cascading architectures for vehicle understanding, which we define as sequential, conditional, multi-level networks that process raw audio to extract highly-granular insights. To showcase the viability of cascading architectures, we build a multi-task convolutional neural network that predicts and cascades vehicle attributes to enhance fault detection. We train and test these models on a synthesized dataset reflecting more than 40 hours of augmented audio and achieve >92% validation set accuracy on attributes (fuel type, engine configuration, cylinder count and aspiration type). Our cascading architecture additionally achieved 93.6% validation and 86.8% test set accuracy on misfire fault prediction, demonstrating margins of 16.4% / 7.8% and 4.2% / 1.5% improvement over na\"ive and parallel baselines. We explore experimental studies focused on acoustic features, data augmentation, feature fusion, and data reliability. Finally, we conclude with a discussion of broader implications, future directions, and application areas for this work.
[ -0.006714215502142906, 0.016482699662446976, -0.03016996756196022, -0.07719536125659943, 0.013966810889542103, 0.06750452518463135, -0.03636133298277855, 0.013324896804988384, -0.035802245140075684, 0.035843659192323685, 0.006859163753688335, -0.049033962190151215, 0.036174971610307693, -0.003936901222914457, -0.03839061036705971, 0.016420578584074974, -0.03812142089009285, -0.028658362105488777, 0.019319547340273857, -0.025096774101257324, -0.009654596447944641, 0.012434499338269234, -0.03781081736087799, 0.003320870688185096, 0.016565527766942978, 0.028596242889761925, 0.014474130235612392, 0.0048868306912481785, -0.06278335303068161, 0.05603289604187012, 0.026463430374860764, 0.011689050123095512, -0.039695147424936295, 0.007029995787888765, 0.016223862767219543, 0.0014637196436524391, 0.015820078551769257, 0.01350090466439724, -0.033048227429389954, 0.010042850859463215, -0.0006166776292957366, -0.05744096636772156, 0.009923786856234074, -0.004653878044337034, 0.02532455138862133, -0.011295619420707226, -0.042449165135622025, 0.04646630585193634, -0.035160332918167114, 0.07181156426668167, -0.01785971038043499, -0.02186649665236473, -0.007754737511277199, 0.021245289593935013, -0.0035641768481582403, 0.028596242889761925, 0.022611945867538452, 0.022777600213885307, 0.04064766317605972, 0.012082481756806374, 0.01785971038043499, 0.02638060227036476, -0.06427424401044846, 0.009488941170275211, 0.02047913335263729, -0.019640503451228142, 0.012538033537566662, 0.017942536622285843, 0.02594575844705105, 0.02259123884141445, -0.03501538559794426, -0.0048635355196893215, -0.04180724918842316, 0.037976473569869995, 0.0329032801091671, -0.012444852851331234, 0.0009259871440008283, 0.06464697420597076, 0.028927553445100784, 0.0047625890001654625, 0.0450996495783329, 0.058683380484580994, -0.04721175506711006, 0.035802245140075684, 0.05242989584803581, -0.0053734430111944675, -0.007180120795965195, -0.07570446282625198, 0.04373299330472946, -0.017393803223967552, -0.024413445964455605, -0.016793303191661835, 0.007889332249760628, 0.03435276448726654, 0.008707255125045776, 0.020468780770897865, -0.016306690871715546, 0.006501969415694475, -0.04468551278114319, 0.0023139971308410168, 0.0450996495783329, 0.006677978206425905, 0.029031086713075638, -0.011005722917616367, 0.011264558881521225, -0.07711253315210342, -0.029900778084993362, 0.02184578962624073, 0.00177691166754812, 0.13053636252880096, 0.02811998315155506, -0.019588736817240715, 0.050483446568250656, -0.009784014895558357, -0.0031422735191881657, 0.010053204372525215, -0.012072128243744373, -0.03422852233052254, -0.011409507133066654, 0.015002155676484108, 0.04066837206482887, 0.03859768062829971, 0.009882372803986073, -0.0035072327591478825, -0.031702280044555664, 0.08638922870159149, 0.03754162788391113, -0.049033962190151215, -0.001323300995863974, 0.025241723284125328, 0.029383104294538498, 0.009892726317048073, -0.036547694355249405, 0.04750164970755577, 0.03497397154569626, -0.02395789511501789, 0.002888613846153021, 0.039011817425489426, 0.01590290665626526, -0.04642489179968834, 0.026235654950141907, 0.005003307014703751, -0.06137527897953987, 0.03213712200522423, 0.011202437803149223, -0.0006267075659707189, 0.003175922203809023, 0.09193868190050125, -0.01301429234445095, -0.0007098587229847908, -0.08063270896673203, 0.010436282493174076, 0.009219751693308353, 0.04543095827102661, 0.02292254939675331, 0.011854705400764942, -0.013946103863418102, -0.018905408680438995, 0.0005280261975713074, -0.012869344092905521, 0.023129617795348167, -0.08928819745779037, -0.027975035831332207, 0.013293836265802383, 0.04791579023003578, 0.023046789690852165, 0.04340168088674545, -0.03565729781985283, -0.051435962319374084, 0.05479048192501068, 0.025738688185811043, -0.006434672046452761, -0.011181730777025223, -0.03288257122039795, 0.027871500700712204, 0.009307756088674068, 0.01653446815907955, 0.049779411405324936, -0.0414966456592083, 0.03435276448726654, -0.05259555205702782, -0.047004684805870056, 0.055660173296928406, -0.012827930971980095, 0.0553702749311924, 0.05027637630701065, 0.04236633703112602, -0.004607287235558033, 0.0008392769377678633, 0.03402145206928253, -0.022011445835232735, 0.008023927919566631, 0.06361162662506104, -0.003002501791343093, -0.009406113997101784, -0.004692703485488892, -0.016700122505426407, -0.05379655212163925, -0.0036910066846758127, 0.014836500398814678, -0.03226136416196823, -0.026939690113067627, 0.002207874320447445, 0.04480975121259689, 0.006833279971033335, 0.03327600285410881, 0.013770095072686672, 0.046631962060928345, 0.03820424899458885, -0.06328031420707703, -0.022322049364447594, 0.02673261985182762, -0.037603747099637985, -0.000999755458906293, 0.007237065117806196, -0.006869517266750336, 0.012579447589814663, -0.058931864798069, 0.02422708459198475, 0.0010372867109254003, 0.03364872932434082, -0.0034787608310580254, 0.022301342338323593, 0.03988150879740715, -0.01695895940065384, -0.07686404883861542, 0.021245289593935013, -0.009908256120979786, -0.0330689363181591, 0.0056322794407606125, -0.019298840314149857, 0.008484655991196632, -0.01909177005290985, -0.015302406623959541, 0.017538752406835556, -0.06746311485767365, 0.017455924302339554, -0.027146758511662483, -0.0099859070032835, 0.010860773734748363, -0.014070345088839531, 0.006481262855231762, -0.06336314231157303, -0.05031779035925865, 0.05930458754301071, -0.0294038113206625, -0.010068735107779503, -0.00658479705452919, -0.01368726696819067, 0.02493111975491047, -0.011854705400764942, -0.00002618696089484729, 0.012320611625909805, -0.013966810889542103, -0.005228494759649038, 0.05595007166266441, 0.0658479705452919, -0.035802245140075684, -0.002374823670834303, -0.06361162662506104, -0.019847573712468147, -0.009732247330248356, -0.03420781344175339, 0.05056627467274666, -0.06323890388011932, -0.0050343675538897514, 0.015188517980277538, 0.047004684805870056, -0.012041067704558372, -0.05305110290646553, 0.012465559877455235, -0.021555893123149872, -0.02669120579957962, -0.0029455579351633787, -0.03503609076142311, -0.05027637630701065, -0.0006658565835095942, -0.02567656710743904, -0.027457362040877342, 0.0024136491119861603, 0.030273502692580223, -0.04795720428228378, 0.06713180243968964, -0.04114462807774544, -0.06141669303178787, -0.03495326265692711, -0.01371832750737667, 0.006051594391465187, -0.017911477014422417, 0.007237065117806196, -0.007356129586696625, -0.056695517152547836, -0.048329927027225494, -0.01440165564417839, 0.005352735985070467, 0.01353196520358324, 0.0015090160304680467, -0.05967731401324272, 0.0173316840082407, -0.01858445070683956, -0.0518915168941021, 0.009690833278000355, 0.020209943875670433, 0.018304908648133278, 0.01455695740878582, 0.028637656942009926, 0.008660664781928062, 0.016109975054860115, 0.02424779161810875, -0.01905035600066185, 0.03079117462038994, 0.03089470975100994, -0.056654103100299835, -0.02283972129225731, -0.029590174555778503, 0.024516981095075607, 0.02422708459198475, -0.03505679965019226, -0.013107473962008953, -0.00008573954983148724, 0.008650311268866062, 0.0018700928194448352, -0.08746598660945892, 0.040730491280555725, -0.046259235590696335, -0.0156544242054224, 0.0415794737637043, -0.0260285846889019, -0.03284115716814995, -0.011471628211438656, -0.04721175506711006, -0.019516263157129288, 0.0005513214855454862, 0.025469498708844185, 0.014267060905694962, -0.0026815447490662336, -0.053506653755903244, 0.05922176316380501, -0.023046789690852165, -0.03882545605301857, -0.015706190839409828, -0.024040721356868744, -0.09914468228816986, -0.011098903603851795, -0.00900750607252121, -0.05955307185649872, 0.0026194241363555193, 0.015302406623959541, -0.01858445070683956, -0.05661269277334213, 0.0011854706099256873, -0.05259555205702782, -0.022032150998711586, -0.05715107172727585, 0.006056771147996187, -0.0012877109693363309, -0.019184952601790428, -0.01938166655600071, 0.040047165006399155, 0.03253055363893509, 0.017445571720600128, -0.07773374021053314, -0.018636219203472137, -0.003991256933659315, -0.019164245575666428, 0.013946103863418102, 0.018646571785211563, -0.04439561441540718, -0.011005722917616367, 0.0030568575020879507, 0.007946276105940342, 0.05831065773963928, -0.00007712515071034431, 0.005772050935775042, -0.01542664784938097, -0.02030312456190586, -0.006538206711411476, -0.05727531388401985, -0.023730117827653885, 0.0554945170879364, 0.007682263385504484, -0.02426849864423275, 0.050110720098018646, 0.005601218901574612, -0.06738028675317764, 0.08721750229597092, -0.0043639810755848885, -0.010177446529269218, -0.023046789690852165, 0.06129245087504387, 0.007708147168159485, -0.00901785958558321, 0.0138736292719841, -0.05292686074972153, 0.05818641558289528, -0.005207787733525038, -0.016772596165537834, -0.0381835401058197, 0.005275085102766752, -0.05822782963514328, -0.0009499294683337212, 0.05644703656435013, 0.022032150998711586, 0.03393862396478653, -0.043443094938993454, 0.022736186161637306, -0.060174278914928436, -0.0033105171751230955, 0.011854705400764942, 0.017010726034641266, -0.03735526651144028, -0.028327051550149918, 0.00883149728178978, -0.04480975121259689, 0.011740817688405514, 0.023357393220067024, 0.005896292626857758, -0.03476690128445625, 0.011067843064665794, 0.031018950045108795, -0.029300278052687645, 0.07114893943071365, 0.016710476949810982, 0.004136205185204744, -0.037231024354696274, 0.009716717526316643, 0.007516608107835054, 0.025842223316431046, -0.04804002866148949, -0.04265623539686203, 0.04056483507156372, -0.05164303258061409, 0.04199361428618431, -0.01594432070851326, 0.024372031912207603, -0.02737453393638134, 0.03226136416196823, -0.012765809893608093, -0.043484508991241455, -0.00004282933150534518, -0.03874262794852257, -0.027271000668406487, -0.05172586068511009, 0.011533748358488083, -0.07164590805768967, -0.06853987276554108, 0.01403928454965353, -0.061168212443590164, -0.019184952601790428, -0.038307782262563705, -0.07462770491838455, 0.046673376113176346, -0.04924103245139122, -0.030956828966736794, -0.024185670539736748, -0.03395933285355568, 0.03012855350971222, -0.02909320779144764, -0.03598861023783684, -0.0381421260535717, 0.04089614748954773, 0.09061343967914581, 0.000744154560379684, 0.015933966264128685, 0.0311638992279768, 0.016948604956269264, -0.030335621908307076, -0.03323458880186081, -0.0008075694786384702, 0.022259928286075592, 0.030397742986679077, -0.07736101746559143, 0.047294583171606064, 0.041765835136175156, -0.002430473454296589, -0.02673261985182762, -0.01961979642510414, -0.00898679904639721, 0.039384543895721436, -0.006874694023281336, 0.0078272121027112, 0.0450582355260849, 0.010027321055531502, -0.03315176069736481, 0.006967875175178051, 0.006015357095748186, 0.06535100936889648, -0.046631962060928345, -0.03921888768672943, -0.0055080377496778965, -0.035139624029397964, -0.01454660389572382, -0.027105344459414482, -0.015716545283794403, 0.000716976763214916, -0.004099967889487743, -0.03317246958613396, 0.011751171201467514, 0.03435276448726654, 0.03547093644738197, 0.012983232736587524, -0.02836846560239792, 0.047625891864299774, 0.007019642274826765, -0.030977535992860794, -0.004162088967859745, -0.006910931318998337, -0.03631991893053055, 0.014681198634207249, 0.02981794998049736, 0.05785510689020157, 0.013283482752740383, 0.027809379622340202, 0.0019710389897227287, 0.035450227558612823, -0.026774033904075623, 0.0277265515178442, -0.0073820133693516254, -0.026939690113067627, 0.03128813952207565, 0.032054297626018524, -0.014795087277889252, -0.014422362670302391, 0.054956138134002686, -0.035201746970415115, 0.05085616931319237, 0.020365245640277863, -0.0010372867109254003, 0.054914724081754684, -0.04712892696261406, -0.03965373337268829, 0.03741738572716713, -0.0450582355260849, -0.04102038964629173, 0.0013343015452846885, 0.008319000713527203, 0.0027333120815455914, 0.07036207616329193, -0.03464265912771225, -0.025925051420927048, -0.046921856701374054, -0.008308647200465202, 0.006320784334093332, 0.0020435131154954433, -0.036609817296266556, -0.004483046010136604, 0.023647291585803032, -0.03327600285410881, 0.017424864694476128, 0.0015530182281509042, 0.021762961521744728, -0.020934686064720154, 0.023854359984397888, 0.04605216532945633, -0.02671191282570362, 0.005580512341111898, -0.010239566676318645, 0.0019322135485708714, 0.014256707392632961, -0.0006910930969752371, -0.05060768872499466, -0.025904344394803047, -0.011854705400764942, 0.05661269277334213, 0.01541629433631897, 0.011026429012417793, 0.012941818684339523, 0.07566304504871368, -0.0449339933693409, 0.03230277821421623, -0.02739524096250534, -0.03878404200077057, -0.03839061036705971, -0.045555200427770615, 0.01852233149111271, -0.0015310171293094754, 0.02561444789171219, -0.06406717747449875, -0.01616174355149269, 0.04576227068901062, 0.025469498708844185, -0.002495182678103447, -0.009054096415638924, 0.06609645485877991, -0.033793676644563675, 0.03079117462038994, -0.03644416108727455, -0.026069998741149902, 0.004506341181695461, 0.0038980757817626, -0.007858272641897202, 0.03843202441930771, -0.04787437617778778, -0.005761697422713041, -0.026504844427108765, -0.03636133298277855, -0.004609875846654177, 0.019360961392521858, 0.03081188164651394, -0.020313479006290436, 0.013304189778864384, 0.04953092709183693, 0.010073911398649216, 0.05445917323231697, 0.026981104165315628, -0.0005846466519869864, 0.03081188164651394, -0.012506972998380661, -0.03542952239513397, 0.052802618592977524, 0.015996087342500687, -0.02739524096250534, 0.06299041956663132, -0.029320983216166496, 0.039281006902456284, 0.03698254004120827, 0.05313393101096153, 0.039715852588415146, -0.005539098288863897, -0.005202610976994038, 0.008919501677155495, 0.018781166523694992, 0.007915216498076916, -0.02248770371079445, 0.012506972998380661, 0.02107963338494301, 0.006719392258673906, -0.0007085645920597017, -0.01783900335431099, -0.004609875846654177, -0.006051594391465187, -0.02598717249929905, -0.035491641610860825, -0.02836846560239792, 0.04203502833843231, 0.0138736292719841, 0.00711800018325448, -0.018066778779029846, 0.01334560289978981, -0.03288257122039795, -0.03460124507546425, -0.028161397203803062, -0.026214947924017906, 0.016596587374806404, -0.011440567672252655, 0.018087485805153847, -0.027975035831332207, -0.03267550468444824, 0.007759914267808199, 0.022736186161637306, 0.013159241527318954, 0.03785223141312599, 0.018781166523694992, 0.05156020447611809, 0.006269016768783331, 0.003155215410515666, 0.04654913395643234, -0.004120674915611744, -0.001663023722358048, 0.01470190566033125, 0.02184578962624073, 0.01682436466217041, 0.02840987965464592, -0.007925570011138916, 0.02085185796022415, 0.008541599847376347, 0.005231082905083895, -0.0328204520046711, -0.028327051550149918, 0.07119035720825195, 0.020406659692525864, -0.042780473828315735, -0.02188720367848873, 0.017083199694752693, 0.017321329563856125, -0.020976100116968155, 0.020603375509381294, 0.03331741690635681, 0.011409507133066654, 0.01580972597002983, 0.006698685232549906, -0.02671191282570362, -0.02281901426613331, 0.04435420036315918, -0.06464697420597076, -0.016348104923963547, 0.014422362670302391, 0.04928244650363922, -0.0032069827429950237, -0.019982168450951576, -0.008779729716479778, 0.015996087342500687, 0.060132864862680435, 0.002356705255806446, -0.006952344905585051, 0.015933966264128685, -0.013956457376480103, 0.0030516807455569506, 0.010498403571546078, -0.009033389389514923, -0.022715479135513306, -0.007920392788946629, -0.03232348710298538, -0.009835782460868359, 0.009903079830110073, -0.005932529456913471, 0.006677978206425905, -0.02426849864423275, -0.010368985123932362, -0.04538954421877861, -0.009571769274771214, 0.020344538614153862, 0.017062492668628693, 0.02352304942905903, 0.0692439079284668, 0.03395933285355568, 0.006186189129948616, 0.0005018190131522715, -0.030314914882183075, 0.012869344092905521, 0.030749760568141937, -0.03507750481367111, -0.04327744245529175, -0.03946736827492714, -0.00848983321338892, 0.025821516290307045, 0.02430991269648075, 0.008111931383609772, -0.0138425687327981, -0.010684764944016933, -0.021069280803203583, -0.04924103245139122, -0.01544735487550497, 0.0037738343235105276, -0.005885939113795757, 0.04712892696261406, 0.039281006902456284, 0.026566965505480766, 0.002257053041830659, 0.01746627874672413, 0.018998589366674423, -0.0078272121027112, 0.0277058444917202, 0.03781081736087799, -0.01832561567425728, 0.03640274703502655, 0.02045842632651329, 0.002185873221606016, 0.00676598260179162, 0.014826146885752678, 0.03279974311590195, -0.06497827917337418, 0.018998589366674423, -0.010943601839244366, -0.011337033472955227, -0.009343992918729782, 0.015892552211880684, -0.02397860214114189, -0.029652293771505356, -0.01030686404556036, -0.023357393220067024, 0.024703342467546463, -0.029258864000439644, 0.0020862212404608727, 0.06319748610258102, -0.03393862396478653, -0.038017887622117996, -0.03052198514342308, -0.0015167811652645469, -0.003152627032250166, 0.0039058409165591, -0.001580196083523333, 0.05930458754301071, -0.026815447956323624, 0.03019067458808422, -0.035201746970415115, 0.08021856844425201, 0.016327397897839546, 0.031764399260282516, -0.04102038964629173, -0.03567800670862198, 0.02708463743329048, -0.029880071058869362, 0.009509648196399212, 0.000415755930589512, 0.005249201785773039, -0.03501538559794426, -0.04824709892272949, -0.02704322338104248, 0.043898649513721466, 0.019081417471170425, -0.010006614029407501, 0.049033962190151215, -0.03296539932489395, 0.01623421721160412, -0.012817577458918095, -0.03526386618614197, 0.021328117698431015, -0.01401857752352953, -0.007350952830165625, 0.03087400272488594, -0.025407377630472183, 0.02327456697821617, 0.02638060227036476, -0.019102124497294426, -0.011399153620004654, 0.0016397284343838692, -0.022052858024835587, -0.028906846418976784, -0.019184952601790428, 0.02673261985182762, 0.012569094076752663, 0.014256707392632961, 0.014463776722550392, 0.02188720367848873, 0.0070714098401367664, -0.004633171018213034, 0.011047136038541794, -0.018222080543637276, 0.027892207726836205, -0.03882545605301857, -0.011947887018322945, 0.00676598260179162, -0.005658163223415613, -0.04472692310810089, -0.030708346515893936, 0.050731927156448364, -0.008381121791899204, 0.012196369469165802, 0.009483764879405499, 0.010058381594717503, 0.04679761454463005, -0.02882401831448078, 0.030604813247919083, -0.0623692125082016, 0.00847947970032692, 0.030998243018984795, -0.03228207305073738, -0.0008580425637774169, 0.041041094809770584, 0.0027100169099867344, 0.004915302619338036, 0.006103361491113901, 0.018139252439141273, -0.05300968885421753, 0.0008748669060878456, 0.001322006806731224, -0.04160018265247345, 0.0031940408516675234, -0.010891834273934364, 0.01852233149111271, 0.01507463026791811, 0.03834919631481171, -0.005029190797358751, 0.020230650901794434, 0.02090362459421158, 0.012424145825207233, -0.002549538156017661, -0.002380000427365303, -0.004765177611261606, 0.04290471598505974, -0.024724049493670464, -0.02708463743329048, -0.0004099321085959673, 0.022736186161637306, -0.00475741270929575, -0.016638001427054405, -0.05151879042387009, -0.029631588608026505, -0.07342670112848282, -0.021762961521744728, -0.016089268028736115, -0.008883263915777206, -0.0013808920048177242, -0.003784187836572528, 0.02428920567035675, 0.0008120991406030953, 0.01542664784938097, -0.008903970941901207, -0.011026429012417793, 0.018304908648133278, 0.0018480917206034064, 0.04365016520023346, -0.019474849104881287, 0.0023955306969583035, -0.02911391481757164, -0.008572660386562347, 0.025428084656596184, 0.02664979360997677, -0.0694095641374588, 0.03547093644738197, 0.04688044264912605, -0.006574444007128477, -0.010643351823091507, 0.045223891735076904, 0.013563025742769241, 0.0007868625689297915, -0.023046789690852165, -0.04151735454797745, -0.012144602835178375, 0.02147306501865387, -0.028306346386671066, -0.0260285846889019, -0.011709757149219513, -0.03437346965074539, 0.03364872932434082, 0.00012731514289043844, -0.013573379255831242, 0.07359235733747482, -0.02323315292596817, -0.05930458754301071, -0.0138632757589221, 0.01955767534673214, 0.01909177005290985, 0.007350952830165625, -0.017093554139137268, -0.04737740755081177, -0.026836154982447624, 0.038059301674366, 0.0008852203609421849, 0.008608897216618061, 0.006051594391465187, -0.011751171201467514, 0.02092433162033558, -0.032406315207481384, 0.0076460265554487705, 0.012341317720711231, 0.017248855903744698, 0.03197146952152252, -0.0046279942616820335, -0.021742254495620728, 0.04567944258451462, 0.029300278052687645, 0.05831065773963928, 0.051104653626680374, -0.0039084292948246, -0.0036599463783204556, -0.0138322152197361, -0.034187108278274536, -0.017217794433236122, -0.0063414908945560455, -0.028202811256051064, 0.002779902657493949, -0.000602765183430165, 0.01525063905864954, -0.02880331128835678, -0.0035771187394857407, -0.0009188691037707031, -0.028285639360547066, 0.013801155611872673, -0.041765835136175156, 0.04377440735697746, -0.00763567304238677, 0.005368266254663467, -0.011595869436860085, 0.02045842632651329, -0.0017290269024670124, -0.010809007100760937, 0.0034295818768441677, -0.002438238589093089, -0.017383450642228127, -0.006610680837184191, -0.0010683471336960793, -0.005223318003118038, -0.019630150869488716, 0.019360961392521858, -0.011927179992198944, -0.028699776157736778, 0.025883637368679047, 0.0008735727751627564, -0.010182622820138931, -0.029010379686951637, -0.011916826479136944, -0.01457766443490982, 0.03540881723165512, 0.005212964490056038, 0.009157630614936352, -0.03128813952207565, -0.01783900335431099, 0.012517326511442661, 0.019329899922013283, -0.012237783521413803, 0.0345805399119854, 0.005533921532332897, 0.0049515399150550365, -0.019692271947860718, 0.015996087342500687, -0.0041180867701768875, -0.08796295523643494, 0.019702624529600143, -0.0022272870410233736, 0.0043924530036747456, 0.017787234857678413, 0.025925051420927048, -0.017362743616104126, -0.020313479006290436, -0.02836846560239792, -0.005295792128890753, 0.043194614350795746, 0.00515343202278018, -0.06738028675317764, -0.016720829531550407, 0.008629604242742062, 0.013935750350356102, -0.0363406278192997, 0.004568461794406176, 0.025842223316431046, -0.03350377827882767, -0.02739524096250534, -0.0029973252676427364, 0.0008709843968972564, -0.005973943509161472, 0.002470593200996518, 0.02874119020998478, -0.029983604326844215, 0.015975380316376686, -0.023046789690852165, -0.010441458784043789, -0.03472548723220825, -0.01680365763604641, 0.01470190566033125, 0.0008438065415248275, 0.00008145257015712559, -0.02184578962624073 ]
Multi-access edge computing (MEC) and network function virtualization (NFV) are promising technologies to support emerging IoT applications, especially those computation-intensive. In NFV-enabled MEC environment, service function chain (SFC), i.e., a set of ordered virtual network functions (VNFs), can be mapped on MEC servers. Mobile devices (MDs) can offload computation-intensive applications, which can be represented by SFCs, fully or partially to MEC servers for remote execution. This paper studies the partial offloading and SFC mapping joint optimization (POSMJO) problem in an NFV-enabled MEC system, where an incoming task can be partitioned into two parts, one for local execution and the other for remote execution. The objective is to minimize the average cost in the long term which is a combination of execution delay, MD's energy consumption, and usage charge for edge computing. This problem consists of two closely related decision-making steps, namely task partition and VNF placement, which is highly complex and quite challenging. To address this, we propose a cooperative dual-agent deep reinforcement learning (CDADRL) algorithm, where we design a framework enabling interaction between two agents. Simulation results show that the proposed algorithm outperforms three combinations of deep reinforcement learning algorithms in terms of cumulative and average episodic rewards and it overweighs a number of baseline algorithms with respect to execution delay, energy consumption, and usage charge.
[ -0.033584222197532654, -0.006130008026957512, -0.033696357160806656, -0.004492380190640688, -0.008910004049539566, 0.023809848353266716, -0.05150701850652695, 0.026164669543504715, -0.05128275230526924, 0.05778653919696808, 0.045489147305488586, -0.06529954075813293, -0.0002660269383341074, 0.003847608109936118, 0.029584765434265137, 0.045489147305488586, -0.0010086246766149998, 0.004457338247448206, -0.009923885576426983, -0.059319041669368744, -0.012830032035708427, -0.0076157874427735806, -0.011998369358479977, 0.008064324967563152, -0.021604541689157486, 0.02999592386186123, 0.01866101659834385, 0.013101023621857166, -0.08925890177488327, 0.0652247816324234, 0.03177138417959213, 0.03337864205241203, -0.008377366699278355, -0.020427130162715912, -0.038349930197000504, 0.0063589490018785, 0.021548474207520485, -0.0016528128180652857, 0.021997010335326195, 0.06548643112182617, -0.009998640976846218, 0.0031701300758868456, -0.06156172975897789, -0.0016528128180652857, 0.027024365961551666, 0.00885860901325941, -0.03883584588766098, -0.018446091562509537, -0.018642326816916466, -0.015016650781035423, 0.028631623834371567, -0.04851677268743515, 0.017520984634757042, -0.027360768988728523, -0.02820177562534809, 0.015437155030667782, 0.08514730632305145, 0.0397329181432724, 0.011222774162888527, 0.016623908653855324, 0.0017287370283156633, -0.03842468559741974, -0.06593496352434158, -0.022109145298600197, -0.0003413671802263707, 0.008512862026691437, 0.00016484325169585645, 0.027005676180124283, 0.027267323806881905, -0.018885284662246704, -0.07729791104793549, 0.03079955279827118, -0.04223725199699402, -0.04115328565239906, -0.0041840109042823315, -0.04055523872375488, -0.010690135881304741, 0.006718713324517012, 0.04545176774263382, -0.03164055943489075, 0.014241055585443974, 0.05595501512289047, -0.016437018290162086, -0.012147882021963596, 0.09905195981264114, 0.011306874454021454, 0.023809848353266716, -0.09800537675619125, 0.03646233677864075, -0.005578681360930204, -0.04459207132458687, 0.007139216642826796, -0.028874581679701805, 0.02293146401643753, 0.06268306821584702, 0.0035298941656947136, -0.0007534023025073111, -0.03259370103478432, -0.024800367653369904, -0.02794012799859047, -0.029491320252418518, 0.010634069330990314, -0.0034247683361172676, -0.001749762217514217, 0.03492983430624008, -0.024875124916434288, -0.024202318862080574, -0.004123271442949772, -0.0026094585191458464, 0.10510721057653427, 0.0008363349479623139, -0.025043325498700142, -0.010905059985816479, 0.05778653919696808, -0.014072854071855545, 0.0032355417497456074, 0.023211799561977386, -0.08970743417739868, -0.0063309152610599995, 0.01352152694016695, 0.003983103670179844, 0.08193279057741165, 0.010166842490434647, -0.03281797096133232, -0.016792111098766327, 0.07894254475831985, -0.011484420858323574, -0.03109857812523842, 0.03197696432471275, -0.002417895710095763, -0.018221823498606682, -0.005578681360930204, -0.010045363567769527, -0.03220123052597046, 0.021997010335326195, 0.05296476557850838, 0.014904516749083996, -0.016175372526049614, 0.010241598822176456, -0.025435796007514, 0.036593157798051834, -0.03506065532565117, -0.025248905643820763, 0.037602368742227554, 0.10062184184789658, 0.059281665831804276, -0.00013126137491781265, 0.04504060745239258, -0.005172194447368383, 0.01956743374466896, -0.04690951481461525, 0.03449998423457146, 0.01841805875301361, 0.020146794617176056, 0.035340990871191025, -0.011727378703653812, 0.05759964883327484, -0.05206768959760666, 0.018184445798397064, 0.004646564833819866, 0.021193381398916245, -0.010222909972071648, -0.006335587706416845, -0.0068074860610067844, -0.04130280017852783, 0.022239968180656433, 0.01006405334919691, 0.006971015594899654, -0.05905739590525627, 0.04354548454284668, -0.026258114725351334, -0.020352374762296677, -0.011605899780988693, -0.004020481836050749, -0.006849536672234535, 0.02293146401643753, 0.08724047988653183, -0.030220191925764084, 0.008111047558486462, 0.02975296601653099, -0.049040064215660095, 0.023193109780550003, 0.01651177555322647, 0.030687419697642326, -0.002013745019212365, 0.036593157798051834, 0.015567977912724018, -0.02674403041601181, 0.026071224361658096, -0.062085021287202835, -0.004499388858675957, 0.04268578812479973, 0.07886778563261032, -0.023791160434484482, 0.027977507561445236, -0.10234123468399048, 0.005317034665495157, 0.046124573796987534, 0.026781408116221428, -0.015110095962882042, -0.038200415670871735, 0.008036291226744652, -0.008942710235714912, 0.04365761950612068, 0.029510008171200752, -0.03631282225251198, 0.03646233677864075, -0.04530225694179535, 0.04533963277935982, -0.024164941161870956, 0.04100377485156059, 0.02308097667992115, -0.004975959192961454, -0.0006745578721165657, 0.004258767236024141, 0.02909884974360466, 0.028762446716427803, -0.0430595688521862, -0.04597506299614906, -0.016035204753279686, -0.01841805875301361, 0.02162322960793972, -0.03216385468840599, -0.02012810669839382, -0.01093309372663498, -0.007041099481284618, -0.009022139012813568, 0.027229944244027138, -0.018988074734807014, -0.0022999211214482784, 0.016493085771799088, 0.024314453825354576, 0.005438513588160276, -0.030575284734368324, 0.008914676494896412, -0.042125117033720016, 0.02087566815316677, -0.002747290302067995, -0.040517859160900116, 0.019847771152853966, -0.04384450986981392, 0.02141765132546425, -0.048142991960048676, -0.03803221508860588, 0.05715111270546913, -0.02523021586239338, -0.026052534580230713, 0.07610180974006653, 0.01995990425348282, -0.015437155030667782, -0.02629549242556095, -0.0652247816324234, 0.017025724053382874, 0.007849400863051414, 0.007798005826771259, 0.0063589490018785, 0.024295764043927193, -0.014231710694730282, 0.013101023621857166, -0.009970608167350292, 0.015390432439744473, 0.01815641112625599, 0.022202590480446815, 0.012923477217555046, -0.0015967456856742501, -0.011101295240223408, 0.0367426723241806, 0.017941487953066826, -0.004235405940562487, -0.023510824888944626, -0.06477624177932739, -0.024314453825354576, -0.05920690670609474, 0.00392703665420413, -0.013026267290115356, -0.049787625670433044, -0.0351354144513607, -0.011119984090328217, 0.07565326988697052, 0.005303017795085907, 0.020744845271110535, -0.017586395144462585, 0.043769754469394684, -0.026314182206988335, -0.06268306821584702, -0.026351559907197952, -0.01469893753528595, -0.03638757765293121, -0.03909749165177345, -0.008839920163154602, -0.02072615548968315, 0.016521120443940163, 0.04489109665155411, 0.009494037367403507, 0.04238676279783249, 0.002845407696440816, 0.001934316591359675, -0.01791345328092575, 0.03676135838031769, -0.009293129667639732, 0.0013818215811625123, 0.01188623532652855, 0.0654490515589714, 0.06399130821228027, -0.0018724091351032257, -0.0042634392157197, -0.026071224361658096, 0.019137587398290634, 0.0430595688521862, -0.013839241117238998, -0.002183114644140005, -0.03300486132502556, -0.0071765948086977005, -0.06638350337743759, -0.015268953517079353, 0.04418091103434563, 0.010877027176320553, -0.03777056932449341, -0.012512318789958954, -0.042573653161525726, 0.048442017287015915, 0.004933909047394991, -0.06290733814239502, 0.0349111445248127, -0.0068635535426437855, -0.004473691340535879, 0.043321214616298676, 0.008947382681071758, -0.05554385483264923, 0.013614972122013569, -0.009302474558353424, 0.006891586817800999, -0.026856163516640663, -0.030126746743917465, -0.01557732280343771, 0.028687691316008568, -0.01845543645322323, 0.07277515530586243, -0.012652486562728882, -0.005022681783884764, 0.014876483008265495, -0.017801320180296898, -0.009395919740200043, 0.03788270428776741, -0.02111862599849701, -0.010073397308588028, -0.03939651697874069, 0.02623942494392395, -0.026781408116221428, 0.023361312225461006, 0.0010314019164070487, -0.04152706637978554, 0.01890397258102894, -0.030967755243182182, 0.08342791348695755, -0.05442251265048981, -0.03876108676195145, -0.005728193558752537, -0.07423290610313416, -0.007115855347365141, 0.007952190935611725, -0.021342894062399864, -0.04496585205197334, 0.0025440468452870846, -0.04264841228723526, 0.020240239799022675, -0.026781408116221428, -0.03678004816174507, 0.031135955825448036, 0.016792111098766327, -0.015054029412567616, 0.012773965485394001, 0.033397331833839417, -0.01851150393486023, -0.06115056946873665, 0.024762989953160286, 0.016287505626678467, -0.05214244872331619, -0.034481294453144073, 0.04044310376048088, -0.008709097281098366, 0.04489109665155411, -0.056515686213970184, 0.010447178967297077, -0.008765163831412792, 0.020632710307836533, 0.03216385468840599, -0.08021339774131775, -0.022912774235010147, 0.07662510126829147, -0.0037471544928848743, -0.03612593188881874, -0.04945122450590134, -0.013764484785497189, 0.008685735985636711, -0.0365184023976326, -0.002009072806686163, 0.012755276635289192, 0.005092766135931015, -0.06903734803199768, -0.055170074105262756, 0.03025757148861885, 0.033042240887880325, 0.054310377687215805, -0.027753237634897232, -0.02784668281674385, 0.017932143062353134, -0.07030820101499557, -0.02072615548968315, 0.019530056044459343, 0.017081791535019875, -0.056366171687841415, 0.013811207376420498, -0.04619932919740677, 0.015437155030667782, 0.025304973125457764, -0.04384450986981392, 0.004679270554333925, -0.007643821183592081, -0.04178871586918831, -0.0238846056163311, 0.013381359167397022, 0.05352543666958809, 0.004812430124729872, 0.05303952097892761, 0.03668660297989845, 0.03231336548924446, -0.03294879570603371, -0.002218156587332487, 0.054310377687215805, 0.008040963672101498, 0.006653301417827606, 0.010624724440276623, -0.05143226310610771, -0.009680927731096745, 0.012502973899245262, 0.04115328565239906, 0.06959801912307739, -0.06653301417827606, 0.01023225486278534, 0.06107581406831741, -0.03780794516205788, -0.054721537977457047, -0.017390159890055656, -0.01081161480396986, -0.02126813866198063, -0.008391383104026318, -0.04343334957957268, 0.028332598507404327, -0.03578953072428703, -0.04418091103434563, 0.004310161806643009, -0.048442017287015915, 0.02764110453426838, 0.035041969269514084, -0.017231304198503494, -0.007858744822442532, -0.06107581406831741, 0.027753237634897232, -0.02844473347067833, 0.021455029025673866, 0.04956335946917534, 0.043022193014621735, -0.03210778534412384, -0.017240647226572037, 0.044031400233507156, -0.05442251265048981, -0.03831255063414574, -0.00722331739962101, -0.00039889439358375967, 0.019137587398290634, -0.04474158585071564, 0.07412076741456985, 0.03425702825188637, -0.000731209060177207, 0.030986443161964417, 0.025211527943611145, -0.10503245890140533, -0.026669273152947426, -0.008260560221970081, 0.017390159890055656, 0.013381359167397022, 0.03737809881567955, -0.025622686371207237, 0.0025440468452870846, 0.000036921821447322145, 0.007022410165518522, 0.000930948241148144, 0.009587482549250126, 0.012157226912677288, 0.07311156392097473, -0.025267595425248146, -0.021810119971632957, 0.027585037052631378, -0.02754765935242176, -0.026949608698487282, 0.011007850058376789, -0.01584831438958645, 0.016137994825839996, 0.03638757765293121, -0.03633151203393936, -0.02588433399796486, 0.06559856235980988, 0.049189578741788864, -0.02132420614361763, -0.03175269439816475, 0.03606986626982689, 0.014147610403597355, -0.0397329181432724, -0.006690679583698511, 0.0334160216152668, 0.049787625670433044, 0.01472697127610445, -0.0006033058743923903, 0.002268383279442787, 0.04832988232374191, -0.0025767525658011436, -0.002962214406579733, -0.002213484374806285, 0.09950049966573715, 0.006073941010981798, -0.021585851907730103, 0.021249448880553246, 0.008648357354104519, -0.015558633953332901, 0.007428897079080343, 0.03079955279827118, -0.024557411670684814, 0.08821231126785278, 0.001732241245917976, -0.055805500596761703, 0.036051176488399506, -0.03177138417959213, -0.003371037309989333, -0.017791975289583206, 0.018885284662246704, -0.009045500308275223, -0.01294216699898243, -0.010578001849353313, -0.013222502544522285, 0.01886659488081932, 0.047731831669807434, -0.012390839867293835, -0.02186618745326996, -0.014708281494677067, 0.010718169622123241, 0.027379456907510757, -0.02653845027089119, 0.023921983316540718, -0.004270447883754969, 0.015511911362409592, -0.04747018590569496, -0.028369976207613945, 0.0043241786770522594, -0.05423562228679657, -0.02272588387131691, 0.013213157653808594, -0.020539265125989914, -0.05117061734199524, -0.03386455774307251, -0.00003723209010786377, 0.01870773918926716, 0.023137042298913002, 0.007620459888130426, 0.013829896226525307, 0.0073027461767196655, -0.04062999412417412, 0.04320908337831497, 0.01279265433549881, 0.020333684980869293, 0.017287369817495346, -0.037396788597106934, -0.005676798522472382, -0.015941759571433067, 0.027061743661761284, 0.007522342260926962, 0.014409257099032402, 0.035247545689344406, 0.007129872217774391, -0.022314725443720818, -0.02293146401643753, -0.016287505626678467, 0.01810968853533268, 0.003941053058952093, -0.013259880244731903, 0.013026267290115356, 0.015511911362409592, -0.031135955825448036, 0.027211256325244904, 0.0019775349646806717, 0.020184174180030823, -0.015465188771486282, -0.048292502760887146, 0.016446363180875778, 0.03853682056069374, -0.023716403171420097, 0.01856757141649723, 0.004212044645100832, 0.01359628327190876, -0.030519217252731323, -0.027958817780017853, 0.06058989837765694, -0.04395664483308792, 0.022707194089889526, -0.016773421317338943, -0.011007850058376789, 0.023903293535113335, 0.08529682457447052, 0.03255632519721985, -0.0015418465482071042, 0.04840463772416115, 0.06515002250671387, 0.03717251867055893, -0.017633117735385895, 0.004029826261103153, -0.01439991220831871, 0.013110368512570858, -0.0011009018635377288, 0.008587618358433247, -0.022296035662293434, 0.008349332958459854, -0.04062999412417412, 0.023417379707098007, 0.02427707426249981, -0.017334092408418655, 0.04074212908744812, 0.01776394061744213, -0.0382377952337265, -0.01000798586755991, -0.04993714019656181, 0.009522070176899433, -0.018240511417388916, -0.003508869092911482, -0.05161915346980095, 0.00890533160418272, -0.023641647771000862, -0.026108602061867714, 0.024314453825354576, -0.004915220197290182, 0.018548881635069847, -0.03522885963320732, 0.02347344532608986, -0.008545568212866783, 0.07157906144857407, -0.0073167625814676285, -0.004578817170113325, -0.02272588387131691, 0.005709504708647728, 0.029080159962177277, 0.04922695457935333, 0.029921168461441994, 0.02156716212630272, 0.027117811143398285, 0.03350946679711342, -0.01467090379446745, -0.012540352530777454, 0.020950423553586006, -0.02012810669839382, -0.025323661044239998, 0.025846954435110092, 0.03636889159679413, -0.012278705835342407, -0.0010424985084682703, 0.016894901171326637, -0.0020149131305515766, -0.029883790761232376, 0.011045227758586407, 0.05950593203306198, -0.008900660090148449, 0.02739814668893814, -0.044666826725006104, 0.018277890980243683, -0.035939041525125504, 0.009475347585976124, 0.00583098316565156, 0.003293944988399744, 0.028986714780330658, 0.022109145298600197, -0.02889326959848404, -0.016633253544569016, -0.04380713030695915, -0.03010805882513523, -0.037153828889131546, -0.0033803817350417376, 0.0032332055270671844, -0.017932143062353134, -0.014110232703387737, 0.019305787980556488, -0.03070610761642456, 0.03606986626982689, -0.023062286898493767, -0.0022228287998586893, 0.04590030387043953, -0.008844592608511448, -0.0015383423306047916, 0.011325564235448837, 0.014334500767290592, -0.02418362908065319, 0.029715588316321373, -0.02182880975306034, -0.008209165185689926, -0.03386455774307251, 0.023118354380130768, -0.00320984423160553, 0.005639420822262764, -0.013026267290115356, 0.00411626324057579, 0.02954738773405552, -0.024669544771313667, -0.006130008026957512, 0.010970472358167171, -0.005209572613239288, -0.0041629858314991, 0.02954738773405552, 0.03902273625135422, 0.02046450972557068, -0.029173605144023895, -0.0037938770838081837, -0.014390568248927593, 0.0032051720190793276, -0.004971287213265896, -0.006209436804056168, -0.020389752462506294, -0.051955558359622955, 0.0015056364936754107, 0.012661830522119999, 0.031173333525657654, 0.03478031978011131, -0.021156003698706627, 0.0029411891009658575, 0.05939379706978798, -0.005396462976932526, -0.0681028962135315, 0.025753509253263474, -0.008349332958459854, -0.005022681783884764, 0.051806043833494186, 0.026351559907197952, 0.0005221253377385437, 0.026052534580230713, 0.01554928906261921, -0.020240239799022675, 0.02358558028936386, -0.0000598268597968854, -0.001842039404436946, -0.0012089478550478816, 0.007671854924410582, 0.021810119971632957, -0.02298753149807453, -0.011923613026738167, 0.048142991960048676, -0.006569200661033392, 0.04541438817977905, -0.015483877621591091, -0.04130280017852783, 0.03375242277979851, 0.015670767053961754, 0.012166570872068405, 0.07505521923303604, 0.03777056932449341, 0.027753237634897232, 0.0396207831799984, 0.010297666303813457, 0.02237079292535782, 0.023454757407307625, 0.0005335139576345682, -0.012129193171858788, -0.026706650853157043, 0.024520032107830048, -0.001312905689701438, 0.028556866571307182, 0.0017252328107133508, 0.011559177190065384, -0.05281525477766991, -0.007648493628948927, -0.015923069790005684, -0.02061402052640915, -0.022744573652744293, -0.0016107624396681786, -0.008825903758406639, -0.05057256668806076, 0.009821095503866673, -0.03692956268787384, 0.03797614946961403, -0.028519488871097565, 0.0053450679406523705, -0.01885724999010563, -0.021585851907730103, 0.02980903349816799, 0.03156580403447151, 0.012213293462991714, 0.007115855347365141, -0.009671582840383053, 0.027416834607720375, 0.04238676279783249, -0.029827723279595375, -0.027061743661761284, 0.03683611750602722, -0.034238338470458984, -0.013306602835655212, 0.021361583843827248, -0.014755004085600376, -0.012960855849087238, 0.03752760961651802, -0.031173333525657654, 0.024762989953160286, -0.005018009804189205, 0.005835655611008406, -0.02904278226196766, 0.02248292602598667, 0.02287539653480053, 0.023847226053476334, -0.03711645305156708, 0.03309830650687218, -0.0026888870634138584, -0.015539944171905518, -0.028837203979492188, 0.03831255063414574, -0.025155460461974144, -0.035490505397319794, 0.03455605357885361, 0.015764212235808372, 0.016530463472008705, 0.06967277824878693, -0.00781202269718051, -0.036256756633520126, 0.0541982427239418, -0.011624588631093502, 0.039209626615047455, 0.026930920779705048, 0.05819769948720932, 0.02293146401643753, 0.004840463865548372, -0.004550783429294825, -0.04358286410570145, 0.010671447031199932, 0.012680520303547382, 0.035247545689344406, -0.026351559907197952, 0.03558395057916641, -0.01349349319934845, -0.004097573924809694, -0.030332326889038086, -0.015521255321800709, -0.057263247668743134, 0.01462418120354414, -0.018231168389320374, 0.00840539950877428, -0.008536223322153091, -0.013540215790271759, 0.02519283816218376, 0.004022818058729172, 0.07841925323009491, 0.007933501154184341, -0.03528492525219917, 0.024052806198596954, -0.023548202589154243, -0.01690424419939518, 0.025323661044239998, -0.018801184371113777, 0.0072326622903347015, 0.010615380480885506, 0.034294404089450836, -0.018754461780190468, 0.017745252698659897, -0.03646233677864075, -0.01932447776198387, -0.010531279258430004, 0.003074348671361804, -0.04152706637978554, 0.014811071567237377, -0.017231304198503494, 0.008564257062971592, 0.031621869653463364, -0.014241055585443974, -0.0032448861747980118, -0.01560535654425621, 0.024893812835216522, 0.05191817879676819, 0.01013880968093872, 0.0004091149603482336, 0.0017953168135136366, 0.013381359167397022, -0.02412756346166134, 0.03868633136153221, -0.007755955681204796, -0.0054338411428034306, -0.039957188069820404, 0.02338000014424324, -0.05438513308763504, -0.007452258374541998, -0.0000705584607203491, 0.004083557054400444, -0.0018794175703078508, 0.02808964066207409, 0.015110095962882042, -0.03405144810676575, -0.0019588458817452192, 0.0037074401043355465, 0.02879982441663742, -0.00830728281289339, -0.03132284805178642, -0.03988243266940117, -0.03631282225251198, 0.0571884922683239, -0.006779452785849571, -0.01261510793119669, -0.023604270070791245, 0.004174666479229927, -0.010624724440276623, 0.018745116889476776, -0.023492135107517242, 0.01861429400742054, 0.014736315235495567, -0.009727650322020054, -0.016736043617129326, -0.02046450972557068, -0.012886099517345428, 0.03767712414264679, 0.01584831438958645, -0.0018338629743084311, -0.0005048963357694447, -0.03025757148861885, 0.02266981638967991, -0.02633287012577057, 0.02347344532608986, 0.010942438617348671, 0.04223725199699402, 0.010316355153918266, -0.013540215790271759, -0.0171658918261528, 0.02266981638967991, 0.019305787980556488, -0.0035649361088871956, 0.012306738644838333, 0.010428489185869694, -0.025566618889570236, -0.03326650708913803, -0.047582320868968964, 0.006073941010981798, -0.03506065532565117, 0.03769581392407417, 0.02493119239807129, 0.02081960067152977, 0.017539672553539276, 0.002173769986256957, 0.03150973841547966, 0.01896004006266594, 0.016567843034863472, 0.03947127237915993, -0.01790410839021206, -0.02990247868001461, 0.007639148738235235, -0.047283295542001724, 0.001842039404436946, -0.044778961688280106, -0.012101159431040287, -0.045937683433294296, 0.01750229485332966, 0.0668320432305336, 0.02010941691696644, 0.015362398698925972, -0.00845212209969759, 0.009195012040436268, -0.004090565722435713, 0.022894086316227913, -0.020333684980869293, 0.02102518081665039, -0.027603724971413612, 0.020800912752747536, 0.03898535668849945, -0.05023616552352905, -0.0025090049020946026, 0.016390295699238777, -0.03683611750602722, -0.010465867817401886, -0.021062558516860008, -0.02603384479880333, -0.04687213525176048, 0.013540215790271759, 0.029491320252418518, -0.006545839365571737, 0.019530056044459343, -0.001714720274321735, -0.013558905571699142, -0.009708961471915245, 0.04750756174325943, -0.018240511417388916, -0.014960584230720997, 0.017773285508155823, -0.034742943942546844, 0.02263243868947029, 0.0034598102793097496, -0.005700159817934036, -0.017932143062353134, 0.005672126542776823, 0.025118082761764526, -0.05774916335940361, -0.016035204753279686, 0.0017801319481804967, -0.03207040950655937, 0.00292950845323503, -0.02177274227142334, 0.04268578812479973, 0.02412756346166134, -0.015016650781035423, 0.024800367653369904, -0.007129872217774391, -0.022146522998809814, 0.04679737985134125, -0.03792008012533188, 0.029435252770781517, 0.03235074505209923, 0.028762446716427803, -0.022894086316227913, 0.04115328565239906, -0.041975606232881546, 0.016044549643993378, -0.025753509253263474, -0.04190084710717201, 0.008961399085819721, -0.01574552431702614, -0.002058131620287895, 0.010344388894736767 ]
Dyson spheres are hypothetical megastructures encircling stars in order to harvest most of their energy output. During the 11th edition of the GTOC challenge, participants were tasked with a complex trajectory planning related to the construction of a precursor Dyson structure, a heliocentric ring made of twelve stations. To this purpose, we developed several new approaches that synthesize techniques from machine learning, combinatorial optimization, planning and scheduling, and evolutionary optimization effectively integrated into a fully automated pipeline. These include a machine learned transfer time estimator, improving the established Edelbaum approximation and thus better informing a Lazy Race Tree Search to identify and collect asteroids with high arrival mass for the stations; a series of optimally-phased low-thrust transfers to all stations computed by indirect optimization techniques, exploiting the synodic periodicity of the system; and a modified Hungarian scheduling algorithm, which utilizes evolutionary techniques to arrange a mass-balanced arrival schedule out of all transfer possibilities. We describe the steps of our pipeline in detail with a special focus on how our approaches mutually benefit from each other. Lastly, we outline and analyze the final solution of our team, ACT&Friends, which ranked second at the GTOC 11 challenge.
[ -0.004889079835265875, -0.06710480898618698, -0.034464962780475616, -0.05454122647643089, -0.014356863684952259, 0.004263022914528847, 0.020744765177369118, 0.046264540404081345, -0.06608613580465317, 0.007040487136691809, 0.016754979267716408, 0.03552607446908951, 0.008801935240626335, -0.03329773619771004, -0.03306429088115692, 0.06566169112920761, 0.018336039036512375, -0.014685808680951595, 0.007592265959829092, -0.09074641019105911, 0.018749872222542763, -0.006929070223122835, -0.03951586037874222, 0.04452431574463844, 0.021370822563767433, -0.033785849809646606, 0.020299097523093224, -0.0013058326439931989, -0.04813209921121597, 0.0016128922579810023, 0.0073004597797989845, 0.014685808680951595, -0.0035892159212380648, -0.009831215254962444, 0.007958349771797657, -0.045585427433252335, 0.055305227637290955, 0.03149384260177612, 0.028713727369904518, 0.006568291690200567, -0.015386143699288368, -0.011948135681450367, -0.07864972203969955, -0.005745928734540939, -0.015322476625442505, 0.041107531636953354, -0.02159365639090538, 0.023471826687455177, 0.04123486578464508, -0.0012879263376817107, 0.00009848458284977823, -0.04550053924322128, 0.05288589000701904, -0.013921806588768959, -0.05649367347359657, 0.0023397549521178007, 0.05241899937391281, 0.07555127143859863, 0.05933745577931404, 0.05263122171163559, 0.0712643712759018, -0.03092084266245365, -0.01585303246974945, 0.007507376838475466, 0.06765658408403397, -0.060271237045526505, 0.008090988732874393, 0.08060216903686523, 0.006992736831307411, 0.01838909462094307, 0.019609374925494194, -0.06506747007369995, -0.08586528897285461, -0.05713034048676491, 0.024936163797974586, -0.04350564628839493, 0.06774147599935532, -0.007740821689367294, -0.04503364861011505, -0.03123917616903782, -0.052970778197050095, 0.033318959176540375, -0.03387073799967766, -0.006398513447493315, 0.062011461704969406, -0.005613289307802916, -0.008197100833058357, -0.07966838777065277, 0.04915076866745949, 0.008966407738626003, -0.044396981596946716, 0.0017017604550346732, -0.047622766345739365, -0.012139136902987957, -0.04584009572863579, 0.034401293843984604, 0.04350564628839493, 0.015248198993504047, -0.018834762275218964, -0.004103855695575476, -0.0848466232419014, -0.06315746903419495, 0.0010863147908821702, -0.03834863752126694, 0.015831811353564262, -0.012903138063848019, 0.017179423943161964, 0.014728252775967121, 0.03898530453443527, 0.10008420795202255, -0.013401861302554607, -0.00806976668536663, 0.019418373703956604, -0.003212520619854331, -0.0567907840013504, -0.006769903004169464, -0.050169438123703, -0.01985342986881733, 0.02559405378997326, -0.007252709474414587, 0.047919876873493195, 0.05730012059211731, 0.014271974563598633, -0.04821699112653732, -0.018749872222542763, 0.030814731493592262, -0.008515434339642525, -0.02811950258910656, 0.009125574491918087, 0.010961300693452358, -0.06112012639641762, 0.010298104956746101, -0.001380773726850748, 0.028756171464920044, 0.022453157231211662, 0.02822561375796795, 0.01732798106968403, -0.001215638010762632, -0.020850876346230507, 0.0422535315155983, -0.03202439844608307, 0.013486750423908234, 0.011258412152528763, -0.010011604055762291, -0.05135788396000862, 0.0009656131151132286, -0.06808102875947952, 0.06031368300318718, -0.06510991603136063, 0.026294387876987457, -0.012775804847478867, 0.07198593020439148, -0.008897434920072556, -0.009396158158779144, -0.03325529024004936, 0.004212619736790657, -0.05814900994300842, -0.010918856598436832, 0.011608580127358437, 0.040789198130369186, 0.0042815920896828175, -0.01830420456826687, 0.019142484292387962, 0.003525549080222845, 0.003541465848684311, -0.05483833700418472, 0.014420529827475548, 0.03879430517554283, -0.09541530907154083, 0.0179009810090065, 0.01483436394482851, 0.005414330866187811, -0.011810190975666046, 0.02674005553126335, -0.013762639835476875, -0.006138540804386139, 0.017932815477252007, 0.015258809551596642, 0.057554785162210464, -0.006440958008170128, -0.05534766986966133, 0.04367542639374733, 0.038178857415914536, 0.04613720625638962, 0.05925256758928299, 0.08514373004436493, 0.05904034525156021, -0.002819908782839775, 0.04660409688949585, -0.0031435482669621706, 0.020405208691954613, -0.011502468958497047, 0.029350394383072853, -0.005745928734540939, 0.006727458443492651, -0.05730012059211731, -0.026824945583939552, 0.007714293897151947, -0.07117947936058044, -0.041404642164707184, -0.024745162576436996, -0.033021848648786545, -0.04622209817171097, 0.014240141026675701, 0.0315362885594368, 0.011428190395236015, 0.021965045481920242, -0.010154854506254196, 0.029350394383072853, -0.03550485149025917, -0.0076612383127212524, 0.03026295267045498, -0.07410815358161926, -0.037117745727300644, -0.011078023351728916, -0.002522796858102083, 0.010027521289885044, 0.05581456050276756, 0.009427991695702076, -0.0778857171535492, 0.01114169042557478, -0.0006608746480196714, 0.036035407334566116, -0.0019113303860649467, 0.019418373703956604, 0.0035096323117613792, -0.018208704888820648, -0.005761845503002405, -0.020288486033678055, -0.04331464692950249, -0.017582647502422333, 0.04855654761195183, 0.01983220875263214, -0.022729046642780304, -0.006027123890817165, -0.04121364280581474, 0.007719599641859531, -0.012945583090186119, -0.013624695129692554, -0.03996152803301811, -0.007162515074014664, -0.04017375037074089, -0.03480451554059982, -0.0003916171262972057, 0.05933745577931404, -0.009465130977332592, -0.03656596690416336, 0.05055144056677818, 0.026124609634280205, 0.03820008039474487, 0.01761448197066784, 0.016394201666116714, -0.02869250439107418, 0.026676388457417488, 0.03531385213136673, 0.028034614399075508, 0.040513306856155396, -0.017349202185869217, -0.008032628335058689, 0.03200317919254303, 0.010282187722623348, -0.0009225053945556283, 0.020543154329061508, 0.0665530264377594, -0.0025029010139405727, 0.04202008619904518, 0.0317060649394989, 0.01915309578180313, -0.03363729268312454, -0.009603075683116913, -0.036523520946502686, -0.07937127351760864, -0.012839470990002155, -0.019195539876818657, 0.01551347691565752, -0.062096353620290756, -0.029201839119195938, 0.0037404245231300592, 0.062308575958013535, -0.0034300489351153374, 0.03550485149025917, -0.07241037487983704, 0.031005730852484703, -0.03297940269112587, -0.05984679237008095, -0.016786813735961914, -0.031005730852484703, -0.011406968347728252, -0.003220479004085064, -0.025169609114527702, -0.040725529193878174, 0.00330536812543869, 0.019206151366233826, 0.03043273091316223, 0.06765658408403397, -0.01303047128021717, 0.02625194378197193, -0.042741645127534866, -0.03764830157160759, -0.018452761694788933, -0.054923225194215775, 0.036523520946502686, 0.004289550706744194, 0.05713034048676491, -0.0425930880010128, 0.010876411572098732, -0.006950292270630598, 0.0534801110625267, -0.03962197154760361, -0.019397152587771416, 0.002356997923925519, 0.03308551385998726, 0.019535096362233162, 0.005841428879648447, 0.03463473916053772, 0.019407762214541435, 0.08280928432941437, 0.019980764016509056, -0.03221540153026581, -0.018728651106357574, 0.04157441854476929, -0.05912523344159126, -0.08115394413471222, 0.003114367602393031, 0.01672314666211605, 0.031111842021346092, 0.055602338165044785, -0.006796430796384811, -0.02092515490949154, 0.02850150316953659, -0.018558872863650322, 0.007231487426906824, -0.023620381951332092, -0.03716018795967102, -0.016882313415408134, -0.05713034048676491, -0.009687964804470539, -0.0035122851841151714, 0.01732798106968403, 0.04098019748926163, 0.015258809551596642, 0.027376724407076836, 0.0232596043497324, 0.0015226976247504354, -0.0550505593419075, -0.04554298520088196, 0.024660274386405945, -0.01633053459227085, -0.011067411862313747, -0.014908642508089542, 0.001272672787308693, 0.010398910380899906, -0.0416380874812603, -0.012531748041510582, 0.0258699432015419, -0.011905691586434841, -0.016606424003839493, -0.07516926527023315, 0.004446065053343773, -0.0030029506888240576, 0.06018634885549545, -0.08348839730024338, 0.03679940849542618, 0.02099943347275257, -0.04613720625638962, 0.01830420456826687, 0.030984509736299515, 0.009502270258963108, -0.050424106419086456, 0.016606424003839493, -0.024872496724128723, 0.05377722531557083, 0.026909833773970604, -0.022240934893488884, -0.013338194228708744, -0.01225585862994194, 0.031472619622945786, -0.016075866296887398, -0.038178857415914536, 0.024172160774469376, -0.010038131847977638, 0.031748510897159576, 0.05904034525156021, 0.040513306856155396, -0.0051066079176962376, 0.06001656875014305, 0.011788968928158283, -0.020787209272384644, -0.009454519487917423, 0.027100834995508194, 0.0034618822392076254, 0.013072916306555271, -0.018558872863650322, 0.0005710116238333285, 0.005220677703619003, -0.03217295557260513, 0.07988061010837555, 0.00685479212552309, -0.004522995557636023, 0.03616274148225784, -0.03092084266245365, 0.035356294363737106, -0.021370822563767433, 0.058615900576114655, 0.009030074812471867, -0.03718141093850136, -0.005387803073972464, -0.03588685393333435, -0.015555921010673046, 0.06112012639641762, -0.0027376723010092974, 0.002654109615832567, 0.02217726781964302, -0.06820836663246155, 0.028522726148366928, 0.048004768788814545, 0.05649367347359657, 0.0026010540314018726, -0.005650428589433432, -0.06370924413204193, -0.060271237045526505, 0.04987232759594917, -0.04728320986032486, 0.029647506773471832, 0.033807069063186646, 0.02975361794233322, 0.02198626846075058, 0.002684616716578603, -0.025912387296557426, 0.01732798106968403, 0.036523520946502686, 0.026145832613110542, 0.00039460152038373053, -0.01642603427171707, 0.009990382008254528, -0.003262923564761877, -0.017274925485253334, 0.00036376292700879276, 0.023662827908992767, 0.04893854632973671, -0.0006515898858197033, -0.014781308360397816, -0.0266551673412323, -0.028055837377905846, 0.02207115665078163, 0.01161919068545103, -0.049447882920503616, 0.016882313415408134, 0.032363954931497574, -0.035950519144535065, -0.059295013546943665, -0.0274403914809227, -0.0648128017783165, 0.006122624035924673, 0.0389428585767746, -0.008573795668780804, 0.013698972761631012, -0.061247460544109344, 0.002127532148733735, 0.0073216818273067474, 0.04609476402401924, 0.023556716740131378, 0.03805152326822281, -0.06901481002569199, 0.04690120741724968, 0.056366339325904846, -0.03278840333223343, -0.04350564628839493, 0.01700964756309986, 0.060568347573280334, -0.00387836922891438, -0.04066186398267746, 0.02159365639090538, 0.0681234747171402, 0.01642603427171707, -0.012733359821140766, 0.002070497488602996, -0.014367474243044853, -0.04613720625638962, -0.03898530453443527, -0.027461612597107887, 0.04123486578464508, 0.060950350016355515, -0.023853827267885208, -0.008870907127857208, -0.0035202435683459044, 0.03189706802368164, -0.010653577744960785, -0.015386143699288368, 0.009152102284133434, 0.06791125237941742, -0.015014753676950932, 0.007135987281799316, -0.0054090251214802265, -0.024278273805975914, -0.0182935930788517, -0.02296249195933342, -0.01593792252242565, 0.02188015729188919, 0.01761448197066784, 0.008998241275548935, -0.04038597270846367, -0.04758032038807869, -0.014314418658614159, 0.005878567695617676, 0.029498949646949768, 0.0566210076212883, 0.0359717421233654, -0.0022164005786180496, -0.007236792705953121, 0.01114169042557478, 0.009884270839393139, 0.01993831992149353, 0.041001420468091965, 0.030666174367070198, 0.02226215787231922, 0.005141093861311674, 0.03503796085715294, -0.004642370622605085, 0.004008355550467968, -0.01975793018937111, -0.02130715548992157, 0.0038651053328067064, 0.026421722024679184, 0.0013980168150737882, 0.025021051988005638, 0.023132270202040672, -0.006281790789216757, 0.03790296986699104, 0.009083130396902561, -0.016394201666116714, 0.039728082716464996, -0.02022482082247734, -0.05653611943125725, -0.010722550563514233, -0.013741417787969112, -0.018887817859649658, 0.022729046642780304, -0.022474380210042, -0.02489371784031391, -0.028374170884490013, 0.04970254749059677, -0.03238517791032791, 0.04195642098784447, -0.0017349203117191792, -0.006340152118355036, 0.05496567115187645, -0.0053241360001266, 0.0018370524048805237, 0.01114169042557478, -0.01964120753109455, -0.00967735331505537, -0.017540203407406807, 0.005218024831265211, -0.022516824305057526, -0.048386767506599426, -0.00568756740540266, -0.05076366290450096, 0.016479089856147766, 0.006976820062845945, -0.016574589535593987, -0.02576383203268051, -0.0011513079516589642, -0.07075503468513489, -0.03276718035340309, -0.012584804557263851, 0.0023225117474794388, 0.011778358370065689, 0.02217726781964302, 0.01693536899983883, 0.02101004309952259, -0.007353515364229679, -0.037011634558439255, 0.01264847069978714, -0.01956692896783352, 0.015301254577934742, -0.02947772853076458, -0.0186862051486969, -0.01046257745474577, -0.021232876926660538, 0.03510162979364395, -0.034762073308229446, 0.0030162145849317312, -0.019089428707957268, 0.013210861012339592, -0.04579764977097511, -0.01926981844007969, -0.034783296287059784, 0.02529694139957428, -0.026803722605109215, -0.02958383969962597, -0.0036183963529765606, -0.002014789031818509, 0.014049140736460686, 0.006647875066846609, 0.030708620324730873, 0.045585427433252335, -0.018718039616942406, 0.025657720863819122, -0.06286035478115082, 0.044609203934669495, 0.024193383753299713, -0.012478692457079887, -0.004345259163528681, -0.03454985097050667, 0.0146327530965209, 0.023280827328562737, 0.013730806298553944, -0.03387073799967766, 0.010054049082100391, 0.0007043139776214957, 0.012850082479417324, 0.0400676392018795, -0.011364523321390152, 0.06048345938324928, 0.0066531808115541935, 0.0029631590005010366, 0.03493184968829155, -0.024002384394407272, -0.05008454993367195, 0.002496269065886736, 0.03240640088915825, 0.040704306215047836, 0.011852636002004147, 0.003615743713453412, 0.038178857415914536, 0.035653408616781235, -0.010669494979083538, -0.030369063839316368, 0.01172530185431242, 0.041404642164707184, -0.0028862282633781433, -0.0199489314109087, -0.032257843762636185, -0.001027953578159213, -0.019630596041679382, 0.001420565415173769, 0.01749775931239128, 0.016945980489253998, 0.06349702179431915, -0.057724565267562866, 0.01700964756309986, 0.008690518327057362, 0.015555921010673046, -0.0031886454671621323, 0.039346083998680115, 0.004719301592558622, -0.035165295004844666, 0.0566210076212883, 0.030411507934331894, 0.03395562618970871, 0.01895148493349552, 0.012828860431909561, 0.0531405545771122, 0.036141518503427505, -0.021031266078352928, -0.005019065923988819, 0.03932486101984978, -0.0013860792387276888, 0.019015150144696236, 0.020787209272384644, -0.0038332717958837748, 0.01633053459227085, 0.018548261374235153, 0.017879759892821312, 0.02207115665078163, 0.023599160835146904, 0.03732996806502342, -0.02169976755976677, 0.0011108530452474952, -0.004785621073096991, 0.01936531811952591, -0.03887919336557388, 0.003705938346683979, 0.01830420456826687, -0.019110651686787605, -0.008133433759212494, 0.06880258768796921, -0.029796062037348747, -0.018919650465250015, 0.03134528920054436, -0.017296146601438522, -0.016404811292886734, -0.04015252739191055, -0.03414662554860115, -0.011152300983667374, -0.01692475751042366, 0.010011604055762291, -0.014080974273383617, 0.03247006610035896, -0.047919876873493195, -0.01575753279030323, -0.03338262438774109, 0.0783950537443161, -0.011184134520590305, 0.014813141897320747, -0.020468875765800476, 0.020574986934661865, 0.028140725567936897, -0.04308120161294937, -0.024532940238714218, 0.03270351141691208, -0.0030692704021930695, 0.024002384394407272, 0.0015425934689119458, 0.054329004138708115, 0.0006943660555407405, -0.004841329529881477, -0.02811950258910656, -0.019206151366233826, -0.02801339142024517, 0.025551609694957733, 0.004005702678114176, 0.024066049605607986, 0.042656756937503815, -0.013943029567599297, -0.021572433412075043, -0.0041197724640369415, 0.011778358370065689, 0.014303808100521564, -0.00987365934997797, -0.00039791749441064894, -0.011343301273882389, -0.028925949707627296, -0.054626114666461945, 0.0025665678549557924, -0.01445236336439848, -0.019821597263216972, -0.0030268258415162563, -0.006685013882815838, 0.0034645351115614176, -0.04055575281381607, 0.017572036013007164, 0.0041595641523599625, -0.011820802465081215, -0.004337300546467304, -0.00236893561668694, 0.022983714938163757, -0.034698404371738434, -0.00685479212552309, 0.0348469614982605, 0.007942433468997478, -0.006356068886816502, -0.01575753279030323, -0.0020360113121569157, -0.017678147181868553, 0.029689950868487358, 0.026145832613110542, 0.02112676575779915, 0.0029207144398242235, 0.03705407679080963, -0.041489530354738235, 0.01713697984814644, 0.03168484568595886, -0.0365871861577034, -0.018707428127527237, -0.01672314666211605, -0.0400676392018795, -0.007677155081182718, 0.025933610275387764, 0.0024697412736713886, 0.004398314747959375, 0.01240441482514143, 0.06782636046409607, 0.013889973051846027, -0.03841230273246765, 0.01317902747541666, 0.005069469101727009, 0.011460023932158947, 0.0307510644197464, 0.018410315737128258, 0.008319128304719925, 0.014664586633443832, -0.057427454739809036, -0.010547466576099396, 0.009618991985917091, 0.0025639149826020002, 0.024278273805975914, -0.033043067902326584, -0.03450740501284599, 0.0022164005786180496, -0.013433694839477539, -0.014558474533259869, -0.002646151464432478, 0.03227906674146652, 0.021328378468751907, 0.020691709592938423, 0.012818248942494392, -0.012563581578433514, 0.02939283847808838, -0.03157873451709747, 0.013974862173199654, -0.0116298021748662, 0.0257850531488657, 0.037796854972839355, -0.013274528086185455, 0.013189638964831829, -0.0258699432015419, -0.015524088405072689, -0.022347046062350273, 0.03599296510219574, 0.03813641145825386, -0.022686602547764778, 0.0068388753570616245, 0.036120299249887466, -0.05517789348959923, 0.0036794105544686317, -0.03221540153026581, 0.006791125517338514, -0.0049474406987428665, 0.013518583960831165, -0.0013164436677470803, -0.007740821689367294, 0.06260568648576736, 0.022835159674286842, 0.01915309578180313, -0.04117119684815407, -0.00977815967053175, -0.0024684148374944925, -0.021816490218043327, 0.04503364861011505, -0.012213414534926414, 0.000903272710274905, 0.042380865663290024, -0.03064495325088501, 0.03230028972029686, 0.057257674634456635, 0.028161948546767235, 0.057724565267562866, 0.0031992567237466574, 0.017678147181868553, 0.033807069063186646, -0.02985972911119461, 0.04592498391866684, -0.02121165581047535, -0.010382994078099728, -0.059889234602451324, -0.017954038456082344, 0.003957952838391066, 0.0583612322807312, 0.03454985097050667, -0.006690319627523422, -0.007517987862229347, -0.022431936115026474, -0.03325529024004936, 0.013210861012339592, -0.010775606147944927, -0.0015518782893195748, -0.008913352154195309, 0.011024967767298222, 0.020490098744630814, 0.03558973968029022, 0.038560859858989716, 0.013911196030676365, -0.05292833223938942, -0.004456676077097654, 0.018802927806973457, 0.01643664576113224, -0.020394599065184593, -0.05067877098917961, 0.0498298816382885, 0.024193383753299713, -0.016203200444579124, -0.0030162145849317312, 0.03374340385198593, 0.02012931928038597, 0.034082960337400436, -0.019970152527093887, -0.010361772030591965, -0.08000794798135757, -0.035547297447919846, 0.01751898042857647, 0.0016288089100271463, 0.003082534298300743, 0.02139204554259777, -0.009995687752962112, -0.03183339908719063, -0.03172728791832924, -0.03870941326022148, -0.0006864076713100076, -0.004515037406235933, -0.001553204609081149, 0.005454122554510832, 0.008589711971580982, 0.018601316958665848, -0.01332758367061615, -0.04647676274180412, -0.005761845503002405, -0.002537387190386653, -0.019917096942663193, -0.03191828727722168, 0.03541996330022812, -0.06960903108119965, -0.022240934893488884, -0.003522896207869053, -0.009120268747210503, -0.03957952558994293, -0.016309311613440514, -0.00447259284555912, 0.016585201025009155, 0.0053241360001266, -0.026782499626278877, -0.017338592559099197, -0.026124609634280205, 0.04690120741724968, 0.003459229366853833, -0.0027151238173246384, 0.0017269619274884462, 0.023853827267885208, 0.0032310900278389454, -0.018176870420575142, 0.04617965221405029, 0.021349599584937096, -0.007677155081182718, 0.006934375502169132, -0.03291573375463486, 0.00751268258318305, -0.03620518743991852, 0.053947001695632935, -0.01711575873196125, 0.020309709012508392, 0.01278641540557146, -0.03592929616570473, 0.018834762275218964, -0.00744371023029089, -0.018516426905989647, -0.04025863856077194, 0.00632423534989357, 0.028246836736798286, -0.010245049372315407, 0.002687269588932395, 0.03431640565395355, 0.03890041634440422, -0.022474380210042, 0.0465192086994648, 0.0012932318495586514, 0.005334747489541769, 0.022792713716626167, -0.0057936785742640495, 0.005613289307802916, -0.005098649766296148, -0.03512285277247429, 0.035059183835983276, 0.0038412301801145077, 0.03588685393333435, -0.021476933732628822, 0.007311070803552866, 0.03034784086048603, -0.005899790208786726, 0.0018622538773342967, 0.012022414244711399, -0.010101798921823502, 0.0037245077546685934, -0.0039420360699296, -0.01799648255109787, 0.010738466866314411, -0.005926318001002073, -0.012903138063848019, -0.03940974920988083, 0.012903138063848019, 0.021381434053182602, 0.042847756296396255, -0.05797923356294632, 0.0038810221012681723, 0.007003347855061293, 0.008228933438658714, -0.02060682140290737, -0.004024272318929434, -0.01712636835873127, -0.006287096533924341, 0.011353912763297558, -0.003870410844683647, 0.032066844403743744, -0.02752527967095375, -0.013794473372399807, 0.005149052478373051, 0.0012196170864626765, 0.002366282744333148, -0.0017269619274884462, -0.042380865663290024, 0.009332492016255856, -0.024002384394407272, -0.024554163217544556, 0.0047617461532354355, -0.017264313995838165, -0.02850150316953659, -0.031472619622945786, 0.010064659640192986, -0.026230720803141594, 0.003475146135315299, -0.012351359240710735, 0.027313057333230972, 0.03200317919254303, -0.06884503364562988, -0.031111842021346092, 0.010802133940160275, -0.02003381960093975, 0.005199455190449953, -0.0008011405589058995, 0.004552176222205162, -0.023768939077854156, -0.010701327584683895, -0.038857970386743546, 0.03230028972029686, 0.018314816057682037, 0.022813936695456505, -0.002758894581347704, 0.024087272584438324, -0.014399307779967785, 0.02060682140290737, -0.00182378850877285, 0.006334846373647451, -0.0026236027479171753, 0.0182935930788517, -0.016075866296887398, 0.00724740419536829, 0.03261862322688103, 0.014505418948829174, 0.016510924324393272, -0.006016512401401997, 0.0005361938383430243, -0.02822561375796795, -0.0365871861577034, -0.0027748113498091698 ]
Federated learning (FL) enables multiple clients to collaboratively train models without sharing their local data, and becomes an important privacy-preserving machine learning framework. However, classical FL faces serious security and robustness problem, e.g., malicious clients can poison model updates and at the same time claim large quantities to amplify the impact of their model updates in the model aggregation. Existing defense methods for FL, while all handling malicious model updates, either treat all quantities benign or simply ignore/truncate the quantities of all clients. The former is vulnerable to quantity-enhanced attack, while the latter leads to sub-optimal performance since the local data on different clients is usually in significantly different sizes. In this paper, we propose a robust quantity-aware aggregation algorithm for federated learning, called FedRA, to perform the aggregation with awareness of local data quantities while being able to defend against quantity-enhanced attacks. More specifically, we propose a method to filter malicious clients by jointly considering the uploaded model updates and data quantities from different clients, and performing quantity-aware weighted averaging on model updates from remaining clients. Moreover, as the number of malicious clients participating in the federated learning may dynamically change in different rounds, we also propose a malicious client number estimator to predict how many suspicious clients should be filtered in each round. Experiments on four public datasets demonstrate the effectiveness of our FedRA method in defending FL against quantity-enhanced attacks.
[ -0.04147191345691681, -0.05512090027332306, -0.017623689025640488, -0.031797636300325394, 0.019151700660586357, -0.03520987927913666, -0.042184360325336456, 0.031141433864831924, -0.03819090873003006, 0.015373856760561466, -0.027504203841090202, -0.00804315134882927, 0.007035414222627878, -0.01378959883004427, -0.06520765274763107, 0.020473476499319077, 0.007968157529830933, -0.05778320133686066, 0.008418124169111252, -0.04897135868668556, 0.031122684478759766, -0.02105468325316906, 0.017201844602823257, 0.05422096699476242, 0.021410906687378883, 0.04627155885100365, 0.004323896951973438, 0.026997990906238556, -0.055008407682180405, 0.08451871573925018, 0.024898147210478783, 0.01885172352194786, -0.02714798040688038, -0.0060183024033904076, -0.021223420277237892, 0.016836248338222504, 0.06667003780603409, 0.061082955449819565, -0.015476973727345467, 0.04237184673547745, -0.06756997108459473, -0.018767353147268295, -0.05474592745304108, 0.042221859097480774, 0.015598839148879051, -0.02517937682569027, -0.022442080080509186, -0.0032294471748173237, -0.05624581500887871, -0.00006796369416406378, -0.020285990089178085, -0.02669801376760006, 0.004930883180350065, -0.022404583171010017, -0.002896659541875124, -0.023060783743858337, 0.0818939059972763, 0.0038809613324701786, 0.013002158142626286, -0.04818391427397728, 0.030503980815410614, 0.020136002451181412, -0.01627378910779953, 0.005366788245737553, -0.008943084627389908, 0.017342459410429, 0.02624804712831974, 0.00945398397743702, -0.03324127569794655, -0.0048605757765471935, -0.04600907862186432, 0.03084145486354828, 0.018757980316877365, -0.02322952263057232, -0.018729856237769127, 0.018167398869991302, 0.011221040040254593, -0.0045113833621144295, 0.010246112942695618, 0.041134439408779144, -0.025966817513108253, 0.05313354730606079, -0.002889628754928708, 0.03406621515750885, 0.04075946658849716, -0.005273045040667057, -0.041546911001205444, -0.060632988810539246, 0.037422217428684235, -0.0059854923747479916, -0.023773230612277985, 0.07210713624954224, 0.013639610260725021, -0.010696079581975937, 0.009397738613188267, 0.038059670478105545, -0.047358978539705276, -0.01841112971305847, -0.08789346367120743, 0.012167844921350479, -0.061945393681526184, 0.02103593572974205, -0.010696079581975937, 0.031085187569260597, -0.002828695811331272, -0.04379674047231674, -0.05485842004418373, 0.027410460636019707, 0.014473923482000828, 0.15463849902153015, -0.010958559811115265, 0.033747490495443344, -0.06633256375789642, 0.07233212143182755, 0.0006105014472268522, 0.0002932398929260671, -0.03907209262251854, -0.021785879507660866, 0.0038317462895065546, -0.02776668407022953, -0.007897850126028061, 0.021148426458239555, 0.0048605757765471935, 0.018926717340946198, -0.059133101254701614, 0.0011424930999055505, 0.04383423924446106, -0.0028263521380722523, -0.0025052824057638645, -0.00737757608294487, -0.04300929978489876, 0.027860427275300026, 0.019779779016971588, -0.0652451440691948, 0.019779779016971588, -0.013030280359089375, 0.031572651118040085, 0.0316101498901844, 0.011146046221256256, 0.02909783460199833, 0.02733546681702137, -0.016958113759756088, 0.0012327207950875163, 0.045221634209156036, -0.012842794880270958, 0.027635443955659866, 0.00422781053930521, 0.029397813603281975, 0.008099397644400597, 0.08879339694976807, -0.030672717839479446, 0.056283313781023026, 0.04908384755253792, 0.02191711962223053, 0.022029610350728035, -0.047396473586559296, 0.0143145602196455, -0.034834910184144974, 0.031160181388258934, -0.050208766013383865, 0.02427944354712963, -0.005474592559039593, 0.04844639450311661, 0.05103370547294617, 0.005015251692384481, 0.059358082711696625, 0.04297180473804474, 0.0017272152472287416, -0.0611579492688179, 0.06577010452747345, 0.020698459818959236, -0.0035200505517423153, -0.01516762189567089, 0.008502492681145668, 0.04229685291647911, 0.027654193341732025, 0.054145973175764084, -0.006927609443664551, -0.002800572896376252, -0.010002381168305874, -0.016217542812228203, 0.04060947895050049, -0.002088126027956605, 0.03434744477272034, 0.04728398099541664, 0.010292984545230865, 0.019001711159944534, -0.006013615056872368, 0.03929707780480385, -0.0017131537897512317, 0.03147890791296959, 0.01869235932826996, -0.013199018314480782, -0.017070604488253593, 0.030054014176130295, -0.005460531450808048, 0.010255486704409122, -0.033316273242235184, 0.05365850776433945, -0.010217989794909954, -0.022404583171010017, -0.02669801376760006, 0.0033770925365388393, -0.015345733612775803, 0.03453493118286133, -0.0018443940207362175, 0.058270666748285294, 0.003002120414748788, -0.0026997991371899843, -0.04833390563726425, -0.029416561126708984, -0.0525335930287838, -0.03732847422361374, 0.02124216966331005, 0.01953604631125927, -0.012927163392305374, 0.028947846964001656, -0.01905795745551586, 0.017858047038316727, 0.028385387733578682, 0.004567629192024469, -0.012533443048596382, 0.004865263123065233, 0.010283609852194786, -0.04878387227654457, -0.019892269745469093, 0.0008050182368606329, -0.00007221142732305452, -0.01972353272140026, 0.03603481873869896, -0.04360925406217575, -0.010386727750301361, 0.005010564811527729, 0.020435979589819908, -0.0009362584678456187, -0.016451900824904442, -0.01476452685892582, 0.03189137578010559, -0.02426069602370262, -0.005605833139270544, -0.039184585213661194, 0.02581682987511158, -0.014680158346891403, -0.08421873301267624, 0.05095870792865753, 0.007640056777745485, -0.06595759093761444, 0.057820700109004974, -0.0001467664260417223, 0.01951729878783226, -0.044321704655885696, -0.061907894909381866, -0.006515140179544687, 0.002063518390059471, -0.0650576576590538, -0.027672940865159035, -0.025235623121261597, -0.01562696322798729, -0.016789376735687256, -0.03564110025763512, 0.09636782854795456, 0.024654416367411613, -0.01992976665496826, 0.01711747609078884, 0.023904472589492798, -0.010789822787046432, 0.018486125394701958, -0.010283609852194786, 0.0654701292514801, 0.003674726700410247, -0.034366194158792496, -0.008441559970378876, -0.07844416797161102, -0.03768469765782356, 0.0026341790799051523, 0.0009913324611261487, -0.012552191503345966, 0.015458225272595882, 0.01346149854362011, 0.01475515216588974, 0.06449520587921143, 0.002295532263815403, 0.030728964135050774, 0.00445279385894537, 0.022667063400149345, -0.026529276743531227, -0.02711048349738121, -0.010789822787046432, -0.06865739077329636, -0.0004326826601754874, -0.02036098577082157, 0.009332118555903435, -0.004935570526868105, -0.014398928731679916, 0.040047019720077515, 0.00934617966413498, -0.017201844602823257, 0.027691690251231194, 0.021223420277237892, 0.030522730201482773, -0.07686927914619446, -0.044359199702739716, 0.054558441042900085, -0.026173053309321404, 0.03146015852689743, -0.008052526041865349, -0.03057897463440895, 0.015298862010240555, -0.023979466408491135, -0.014970761723816395, 0.010705453343689442, -0.05092121288180351, -0.015992559492588043, -0.07994405180215836, -0.05579584836959839, -0.010958559811115265, -0.02324827015399933, 0.021954616531729698, 0.007457257714122534, -0.051108699291944504, -0.006693251896649599, 0.05272107943892479, -0.07446946203708649, 0.0075603751465678215, -0.009416487067937851, -0.07446946203708649, 0.006819805130362511, 0.049346327781677246, -0.07180716097354889, 0.004129380453377962, -0.03387872874736786, -0.014230191707611084, -0.09531790763139725, -0.03729097545146942, -0.05722074210643768, -0.02150464989244938, -0.07971906661987305, 0.034178707748651505, 0.004494978114962578, -0.004267651122063398, -0.057408228516578674, -0.03339126706123352, -0.030541477724909782, 0.03768469765782356, -0.00006393567309714854, 0.027916673570871353, -0.04627155885100365, 0.005141804926097393, 0.055420875549316406, 0.011042928323149681, 0.0009093073313124478, 0.00008327016985276714, 0.004190313164144754, 0.021635890007019043, 0.013414626941084862, -0.058045681565999985, 0.012430325150489807, -0.006730749271810055, -0.03389747813344002, -0.028104159981012344, -0.005427721422165632, -0.011071051470935345, -0.03907209262251854, 0.022704560309648514, -0.044996652752161026, -0.03888460621237755, -0.036784764379262924, -0.017276840284466743, -0.02296704240143299, 0.04747146740555763, -0.03296004980802536, 0.07709426432847977, 0.04364675283432007, 0.033747490495443344, -0.018261142075061798, -0.021429656073451042, -0.026848003268241882, -0.009107135236263275, -0.04105944558978081, 0.04930883273482323, 0.019573543220758438, 0.008207201957702637, 0.03168514370918274, -0.021148426458239555, 0.08121895790100098, -0.011071051470935345, -0.012327208183705807, -0.023079533129930496, 0.028047913685441017, 0.045221634209156036, 0.009182129055261612, -0.011146046221256256, 0.00804315134882927, -0.0061401682905852795, 0.04105944558978081, -0.018514247611165047, 0.017933040857315063, -0.011024179868400097, 0.05815817415714264, -0.058870621025562286, -0.02643553353846073, 0.047658953815698624, -0.025535600259900093, 0.03925957903265953, -0.0025732461363077164, -0.015355107374489307, 0.00025632858159951866, -0.0017412767047062516, 0.06220787391066551, 0.0041551594622433186, 0.0019850085955113173, -0.026079310104250908, 0.004874637350440025, -0.021804627031087875, 0.03530362248420715, 0.007410386111587286, -0.05193363502621651, 0.013180269859731197, -0.05763321369886398, -0.042634326964616776, -0.0033864667639136314, 0.005427721422165632, 0.07233212143182755, 0.030747713521122932, -0.021110929548740387, 0.05549587309360504, -0.016817498952150345, -0.0032083550468087196, 0.0008677088771946728, -0.021129678934812546, 0.028422886505723, 0.052608586847782135, -0.006721375044435263, -0.042859312146902084, -0.03281005844473839, 0.015720706433057785, 0.012720928527414799, -0.023304516449570656, 0.0005899951793253422, 0.008160330355167389, -0.008375938981771469, 0.01542072743177414, -0.015898818150162697, 0.018748605623841286, -0.030747713521122932, -0.0377596914768219, 0.0026177740655839443, -0.03475991263985634, -0.016348782926797867, 0.008272822014987469, -0.07919410616159439, 0.014295811764895916, -0.08841842412948608, -0.006861989386379719, 0.04619656503200531, -0.017436202615499496, 0.03952205926179886, -0.036091066896915436, 0.022217096760869026, -0.026379287242889404, 0.004105944652110338, 0.04402172565460205, 0.0008436872158199549, 0.026960493996739388, -0.009955509565770626, 0.021373409777879715, 0.0156457107514143, -0.1075420007109642, 0.0013440406182780862, -0.012074101716279984, -0.0389970988035202, -0.021298415958881378, -0.003545830026268959, 0.0030372741166502237, -0.014614538289606571, 0.0599205419421196, -0.008315006271004677, -0.08759348094463348, 0.023698236793279648, -0.0206234659999609, 0.0026037124916911125, 0.011980358511209488, 0.0010505077661946416, -0.009796146303415298, -0.002375213894993067, -0.012524068355560303, 0.02474815957248211, -0.0011085112346336246, -0.03102894127368927, -0.050883714109659195, 0.014858270063996315, -0.04923383891582489, 0.026773007586598396, -0.013808348216116428, 0.008188453502953053, -0.01346149854362011, -0.020435979589819908, -0.008258760906755924, 0.08429373055696487, -0.024016963317990303, 0.05902060866355896, 0.009594598785042763, 0.029229076579213142, 0.007836917415261269, -0.013227141462266445, -0.03704724460840225, -0.006388587411493063, -0.01690186746418476, -0.031797636300325394, -0.017895543947815895, 0.017736179754137993, 0.050696227699518204, -0.020435979589819908, -0.043309278786182404, -0.04627155885100365, -0.0011594840325415134, 0.003984078764915466, -0.022292092442512512, 0.0025380924344062805, 0.043946731835603714, 0.02296704240143299, 0.04878387227654457, -0.016001934185624123, -0.006758872419595718, -0.0045113833621144295, 0.013639610260725021, 0.019170448184013367, 0.037403468042612076, 0.033503755927085876, -0.03487240523099899, -0.020061006769537926, 0.06055799499154091, -0.044584184885025024, -0.010508593171834946, 0.028160404413938522, 0.01715497300028801, -0.009739900007843971, -0.016826873645186424, -0.025066886097192764, -0.012411576695740223, -0.05275857448577881, 0.05047124624252319, 0.004098913632333279, 0.006412023212760687, -0.002178353490307927, 0.05605832859873772, 0.03933457285165787, -0.058045681565999985, -0.03127267211675644, -0.012299085035920143, 0.038097165524959564, -0.027447957545518875, 0.0011014805641025305, 0.02649177983403206, -0.002082267077639699, 0.012111598625779152, 0.04293430596590042, -0.01235533133149147, -0.025348113849759102, -0.035697344690561295, 0.010789822787046432, 0.005179302301257849, 0.024673163890838623, -0.020548472180962563, 0.01931106299161911, -0.03378498554229736, 0.0018994681304320693, 0.0447341725230217, -0.032903801649808884, -0.003784874686971307, 0.020492225885391235, -0.017933040857315063, 0.009514917619526386, -0.04102194681763649, 0.022517075762152672, -0.01007737498730421, -0.029416561126708984, 0.028797857463359833, 0.03147890791296959, -0.009486794471740723, -0.028722863644361496, -0.03507864102721214, -0.015908190980553627, 0.041546911001205444, 0.04454668611288071, 0.022854549810290337, -0.01629253849387169, -0.019011085852980614, -0.012224090285599232, -0.03494739904999733, -0.02604181319475174, 0.04098445177078247, 0.003613793756812811, 0.0054558441042900085, -0.01757681742310524, 0.017023732885718346, 0.00934617966413498, -0.03039149008691311, 0.053246039897203445, -0.02322952263057232, -0.04282181337475777, 0.0011981530115008354, 0.004216092638671398, 0.03820965811610222, 0.00585893914103508, -0.005062123294919729, 0.016836248338222504, 0.014942638576030731, -0.016095677390694618, -0.002962279599159956, 0.04443419352173805, 0.0030747712589800358, 0.007054162677377462, -0.028422886505723, 0.032191354781389236, -0.0013475560117512941, 0.016330035403370857, -0.02992277406156063, -0.022254593670368195, 0.031366415321826935, 0.06303281337022781, -0.006852615159004927, 0.02802916429936886, 0.04143441841006279, 0.009322743862867355, 0.02084844931960106, -0.02171088568866253, -0.03835964575409889, -0.0012983409687876701, -0.005779257509857416, -0.010555464774370193, -0.004940257407724857, -0.04008451849222183, -0.00901807937771082, -0.06933233886957169, -0.04019701108336449, 0.045221634209156036, 0.05163365975022316, -0.000703658617567271, 0.020079756155610085, 0.0136489849537611, -0.003452087054029107, 0.013658358715474606, 0.031816381961107254, -0.01802678406238556, -0.025216873735189438, -0.0040895394049584866, -0.025685589760541916, 0.03558485209941864, 0.02212335355579853, 0.00552615150809288, 0.01093981135636568, 0.01453016884624958, 0.018504872918128967, -0.004434044938534498, -0.0355098582804203, -0.011436649598181248, -0.022817052900791168, -0.010892939753830433, 0.03084145486354828, 0.004654341377317905, -0.0032950674649327993, -0.004319210071116686, -0.028160404413938522, 0.03342876210808754, -0.04923383891582489, 0.02472941018640995, 0.04278431832790375, 0.05103370547294617, 0.08294382691383362, -0.003850494744256139, 0.01911420375108719, 0.004527788143604994, 0.03929707780480385, 0.02690424770116806, -0.002866192953661084, 0.01887047104537487, 0.03012900799512863, -0.011924113146960735, -0.027072986587882042, -0.032191354781389236, -0.004253590013831854, -0.0006415538373403251, 0.004180938936769962, -0.09186816960573196, -0.014173945412039757, -0.013836470432579517, 0.045671600848436356, -0.037009745836257935, -0.044321704655885696, 0.0008249386446550488, -0.04184688627719879, -0.018598616123199463, -0.008732163347303867, 0.0092336880043149, 0.008179078809916973, -0.0038481513038277626, -0.01955479569733143, -0.03562235087156296, 0.00998363271355629, 0.0025170003063976765, -0.004195000510662794, -0.03586608171463013, -0.020285990089178085, -0.026191800832748413, -0.03933457285165787, -0.009243062697350979, 0.04488416016101837, 0.03790967911481857, 0.02709173411130905, -0.001416691462509334, 0.011352280154824257, -0.00866654235869646, -0.004823078867048025, -0.0009421174181625247, -0.0025966819375753403, 0.0010223848512396216, -0.009786771610379219, -0.011952236294746399, 0.03404746577143669, 0.025310616940259933, 0.04008451849222183, 0.01160538662225008, -0.041134439408779144, -0.01430518552660942, -0.015776950865983963, 0.014136448502540588, -0.0143145602196455, -0.033110037446022034, 0.002058831276372075, 0.049608808010816574, -0.009458671323955059, -0.03997202590107918, 0.018579868599772453, -0.007682241033762693, 0.002104531042277813, 0.027054237201809883, 0.036109812557697296, 0.004305148497223854, 0.011952236294746399, 0.06205788254737854, 0.0016522208461537957, 0.027241723611950874, -0.010705453343689442, 0.004042667802423239, 0.028460383415222168, 0.0009919183794409037, 0.00974927470088005, -0.007522877771407366, -0.0033044416923075914, -0.019592292606830597, -0.025760583579540253, 0.05658328905701637, -0.0024959081783890724, -0.07904411852359772, 0.01509262714534998, 0.031085187569260597, 0.00986176636070013, 0.008821219205856323, 0.025085633620619774, -0.040871959179639816, 0.05275857448577881, 0.007293207570910454, -0.023716986179351807, 0.08384376019239426, 0.013255263678729534, -0.055008407682180405, -0.027241723611950874, -0.009918012656271458, -0.05358351394534111, 0.015430102124810219, 0.0180080346763134, -0.03948456421494484, -0.009435235522687435, -0.01105230301618576, 0.01183036994189024, 0.030297746881842613, -0.020136002451181412, 0.022498326376080513, 0.018176773563027382, -0.0011184714967384934, 0.009599286131560802, -0.012842794880270958, -0.0015549624804407358, -0.00006199489871505648, 0.022873299196362495, 0.007288520224392414, -0.010377353057265282, -0.0136489849537611, 0.01912357658147812, -0.01378959883004427, 0.011061676777899265, -0.00975864939391613, 0.01824239268898964, 0.05512090027332306, -0.002795885782688856, -0.04852139204740524, 0.04135942459106445, -0.01398645993322134, -0.006712000817060471, 0.04627155885100365, -0.012617811560630798, -0.005362100899219513, 0.005343352444469929, -0.0424843393266201, -0.00018499600992072374, 0.002115077106282115, -0.017033107578754425, -0.02581682987511158, 0.003524737898260355, 0.021598393097519875, 0.005263670813292265, -0.002840413711965084, -0.004855888895690441, -0.028385387733578682, -0.013817721977829933, 0.04094695299863815, 0.02060471661388874, -0.00754631357267499, -0.03843463957309723, -0.018392382189631462, 0.003063053358346224, -0.02086719684302807, 0.023323265835642815, -0.012289710342884064, -0.0016885462682694197, -0.008432185277342796, 0.0013803660403937101, 0.008038464933633804, 0.023192023858428, -0.005132430698722601, -0.005704263225197792, -0.028085410594940186, -0.008732163347303867, -0.04233435168862343, -0.0272979699075222, -0.015336358919739723, 0.042221859097480774, -0.01126791164278984, 0.005830816458910704, -0.009130571037530899, -0.015111375600099564, -0.01238345354795456, -0.026754260063171387, -0.04510914534330368, -0.03106643818318844, -0.00964615773409605, -0.008807157166302204, 0.030428986996412277, -0.005366788245737553, 0.013264638371765614, 0.0074947550892829895, 0.045896586030721664, -0.014164571650326252, -0.006585447583347559, -0.01608630269765854, 0.0026552712079137564, 0.012749051675200462, 0.011446023359894753, -0.014070828445255756, -0.08594360947608948, 0.010808571241796017, -0.005169928073883057, -0.025910573080182076, 0.0416593998670578, -0.014905141666531563, -0.008357190527021885, -0.05440845340490341, -0.05204612761735916, -0.04338427260518074, 0.049383826553821564, -0.01652689464390278, -0.002784167882055044, 0.03862212598323822, 0.016301913186907768, 0.012805297039449215, 0.006290156859904528, 0.02212335355579853, -0.0163112860172987, -0.03755345568060875, 0.008399374783039093, 0.012814671732485294, 0.019798526540398598, -0.01378959883004427, 0.029847780242562294, -0.056733280420303345, -0.0052589839324355125, -0.04150941222906113, -0.01648939773440361, -0.05534588173031807, -0.00782285537570715, -0.002342403866350651, 0.001468250178731978, 0.022498326376080513, 0.04443419352173805, -0.020304739475250244, -0.0163112860172987, 0.032903801649808884, 0.008633732795715332, 0.028779109939932823, -0.001981493318453431, -0.021354662254452705, -0.013264638371765614, -0.002177181886509061, 0.0385846309363842, 0.02302328683435917, -0.01409895159304142, -0.01843925379216671, 0.007218212820589542, 0.008071274496614933, -0.011530391871929169, -0.031797636300325394, -0.014717655256390572, -0.015542593784630299, 0.00996488332748413, -0.016414403915405273, -0.046309053897857666, -0.01161476131528616, -0.0011231586104258895, 0.039822038263082504, 0.0012643591035157442, 0.04079696536064148, -0.00552615150809288, 0.0024701287038624287, -0.007485380861908197, 0.003501302096992731, -0.017951790243387222, 0.00942117441445589, 0.007986905984580517, 0.010883565060794353, -0.01453954353928566, 0.0053152297623455524, 0.015973811969161034, 0.04792143404483795, -0.022873299196362495, 0.05898311361670494, -0.0053902240470051765, 0.02384822629392147, -0.01603943109512329, -0.004546536598354578, -0.033541254699230194, -0.02802916429936886, -0.005132430698722601, 0.0028216650243848562, 0.03607231751084328, -0.0330350436270237, 0.012749051675200462, -0.023342013359069824, -0.0041340673342347145, 0.0420718714594841, -0.021448403596878052, -0.005132430698722601, 0.024673163890838623, 0.012655308470129967, -0.03380373492836952, 0.016836248338222504, -0.012195968069136143, 0.00423015421256423, -0.021317163482308388, 0.048671379685401917, -0.04267182573676109, -0.003529425011947751, -0.03877211734652519, -0.01161476131528616, -0.04949631914496422, 0.005474592559039593, -0.027391713112592697, -0.054145973175764084, -0.030691467225551605, -0.005540213081985712, -0.02362324297428131, -0.0309914443641901, -0.007860353216528893, -0.00001876691385405138, 0.02429819293320179, 0.03496614843606949, 0.023173276335000992, -0.009510230273008347, -0.0337662398815155, 0.03316628187894821, -0.024598170071840286, -0.00997425802052021, 0.011511643417179585, 0.044359199702739716, -0.010855442844331264, -0.014727029018104076, -0.0045441933907568455, 0.009186816401779652, -0.02039848268032074, -0.002261550398543477, -0.01583319716155529, -0.02255457267165184, 0.012439699843525887, -0.045559111982584, -0.027916673570871353, 0.017942415550351143, -0.037459712475538254, -0.017033107578754425, -0.012195968069136143, 0.01629253849387169, -0.040459491312503815, 0.002341232029721141, -0.011464771814644337, 0.0048277657479047775, 0.003030243329703808, -0.04874637350440025, 0.04510914534330368, 0.012224090285599232, -0.0769442766904831, -0.005076184868812561, -0.046309053897857666, -0.028122907504439354, 0.027429210022091866, -0.002143200021237135, -0.07615683227777481, 0.01302090659737587, -0.006430771667510271, 0.036578528583049774, 0.004129380453377962, 0.0034356818068772554, 0.051296185702085495, -0.017698682844638824, 0.015598839148879051, -0.01149289496243 ]
Sequential recommendation (SR) learns users' preferences by capturing the sequential patterns from users' behaviors evolution. As discussed in many works, user-item interactions of SR generally present the intrinsic power-law distribution, which can be ascended to hierarchy-like structures. Previous methods usually handle such hierarchical information by making user-item sectionalization empirically under Euclidean space, which may cause distortion of user-item representation in real online scenarios. In this paper, we propose a Poincar\'{e}-based heterogeneous graph neural network named PHGR to model the sequential pattern information as well as hierarchical information contained in the data of SR scenarios simultaneously. Specifically, for the purpose of explicitly capturing the hierarchical information, we first construct a weighted user-item heterogeneous graph by aliening all the user-item interactions to improve the perception domain of each user from a global view. Then the output of the global representation would be used to complement the local directed item-item homogeneous graph convolution. By defining a novel hyperbolic inner product operator, the global and local graph representation learning are directly conducted in Poincar\'{e} ball instead of commonly used projection operation between Poincar\'{e} ball and Euclidean space, which could alleviate the cumulative error issue of general bidirectional translation process. Moreover, for the purpose of explicitly capturing the sequential dependency information, we design two types of temporal attention operations under Poincar\'{e} ball space. Empirical evaluations on datasets from the public and financial industry show that PHGR outperforms several comparison methods.
[ 0.006789605598896742, -0.011162111535668373, -0.03639228641986847, -0.006078960373997688, 0.01566135697066784, -0.04555372893810272, -0.026434198021888733, 0.0169559083878994, -0.05087677761912346, 0.0021296730265021324, 0.022288011386990547, 0.02006102167069912, 0.014728917740285397, -0.029186252504587173, -0.004879463464021683, 0.02335624396800995, 0.034255824983119965, -0.02018776163458824, -0.010311148129403591, -0.02006102167069912, 0.018159931525588036, -0.04102732241153717, -0.031069235876202583, 0.04182397201657295, 0.04073763266205788, 0.03907191753387451, 0.022831181064248085, 0.004535456653684378, -0.08031650632619858, 0.03711651265621185, -0.010474097914993763, 0.02886035107076168, 0.003879128023982048, -0.01087242178618908, -0.015760937705636024, 0.006364123895764351, 0.08227191865444183, 0.025619445368647575, 0.01904710754752159, 0.009514500387012959, 0.00977703183889389, 0.049174848943948746, -0.02288549765944481, 0.02889656089246273, 0.012112656608223915, -0.02755674533545971, 0.03878222778439522, 0.01672053523361683, -0.010600837878882885, -0.01656663790345192, 0.008120368234813213, -0.003539647674188018, -0.02301223762333393, -0.024641742929816246, -0.03436445817351341, 0.004386085085570812, 0.0444311797618866, -0.006336965132504702, 0.03639228641986847, 0.03097870759665966, -0.036410391330718994, 0.019300585612654686, -0.0719517171382904, 0.0022518858313560486, 0.03588533028960228, -0.03878222778439522, 0.010446939617395401, -0.0069887675344944, 0.05109404772520065, -0.028552554547786713, -0.08140284568071365, -0.002555154962465167, 0.0837927833199501, -0.025384072214365005, -0.0035532270558178425, 0.04291030764579773, 0.06499915570020676, 0.012139814905822277, 0.04008583351969719, -0.01661190204322338, 0.02127409726381302, 0.04345347732305527, 0.0018456411780789495, 0.02929488569498062, 0.07539178431034088, -0.0584087148308754, 0.03827527165412903, -0.039325397461652756, 0.026325564831495285, 0.02069471776485443, -0.03498004749417305, 0.016593797132372856, -0.007690359838306904, -0.03914434090256691, -0.02532975561916828, -0.019717015326023102, 0.013361943885684013, -0.004644090309739113, -0.032336629927158356, 0.014792287722229958, -0.005893377587199211, 0.038963284343481064, -0.010890527628362179, -0.0017720870673656464, 0.021418942138552666, -0.03671818599104881, -0.022505279630422592, 0.024641742929816246, -0.04153428226709366, 0.08799328655004501, 0.0005530699854716659, 0.011370326392352581, 0.012873092666268349, 0.021853476762771606, -0.05645330622792244, -0.03085196763277054, -0.0606900230050087, -0.01782497763633728, 0.03662765771150589, -0.06293512135744095, 0.0013296310789883137, 0.0011983653530478477, -0.009048281237483025, -0.011850125156342983, -0.013063201680779457, 0.01154232956469059, -0.0032861691433936357, -0.0000987321836873889, 0.0013522631488740444, 0.009767979383468628, -0.05721374228596687, 0.01908331923186779, 0.0012526822974905372, -0.06072623282670975, 0.0396512970328331, 0.023917516693472862, 0.04533645883202553, 0.0025709974579513073, -0.030182059854269028, -0.039397817105054855, -0.03947024047374725, -0.035668060183525085, -0.0012085498310625553, -0.0795198604464531, 0.0279188584536314, 0.046857330948114395, -0.015760937705636024, 0.058988094329833984, -0.056598152965307236, 0.043598320335149765, -0.039361607283353806, 0.049102429300546646, -0.00912975613027811, 0.0018716679187491536, -0.014086168259382248, 0.011723386123776436, -0.009985246695578098, -0.04396043345332146, 0.019662698730826378, -0.039832353591918945, 0.0700325220823288, 0.017109805718064308, -0.017616763710975647, 0.03548700734972954, -0.010682312771677971, 0.03206504508852959, 0.03488951921463013, -0.03130460903048515, -0.06579580903053284, 0.03834769129753113, -0.05170963704586029, 0.03682682290673256, -0.01881173439323902, 0.04041173309087753, -0.017680132761597633, -0.005703268572688103, 0.06615791469812393, -0.07039463520050049, -0.03483520448207855, -0.0001051681610988453, -0.018313828855752945, 0.017010224983096123, 0.028244759887456894, 0.045408882200717926, 0.03664576634764671, 0.04464844614267349, 0.053846098482608795, 0.043562110513448715, 0.005630846135318279, -0.003123218659311533, 0.029747525230050087, 0.03863738104701042, 0.06409388035535812, -0.02362782694399357, 0.0037071246188133955, -0.026832520961761475, 0.01464744284749031, -0.033350542187690735, 0.008405531756579876, 0.03275305777788162, -0.039796143770217896, -0.053411565721035004, 0.015607040375471115, -0.01986186020076275, 0.05268733948469162, 0.0047074598260223866, 0.02940351888537407, -0.010293042287230492, -0.027538640424609184, -0.03184777870774269, -0.006400335114449263, -0.022740652784705162, -0.03881843760609627, -0.029584575444459915, -0.015199664048850536, 0.00338122365064919, 0.023030342534184456, 0.005721374414861202, 0.025945346802473068, -0.02637988142669201, -0.010211567394435406, 0.00007305898907361552, 0.09987057000398636, 0.01904710754752159, 0.006789605598896742, 0.03726135566830635, -0.056163616478443146, 0.02362782694399357, -0.006907292176038027, -0.04609689489006996, 0.030906284227967262, -0.00877669733017683, 0.0008141868747770786, -0.003109639510512352, 0.0011117978719994426, 0.006183067802339792, -0.043598320335149765, -0.05312187597155571, -0.01601441577076912, -0.028407709673047066, 0.025854818522930145, 0.002600418869405985, -0.007002346683293581, 0.037080299109220505, 0.023464877158403397, 0.005965800024569035, -0.06691835075616837, 0.03416529670357704, 0.045046769082546234, 0.04834199324250221, -0.035269737243652344, -0.051021624356508255, 0.007065716199576855, 0.033314332365989685, -0.04146185889840126, 0.04095490276813507, 0.021527577191591263, -0.023501088842749596, 0.03702598437666893, -0.04761776700615883, 0.008980385027825832, 0.040810056030750275, -0.017028331756591797, 0.032409049570560455, 0.015081977471709251, 0.034219611436128616, 0.06652002781629562, -0.016168314963579178, 0.03994098678231239, 0.02281307429075241, 0.05547560378909111, -0.08248918503522873, -0.0062147523276507854, -0.04511919245123863, -0.01908331923186779, -0.03784073516726494, 0.03530595079064369, -0.06623034179210663, 0.07684022933244705, 0.02802749164402485, -0.016159260645508766, -0.013171834871172905, -0.014312488958239555, 0.015588934533298016, -0.0257099736481905, -0.025112487375736237, -0.0720241367816925, -0.03034501150250435, -0.06644760817289352, 0.005318524315953255, -0.038383904844522476, -0.07408817857503891, -0.05047845467925072, 0.008161106146872044, 0.039325397461652756, 0.08929689228534698, -0.02735758386552334, 0.03400234505534172, 0.05641709640622139, -0.06829438358545303, -0.04410528019070625, -0.004306873306632042, 0.007052137050777674, 0.03224610164761543, -0.07539178431034088, -0.023609722033143044, 0.0002606925554573536, 0.04975423216819763, -0.03608449175953865, -0.025112487375736237, 0.04703838750720024, -0.013787426054477692, 0.0017856663325801492, 0.01547124795615673, -0.04001341015100479, -0.004392874892801046, 0.05822765827178955, 0.01663905940949917, 0.001725691487081349, -0.0678960531949997, -0.0012515506241470575, 0.022125061601400375, -0.09487342089414597, -0.04012204334139824, -0.005151047371327877, 0.0558377169072628, 0.012293712235987186, 0.0017189017962664366, 0.005318524315953255, -0.009840401820838451, -0.01466554868966341, -0.06405766308307648, 0.002939899219200015, -0.03161240369081497, -0.021056830883026123, -0.020169654861092567, 0.0022417015861719847, 0.01107158325612545, -0.036917347460985184, -0.059386417269706726, 0.000794949650298804, 0.010202514007687569, 0.010356412269175053, 0.01581525430083275, -0.006196646951138973, -0.00964124035090208, -0.023374348878860474, 0.03034501150250435, 0.018866050988435745, 0.04580720514059067, 0.0008860435336828232, 0.022867392748594284, -0.015362614765763283, -0.010057669132947922, 0.08053377270698547, -0.032879795879125595, 0.03423772007226944, 0.0053411563858389854, 0.06405766308307648, -0.006884660106152296, 0.03050796128809452, -0.05442547798156738, -0.050043921917676926, 0.030200166627764702, -0.04396043345332146, -0.013081306591629982, -0.05500485748052597, 0.016358423978090286, 0.031395137310028076, -0.0030462697613984346, -0.0628264844417572, 0.029258674010634422, -0.004023972898721695, -0.02406236343085766, -0.00006938128353795037, 0.04149806872010231, -0.006219279021024704, -0.014339647255837917, 0.015344508923590183, 0.04975423216819763, 0.016304105520248413, 0.023917516693472862, -0.0024397317320108414, -0.0122303431853652, 0.025293543934822083, 0.036138806492090225, 0.012773511931300163, -0.02909572422504425, -0.017616763710975647, 0.0027678958140313625, -0.0017720870673656464, -0.04410528019070625, -0.010238725692033768, -0.0312683992087841, 0.02896898426115513, -0.017598658800125122, 0.03027258813381195, -0.0034921204205602407, 0.01758960448205471, -0.016195472329854965, -0.02382699027657509, -0.028172336518764496, -0.015996310859918594, 0.03881843760609627, -0.020205866545438766, -0.014176696538925171, 0.013334785588085651, -0.037478622049093246, 0.02697736583650112, 0.01778876595199108, 0.04055657610297203, 0.002018776023760438, -0.0673891007900238, -0.01367879193276167, 0.012755406089127064, 0.031195973977446556, -0.05717753246426582, 0.010908633470535278, -0.007857836782932281, 0.015435037203133106, -0.004191449843347073, 0.038999494165182114, 0.09045565128326416, -0.012873092666268349, -0.04363453388214111, 0.03427392989397049, 0.015208716504275799, -0.022994130849838257, 0.013217099010944366, -0.042186085134744644, 0.04377937689423561, -0.014593126252293587, 0.02308465912938118, -0.03994098678231239, -0.05638088658452034, 0.013380049727857113, 0.022161273285746574, 0.012194131501019001, -0.006925398018211126, -0.016430845484137535, -0.01888415589928627, -0.00824258103966713, -0.02395372837781906, -0.017716344445943832, 0.041751548647880554, 0.037913158535957336, -0.02735758386552334, -0.010727576911449432, -0.007989102974534035, -0.024044256657361984, -0.04569857195019722, 0.014249118976294994, -0.006622128654271364, -0.06550611555576324, 0.043562110513448715, -0.0312683992087841, 0.003849706379696727, -0.00739161716774106, 0.014955238439142704, -0.0019373007817193866, -0.0011723386123776436, 0.04023067653179169, 0.020006705075502396, -0.08538608253002167, -0.011252639815211296, 0.009595976211130619, -0.05091299116611481, 0.01636747643351555, 0.0035147524904459715, -0.0350886806845665, -0.002666051732376218, -0.011614752002060413, 0.03034501150250435, 0.011786755174398422, -0.011415590532124043, 0.007921206764876842, 0.012429504655301571, -0.0419326052069664, 0.005350209306925535, -0.00697971461340785, 0.019029000774025917, 0.0004503771779127419, 0.08133042603731155, 0.018168983981013298, 0.0028697398956865072, 0.0001800659956643358, 0.044938135892152786, 0.021328413859009743, -0.0244606863707304, 0.015543670393526554, -0.013733109459280968, 0.019807543605566025, -0.024641742929816246, 0.010727576911449432, 0.03389371186494827, -0.014909974299371243, -0.018594466149806976, -0.006789605598896742, 0.07300183922052383, 0.017182229086756706, 0.0011610225774347782, -0.00912975613027811, 0.03581290692090988, 0.008514165878295898, 0.009858507663011551, 0.014393963851034641, 0.03990477696061134, -0.011578541249036789, -0.05181827023625374, 0.0057259006425738335, 0.022450963035225868, 0.046857330948114395, -0.006789605598896742, -0.011922547593712807, 0.004716512747108936, -0.005830008070915937, -0.019608380272984505, -0.007350879721343517, 0.03326001390814781, 0.036573342978954315, -0.0044132438488304615, 0.0244244746863842, -0.023138975724577904, 0.007952891290187836, -0.05319429561495781, 0.018793627619743347, 0.019373008981347084, -0.009025649167597294, 0.0467124879360199, -0.03431013971567154, -0.006422967184334993, 0.013805531896650791, -0.03097870759665966, -0.03070712275803089, 0.027828330174088478, -0.014891868457198143, 0.021853476762771606, 0.03349538892507553, 0.03152187541127205, -0.03202883154153824, -0.03740620240569115, 0.06286269426345825, -0.013416260480880737, 0.04750913381576538, 0.007590779103338718, 0.019373008981347084, -0.007943838834762573, -0.03662765771150589, -0.04515540599822998, 0.020821457728743553, 0.0058164289221167564, -0.012927409261465073, 0.010709471069276333, -0.03175725042819977, -0.02073092944920063, -0.008292371407151222, -0.00918859988451004, -0.0058164289221167564, 0.015516512095928192, -0.010302094742655754, -0.006060854531824589, 0.02281307429075241, -0.016403688117861748, -0.05641709640622139, 0.0015966889914125204, 0.0014710812829434872, 0.01199497003108263, 0.0560549832880497, 0.02237853966653347, 0.021581893786787987, -0.03184777870774269, 0.017607711255550385, 0.0017109806649386883, 0.0011632858077064157, 0.015996310859918594, 0.015045765787363052, 0.011859177611768246, -0.017499076202511787, 0.01653042621910572, 0.002930846530944109, -0.01107158325612545, -0.019300585612654686, 0.017870241776108742, 0.006422967184334993, -0.004008130636066198, -0.02728516235947609, -0.026923049241304398, -0.05018876492977142, 0.005449790041893721, -0.024822797626256943, -0.014077115803956985, 0.06785984337329865, 0.01661190204322338, 0.02536596730351448, -0.02893277257680893, -0.023138975724577904, 0.0074866716749966145, -0.004100922029465437, 0.06720804423093796, -0.062210895121097565, 0.006178541108965874, 0.024822797626256943, 0.007314668502658606, -0.0030168481171131134, -0.024116680026054382, -0.04109974578022957, 0.08299613744020462, -0.040810056030750275, 0.018974684178829193, 0.015127241611480713, 4.994957407689071e-7, 0.030652806162834167, 0.03572237864136696, -0.07720234245061874, 0.04986286535859108, 0.027538640424609184, 0.05594635009765625, 0.024243418127298355, -0.006594970356673002, -0.0558377169072628, 0.06630276143550873, 0.0018422463908791542, 0.08531365543603897, 0.025764290243387222, -0.034726571291685104, -0.005793796852231026, -0.0006416177493520081, -0.0043498738668859005, 0.009414919652044773, -0.004870410542935133, -0.013226151466369629, 0.0045015085488557816, -0.0489213727414608, -0.039832353591918945, -0.03733377903699875, 0.03396613523364067, 0.00092621537623927, 0.033078957349061966, 0.02163621038198471, 0.056091196835041046, -0.011316009797155857, 0.005875272210687399, -0.013226151466369629, 0.012809722684323788, -0.004748197738081217, -0.005409052595496178, -0.021056830883026123, -0.005033360794186592, 0.027267055585980415, -0.0009499790030531585, -0.0012062866007909179, -0.01018440816551447, 0.024949537590146065, 0.02712221071124077, 0.017969822511076927, -0.03628365322947502, -0.016204524785280228, -0.026832520961761475, -0.008880804292857647, -0.03215557336807251, -0.02398994006216526, 0.011478959582746029, 0.012456662952899933, 0.0035056998021900654, 0.016892539337277412, 0.022831181064248085, -0.0009403603617101908, -0.010446939617395401, 0.015588934533298016, 0.027864541858434677, -0.016123050823807716, -0.05076814442873001, -0.06416629999876022, 0.018078457564115524, 0.049174848943948746, -0.06007442995905876, 0.0025053645949810743, -0.00785331055521965, 0.011886335909366608, 0.001157062011770904, -0.004193712957203388, -0.005418105516582727, -0.028335288166999817, -0.04580720514059067, -0.010519362054765224, -0.023808883503079414, 0.00249857478775084, -0.025456495583057404, -0.017834030091762543, 0.011678121984004974, -0.026361776515841484, -0.023138975724577904, 0.019807543605566025, 0.006780552677810192, 0.05471516773104668, 0.0037727574817836285, 0.003428750904276967, 0.00369580858387053, 0.0034536460880190134, 0.0244968980550766, -0.025221122428774834, 0.002408046741038561, 0.005132941994816065, -0.005037887487560511, 0.00415071239694953, 0.010627996176481247, 0.0007140401867218316, 0.024370158091187477, -0.04189639165997505, -0.034961942583322525, 0.03344107046723366, 0.006020117085427046, -0.05797417834401131, 0.045445095747709274, 0.03230041638016701, 0.03050796128809452, 0.0007525146356783807, -0.02983805350959301, -0.019608380272984505, 0.012357082217931747, 0.011261692270636559, 0.019409218803048134, 0.046821121126413345, -0.03592154011130333, -0.008034367114305496, -0.030996812507510185, 0.022722547873854637, 0.00478893518447876, -0.02590913511812687, -0.00019604986300691962, 0.07111885398626328, -0.03374886512756348, 0.002672841539606452, 0.006192120257765055, -0.046857330948114395, 0.027737801894545555, -0.023935623466968536, 0.02775590866804123, -0.012293712235987186, 0.006151382811367512, 0.021455153822898865, -0.01951785385608673, -0.007482145447283983, -0.035124894231557846, 0.009102597832679749, 0.009586922824382782, 0.01904710754752159, -0.002057250589132309, -0.0004336860729381442, 0.008043419569730759, 0.02681441605091095, -0.015887677669525146, 0.06355071067810059, -0.029910476878285408, -0.08965900540351868, 0.009894718416035175, 0.00499714957550168, -0.02768348529934883, 0.010646102018654346, -0.036844927817583084, -0.0030281641520559788, 0.059458840638399124, -0.006323385983705521, 0.02905951254069805, 0.07108264416456223, 0.01648516207933426, -0.06568717211484909, -0.0013771583326160908, -0.007219613995403051, -0.04718323424458504, 0.025746185332536697, -0.0017709555104374886, 0.059965796768665314, -0.02976563200354576, 0.008043419569730759, 0.017607711255550385, 0.0008294634753838181, 0.023645933717489243, 0.00010658266546670347, 0.019463535398244858, -0.012728247791528702, -0.012357082217931747, 0.02332003228366375, 0.057105109095573425, -0.008179211989045143, -0.02277686446905136, -0.009858507663011551, -0.03253579139709473, 0.05029739812016487, -0.0008339898777194321, 0.03431013971567154, 0.020278288051486015, 0.0007666596211493015, 0.03387560695409775, 0.05257870629429817, 0.03456361964344978, -0.02607208490371704, -0.014049957506358624, -0.008446269668638706, -0.00229714997112751, 0.04251198470592499, -0.002521206857636571, 0.017698239535093307, 0.03226420655846596, -0.004227661062031984, 0.01931869052350521, 0.021364625543355942, 0.019572170451283455, 0.018902262672781944, -0.005906956735998392, -0.029457835480570793, 0.015100083313882351, 0.004725565668195486, 0.013343838043510914, 0.009767979383468628, -0.007273931056261063, -0.007070242892950773, 0.010338306427001953, -0.05424442142248154, -0.03050796128809452, 0.014185749925673008, -0.030489856377243996, -0.028244759887456894, -0.02677820436656475, -0.00977703183889389, -0.024877116084098816, 0.00894870050251484, 0.005042413715273142, 0.02775590866804123, 0.00065519695635885, 0.030924391001462936, 0.05257870629429817, -0.029005195945501328, 0.008681642822921276, -0.02513059414923191, 0.03659144788980484, 0.008369321003556252, 0.03353159874677658, 0.018458673730492592, 0.04084626957774162, 0.014104274101555347, 0.004119027405977249, 0.0027882647700607777, -0.01070041861385107, -0.014973343349993229, 0.01978943683207035, -0.04396043345332146, 0.008722379803657532, 0.03353159874677658, 0.02265012450516224, 0.042729251086711884, 0.015226822346448898, 0.03921676054596901, 0.005309471860527992, -0.015100083313882351, -0.002127409679815173, 0.0057259006425738335, 0.024152889847755432, 0.016738642007112503, -0.029747525230050087, 0.07379848510026932, -0.030417433008551598, -0.04653143137693405, 0.0021115674171596766, 0.04142564907670021, -0.018123719841241837, 0.034762781113386154, -0.04015825316309929, -0.006327912677079439, -0.029113829135894775, 0.008432690054178238, 0.0419326052069664, -0.05344777554273605, 0.023537300527095795, 0.04526403918862343, -0.0044675604440271854, 0.004625984467566013, -0.013162782415747643, -0.019680803641676903, -0.02147325873374939, 0.023464877158403397, 0.0005021479446440935, -0.01621357910335064, 0.01834098808467388, 0.06785984337329865, -0.026198824867606163, -0.0022960184141993523, -0.02771969698369503, -0.034255824983119965, -0.020875774323940277, -0.016811063513159752, 0.027701592072844505, -0.005399999674409628, -0.00763604324311018, -0.009822295978665352, -0.0032861691433936357, 0.007690359838306904, 0.01829572394490242, 0.0018660100176930428, 0.02933109737932682, 0.005083151627331972, -0.01478323433548212, -0.0001456936151953414, -0.03356781229376793, 0.02590913511812687, 0.010329253040254116, 0.03324190899729729, -0.020314499735832214, 0.023229504004120827, -0.002319782041013241, -0.009722715243697166, -0.01501860748976469, 0.023736461997032166, -0.07068432122468948, 0.03921676054596901, -0.0028222128748893738, -0.014149538241326809, 0.01115305908024311, -0.005834534298628569, -0.022197484970092773, 0.032372839748859406, 0.021020619198679924, -0.00830595102161169, 0.01728180982172489, -0.030399328097701073, -0.0009861902799457312, -0.028118019923567772, 0.034998152405023575, 0.013705950230360031, 0.025528917089104652, -0.035867225378751755, 0.00201764446683228, 0.014756076037883759, 0.02351919375360012, 0.014448280446231365, 0.01951785385608673, -0.063261017203331, -0.03903570771217346, 0.01661190204322338, 0.024116680026054382, 0.011632857844233513, 0.015751885250210762, -0.039796143770217896, 0.037044089287519455, -0.014946185052394867, 0.011370326392352581, 0.05109404772520065, -0.0018252723384648561, 0.0186849944293499, -0.008378373458981514, -0.036410391330718994, 0.00542715797200799, -0.014031851664185524, -0.03219178318977356, -0.02006102167069912, -0.012728247791528702, -0.020839562639594078, -0.01488281600177288, -0.040303099900484085, 0.04327242076396942, -0.011279798112809658, 0.011261692270636559, -0.019246269017457962, -0.007255825214087963, -0.06771500408649445, -0.00763604324311018, -0.0037433358374983072, 0.011859177611768246, -0.02265012450516224, 0.0291681457310915, 0.008898910135030746, -0.013805531896650791, 0.05453411117196083, 0.027900753542780876, 0.026796311140060425, 0.04609689489006996, -0.024677952751517296, -0.018866050988435745, -0.03396613523364067, 0.05185448005795479, 0.011261692270636559, 0.04834199324250221, 0.03863738104701042, 0.004223134834319353, 0.03711651265621185, -0.04609689489006996, 0.018159931525588036, 0.005495054181665182, -0.029222462326288223, -0.004775356035679579, -0.015588934533298016, 0.02116546407341957, 0.04486571252346039, -0.062971331179142, 0.0034830677323043346, 0.0209663026034832, 0.002362782834097743, 0.018757417798042297, -0.03816663846373558, 0.004675775300711393, 0.008224476128816605, -0.04084626957774162, -0.019065212458372116, -0.003969656303524971, 0.009138809517025948, 0.0002688966633286327, 0.0606175996363163, 0.028063703328371048, 0.0004450020787771791, 0.05438926815986633, 0.002101382939144969, -0.01009388081729412, -0.042693041265010834, -0.0014778708573430777, -0.011478959582746029, -0.0008702011546120048, -0.0653974786400795, 0.013905112631618977, 0.05931399390101433, -0.0019373007817193866, -0.004275188315659761, 0.014991449192166328, 0.05493243783712387, -0.029729420319199562 ]
Stochastic Programming is a powerful modeling framework for decision-making under uncertainty. In this work, we tackle two-stage stochastic programs (2SPs), the most widely used class of stochastic programming models. Solving 2SPs exactly requires optimizing over an expected value function that is computationally intractable. Having a mixed-integer linear program (MIP) or a nonlinear program (NLP) in the second stage further aggravates the intractability, even when specialized algorithms that exploit problem structure are employed. Finding high-quality (first-stage) solutions -- without leveraging problem structure -- can be crucial in such settings. We develop Neur2SP, a new method that approximates the expected value function via a neural network to obtain a surrogate model that can be solved more efficiently than the traditional extensive formulation approach. Neur2SP makes no assumptions about the problem structure, in particular about the second-stage problem, and can be implemented using an off-the-shelf MIP solver. Our extensive computational experiments on four benchmark 2SP problem classes with different structures (containing MIP and NLP second-stage problems) demonstrate the efficiency (time) and efficacy (solution quality) of Neur2SP. In under 1.66 seconds, Neur2SP finds high-quality solutions across all problems even as the number of scenarios increases, an ideal property that is difficult to have for traditional 2SP solution techniques. Namely, the most generic baseline method typically requires minutes to hours to find solutions of comparable quality.
[ 0.025302499532699585, -0.007651741616427898, -0.03973730653524399, -0.022437715902924538, 0.0625816360116005, -0.008783793076872826, -0.01674511656165123, 0.04258360713720322, -0.02631903439760208, 0.05481899902224541, 0.05773923173546791, 0.014832180924713612, -0.009980532340705395, -0.002207499695941806, -0.021347250789403915, -0.020386163145303726, 0.017724687233567238, 0.0025413392577320337, 0.02108849585056305, -0.01864881068468094, 0.028888097032904625, 0.06516918540000916, -0.018094336614012718, 0.05456024408340454, -0.03631804883480072, -0.006935546174645424, -0.00502723129466176, 0.008954755961894989, -0.120505690574646, 0.055595263838768005, 0.04332290589809418, 0.03332389146089554, -0.014157570898532867, -0.015321966260671616, 0.022641023620963097, -0.024138104170560837, 0.024378376081585884, 0.03234431892633438, -0.014628873206675053, 0.06387540698051453, 0.02744646556675434, -0.013205723837018013, 0.023269427940249443, -0.022105032578110695, 0.0796964019536972, 0.00019045606313738972, 0.013381307013332844, 0.010008256882429123, -0.014656596817076206, 0.01859336346387863, -0.01505396980792284, -0.03136475011706352, 0.005826598033308983, -0.011754849925637245, -0.008303248323500156, 0.01815902441740036, 0.046538855880498886, 0.025302499532699585, 0.031919222325086594, 0.03045910783112049, 0.010867691598832607, 0.017345795407891273, -0.03757485747337341, -0.016486361622810364, 0.02615269273519516, -0.003294499823823571, 0.10143178701400757, -0.011939674615859985, 0.06413416564464569, -0.04934819042682648, -0.08346682786941528, -0.0004961387603543699, 0.00007847828965168446, 0.01279910933226347, -0.0009691744344308972, -0.004110038746148348, 0.01694842241704464, 0.03204859793186188, -0.008635933510959148, 0.057628337293863297, 0.047352083027362823, 0.04191823676228523, 0.01916631869971752, -0.03308361768722534, 0.07666527479887009, -0.010839967988431454, 0.009934326633810997, -0.08635009080171585, 0.05566919222474098, 0.029257746413350105, -0.033619608730077744, -0.020959118381142616, -0.006958649028092623, 0.037500929087400436, 0.023768454790115356, 0.02935015968978405, 0.014859904535114765, -0.0022121204528957605, -0.013649302534759045, -0.013935781084001064, 0.012096775695681572, 0.012383253313601017, 0.019646864384412766, 0.007420710753649473, 0.04236181825399399, -0.007679465692490339, -0.005235159303992987, 0.04047660529613495, 0.03286182880401611, 0.09817887097597122, 0.06428202241659164, -0.0022386889904737473, 0.0189999770373106, 0.003331464948132634, -0.04077232629060745, -0.02801942080259323, -0.07241430878639221, -0.08664581179618835, 0.07533454149961472, -0.061435725539922714, -0.002843989757820964, 0.07792208343744278, -0.03160502016544342, -0.014859904535114765, -0.06535400450229645, 0.022899778559803963, 0.03683555871248245, 0.04775869846343994, 0.007674844935536385, 0.01657877303659916, -0.027409499511122704, -0.030773309990763664, -0.02330639213323593, -0.05847853049635887, -0.001856332877650857, 0.03992212936282158, 0.014573425985872746, -0.039626412093639374, -0.05492989346385002, -0.011699402704834938, 0.010026738978922367, -0.05001355707645416, -0.041105009615421295, -0.055410441011190414, 0.0356157161295414, -0.013288894668221474, -0.028906580060720444, 0.0728948563337326, -0.05929175764322281, -0.0025297878310084343, -0.06450381129980087, 0.04003302752971649, -0.00004010551128885709, 0.04923729598522186, 0.03234431892633438, -0.018029646947979927, -0.014157570898532867, -0.0074992612935602665, 0.019332662224769592, -0.061066076159477234, 0.031734399497509, 0.018944529816508293, -0.03106902912259102, -0.004916336387395859, 0.002344963140785694, 0.02988615073263645, 0.03410015255212784, -0.009980532340705395, -0.06213805824518204, 0.020071960985660553, -0.037741199135780334, -0.0018632637802511454, -0.027427982538938522, 0.0030519175343215466, -0.008866963908076286, -0.01157926581799984, 0.022511646151542664, -0.008437247015535831, -0.03899800777435303, 0.03154957294464111, -0.03031124733388424, -0.015090934932231903, 0.04871978610754013, 0.0005536076496355236, 0.003962179180234671, 0.08198823034763336, 0.05847853049635887, 0.0017188695492222905, 0.056519389152526855, -0.04572562500834465, 0.018787428736686707, 0.04084625467658043, 0.03315754607319832, -0.04214002564549446, -0.021365733817219734, -0.03947855159640312, -0.038480497896671295, 0.01750289648771286, -0.03777816519141197, 0.0395524799823761, -0.07208162546157837, -0.029035957530140877, 0.0049209571443498135, -0.0013734784442931414, -0.011246581561863422, 0.006972511298954487, 0.013519925065338612, -0.02785307914018631, 0.017724687233567238, -0.07448434829711914, -0.01898149400949478, -0.03419256582856178, -0.0723034143447876, -0.009329025633633137, -0.06742404401302338, -0.024581681936979294, -0.02578304335474968, -0.03142019733786583, 0.003946006763726473, -0.06864388287067413, -0.01692994125187397, 0.07814387232065201, 0.024544717743992805, -0.0429532565176487, 0.008391040377318859, -0.0023357218597084284, -0.03182680904865265, -0.0000471808307338506, 0.0041054184548556805, 0.013316618278622627, -0.006020663771778345, 0.02914685197174549, 0.017900269478559494, 0.03088420443236828, 0.003936765715479851, -0.021569039672613144, 0.014222259633243084, 0.0033129823859781027, -0.02217896096408367, 0.010451835580170155, 0.021199390292167664, 0.014481013640761375, -0.024008726701140404, 0.010100669227540493, -0.03119840659201145, -0.021883241832256317, -0.034118637442588806, 0.06668474525213242, 0.043729521334171295, 0.08087927848100662, -0.07829173654317856, -0.026041798293590546, 0.001627612393349409, 0.013593855313956738, -0.03702038526535034, 0.005858942400664091, 0.0018031958024948835, 0.0060299052856862545, 0.029812220484018326, 0.020663399249315262, 0.046390995383262634, 0.02160600572824478, 0.04114197567105293, 0.05888514220714569, -0.012272358871996403, 0.03476552292704582, 0.03862835839390755, -0.004703788086771965, -0.0007179283420555294, 0.03204859793186188, 0.016874494031071663, -0.0440252386033535, 0.05474507063627243, -0.02537642791867256, 0.0158394742757082, -0.027612807229161263, 0.026411447674036026, -0.03027428314089775, 0.015100176446139812, -0.015756303444504738, -0.019517486914992332, 0.023047637194395065, -0.026984402909874916, -0.010498042218387127, -0.043729521334171295, -0.03193770349025726, -0.014286947436630726, -0.03888711333274841, -0.022696470841765404, -0.00014092882338445634, -0.035283032804727554, -0.009860396385192871, 0.0035832885187119246, 0.015571479685604572, 0.06376451253890991, 0.017650756984949112, -0.013547648675739765, -0.005115022882819176, 0.02672564797103405, 0.01936962641775608, -0.039071936160326004, 0.0263375174254179, 0.008589726872742176, 0.012863798066973686, -0.03663225099444389, -0.003678011242300272, 0.02521008625626564, 0.03862835839390755, -0.024138104170560837, 0.03029276430606842, -0.0004268295015208423, 0.014832180924713612, -0.017059318721294403, -0.031346265226602554, -0.031161440536379814, 0.03910890221595764, 0.06912443041801453, -0.008386420086026192, -0.007892013527452946, -0.0019164008554071188, -0.0002828683936968446, 0.05367308855056763, -0.063468798995018, 0.028721755370497704, 0.03217797726392746, -0.0008756069000810385, 0.02166145294904709, 0.054079700261354446, 0.007822704501450062, -0.024766506627202034, -0.02764977142214775, -0.030717862769961357, -0.08036176860332489, 0.02877720259130001, -0.00350011745467782, -0.053894877433776855, -0.04158555343747139, 0.020755812525749207, 0.018778188154101372, -0.06930925697088242, 0.035467855632305145, -0.039589446038007736, -0.010784519836306572, 0.03554178774356842, 0.017632273957133293, -0.06269253045320511, -0.016957664862275124, 0.027169227600097656, -0.026097245514392853, 0.017022352665662766, 0.0010714055970311165, -0.023620594292879105, 0.003580978140234947, 0.027224674820899963, 0.04454274848103523, -0.010285493917763233, -0.021772347390651703, 0.011570025235414505, -0.019517486914992332, 0.016569532454013824, 0.018371572718024254, -0.02933167666196823, -0.048830680549144745, 0.02822272852063179, -0.020404644310474396, 0.028906580060720444, 0.005683358758687973, -0.00932440534234047, 0.004962542559951544, -0.008261662907898426, 0.013094828464090824, 0.07821780443191528, 0.03683555871248245, 0.010969344526529312, -0.01043335348367691, 0.004548997618257999, 0.007656362373381853, 0.020367680117487907, -0.07873531430959702, 0.016606496647000313, -0.018537916243076324, 0.0010910432320088148, -0.014379359781742096, -0.03291727602481842, -0.009389094077050686, 0.0673501119017601, 0.013390548527240753, 0.03384139761328697, -0.040920183062553406, 0.0325106605887413, 0.010719831101596355, -0.0500505231320858, 0.010729072615504265, 0.017345795407891273, 0.04724118858575821, -0.019462039694190025, -0.02916533499956131, -0.04398827254772186, -0.011736366897821426, -0.0077811190858483315, -0.04683457314968109, -0.031882256269454956, -0.06147268787026405, 0.0237130057066679, -0.04679761081933975, 0.0044219302944839, -0.0424727126955986, -0.026411447674036026, -0.025672148913145065, 0.011218857951462269, -0.01844550296664238, -0.04483846575021744, -0.037353068590164185, 0.004981025122106075, -0.010997068136930466, 0.01089541520923376, -0.02164296992123127, -0.03458069637417793, -0.012836074456572533, -0.06479953229427338, -0.007734912913292646, 0.05836763605475426, 0.04040267691016197, -0.004777717869728804, -0.00653817318379879, 0.00588204525411129, -0.05470810458064079, 0.01573782227933407, 0.027150746434926987, 0.012937727384269238, 0.0794006809592247, 0.009019444696605206, -0.027409499511122704, -0.006182385608553886, 0.010137633420526981, -0.014111364260315895, -0.03873925283551216, -0.0033938433043658733, -0.02369452454149723, -0.03201163560152054, 0.048608891665935516, -0.029682843014597893, -0.025468841195106506, 0.0034747039899230003, -0.008192353881895542, -0.02277040109038353, -0.0659824088215828, -0.001902539050206542, 0.029276229441165924, -0.004851647652685642, -0.047130294144153595, 0.01627381332218647, -0.08908549696207047, 0.001636853558011353, 0.02184627763926983, 0.006399554666131735, 0.002885575406253338, -0.029072921723127365, 0.021864760667085648, 0.013926539570093155, -0.002691509434953332, 0.003456221427768469, 0.00667217094451189, -0.0840582624077797, 0.021033048629760742, 0.017244143411517143, -0.027501912787556648, 0.006741480436176062, 0.012013603933155537, 0.011819538660347462, -0.02029374986886978, -0.00847421120852232, 0.03045910783112049, 0.07226645201444626, 0.037926025688648224, 0.030422141775488853, -0.01793723553419113, -0.08272752910852432, -0.006981752347201109, -0.0244892705231905, 0.02408265508711338, -0.007083405740559101, 0.05781316012144089, -0.005572464317083359, -0.023454252630472183, 0.008284766227006912, 0.01325192954391241, 0.03271396830677986, 0.033748988062143326, -0.01005446258932352, -0.011089480482041836, 0.019314179196953773, -0.01997954770922661, -0.02596786804497242, -0.014249983243644238, 0.011292788200080395, -0.012004363350570202, -0.07363415509462357, 0.06694349646568298, 0.03822174295783043, 0.013750956393778324, -0.054264526814222336, 0.004043039865791798, 0.02916533499956131, -0.026947438716888428, -0.013177999295294285, 0.03859139233827591, -0.019258731976151466, -0.01469356194138527, 0.024138104170560837, 0.0158671997487545, 0.0542275607585907, -0.030422141775488853, -0.029054440557956696, 0.03068089671432972, 0.008428005501627922, -0.003657218301668763, 0.008885446935892105, 0.03541240841150284, 0.01817750744521618, 0.03195618838071823, -0.02899899333715439, 0.001780092716217041, 0.011791815049946308, -0.0406244657933712, 0.02160600572824478, 0.027372535318136215, -0.027908526360988617, 0.03130929917097092, 0.014102122746407986, -0.04912640154361725, 0.040513571351766586, -0.05249020829796791, -0.016504844650626183, -0.03232583776116371, -0.02748342975974083, 0.016514085233211517, 0.04188127443194389, -0.03241824731230736, -0.025727596133947372, -0.01852867379784584, 0.03531999513506889, 0.041659481823444366, -0.022548610344529152, 0.02539491094648838, 0.007448434829711914, 0.0022306027822196484, -0.02312156744301319, -0.024378376081585884, 0.010673625394701958, -0.05433845520019531, 0.026282070204615593, 0.00926433689892292, -0.0027307847049087286, -0.018020406365394592, -0.03260307386517525, -0.023823902010917664, -0.02994159795343876, 0.006371831055730581, -0.03088420443236828, -0.009546195156872272, -0.043027184903621674, -0.021106978878378868, -0.0353754423558712, 0.03670618310570717, 0.02615269273519516, 0.0186118446290493, 0.07962246984243393, -0.041326798498630524, 0.03350871428847313, 0.003652597777545452, 0.007420710753649473, -0.007799601648002863, -0.007591673638671637, 0.011366717517375946, 0.04350772872567177, 0.003911352250725031, 0.0387762188911438, -0.011902709491550922, -0.045836519449949265, 0.03598536550998688, -0.007554708980023861, 0.028925063088536263, 0.016486361622810364, 0.027354052290320396, 0.014194535091519356, 0.009980532340705395, -0.021143943071365356, -0.01533120684325695, -0.009814190678298473, 0.009610882960259914, 0.01307634636759758, 0.01334434188902378, 0.004311035852879286, -0.010950862430036068, -0.01251263078302145, 0.027963973581790924, -0.02971980907022953, 0.01241097692400217, -0.058071915060281754, -0.0174197256565094, 0.012096775695681572, -0.029109887778759003, -0.007822704501450062, 0.012438701465725899, 0.035671163350343704, 0.04539294168353081, 0.03101358190178871, 0.025690630078315735, -0.004389586392790079, -0.035283032804727554, -0.008899308741092682, 0.05507775396108627, -0.018565639853477478, 0.024951331317424774, -0.011089480482041836, -0.018214471638202667, 0.016449397429823875, -0.028185764327645302, 0.013113311491906643, 0.006126938387751579, -0.04121590405702591, 0.022123513743281364, -0.02668868377804756, -0.004495860543102026, 0.07078785449266434, -0.012993174605071545, -0.017835581675171852, -0.013640061020851135, -0.02295522578060627, -0.013233447447419167, -0.020848223939538002, 0.0010263546137139201, -0.02143966220319271, 0.01922176592051983, -0.013806403614580631, 0.005124264396727085, 0.047721732407808304, -0.0008946669986471534, 0.031734399497509, -0.01817750744521618, -0.004209381993860006, 0.028185764327645302, 0.057295650243759155, -0.00793359987437725, -0.027612807229161263, -0.000875029363669455, -0.016061265021562576, 0.05123339965939522, 0.029461054131388664, 0.01592264696955681, 0.033176030963659286, 0.03554178774356842, 0.04457971453666687, -0.01738276146352291, 0.008391040377318859, -0.00881151668727398, 0.030921168625354767, 0.021384214982390404, 0.014268465340137482, -0.020792776718735695, -0.01400046981871128, -0.011200375854969025, 0.005664876662194729, 0.006053008139133453, 0.03258459270000458, -0.015137141570448875, 0.03008945845067501, 0.006242453586310148, 0.020182855427265167, -0.029442571103572845, 0.02406417392194271, -0.012632766738533974, 0.05119643732905388, 0.022511646151542664, -0.017733927816152573, -0.015571479685604572, 0.017308831214904785, 0.023971760645508766, -0.04029177874326706, -0.031179923564195633, 0.025265533477067947, 0.0031859155278652906, 0.012826832942664623, -0.053525228053331375, -0.016514085233211517, -0.002876334125176072, -0.014259223826229572, 0.02275191806256771, -0.006898581050336361, -0.048239242285490036, -0.052564140409231186, 0.02635599859058857, 0.0020561746787279844, 0.07359718531370163, 0.008857722394168377, 0.022345304489135742, 0.00479157967492938, 0.0203122328966856, -0.009934326633810997, -0.010784519836306572, -0.0006694119074381888, -0.022622540593147278, -0.042805396020412445, 0.05474507063627243, 0.0710466057062149, 0.010738314129412174, -0.02898051030933857, -0.030791791155934334, -0.022659506648778915, 0.025320980697870255, 0.015377413481473923, -0.02465561218559742, 0.00899634137749672, 0.03367505595088005, 0.03384139761328697, 0.012022845447063446, -0.015913404524326324, -0.019092390313744545, 0.012558837421238422, 0.013409030623733997, 0.014804457314312458, 0.009629365988075733, -0.02951650135219097, -0.025709113106131554, 0.0020469333976507187, -0.00010872889106394723, -0.012447942048311234, -0.0019857101142406464, 0.006126938387751579, -0.018232954666018486, -0.02933167666196823, -0.008053735829889774, -0.009093374013900757, 0.011255823075771332, -0.022548610344529152, -0.010183840058743954, 0.010969344526529312, -0.017576826736330986, -0.01731807179749012, 0.05038320645689964, -0.015710098668932915, -0.006616723723709583, 0.004315656144171953, -0.013335100375115871, -0.006510449573397636, 0.015506790950894356, -0.013741714879870415, 0.003682631766423583, 0.006510449573397636, 0.05877424776554108, -0.04609527438879013, 0.016532568261027336, -0.018704257905483246, -0.03633653372526169, 0.018787428736686707, -0.004454274661839008, -0.010562730953097343, 0.0008975548553280532, -0.040920183062553406, 0.007702568545937538, 0.04868282005190849, 0.058219775557518005, 0.01918480172753334, 0.015303483232855797, -0.012078292667865753, 0.0036595286801457405, -0.012152222916483879, 0.013390548527240753, -0.01224463526159525, -0.01023928727954626, -0.012087534181773663, 0.025080708786845207, -0.046354029327631, -0.03147564455866814, 0.0016703529981896281, -0.0018632637802511454, 0.02238226868212223, 0.011625472456216812, 0.04003302752971649, 0.011819538660347462, 0.02408265508711338, 0.011911951005458832, 0.03666921705007553, -0.03347174823284149, -0.0024697198532521725, -0.0032367422245442867, -0.03156805410981178, 0.016902217641472816, -0.011329753324389458, 0.009430679492652416, -0.04454274848103523, -0.06369058787822723, 0.008705242536962032, 0.02916533499956131, -0.006884719245135784, -0.027335571125149727, 0.020737329497933388, -0.02180931158363819, -0.010960103943943977, -0.00017125162412412465, -0.01664346270263195, 0.011708643287420273, 0.02142118103802204, 0.007637879811227322, -0.008127665147185326, -0.04276842996478081, -0.04343380033969879, 0.010488800704479218, 0.0013238068204373121, -0.03031124733388424, -0.02842603623867035, -0.04886764660477638, 0.03522758558392525, 0.005036472342908382, -0.020404644310474396, -0.014887628145515919, 0.050124455243349075, -0.04853495955467224, -0.013307376764714718, -0.005230538547039032, -0.06801548600196838, 0.008123044855892658, -0.015192588791251183, -0.04254664108157158, -0.016181400045752525, -0.019905617460608482, -0.024119621142745018, 0.056926000863313675, 0.0018979184096679091, -0.007101888302713633, 0.05718475580215454, -0.058811213821172714, 0.018390055745840073, -0.03535696119070053, 0.03533848002552986, -0.06324700266122818, 0.009042547084391117, -0.03365657478570938, 0.01883363537490368, 0.004981025122106075, 0.025727596133947372, 0.028832649812102318, -0.03008945845067501, -0.017780134454369545, -0.004745373502373695, 0.01836233213543892, 0.05999409034848213, -0.013640061020851135, 0.0193881094455719, -0.0004996042116545141, 0.0193881094455719, 0.04088322073221207, -0.007822704501450062, -0.02990463376045227, -0.013750956393778324, -0.002282584784552455, 0.022345304489135742, 0.003488565795123577, -0.006108455825597048, 0.03925676271319389, 0.0015328896697610617, 0.03833263739943504, -0.04531901329755783, 0.03422953188419342, -0.03166046738624573, -0.02389783039689064, -0.05356219410896301, -0.02426747977733612, -0.08553685992956161, 0.002193637890741229, 0.0024581681936979294, -0.013935781084001064, 0.022456198930740356, 0.04084625467658043, 0.012457183562219143, 0.021199390292167664, -0.044283993542194366, -0.018482467159628868, -0.007864289917051792, -0.002045778091996908, 0.005868183448910713, 0.0048377858474850655, -0.03446980193257332, 0.04276842996478081, -0.008229319006204605, -0.01515562366694212, -0.033379338681697845, 0.020460091531276703, -0.04387737810611725, 0.022345304489135742, 0.007402228657156229, -0.0395524799823761, 0.016079748049378395, 0.021384214982390404, -0.020034994930028915, -0.00890392903238535, 0.01889832317829132, 0.045651696622371674, -0.01204132754355669, 0.019277215003967285, 0.012725179083645344, -0.013797162100672722, -0.028555413708090782, 0.05603884160518646, -0.005895907524973154, 0.005669496953487396, -0.024396857246756554, 0.02953498438000679, -0.01901846006512642, 0.010267010889947414, 0.006958649028092623, -0.006773824337869883, -0.03234431892633438, 0.035689644515514374, 0.020774293690919876, -0.020219819620251656, -0.030921168625354767, 0.02223440818488598, -0.048091381788253784, 0.0059929401613771915, -0.01551603153347969, 0.04258360713720322, 0.012401736341416836, -0.04029177874326706, 0.02387934923171997, 0.006926305126398802, 0.004204761702567339, 0.010608936659991741, 0.00940757617354393, -0.03628108650445938, 0.027705220505595207, 0.042250923812389374, 0.0035324618220329285, 0.02916533499956131, 0.014425566419959068, 0.031697433441877365, 0.01703159511089325, 0.006570517551153898, 0.018066613003611565, -0.02461864799261093, 0.00876068975776434, -0.02936864085495472, 0.005687979515641928, -0.02068188227713108, -0.029405606910586357, 0.019499003887176514, -0.024988297373056412, -0.037131279706954956, 0.023639077320694923, 0.0012891521910205483, -0.013510684482753277, 0.028499966487288475, -0.013002416118979454, -0.026041798293590546, 0.05777619406580925, -0.025357946753501892, 0.01111720409244299, -0.029812220484018326, 0.025524288415908813, 0.037889059633016586, 0.005627911537885666, -0.07762636244297028, -0.005734185688197613, 0.013372065499424934, -0.005960595794022083, -0.01542361918836832, -0.02539491094648838, -0.056519389152526855, 0.038850147277116776, 0.011329753324389458, -0.035855989903211594, -0.019332662224769592, -0.0006486191414296627, 0.0028786445036530495, -0.005683358758687973, 0.01157926581799984, -0.014859904535114765, -0.014647356234490871, 0.01994258351624012, 0.03312058374285698, 0.0010303976014256477, -0.015377413481473923, 0.015035487711429596, 0.042620573192834854, -0.03936765715479851, 0.008464970625936985, -0.005567843560129404, -0.001708473195321858, 0.026004832237958908, 0.005147367250174284, 0.03711279481649399, 0.0005879735108464956, 0.0014069778844714165, -0.017327314242720604, 0.038850147277116776, -0.01590416394174099, -0.015626925975084305, 0.03419256582856178, -0.001606819569133222, -0.013325859792530537, -0.014887628145515919, -0.028444519266486168, 0.039774272590875626, 0.0670543909072876, 0.012854556553065777, 0.023934796452522278, 0.00593287218362093, -0.0849454253911972, 0.06361665576696396, -0.029812220484018326, -0.035855989903211594, -0.01006370410323143, -0.009518470615148544, -0.01959141530096531, 0.007836566306650639, -0.008164630271494389, 0.03768575191497803, 0.052046630531549454, -0.008377178572118282, 0.004456585273146629, 0.006746100727468729, -0.010997068136930466, 0.03485793620347977 ]
Artificial Intelligence is now recognized as a general-purpose technology with ample impact on human life. In this work, we aim to understand the evolution of AI and Machine learning over the years by analyzing researchers' impact, influence, and leadership over the last decades. This work also intends to shed new light on the history and evolution of AI by exploring the dynamics involved in the field's evolution through the lenses of the papers published on AI conferences since the first International Joint Conference on Artificial Intelligence (IJCAI) in 1969. AI development and evolution have led to increasing research output, reflected in the number of articles published over the last sixty years. We construct comprehensive citation-collaboration and paper-author datasets and compute corresponding centrality measures to carry out our analyses. These analyses allow a better understanding of how AI has reached its current state of affairs in research. Throughout the process, we correlate these datasets with the work of the ACM Turing Award winners and the so-called two AI winters the field has gone through. We also look at self-citation trends and new authors' behaviors. Finally, we present a novel way to infer the country of affiliation of a paper from its organization. Therefore, this work provides a deep analysis of Artificial Intelligence history from information gathered and analyzed from large technical venues datasets and suggests novel insights that can contribute to understanding and measuring AI's evolution.
[ -0.0048223696649074554, 0.0018658243352547288, -0.04996349662542343, -0.01996755413711071, 0.01813853345811367, -0.02583826519548893, 0.013864870183169842, 0.017255250364542007, 0.01568496972322464, 0.015435151755809784, -0.021948250010609627, -0.059099677950143814, 0.04571659862995148, -0.04296860843896866, -0.04953523725271225, 0.007222401909530163, 0.03317219391465187, -0.025338631123304367, -0.025713356211781502, -0.043218422681093216, -0.020342281088232994, -0.02956768311560154, -0.039471160620450974, -0.016871601343154907, -0.0038387132808566093, 0.013731039129197598, 0.014980127103626728, -0.007436531130224466, -0.04692999646067619, 0.048607345670461655, -0.03368967026472092, 0.00508110923692584, -0.004675155505537987, -0.05645875260233879, 0.002567320829257369, 0.007146564312279224, 0.01133100688457489, 0.04650174081325531, -0.004737609997391701, 0.017326626926660538, 0.04378943517804146, -0.0016238136449828744, -0.004262510687112808, -0.03875739872455597, -0.0006786336307413876, -0.009698271751403809, -0.05099845305085182, -0.03807932138442993, -0.07544487714767456, 0.007191174663603306, 0.03634844347834587, -0.015113957226276398, 0.024428579956293106, 0.003194094868376851, -0.011812797747552395, 0.03315434977412224, 0.043218422681093216, -0.036437664180994034, 0.05752939730882645, 0.008404573425650597, -0.0017899868544191122, 0.07730066776275635, -0.03310081735253334, 0.02189471758902073, 0.04821477457880974, -0.017549678683280945, -0.051997724920511246, 0.006869980599731207, 0.01996755413711071, 0.02555275894701481, -0.025891797617077827, 0.026891067624092102, -0.0016059695044532418, -0.008743612095713615, 0.016951899975538254, -0.04357530549168587, 0.053639382123947144, 0.021127421408891678, -0.048607345670461655, -0.012696080841124058, 0.049499548971652985, 0.028175843879580498, -0.028978828340768814, -0.001236819545738399, 0.039685290306806564, -0.01471246499568224, 0.014373427256941795, -0.07194743305444717, -0.008730228990316391, -0.012945898808538914, -0.07394597679376602, 0.028479192405939102, -0.03629491105675697, -0.016389811411499977, -0.01765674352645874, 0.015265632420778275, 0.03131640702486038, -0.0049294340424239635, -0.03840051591396332, -0.028711166232824326, -0.009412765502929688, -0.0186470914632082, 0.08679372817277908, -0.0681287944316864, 0.014757075347006321, -0.08715061098337173, -0.031245028600096703, -0.002082184189930558, -0.006624624133110046, 0.14468000829219818, -0.014034389518201351, 0.011554058641195297, -0.04054180905222893, 0.004121988546103239, -0.057315267622470856, 0.03490307182073593, -0.04050612077116966, -0.025927485898137093, 0.003218630561605096, -0.009038039483129978, -0.05520966276526451, 0.039007216691970825, 0.04293292015790939, -0.002841673791408539, -0.006285586394369602, 0.07901369780302048, -0.033332791179418564, -0.039542537182569504, 0.024089543148875237, 0.00035214226227253675, -0.033814579248428345, 0.08479519188404083, 0.0016784612089395523, 0.03843620419502258, 0.025338631123304367, -0.015551138669252396, 0.03936409577727318, 0.011670045554637909, -0.02742638997733593, -0.020431501790881157, -0.00877930037677288, -0.03026360273361206, -0.018415117636322975, -0.002701151417568326, 0.016327356919646263, 0.003252088325098157, -0.012205367907881737, 0.046680182218551636, -0.018700622022151947, -0.010099763981997967, -0.007699731737375259, 0.05349662899971008, -0.011036579497158527, -0.027123041450977325, -0.006740611046552658, -0.017183873802423477, 0.009261091239750385, -0.007646199315786362, -0.01433773897588253, -0.00010295212268829346, 0.0034372208174318075, 0.004737609997391701, 0.005879632662981749, 0.07194743305444717, 0.04792926833033562, -0.019842645153403282, 0.013873792253434658, 0.0371871180832386, -0.07258982211351395, 0.0515337772667408, 0.006330196745693684, -0.02928217686712742, -0.007793413009494543, -0.033261414617300034, 0.018290208652615547, 0.02742638997733593, -0.0023130422923713923, 0.011072267778217793, -0.051926348358392715, 0.019646359607577324, -0.005121258553117514, 0.029603371396660805, 0.031262874603271484, 0.020841915160417557, 0.06220455467700958, -0.003970313351601362, 0.0872933641076088, 0.006490793544799089, 0.012410575523972511, -0.010599398985505104, 0.004320504143834114, -0.025945330038666725, 0.06277556717395782, -0.019021816551685333, 0.0013695351080968976, -0.015033659525215626, 0.0011336583411321044, 0.023732660338282585, -0.01799578033387661, -0.017674587666988373, -0.033065129071474075, -0.07894232124090195, -0.02632005698978901, 0.06302538514137268, 0.0381150096654892, -0.01222321204841137, -0.03172681853175163, -0.04871441051363945, 0.02239435352385044, -0.01036742515861988, -0.028033090755343437, -0.01278530154377222, -0.03445696830749512, -0.05438883602619171, -0.03108443319797516, -0.005723496899008751, 0.03704436495900154, 0.04089869186282158, -0.009127260185778141, -0.014114688150584698, 0.011768187396228313, 0.03529564291238785, 0.04136263579130173, 0.00604469096288085, -0.002567320829257369, -0.06477410346269608, -0.0031294100917875767, -0.051569465547800064, 0.00562981516122818, -0.01016221847385168, 0.01184848602861166, 0.023786192759871483, -0.0076105110347270966, 0.05463865026831627, 0.04243328422307968, -0.024767618626356125, 0.04125557094812393, -0.012026927433907986, -0.031173652037978172, 0.004710843786597252, 0.014373427256941795, -0.05346094071865082, -0.020770538598299026, 0.010403113439679146, 0.044110629707574844, -0.048678722232580185, -0.01982480101287365, 0.01119717676192522, 0.025053124874830246, 0.03611646965146065, 0.0004714747192338109, -0.0013293859083205462, -0.017567522823810577, 0.003225322114303708, -0.005861788988113403, 0.008172600530087948, 0.03743693232536316, -0.0009970393730327487, -0.06134803593158722, -0.006196365691721439, 0.029246488586068153, 0.017041120678186417, 0.008641008287668228, 0.07219725102186203, -0.04717981442809105, 0.03567036613821983, 0.013980857096612453, 0.01698758825659752, 0.026819691061973572, 0.009287857450544834, -0.021180953830480576, -0.013597209006547928, 0.02888960763812065, -0.033332791179418564, -0.02797955833375454, -0.02025306038558483, 0.0008732459391467273, -0.019235946238040924, 0.005018654745072126, 0.02285829931497574, -0.005790412425994873, -0.052069101482629776, 0.0680217295885086, 0.002848365344107151, -0.06427446752786636, -0.08415280282497406, -0.056351687759160995, 0.008538404479622841, -0.022055314853787422, -0.03368967026472092, 0.010340658947825432, 0.005719035863876343, -0.049356795847415924, 0.030495576560497284, 0.0041688294149935246, -0.035474080592393875, 0.035830963402986526, 0.004599318373948336, 0.0012780841207131743, -0.009113877080380917, 0.035741742700338364, 0.014105766080319881, 0.025856109336018562, 0.005986697506159544, 0.00138180295471102, 0.01142914965748787, 0.04400356486439705, 0.08529482781887054, -0.030352823436260223, -0.04486008360981941, -0.03633059933781624, 0.02259063720703125, -0.013579364866018295, -0.03822207450866699, 0.06213317811489105, 0.031744662672281265, 0.03590233996510506, -0.020502878352999687, 0.018682777881622314, -0.05838591605424881, 0.04614485800266266, -0.05417470633983612, -0.08036985248327255, 0.057315267622470856, -0.05906398966908455, -0.010929514653980732, 0.020627785474061966, -0.002069916343316436, -0.016354123130440712, -0.02901451662182808, -0.0396496020257473, -0.03592018410563469, 0.022822611033916473, -0.04157676547765732, 0.04097006842494011, -0.019878333434462547, 0.006093762349337339, 0.03861464560031891, -0.03697298839688301, -0.03925703093409538, -0.02396463416516781, -0.027818961068987846, -0.0483575277030468, -0.0027457617688924074, 0.006646929308772087, -0.049856431782245636, 0.0107064638286829, 0.0182634424418211, 0.026409275829792023, -0.007414225954562426, 0.000950756249949336, -0.028532724827528, -0.009894556365907192, -0.037472620606422424, 0.00016045755182858557, 0.020056774839758873, -0.030227914452552795, -0.04493146017193794, 0.010340658947825432, -0.02044934593141079, -0.005174790509045124, -0.05956362560391426, 0.05049882084131241, 0.0005855096969753504, -0.07126935571432114, -0.049356795847415924, 0.0009334697970189154, 0.026409275829792023, -0.002694459864869714, 0.025945330038666725, -0.04054180905222893, 0.03315434977412224, -0.04635898768901825, -0.012687158770859241, 0.0001572511828271672, 0.017478302121162415, -0.01762997731566429, -0.009653661400079727, -0.015381619334220886, 0.024303672835230827, 0.0033859191462397575, 0.004387419670820236, 0.03322572633624077, 0.043967876583337784, -0.06869980692863464, -0.01722848415374756, 0.07580175995826721, -0.032297831028699875, 0.028639789670705795, 0.040184926241636276, 0.03345770016312599, -0.019646359607577324, -0.039899419993162155, -0.054353147745132446, 0.014070077799260616, -0.0281223114579916, 0.05253304913640022, -0.01140238344669342, 0.021109577268362045, -0.03274393454194069, 0.012678237631917, 0.01813853345811367, -0.010081919841468334, -0.0030937218107283115, -0.010278205387294292, 0.015194255858659744, -0.008074457757174969, 0.03377889096736908, 0.019806956872344017, -0.014319894835352898, 0.001384033472277224, 0.032511960715055466, -0.047215502709150314, -0.031887415796518326, -0.031405627727508545, 0.006093762349337339, 0.013641818426549435, 0.007561439648270607, -0.007128720171749592, -0.009493064135313034, -0.0027435312513262033, -0.014650010503828526, 0.028175843879580498, -0.03697298839688301, -0.060420140624046326, -0.013276014477014542, -0.004773298278450966, -0.0095287524163723, 0.012553328648209572, 0.00004722414814750664, 0.04007786139845848, -0.012767457403242588, 0.07965608686208725, 0.03054910898208618, 0.0011130260536447167, -0.021805496886372566, 0.0028238296508789062, -0.010822449810802937, -0.004880363121628761, -0.023197337985038757, -0.05892123654484749, -0.009403843432664871, 0.01191986259073019, -0.014293128624558449, -0.0428258553147316, 0.003948008641600609, -0.008895286358892918, -0.04614485800266266, -0.022893987596035004, -0.0816546306014061, -0.059670690447092056, 0.033065129071474075, -0.05513828620314598, -0.03939978405833244, 0.03875739872455597, 0.017460457980632782, 0.010777839459478855, -0.010519100353121758, 0.010715385898947716, -0.03463540971279144, 0.01018898468464613, 0.04132694751024246, 0.024143075570464134, -0.013739961199462414, 0.02410738728940487, 0.02937139756977558, -0.04082731530070305, -0.08251114189624786, -0.0076417382806539536, 0.050748635083436966, 0.039471160620450974, -0.008997890166938305, 0.007507907692342997, 0.04386081174015999, 0.018272364512085915, 0.0021992861293256283, 0.03504582494497299, -0.004266971722245216, 0.007159947417676449, 0.005777029320597649, 0.04229053109884262, 0.08650822192430496, -0.02037796936929226, -0.04179089516401291, -0.03019222617149353, 0.04967799037694931, -0.0071510253474116325, 0.024821151047945023, -0.040184926241636276, -0.04179089516401291, -0.026034550741314888, 0.04125557094812393, 0.008123529143631458, -0.0030067318584769964, -0.04478870704770088, -0.019235946238040924, -0.02908589318394661, -0.006847675424069166, 0.033350635319948196, 0.04932110756635666, -0.04732256755232811, -0.009769648313522339, -0.025267254561185837, 0.052961304783821106, 0.0057502631098032, 0.030923835933208466, 0.05099845305085182, -0.01650579832494259, -0.04539540410041809, 0.03911428153514862, 0.03238705173134804, 0.018504338338971138, -0.0006959201418794692, -0.014971205033361912, 0.014212829992175102, 0.04914266616106033, 0.03301159664988518, 0.017282016575336456, 0.025106657296419144, 0.014542946591973305, 0.02080622687935829, 0.011000891216099262, 0.03343985602259636, 0.023250870406627655, 0.006348040420562029, 0.03722280636429787, -0.014596479013562202, -0.016800224781036377, 0.0371871180832386, 0.004447643179446459, -0.014453725889325142, 0.0241787638515234, -0.042397595942020416, -0.039899419993162155, -0.004171059932559729, 0.008583014830946922, 0.017737040296196938, 0.025659823790192604, -0.003832021728157997, -0.005063265096396208, -0.0021803267300128937, 0.025178033858537674, -0.004916050937026739, 0.023750504478812218, 0.007293778471648693, 0.0032922374084591866, 0.06081271171569824, -0.004916050937026739, 0.0004062322259414941, 0.0245356447994709, 0.02721226215362549, -0.021091733127832413, -0.018682777881622314, -0.04475301876664162, -0.010501256212592125, 0.0475366972386837, 0.021091733127832413, -0.01105442363768816, -0.01907534897327423, 0.02037796936929226, -0.03343985602259636, -0.05124827101826668, -0.030138695612549782, 0.02078838273882866, -0.013971935026347637, -0.030317135155200958, 0.014141453430056572, 0.08508069813251495, -0.01398977916687727, 0.022715546190738678, -0.0024870221968740225, -0.04150538891553879, -0.03397517651319504, 0.006504176650196314, 0.005732418969273567, 0.036027248948812485, -0.0016795764677226543, -0.04014923796057701, -0.04717981442809105, 0.015800954774022102, 0.0032788545358926058, 0.022893987596035004, 0.03211938962340355, 0.022340821102261543, 0.0006094877608120441, 0.011000891216099262, -0.033529072999954224, 0.004019384738057852, -0.03254764899611473, -0.019931865856051445, -0.00950198620557785, 0.016425499692559242, -0.0340643972158432, -0.009974854998290539, -0.03172681853175163, 0.010420957580208778, 0.008065535686910152, 0.022715546190738678, 0.022001782432198524, -0.020556410774588585, 0.046394675970077515, 0.009006812237203121, 0.05638737604022026, 0.056066181510686874, -0.003997079562395811, 0.0010500140488147736, 0.004362883977591991, -0.012410575523972511, 0.003675885731354356, 0.02508881315588951, -0.0038164081051945686, -0.0515337772667408, 0.008819449692964554, -0.001176595687866211, 0.03135209530591965, -0.023179493844509125, 0.033546917140483856, 0.04125557094812393, -0.05570929870009422, -0.036241378635168076, 0.0217698086053133, 0.01258009485900402, 0.043361175805330276, 0.009096032939851284, -0.002538324100896716, 0.04139832407236099, -0.0026364666409790516, 0.009207558818161488, -0.022679857909679413, -0.018504338338971138, 0.00019530931604094803, -0.04767945036292076, -0.03310081735253334, 0.0012769688619300723, 0.008275204338133335, -0.016318434849381447, -0.003934625536203384, 0.017326626926660538, 0.016184603795409203, -0.04264741390943527, -0.006303430534899235, 0.017915481701493263, -0.019717736169695854, 0.07076972723007202, -0.00559858838096261, 0.05092707648873329, -0.025517070665955544, -0.04882147163152695, 0.02032443694770336, 0.03722280636429787, 0.0404704324901104, 0.009974854998290539, -0.015310242772102356, 0.053104057908058167, -0.013579364866018295, -0.040256302803754807, 0.01450725831091404, -0.024000322446227074, 0.050677262246608734, 0.022554948925971985, 0.02342931181192398, -0.02196609415113926, 0.03904290497303009, -0.011518370360136032, 0.03829345107078552, -0.002881823107600212, 0.04739394411444664, 0.025820421054959297, -0.05035606771707535, 0.027747584506869316, -0.0014018776128068566, 0.03211938962340355, -0.007958470843732357, -0.0023955712094902992, 0.03522426635026932, -0.011446993798017502, 0.013623975217342377, 0.0491783544421196, 0.03156622499227524, 0.007695270702242851, -0.04154107719659805, -0.02480330690741539, -0.009617973119020462, -0.02444642409682274, -0.03308297321200371, -0.018325896933674812, -0.01878984272480011, 0.0498921200633049, -0.008676696568727493, -0.03399302065372467, -0.021377239376306534, -0.0213593952357769, -0.03850758075714111, -0.003629045095294714, 0.01871846616268158, 0.04664449393749237, -0.05581636354327202, -0.009689349681138992, 0.021519992500543594, -0.02992456592619419, -0.013802415691316128, -0.01768350973725319, -0.01081352774053812, 0.040113549679517746, -0.016175681725144386, 0.0241252314299345, 0.011678967624902725, -0.030174382030963898, -0.05934949591755867, -0.005317543633282185, 0.010519100353121758, 0.04382512345910072, 0.0018535564886406064, 0.05264011397957802, 0.018254520371556282, 0.031137963756918907, -0.04889284819364548, -0.004706382751464844, -0.02044934593141079, -0.0035063668619841337, 0.0023732660338282585, -0.023946790024638176, 0.008846215903759003, -0.03531348705291748, -0.06195473670959473, -0.0063391188159585, -0.01554221659898758, 0.029264332726597786, -0.06527373939752579, 0.004898207262158394, 0.004670694470405579, -0.014721387065947056, -0.0005537248798646033, -0.003990388009697199, 0.02066347375512123, 0.012455185875296593, 0.02307242900133133, 0.04357530549168587, 0.030941680073738098, -0.021091733127832413, -0.0033546919003129005, 0.00786479003727436, 0.04014923796057701, -0.015524372458457947, -0.00891313049942255, 0.028925295919179916, -0.02978181280195713, 0.02985318936407566, -0.024143075570464134, -0.000777333858422935, 0.02896098420023918, -0.014944438822567463, 0.04939248412847519, -0.02701597660779953, 0.02369697205722332, -0.027676207944750786, -0.014551868662238121, -0.0013427690137177706, 0.011652201414108276, 0.021163109689950943, -0.03497444838285446, 0.03276177868247032, -0.006861058529466391, 0.010715385898947716, 0.04022061452269554, 0.017665665596723557, 0.010590476915240288, -0.0006317928782664239, -0.021056044846773148, 0.004556938540190458, 0.010269283317029476, -0.025249410420656204, 0.06680833548307419, -0.008667774498462677, 0.010742152109742165, 0.0045948573388159275, 0.0381150096654892, -0.0594208724796772, 0.00023308863455895334, 0.002906358800828457, -0.029763968661427498, 0.0073473104275763035, -0.08607997000217438, 0.00802538637071848, -0.03986373171210289, 0.040256302803754807, 0.00530416052788496, -0.034653253853321075, 0.028479192405939102, 0.08379592001438141, -0.03490307182073593, -0.03490307182073593, 0.029799656942486763, -0.0016963053494691849, 0.05528103932738304, 0.037401244044303894, -0.027408545836806297, -0.021519992500543594, 0.009029117412865162, 0.004817908629775047, 0.05742233246564865, -0.0027167650405317545, -0.02383972518146038, -0.02405385486781597, 0.0023375777527689934, -0.06156216561794281, 0.019360855221748352, -0.004001540597528219, 0.0057725682854652405, 0.019467920064926147, 0.04953523725271225, 0.011277474462985992, -0.008881903253495693, 0.055031221359968185, 0.025802576914429665, -0.013650740496814251, -0.025927485898137093, 0.007811257150024176, -0.051498088985681534, -0.010688619688153267, -0.027961714193224907, -0.04146970063447952, -0.018058234825730324, 0.00821721088141203, -0.04029199108481407, -0.0037338791880756617, 0.0245356447994709, 0.0022885065991431475, 0.008284126408398151, -0.00241787638515234, 0.02391110174357891, 0.032155077904462814, -0.04214777797460556, 0.03108443319797516, -0.022430041804909706, 0.01337415724992752, -0.03161975368857384, 0.0030870302580296993, -0.018771998584270477, 0.03219076618552208, 0.00814137328416109, 0.009653661400079727, -0.012401653453707695, -0.0015490914229303598, 0.011170410551130772, -0.00691012991592288, -0.051854971796274185, -0.004724226891994476, 0.008752534165978432, 0.009725037962198257, 0.011036579497158527, -0.0006780760013498366, 0.025124501436948776, 0.002152445260435343, -0.008284126408398151, 0.010180062614381313, 0.0206456296145916, -0.019396543502807617, 0.023197337985038757, -0.020270904526114464, 0.0388287752866745, 0.04339686408638954, -0.0070885708555579185, -0.012151836417615414, -0.0033167731016874313, -0.04214777797460556, 0.005072187166661024, -0.04250466078519821, 0.019325166940689087, -0.012133992277085781, 0.014694620855152607, 0.026230836287140846, 0.010287127457559109, 0.07109091430902481, -0.003113796468824148, 0.029050204902887344, 0.019878333434462547, 0.012892366386950016, -0.020681317895650864, -0.032511960715055466, -0.013356313109397888, -0.0023442693054676056, 0.0357060544192791, 0.04475301876664162, -0.01471246499568224, 0.011446993798017502, -0.0832962840795517, -0.010777839459478855, 0.014650010503828526, 0.004075147677212954, -0.006883363705128431, 0.014302050694823265, 0.032297831028699875, -0.0009044731268659234, 0.015328086912631989, 0.017014354467391968, 0.017478302121162415, -0.009680427610874176, 0.014239596202969551, -0.004188903607428074, 0.01274069119244814, 0.0012602399801835418, 0.03161975368857384, -0.0009769648313522339, -0.021109577268362045, -0.04746532067656517, 0.006419416982680559, -0.05735095590353012, 0.007387459743767977, -0.018754154443740845, 0.0007907169638201594, -0.03470678627490997, -0.019592829048633575, -0.01606861688196659, 0.03211938962340355, -0.01088490430265665, -0.09143319725990295, -0.03793656826019287, -0.013561520725488663, 0.0022015166468918324, 0.04254034906625748, 0.012571172788739204, 0.009814257733523846, -0.010331736877560616, -0.04821477457880974, 0.01700543239712715, -0.011116878129541874, 0.0016483492217957973, -0.005616432521492243, -0.029246488586068153, -0.020913291722536087, 0.05160515382885933, 0.025873953476548195, 0.014551868662238121, 0.02749776653945446, -0.020502878352999687, -0.019021816551685333, 0.044039253145456314, -0.028550568968057632, -0.006406033877283335, -0.021609211340546608, -0.04428907111287117, 0.006120528094470501, 0.020467190071940422, -0.006843214388936758, -0.018540026620030403, 0.06605888158082962, 0.02874685451388359, 0.01975342445075512, 0.034028708934783936, -0.03158406913280487, 0.04796495661139488, 0.018174221739172935, -0.023928945884108543, -0.04482439532876015, -0.009885634295642376, -0.006240976043045521, -0.05349662899971008, -0.0033569224178791046, -0.009234325028955936, -0.0012044771574437618, 0.03627706691622734, -0.01724632829427719, -0.013070807792246342, -0.02569551207125187, 0.036437664180994034, 0.016657473519444466, -0.016184603795409203, -0.04064887389540672, -0.010046231560409069, 0.010064075700938702, -0.02292967587709427, -0.036580417305231094, -0.027319325134158134, 0.017888715490698814, -0.027462078258395195, 0.007365154568105936, 0.0017888715956360102, -0.017906559631228447, -0.002915280871093273, -0.04346824064850807, 0.003216400044038892, 0.005982236471027136, -0.023250870406627655, 0.017264172434806824, 0.0026253140531480312, -0.02549922652542591, -0.015426229685544968, -0.010340658947825432, 0.05228323116898537, 0.03722280636429787, 0.04807202145457268, 0.025267254561185837, -0.02880038693547249, 0.012990509159862995, -0.028853919357061386, 0.0030045013409107924, -0.009591206908226013, 0.03957822546362877, 0.0515337772667408, -0.0325298048555851, 0.013552598655223846, 0.01575634628534317, 0.04710843786597252, 0.02066347375512123, 0.08415280282497406, 0.02499959245324135, 0.013088651932775974, -0.008859598077833652, -0.008105685003101826, 0.025731200352311134, 0.021787652745842934, 0.00720455776900053, -0.008520560339093208, 0.035884495824575424, 0.02451780065894127, -0.009403843432664871, -0.003680346766486764, -0.01845080591738224, -0.08929190784692764, 0.004362883977591991, -0.01461432222276926, 0.015818798914551735, 0.0007377422298304737 ]
Embodied agents in continuous control domains have had limited exposure to tasks allowing to explore musculoskeletal properties that enable agile and nimble behaviors in biological beings. The sophistication behind neuro-musculoskeletal control can pose new challenges for the motor learning community. At the same time, agents solving complex neural control problems allow impact in fields such as neuro-rehabilitation, as well as collaborative-robotics. Human biomechanics underlies complex multi-joint-multi-actuator musculoskeletal systems. The sensory-motor system relies on a range of sensory-contact rich and proprioceptive inputs that define and condition muscle actuation required to exhibit intelligent behaviors in the physical world. Current frameworks for musculoskeletal control do not support physiological sophistication of the musculoskeletal systems along with physical world interaction capabilities. In addition, they are neither embedded in complex and skillful motor tasks nor are computationally effective and scalable to study large-scale learning paradigms. Here, we present MyoSuite -- a suite of physiologically accurate biomechanical models of elbow, wrist, and hand, with physical contact capabilities, which allow learning of complex and skillful contact-rich real-world tasks. We provide diverse motor-control challenges: from simple postural control to skilled hand-object interactions such as turning a key, twirling a pen, rotating two balls in one hand, etc. By supporting physiological alterations in musculoskeletal geometry (tendon transfer), assistive devices (exoskeleton assistance), and muscle contraction dynamics (muscle fatigue, sarcopenia), we present real-life tasks with temporal changes, thereby exposing realistic non-stationary conditions in our tasks which most continuous control benchmarks lack.
[ 0.056340642273426056, 0.002111805370077491, -0.031812701374292374, -0.054325707256793976, 0.04444478452205658, 0.05145830288529396, -0.041577380150556564, 0.007517252117395401, -0.005686374846845865, 0.006882741581648588, 0.03218081220984459, 0.00405408488586545, 0.07943487912416458, -0.01844439096748829, 0.01677819713950157, 0.011295252479612827, -0.011692427098751068, 0.0018490406218916178, -0.06471036374568939, -0.0399886816740036, 0.01670069992542267, 0.005468413233757019, -0.03648192062973976, 0.01676850952208042, 0.008762055076658726, -0.020556196570396423, 0.007899895310401917, 0.0002959130797535181, -0.07315758615732193, 0.016313211992383003, 0.03047586977481842, 0.030165880918502808, -0.030301500111818314, 0.09454688429832458, -0.02421795204281807, -0.06614407151937485, -0.005507162306457758, 0.028790300711989403, -0.04467727616429329, 0.02074994146823883, -0.0024557001888751984, 0.005366697907447815, -0.021873652935028076, -0.030650239437818527, 0.01296144723892212, -0.0028117040637880564, -0.014927945099771023, 0.002838343847543001, 0.013077693991363049, 0.03528071194887161, 0.04138363525271416, -0.01484076026827097, 0.03165770694613457, -0.04417354241013527, 0.017853474244475365, 0.01023934967815876, 0.09415939450263977, 0.026058515533804893, 0.04448353126645088, 0.009595151990652084, -0.008573154918849468, -0.013474867679178715, -0.05269826203584671, 0.01893843710422516, 0.03925245627760887, -0.057580601423978806, 0.0032258310820907354, -0.012108976021409035, 0.011072447523474693, -0.010617149993777275, -0.03824498876929283, 0.04890088737010956, -0.033595141023397446, -0.02774408459663391, 0.015296057797968388, -0.008403629064559937, 0.03524196147918701, 0.05428696051239967, 0.038806844502687454, -0.04138363525271416, 0.015150750055909157, 0.047350939363241196, -0.028790300711989403, -0.006824618671089411, 0.08075233548879623, 0.011334001086652279, 0.03520321473479271, -0.08695213496685028, 0.008752367459237576, 0.021776782348752022, -0.022609880194067955, 0.02846093662083149, 0.002398787997663021, 0.02667849510908127, -0.01970372535288334, -0.00462562870234251, 0.03652067109942436, 0.006989300716668367, 0.022803623229265213, -0.028131572529673576, 0.04452228173613548, 0.018802817910909653, 0.0007598382071591914, -0.03264579921960831, -0.030398372560739517, -0.015325119718909264, 0.03303328529000282, 0.03772187978029251, -0.03169645369052887, 0.08974204212427139, 0.001118869404308498, -0.0424298495054245, 0.012942072935402393, 0.009091419167816639, -0.061571720987558365, -0.009338442236185074, -0.05444195494055748, -0.04471602663397789, 0.020517447963356972, -0.04696344956755638, 0.06556283682584763, 0.06912772357463837, 0.008810490369796753, -0.034118250012397766, -0.05374447628855705, 0.04924962669610977, -0.04800966754555702, -0.01361048873513937, 0.05014084652066231, 0.04022117331624031, 0.05269826203584671, 0.0249541774392128, 0.015867602080106735, 0.0059043364599347115, -0.012060539796948433, 0.007526939269155264, 0.012302719056606293, 0.054054468870162964, 0.00474671833217144, 0.011149944737553596, -0.02043995074927807, -0.01894812472164631, -0.064981609582901, -0.0020609477069228888, 0.021021181717514992, -0.042081113904714584, -0.030766485258936882, 0.08540218323469162, -0.009541872888803482, 0.0029085760470479727, -0.0548681914806366, 0.02520604431629181, -0.022319264709949493, 0.014569519087672234, 0.06412913650274277, -0.02547728456556797, -0.07412630319595337, 0.005584659520536661, 0.047350939363241196, 0.030069008469581604, 0.03650129586458206, -0.002297072671353817, -0.004431885201483965, 0.05374447628855705, 0.049520865082740784, -0.03218081220984459, -0.02071119099855423, -0.01948091946542263, 0.003557617077603936, 0.034854475408792496, -0.08912205696105957, 0.00413158256560564, 0.028402812778949738, 0.03154145926237106, 0.047312188893556595, 0.03268454596400261, 0.06095173954963684, -0.006175577640533447, -0.004744296427816153, -0.020788690075278282, -0.024295449256896973, 0.028635306283831596, -0.0074397544376552105, 0.02898404374718666, 0.04149988293647766, 0.0048944479785859585, 0.05099331960082054, -0.00861190352588892, 0.023307356983423233, -0.02043995074927807, 0.01722380705177784, -0.03816749155521393, 0.010442780330777168, -0.00737194437533617, -0.016807258129119873, -0.030630864202976227, 0.0019689195323735476, 0.03940745070576668, 0.01925811544060707, 0.04343731701374054, -0.035125717520713806, -0.07788493484258652, -0.01573198102414608, -0.026523500680923462, 0.03551320359110832, -0.0022728547919541597, -0.02226114086806774, -0.056844376027584076, 0.03303328529000282, -0.06412913650274277, 0.024896053597331047, 0.039794936776161194, -0.06405163556337357, -0.054829441010951996, -0.05823932960629463, -0.051032066345214844, 0.019771534949541092, 0.010423406027257442, -0.02049807459115982, -0.023346105590462685, -0.009449844248592854, 0.011111196130514145, 0.01285488810390234, -0.009939047507941723, -0.062036704272031784, 0.053047001361846924, 0.036326926201581955, 0.0037755786906927824, 0.04572349041700363, -0.012680519372224808, 0.0449485182762146, 0.00462562870234251, 0.047040946781635284, 0.0005225022905506194, 0.0324908047914505, 0.07327383011579514, 0.05339574068784714, -0.010723709128797054, 0.013562052510678768, 0.03772187978029251, 0.015877289697527885, 0.012699893675744534, -0.013164877891540527, -0.019916843622922897, 0.010810893028974533, -0.011789298616349697, 0.0019277489045634866, 0.0750562772154808, -0.021176176145672798, -0.013387683779001236, -0.023617345839738846, -0.014065786264836788, 0.004189705476164818, 0.00911563728004694, -0.0034801196306943893, 0.04642096906900406, 0.05076082423329353, -0.06347040832042694, 0.05045083537697792, -0.01474388875067234, 0.03022400289773941, 0.014191719703376293, 0.012913011945784092, 0.03477697819471359, -0.01798909343779087, -0.028150945901870728, 0.07083266228437424, 0.030533993616700172, 0.008330975659191608, -0.020304329693317413, -0.038109369575977325, -0.008868614211678505, -0.0030635709408670664, 0.03913620859384537, 0.04343731701374054, -0.039949931204319, 0.018531575798988342, -0.02173803374171257, 0.05947928875684738, -0.010035919025540352, 0.04076365381479263, -0.029313407838344574, 0.07831116765737534, 0.0449872650206089, 0.010510590858757496, -0.03022400289773941, -0.0018284553661942482, 0.013077693991363049, -0.028596557676792145, 0.06184295937418938, 0.007144295610487461, -0.004385870881378651, -0.018105341121554375, 0.005565285217016935, 0.041073646396398544, -0.035086967051029205, -0.017611294984817505, -0.0004331986128818244, 0.015208872966468334, -0.06141672283411026, -0.03318827971816063, 0.013842981308698654, 0.0009130167891271412, -0.014317653141915798, -0.008156605996191502, 0.00007893538713688031, 0.05021834373474121, 0.059789277613162994, -0.02973964437842369, -0.022048022598028183, 0.03867122530937195, 0.010820580646395683, -0.0548681914806366, -0.04018242657184601, 0.006781026255339384, 0.057038117200136185, 0.05048958584666252, 0.007536626420915127, -0.03154145926237106, -0.002608273411169648, -0.04816466197371483, 0.0249348022043705, -0.062307946383953094, 0.01424015499651432, 0.038089994341135025, -0.036094434559345245, 0.01970372535288334, 0.011275878176093102, -0.0018405643058940768, -0.046575963497161865, -0.025516033172607422, 0.01946154609322548, -0.07091016322374344, 0.022687377408146858, 0.021796155720949173, -0.0074688163585960865, -0.029662147164344788, 0.011111196130514145, -0.05467444658279419, -0.03514508903026581, -0.016536017879843712, -0.03297516331076622, -0.03349826857447624, 0.00487749557942152, 0.03140584006905556, -0.013639549724757671, 0.01459858100861311, 0.04370855912566185, 0.011692427098751068, 0.036559417843818665, 0.0012411699863150716, -0.05165204778313637, 0.01098526269197464, -0.026562249287962914, 0.05587565898895264, -0.04273984208703041, 0.06471036374568939, 0.009958421811461449, -0.05971178039908409, 0.02148616686463356, -0.028286566957831383, -0.048319656401872635, 0.0056815315037965775, 0.03646254912018776, -0.06327666342258453, -0.011924918740987778, -0.0072169494815170765, -0.05870431289076805, 0.045607246458530426, 0.03886496648192406, -0.04490976780653, -0.031328342854976654, 0.03456386178731918, -0.05789059028029442, -0.008762055076658726, 0.009900298900902271, 0.008292226120829582, -0.005221390165388584, -0.01719474606215954, 0.06378039717674255, -0.026058515533804893, -0.01644883304834366, -0.035823192447423935, 0.02045932598412037, 0.0021759828086942434, 0.04692470282316208, 0.028674054890871048, -0.01371704787015915, 0.03520321473479271, 0.02617476135492325, 0.02200927399098873, -0.02394670993089676, -0.020653069019317627, -0.024314822629094124, -0.02900341898202896, 0.00549263134598732, 0.027337223291397095, -0.010665585286915302, -0.050295840948820114, 0.02570977620780468, 0.0211955513805151, -0.04425103962421417, -0.015179811976850033, 0.026097264140844345, 0.035610076040029526, -0.01969403773546219, -0.011159632354974747, -0.014617955312132835, 0.003322702832520008, -0.06622156500816345, 0.005129361990839243, -0.024586064741015434, 0.02898404374718666, 0.017901910468935966, -0.00838425476104021, 0.014046411961317062, 0.0048193722032010555, 0.02799595147371292, 0.018686572089791298, -0.109891377389431, 0.009275475516915321, -0.013155191205441952, 0.02344297617673874, 0.013523303903639317, -0.02725972607731819, 0.04479352384805679, -0.014918258413672447, -0.004664377309381962, -0.04824215918779373, -0.024082330986857414, -0.022668002173304558, 0.024760432541370392, -0.0034365272149443626, -0.07377756386995316, 0.053589481860399246, -0.010539652779698372, -0.0020972746424376965, -0.0026300696190446615, -0.02797657810151577, -0.022687377408146858, -0.03892309218645096, -0.0055410671047866344, 0.013707360252737999, -0.021156802773475647, 0.03518383949995041, -0.02071119099855423, -0.014230468310415745, -0.01575135625898838, 0.03894246742129326, -0.01971341297030449, -0.0774974450469017, 0.03438949212431908, -0.026794740930199623, -0.009425627067685127, -0.01825064793229103, -0.016894442960619926, 0.041344884783029556, -0.024818556383252144, 0.005700905807316303, -0.05172954499721527, 0.0075656878761947155, 0.02301674149930477, 0.04696344956755638, -0.03096022829413414, 0.05172954499721527, 0.024605438113212585, 0.022319264709949493, -0.020614320412278175, 0.011111196130514145, 0.06083549186587334, 0.014782637357711792, -0.01246740110218525, -0.045103512704372406, -0.008839552290737629, 0.05273701250553131, -0.010045606642961502, -0.004584458190947771, -0.05064458027482033, 0.010423406027257442, -0.014937632717192173, 0.03369201347231865, -0.023811088874936104, 0.0060060517862439156, -0.019800597801804543, 0.006228857208043337, -0.04169362410902977, 0.022125519812107086, 0.02725972607731819, 0.003211300354450941, -0.022435510531067848, 0.038535602390766144, -0.034835100173950195, -0.007812711410224438, 0.02747284434735775, -0.02600039169192314, -0.033575765788555145, 0.034990094602108, 0.009919673204421997, 0.03677253797650337, 0.03452511131763458, 0.006674467585980892, -0.021428043022751808, -0.012544898316264153, 0.022048022598028183, 0.0398724339902401, 0.03320765495300293, -0.0024266387335956097, 0.012234908528625965, 0.013658924959599972, -0.03541633114218712, 0.018027842044830322, 0.02973964437842369, -0.01728193089365959, -0.025070423260331154, 0.014705140143632889, -0.01346518099308014, 0.03640442341566086, -0.0021142270416021347, 0.07474628835916519, 0.04626597464084625, 0.010907765477895737, 0.04521976038813591, 0.024527940899133682, 0.023539848625659943, -0.06168796494603157, 0.018124714493751526, -0.001204237574711442, -0.02448919229209423, 0.042042363435029984, 0.0030127130448818207, -0.06885647773742676, 0.01703006401658058, -0.04692470282316208, -0.018667196854948997, -0.010936826467514038, 0.004109786357730627, 0.03216144070029259, 0.0450260154902935, -0.014307965524494648, -0.03911683335900307, -0.00606417516246438, 0.02995276264846325, 0.012535211630165577, -0.03615255653858185, -0.030282126739621162, 0.00887830089777708, 0.029139038175344467, -0.002280120039358735, 0.02818969450891018, -0.0001266901526832953, -0.033110782504081726, 0.027337223291397095, -0.0015584251377731562, -0.014278903603553772, -0.022609880194067955, -0.0349125973880291, -0.016671637073159218, -0.04564599320292473, 0.01010372955352068, -0.04227485507726669, -0.031347714364528656, 0.013455493375658989, 0.000923309416975826, 0.03347889706492424, 0.01993621699512005, -0.04603348299860954, -0.013126129284501076, 0.0449872650206089, 0.04215861111879349, 0.013145503588020802, -0.0002692733542062342, -0.022144895046949387, 0.03446698933839798, 0.0019362252205610275, 0.006073862314224243, 0.037799376994371414, 0.019141867756843567, -0.017407862469553947, -0.033595141023397446, -0.001679514884017408, 0.014046411961317062, -0.012893637642264366, 0.021815530955791473, 0.009028452448546886, 0.028364064171910286, 0.01558667328208685, -0.002297072671353817, -0.013881729915738106, 0.007367100566625595, 0.00024702309747226536, 0.040066178888082504, 0.017553171142935753, -0.004431885201483965, 0.006785870064049959, -0.024101704359054565, -0.032064568251371384, -0.03169645369052887, -0.013145503588020802, 0.07350632548332214, -0.05262076482176781, 0.0249541774392128, 0.026232885196805, 0.02071119099855423, 0.002508979756385088, -0.003954791463911533, -0.019354986026883125, 0.0599055252969265, 0.03719877451658249, -0.05889805778861046, 0.005943085066974163, 0.022086771205067635, 0.03592006489634514, 0.05719311535358429, -0.013581426814198494, 0.044057298451662064, -0.010898077860474586, 0.0033251247368752956, 0.001669827732257545, 0.03406012803316116, -0.004511804319918156, 0.006848836783319712, 0.04564599320292473, 0.006330572534352541, -0.003899090224877, 0.029875265434384346, 0.013804231770336628, -0.006538846995681524, -0.0374506413936615, 0.03375013545155525, -0.0037852658424526453, 0.014947319403290749, 0.008054890669882298, -0.006059331353753805, -0.022900493815541267, 0.03303328529000282, 0.024043582379817963, -0.00630635442212224, 0.013784857466816902, -0.024353571236133575, 0.017843786627054214, 0.0036133183166384697, 0.020110586658120155, -0.008364880457520485, 0.025419160723686218, -0.026639746502041817, 0.04394105076789856, -0.009779208339750767, 0.028906546533107758, 0.03549382835626602, 0.009827644564211369, 0.029875265434384346, -0.006829462479799986, 0.003848232561722398, 0.03200644254684448, -0.043088577687740326, -0.010355595499277115, 0.004029867239296436, -0.044328536838293076, 0.0037319862749427557, -0.020575571805238724, 0.016594139859080315, -0.000847022864036262, 0.0036496452521532774, 0.005105144344270229, 0.024527940899133682, -0.011053073219954967, 0.03543570637702942, 0.039349328726530075, -0.011295252479612827, 0.054829441010951996, 0.014685765840113163, -0.07013518363237381, -0.023520473390817642, 0.006073862314224243, -0.013775170780718327, -0.02518666908144951, 0.012680519372224808, 0.0019967700354754925, 0.0054054465144872665, -0.03952369466423988, -0.006098079960793257, -0.0044197761453688145, 0.0005639755399897695, -0.02772471122443676, -0.0033832478802651167, -0.013310185633599758, 0.016603827476501465, 0.02849968522787094, -0.023326730355620384, 0.006311198230832815, 0.009643588215112686, 0.007730369921773672, 0.0006926333880983293, 0.012283344753086567, 0.046808455139398575, 0.007933801040053368, 0.001881734817288816, -0.0549069382250309, 0.058084335178136826, -0.008471439592540264, -0.02022683247923851, -0.020808063447475433, 0.00025731572532095015, 0.011421185918152332, 0.0925319492816925, -0.02650412544608116, 0.0004940461949445307, 0.010588088072836399, -0.020091213285923004, 0.015044190920889378, 0.0011497472878545523, 0.03355639427900314, -0.019296864047646523, -0.006839149631559849, 0.05436445772647858, 0.015431678853929043, 0.026136012747883797, 0.014230468310415745, -0.007643185555934906, 0.04967586323618889, 0.01724318042397499, -0.013523303903639317, 0.020769314840435982, -0.05444195494055748, -0.03448636084794998, 0.061804212629795074, -0.03466073051095009, -0.04390230029821396, -0.004376183729618788, -0.014443586580455303, 0.026639746502041817, -0.06168796494603157, 0.020808063447475433, 0.021137427538633347, 0.0450260154902935, -0.019364673644304276, 0.005235921125859022, 0.04068615660071373, -0.015315432101488113, 0.007807867601513863, -0.00897517241537571, -0.024043582379817963, 0.005754185374826193, 0.018328145146369934, 0.007284759543836117, 0.00499858520925045, 0.0024096861016005278, 0.007241167593747377, -0.015276683494448662, -0.012544898316264153, 0.07803992927074432, 0.011924918740987778, 0.04401854798197746, -0.02073056623339653, -0.024837931618094444, -0.011324314400553703, 0.04653721675276756, 0.005013115704059601, -0.003715033642947674, 0.0054199774749577045, 0.01571260765194893, 0.05835557356476784, -0.0063790082931518555, 0.04091865196824074, 0.03148333728313446, 0.00499858520925045, -0.04068615660071373, 0.0015669014537706971, 0.03667566552758217, -0.0018998982850462198, 0.03714064881205559, -0.01950998231768608, 0.04549099877476692, -0.025070423260331154, -0.007376788184046745, -0.017650043591856956, -0.026232885196805, -0.018037529662251472, -0.057813093066215515, 0.02173803374171257, 0.004242985043674707, -0.03398263081908226, -0.008098483085632324, 0.06769401580095291, -0.0005100906128063798, 0.004255094099789858, -0.020362453535199165, -0.01651664264500141, -0.0028698272071778774, -0.00025898072635754943, -0.02499292604625225, -0.023074863478541374, 0.0008585263858549297, 0.05145830288529396, 0.01602259650826454, -0.03617193177342415, -0.010297472588717937, 0.0056573133915662766, -0.03280079364776611, 0.019325925037264824, -0.00998748280107975, -0.008437533862888813, 0.02944902889430523, 0.04514225944876671, -0.01285488810390234, 0.02698848396539688, -0.05277575924992561, 0.024024207144975662, -0.001034106477163732, 0.02197052538394928, -0.027124105021357536, -0.002806860487908125, 0.015925724059343338, 0.018085965886712074, -0.006127141881734133, 0.010219975374639034, 0.005729967262595892, 0.01533480640500784, 0.046808455139398575, 0.0016734604723751545, -0.00517295440658927, -0.05370572954416275, 0.01271926797926426, 0.019287176430225372, -0.020091213285923004, -0.024372946470975876, -0.004005649127066135, 0.022454883903265, 0.02543853595852852, 0.018870627507567406, 0.031618956476449966, -0.0018744694534689188, -0.03355639427900314, -0.005148736294358969, -0.028422188013792038, 0.023036114871501923, 0.045374754816293716, 0.010190913453698158, -0.012418965809047222, 0.0450260154902935, -0.01123712956905365, -0.03268454596400261, -0.018124714493751526, -0.029797766357660294, -0.01172148808836937, 0.00423814170062542, 0.019616540521383286, 0.041344884783029556, -0.021854279562830925, 0.00655822129920125, 0.02567102760076523, 0.0042938427068293095, 0.07509502023458481, 0.035086967051029205, 0.006785870064049959, -0.010898077860474586, 0.07590874284505844, 0.055604416877031326, -0.030069008469581604, -0.004422198049724102, -0.020924309268593788, -0.048319656401872635, 0.022900493815541267, 0.011450246907770634, 0.04126738756895065, -0.03402137756347656, 0.003296063281595707, 0.0068536801263689995, -0.03047586977481842, -0.06040925905108452, 0.029080916196107864, -0.002983651589602232, 0.009692024439573288, 0.018027842044830322, -0.01138243731111288, 0.032083943486213684, -0.06381914764642715, -0.019287176430225372, -0.008737836964428425, -0.001898687332868576, 0.007933801040053368, -0.002838343847543001, 0.05575941130518913, -0.02272612601518631, 0.04897838458418846, 0.036307550966739655, -0.00007004285725997761, -0.030088381841778755, 0.00013039853365626186, -0.033323902636766434, -0.012980821542441845, 0.0037997965700924397, -0.02198990061879158, -0.033343274146318436, 0.015615735203027725, -0.0007640763651579618, -0.048590898513793945, 0.02598101831972599, -0.028112197294831276, 0.02425670064985752, 0.0016068610129877925, -0.0499083548784256, -0.05696061998605728, -0.04339857026934624, -0.008452065289020538, 0.010810893028974533, 0.0043447003699839115, -0.0032597363460808992, 0.040337421000003815, -0.003736829850822687, -0.024818556383252144, -0.008829864673316479, 0.005216546822339296, 0.01271926797926426, 0.009377190843224525, -0.007095859851688147, -0.036346301436424255, -0.029371531680226326, 0.05975053086876869, 0.01577072963118553, 0.011818360537290573, -0.018676884472370148, -0.015073252841830254, 0.010307160206139088, -0.03024337813258171, 0.01197335496544838, 0.013920478522777557, 0.02474105916917324, 0.031560834497213364, -0.016671637073159218, -0.04564599320292473, 0.027317849919199944, 0.019277488812804222, 0.010859329253435135, 0.0275115929543972, -0.013920478522777557, 0.01799878105521202, 0.0029400591738522053, -0.017185058444738388, -0.006718059536069632, -0.01944217085838318, -0.05444195494055748, 0.001178808743134141, 0.04549099877476692, 0.008631277829408646, -0.009948734194040298, 0.027840957045555115, 0.04374730587005615, -0.020362453535199165, -0.014123909175395966, -0.020149335265159607, -0.03704378008842468, 0.018134402111172676, -0.01424015499651432, -0.022648628801107407, 0.02826719358563423, -0.02443106845021248, -0.0031967696268111467, -0.016342272982001305, 0.023869212716817856, -0.01827002316713333, 0.001516043790616095, -0.06835274398326874, 0.01097557507455349, -0.03595881536602974, 0.023869212716817856, -0.016071032732725143, -0.047505933791399, -0.04196486622095108, 0.01212835032492876, -0.02801532670855522, 0.005604033824056387, 0.003237940138205886, 0.024314822629094124, -0.007662559859454632, 0.006475880276411772, -0.016400396823883057, -0.031580209732055664, -0.008020985871553421, -0.0018175572622567415, 0.018531575798988342, -0.023346105590462685, 0.03597818687558174, -0.02497355081140995, -0.029294034466147423, 0.015363868325948715, -0.0026034298352897167, -0.01974247395992279, -0.03140584006905556, -0.0060157389380037785, -0.005153580103069544, -0.02276487462222576, 0.022881120443344116, -0.06463287025690079, -0.03671441227197647, 0.011944293975830078, 0.007163669914007187, 0.006286980118602514, 0.01335862185806036, -0.0162163395434618, -0.03576507046818733, -0.05110956355929375, -0.04025992378592491, 0.02625225856900215, 0.022319264709949493, 0.01510231476277113, 0.023074863478541374, 0.021815530955791473, -0.013930165208876133, -0.019364673644304276, -0.01013279054313898, -0.020381826907396317, 0.0029981823172420263, -0.017901910468935966, 0.007672247011214495, 0.006718059536069632, -0.00725085474550724, 0.006945708300918341, -0.008926737122237682, -0.02671724371612072, 0.03099897690117359, -0.02848030999302864, 0.01325206272304058, -0.09508936107158661 ]
The Streaming Engine (SE) is a Coarse-Grained Reconfigurable Array which provides programming flexibility and high-performance with energy efficiency. An application program to be executed on the SE is represented as a combination of Synchronous Data Flow (SDF) graphs, where every instruction is represented as a node. Each node needs to be mapped to the right slot and array in the SE to ensure the correct execution of the program. This creates an optimization problem with a vast and sparse search space for which finding a mapping manually is impractical because it requires expertise and knowledge of the SE micro-architecture. In this work we propose a Reinforcement Learning framework with Global Graph Attention (GGA) module and output masking of invalid placements to find and optimize instruction schedules. We use Proximal Policy Optimization in order to train a model which places operations into the SE tiles based on a reward function that models the SE device and its constraints. The GGA module consists of a graph neural network and an attention module. The graph neural network creates embeddings of the SDFs and the attention block is used to model sequential operation placement. We show results on how certain workloads are mapped to the SE and the factors affecting mapping quality. We find that the addition of GGA, on average, finds 10% better instruction schedules in terms of total clock cycles taken and masking improves reward obtained by 20%.
[ 0.010397092439234257, -0.006630231160670519, -0.03760374337434769, -0.018737005069851875, 0.005041014403104782, 0.04781550541520119, -0.01261180266737938, 0.04889042675495148, -0.07643067091703415, 0.029764223843812943, 0.014770912937819958, 0.002012004144489765, 0.03085768036544323, -0.025427469983696938, 0.02842983789741993, 0.02889316715300083, 0.01996019296348095, 0.0028772701043635607, -0.0389566607773304, -0.05730447173118591, 0.03096887841820717, -0.060492172837257385, -0.01843120902776718, -0.01709682308137417, -0.011379348114132881, 0.02305522747337818, -0.01595703512430191, 0.0428486205637455, -0.08636444061994553, 0.026706255972385406, 0.022258302196860313, 0.05189279466867447, -0.00800168327987194, -0.01895013637840748, -0.027892377227544785, -0.02590933069586754, 0.02403748407959938, 0.017865948379039764, -0.008900540880858898, 0.0009544567437842488, -0.02305522747337818, 0.013325328007340431, -0.04892749339342117, -0.0024718577042222023, 0.012296739034354687, 0.013751590624451637, 0.02804064191877842, -0.02694718725979328, -0.04751897230744362, -0.001743273576721549, -0.005722107365727425, -0.022239768877625465, 0.0015046594198793173, -0.018190277740359306, -0.04158836975693703, -0.00695919431746006, 0.032859258353710175, 0.03980918601155281, 0.024890007451176643, 0.010258093476295471, 0.005328278057277203, -0.027818243950605392, -0.08866254985332489, 0.01066582277417183, 0.027873843908309937, -0.09585340321063995, 0.002197335474193096, 0.0007262674625962973, 0.04644405096769333, 0.02081271819770336, -0.06582971662282944, -0.08347326517105103, -0.03825240209698677, 0.0019610379822552204, 0.01757868379354477, 0.03862306475639343, 0.028541037812829018, 0.004674984607845545, -0.00047462215297855437, -0.009766965173184872, 0.032173532992601395, 0.03873426467180252, -0.04295982047915459, 0.04314515367150307, 0.10845594108104706, -0.0622713528573513, 0.009428735822439194, -0.07476268708705902, -0.0035166635643690825, -0.0017143154982477427, -0.046184588223695755, -0.016837358474731445, 0.015299107879400253, -0.00800168327987194, 0.02559426799416542, 0.026910120621323586, 0.008154582232236862, -0.04221849516034126, -0.03378591686487198, 0.04948348551988602, -0.04080997779965401, -0.014131519943475723, -0.021850572898983955, -0.038993727415800095, 0.0018961719470098615, -0.014298317953944206, -0.04203316196799278, -0.0002723502984736115, 0.0017814981983974576, 0.11505373567342758, -0.008923707529902458, -0.030116353183984756, 0.011499813757836819, 0.0011339965276420116, -0.05211519077420235, -0.03634348884224892, -0.014437316916882992, -0.015465905889868736, -0.003966092132031918, -0.016309164464473724, 0.018662873655557632, 0.04358994588255882, -0.014465116895735264, -0.0162998978048563, -0.02881903387606144, 0.0632350742816925, -0.0030440683476626873, -0.014001787640154362, 0.019015002995729446, 0.005898172035813332, -0.03563923016190529, -0.03491643816232681, -0.025038274005055428, -0.0486680269241333, -0.006162269506603479, 0.04514672979712486, -0.0257981326431036, 0.024871475994586945, -0.0028680036775767803, -0.03717748075723648, 0.026354126632213593, -0.007672720588743687, -0.017689883708953857, -0.04403474181890488, 0.06460653245449066, -0.004392354283481836, -0.02318495884537697, 0.09511207789182663, -0.023129360750317574, 0.05945431813597679, -0.06119643151760101, 0.05826819688081741, -0.016309164464473724, 0.013603325933218002, 0.002976885763928294, 0.030709413811564445, -0.016652027145028114, 0.007079659961163998, -0.0037645441479980946, 0.021257512271404266, 0.011129151098430157, -0.05341251194477081, -0.025075340643525124, 0.02296256087720394, -0.019237400963902473, 0.03447164222598076, 0.0170319564640522, 0.01641109585762024, -0.07657893747091293, 0.03854893147945404, 0.006852628663182259, 0.007723686285316944, 0.009692832827568054, -0.009952296502888203, 0.003162217093631625, -0.04826029762625694, 0.04981708154082298, -0.03074648045003414, -0.058453526347875595, 0.030134886503219604, -0.08265780657529831, 0.023333225399255753, 0.025927864015102386, 0.04922402277588844, 0.00589353870600462, 0.04889042675495148, 0.041217707097530365, -0.01916326768696308, 0.02666918933391571, -0.001096351072192192, 0.03584309294819832, 0.0398833192884922, 0.06690464168787003, -0.04095824062824249, -0.005411677062511444, -0.059713780879974365, -0.05589595437049866, 0.008937607519328594, 0.03282219171524048, 0.006514398846775293, -0.06542199105024338, -0.0167817585170269, 0.017689883708953857, -0.020775651559233665, -0.0141222532838583, 0.012704468332231045, 0.036843884736299515, -0.018282944336533546, -0.012065074406564236, -0.026150261983275414, -0.004049491137266159, 0.02211003750562668, -0.04937228932976723, -0.025242138653993607, 0.05100320279598236, -0.0102302934974432, 0.019052069634199142, 0.01541957352310419, -0.006046437192708254, -0.03449017554521561, 0.01541957352310419, 0.03056114912033081, 0.04147716984152794, -0.006393933668732643, -0.03943852335214615, 0.01508597657084465, -0.006004737690091133, -0.004283472429960966, 0.017152421176433563, 0.0006776179652661085, -0.05960258096456528, 0.06023270636796951, 0.011518347077071667, 0.011110617779195309, 0.004366871435195208, -0.030320217832922935, 0.028985831886529922, -0.00035560462856665254, 0.02570546604692936, -0.008316746912896633, -0.04447953775525093, -0.0038525767158716917, -0.05704500898718834, 0.024760276079177856, 0.02980129048228264, 0.008469645865261555, -0.010980886407196522, 0.09355529397726059, 0.048816293478012085, -0.017736215144395828, -0.07116726040840149, -0.03106154501438141, -0.025631334632635117, -0.002974569099023938, -0.06319800764322281, 0.047259509563446045, 0.037622276693582535, -0.03365618363022804, 0.050076548010110855, -0.006366134155541658, -0.0039058595430105925, 0.017013423144817352, 0.026150261983275414, 0.015567838214337826, -0.037714943289756775, -0.009470434859395027, 0.026224395260214806, 0.0021069864742457867, -0.0024695410393178463, 0.01957099698483944, 0.004753750748932362, -0.08021143078804016, -0.021869106218218803, -0.012834199704229832, -0.006398566998541355, -0.042107295244932175, -0.025242138653993607, 0.017430419102311134, 0.03447164222598076, 0.012519137002527714, -0.01753235049545765, 0.004234822932630777, 0.011286682449281216, 0.04496140033006668, -0.05856472626328468, 0.008752276189625263, -0.022758696228265762, -0.04447953775525093, -0.06338334083557129, -0.003208549926057458, -0.026446791365742683, 0.004392354283481836, 0.031098609790205956, 0.06275321543216705, 0.0651625245809555, 0.004014741629362106, -0.01751381903886795, -0.01066582277417183, 0.034323375672101974, -0.004586952272802591, -0.004403937608003616, 0.03828946873545647, 0.03376738354563713, 0.005810139700770378, -0.06953634321689606, -0.014289051294326782, -0.043552882969379425, 0.03180287033319473, -0.01455778256058693, -0.02705838531255722, 0.060010310262441635, 0.03378591686487198, 0.03617669269442558, -0.015178642235696316, -0.0009810981573536992, 0.04218142852187157, 0.0189964696764946, 0.015354706905782223, -0.02950476109981537, -0.04147716984152794, 0.030931811779737473, -0.03019048646092415, -0.07872878015041351, 0.03137660771608353, -0.01751381903886795, 0.011082818731665611, 0.04232969507575035, 0.0023050594609230757, -0.04788963496685028, 0.008659610524773598, -0.010767755098640919, 0.038993727415800095, -0.04329341650009155, -0.04006865248084068, 0.02327762544155121, -0.004471120424568653, -0.05367197468876839, 0.06149296090006828, -0.019886059686541557, -0.04714830964803696, -0.011648079380393028, -0.006505132652819157, 0.011990942060947418, -0.000008642163265903946, -0.020571786910295486, -0.06075163558125496, -0.026113195344805717, 0.016355497762560844, -0.01955246366560459, -0.02296256087720394, 0.001030326820909977, -0.02785531058907509, 0.02044205367565155, 0.0028842200990766287, 0.04555445909500122, -0.030876213684678078, -0.06660810858011246, 0.004994681570678949, -0.004781550262123346, -0.006505132652819157, 0.05011361464858055, -0.053004782646894455, -0.03710334748029709, 0.0418478325009346, -0.04559152573347092, 0.04455367103219032, -0.03847480192780495, -0.008261147886514664, 0.007176958955824375, 0.04058757796883583, -0.03484230488538742, 0.038104139268398285, 0.033248454332351685, -0.004262622445821762, 0.03862306475639343, 0.02201737090945244, -0.019404198974370956, -0.0008727951208129525, -0.04685178026556969, 0.0496317520737648, 0.0015289841685444117, 0.08043383061885834, -0.028151841834187508, 0.00004922865628032014, 0.003674195148050785, 0.05900952219963074, 0.026706255972385406, -0.05263411998748779, -0.052226390689611435, 0.01391838863492012, 0.01726362109184265, -0.05322718247771263, -0.05826819688081741, -0.023240558803081512, 0.01854240708053112, -0.013723790645599365, -0.008061916567385197, -0.04822323098778725, 0.06219721958041191, -0.02279576286673546, -0.02707691863179207, -0.04333048313856125, 0.024945607408881187, 0.06497719138860703, -0.03183993697166443, -0.02316642552614212, -0.03814120590686798, -0.06449533253908157, 0.028263039886951447, -0.014650448225438595, 0.0350276380777359, -0.05055840685963631, -0.002826303942129016, 0.004369188100099564, 0.018468275666236877, 0.04110650718212128, -0.049409352242946625, -0.008446479216217995, -0.027669979259371758, -0.027484647929668427, -0.03487937152385712, 0.04559152573347092, -0.0006660347571596503, 0.021832039579749107, 0.021924706175923347, 0.007668087258934975, 0.07872878015041351, 0.01968219503760338, -0.01074922177940607, -0.05889832228422165, 0.027892377227544785, 0.013797923922538757, -0.0014409517170861363, -0.03680681809782982, -0.03486083820462227, 0.03386005014181137, -0.01890380308032036, 0.03417511284351349, -0.03706628084182739, -0.019904593005776405, -0.051447998732328415, -0.04759310558438301, -0.021869106218218803, -0.05137386545538902, -0.015058176591992378, -0.011184750124812126, -0.018709205090999603, -0.03866013139486313, -0.012945398688316345, -0.0335635170340538, -0.05437623709440231, 0.006926761474460363, -0.05307891592383385, 0.003681145142763853, 0.06104816496372223, 0.02042352221906185, 0.008863474242389202, -0.019719261676073074, 0.010137627832591534, -0.016670560464262962, 0.01782888174057007, 0.03311872109770775, 0.016883691772818565, -0.08740229159593582, -0.029078498482704163, 0.024204282090067863, -0.04748190566897392, -0.066126249730587, -0.002643289277330041, -0.0037877107970416546, 0.010350759141147137, -0.008043383248150349, 0.02042352221906185, 0.02151697687804699, -0.0038340436294674873, 0.051633331924676895, 0.007834885269403458, -0.0925174430012703, -0.030005155131220818, 0.01275080069899559, 0.03224766626954079, 0.03604695945978165, 0.03137660771608353, 0.009368502534925938, -0.010739955119788647, -0.0008484703721478581, 0.04195903241634369, 0.020293788984417915, 0.01246353704482317, -0.01168514508754015, 0.00898393988609314, 0.022462166845798492, -0.058750055730342865, 0.014974777586758137, 0.004278839100152254, -0.008914440870285034, -0.0002287684619659558, -0.017106089740991592, 0.05530289188027382, 0.024556411430239677, -0.03065381571650505, 0.005708207376301289, 0.047741372138261795, 0.012370871379971504, -0.02600199729204178, 0.02676185593008995, 0.05871298909187317, 0.04796376824378967, -0.028559571132063866, 0.011750011704862118, 0.01567903719842434, 0.015410306863486767, 0.010424891486763954, 0.013686724938452244, -0.008043383248150349, 0.0535237118601799, -0.013973988592624664, -0.010823354125022888, 0.03984625265002251, 0.03137660771608353, 0.030134886503219604, -0.004698151256889105, -0.0011432631872594357, 0.03330405429005623, -0.01799567975103855, 0.04014278203248978, 0.030487017706036568, -0.04662938416004181, 0.02570546604692936, 0.002895803190767765, -0.032859258353710175, 0.013269728980958462, -0.0010187436128035188, -0.011518347077071667, -0.0014328435063362122, -0.00882640853524208, -0.010832620784640312, -0.013881322927772999, -0.02305522747337818, -0.0389566607773304, -0.00871984288096428, 0.05307891592383385, -0.03623228892683983, -0.007302057463675737, -0.01975632831454277, 0.003331332001835108, 0.03790027275681496, -0.025835199281573296, -0.03376738354563713, 0.014539249241352081, -0.032173532992601395, 0.006236401852220297, -0.011657346040010452, -0.016559360548853874, 0.000834570499137044, -0.03007928840816021, -0.04125477001070976, 0.010786288417875767, -0.02696572057902813, 0.004966881591826677, 0.03463844209909439, -0.01631843112409115, 0.027688512578606606, -0.010007896460592747, -0.015299107879400253, -0.05385730788111687, -0.004809350240975618, 0.04659231752157211, 0.0011739586479961872, -0.010054228827357292, 0.006847995799034834, 0.002513557206839323, 0.009924497455358505, 0.024871475994586945, 0.011027218773961067, 0.03465697541832924, 0.0024788076989352703, 0.00027683880762197077, 0.013705257326364517, 0.010044962167739868, -0.007663453929126263, -0.013278995640575886, 0.027762645855545998, 0.027688512578606606, 0.02707691863179207, -0.01815321110188961, -0.025464536622166634, -0.04681471362709999, -0.006898961961269379, -0.021943239495158195, -0.03925319388508797, 0.0476672388613224, -0.02307376079261303, -0.011379348114132881, -0.04036518186330795, -0.03211793303489685, 0.011258883401751518, -0.009331436827778816, 0.016855891793966293, -0.06397639960050583, 0.009572367183864117, 0.016031166538596153, -0.047556038945913315, 0.004705101251602173, -0.03534270077943802, -0.02822597324848175, 0.015512239187955856, 0.005272678565233946, 0.05771220102906227, 0.0028749534394592047, 0.017013423144817352, 0.011045752093195915, 0.04759310558438301, -0.03958678990602493, 0.012639601714909077, 0.006945294793695211, 0.025483068078756332, 0.009275836870074272, -0.011592479422688484, -0.06827609241008759, 0.04021691530942917, -0.0325997956097126, 0.053004782646894455, 0.026724789291620255, -0.025464536622166634, 0.05022481083869934, 0.020682984963059425, -0.020201124250888824, -0.014094453305006027, -0.031283941119909286, -0.008136048913002014, -0.018375609070062637, -0.06468066573143005, -0.02248070016503334, -0.007033327128738165, 0.009062705561518669, -0.00283557060174644, 0.05211519077420235, -0.0167817585170269, -0.03146927431225777, -0.02318495884537697, 0.02522360533475876, 0.01148128043860197, 0.07316884398460388, -0.003569946391507983, 0.003732111304998398, -0.017448952421545982, -0.020293788984417915, -0.015827301889657974, 0.018329275771975517, 0.05167039856314659, 0.025946397334337234, 0.0306723490357399, 0.03880839794874191, -0.005833306349813938, -0.04700004681944847, 0.045888058841228485, 0.0102302934974432, -0.051929861307144165, 0.02122044563293457, -0.013927655294537544, 0.0219061728566885, 0.008316746912896633, -0.02804064191877842, 0.011518347077071667, 0.004700467921793461, 0.005212445743381977, 0.05207812786102295, -0.015039644204080105, 0.04903868958353996, -0.04047637805342674, -0.02451934479176998, -0.027002787217497826, -0.0009753065533004701, 0.04173663258552551, -0.03828946873545647, 0.006824829149991274, 0.038697198033332825, -0.014372451230883598, 0.022517766803503036, -0.015845835208892822, -0.04518379643559456, -0.024278415367007256, -0.001032064319588244, 0.024463746696710587, -0.015252774581313133, -0.03478670492768288, -0.0017838148633018136, -0.057193271815776825, 0.0036626120563596487, -0.01838487572968006, -0.007895117625594139, 0.0008189331856556237, 0.007668087258934975, 0.034026846289634705, 0.03113567642867565, -0.011750011704862118, 0.016244297847151756, 0.04129183664917946, 0.006083503365516663, -0.052411723881959915, 0.020219657570123672, -0.0015000260900706053, -0.0010720263235270977, 0.04010571539402008, 0.010934553109109402, 0.004508186597377062, -0.004304321948438883, 0.018848204985260963, -0.005319011397659779, 0.004804716911166906, -0.016577893868088722, -0.021776441484689713, 0.06241961941123009, 0.011351549066603184, -0.0009231820586137474, 0.0026224395260214806, -0.005606275051832199, -0.04611045494675636, 0.026354126632213593, 0.02198030613362789, 0.0026710890233516693, -0.007496655452996492, -0.06475479155778885, -0.050854939967393875, 0.020089924335479736, -0.0011710628168657422, -0.012185540050268173, -0.007561521604657173, -0.011777810752391815, 0.019700728356838226, -0.03884546458721161, -0.04933522269129753, -0.0037761274725198746, 0.001217395649291575, -0.02296256087720394, 0.010304426774382591, 0.03951265662908554, 0.019404198974370956, -0.007158425636589527, 0.013445793651044369, -0.01518790889531374, 0.01938566565513611, 0.008682776242494583, 0.005152213387191296, 0.04095824062824249, 0.028578102588653564, 0.0012428787304088473, -0.018273677676916122, 0.022944029420614243, 0.04507260024547577, -0.049298156052827835, 0.05400557443499565, -0.006505132652819157, -0.057675134390592575, 0.019015002995729446, -0.00503638107329607, -0.03330405429005623, 0.018486808985471725, -0.01817174442112446, 0.003173800418153405, 0.020571786910295486, 0.014011054299771786, 0.014363184571266174, 0.034212179481983185, 0.016791025176644325, -0.0238336194306612, 0.007260357961058617, 0.0002659795281942934, -0.0030649180989712477, 0.04703711345791817, -0.008085083216428757, 0.03484230488538742, -0.039772119373083115, 0.015252774581313133, 0.012723001651465893, -0.030635282397270203, 0.013760857284069061, -0.009021006524562836, -0.04370114579796791, -0.0017699149902909994, 0.04358994588255882, -0.007607854437083006, 0.03224766626954079, -0.009776231832802296, -0.020479120314121246, 0.014928445219993591, -0.02483440935611725, -0.02103511430323124, -0.015947768464684486, 0.0028587370179593563, 0.013612591661512852, -0.020664451643824577, 0.002437107963487506, 0.05763806775212288, -0.007505922112613916, -0.022999627515673637, 0.030301686376333237, -0.01634623110294342, -0.01938566565513611, 0.03719601407647133, 0.009261936880648136, -0.03200673311948776, 0.04837149754166603, -0.013872056268155575, -0.0447760671377182, -0.013556992635130882, 0.00835381355136633, -0.022147104144096375, -0.00882640853524208, 0.04244089126586914, 0.01782888174057007, 0.010146894492208958, 0.013334594666957855, 0.018496073782444, -0.021869106218218803, 0.027206651866436005, -0.002640972612425685, -0.005754540208727121, -0.05092907324433327, -0.00888200756162405, -0.005439477041363716, -0.010777021758258343, 0.012500603683292866, -0.018273677676916122, -0.01918180100619793, -0.012037275359034538, 0.030097821727395058, 0.07038886845111847, 0.004086557775735855, 0.004855683073401451, 0.01785668171942234, -0.0398833192884922, 0.025631334632635117, -0.04207022860646248, 0.043849412351846695, -0.02227683551609516, -0.004776916932314634, -0.0010702889412641525, 0.04040224850177765, -0.011546147055923939, 0.027818243950605392, -0.007728319615125656, -0.03404537960886955, -0.035583630204200745, 0.015947768464684486, -0.026242926716804504, -0.032859258353710175, 0.00822871457785368, -0.027873843908309937, 0.03195113688707352, 0.048519764095544815, 0.05600715056061745, -0.012343072332441807, -0.04236676171422005, -0.0027405882719904184, 0.00026192539371550083, 0.004767650738358498, -0.038919597864151, -0.028985831886529922, 0.033637650310993195, 0.012584002688527107, 0.019496863707900047, -0.005592375062406063, 0.00017273466801270843, 0.016077499836683273, -0.009998629800975323, -0.026595057919621468, -0.0214057769626379, -0.027391983196139336, -0.013584792613983154, 0.0233702901750803, -0.05003948137164116, 0.017986413091421127, 0.006217868998646736, 0.02211003750562668, -0.00403559161350131, -0.023036694154143333, -0.02229536883533001, -0.036936551332473755, 0.01139788143336773, -0.011268150061368942, 0.05667434632778168, -0.013547725975513458, 0.09422248601913452, 0.029615959152579308, -0.03154340758919716, -0.05107733607292175, -0.006027903873473406, -0.017801081761717796, -0.014465116895735264, 0.009034906513988972, -0.005875005852431059, -0.0020432788878679276, 0.04114357382059097, 0.0010123727843165398, -0.009776231832802296, 0.012908332981169224, -0.005277311895042658, 0.01916326768696308, -0.006208602339029312, -0.030690882354974747, -0.01693929173052311, -0.032655395567417145, 0.03678828477859497, -0.029523294419050217, 0.01721728779375553, 0.0005058968090452254, -0.0013807190116494894, -0.03534270077943802, -0.020182590931653976, -0.007510555442422628, 0.06223428621888161, -0.01840340904891491, -0.024296948686242104, -0.032951924949884415, 0.0008913282654248178, -0.0020270622335374355, 0.009113672189414501, -0.012296739034354687, -0.01964513026177883, 0.03195113688707352, -0.030097821727395058, 0.015428840182721615, 0.004332121927291155, 0.019126201048493385, -0.021776441484689713, 0.03814120590686798, -0.00220660213381052, -0.050966136157512665, -0.029356494545936584, 0.02394481748342514, 0.0172821544110775, 0.002761438023298979, 0.02957889251410961, -0.006885061971843243, -0.05585888773202896, -0.0016506079118698835, -0.00011040249955840409, 0.034508708864450455, -0.023110827431082726, 0.03925319388508797, 0.015827301889657974, 0.01851460710167885, 0.017504552379250526, -0.009822565130889416, 0.030505549162626266, 0.0033869314938783646, -0.00869667623192072, 0.05489516258239746, -0.03254419565200806, -0.024371080100536346, -0.028559571132063866, -0.004167640116065741, 0.002368767047300935, -0.047556038945913315, -0.03172873705625534, -0.04162543639540672, 0.005448743235319853, 0.04877922683954239, -0.020682984963059425, -0.01977486163377762, -0.006662664003670216, -0.009943029843270779, 0.02073858492076397, 0.01474311389029026, -0.05400557443499565, -0.016772491857409477, 0.011777810752391815, -0.004841783083975315, 0.025742532685399055, -0.05897245556116104, 0.0030070021748542786, 0.025093872100114822, -0.019237400963902473, 0.013936921954154968, -0.02716958522796631, 0.008474278263747692, -0.011518347077071667, -0.010452691465616226, 0.023611221462488174, -0.03280365839600563, 0.03682535141706467, 0.008363080210983753, 0.013853522948920727, -0.04422007501125336, -0.0021035114768892527, -0.011073552072048187, -0.0374925434589386, -0.02170230820775032, -0.01581803523004055, 0.02891170047223568, 0.033341120928525925, -0.01872773841023445, -0.007959984242916107, -0.022462166845798492, -0.006894328631460667, -0.029949555173516273, 0.0025529402773827314, 0.0003194070886820555, 0.03741841018199921, -0.05278238654136658, -0.03322992101311684, 0.041996099054813385, -0.003790027229115367, 0.018486808985471725, 0.03715894743800163, 0.005031747743487358, 0.007478122599422932, 0.05215225741267204, 0.014075920917093754, -0.013455060310661793, -0.015567838214337826, 0.028263039886951447, -0.006727530155330896, 0.017476752400398254, -0.020905382931232452, 0.004186173435300589, 0.003227083245292306, -0.014780179597437382, 0.03417511284351349, -0.0564890131354332, 0.03171020373702049, -0.018032746389508247 ]
We present a machine sound dataset to benchmark domain generalization techniques for anomalous sound detection (ASD). Domain shifts are differences in data distributions that can degrade the detection performance, and handling them is a major issue for the application of ASD systems. While currently available datasets for ASD tasks assume that occurrences of domain shifts are known, in practice, they can be difficult to detect. To handle such domain shifts, domain generalization techniques that perform well regardless of the domains should be investigated. In this paper, we present the first ASD dataset for the domain generalization techniques, called MIMII DG. The dataset consists of five machine types and three domain shift scenarios for each machine type. The dataset is dedicated to the domain generalization task with features such as multiple different values for parameters that cause domain shifts and introduction of domain shifts that can be difficult to detect, such as shifts in the background noise. Experimental results using two baseline systems indicate that the dataset reproduces domain shift scenarios and is useful for benchmarking domain generalization techniques.
[ -0.010710019618272781, 0.016481321305036545, -0.03684171289205551, -0.015393288806080818, 0.033076174557209015, 0.017834264785051346, -0.041364140808582306, 0.03529008477926254, 0.0009608978871256113, -0.002146498067304492, 0.0074270013719797134, -0.04685160517692566, 0.03421151265501976, 0.001122920075431466, -0.06982327252626419, -0.010757326148450375, -0.028724046424031258, -0.028799735009670258, -0.023217657580971718, -0.02760763093829155, 0.017862647771835327, 0.013359141536056995, -0.05903756618499756, 0.04836539179086685, -0.021741719916462898, 0.03383306786417961, 0.03237605094909668, -0.0248260535299778, -0.02011440135538578, 0.061194706708192825, -0.026831816881895065, -0.014655319042503834, -0.03247066214680672, -0.0041085039265453815, -0.034400735050439835, 0.013415908440947533, -0.015800118446350098, 0.04647316038608551, -0.03127855807542801, 0.019546732306480408, -0.007403348572552204, 0.00011190764780621976, -0.019073674455285072, -0.047986943274736404, -0.03406013548374176, -0.013983577489852905, -0.06615234911441803, 0.025564022362232208, -0.048554614186286926, 0.10649468749761581, -0.019622422754764557, -0.01614071987569332, -0.01593257486820221, 0.02643444947898388, -0.061346087604761124, 0.03782567009329796, 0.03265988454222679, 0.04677591845393181, 0.03729584813117981, -0.04427817463874817, 0.031392090022563934, -0.019641343504190445, -0.04265085607767105, 0.036160510033369064, 0.009068510495126247, -0.04053156077861786, 0.013169918209314346, -0.013491597957909107, 0.022479688748717308, 0.04991701990365982, -0.05801576375961304, -0.036822788417339325, -0.009399650618433952, 0.019073674455285072, -0.00640519754961133, -0.036898478865623474, 0.043710507452487946, 0.0546097494661808, 0.002821787493303418, -0.0338519886136055, 0.03829872980713844, -0.013718665577471256, 0.017503123730421066, 0.02965123951435089, 0.0657360628247261, 0.03634973242878914, -0.0422724112868309, -0.051809247583150864, 0.017247673124074936, -0.0725102424621582, 0.00622070487588644, -0.01791941560804844, 0.043142836540937424, 0.04582980275154114, -0.03326539695262909, 0.001200383179821074, 0.006953943986445665, -0.0015989340608939528, -0.10445107519626617, -0.018004564568400383, -0.015554128214716911, -0.017938338220119476, -0.0003887940547429025, -0.024769285693764687, -0.0371633917093277, -0.0060125598683953285, -0.01089924294501543, -0.00019868412346113473, -0.011684518307447433, 0.13828414678573608, 0.025828935205936432, 0.04155336320400238, 0.04677591845393181, 0.0016698926920071244, -0.005728725343942642, 0.011447989381849766, -0.04734358564019203, -0.0613839291036129, -0.026623671874403954, -0.06460072100162506, 0.009172582998871803, 0.05249045044183731, 0.0034154746681451797, -0.006689032074064016, -0.012081886641681194, 0.02862943522632122, 0.01927235908806324, -0.03407905623316765, -0.014153878204524517, 0.062216512858867645, 0.011258766986429691, 0.011845357716083527, -0.008127126842737198, 0.03165700286626816, -0.015696045011281967, -0.013964654877781868, -0.01177912950515747, 0.04582980275154114, -0.04552704468369484, 0.009830133058130741, -0.0248260535299778, -0.010956009849905968, -0.02283921279013157, 0.023104123771190643, -0.030218908563256264, -0.015204065479338169, 0.008363654837012291, 0.10187764465808868, 0.023520415648818016, 0.018950680270791054, -0.01222380343824625, 0.016178563237190247, 0.033511389046907425, 0.005738186649978161, 0.04075862839818001, 0.014825619757175446, 0.003297210205346346, -0.01934804767370224, 0.010842476040124893, -0.05154433846473694, 0.0550638847053051, -0.015516282990574837, 0.03326539695262909, 0.024352995678782463, 0.024712519720196724, -0.007975747808814049, 0.008231199346482754, -0.05078744515776634, 0.02246076613664627, 0.05021977424621582, 0.04617040604352951, 0.0019076040480285883, -0.005705072544515133, -0.00429536122828722, -0.0013742317678406835, 0.07375911623239517, 0.01873307302594185, 0.048403237015008926, -0.0015114184934645891, -0.0013541268417611718, -0.0421210341155529, 0.030521664768457413, 0.0062774717807769775, 0.03950975462794304, 0.046359628438949585, 0.011012776754796505, 0.036311887204647064, -0.028837580233812332, 0.029689082875847816, 0.00945641752332449, 0.02541264519095421, -0.026169536635279655, 0.03574422001838684, 0.009101624600589275, -0.02857266739010811, 0.0038435915485024452, -0.04779772087931633, 0.010956009849905968, -0.01832624524831772, -0.04938719421625137, -0.0032096945215016603, -0.023160891607403755, 0.03377629816532135, -0.03390875458717346, 0.0017384859966114163, 0.05975661426782608, -0.03383306786417961, 0.049008749425411224, -0.00791425071656704, -0.07497014105319977, -0.00555842462927103, -0.005090097896754742, -0.047835566103458405, -0.015620356425642967, 0.028383444994688034, -0.004300091881304979, -0.000452065491117537, 0.015913652256131172, -0.020738838240504265, -0.05040900036692619, 0.03561176359653473, -0.05090097710490227, 0.0273805633187294, -0.006111901719123125, -0.051506493240594864, -0.04458093270659447, 0.022006630897521973, 0.025658635422587395, 0.0303135197609663, 0.024277307093143463, -0.01600826345384121, 0.022725678980350494, -0.018468162044882774, -0.018818223848938942, 0.068006731569767, 0.03311401978135109, -0.000578608363866806, 0.021344350650906563, -0.051128044724464417, -0.0165475495159626, -0.020284703001379967, -0.00037312402855604887, -0.07765710353851318, -0.05154433846473694, 0.05922678858041763, -0.035271160304546356, 0.0726616233587265, 0.0046856338158249855, 0.058621276170015335, 0.019717033952474594, -0.039396222680807114, 0.008557608351111412, -0.055101729929447174, -0.001537436619400978, -0.02452329732477665, 0.015762273222208023, 0.05998368188738823, 0.011883202008903027, 0.014806697145104408, -0.09249218553304672, 0.02870512381196022, 0.005884834099560976, -0.06478994339704514, 0.008075090125203133, -0.04957641661167145, 0.021930942311882973, 0.03634973242878914, -0.010435646399855614, -0.007209395058453083, -0.03258419409394264, -0.023520415648818016, 0.016651621088385582, -0.06391952186822891, 0.011249305680394173, 0.0015740985982120037, -0.016225868836045265, 0.08696687966585159, 0.029178181663155556, 0.05226338282227516, -0.023520415648818016, 0.03782567009329796, 0.052376918494701385, 0.0309190321713686, -0.03421151265501976, 0.001996302278712392, -0.02724810689687729, -0.0010892146965488791, -0.034835949540138245, -0.054874662309885025, -0.0368606336414814, 0.022120164707303047, -0.07864106446504593, -0.0725102424621582, 0.04594333842396736, -0.0073749651201069355, -0.008789407089352608, 0.027929309755563736, -0.022366154938936234, 0.020246857777237892, -0.01761665754020214, -0.06592528522014618, -0.017607197165489197, 0.03669033199548721, 0.03158131241798401, 0.012346798554062843, -0.004924527835100889, 0.02217693254351616, 0.06906638294458389, 0.0007225951994769275, -0.027569785714149475, 0.0016923629445955157, 0.014910769648849964, -0.045337822288274765, 0.0004547264543361962, -0.03839334100484848, 0.00792844220995903, 0.019773799926042557, -0.05438268184661865, 0.04567842558026314, -0.00006474973633885384, -0.009234081022441387, -0.023160891607403755, -0.10066661983728409, 0.04458093270659447, 0.02159034088253975, -0.03780674934387207, -0.01562981680035591, 0.03621727600693703, -0.021249739453196526, -0.0014014325570315123, -0.051430802792310715, -0.01449447963386774, -0.0062916637398302555, -0.029121415689587593, 0.014513401314616203, -0.0041983844712376595, 0.012091347947716713, 0.03180838003754616, -0.010766786523163319, 0.0012334971688687801, -0.008406230248510838, -0.009309769608080387, -0.07682452350854874, -0.0683094933629036, -0.023387959226965904, 0.016869228333234787, -0.00574291730299592, -0.002838344546034932, -0.051279425621032715, -0.026264147832989693, 0.0008970351191237569, -0.051506493240594864, -0.016358325257897377, 0.001393154147081077, -0.01863846182823181, -0.03002968430519104, -0.006982327438890934, -0.0023960359394550323, 0.01858169585466385, -0.011798052117228508, -0.051355112344026566, -0.0747809186577797, 0.0167746152728796, -0.012971234507858753, -0.07568918913602829, -0.01200619712471962, -0.028761891648173332, 0.009631449356675148, -0.030370285734534264, 0.00491979718208313, -0.005284051410853863, 0.02283921279013157, 0.032413896173238754, 0.022706756368279457, -0.03576314076781273, 0.026547983288764954, 0.05139295756816864, 0.0014936787774786353, -0.008065628819167614, 0.024617908522486687, -0.0273048747330904, 0.05449621379375458, 0.00471638236194849, -0.052679672837257385, 0.006651187315583229, 0.04787341132760048, 0.04246163368225098, 0.01263063307851553, 0.00922934990376234, 0.03230036050081253, 0.0036827519070357084, 0.026831816881895065, -0.052906740456819534, -0.017474740743637085, 0.02268783375620842, 0.005217823199927807, -0.0009691764134913683, -0.018496545031666756, 0.03737153485417366, -0.04654885083436966, -0.01912098005414009, 0.05192278325557709, 0.01156152319163084, 0.014664780348539352, -0.029916150495409966, -0.016869228333234787, -0.0011045890860259533, 0.030445976182818413, -0.019357509911060333, 0.0009774549398571253, 0.0035100860986858606, -0.047911256551742554, 0.0248260535299778, -0.004690364468842745, -0.006651187315583229, 0.031467780470848083, -0.06687139719724655, 0.0025663364212960005, -0.0036567337810993195, -0.015024303458631039, -0.04249947890639305, -0.017143601551651955, 0.07092076539993286, 0.029026802629232407, -0.04499722272157669, 0.012687399983406067, -0.018260017037391663, 0.027361640706658363, 0.016273174434900284, -0.07198041677474976, 0.007398617919534445, 0.02312304638326168, 0.0430293045938015, -0.04458093270659447, 0.004449104890227318, 0.04726789891719818, 0.0279103871434927, -0.03046489879488945, -0.01848708465695381, 0.03561176359653473, -0.009314500726759434, 0.004214941523969173, 0.005671958439052105, -0.025147732347249985, -0.06747691333293915, -0.09317339211702347, -0.013898426666855812, 0.04514859989285469, -0.036292966455221176, 0.007791255600750446, -0.07523505389690399, 0.04458093270659447, -0.030673043802380562, 0.0010862580966204405, 0.010113967582583427, -0.02230938710272312, 0.014418790116906166, -0.008368385955691338, 0.017294978722929955, -0.025072043761610985, 0.02473144233226776, 0.05601000040769577, 0.044808000326156616, 0.010851937346160412, 0.03392767906188965, 0.03680386766791344, -0.05926463380455971, -0.03504409268498421, -0.009744983166456223, 0.024050239473581314, 0.04060724750161171, -0.023898860439658165, 0.019215593114495277, 0.009025936014950275, 0.029026802629232407, 0.013747048564255238, -0.04927366226911545, -0.010530258528888226, 0.037106625735759735, 0.0038483222015202045, 0.009295578114688396, -0.018695229664444923, -0.007304006721824408, -0.03897993266582489, 0.014787774533033371, 0.012100809253752232, 0.02348257042467594, -0.022555377334356308, -0.03848795220255852, 0.03714446723461151, -0.019622422754764557, 0.03165700286626816, -0.006471425294876099, -0.008231199346482754, -0.016055569052696228, -0.0017893397016450763, -0.034987326711416245, -0.016065029427409172, 0.07610547542572021, -0.003025202313438058, -0.03353030979633331, -0.04310499131679535, 0.016765154898166656, -0.037106625735759735, 0.013709204271435738, 0.0031458318699151278, -0.009300309233367443, 0.027342718094587326, 0.023179814219474792, 0.010047739371657372, 0.02459898591041565, -0.012800933793187141, 0.05188493803143501, -0.008562339469790459, 0.00035981929977424443, 0.019868411123752594, -0.01343483105301857, -0.040115270763635635, 0.02651013806462288, 0.006745798978954554, 0.02085237205028534, 0.0057996842078864574, -0.0024551679380238056, 0.044240329414606094, -0.02495850995182991, 0.01799510419368744, 0.05820498615503311, 0.014825619757175446, 0.08477188646793365, -0.03205437213182449, -0.0010371784446761012, 0.006315316539257765, -0.02722918428480625, -0.050181932747364044, -0.004489314742386341, 0.006925560534000397, -0.010113967582583427, 0.02959447167813778, -0.011618290096521378, -0.03510086238384247, -0.041364140808582306, 0.017399052157998085, -0.017881570383906364, -0.036084819585084915, -0.01981164515018463, 0.03250850737094879, 0.0165475495159626, -0.015800118446350098, 0.0490465946495533, 0.05381501093506813, 0.04420248419046402, 0.016452936455607414, 0.02613169141113758, 0.0008177980198524892, -0.014125494286417961, -0.02819422259926796, -0.03288695216178894, -0.007039094343781471, -0.003543199971318245, -0.01277255080640316, -0.015308137983083725, 0.0073418510146439075, 0.009697677567601204, 0.04102354124188423, 0.0039192805998027325, -0.0010371784446761012, 0.01611233502626419, 0.04389972984790802, 0.003914549946784973, 0.0007746315095573664, -0.004255151376128197, -0.047835566103458405, -0.022479688748717308, -0.047381430864334106, 0.026301993057131767, 0.010511335916817188, -0.035271160304546356, -0.0658874362707138, -0.029897229745984077, 0.029783695936203003, 0.001115824212320149, -0.045564889907836914, 0.029897229745984077, 0.03856364265084267, -0.01240356545895338, -0.0014771218411624432, -0.01108846627175808, -0.04677591845393181, 0.002949513029307127, 0.0020424253307282925, 0.05305812135338783, 0.02656690403819084, -0.043710507452487946, -0.001259515411220491, -0.04700298607349396, 0.005307704210281372, -0.012659016996622086, 0.0021583244670182467, 0.03337893262505531, -0.002293145749717951, 0.02283921279013157, 0.0077108358964324, 0.0023439994547516108, 0.02039823681116104, 0.020322546362876892, -0.03283018618822098, 0.03617943078279495, -0.02172279730439186, -0.0010425002546980977, -0.02643444947898388, 0.034911636263132095, 0.007181011606007814, 0.034249357879161835, -0.005856450647115707, 0.032489582896232605, 0.07084508240222931, 0.07167766243219376, 0.016755694523453712, -0.02342580258846283, -0.043067146092653275, 0.0019809280056506395, 0.005416507367044687, 0.01391734927892685, 0.027872543781995773, 0.04128845036029816, 0.05835636332631111, -0.02908357046544552, -0.0364064984023571, 0.0051941704005002975, 0.03349246457219124, -0.003945298958569765, 0.04397541657090187, -0.0607784166932106, -0.042991459369659424, 0.011429067701101303, 0.0027342718094587326, 0.03273557499051094, -0.017777498811483383, -0.004042275715619326, -0.06312478333711624, -0.0077108358964324, -0.013945733197033405, -0.0006374449003487825, 0.00373478839173913, -0.0013505789684131742, 0.050333309918642044, -0.00039855088107287884, -0.0307676550000906, 0.02651013806462288, 0.061497464776039124, -0.01698276214301586, 0.01472154725342989, -0.00407775491476059, 0.03207329288125038, -0.029386326670646667, 0.033454619348049164, 0.03699309006333351, -0.005842259153723717, 0.005459082778543234, 0.021249739453196526, 0.030748732388019562, -0.04866814613342285, -0.02159034088253975, -0.0030535857658833265, 0.03413582220673561, -0.009972050786018372, 0.0036046975292265415, 0.008041976019740105, 0.010984393768012524, 0.02768331952393055, 0.0273805633187294, -0.08144156634807587, -0.010757326148450375, -0.019925178959965706, -0.003498259698972106, -0.026320915669202805, 0.026415526866912842, 0.004962372127920389, 0.007663530297577381, -0.06304909288883209, 0.02268783375620842, -0.02796715497970581, -0.026472292840480804, 0.03441965952515602, 0.007658799644559622, 0.0018863164586946368, 0.03377629816532135, 0.00363308098167181, -0.02276352234184742, -0.014343100599944592, 0.02282029017806053, -0.015005381777882576, 0.0030370287131518126, 0.021836331114172935, -0.02656690403819084, -0.04757065325975418, -0.025299111381173134, -0.004051737021654844, -0.0050191390328109264, 0.018364088609814644, -0.026226302608847618, -0.005397585220634937, -0.03920700028538704, 0.03790136054158211, 0.0303892083466053, 0.03767429292201996, 0.007961556315422058, -0.01032211259007454, 0.030445976182818413, -0.021741719916462898, 0.006329508498311043, 0.014163339510560036, -0.021684952080249786, 0.015506822615861893, 0.02282029017806053, -0.005884834099560976, -0.026453370228409767, -0.012271109968423843, 0.009125277400016785, 0.03419259190559387, 0.02041715756058693, 0.022555377334356308, 0.008940785191953182, -0.04598117992281914, -0.037920281291007996, 0.022271543741226196, 0.013226685114204884, -0.0340033657848835, -0.0277590099722147, 0.003869609674438834, -0.006301125045865774, -0.037995971739292145, -0.011864280328154564, 0.0014002500101923943, -0.0013718665577471256, -0.03612266480922699, 0.012536021880805492, 0.0277590099722147, -0.005634113680571318, 0.010492413304746151, -0.018032949417829514, 0.0013553095050156116, 0.06437365710735321, -0.018960140645503998, -0.016680004075169563, 0.015894729644060135, 0.045186445116996765, -0.020719915628433228, -0.03377629816532135, 0.004037545062601566, 0.024201618507504463, -0.002264762297272682, -0.014920230954885483, -0.03538469597697258, 0.019584577530622482, -0.007971017621457577, 0.05653982236981392, 0.0026680438313633204, -0.037636447697877884, -0.01299015711992979, -0.0065707676112651825, 0.01596095785498619, -0.009409111924469471, 0.0017562257125973701, 0.01148583460599184, 0.006670109461992979, -0.013103690929710865, 0.0016438745660707355, 0.007370234467089176, 0.03237605094909668, 0.03392767906188965, -0.04711651802062988, 0.01996302232146263, -0.007384426426142454, 0.0604756623506546, 0.02113620564341545, -0.0034462232142686844, -0.023160891607403755, -0.009849055670201778, 0.012384642846882343, -0.028515901416540146, -0.0052462066523730755, -0.010814093053340912, 0.029253870248794556, 0.013936271890997887, 0.04957641661167145, -0.01093708723783493, -0.0016533356392756104, -0.004770784173160791, 0.04091000556945801, -0.032565273344516754, -0.025431567803025246, 0.015090531669557095, -0.045110754668712616, 0.02365287020802498, -0.002164237666875124, -0.004626501351594925, 0.04022880271077156, -0.06369245052337646, -0.02378532662987709, 0.0371633917093277, 0.0077108358964324, 0.010350496508181095, 0.0007444741204380989, -0.01325506903231144, -0.0359523631632328, -0.017635580152273178, 0.042991459369659424, -0.019622422754764557, 0.02643444947898388, 0.035573918372392654, 0.006457233801484108, 0.032130058854818344, 0.0054874662309885025, 0.03661464527249336, 0.002105105435475707, -0.020209012553095818, -0.03186514973640442, 0.0038270344957709312, -0.004645423963665962, -0.05434483662247658, -0.03177053481340408, -0.013822738081216812, 0.012167036533355713, -0.013775432482361794, 0.0004047597467433661, 0.03169484809041023, 0.018524928018450737, 0.03803381696343422, -0.024655751883983612, 0.012308954261243343, -0.029405249282717705, -0.013387525454163551, 0.00724723981693387, -0.014021421782672405, 0.018979063257575035, 0.03406013548374176, 0.022933823987841606, 0.006911369040608406, 0.042840078473091125, 0.05805360525846481, 0.01680300012230873, -0.03002968430519104, -0.019660266116261482, 0.01631101965904236, -0.024561140686273575, 0.003990239463746548, 0.011107387952506542, 0.026491215452551842, 0.027323797345161438, 0.030048606917262077, 0.009262464009225368, 0.01148583460599184, -0.018997985869646072, -0.024334073066711426, 0.016254253685474396, -0.01134391687810421, 0.017143601551651955, -0.0030299327336251736, -0.011996735818684101, 0.04094785079360008, -0.0010454568546265364, -0.0332464762032032, 0.017730191349983215, 0.020682070404291153, 0.016632698476314545, -0.014617474749684334, -0.061346087604761124, 0.019395355135202408, -0.010814093053340912, -0.012649555690586567, -0.018676307052373886, -0.0021535938140004873, 0.001122920075431466, -0.04030449315905571, 0.02106051705777645, -0.02151465229690075, -0.003491163719445467, -0.03141101449728012, 0.009063780307769775, 0.00047719667782075703, 0.06509269773960114, 0.048933058977127075, -0.06342753767967224, 0.01682192273437977, -0.004562638700008392, -0.002213908825069666, 0.021760640665888786, 0.003897993126884103, -0.030067529529333115, -0.010407263413071632, 0.0033019408583641052, -0.04579195752739906, -0.03604697436094284, 0.055101729929447174, 0.008160240948200226, 0.0006888898788020015, -0.0018709420692175627, -0.024844976142048836, -0.007365503814071417, -0.007772333454340696, -0.037768904119729996, -0.018420856446027756, 0.010397802107036114, 0.02766439877450466, 0.027853621169924736, 0.004399434197694063, 0.00873264018446207, 0.03392767906188965, -0.008089281618595123, -0.004844108130782843, -0.002223369898274541, 0.04185612127184868, -0.03752291575074196, 0.01967918872833252, -0.003888532053679228, 0.017985643818974495, 0.01009504497051239, 0.04200749844312668, 0.02047392539680004, 0.007460115477442741, 0.0482897013425827, -0.012876623310148716, 0.014551246538758278, -0.07198041677474976, -0.00921515841037035, -0.014153878204524517, 0.01028426829725504, 0.020890215411782265, 0.017143601551651955, -0.018950680270791054, 0.04053156077861786, 0.011883202008903027, 0.010113967582583427, 0.052831053733825684, -0.03563068434596062, 0.01032211259007454, 0.025866780430078506, -0.02092806063592434, -0.0038435915485024452, 0.0006705588893964887, 0.019215593114495277, 0.02584785781800747, 0.024409763514995575, 0.06944482773542404, 0.0541556142270565, -0.004141617566347122, -0.03735261410474777, -0.020019790157675743, 0.005530041176825762, 0.016509704291820526, -0.03474133834242821, -0.022858135402202606, 0.003330324310809374, -0.045186445116996765, 0.015800118446350098, -0.015260832384228706, 0.031032565981149673, 0.0024196887388825417, 0.002798134693875909, -0.001174956327304244, 0.038733940571546555, -0.0686122477054596, 0.013245607726275921, 0.010918165557086468, -0.01329291332513094, -0.027134573087096214, 0.009792288765311241, 0.021533573046326637, -0.014437712728977203, -0.03235712647438049, 0.005530041176825762, 0.007933173328638077, -0.012110269628465176, -0.018411394208669662, -0.01641509309411049, 0.018515467643737793, -0.0036709255073219538, -0.03466564789414406, -0.029916150495409966, 0.005463813431560993, 0.017635580152273178, 0.026018157601356506, 0.003592871129512787, -0.021779563277959824, -0.0022765889298170805, 0.012072425335645676, -0.053928546607494354, -0.05116588994860649, -0.04098569601774216, -0.03180838003754616, -0.03112717904150486, -0.013046924024820328, -0.019433198496699333, -0.05710749328136444, 0.014466095715761185, -0.034400735050439835, -0.007658799644559622, 0.009243542328476906, 0.06940698623657227, -0.04734358564019203, -0.0550638847053051, 0.002485916716977954, 0.027210263535380363, -0.02906464785337448, 0.008656950667500496, 0.023974550887942314, -0.05513957142829895, -0.018184326589107513, -0.0035881404764950275, 0.007819639518857002, -0.030275674536824226, 0.033870913088321686, -0.014816158451139927, 0.0013068211264908314, -0.006007829215377569, -0.0167746152728796, 0.011722362600266933, -0.0361037440598011, -0.005530041176825762, -0.0017893397016450763, -0.015573049895465374, -0.011334455572068691, -0.015147298574447632 ]
Though PINNs (physics-informed neural networks) are now deemed as a complement to traditional CFD (computational fluid dynamics) solvers rather than a replacement, their ability to solve the Navier-Stokes equations without given data is still of great interest. This report presents our not-so-successful experiments of solving the Navier-Stokes equations with PINN as a replacement for traditional solvers. We aim to, with our experiments, prepare readers for the challenges they may face if they are interested in data-free PINN. In this work, we used two standard flow problems: 2D Taylor-Green vortex at Re=100 and 2D cylinder flow at Re=200. The PINN method solved the 2D Taylor-Green vortex problem with acceptable results, and we used this flow as an accuracy and performance benchmark. About 32 hours of training were required for the PINN method's accuracy to match the accuracy of a 16x16 finite-difference simulation, which took less than 20 seconds. The 2D cylinder flow, on the other hand, did not produce a physical solution. The PINN method behaved like a steady-flow solver and did not capture the vortex shedding phenomenon. By sharing our experience, we would like to emphasize that the PINN method is still a work-in-progress, especially in terms of solving flow problems without any given data. More work is needed to make PINN feasible for real-world problems in such applications.
[ -0.03709496930241585, 0.040938910096883774, -0.03291018679738045, -0.048702534288167953, 0.02418084628880024, 0.026206962764263153, -0.006040477659553289, 0.020526262000203133, -0.07703028619289398, 0.011853726580739021, 0.0020616205874830484, -0.009884417988359928, 0.006210898514837027, -0.051694367080926895, -0.009482034482061863, 0.05589808523654938, 0.000013508304618881084, 0.0112477857619524, -0.02399148978292942, -0.064457006752491, -0.005178904626518488, 0.03593989461660385, -0.015981702134013176, -0.016464561223983765, 0.0255820844322443, 0.025298049673438072, -0.0026746627409011126, 0.01781846210360527, -0.011531820520758629, 0.028100527822971344, 0.0521109513938427, 0.044423073530197144, 0.014570995233952999, 0.0410146526992321, 0.03171724081039429, -0.03440610691905022, 0.011304592713713646, 0.028422435745596886, -0.01164543442428112, 0.039954256266355515, -0.030524292960762978, 0.002783542964607477, 0.015413632616400719, 0.009657190181314945, 0.009065450169146061, -0.03711390495300293, -0.03152788430452347, 0.007825164124369621, 0.018178239464759827, -0.011882130056619644, 0.00875774584710598, -0.034178879112005234, 0.006068881135433912, -0.006135155912488699, -0.013709422200918198, -0.002518443623557687, 0.009661924093961716, 0.05036887153983116, 0.029918352141976357, -0.013860907405614853, 0.007938778027892113, 0.022647056728601456, -0.02993728779256344, 0.014372170902788639, -0.004620302468538284, -0.04389287531375885, -0.010727054439485073, -0.031982339918613434, 0.02020435594022274, -0.03370548412203789, -0.06441913545131683, 0.0022687294986099005, -0.03779558837413788, 0.043249063193798065, -0.016455093398690224, -0.07362186908721924, 0.0401814840734005, 0.04889189079403877, 0.057375069707632065, 0.04480178654193878, 0.02079136110842228, 0.05105055496096611, -0.05017951503396034, -0.00004619266837835312, 0.02717268094420433, 0.05745081230998039, -0.004509055521339178, -0.04919486120343208, 0.04332480579614639, -0.03753048926591873, 0.007938778027892113, 0.034197814762592316, 0.03908321633934975, -0.058473337441682816, -0.002310151234269142, 0.00032397740869782865, 0.02081029675900936, 0.0020699049346148968, -0.023006834089756012, 0.018651630729436874, -0.014940240420401096, -0.0030675779562443495, 0.030221322551369667, 0.07725752145051956, 0.005112629849463701, -0.05165649577975273, 0.0002396545314695686, 0.02289322018623352, 0.02607441321015358, 0.160725936293602, -0.03800388053059578, 0.007796760648488998, -0.00970452930778265, -0.0024142975453287363, -0.025998668745160103, 0.007233424577862024, 0.02887689135968685, -0.03550437465310097, 0.054572589695453644, -0.03251253813505173, 0.06547953188419342, 0.06525230407714844, 0.025922926142811775, 0.03671625629067421, -0.00944889709353447, 0.014447913505136967, 0.005893725901842117, -0.043741390109062195, -0.011654902249574661, 0.015385229140520096, 0.02946389652788639, -0.004362304229289293, 0.013008802197873592, -0.04150697961449623, -0.0002124345046468079, -0.02696438878774643, -0.008890295401215553, -0.003664051415398717, -0.003365814685821533, -0.02607441321015358, 0.011465545743703842, -0.03931044414639473, 0.0008905680733732879, -0.02039371244609356, 0.023252997547388077, 0.013576872646808624, -0.08846743404865265, 0.009112789295613766, 0.009856014512479305, 0.03077045828104019, -0.08308970183134079, 0.021056460216641426, -0.004260525107383728, 0.0017077603843063116, -0.006537538953125477, -0.016152122989296913, 0.021567724645137787, -0.019229168072342873, -0.00122608442325145, -0.07066790759563446, 0.04574856907129288, -0.034500785171985626, 0.011427674442529678, -0.009330549277365208, -0.01901140809059143, -0.010755457915365696, 0.0436277762055397, 0.01154128834605217, -0.06547953188419342, 0.03874237462878227, 0.030618973076343536, -0.005339857656508684, -0.028725406154990196, -0.01298986654728651, -0.023745324462652206, 0.04033296927809715, 0.01258275005966425, 0.0034557590261101723, -0.02577144093811512, 0.04082529619336128, -0.051580753177404404, -0.037776652723550797, 0.04177207872271538, 0.0364132858812809, 0.009174330160021782, 0.029634317383170128, 0.032985929399728775, -0.01592489518225193, 0.01562192477285862, -0.0018048057099804282, -0.01323603093624115, -0.006210898514837027, 0.02238195762038231, 0.02397255413234234, -0.0016000637551769614, -0.019238635897636414, -0.0253737922757864, -0.02507082186639309, 0.007200287189334631, 0.03451972082257271, -0.05862482264637947, -0.0728265717625618, -0.005893725901842117, -0.028592856600880623, -0.05782952532172203, 0.055860213935375214, 0.028990505263209343, 0.032777637243270874, 0.029123054817318916, -0.03864769637584686, -0.007725751958787441, -0.003112550126388669, -0.07032706588506699, -0.04620302468538284, -0.03624286502599716, 0.0032782373018562794, -0.04972505941987038, 0.03361080586910248, -0.04510475695133209, -0.06752458214759827, -0.04192356392741203, -0.01143714226782322, 0.017638573423027992, 0.010888008400797844, -0.012118826620280743, -0.06138943135738373, 0.011588627472519875, 0.022230472415685654, -0.04245376214385033, -0.05661763995885849, 0.07706816494464874, 0.0026841305661946535, 0.036678384989500046, 0.01980670727789402, -0.03393271192908287, 0.002201271243393421, 0.004620302468538284, -0.00791984237730503, -0.030732586979866028, -0.015745006501674652, -0.007593201939016581, 0.023915747180581093, 0.01218510139733553, 0.02775968611240387, -0.0015740272356197238, -0.028024785220623016, -0.02715374529361725, 0.03783345967531204, 0.05366367846727371, -0.03999212756752968, 0.01630360819399357, -0.04021935537457466, 0.005226243752986193, 0.028517113998532295, -0.046733222901821136, 0.05820823833346367, 0.0587005652487278, 0.005074758548289537, 0.011626498773694038, 0.013018270023167133, 0.055860213935375214, 0.045142628252506256, -0.011948405764997005, 0.020033935084939003, -0.016057444736361504, 0.04805872216820717, -0.00135626713745296, 0.040370840579271317, 0.0076026697643101215, 0.008397967554628849, -0.017240924760699272, -0.010443019680678844, -0.01730719953775406, -0.05521640181541443, 0.03671625629067421, -0.05888992175459862, -0.0405980683863163, -0.042378019541502, -0.01661604642868042, -0.0012746070278808475, 0.015991169959306717, -0.04927060380578041, 0.007763623259961605, -0.0035078320652246475, -0.05942011997103691, -0.05570872873067856, -0.06354809552431107, -0.02707800269126892, -0.008487911894917488, 0.003763463580980897, 0.018481209874153137, -0.03241785988211632, -0.08733129501342773, 0.05184585228562355, 0.05900353565812111, 0.037947073578834534, -0.04309757798910141, -0.07142533361911774, 0.004369405098259449, 0.0049469429068267345, -0.008682003244757652, 0.04412010312080383, 0.04158272221684456, 0.017193585634231567, -0.04843743517994881, -0.025298049673438072, 0.017837397754192352, -0.02327193319797516, 0.05052035674452782, -0.05820823833346367, -0.006878380663692951, 0.025998668745160103, -0.01572607085108757, -0.0828624740242958, 0.021113267168402672, -0.017269328236579895, 0.07615924626588821, 0.012421797029674053, -0.03351612761616707, -0.034500785171985626, 0.030088772997260094, -0.00979920756071806, -0.05843546614050865, 0.018784180283546448, 0.005136299412697554, -0.05366367846727371, 0.0037019227165728807, 0.0194090586155653, 0.008644131943583488, -0.008819286711513996, 0.024048296734690666, -0.025903990492224693, -0.004485385958105326, -0.01068918313831091, -0.016634982079267502, 0.0011018190998584032, -0.04786936566233635, -0.002589452313259244, -0.037454746663570404, -0.03730326145887375, -0.0569206140935421, -0.0025847184006124735, -0.0471876785159111, -0.044726043939590454, 0.03811749443411827, -0.05453471839427948, 0.011910534463822842, 0.00856838934123516, -0.029293475672602654, -0.01672966033220291, 0.0010467872489243746, 0.003091247519478202, -0.004724448546767235, -0.0010349524673074484, 0.09301199018955231, -0.05112629756331444, -0.011768516153097153, 0.007971915416419506, 0.0011183877941220999, -0.024427009746432304, 0.05544362962245941, -0.031584691256284714, 0.001245020073838532, 0.01969309337437153, -0.10073774307966232, 0.033875904977321625, -0.02596079744398594, -0.01249753963202238, 0.009605116210877895, 0.0033587138168513775, 0.026528868824243546, 0.017581766471266747, 0.0029657986015081406, -0.0604805164039135, -0.025222307071089745, -0.029918352141976357, 0.008734076283872128, 0.02787330001592636, -0.0798327699303627, 0.03251253813505173, -0.06987261027097702, 0.008284353651106358, 0.06566888839006424, 0.021132202818989754, -0.004951676819473505, 0.02666141837835312, 0.016767531633377075, -0.004755218978971243, 0.07634860277175903, 0.044347330927848816, 0.025525277480483055, -0.048929762095212936, -0.025032950565218925, -0.015101193450391293, 0.010906944051384926, -0.016559239476919174, 0.0069304537028074265, -0.02389681152999401, 0.008369564078748226, -0.0066038137301802635, -0.028498178347945213, 0.0251655001193285, -0.07157681882381439, -0.0295585747808218, 0.005467673763632774, 0.017449216917157173, -0.00955304317176342, -0.061843886971473694, -0.060934972018003464, -0.003557538380846381, -0.010566101409494877, -0.01163596659898758, 0.054004520177841187, -0.018632695078849792, 0.05052035674452782, 0.014220685698091984, -0.02010967768728733, -0.016985291615128517, -0.03681093454360962, -0.032985929399728775, 0.0018592457054182887, 0.04287034645676613, 0.022211536765098572, -0.040370840579271317, -0.04476391524076462, 0.03821217268705368, 0.05476194620132446, 0.023953618481755257, 0.03075152263045311, -0.008445306681096554, -0.021075395867228508, 0.015309486538171768, 0.025222307071089745, -0.009363686665892601, -0.03501204773783684, -0.04347629100084305, 0.048020850867033005, -0.005671232007443905, 0.02277960628271103, -0.021870695054531097, -0.0010272598592564464, 0.02009074203670025, -0.023139383643865585, 0.0017077603843063116, 0.048020850867033005, -0.027115873992443085, -0.019560543820261955, -0.03300486505031586, -0.031092364341020584, 0.01610478386282921, -0.028384564444422722, -0.024048296734690666, -0.0222872793674469, -0.004217919427901506, 0.029804738238453865, -0.013709422200918198, -0.039272572845220566, -0.03323209285736084, -0.004253424238413572, -0.015015983022749424, -0.01373782567679882, 0.01959841512143612, -0.0050652907229959965, -0.033686548471450806, 0.031490013003349304, -0.02289322018623352, -0.008790883235633373, -0.040938910096883774, 0.012204037047922611, 0.03639435023069382, 0.07657583057880402, 0.036280736327171326, 0.0018781813560053706, 0.042832475155591965, 0.043552033603191376, 0.055973827838897705, -0.012516475282609463, -0.04400648921728134, 0.0359967015683651, -0.05192159488797188, 0.03436823561787605, 0.007702082395553589, -0.013671550899744034, -0.025127628818154335, -0.04446094483137131, 0.031603626906871796, 0.03175511211156845, 0.0009527006768621504, -0.02993728779256344, 0.0010935347527265549, 0.00905124843120575, 0.022154729813337326, -0.019636286422610283, -0.040143612772226334, 0.005709103308618069, -0.03868556767702103, -0.0006408539484255016, -0.04082529619336128, 0.08248376101255417, -0.015584053471684456, 0.0855892077088356, -0.019541608169674873, -0.008634664118289948, -0.007702082395553589, -0.021075395867228508, 0.07930257171392441, 0.03953767195343971, 0.005552884191274643, -0.009676125831902027, 0.015801813453435898, 0.00472681550309062, -0.03171724081039429, 0.002126712119206786, 0.03823110833764076, 0.009595648385584354, 0.005084226373583078, -0.0021444642916321754, -0.019768835976719856, 0.01298986654728651, 0.020961781963706017, 0.004885402042418718, 0.0008609810611233115, -0.009941224940121174, 0.019390122964978218, -0.04040871188044548, 0.010130581445991993, 0.012260843999683857, -0.02378319576382637, 0.05351219326257706, 0.04230227693915367, -0.01392718218266964, 0.053587935864925385, 0.023234061896800995, -0.056882742792367935, -0.013472726568579674, -0.012563814409077168, -0.007560064550489187, -0.0038889124989509583, 0.003453392069786787, -0.02497614361345768, -0.09695061296224594, 0.043438419699668884, 0.03781452402472496, -0.024124039337038994, 0.008719874545931816, 0.02605547569692135, -0.004362304229289293, -0.026888646185398102, 0.02418084628880024, -0.035883087664842606, -0.009912821464240551, 0.039272572845220566, 0.022647056728601456, -0.005690167658030987, -0.0035883088130503893, -0.01174011267721653, 0.020658811554312706, 0.0036474827211350203, 0.03005090169608593, -0.024654237553477287, -0.01531895436346531, 0.025354856625199318, -0.04002999886870384, -0.04779362305998802, -0.07138746231794357, -0.0388181172311306, 0.017846865579485893, 0.029804738238453865, -0.030107708647847176, -0.03493630513548851, 0.003150421427562833, 0.01383250392973423, -0.008364830166101456, 0.025392727926373482, 0.027210552245378494, 0.0048001911491155624, -0.009789739735424519, -0.0027740751393139362, 0.01279104221612215, 0.020071806386113167, 0.0025350123178213835, -0.016483496874570847, -0.025506341829895973, 0.024029361084103584, -0.0419614352285862, 0.013188691809773445, 0.012014680542051792, -0.005893725901842117, 0.0006373035139404237, -0.021567724645137787, -0.01123831793665886, 0.0643433928489685, 0.0034391903318464756, 0.0010953099699690938, 0.007697348482906818, -0.01839599944651127, -0.020431583747267723, 0.02974793128669262, 0.04487752914428711, -0.028119463473558426, -0.03084620088338852, 0.03336464241147041, 0.045634955167770386, 0.013775696977972984, -0.0025042418856173754, 0.009008643217384815, 0.016767531633377075, 0.03669732064008713, 0.05476194620132446, -0.02209792286157608, 0.02209792286157608, -0.014646737836301327, 0.031111299991607666, -0.04571069777011871, 0.06290428340435028, -0.00195392407476902, 0.02088603936135769, 0.047111935913562775, -0.04120400920510292, -0.012724767439067364, -0.003091247519478202, 0.0056380946189165115, 0.0679032951593399, -0.009164862334728241, 0.0036995557602494955, 0.05305773764848709, -0.0003813761577475816, 0.001229634857736528, -0.016350947320461273, -0.05180798098444939, -0.00990335363894701, -0.025430599227547646, -0.025316985324025154, 0.0021539321169257164, 0.022647056728601456, 0.04699832201004028, 0.012317650951445103, 0.029975159093737602, 0.016275204718112946, -0.030827265232801437, 0.01393665000796318, 0.006646418944001198, 0.03968915715813637, 0.051883723586797714, 0.006371851544827223, 0.027418844401836395, 0.01218510139733553, -0.02298789843916893, 0.0038699768483638763, 0.0525275394320488, 0.00801452063024044, -0.02518443576991558, 0.034974176436662674, 0.04328693449497223, -0.01652136817574501, -0.04586218297481537, 0.036375414580106735, 0.015953298658132553, -0.008128134533762932, 0.02050732634961605, 0.00592212937772274, 0.04487752914428711, 0.003003670135512948, -0.004909071605652571, 0.01372835785150528, 0.023650646209716797, 0.007773091085255146, 0.0049469429068267345, 0.034500785171985626, 0.0196173507720232, -0.009652456268668175, -0.02181388810276985, 0.000955659372266382, 0.03311847895383835, 0.03236105293035507, -0.030600037425756454, 0.008483177982270718, 0.04002999886870384, 0.026206962764263153, -0.05404239147901535, -0.020223291590809822, -0.009912821464240551, -0.014731948263943195, 0.015091725625097752, 0.007891438901424408, 0.011295124888420105, -0.041847821325063705, -0.045634955167770386, -0.0005080084083601832, -0.02190856635570526, -0.008776681497693062, -0.04146910831332207, 0.041658464819192886, 0.01950373686850071, 0.03451972082257271, 0.02427552454173565, -0.042643118649721146, -0.008379031904041767, -0.01497811172157526, 0.009571978822350502, -0.04487752914428711, 0.0009402741561643779, -0.028024785220623016, -0.017155714333057404, 0.0010964934481307864, -0.012204037047922611, 0.002793010789901018, -0.015470439568161964, -0.007455918472260237, 0.006774234585464001, 0.0045824311673641205, -0.03124384954571724, 0.014201750047504902, 0.03166043385863304, 0.009723464958369732, -0.007616871502250433, 0.021643467247486115, 0.014788755215704441, 0.0043291668407619, -0.017098907381296158, -0.02675609663128853, -0.024029361084103584, -0.0318119190633297, -0.04347629100084305, -0.01476981956511736, 0.02775968611240387, -0.01782792992889881, -0.024351267144083977, -0.006404988933354616, 0.018727373331785202, 0.024067232385277748, -0.013075077906250954, 0.01692848466336727, 0.014722480438649654, -0.0031740909907966852, -0.01352953352034092, 0.07744687795639038, 0.006646418944001198, 0.029899416491389275, 0.008345894515514374, -0.000587893242482096, -0.02726735919713974, -0.013520065695047379, 0.0061209541745483875, 0.00758373411372304, 0.006849977187812328, 0.008383765816688538, -0.005926863290369511, 0.01019685622304678, -0.025922926142811775, 0.057375069707632065, -0.0072854976169764996, -0.0105945048853755, -0.04847530648112297, -0.042832475155591965, -0.010111645795404911, 0.030713651329278946, -0.04090103879570961, 0.0026557270903140306, -0.002112510148435831, 0.011162575334310532, 0.04082529619336128, -0.011957873590290546, 0.035068854689598083, 0.010177920572459698, -0.017240924760699272, -0.02168133854866028, -0.006225100252777338, -0.007721018046140671, -0.029388153925538063, -0.013349644839763641, 0.057375069707632065, 0.029482832178473473, 0.0048380629159510136, -0.02607441321015358, -0.025411663576960564, -0.007545862812548876, 0.010575569234788418, 0.0029468629509210587, 0.034974176436662674, 0.02109433151781559, 0.007328102830797434, -0.013898778706789017, 0.0008763662772253156, 0.02916092611849308, 0.023234061896800995, -0.0024569027591496706, -0.011209914460778236, 0.003874710761010647, -0.028119463473558426, -0.004587165080010891, -0.005117363762110472, 0.014807690866291523, -0.03315635025501251, 0.05741294100880623, 0.011314060539007187, -0.004894869867712259, 0.009264274500310421, -0.038344722241163254, 0.0032711364328861237, 0.011759048327803612, -0.028005849570035934, -0.04408223181962967, 0.046127282083034515, -0.008814552798867226, -0.013169756159186363, -0.017487088218331337, 0.011711709201335907, -0.01919129677116871, 0.002285298192873597, -0.01164543442428112, -0.034197814762592316, -0.004026195965707302, 0.011067897081375122, -0.008587324991822243, -0.023953618481755257, -0.02478678710758686, 0.005141033325344324, -0.01279104221612215, 0.006561208516359329, -0.04768000915646553, 0.008871359750628471, 0.005533948540687561, -0.03194446861743927, -0.04737703502178192, -0.014892901293933392, 0.0009006276377476752, -0.015792345628142357, 0.03980277106165886, 0.02944496087729931, -0.0038794446736574173, 0.0432111918926239, -0.018926197662949562, 0.01164543442428112, -0.01372835785150528, -0.009164862334728241, 0.030884072184562683, 0.08240801841020584, -0.06517656147480011, 0.004452248569577932, 0.01730719953775406, 0.0026225897017866373, -0.04218866303563118, -0.029331346973776817, 0.01068918313831091, 0.027305230498313904, -0.0037303261924535036, -0.0012710565933957696, -0.010263131000101566, -0.024900401011109352, 0.018746308982372284, -0.01019685622304678, 0.015650328248739243, -0.0017977048410102725, -0.04885401949286461, -0.0016178159276023507, 0.06987261027097702, 0.03501204773783684, -0.028725406154990196, -0.014268024824559689, 0.04756639152765274, 0.003685354022309184, 0.024029361084103584, -0.014741416089236736, 0.007607403676956892, -0.033686548471450806, 0.013624211773276329, -0.014760351739823818, -0.00624403590336442, -0.08225653320550919, -0.0324367955327034, -0.025127628818154335, 0.031792983412742615, 0.012658492662012577, -0.026415254920721054, 0.011948405764997005, -0.003794234013184905, -0.01115310750901699, -0.016985291615128517, -0.00875774584710598, -0.018585355952382088, 0.016776999458670616, -0.0033989520743489265, 0.005245179403573275, 0.014930772595107555, -0.02137836627662182, -0.021170074120163918, -0.031168106943368912, -0.028706470504403114, -0.06097284331917763, 0.01467514131218195, 0.018935665488243103, -0.0028356160037219524, 0.020753489807248116, 0.021851759403944016, -0.033970583230257034, -0.04836169257760048, -0.001181703875772655, -0.011266721412539482, -0.002260445151478052, -0.03552331030368805, 0.035068854689598083, -0.040370840579271317, -0.05461046099662781, 0.016795935109257698, -0.04824807867407799, 0.045029014348983765, -0.027115873992443085, 0.02866859920322895, -0.001365734962746501, -0.06157878786325455, -0.049800802022218704, -0.038780245929956436, 0.006177761126309633, -0.007181351538747549, 0.05317135155200958, -0.046808965504169464, 0.04226440563797951, 0.04396861791610718, -0.026831839233636856, -0.00970452930778265, 0.033970583230257034, -0.04241589084267616, 0.013785164803266525, -0.012933059595525265, 0.010859604924917221, 0.0410146526992321, 0.06600973010063171, -0.013472726568579674, 0.014921304769814014, 0.02953963913023472, 0.04127975180745125, 0.04377926141023636, 0.019560543820261955, 0.008942368440330029, 0.032872315496206284, 0.004182415083050728, 0.00696359109133482, 0.0067126937210559845, -0.01532842218875885, -0.022552378475666046, -0.010433551855385303, -0.02357490360736847, -0.002558681881055236, 0.007110342849045992, -0.02476785145699978, 0.07138746231794357, 0.009411025792360306, -0.0255820844322443, 0.006878380663692951, 0.004393074661493301, -0.006404988933354616, -0.014836094342172146, 0.007971915416419506, -0.02188963070511818, -0.000037797366530867293, -0.04987654462456703, 0.006523337215185165, 0.0025137097109109163, 0.014599398709833622, -0.006627483293414116, -0.0224955715239048, -0.009524639695882797, -0.028005849570035934, 0.0003248650173190981, 0.0034888964146375656, -0.012128294445574284, -0.06381319463253021, -0.0016982925590127707, 0.012412329204380512, 0.0036001435946673155, 0.009226403199136257, -0.0026320575270801783, 0.056466154754161835, 0.0017977048410102725, -0.012961463071405888, -0.03186872601509094, -0.04029509797692299, -0.03245573118329048, 0.01458046305924654, 0.01393665000796318, 0.01612371951341629, -0.007138746324926615, -0.0388181172311306, -0.03173617646098137, -0.012279779650270939, -0.01458046305924654, -0.0038889124989509583, -0.05226244032382965, -0.009079651907086372, -0.00400252640247345, -0.01801728643476963, 0.07150107622146606, -0.04218866303563118, -0.008871359750628471, 0.0676003247499466, 0.01229871530085802, -0.0209807176142931, 0.02387787587940693, 0.01742081344127655, -0.01901140809059143, 0.012279779650270939, 0.004225020296871662, 0.01531895436346531, 0.03495524078607559, -0.005112629849463701, 0.04309757798910141, 0.003292439039796591, -0.018585355952382088, 0.027040131390094757, -0.017070503905415535, -0.016057444736361504, 0.0048001911491155624, -0.024654237553477287, -0.00415164465084672, 0.008473710156977177, -0.06945602595806122, -0.028611792251467705, -0.016341479495167732, -0.008090263232588768, 0.03559905290603638, -0.0006020950386300683, 0.03126278519630432, -0.02696438878774643 ]
Rational approximations are introduced and studied in granular graded rough sets and generalizations thereof by the first author in recent research papers. The concept of rationality is determined by related ontologies and coherence between granularity, mereology and approximations in the context. In addition, a framework for rational approximations is introduced by her in the mentioned paper(s). Granular approximations constructed as per the procedures of variable precision rough sets (VPRS) are likely to be more rational than those constructed from a classical perspective under certain conditions. This may continue to hold for some generalizations of the former. However, a formal characterization of such conditions is not available in the previously published literature. In this research, theoretical aspects of the problem are critically examined, uniform generalizations of granular VPRS are introduced, new connections with granular graded rough sets are proved, appropriate concepts of substantial parthood are introduced, their extent of compatibility with the framework is accessed, and the framework is extended. Basic assumptions are explained in detail, and additional examples are constructed for readability. Furthermore, meta applications to cluster validation, image segmentation and dynamic sorting are invented. Extensions to direct generalizations of VPRS such as probabilistic rough sets are a natural consequence of the work.
[ -0.05167648568749428, -0.008443742990493774, -0.05928170308470726, 0.027807798236608505, 0.04621632769703865, 0.0006429090863093734, 0.023303169757127762, -0.004426626954227686, 0.011242073029279709, 0.004265747498720884, 0.024999717250466347, 0.012792367488145828, 0.04492929205298424, -0.040288157761096954, -0.04574831575155258, 0.026754768565297127, 0.016721731051802635, 0.00843399204313755, 0.009482147172093391, -0.04641133174300194, -0.024317199364304543, 0.02774929627776146, -0.029972361400723457, -0.00006394812953658402, -0.0011334700975567102, 0.020319582894444466, 0.04368125647306442, -0.046294331550598145, -0.06224578991532326, 0.07410212606191635, 0.004836138803511858, -0.0032005293760448694, 0.01886679232120514, 0.02451220341026783, -0.046567339450120926, -0.012646113522350788, 0.032780442386865616, -0.011125070042908192, 0.08268237859010696, 0.004065866582095623, 0.022191638126969337, 0.031629908829927444, -0.02421969547867775, 0.0381040945649147, 0.005016519222408533, -0.037772584706544876, 0.007254208438098431, -0.01666322909295559, -0.025136221200227737, -0.05690263584256172, -0.00756134232506156, -0.048634398728609085, 0.08081032335758209, -0.013796646147966385, -0.03215642273426056, -0.046606339514255524, 0.09742479771375656, 0.03857210651040077, 0.03827960044145584, -0.004514379892498255, 0.02494121715426445, -0.039722640067338943, -0.05799466744065285, -0.016916735097765923, 0.0066984426230192184, -0.032643936574459076, 0.0024412262719124556, -0.02024158090353012, 0.009906284511089325, -0.020885100588202477, -0.016000209376215935, 0.017843011766672134, 0.03607603535056114, 0.010735058225691319, 0.012519359588623047, 0.005333403125405312, 0.011739336885511875, -0.019325055181980133, -0.046567339450120926, 0.07020201534032822, 0.004092680290341377, 0.09422671049833298, 0.008721625432372093, -0.011183571070432663, 0.004811763297766447, 0.007322460412979126, 0.04520229995250702, -0.05791666358709335, 0.05811166763305664, -0.0013504137750715017, 0.00902875978499651, -0.022328142076730728, 0.013172628358006477, -0.014488915912806988, 0.06977300345897675, 0.02098260261118412, 0.01562969945371151, -0.007619843818247318, -0.0322539247572422, -0.02012457884848118, -0.013094626367092133, -0.007419963367283344, 0.00620605330914259, -0.016117213293910027, 0.06700392812490463, -0.06232379004359245, -0.007688095793128014, -0.02217213623225689, -0.011554081924259663, 0.13455386459827423, -0.019617563113570213, 0.06283080577850342, -0.011339575983583927, -0.0425112210214138, -0.039722640067338943, -0.06415684521198273, -0.032643936574459076, -0.057019639760255814, 0.05916469916701317, 0.025311727076768875, -0.04684034734964371, 0.020729094743728638, 0.023985689505934715, -0.01006228942424059, -0.0631818175315857, 0.037928588688373566, -0.025194723159074783, 0.01590270735323429, 0.009257891215384007, 0.028821827843785286, -0.040288157761096954, 0.0381430946290493, 0.009394395165145397, -0.0329754464328289, -0.020163578912615776, 0.03923512622714043, 0.08276037871837616, -0.020651092752814293, 0.014030653052031994, 0.018749788403511047, -0.020495088770985603, -0.05280751734972, 0.014118405990302563, 0.009248140268027782, 0.009316392242908478, -0.0020049014128744602, -0.05105246603488922, 0.03987864404916763, -0.02466820925474167, 0.018925294280052185, -0.003446724032983184, -0.008404741063714027, 0.04680134356021881, 0.037909090518951416, 0.07753422856330872, 0.05179348960518837, -0.016682729125022888, 0.0484783910214901, 0.031025391072034836, -0.010267045348882675, 0.02464870736002922, -0.04091217368841171, -0.00535777909681201, 0.010978815145790577, 0.020748596638441086, 0.0329754464328289, -0.02258164808154106, 0.057877663522958755, -0.011583332903683186, 0.03627104312181473, -0.019442059099674225, 0.009296892210841179, 0.025428730994462967, 0.03504250571131706, 0.008424242027103901, 0.05042845010757446, 0.01590270735323429, 0.024882715195417404, -0.015200686641037464, -0.00602079788222909, -0.006986075546592474, -0.007093328982591629, 0.014079404063522816, 0.02024158090353012, 0.03463299572467804, 0.04317424073815346, 0.11325925588607788, 0.015512695536017418, 0.012441357597708702, -0.01996857300400734, -0.016614478081464767, 0.058462679386138916, -0.016029460355639458, 0.031629908829927444, -0.014079404063522816, -0.07425813376903534, -0.040600165724754333, -0.013845398090779781, -0.01655597612261772, 0.009501648135483265, -0.01936405710875988, -0.09009258449077606, -0.004119493532925844, -0.0425892248749733, 0.07952328771352768, -0.04344724863767624, 0.047152355313301086, -0.00466550886631012, 0.002003682544454932, -0.015249437652528286, -0.01846703141927719, -0.011047067120671272, 0.04227721318602562, 0.03260493651032448, -0.06649690866470337, 0.01370889414101839, 0.005806291941553354, -0.02375168167054653, -0.0043169367127120495, -0.054289560765028, -0.0018781477119773626, -0.03159090876579285, 0.05074045807123184, 0.0003281578538008034, 0.0359785333275795, 0.06423484534025192, 0.03317045420408249, 0.02993335947394371, -0.04021015390753746, 0.013455386273562908, -0.013036124408245087, 0.023244667798280716, 0.008419366553425789, -0.04726935923099518, -0.02408319152891636, -0.0016599851660430431, -0.033365458250045776, 0.01635121926665306, 0.022074634209275246, 0.023985689505934715, -0.03841610252857208, 0.022347642108798027, -0.024590207263827324, -0.0007056765025481582, 0.0763251930475235, -0.030615879222750664, -0.00917501375079155, 0.047464363276958466, 0.05386054888367653, 0.001723362016491592, -0.031746912747621536, -0.021372614428400993, 0.015454193577170372, 0.0150446817278862, -0.051871489733457565, 0.011846589855849743, 0.049063410609960556, 0.019471310079097748, -0.011944092810153961, -0.01619521528482437, 0.03753857687115669, -0.002632575575262308, 0.02041708678007126, -0.0315324068069458, 0.0010414518183097243, -0.008789877407252789, 0.010696057230234146, -0.023654179647564888, -0.016945986077189445, 0.07203506678342819, 0.02849031798541546, -0.04633333161473274, -0.028568319976329803, -0.004775199573487043, 0.013133627362549305, -0.06388383358716965, 0.0035661649890244007, -0.005801416467875242, 0.02683277055621147, 0.012304853647947311, -0.006249929312616587, 0.01232435368001461, -0.0323319286108017, -0.007224957458674908, -0.01938355714082718, 0.024902215227484703, -0.05116946995258331, 0.03915712609887123, -0.06922698765993118, -0.013962401077151299, 0.041302185505628586, -0.00954552460461855, -0.10031088441610336, 0.014635170809924603, 0.012363355606794357, 0.0064351847395300865, 0.011690585874021053, -0.013016624376177788, 0.004099992569535971, -0.02187962830066681, 0.030713383108377457, -0.0359785333275795, 0.02613075077533722, 0.011066568084061146, 0.015707701444625854, -0.012061096727848053, -0.009808781556785107, 0.029309341683983803, -0.023088663816452026, -0.016477974131703377, 0.00998428650200367, 0.04461728036403656, -0.020456086844205856, 0.02304966188967228, -0.018135521560907364, 0.008238987065851688, 0.02538972906768322, -0.03568602353334427, 0.013952651061117649, -0.03276094049215317, 0.03038187325000763, -0.0032102796249091625, -0.09048260003328323, -0.027398286387324333, -0.033813972026109695, -0.01785276271402836, -0.02363467961549759, 0.01848653145134449, -0.04375925660133362, -0.008204860612750053, -0.017394499853253365, 0.0017160492716357112, -0.006722818128764629, 0.006864197086542845, -0.03845510631799698, 0.01232435368001461, 0.06279180198907852, 0.04859539493918419, -0.015493195503950119, -0.003992739599198103, -0.013279881328344345, -0.010676556266844273, -0.006201178301125765, 0.0011791745200753212, 0.013016624376177788, -0.0070738280192017555, 0.0030006486922502518, -0.040600165724754333, -0.001037795445881784, 0.031064392998814583, 0.0011054379865527153, -0.010520552285015583, -0.053938549011945724, 0.02730078436434269, 0.04808838292956352, -0.06653591245412827, 0.02550673298537731, -0.03330695629119873, -0.004626507870852947, 0.010306046344339848, 0.017209244892001152, -0.06860297173261642, -0.0425892248749733, 0.05257350951433182, -0.0469963513314724, -0.020066076889634132, 0.003880611388012767, 0.062440793961286545, -0.00997453648597002, -0.009516273625195026, -0.07882126420736313, 0.04021015390753746, 0.06130976229906082, -0.02213313616812229, -0.007356586400419474, 0.006844696588814259, -0.0015637011965736747, -0.021080104634165764, -0.03566652536392212, 0.02213313616812229, 0.028412315994501114, 0.007761222776025534, 0.03051837719976902, 0.03480850160121918, -0.013689393177628517, 0.0015880768187344074, -0.00355885224416852, 0.002596012083813548, 0.027944302186369896, 0.04711335524916649, -0.01912030018866062, 0.0381430946290493, 0.013767395168542862, -0.061270758509635925, 0.03921562805771828, -0.004207246005535126, -0.0586576834321022, -0.022074634209275246, 0.00045064574806019664, 0.01512268465012312, -0.03623203933238983, -0.010657056234776974, -0.04134118929505348, 0.0026447635609656572, 0.0439932644367218, -0.0009664965327829123, -0.02289365790784359, 0.036193039268255234, 0.023264167830348015, 0.017648007720708847, -0.02700827643275261, 0.02950434759259224, -0.005586910527199507, -0.06041273474693298, -0.022328142076730728, 0.04200420528650284, -0.032370928674936295, 0.029133837670087814, -0.026169750839471817, -0.01114457007497549, -0.020768096670508385, -0.015073932707309723, 0.04925841465592384, 0.001688017277047038, -0.03900112211704254, 0.0330534502863884, -0.02379068359732628, 0.014215908013284206, 0.028821827843785286, 0.02521422505378723, 0.0007794130360707641, 0.03492550179362297, 0.01006228942424059, -0.001677048159763217, 0.0024790086317807436, -0.007137204986065626, -0.03595903143286705, 0.02320566587150097, 0.012236601673066616, -0.02804180607199669, 0.0013577265199273825, -0.02687177248299122, 0.02936784364283085, 0.03654405102133751, 0.007936728186905384, 0.013923400081694126, -0.029387343674898148, -0.036329545080661774, -0.04383726045489311, 0.0381430946290493, -0.00945777166634798, 0.006815445609390736, -0.06552188098430634, 0.013016624376177788, 0.06193377822637558, -0.020046574994921684, 0.06571688503026962, -0.04929741472005844, 0.007249333430081606, -0.012958122417330742, -0.01912030018866062, 0.03679755702614784, -0.002698390046134591, 0.016741231083869934, -0.013933150097727776, 0.01729699596762657, -0.0012833806686103344, 0.015424943529069424, -0.009233515709638596, 0.02246464602649212, -0.024590207263827324, -0.03671955317258835, -0.05986671894788742, 0.008936131373047829, 0.017014238983392715, 0.0020353710278868675, 0.03775308281183243, -0.045397303998470306, -0.019100798293948174, 0.008984883315861225, 0.021977132186293602, 0.030615879222750664, 0.009189639240503311, 0.03592003136873245, -0.0132213793694973, -0.003271218854933977, 0.018749788403511047, 0.02640375867486, 0.024317199364304543, -0.017082490026950836, -0.05491357669234276, 0.013942900113761425, 0.008911755867302418, 0.019393306225538254, -0.00791722722351551, 0.006274305284023285, 0.02466820925474167, -0.04095117747783661, 0.018515782430768013, 0.027534790337085724, -0.017599254846572876, -0.030752383172512054, -0.06832996010780334, -0.030596379190683365, -0.0040536788292229176, -0.03592003136873245, 0.003132277401164174, -0.03923512622714043, -0.017101991921663284, -0.017911264672875404, 0.020748596638441086, -0.04067816957831383, -0.0047191353514790535, 0.00602079788222909, 0.047191355377435684, 0.02683277055621147, -0.021606620401144028, -0.010910563170909882, 0.012275602668523788, 0.03346296027302742, 0.00013170496094971895, 0.0008836191263981164, -0.0557716004550457, 0.03535451740026474, -0.036173537373542786, 0.012392605654895306, 0.005601536016911268, -0.020631592720746994, -0.02156762033700943, -0.05280751734972, -0.01349438726902008, 0.024102691560983658, -0.019890571013092995, -0.00942364614456892, -0.004568006377667189, -0.008243861608207226, 0.06060774251818657, 0.01958831213414669, -0.019646814092993736, -0.011817339807748795, -0.00998428650200367, 0.06173877418041229, 0.011203072033822536, -0.05370454117655754, 0.006815445609390736, 0.03332645818591118, 0.01738474890589714, -0.03420398384332657, -0.0018671785946935415, 0.01900329627096653, 0.014352411963045597, -0.016516974195837975, -0.04652833566069603, -0.00016529772256035358, 0.008921505883336067, 0.035276513546705246, -0.007015326526015997, 0.023147165775299072, -0.007902601733803749, -0.005192024167627096, 0.024102691560983658, 0.000014844420547888149, 0.03258543461561203, 0.012519359588623047, 0.026150250807404518, 0.013533389195799828, 0.03186391666531563, 0.04009314998984337, -0.08283837884664536, 0.016000209376215935, -0.03151290491223335, -0.02788580022752285, -0.02995286136865616, -0.03227342665195465, 0.014693671837449074, 0.05955471098423004, -0.016926486045122147, -0.010666806250810623, 0.000695316877681762, -0.027827300131320953, 0.040717169642448425, -0.024609707295894623, -0.01891554333269596, 0.009126261807978153, 0.03240993246436119, -0.016097713261842728, -0.0440322645008564, -0.03024536930024624, 0.01637072116136551, -0.04208220914006233, 0.007249333430081606, 0.05811166763305664, 0.0220161322504282, -0.012860619463026524, 0.017735758796334267, 0.0077465977519750595, 0.030128365382552147, -0.0014479166129603982, -0.022503646090626717, -0.0439932644367218, -0.04933641850948334, 0.02084609866142273, -0.022991159930825233, 0.0016782669117674232, -0.02964085154235363, 0.015892956405878067, 0.035432517528533936, -0.017599254846572876, 0.0011042192345485091, 0.01621471531689167, -0.019939322024583817, -0.025877242907881737, 0.003865986131131649, -0.015688201412558556, -0.0069763255305588245, -0.0110080661252141, 0.044227272272109985, -0.044812288135290146, -0.009092136286199093, 0.022815655916929245, 0.05783865973353386, -0.04021015390753746, -0.024609707295894623, -0.004399813711643219, -0.009516273625195026, 0.01711174100637436, 0.006240179296582937, -0.007658844813704491, -0.01875953935086727, 0.002530197612941265, -0.03123989701271057, -0.007171330973505974, -0.0065375627018511295, 0.013640642166137695, 0.023654179647564888, 0.012928871437907219, -0.017862513661384583, 0.010793560184538364, 0.02804180607199669, -0.012246351689100266, -0.018457280471920967, 0.0006362057756632566, 0.014547417871654034, 0.021470116451382637, -0.016702229157090187, -0.013738144189119339, 0.06813495606184006, 0.0063328067772090435, 0.00982828252017498, 0.033521462231874466, 0.013903899118304253, 0.020612092688679695, 0.007809974253177643, 0.035998035222291946, 0.0263842586427927, 0.0076393443159759045, 0.008136608637869358, -0.03254643455147743, -0.05358754098415375, -0.03681705892086029, 0.02098260261118412, 0.018905792385339737, -0.038065094500780106, 0.03831860050559044, 0.00730295991525054, 0.04606032371520996, 0.05518658459186554, 0.05241750553250313, 0.013835647143423557, 0.04726935923099518, -0.02041708678007126, -0.020456086844205856, 0.0035003505181521177, 0.006327931769192219, 0.009179888293147087, -0.024395201355218887, -0.011203072033822536, 0.03432098776102066, 0.01571745239198208, -0.01722874492406845, 0.009955035522580147, 0.0039781141094863415, 0.0300893634557724, -0.018535282462835312, -0.053197529166936874, 0.019481059163808823, -0.004448565188795328, -0.027047276496887207, -0.01525918859988451, -0.017033739015460014, -0.009326143190264702, -0.0069714500568807125, -0.0005889778840355575, -0.004031740594655275, -0.0020792472641915083, 0.022815655916929245, -0.004780075047165155, 0.015093433670699596, 0.04875139892101288, -0.028841327875852585, -0.048361390829086304, -0.02332266978919506, 0.007970853708684444, 0.03566652536392212, 0.023303169757127762, 0.030440375208854675, 0.029679853469133377, 0.0005996422260068357, -0.0009329799213446677, -0.0037952964194118977, 0.007809974253177643, 0.07137204706668854, 0.0007976947817951441, 0.025662736967206, 0.037343572825193405, -0.011349325999617577, -0.005981796886771917, -0.025350729003548622, 0.03069388121366501, 0.018164772540330887, 0.01846703141927719, -0.003865986131131649, -0.007819724269211292, -0.0014759486075490713, -0.0300893634557724, -0.0031542156357318163, 0.06805695593357086, -0.0013138502836227417, 0.01664372719824314, 0.001427197246812284, -0.013611391186714172, 0.04648933559656143, -0.00777097325772047, -0.008307239040732384, 0.016185464337468147, 0.009009258821606636, 0.014410913921892643, -0.002399787772446871, -0.04918041452765465, 0.01871078833937645, 0.037636082619428635, 0.04360325261950493, 0.01180758886039257, -0.02494121715426445, 0.017482252791523933, -0.023576177656650543, 0.011261573061347008, -0.024551205337047577, 0.002305941190570593, 0.06922698765993118, 0.016897235065698624, -0.005903794430196285, -0.032214924693107605, -0.03898162022233009, -0.059515710920095444, -0.016477974131703377, 0.01180758886039257, -0.008594871498644352, -0.007171330973505974, 0.005333403125405312, -0.01839877851307392, 0.030167367309331894, 0.016087962314486504, 0.00892638135701418, 0.024141693487763405, -0.01019879337400198, -0.05315852537751198, 0.006420559249818325, 0.012109847739338875, -0.043954264372587204, 0.02628675475716591, 0.011359076015651226, 0.03307294845581055, -0.1041329950094223, 0.07355611026287079, 0.02390768751502037, -0.04828338697552681, -0.013981902040541172, -0.01594170741736889, 0.06224578991532326, -0.0212556105107069, 0.019412808120250702, -0.01518118567764759, -0.041887205094099045, 0.02244514413177967, -0.011778338812291622, -0.021021604537963867, -0.02671576663851738, 0.0411071814596653, -0.012275602668523788, -0.006795945111662149, -0.03151290491223335, -0.019081298261880875, -0.018613284453749657, 0.05534258857369423, -0.027027776464819908, -0.022932657971978188, -0.01857428438961506, -0.05382154509425163, -0.017306746914982796, 0.0330534502863884, -0.01657547615468502, -0.01136882696300745, 0.06774494796991348, -0.011905091814696789, -0.014313410967588425, -0.033365458250045776, -0.01343588624149561, -0.06544388085603714, 0.026891272515058517, 0.018233023583889008, 0.006513187196105719, -0.011417577974498272, 0.00634255725890398, -0.01525918859988451, 0.014508416876196861, -0.015278688631951809, 0.005777040962129831, 0.004504629410803318, -0.015132434666156769, -0.047893375158309937, -0.04325224086642265, 0.009501648135483265, -0.00840961653739214, -0.03209792077541351, -0.007600343320518732, 0.000019110168068436906, -0.017716258764266968, 0.026598764583468437, -0.04169219732284546, 0.019442059099674225, 0.033248454332351685, 0.016672978177666664, -0.046294331550598145, -0.03065488114953041, -0.00693244906142354, -0.03203941881656647, 0.01048155128955841, 0.03488650172948837, 0.05031144618988037, -0.0469573475420475, -0.012129348702728748, 0.02067059464752674, 0.016877735033631325, 0.009745405055582523, -0.02657926268875599, 0.046723343431949615, 0.003856235882267356, -0.015580947510898113, -0.021489616483449936, 0.02111910656094551, -0.02745678834617138, 0.036602552980184555, 0.05124747380614281, -0.017599254846572876, -0.04816638305783272, -0.02215263620018959, 0.017170242965221405, 0.019715066999197006, -0.017560254782438278, 0.030771883204579353, -0.013903899118304253, 0.051715485751628876, 0.032507434487342834, -0.008336489088833332, -0.002537510357797146, -0.01866203546524048, -0.029991861432790756, -0.01387464813888073, -0.04375925660133362, 0.016897235065698624, 0.006776444613933563, 0.021177608519792557, 0.00029342249035835266, 0.010813060216605663, 0.030498875305056572, 0.004351062700152397, 0.00027544540353119373, 0.041458189487457275, -0.01585395634174347, -0.0030908389016985893, 0.00972590409219265, 0.0007032389403320849, -0.005279776640236378, 0.010237794369459152, -0.06778394430875778, -0.018428029492497444, -0.03375547006726265, -0.012958122417330742, -0.0227571539580822, 0.02964085154235363, 0.030011361464858055, -0.049102410674095154, 0.006318181287497282, 0.03051837719976902, -0.018135521560907364, 0.013552889227867126, 0.03679755702614784, -0.02318616583943367, -0.05401655286550522, -0.007468714378774166, 0.005933045409619808, -0.03342396020889282, -0.012197600677609444, 0.02053409069776535, 0.010296295396983624, -0.015229937620460987, -0.019861320033669472, 0.014917928725481033, -0.05464056879281998, -0.03246843442320824, -0.04383726045489311, -0.024180695414543152, -0.1158333271741867, -0.05389954894781113, -0.03217592462897301, -0.047620367258787155, -0.003112776903435588, 0.025448231026530266, 0.029757855460047722, 0.011261573061347008, 0.03215642273426056, -0.004726448096334934, -0.011963593773543835, -0.019110549241304398, -0.014703422784805298, -0.02774929627776146, -0.0043169367127120495, 0.0705140233039856, -0.054367560893297195, -0.004943391773849726, -0.010598554275929928, 0.04001514986157417, 0.018476780503988266, 0.01166133489459753, 0.04446127638220787, 0.057604655623435974, -0.014674171805381775, 0.03759707883000374, -0.05062345415353775, -0.05506958067417145, 0.0028324562590569258, 0.04067816957831383, -0.027105778455734253, 0.00029997347155585885, 0.015444443561136723, 0.03385297209024429, 0.01167108491063118, -0.03272194042801857, 0.025331227108836174, 0.016253717243671417, -0.01635121926665306, 0.01422565896064043, -0.04001514986157417, -0.002834893995895982, -0.02934834361076355, -0.015883205458521843, 0.025623736903071404, -0.021918630227446556, 0.02860732190310955, -0.0034442865289747715, -0.0073078349232673645, -0.05179348960518837, -0.02392718754708767, -0.062128785997629166, -0.0005432734033092856, 0.0484393909573555, -0.03123989701271057, -0.02936784364283085, 0.02876332588493824, 0.02435619942843914, 0.0018781477119773626, -0.00920913927257061, 0.011095819063484669, -0.009881909005343914, -0.004646008368581533, 0.029309341683983803, -0.019598063081502914, -0.01049130130559206, 0.01828177459537983, 0.020319582894444466, -0.01269486453384161, 0.030888887122273445, 0.030264869332313538, -0.017930764704942703, 0.007351711392402649, 0.016702229157090187, 0.019890571013092995, -0.03812359645962715, -0.0012346291914582253, 0.0014771674759685993, 0.020612092688679695, 0.007819724269211292, 0.04134118929505348, -0.027632294222712517, 0.008863004855811596, -0.004043928813189268, 0.03549101948738098, -0.0352180115878582, -0.03223442658782005, -0.022542648017406464, -0.025584734976291656, -0.027476288378238678, -0.0013077562907710671, 0.014459664933383465, -0.005343153607100248, 0.03697306290268898, 0.03395047411322594, -0.06949999928474426, 0.02966035157442093, -0.06517086923122406, -0.02143111638724804, 0.012441357597708702, 0.02743728831410408, -0.014040403068065643, 0.015483444556593895, -0.03592003136873245, 0.01902279630303383, 0.022679151967167854, -0.05662962794303894, -0.004663071595132351, 0.003914737608283758, -0.006098800338804722, 0.0007196925580501556 ]
Monumental advancements in artificial intelligence (AI) have lured the interest of doctors, lenders, judges, and other professionals. While these high-stakes decision-makers are optimistic about the technology, those familiar with AI systems are wary about the lack of transparency of its decision-making processes. Perturbation-based post hoc explainers offer a model agnostic means of interpreting these systems while only requiring query-level access. However, recent work demonstrates that these explainers can be fooled adversarially. This discovery has adverse implications for auditors, regulators, and other sentinels. With this in mind, several natural questions arise - how can we audit these black box systems? And how can we ascertain that the auditee is complying with the audit in good faith? In this work, we rigorously formalize this problem and devise a defense against adversarial attacks on perturbation-based explainers. We propose algorithms for the detection (CAD-Detect) and defense (CAD-Defend) of these attacks, which are aided by our novel conditional anomaly detection approach, KNN-CAD. We demonstrate that our approach successfully detects whether a black box system adversarially conceals its decision-making process and mitigates the adversarial attack on real-world data for the prevalent explainers, LIME and SHAP.
[ -0.02841116115450859, -0.0401134230196476, -0.03259341046214104, -0.018669329583644867, 0.0518760047852993, 0.034382931888103485, -0.04162144660949707, 0.004290326498448849, -0.018810078501701355, 0.025214150547981262, -0.0016336919507011771, -0.03928903490304947, 0.022942062467336655, -0.04809589311480522, -0.02288174070417881, -0.008781722746789455, -0.0014137718826532364, -0.012235096655786037, 0.01959425024688244, -0.019413288682699203, -0.0068765864707529545, -0.03552903234958649, -0.0003374202351551503, 0.03987213969230652, 0.06357826292514801, 0.049583807587623596, 0.01934291422367096, -0.008012630976736546, -0.04644712060689926, 0.05686253681778908, 0.014828897081315517, 0.02632003463804722, 0.008103112690150738, -0.02404794655740261, -0.048417605459690094, -0.013079589232802391, 0.005831023678183556, 0.001038022805005312, 0.016246438026428223, 0.04938273876905441, 0.002489495323970914, -0.05046851560473442, 0.02290184795856476, 0.02253992296755314, -0.02159489504992962, -0.016306759789586067, -0.040274277329444885, -0.04942295327782631, 0.02276109904050827, 0.01968473196029663, -0.008424824103713036, -0.025535862892866135, 0.03209073841571808, -0.028833407908678055, 0.008646001107990742, 0.03526763990521431, 0.03784133493900299, -0.028089448809623718, 0.03223148733377457, -0.0012705096742138267, -0.0011844267137348652, 0.05268028378486633, -0.013622477650642395, 0.022218210622668266, 0.021072113886475563, -0.00654984824359417, 0.01756344549357891, 0.02748624049127102, -0.0365544855594635, 0.045924339443445206, -0.01316001731902361, -0.022338852286338806, -0.01767403446137905, 0.0017430237494409084, 0.0033050845377147198, -0.0013069536071270704, 0.008299155160784721, 0.02619939297437668, -0.010184184648096561, 0.020669974386692047, 0.034041114151477814, 0.032714053988456726, -0.0065397946164011955, 0.0007527550333179533, 0.09450279921293259, 0.00007438011380145326, -0.02053927816450596, -0.09458322823047638, 0.02617928571999073, -0.05871237814426422, 0.013431461527943611, -0.0005563977756537497, 0.015170715749263763, -0.04202358424663544, 0.005976799409836531, -0.0010110039729624987, -0.0023173291701823473, -0.025214150547981262, -0.03468453884124756, -0.0007571534370072186, -0.004742733668535948, 0.006519687827676535, 0.005710382014513016, 0.05058915913105011, 0.009153702296316624, -0.03643384575843811, -0.047573111951351166, 0.0008784236270003021, -0.019282592460513115, 0.2087908685207367, -0.062210991978645325, 0.017985692247748375, -0.030864212661981583, 0.004209898412227631, -0.028813300654292107, -0.0035011277068406343, -0.042144227772951126, -0.03840433061122894, 0.01551253441721201, -0.02109222114086151, -0.041902944445610046, 0.018216922879219055, 0.11010581254959106, 0.06329676508903503, -0.01815660111606121, 0.09032054990530014, 0.046286266297101974, 0.01102867815643549, 0.018950827419757843, 0.017171360552310944, -0.002319842576980591, 0.020911257714033127, 0.02947683073580265, -0.06164799630641937, 0.01874975673854351, 0.0053484560921788216, 0.03203041851520538, 0.07001250237226486, 0.020931364968419075, -0.016829540953040123, -0.004918669816106558, -0.03235212713479996, -0.04801546409726143, 0.0365343801677227, 0.002131339628249407, 0.02428922988474369, 0.006765998434275389, 0.05388670414686203, -0.06763987243175507, 0.051473863422870636, -0.033679187297821045, 0.01614590361714363, -0.0011454694904386997, -0.031065281480550766, 0.08316246420145035, 0.00791209563612938, 0.010174131020903587, 0.005564606282860041, 0.02229863964021206, -0.0330156572163105, 0.038163043558597565, -0.028692658990621567, -0.005041824653744698, 0.03587085008621216, 0.059154730290174484, 0.007927176542580128, -0.005524392239749432, -0.028370946645736694, -0.09297467023134232, 0.07025378197431564, 0.01150119211524725, -0.018096281215548515, -0.034262292087078094, 0.01186311710625887, -0.0009211509604938328, 0.03170870617032051, 0.04532112926244736, -0.0007383031188510358, -0.04150080308318138, -0.05268028378486633, -0.030964747071266174, -0.02099168486893177, 0.029275760054588318, -0.018357671797275543, -0.004134497605264187, 0.000004437672942003701, 0.10769297927618027, -0.03669523447751999, 0.03619256243109703, 0.05227814242243767, 0.000867113471031189, -0.014225686900317669, 0.011249854229390621, -0.029517045244574547, 0.0020911258179694414, -0.023987624794244766, 0.004109363537281752, -0.10777340829372406, -0.009661403484642506, -0.04162144660949707, -0.024952759966254234, -0.0636184811592102, 0.0036644968204200268, 0.03963085636496544, 0.016326867043972015, -0.00897273886948824, 0.01615595817565918, -0.012315524742007256, -0.030703356489539146, -0.021152541041374207, 0.003998775500804186, 0.004033962730318308, -0.026340141892433167, -0.040173742920160294, -0.04029438644647598, -0.0024517946876585484, -0.006695623975247145, -0.016125796362757683, -0.028752978891134262, -0.0017530771438032389, 0.01162183377891779, 0.0028451373800635338, 0.02372623421251774, 0.011551459319889545, 0.011239800602197647, -0.03478507325053215, 0.013200231827795506, 0.005479151848703623, -0.0034031060058623552, 0.022137783467769623, -0.05710382014513016, -0.022097568958997726, 0.011843010783195496, 0.017754461616277695, 0.03042185865342617, -0.002034574979916215, 0.022258425131440163, 0.012315524742007256, -0.007168137934058905, -0.03192988038063049, -0.05340413376688957, -0.004219952039420605, 0.008857124485075474, -0.05115215480327606, 0.05038808658719063, -0.019996389746665955, 0.00879680272191763, 0.04091770201921463, 0.05533440411090851, 0.02430933713912964, -0.013823547400534153, -0.002158986870199442, -0.012476379983127117, -0.015432106330990791, -0.04117909073829651, 0.018226975575089455, 0.05569633096456528, -0.023324094712734222, 0.039108071476221085, -0.014084938913583755, 0.028089448809623718, 0.015995102003216743, -0.004433588590472937, 0.05633975565433502, -0.05766681581735611, -0.019252432510256767, 0.054530125111341476, 0.017302054911851883, -0.013974349945783615, 0.019654572010040283, 0.029396401718258858, -0.038746148347854614, -0.02569671906530857, -0.042144227772951126, 0.008274021558463573, -0.010897981934249401, -0.007992523722350597, 0.002696848474442959, -0.016336919739842415, -0.027405811473727226, -0.02014719322323799, -0.06659431010484695, 0.027084100991487503, 0.004473802633583546, -0.011249854229390621, -0.046286266297101974, -0.020489010959863663, -0.004056582693010569, -0.0684441551566124, -0.016940129920840263, -0.030341431498527527, -0.004609524738043547, -0.0024216342717409134, 0.0020911258179694414, 0.028129663318395615, 0.0483371764421463, -0.029919184744358063, -0.015170715749263763, 0.042385511100292206, -0.04849803075194359, -0.07596416771411896, -0.05002616345882416, 0.02666185423731804, 0.0967547819018364, 0.005981826223433018, 0.03914828598499298, 0.017523230984807014, 0.0944223701953888, -0.013431461527943611, -0.004466262646019459, -0.0033302183728665113, 0.02052922546863556, -0.014657987281680107, -0.006092414725571871, -0.0412997342646122, 0.023746341466903687, 0.05223793163895607, -0.04588412493467331, 0.035770315676927567, -0.008490171283483505, 0.01590462028980255, 0.0007584100821986794, -0.07166127115488052, 0.011702261865139008, 0.019845588132739067, -0.031045174226164818, -0.0412595197558403, 0.05119236558675766, -0.03454378992319107, -0.009098407812416553, -0.07696951180696487, 0.041098665446043015, -0.03410143405199051, -0.02841116115450859, -0.029315974563360214, -0.009249210357666016, -0.03633331134915352, 0.02440987154841423, -0.025877680629491806, -0.019775213673710823, -0.013300766237080097, -0.027063993737101555, -0.0472111850976944, -0.03134677931666374, -0.014577559195458889, -0.05127279460430145, -0.004989044275134802, -0.035770315676927567, -0.0023738802410662174, -0.0019063928630203009, 0.0012767931912094355, -0.006992201786488295, -0.024148480966687202, -0.012818198651075363, 0.010098730213940144, -0.004989044275134802, -0.04202358424663544, -0.030844105407595634, 0.015070180408656597, 0.03802229464054108, 0.08223754167556763, -0.04266700893640518, -0.03739897906780243, 0.03359876200556755, -0.02217799797654152, -0.03786144033074379, -0.04053566977381706, 0.0159347802400589, -0.05847109481692314, 0.010475736111402512, -0.051594506949186325, 0.05119236558675766, -0.004028935916721821, 0.06402061879634857, 0.023303987458348274, 0.011440870352089405, -0.017292002215981483, -0.0059617189690470695, -0.04218444228172302, 0.0519162192940712, -0.058551520109176636, -0.036715343594551086, 0.038625504821538925, 0.022580137476325035, -0.06072307378053665, 0.027204742655158043, 0.01806611940264702, 0.012285363860428333, 0.04741225391626358, 0.04447663575410843, -0.004323000553995371, 0.018096281215548515, -0.013632531277835369, -0.07351111620664597, 0.034382931888103485, 0.0008105625747703016, 0.00785177480429411, -0.020468903705477715, 0.05316285043954849, -0.06872565299272537, 0.015371785499155521, 0.02264045737683773, -0.047693751752376556, 0.023505058139562607, -0.02145414613187313, 0.031306564807891846, 0.0123858992010355, -0.023505058139562607, 0.023786555975675583, 0.01303937565535307, 0.0012541727628558874, -0.0019365533953532577, -0.019433394074440002, -0.0055193654261529446, 0.014497131109237671, 0.020951472222805023, -0.01696023717522621, -0.009766965173184872, 0.034604109823703766, -0.0006804955773986876, 0.008349423296749592, 0.018779918551445007, 0.013210284523665905, -0.04043513536453247, -0.004674872383475304, 0.006147708743810654, -0.007886962033808231, 0.003197009675204754, 0.023022489622235298, -0.0023286393843591213, 0.0731491893529892, 0.026219500228762627, -0.02003660425543785, -0.0277275238186121, -0.035931169986724854, 0.009048140607774258, -0.011541405692696571, -0.048055678606033325, -0.021856285631656647, -0.010048462077975273, -0.010234451852738857, 0.0005793322925455868, -0.004282786510884762, 0.05199664831161499, -0.06188927963376045, -0.0589938759803772, -0.004453695844858885, -0.04107855632901192, -0.016065476462244987, -0.0038002189248800278, -0.09015969187021255, -0.01900109462440014, -0.07391325384378433, -0.0329955518245697, 0.019986337050795555, 0.010355093516409397, -0.00501669105142355, -0.05493226647377014, 0.039791710674762726, -0.042385511100292206, -0.01102867815643549, 0.08058877289295197, 0.014286008663475513, -0.012456273660063744, 0.019413288682699203, 0.01676921918988228, -0.03729844465851784, -0.04692968726158142, 0.027285169810056686, -0.0011611779918894172, 0.051232580095529556, 0.014607720077037811, -0.0008652284159325063, 0.026983564719557762, 0.009113487787544727, 0.010546110570430756, 0.018689436838030815, -0.009173808619379997, 0.03987213969230652, -0.002807436976581812, 0.024791903793811798, 0.005775729659944773, -0.026259714737534523, -0.02113243378698826, 0.004702519625425339, -0.007504929788410664, 0.027546560391783714, -0.004255139268934727, -0.08235818147659302, -0.06583024561405182, -0.03313630074262619, -0.03263362497091293, 0.024007732048630714, -0.02973822131752968, 0.005099632311612368, 0.0012359508546069264, -0.016236385330557823, -0.010867821983993053, 0.06028072163462639, 0.060079652816057205, 0.01817670837044716, -0.02203724905848503, -0.025435328483581543, -0.03872603923082352, 0.028974156826734543, -0.0035890957806259394, -0.02442997880280018, 0.03866571933031082, 0.04918166995048523, 0.002872784622013569, 0.015231036581099033, -0.05432905629277229, 0.013019268400967121, 0.011320228688418865, -0.003792678937315941, -0.030763676390051842, 0.016417348757386208, 0.021615002304315567, 0.006182895973324776, -0.010395308025181293, 0.03916839510202408, -0.06052200496196747, 0.012999162077903748, 0.04552219808101654, -0.012486433610320091, 0.03514700010418892, 0.044154923409223557, -0.005966745782643557, 0.02879319339990616, -0.03665502369403839, 0.003905780613422394, 0.07166127115488052, -0.007037442643195391, -0.012958947569131851, 0.030100146308541298, -0.0007483566296286881, 0.01875981129705906, 0.031789131462574005, -0.021615002304315567, -0.0007791453972458839, -0.06751923263072968, 0.04423535242676735, 0.03217116743326187, 0.03707726672291756, -0.0009312044712714851, 0.023384416475892067, 0.018478313460946083, -0.017844943329691887, 0.014959592372179031, 0.005034284666180611, 0.012305471114814281, 0.013260552659630775, -0.019905908033251762, -0.0032598439138382673, 0.016598310321569443, -0.010636591352522373, -0.02406805381178856, 0.02642056904733181, -0.00548920501023531, -0.021313397213816643, -0.020106978714466095, -0.017070824280381203, 0.01221498940140009, 0.028873620554804802, -0.02171553671360016, -0.043551716953516006, 0.016688792034983635, 0.07085699588060379, -0.015019913204014301, 0.01661841757595539, -0.028752978891134262, -0.009415092878043652, -0.014728361740708351, -0.0017719274619594216, 0.0002862102701328695, 0.037921760231256485, 0.01897093467414379, -0.015341624617576599, 0.00312663521617651, 0.012054133228957653, -0.035669781267642975, -0.0029180252458900213, -0.005614873953163624, 0.029054583981633186, 0.0067458911798894405, -0.0094452528283, -0.02087104320526123, -0.005182573571801186, -0.0015356704825535417, 0.01755339279770851, 0.0025523295626044273, 0.04351150244474411, 0.006836372893303633, 0.0135722104460001, 0.03160817176103592, 0.02312302589416504, 0.050187017768621445, 0.005454017780721188, 0.005876264534890652, -0.009575948119163513, 0.01227531023323536, -0.0059013981372118, 0.06381954997777939, 0.03735876455903053, 0.005423857364803553, 0.0074948761612176895, -0.0015419538831338286, 0.017271894961595535, -0.0004888509283773601, -0.023404523730278015, -0.0030537473503500223, -0.01746291108429432, 0.0070474958047270775, -0.038846682757139206, 0.049543596804142, -0.02499297447502613, 0.022801313549280167, -0.026722174137830734, 0.015190822072327137, -0.010038409382104874, 0.04845781996846199, -0.004684926010668278, 0.07596416771411896, -0.014728361740708351, 0.030984854325652122, 0.049583807587623596, -0.026702066883444786, -0.0029280786402523518, 0.00020405442046467215, 0.0241886954754591, -0.02358548529446125, -0.007816587574779987, -0.021152541041374207, -0.0003616114554461092, -0.005167493596673012, 0.006464393809437752, 0.01056621689349413, 0.04962402209639549, 0.019503768533468246, 0.0015243602683767676, -0.00932461116462946, -0.0318695604801178, -0.04166166111826897, 0.07290790230035782, -0.020368369296193123, 0.002236901316791773, 0.013763226568698883, -0.011601726524531841, 0.03020068258047104, 0.012828252278268337, -0.015974994748830795, 0.011933491565287113, -0.005941612180322409, 0.024007732048630714, -0.004732680041342974, -0.016457561403512955, 0.03605181351304054, 0.00808803178369999, 0.03707726672291756, -0.003875620197504759, 0.02428922988474369, -0.019724946469068527, 0.020338209345936775, 0.014286008663475513, -0.0035790421534329653, -0.018950827419757843, 0.012848359532654285, 0.002341206418350339, -0.005715408828109503, 0.08420802652835846, -0.0165279358625412, 0.009405039250850677, -0.04672861844301224, 0.052197717130184174, 0.03032132424414158, 0.007580331061035395, 0.027325384318828583, 0.019533930346369743, 0.005896371323615313, -0.024470193311572075, -0.023846875876188278, 0.015753816813230515, -0.0038354061543941498, 0.025857575237751007, -0.07009292393922806, 0.005479151848703623, -0.011692208237946033, 0.028370946645736694, 0.019905908033251762, -0.049221884459257126, 0.018548687919974327, -0.0026867950800806284, 0.013944189995527267, -0.006092414725571871, -0.013109750114381313, -0.025917895138263702, -0.04532112926244736, -0.05597782880067825, 0.03394057974219322, -0.008505252189934254, -0.017764516174793243, 0.029657794162631035, -0.0075903842225670815, 0.043109361082315445, -0.028109556064009666, -0.02101179212331772, 0.01085776835680008, -0.005921505391597748, -0.0023160725831985474, -0.01145092397928238, 0.017503125593066216, 0.05593761429190636, -0.0012635979801416397, 0.008108139038085938, 0.00011490823817439377, 0.04419513791799545, 0.07419475167989731, -0.040957916527986526, -0.012536700814962387, 0.038746148347854614, 0.048296961933374405, 0.0025171423330903053, 0.00021332247706595808, -0.032854802906513214, -0.03558935225009918, 0.04869910329580307, -0.004184764809906483, 0.008867177180945873, -0.03701694682240486, -0.0064392597414553165, 0.03158806264400482, 0.0031769026536494493, -0.03446336090564728, 0.005554552655667067, -0.007716053165495396, -0.019986337050795555, 0.047010116279125214, 0.03928903490304947, 0.03749951347708702, 0.0032422502990812063, 0.0206498671323061, 0.000955709838308394, 0.020237673074007034, -0.04065630957484245, -0.004627118352800608, 0.019845588132739067, -0.009425146505236626, 0.024590834975242615, 0.006519687827676535, 0.02003660425543785, 0.022137783467769623, -0.0022632917389273643, 0.020127085968852043, -0.017844943329691887, -0.008480118587613106, 0.023645807057619095, -0.0030059933196753263, 0.0068112388253211975, 0.02442997880280018, -0.013662692159414291, -0.05316285043954849, 0.05911451578140259, -0.06261312961578369, -0.0008928755414672196, 0.07246555387973785, -0.015371785499155521, -0.003214603289961815, -0.019865695387125015, 0.03848475590348244, -0.015894565731287003, 0.01794547773897648, -0.0008545466116629541, 0.014155312441289425, -0.02111232839524746, 0.0009513114346191287, -0.015894565731287003, 0.043350644409656525, -0.009314557537436485, -0.005916478578001261, 0.00778642762452364, 0.01309969648718834, 0.011360443197190762, -0.032472770661115646, 0.019734999164938927, -0.01851852796971798, -0.005433910991996527, -0.025917895138263702, -0.04608519375324249, -0.007977443747222424, 0.04930230975151062, -0.005886318162083626, -0.02286163531243801, 0.03581053018569946, -0.04387342557311058, 0.011531352065503597, 0.027767736464738846, -0.02690313756465912, 0.005509312264621258, 0.000165254226885736, -0.015321517363190651, 0.04043513536453247, -0.004772894084453583, 0.03492582216858864, -0.022459495812654495, 0.005343429744243622, -0.01639724150300026, 0.0020220079459249973, -0.007831668481230736, 0.011350389569997787, 0.028732871636748314, 0.06619217246770859, 0.03351833298802376, -0.0016977830091491342, 0.051956433802843094, 0.027325384318828583, -0.027265062555670738, 0.0067056771367788315, 0.010576270520687103, -0.02205735631287098, -0.02089115045964718, -0.0400531031191349, -0.02463104948401451, 0.014949538744986057, -0.017754461616277695, -0.027325384318828583, -0.02053927816450596, 0.031447313725948334, -0.006348778493702412, 0.020076818764209747, -0.012416059151291847, -0.0032070630695670843, 0.046165622770786285, -0.013692852109670639, 0.029919184744358063, -0.033779725432395935, 0.01480878982692957, -0.029034476727247238, -0.003998775500804186, 0.041118770837783813, -0.007037442643195391, -0.004888508934527636, 0.002925565466284752, 0.0038127857260406017, -0.022137783467769623, 0.0030663141515105963, 0.006715730763971806, -0.011129212565720081, -0.04894038662314415, -0.020458851009607315, 0.009113487787544727, 0.00897273886948824, -0.014517238363623619, -0.02274099364876747, -0.024349551647901535, -0.0002430116874165833, 0.013662692159414291, 0.019161950796842575, 0.008540439419448376, -0.014738415367901325, -0.039932459592819214, -0.029698006808757782, 0.015763871371746063, -0.017060771584510803, -0.023283882066607475, 0.044275566935539246, 0.002960752695798874, 0.014105045236647129, -0.049221884459257126, -0.0017870076699182391, -0.06205013766884804, -0.012295417487621307, -0.0011228490620851517, -0.03647406026721001, 0.01933285966515541, 0.009626216255128384, 0.01038525439798832, -0.003739898093044758, 0.011048784479498863, 0.03132667392492294, -0.008726428262889385, 0.006720757577568293, 0.01700044982135296, 0.025173937901854515, -0.028049234300851822, 0.009892633184790611, -0.01626654528081417, 0.002631500829011202, 0.0066704899072647095, -0.02111232839524746, -0.03335747867822647, -0.0014728361275047064, 0.03315640613436699, -0.023907197639346123, 0.004745246842503548, 0.03693651780486107, -0.0058259968645870686, 0.00014883876428939402, 0.00838460959494114, -0.009314557537436485, -0.02605864405632019, 0.005232841242104769, 0.02286163531243801, -0.015954887494444847, 0.00401385547593236, 0.005479151848703623, 0.026159178465604782, 0.015140554867684841, -0.031065281480550766, 0.03995256498456001, -0.01709093153476715, -0.016417348757386208, -0.03548881784081459, 0.00654984824359417, 0.007881935685873032, 0.029677899554371834, -0.049704451113939285, -0.039309144020080566, 0.010334987193346024, 0.015411999076604843, 0.00407166313380003, 0.048658888787031174, 0.05722445994615555, -0.015050073154270649, 0.0013949216809123755, -0.0019968743436038494, -0.006147708743810654, -0.02111232839524746, 0.03468453884124756, -0.023625699803233147, 0.029155118390917778, -0.027204742655158043, 0.01067680586129427, -0.023263774812221527, 0.019533930346369743, 0.004649738781154156, 0.07053527981042862, -0.07290790230035782, 0.03267383947968483, -0.029577365145087242, -0.03679576888680458, 0.0019440934993326664, -0.0078015075996518135, 0.02251981571316719, -0.02159489504992962, 0.026621639728546143, -0.035086676478385925, 0.06691602617502213, -0.004405941814184189, -0.01746291108429432, -0.004227492026984692, -0.03466442972421646, 0.006615195889025927, 0.010365147143602371, 0.0065397946164011955, -0.07294812053442001, -0.008364503271877766, -0.013813494704663754, -0.013622477650642395, 0.004451182205229998, 0.0330156572163105, 0.005122252739965916, 0.0005994393141008914, -0.017050717025995255, -0.01073712669312954, -0.034986142069101334, -0.011048784479498863, 0.007057549431920052, -0.04777418076992035, -0.027265062555670738, -0.025736931711435318, -0.007369207683950663, -0.016005154699087143, -0.027305277064442635, 0.03516710549592972, 0.06675516813993454, -0.01723168045282364, 0.014909324236214161, -0.031909774988889694, 0.005403750576078892, 0.00012119167513446882, 0.00956086814403534, -0.04491899162530899, -0.0013069536071270704, 0.04729161411523819, 0.011662047356367111, -0.01156151294708252, 0.04059598967432976, -0.0025812333915382624, -0.022499708458781242, 0.00931958481669426, -0.01837777905166149, -0.02629992738366127, -0.008927498012781143, -0.053001996129751205, -0.030341431498527527, 0.01522098295390606, 0.0016450021648779511, -0.01747296378016472, -0.011420764029026031, -0.0011712315026670694, -0.020710187032818794, 0.03812283277511597, 0.028813300654292107, 0.046648189425468445, -0.010304826311767101, 0.015653282403945923, 0.03965096175670624, -0.02217799797654152, -0.009108461439609528, 0.004978990647941828, -0.024812011048197746, 0.009043113328516483, -0.026601532474160194, 0.0707363486289978, -0.03717780485749245, 0.037439193576574326, -0.029878970235586166, 0.016548043116927147, -0.024228909984230995, 0.001557034207507968, 0.024832118302583694, -0.04612540826201439, 0.006318618077784777, -0.008279048837721348 ]
With the growing popularity of artificial intelligence and machine learning, a wide spectrum of attacks against deep learning models have been proposed in the literature. Both the evasion attacks and the poisoning attacks attempt to utilize adversarially altered samples to fool the victim model to misclassify the adversarial sample. While such attacks claim to be or are expected to be stealthy, i.e., imperceptible to human eyes, such claims are rarely evaluated. In this paper, we present the first large-scale study on the stealthiness of adversarial samples used in the attacks against deep learning. We have implemented 20 representative adversarial ML attacks on six popular benchmarking datasets. We evaluate the stealthiness of the attack samples using two complementary approaches: (1) a numerical study that adopts 24 metrics for image similarity or quality assessment; and (2) a user study of 3 sets of questionnaires that has collected 20,000+ annotations from 1,000+ responses. Our results show that the majority of the existing attacks introduce nonnegligible perturbations that are not stealthy to human eyes. We further analyze the factors that contribute to attack stealthiness. We further examine the correlation between the numerical analysis and the user studies, and demonstrate that some image quality metrics may provide useful guidance in attack designs, while there is still a significant gap between assessed image quality and visual stealthiness of attacks.
[ -0.03753754124045372, -0.04351439327001572, -0.019880319014191628, -0.010131491348147392, 0.058893851935863495, 0.04092685505747795, -0.04832502827048302, 0.010605266317725182, -0.0006981344777159393, 0.022868745028972626, -0.00844139140099287, -0.04858013987541199, 0.03012114390730858, -0.04376950114965439, -0.037829093635082245, 0.039031755179166794, 0.02503717504441738, -0.012053923681378365, -0.006550847552716732, -0.05572320520877838, 0.02111942321062088, -0.032016243785619736, -0.030886471271514893, -0.0027082606684416533, 0.001170770381577313, 0.05473921075463295, 0.03179757669568062, 0.010732821188867092, -0.030285142362117767, 0.04814280942082405, -0.026221612468361855, 0.009238608181476593, -0.007730728946626186, -0.007256954442709684, -0.010723710060119629, -0.007584952283650637, 0.032070908695459366, 0.06446981430053711, 0.015024127438664436, 0.06855157017707825, -0.0273878276348114, -0.08513368666172028, -0.010514155961573124, 0.019880319014191628, 0.00922949705272913, -0.05699875205755234, -0.018540995195508003, -0.03090469352900982, -0.009142942726612091, 0.026185167953372, -0.017629889771342278, -0.032435350120067596, -0.007908394560217857, 0.00943905208259821, -0.03680865839123726, 0.025128286331892014, 0.060716062784194946, -0.04176507145166397, 0.027788713574409485, 0.00038124065031297505, 0.003655810374766588, 0.0136939138174057, 0.029501592740416527, 0.00927960779517889, -0.03837575763463974, -0.04307706281542778, 0.05637919902801514, 0.002653594361618161, 0.02326963096857071, 0.015825901180505753, -0.06778623908758163, 0.01735655777156353, 0.02839004248380661, 0.016837228089571, -0.01840432919561863, -0.03294556960463524, 0.0017777943285182118, -0.0030453696381300688, -0.056852973997592926, 0.02780693583190441, 0.015716567635536194, 0.040853966027498245, -0.03168824315071106, 0.013502581976354122, 0.09096475690603256, -0.02394384890794754, -0.03870375454425812, -0.05947696045041084, -0.014951239340007305, -0.05065745860338211, 0.010723710060119629, 0.00137576914858073, 0.036407772451639175, -0.001707183662801981, -0.01762077771127224, 0.03790198266506195, -0.018422551453113556, -0.049527689814567566, -0.05922184884548187, 0.02028120495378971, 0.025529172271490097, 0.006373181939125061, 0.011279484257102013, 0.029355814680457115, -0.0009948131628334522, -0.029884256422519684, -0.04825213924050331, 0.012017480097711086, -0.0011525482404977083, 0.15350303053855896, -0.0198620967566967, 0.01212681271135807, -0.04198373481631279, -0.0034462560433894396, -0.0018620715709403157, 0.042056623846292496, -0.0643969252705574, -0.029465148225426674, -0.0016217675292864442, -0.02942870371043682, -0.027278494089841843, 0.09366162866353989, 0.01752055622637272, 0.06231960654258728, -0.06122628226876259, 0.08010438084602356, 0.029301147907972336, -0.012819252908229828, 0.02299629896879196, 0.001305158482864499, 0.008906055241823196, 0.007284287363290787, 0.015661900863051414, 0.0018768770387396216, 0.004263973329216242, 0.019114989787340164, 0.013493470847606659, 0.023725183680653572, 0.007666951511055231, 0.03633488342165947, -0.013584581203758717, -0.04223884642124176, -0.01562545634806156, 0.022030528634786606, -0.06829646229743958, -0.008482391014695168, 0.01620856486260891, 0.08819500356912613, -0.03001181036233902, 0.03775620833039284, -0.029720257967710495, 0.0156345684081316, 0.02786160260438919, 0.02660427615046501, 0.0026490387972444296, 0.0046739703975617886, 0.0017720999894663692, 0.0035054779145866632, 0.05462987720966339, -0.05247966945171356, 0.021028311923146248, -0.06815068423748016, 0.058529410511255264, 0.019880319014191628, 0.023925626650452614, 0.0016775727272033691, 0.046867258846759796, 0.046138375997543335, -0.04380594566464424, 0.06228316202759743, 0.06097117066383362, -0.04140062630176544, -0.026130501180887222, 0.018021663650870323, -0.007881061173975468, 0.021137645468115807, 0.036881543695926666, -0.029155371710658073, -0.03115980327129364, -0.018522772938013077, -0.04140062630176544, 0.05473921075463295, 0.031196247786283493, -0.040015749633312225, 0.004774192348122597, -0.017839442938566208, 0.049527689814567566, 0.017110558226704597, 0.029811367392539978, 0.008455057628452778, -0.025911835953593254, -0.006163627840578556, 0.0057946303859353065, -0.04930902272462845, 0.028772708028554916, 0.010386601090431213, -0.008505168370902538, -0.015488791279494762, 0.025346951559185982, -0.008828611113131046, -0.024946065619587898, -0.046867258846759796, 0.013520803302526474, -0.03750109672546387, -0.0005534965312108397, -0.04464416205883026, -0.010186158120632172, -0.008332058787345886, -0.03618910536170006, 0.010723710060119629, -0.009712383151054382, 0.019825652241706848, -0.09176653623580933, 0.029046040028333664, -0.03387489914894104, -0.02551095001399517, -0.005744519177824259, -0.024818509817123413, -0.00258753914386034, -0.0034758669789880514, -0.01152548287063837, 0.014914794825017452, -0.010222602635622025, -0.03597043827176094, -0.0547756552696228, -0.017119670286774635, 0.028517598286271095, 0.0186594370752573, -0.004275362007319927, -0.005940407048910856, -0.02760649286210537, -0.055030763149261475, 0.022394970059394836, -0.004286750685423613, 0.04799703136086464, -0.02576605975627899, -0.006614624988287687, 0.027624715119600296, 0.02995714545249939, -0.017702776938676834, 0.001963432179763913, -0.07369020581245422, 0.004869858268648386, -0.03143313527107239, 0.028790930286049843, 0.0003721296088770032, -0.009849049150943756, -0.009839938022196293, 0.02028120495378971, 0.001953182043507695, 0.002048848196864128, 0.0076851737685501575, -0.05364588275551796, 0.06344937533140182, -0.07409109175205231, 0.008723833598196507, 0.026330946013331413, -0.02310563251376152, 0.04114551842212677, -0.042165957391262054, 0.0595862902700901, -0.012199700810015202, -0.06184583157300949, 0.08141637593507767, -0.03549666702747345, 0.01168037112802267, 0.06665647029876709, 0.004471249412745237, 0.010514155961573124, 0.012035702355206013, -0.03272690623998642, -0.0022367637138813734, -0.04766903445124626, 0.012646142393350601, -0.02729671634733677, -0.00420930702239275, 0.018632104620337486, 0.001319963950663805, -0.00943905208259821, -0.03695443272590637, 0.02290518954396248, -0.028608709573745728, 0.02895492874085903, -0.0007829811656847596, 0.030777139589190483, -0.014677907340228558, -0.0084186140447855, -0.028353599831461906, -0.05320855230093002, 0.008591723628342152, -0.035733550786972046, -0.01809455268085003, -0.03511400148272514, -0.005585075821727514, 0.02117408812046051, 0.0039450861513614655, -0.018495438620448112, 0.022230971604585648, -0.00048601775779388845, -0.035478442907333374, -0.10678154975175858, -0.023870959877967834, 0.013602803461253643, 0.042749062180519104, -0.008947054855525494, -0.007238732185214758, 0.03001181036233902, 0.0715399906039238, -0.043842390179634094, -0.03994286060333252, -0.009694160893559456, -0.006505292374640703, -0.0030180364847183228, -0.026203390210866928, -0.02388918213546276, 0.02170252986252308, -0.004045307636260986, -0.0037924761418253183, 0.002644483232870698, 0.01798521913588047, -0.027788713574409485, 0.03228957578539848, -0.06479781121015549, -0.013420581817626953, -0.035150445997714996, -0.047341033816337585, -0.035478442907333374, 0.01772099919617176, -0.0806146040558815, -0.004514527041465044, -0.019625209271907806, -0.013584581203758717, -0.07081110775470734, -0.01510612666606903, 0.03476778045296669, 0.049746353179216385, -0.026731831952929497, 0.014231465756893158, 0.014605019241571426, 0.0005198994767852128, -0.013211027719080448, -0.031342025846242905, -0.0421295128762722, -0.01506057195365429, 0.006646513473242521, -0.03125091269612312, -0.030248697847127914, -0.017265446484088898, 0.0009703272371552885, -0.009197608567774296, 0.0010272712679579854, -0.0015762122347950935, -0.04719525948166847, 0.006341293454170227, -0.013903467915952206, -0.008436835370957851, 0.023652294650673866, -0.006723957601934671, 0.004938191268593073, -0.0408904105424881, 0.03294556960463524, -0.06133561208844185, 0.0020978201646357775, 0.013065250590443611, -0.01657300628721714, -0.061044059693813324, -0.03418467193841934, 0.03283623605966568, 0.02623983472585678, 0.020117206498980522, 0.013511693105101585, 0.010386601090431213, -0.035988662391901016, 0.04981924220919609, -0.0021422365680336952, -0.04752325639128685, -0.011917258612811565, -0.002683205297216773, -0.04395172372460365, 0.04234817624092102, -0.020463427528738976, 0.018231218680739403, 0.04825213924050331, 0.027843380346894264, -0.034694891422986984, 0.030886471271514893, 0.02002609521150589, 0.0041614738292992115, 0.031542468816041946, 0.04941835626959801, 0.022303858771920204, 0.011033485643565655, -0.0069244010373950005, 0.014677907340228558, 0.04099974036216736, 0.0043004173785448074, 0.02735138311982155, -0.020609203726053238, -0.0016069620614871383, -0.07543952763080597, -0.030175810679793358, 0.040234412997961044, -0.01693744957447052, 0.011060819029808044, -0.012236145325005054, 0.015197237953543663, -0.019880319014191628, -0.03511400148272514, -0.005799185484647751, -0.05379166081547737, -0.0004857330641243607, -0.01893276907503605, -0.031506024301052094, -0.006532625295221806, -0.01803988590836525, 0.040744632482528687, -0.01149814948439598, -0.021374531090259552, 0.018167441710829735, -0.03556955233216286, 0.036990877240896225, 0.0038995309732854366, 0.04209306836128235, -0.04847080633044243, -0.03739176318049431, -0.0031296468805521727, -0.01641811802983284, -0.004696748219430447, 0.044206831604242325, -0.04690370336174965, 0.02808026783168316, -0.013675691559910774, 0.00966682843863964, -0.042056623846292496, -0.0008154393290169537, -0.03648065775632858, 0.03054025210440159, 0.0029907033313065767, -0.010541489347815514, -0.026203390210866928, -0.019898541271686554, -0.003341478994116187, 0.009270497597754002, 0.03407534211874008, -0.08003149926662445, -0.072159543633461, 0.010304601863026619, -0.011981035582721233, -0.04304061830043793, 0.009265941567718983, -0.10277268290519714, 0.06676580011844635, -0.08695589751005173, -0.0352233350276947, 0.024180736392736435, -0.031196247786283493, -0.019169656559824944, -0.056014757603406906, 0.0027447049506008625, -0.04967346414923668, 0.029355814680457115, 0.062392495572566986, 0.011935479938983917, -0.009475495666265488, 0.0006446070619858801, 0.031014027073979378, -0.04355083778500557, 0.0027424271684139967, 0.008983499370515347, 0.008541612885892391, -0.04161929339170456, -0.004906302317976952, -0.009940159507095814, 0.00694262282922864, 0.011470817029476166, 0.013247472234070301, -0.022595413029193878, -0.05087612569332123, 0.03812064975500107, -0.028171377256512642, 0.04052596539258957, 0.025128286331892014, -0.043149951845407486, -0.028681596741080284, 0.013785024173557758, 0.008377613499760628, 0.025693170726299286, -0.02022654004395008, -0.018859881907701492, -0.07190443575382233, -0.04591970890760422, -0.03068602830171585, 0.04220240190625191, -0.0025260397233068943, -0.028572265058755875, -0.000605885055847466, 0.01385791227221489, -0.023962071165442467, 0.07645995914936066, 0.036626435816287994, 0.011361484415829182, -0.04366016760468483, -0.005188744980841875, 0.02682294137775898, 0.06002362072467804, 0.000013239499821793288, -0.0018506827764213085, 0.0038198092952370644, 0.07369020581245422, 0.027752269059419632, 0.008609945885837078, 0.01510612666606903, 0.004970079753547907, -0.0074391751550138, -0.0144319087266922, 0.04103618487715721, 0.01311991736292839, -0.003767420770600438, 0.019934985786676407, 0.03719132021069527, 0.0016969337593764067, -0.021939417347311974, -0.020937200635671616, 0.021319866180419922, 0.006295738276094198, 0.07740750908851624, 0.054083213210105896, -0.014978572726249695, -0.014750796370208263, -0.05488498881459236, 0.00288820406422019, 0.014823684468865395, -0.02352474071085453, -0.005020190495997667, 0.0034576449543237686, 0.017793888226151466, -0.01557990163564682, 0.03815709426999092, -0.02562028355896473, -0.0025807060301303864, -0.013129028491675854, 0.017839442938566208, -0.011261261999607086, -0.017766553908586502, 0.00953927356749773, -0.0014384075766429305, 0.017274558544158936, -0.04967346414923668, -0.003081813920289278, -0.005557742901146412, 0.02321496419608593, -0.001267575309611857, 0.008555279113352299, -0.016664117574691772, -0.017229001969099045, 0.009730605408549309, 0.008751166984438896, 0.07602263242006302, -0.016026344150304794, -0.018112774938344955, -0.02875448577105999, -0.01834966242313385, 0.006245627533644438, 0.026203390210866928, 0.003915475215762854, -0.04730458930134773, -0.01327480562031269, 0.0805417150259018, -0.01975276507437229, 0.020900757983326912, -0.010751043446362019, -0.020663870498538017, -0.017757443711161613, -0.030139366164803505, 0.018950991332530975, -0.0216478630900383, 0.028462931513786316, -0.04668503999710083, -0.011388816870748997, 0.026075836271047592, 0.00423436239361763, 0.004218417685478926, -0.03168824315071106, 0.005571409128606319, -0.010915041901171207, 0.01975276507437229, -0.03216201812028885, -0.007881061173975468, -0.027588270604610443, 0.010022158734500408, 0.022504301741719246, 0.067348912358284, -0.0426761768758297, 0.0026034836191684008, -0.005234300158917904, 0.014331687241792679, 0.0333646796643734, 0.0006787735037505627, 0.028171377256512642, 0.012482143938541412, -0.01819477416574955, 0.02388918213546276, 0.05809208005666733, 0.07973994314670563, 0.016062786802649498, -0.01814010739326477, -0.018130997195839882, 0.04617482051253319, -0.0370091013610363, 0.0047104149125516415, 0.019479433074593544, -0.018258551135659218, 0.02305096574127674, -0.04278550669550896, 0.015461457893252373, 0.020062539726495743, 0.02212163805961609, 0.01584412157535553, 0.010896820574998856, -0.02598472498357296, 0.02937403693795204, -0.023142077028751373, 0.040489520877599716, 0.043842390179634094, 0.029082482680678368, 0.05637919902801514, 0.00023873808095231652, 0.01244569942355156, 0.008459613658487797, -0.011033485643565655, -0.03538733348250389, -0.008213615044951439, -0.017802998423576355, 0.019060324877500534, -0.02645849995315075, 0.01767544448375702, 0.06060672923922539, -0.0026991497725248337, -0.028353599831461906, -0.0024668178521096706, 0.01944298855960369, 0.006714846473187208, -0.0136939138174057, 0.039141084998846054, -0.00534818833693862, 0.030704250559210777, 0.0027743158861994743, -0.000008038903615670279, -0.002626261208206415, 0.037154875695705414, 0.024399401620030403, 0.03628021478652954, 0.006040628533810377, 0.01589878834784031, -0.013156361877918243, -0.01714700274169445, 0.050730347633361816, 0.0352233350276947, 0.059367626905441284, 0.002201458439230919, 0.03874019905924797, -0.013375027105212212, -0.0029018705245107412, 0.009639495052397251, 0.014486575499176979, 0.017602555453777313, 0.031141581013798714, 0.00475597009062767, -0.004257139749825001, 0.04599259793758392, 0.00967593863606453, -0.011042596772313118, -0.048543695360422134, 0.02676827646791935, 0.024089625105261803, -0.014322576113045216, 0.0321984626352787, 0.027114495635032654, 0.023014521226286888, 0.0034485338255763054, -0.017074115574359894, 0.006541736423969269, 0.00045754574239254, 0.0009600772755220532, -0.017921442165970802, -0.018386106938123703, 0.0015044627944007516, 0.03852153569459915, -0.0136939138174057, -0.06567247211933136, 0.0037651429884135723, -0.03177935630083084, 0.001982792979106307, -0.006218294147402048, 0.018285885453224182, 0.009001720696687698, -0.028845595195889473, -0.04559171199798584, -0.004245751071721315, -0.01453213021159172, -0.020882535725831985, 0.01641811802983284, -0.067348912358284, 0.0373188741505146, 0.006464292760938406, 0.011079041287302971, 0.01725633628666401, 0.005548631772398949, -0.005170523189008236, 0.03048558533191681, -0.011151929385960102, 0.052734777331352234, 0.04679437354207039, 0.03895886614918709, 0.021246977150440216, 0.012536809779703617, 0.039031755179166794, -0.00022848814842291176, 0.017001226544380188, 0.05484854429960251, 0.060096509754657745, 0.02500073052942753, 0.02368873916566372, -0.07565818727016449, -0.024235403165221214, 0.024435846135020256, -0.037355318665504456, -0.01782122068107128, -0.06293915957212448, 0.0045646377839148045, 0.05404677242040634, -0.05171434208750725, -0.034640226513147354, 0.01506057195365429, -0.002906426088884473, -0.006313960067927837, 0.001843849546276033, 0.018285885453224182, 0.037100210785865784, -0.023706961423158646, -0.007143066264688969, -0.022103415802121162, 0.01752055622637272, -0.0012163256760686636, 0.02383451722562313, 0.04406105726957321, 0.008696501143276691, 0.012208811938762665, -0.0010409378446638584, 0.027934489771723747, 0.047596145421266556, -0.05426543578505516, 0.04271262139081955, -0.056743644177913666, -0.021684307605028152, -0.007744395639747381, -0.001788044348359108, 0.031870465725660324, -0.0029087038710713387, -0.008318391628563404, -0.020299427211284637, 0.049017470329999924, 0.02833537757396698, 0.012536809779703617, 0.06636491417884827, 0.0011377428891137242, -0.014058356173336506, -0.008427724242210388, 0.006865179166197777, 0.004528193734586239, 0.04664859548211098, 0.008113393560051918, 0.025383396074175835, -0.025182953104376793, -0.05258900299668312, 0.0037446431815624237, 0.041509959846735, -0.049855686724185944, -0.030102921649813652, 0.01933365687727928, -0.023196741938591003, 0.01605367660522461, -0.01082393154501915, 0.05809208005666733, -0.031560689210891724, 0.022814078256487846, 0.005389188416302204, 0.002851759782060981, -0.026750054210424423, 0.02953803539276123, -0.03258112818002701, 0.002242458052933216, 0.0050611901096999645, -0.0024121515452861786, 0.024873176589608192, 0.006323071196675301, -0.028062045574188232, 0.037464652210474014, -0.02086431346833706, -0.04063529893755913, 0.05247966945171356, 0.009484606795012951, 0.0021388197783380747, 0.002268652431666851, -0.02682294137775898, -0.04227529093623161, -0.0071476218290627, 0.023342519998550415, 0.0021399587858468294, 0.010495933704078197, 0.039651304483413696, 0.0038562535773962736, -0.029246482998132706, 0.025583839043974876, -0.027333160862326622, -0.002778871450573206, 0.01678256131708622, 0.022449636831879616, 0.0017664055339992046, -0.058529410511255264, -0.008213615044951439, -0.02755182608962059, 0.017894109711050987, -0.04161929339170456, -0.06272049248218536, -0.004505415912717581, 0.025547394528985023, -0.01139792799949646, -0.000013488630429492332, 0.026895830407738686, -0.008404946886003017, 0.017420334741473198, -0.04464416205883026, 0.04949124529957771, -0.029446925967931747, 0.04103618487715721, -0.01194459106773138, 0.017283668741583824, -0.02702338621020317, 0.004769636783748865, 0.017966998741030693, 0.022303858771920204, -0.0011650760425254703, -0.02461806684732437, 0.008969832211732864, 0.011698593385517597, -0.03815709426999092, 0.020736757665872574, 0.006067961920052767, 0.017475001513957977, 0.014340798370540142, 0.011015264317393303, 0.039031755179166794, 0.0084186140447855, 0.010286379605531693, -0.017156114801764488, 0.002129708882421255, 0.031706467270851135, -0.0619187206029892, -0.024964287877082825, -0.007940283045172691, 0.0595134012401104, 0.012227034196257591, 0.018950991332530975, 0.0475597009062767, 0.0023460963275283575, -0.023652294650673866, -0.031815800815820694, 0.002658149925991893, -0.05364588275551796, -0.005462076514959335, -0.025474505499005318, -0.038776643574237823, 0.031068693846464157, 0.014778128825128078, 0.0007260370766744018, -0.0228505227714777, -0.005876629613339901, -0.017602555453777313, -0.016700562089681625, -0.0044097499921917915, -0.01709233596920967, 0.03518689051270485, -0.023870959877967834, -0.003947364166378975, -0.047924142330884933, -0.008423169143497944, -0.00037753928336314857, -0.021994084119796753, -0.0062684048898518085, 0.0010352435056120157, -0.0020442926324903965, -0.015051460824906826, 0.04621126502752304, 0.04533660411834717, 0.0029497037176042795, 0.011753259226679802, -0.01464146375656128, -0.02290518954396248, -0.008386724628508091, 0.007270620670169592, 0.019206101074814796, 0.03227135166525841, -0.017420334741473198, 0.0024690956342965364, 0.07864661514759064, -0.016117453575134277, -0.019588764756917953, 0.02891848422586918, -0.0018689049175009131, -0.008801277726888657, -0.04344150424003601, -0.03750109672546387, 0.008031393401324749, 0.04427972063422203, -0.007890172302722931, -0.014377242885529995, -0.023962071165442467, 0.021611418575048447, 0.01531568169593811, 0.024636289104819298, 0.008058726787567139, -0.03360156714916229, 0.02055453695356846, -0.016591228544712067, 0.00009118171874433756, 0.0006235377513803542, 0.036626435816287994, -0.021738974377512932, 0.059877846390008926, -0.0013974078465253115, 0.03423934057354927, 0.02467273361980915, 0.011060819029808044, 0.03884953260421753, -0.008564390242099762, -0.04930902272462845, 0.055868979543447495, -0.07886528223752975, -0.023287853226065636, -0.005917629227042198, -0.016755226999521255, 0.002129708882421255, -0.013584581203758717, 0.008701056241989136, -0.04595615342259407, 0.0511312335729599, 0.010259046219289303, -0.03196157515048981, -0.002835815539583564, -0.02818959951400757, -0.007361731491982937, 0.01793055422604084, 0.010887709446251392, -0.051422785967588425, 0.01740211248397827, -0.005575964692980051, -0.011725925840437412, -0.0032731459941715, 0.0030909250490367413, -0.012454810552299023, -0.009502829052507877, -0.028043823316693306, 0.012801030650734901, -0.03675398975610733, -0.002022653818130493, -0.022340303286910057, -0.029137149453163147, -0.0012037979904562235, -0.01793055422604084, 0.005717186257243156, -0.043842390179634094, -0.02567494846880436, 0.0009447023621760309, 0.05258900299668312, 0.008218170143663883, 0.022194527089595795, -0.03434867411851883, 0.010887709446251392, 0.016281453892588615, 0.012135923840105534, -0.008450502529740334, -0.021939417347311974, 0.0363895483314991, 0.02184830605983734, -0.044352609664201736, 0.020408760756254196, -0.014978572726249695, -0.06414181739091873, 0.04402461275458336, 0.02321496419608593, -0.04992857575416565, 0.0020044317934662104, -0.0025510950945317745, -0.0397241935133934, -0.00799494981765747, -0.031014027073979378, -0.00635040458291769, 0.016609450802206993, 0.016901005059480667, -0.0154796801507473, 0.002767482539638877, -0.013238361105322838, 0.04129129648208618, 0.013457026332616806, 0.029610924422740936, 0.05441121384501457, -0.043368615210056305, -0.02593005821108818, -0.0043710279278457165, -0.01929721236228943, -0.02623983472585678, 0.005165967624634504, 0.022704746574163437, 0.020846091210842133, 0.03391134366393089, -0.06326715648174286, 0.018021663650870323, -0.0026604277081787586, -0.00876027811318636, 0.05871162936091423, -0.014103910885751247, 0.022230971604585648, 0.0006565653020516038 ]
The problem of interpreting or aggregating multiple rankings is common to many real-world applications. Perhaps the simplest and most common approach is a weighted rank aggregation, wherein a (convex) weight is applied to each input ranking and then ordered. This paper describes a new tool for visualizing and displaying ranking information for the weighted rank aggregation method. Traditionally, the aim of rank aggregation is to summarize the information from the input rankings and provide one final ranking that hopefully represents a more accurate or truthful result than any one input ranking. While such an aggregated ranking is, and clearly has been, useful to many applications, it also obscures information. In this paper, we show the wealth of information that is available for the weighted rank aggregation problem due to its structure. We apply weight set decomposition to the set of convex multipliers, study the properties useful for understanding this decomposition, and visualize the indifference regions. This methodology reveals information--that is otherwise collapsed by the aggregated ranking--into a useful, interpretable, and intuitive decision support tool. Included are multiple illustrative examples, along with heuristic and exact algorithms for computing the weight set decomposition.
[ -0.027238257229328156, -0.014262480661273003, -0.04269682988524437, 0.007869736291468143, 0.013093573041260242, -0.030717795714735985, 0.0060302927158772945, 0.020152322947978973, -0.0503445640206337, 0.00721732247620821, 0.015358897857367992, -0.03581024333834648, 0.019083090126514435, -0.04813360795378685, -0.08046431094408035, 0.0015347570879384875, 0.03528468683362007, 0.01814071461558342, 0.024048680439591408, -0.03352679684758186, -0.01783263124525547, 0.014606810174882412, -0.03823867067694664, 0.03430606797337532, 0.03015599399805069, 0.03318246826529503, -0.0033073732629418373, -0.026658333837985992, -0.10880804806947708, 0.06850340217351913, 0.01902872323989868, 0.004353953059762716, -0.015105181373655796, -0.016600295901298523, -0.061943020671606064, 0.01398158073425293, 0.055056437849998474, 0.0556001141667366, 0.02321504056453705, 0.06933704018592834, -0.07857955992221832, -0.024229906499385834, 0.0022483342327177525, -0.00441964715719223, -0.00820047315210104, -0.013410719111561775, 0.007588835898786783, 0.034722886979579926, 0.00824124924838543, -0.05904340744018555, 0.025226648896932602, -0.05030831694602966, 0.01004897803068161, -0.02765507623553276, 0.013193247839808464, 0.04675628989934921, -0.008639946579933167, 0.004566893447190523, 0.039869703352451324, -0.006333846133202314, -0.00426787044852972, 0.031913887709379196, -0.10453111678361893, -0.01973550394177437, 0.036988213658332825, -0.06158057227730751, 0.018919987604022026, 0.004159135278314352, -0.02729262411594391, 0.0028225937858223915, -0.04327675327658653, 0.01573041081428528, -0.004331299569457769, -0.014516197144985199, -0.033363692462444305, 0.03474101051688194, 0.030717795714735985, -0.09242521971464157, -0.034106720238924026, 0.04255184903740883, -0.03907230868935585, 0.04527023807168007, -0.059587083756923676, 0.024374887347221375, 0.013963458128273487, -0.028905535116791725, -0.022417647764086723, -0.045161500573158264, -0.01091886218637228, 0.0009967426303774118, 0.022635119035840034, -0.019753625616431236, 0.009423748590052128, -0.017578914761543274, 0.044255372136831284, 0.005926087964326143, 0.054367776960134506, 0.0024125701747834682, -0.023106304928660393, -0.008513088338077068, -0.01152596902102232, -0.010320816189050674, -0.0017023910768330097, -0.006963606458157301, 0.0491122268140316, -0.04874977469444275, 0.038129936903715134, -0.000007685289347136859, -0.05451275780797005, 0.11852175742387772, 0.00356108951382339, 0.07705726474523544, -0.004458157811313868, 0.006687236949801445, -0.049075979739427567, 0.01648249849677086, -0.07133052498102188, -0.05139567330479622, -0.0011349273845553398, -0.012903286144137383, 0.0075978972017765045, 0.010030855424702168, 0.002250599442049861, 0.025117913261055946, -0.051649387925863266, 0.062377963215112686, -0.007588835898786783, -0.012513650581240654, -0.008340923115611076, -0.00525102112442255, -0.0037808259949088097, 0.02328753098845482, -0.017560793086886406, -0.027908792719244957, -0.027709444984793663, 0.02283446677029133, 0.03376239165663719, -0.020061710849404335, -0.019155580550432205, -0.01902872323989868, -0.027999406680464745, -0.04298679158091545, -0.013555699028074741, -0.02691205032169819, -0.03446917235851288, -0.0010307225165888667, -0.01805916428565979, 0.03709694743156433, -0.05733988434076309, 0.020804736763238907, -0.026205269619822502, 0.028379980474710464, -0.0017409016145393252, 0.023450635373592377, 0.004784364718943834, 0.011127271689474583, 0.04860479384660721, 0.04831483215093613, 0.00681862561032176, -0.06183428689837456, 0.019155580550432205, -0.013990641571581364, -0.050743259489536285, 0.05831850320100784, 0.008381699211895466, 0.027872547507286072, -0.0001471044815843925, -0.037060704082250595, -0.04690127074718475, 0.02781818062067032, 0.004240686539560556, -0.0019527093973010778, -0.00477983383461833, 0.010157713666558266, -0.009133786894381046, 0.061544325202703476, 0.03292874991893768, 0.018457861617207527, -0.001974229933694005, -0.0002306383103132248, -0.07481006532907486, -0.05556387081742287, 0.008449658751487732, 0.004802487324923277, -0.022163931280374527, 0.028234999626874924, 0.055962566286325455, -0.024954810738563538, 0.016056617721915245, 0.028234999626874924, 0.06462516635656357, 0.056868694722652435, 0.08307396620512009, 0.023396266624331474, 0.025879062712192535, -0.0652775764465332, -0.007697571534663439, -0.04951092228293419, -0.015404203906655312, 0.021348414942622185, -0.07419389486312866, -0.04316801577806473, -0.007403078954666853, 0.031551435589790344, 0.006197926588356495, 0.00046382509754039347, 0.003130677854642272, -0.05893467366695404, -0.007439324166625738, -0.04965590313076973, -0.050054602324962616, -0.017270831391215324, -0.04755368456244469, 0.04284181073307991, -0.035175953060388565, -0.018113531172275543, 0.01661841757595539, 0.030210362747311592, 0.04610387608408928, -0.007738347165286541, 0.034106720238924026, 0.04298679158091545, 0.045378971844911575, 0.017325198277831078, 0.05781107023358345, -0.002693470334634185, -0.008676190860569477, 0.011163516901433468, 0.024229906499385834, 0.05494770035147667, -0.07575243711471558, -0.02691205032169819, 0.01341977994889021, -0.03484974429011345, 0.0002506014716345817, -0.05476647615432739, -0.007543529383838177, -0.002307232702150941, -0.04668379947543144, -0.0032598013058304787, -0.005862658843398094, -0.008948029950261116, -0.006143558770418167, -0.0072580985724925995, 0.08459626138210297, 0.059732064604759216, -0.006777849514037371, -0.003622253192588687, 0.03158767893910408, 0.0027976753190159798, -0.004369810223579407, 0.000025219427698175423, 0.005078856833279133, -0.001363725052215159, 0.007375895511358976, 0.03863736614584923, 0.0510694682598114, -0.061326853930950165, -0.007480100262910128, -0.03845614194869995, 0.031098369508981705, 0.04940218850970268, -0.029231742024421692, 0.006039354018867016, 0.034867867827415466, -0.018793128430843353, 0.02267136424779892, -0.038419898599386215, -0.012568018399178982, 0.04494402930140495, -0.0297029297798872, -0.015522000379860401, -0.004614465404301882, -0.0613631010055542, -0.031714536249637604, -0.03494035825133324, 0.04896724596619606, -0.04918471723794937, 0.012640508823096752, -0.040848325937986374, -0.02274385467171669, -0.024084925651550293, -0.003436496714130044, 0.030409710481762886, 0.03561089560389519, -0.0122780567035079, 0.060746930539608, 0.01602943427860737, -0.016373762860894203, -0.023160673677921295, 0.01805916428565979, -0.005273674614727497, -0.0044853417202830315, 0.005767515394836664, 0.040993306785821915, -0.0091111334040761, -0.04570518061518669, 0.009958365000784397, 0.01814071461558342, -0.04124702140688896, -0.012830795720219612, 0.04672004282474518, 0.020732246339321136, -0.023233164101839066, -0.027455728501081467, 0.007570713292807341, -0.01602037250995636, 0.08785832673311234, -0.07640485465526581, -0.016455315053462982, 0.0019175969064235687, 0.062088001519441605, -0.012124015018343925, 0.004458157811313868, -0.02477358467876911, 0.04922096058726311, 0.04650257155299187, 0.009351258166134357, 0.02312442846596241, -0.003687947755679488, 0.013120757415890694, -0.008218595758080482, -0.08488622307777405, 0.0017964020371437073, -0.05389659106731415, -0.04124702140688896, -0.021330291405320168, -0.00025782219017855823, -0.009179092943668365, 0.03802119940519333, -0.04556019976735115, 0.012404914945363998, -0.014371216297149658, -0.027981283143162727, -0.0006473163375630975, -0.02999289147555828, -0.024374887347221375, -0.013320106081664562, -0.017134912312030792, 0.009088479913771152, -0.010456736199557781, 0.02343251183629036, -0.020206691697239876, 0.01632845588028431, 0.024229906499385834, -0.02827124483883381, -0.09068545699119568, -0.03133396431803703, 0.06190677732229233, 0.03997844085097313, 0.0011757032480090857, 0.04450908675789833, -0.03142457455396652, 0.057992298156023026, 0.0316058024764061, -0.0601307637989521, -0.010520164854824543, 0.00944187119603157, -0.02417553961277008, -0.06179803982377052, 0.006320254411548376, -0.038709856569767, -0.0808267667889595, 0.02303381636738777, -0.1033712700009346, -0.00189834157936275, -0.012096830643713474, -0.003486333880573511, -0.021203434094786644, -0.0028112672735005617, -0.03494035825133324, 0.0008189146756194532, 0.03407047316431999, 0.002161119133234024, -0.005989517085254192, 0.027528218924999237, -0.013166063465178013, -0.04570518061518669, -0.045596443116664886, 0.01623784378170967, -0.04737245664000511, 0.02334189973771572, -0.00235367170535028, 0.009156440384685993, -0.023450635373592377, 0.03218572586774826, 0.006506010890007019, -0.0055319215171039104, 0.02486419677734375, -0.018421616405248642, 0.011009475216269493, -0.058753445744514465, 0.027111398056149483, -0.033744268119335175, 0.010511104017496109, -0.03606395795941353, 0.020913472399115562, 0.013927212916314602, 0.052700500935316086, -0.011725317686796188, -0.042443111538887024, -0.006519602611660957, 0.01911933533847332, 0.005799229722470045, -0.01730707660317421, 0.00008225958299590275, 0.02758258581161499, -0.0167815200984478, 0.05280923470854759, 0.04585016146302223, 0.0264589861035347, 0.0028724309522658587, -0.030880898237228394, 0.0109641682356596, -0.0013965723337605596, -0.018385371193289757, -0.0219283364713192, -0.010955107398331165, 0.0026005920954048634, -0.047771155834198, -0.05476647615432739, -0.0029879624489694834, 0.03762250393629074, 0.02259887382388115, -0.04831483215093613, 0.01973550394177437, 0.0007764398469589651, -0.013256676495075226, 0.05915214121341705, -0.019753625616431236, 0.04153698310256004, 0.062595434486866, 0.035320933908224106, -0.05465773865580559, 0.0872059166431427, -0.008513088338077068, -0.07517251372337341, 0.027745690196752548, -0.015123303979635239, -0.010039916262030602, 0.0030604528728872538, -0.012848918326199055, -0.01492395531386137, 0.003638110589236021, -0.03236695006489754, -0.005676902364939451, -0.04164571687579155, -0.03091714344918728, -0.004510260187089443, 0.018494106829166412, -0.06350156664848328, 0.0009525687783025205, -0.07959442585706711, -0.05396908149123192, 0.033291202038526535, -0.00702703557908535, 0.043711692094802856, -0.02009795606136322, -0.009015989489853382, -0.052772991359233856, -0.0483873225748539, 0.04932969808578491, -0.01714397221803665, -0.03008350357413292, 0.012305240146815777, 0.03269315883517265, -0.03229445964097977, -0.03954349830746651, -0.01761515997350216, -0.006628338247537613, -0.04353046789765358, -0.05146816372871399, -0.035701509565114975, 0.036770742386579514, 0.015023629181087017, 0.0093693807721138, 0.0536428764462471, -0.0400509312748909, 0.061943020671606064, 0.029358601197600365, 0.04577767103910446, 0.003296046517789364, 0.028923658654093742, 0.005119632463902235, 0.012359607964754105, -0.004444566089659929, 0.03542966768145561, -0.02653147652745247, -0.014189990237355232, 0.013881905935704708, 0.028760554268956184, 0.04048587381839752, -0.010320816189050674, 0.006007639691233635, 0.026422740891575813, 0.04055836424231529, -0.021964581683278084, -0.056578733026981354, 0.04845981299877167, 0.0036902129650115967, 0.055128928273916245, 0.07419389486312866, -0.011544091627001762, 0.0027410420589149, 0.04487153887748718, -0.018648147583007812, -0.006039354018867016, -0.003950725309550762, -0.023251285776495934, -0.018630025908350945, 0.07096807658672333, 0.051431916654109955, 0.02191021479666233, -0.07230914384126663, 0.05183061584830284, 0.004233890678733587, -0.001870025065727532, -0.04755368456244469, 0.001731840311549604, 0.007869736291468143, 0.000009919642252498306, 0.028234999626874924, -0.023939944803714752, 0.06585749983787537, -0.008114391006529331, 0.013764109462499619, -0.014035948552191257, 0.0156488586217165, 0.013927212916314602, -0.023523125797510147, -0.010293632745742798, 0.03700633347034454, -0.017433933913707733, -0.027383238077163696, 0.02372247353196144, -0.00921533815562725, 0.017171157523989677, 0.02606028877198696, -0.0420081689953804, 0.042733073234558105, 0.03484974429011345, 0.06843090802431107, -0.0109641682356596, 0.017859814688563347, -0.030554691329598427, 0.03588273376226425, 0.04063085466623306, -0.04157322645187378, -0.019989220425486565, 0.013401657342910767, 0.03664388135075569, -0.004770772531628609, -0.03098963387310505, -0.029521703720092773, -0.019209949299693108, 0.014987383969128132, 0.0059396796859800816, -0.004367544781416655, -0.006990790367126465, -0.02154776267707348, 0.0034953951835632324, -0.0009746556752361357, 0.05752110853791237, -0.02426615171134472, 0.0030128811486065388, 0.011462540365755558, 0.024374887347221375, 0.07807213068008423, -0.07292531430721283, 0.005821882747113705, 0.005232898518443108, 0.003975643776357174, -0.03535717725753784, 0.001905137556605041, -0.024592358618974686, 0.03921728953719139, -0.027238257229328156, 0.022653240710496902, 0.004104767460376024, 0.0048296707682311535, 0.036227062344551086, -0.028398102149367332, 0.020442284643650055, -0.01971738040447235, 0.037441276013851166, -0.02955794893205166, 0.0013127552811056376, -0.014960200525820255, -0.04737245664000511, -0.011308497749269009, -0.024048680439591408, 0.0358283668756485, -0.004557832144200802, -0.014461829327046871, -0.01496926136314869, -0.011661888100206852, 0.003672090359032154, -0.007928634062409401, 0.01300296001136303, -0.029340477660298347, 0.05926087871193886, -0.00793769583106041, 0.008988806046545506, 0.028053773567080498, 0.0067370738834142685, 0.010302693583071232, 0.03976096957921982, 0.028216877952218056, 0.03950725123286247, 0.010511104017496109, -0.04400165379047394, -0.02047852985560894, 0.01580290123820305, -0.03557464852929115, 0.009876812808215618, -0.0406670980155468, -0.018195083364844322, -0.021294046193361282, 0.0021226087119430304, -0.012268994934856892, 0.04302303493022919, -0.03709694743156433, 0.013954396359622478, 0.029811665415763855, 0.020732246339321136, 0.025661591440439224, -0.02841622568666935, -0.02796316146850586, 0.0005575529066845775, -0.018847497180104256, -0.024682970717549324, 0.0011666419450193644, -0.02698454074561596, -0.012894224375486374, 0.006573970429599285, -0.056796204298734665, 0.004306381102651358, 0.019862361252307892, 0.00032365816878154874, 0.04657506197690964, -0.02283446677029133, -0.006773319095373154, -0.0028928187675774097, 0.04443659633398056, -0.005241959821432829, 0.03597334772348404, -0.015666982159018517, -0.01852129027247429, 0.0364445336163044, -0.008214064873754978, -0.003998297266662121, 0.021022208034992218, -0.004211237654089928, 0.02214580774307251, 0.04421912506222725, -0.03805744647979736, -0.0021973643451929092, 0.009604974649846554, -0.013818477280437946, 0.008562925271689892, 0.00028033385751768947, -0.041971925646066666, -0.004657506477087736, 0.05183061584830284, -0.009396564215421677, -0.0017612895462661982, -0.012676754035055637, 0.02145715057849884, 0.03209511190652847, 0.028543082997202873, 0.016727153211832047, -0.019844239577651024, -0.018485045060515404, 0.007489161565899849, -0.0013909089611843228, -0.023106304928660393, 0.008073614910244942, 0.07056937366724014, -0.014461829327046871, -0.02674894779920578, -0.017886999994516373, 0.009423748590052128, -0.006764257792383432, 0.010438613593578339, -0.04527023807168007, -0.011190701276063919, -0.007833491079509258, 0.027836302295327187, -0.008508557453751564, -0.007711163256317377, -0.0445815771818161, 0.010338938795030117, 0.010058038868010044, 0.0261509008705616, 0.026277760043740273, 0.005038080736994743, -0.015666982159018517, -0.0015562776243314147, 0.017624221742153168, -0.004535178653895855, -0.03347242996096611, 0.0077836536802351475, -0.0007849347894079983, 0.04682878032326698, 0.003558824071660638, 0.011371927335858345, -0.009740893729031086, 0.01640094630420208, -0.0027591646648943424, 0.0013773170066997409, -0.007085933815687895, 0.011797808110713959, -0.03907230868935585, 0.00545943109318614, 0.026622088626027107, 0.007747408468276262, 0.0400509312748909, -0.02653147652745247, -0.03697009012103081, -0.019898606464266777, -0.001316153327934444, -0.007661326322704554, 0.04171820729970932, -0.025226648896932602, -0.0031782498117536306, 0.004093440715223551, 0.009432809427380562, -0.001635564025491476, -0.028506837785243988, -0.008331862278282642, 0.007833491079509258, 0.013211370445787907, -0.01009428407996893, 0.003055922221392393, 0.006546786520630121, 0.02334189973771572, -0.017515486106276512, 0.049982111901044846, -0.035175953060388565, -0.020514775067567825, -0.03635391965508461, -0.0029811665881425142, 0.011680010706186295, -0.036227062344551086, 0.006510541308671236, 0.02116718888282776, 0.011018536053597927, 0.02114906534552574, 0.02915925160050392, -0.027926916256546974, 0.02123967930674553, -0.01820414513349533, 0.019590523093938828, -0.03780372813344002, -0.060565706342458725, -0.05675996094942093, 0.028742432594299316, -0.0067416043020784855, 0.0030038198456168175, 0.013365412130951881, -0.01746111735701561, 0.07035190612077713, 0.035937100648880005, 0.03936227038502693, 0.04411039128899574, -0.012522711418569088, -0.02017044648528099, 0.028090018779039383, 0.015367958694696426, -0.006048415321856737, 0.008263902738690376, 0.032675035297870636, -0.006175273563712835, -0.02818063274025917, 0.01035706140100956, -0.011915604583919048, -0.025027301162481308, 0.0009180225897580385, -0.023559371009469032, 0.023994313552975655, 0.0015528796939179301, -0.00545943109318614, -0.018575657159090042, -0.009931180626153946, 0.0016163086984306574, -0.020224813371896744, 0.03550215810537338, -0.03084465302526951, 0.043494224548339844, 0.019536154344677925, -0.012948592193424702, -0.02200082689523697, -0.028959903866052628, 0.0014033683110028505, 0.06506010890007019, -0.01424435805529356, -0.003672090359032154, 0.004797956440597773, -0.06861213594675064, -0.045233990997076035, 0.015975065529346466, -0.01693556271493435, -0.00827296357601881, 0.01534077525138855, -0.04762617498636246, -0.01553106214851141, -0.00763414241373539, -0.028833044692873955, -0.020134201273322105, 0.029304232448339462, 0.06861213594675064, 0.007661326322704554, -0.019064968451857567, 0.05911589786410332, -0.011326620355248451, -0.00264589861035347, -0.0033413530327379704, 0.030862774699926376, -0.014371216297149658, -0.03008350357413292, -0.05204808712005615, -0.03758625686168671, -0.0021044861059635878, -0.010547349229454994, -0.013601006008684635, -0.02283446677029133, 0.037441276013851166, 0.014026886783540249, 0.016491560265421867, -0.001648023258894682, 0.010628900490701199, 0.03218572586774826, -0.04146449267864227, 0.012151198461651802, 0.001080559566617012, -0.004215768072754145, -0.041754454374313354, 0.02274385467171669, 0.023541247472167015, 0.04751743748784065, -0.014606810174882412, -0.008707906119525433, -0.0012504588812589645, -0.01276736706495285, 0.01208776980638504, -0.0038827655371278524, -0.014235296286642551, 0.013184186071157455, -0.01361006684601307, 0.015105181373655796, 0.02116718888282776, -0.015739472582936287, 0.014425584115087986, -0.019064968451857567, -0.00010625785944284871, -0.027999406680464745, 0.03127959370613098, -0.01409937720745802, -0.0020739042665809393, 0.01851222850382328, 0.03282001614570618, 0.008481373079121113, -0.01698993146419525, -0.04701000452041626, 0.034650396555662155, 0.007326058112084866, 0.028398102149367332, -0.029449213296175003, -0.04113828390836716, -0.026187146082520485, 0.004154604393988848, 0.024139294400811195, 0.01167094986885786, -0.01368255726993084, 0.02259887382388115, 0.006197926588356495, 0.000789465440902859, 0.03220384567975998, 0.042733073234558105, 0.028688063845038414, -0.0024284273386001587, -0.04896724596619606, -0.016600295901298523, -0.01239585317671299, 0.03878234699368477, -0.05077950656414032, -0.0613631010055542, 0.006229641381651163, -0.006329315714538097, -0.01152596902102232, 0.02993852272629738, -0.004671098198741674, -0.04063085466623306, -0.03265691176056862, -0.024465499445796013, -0.021964581683278084, 0.014425584115087986, -0.0020048117730766535, 0.023378144949674606, -0.008327331393957138, 0.025262894108891487, -0.030282853171229362, 0.03425170108675957, -0.015277345664799213, 0.05476647615432739, 0.03602771461009979, 0.01375504769384861, -0.025643469765782356, 0.07259910553693771, -0.03856487572193146, -0.003887296188622713, -0.04142824560403824, -0.012495527975261211, -0.06411773711442947, 0.013773170299828053, -0.036082081496715546, -0.08118921518325806, 0.02138466015458107, 0.0068322173319756985, 0.033744268119335175, -0.0043380954302847385, 0.049837131053209305, 0.04701000452041626, -0.0044241780415177345, -0.027981283143162727, 0.010792003944516182, -0.046973761171102524, -0.0025031832046806812, 0.024157416075468063, 0.009188154712319374, -0.01746111735701561, 0.0148514648899436, -0.013972518965601921, 0.0030151463579386473, 0.023668106645345688, 0.03780372813344002, 0.0049202837981283665, -0.007747408468276262, -0.00780177628621459, -0.0438566729426384, 0.015250162221491337, 0.01322043128311634, 0.02250825986266136, 0.04186318814754486, 0.004061725921928883, -0.042588092386722565, -0.012223688885569572, -0.021275924518704414, 0.016120046377182007, 0.026966417208313942, 0.026422740891575813, -0.002326487796381116, -0.03602771461009979, -0.009156440384685993, -0.022272666916251183, -0.005695024970918894, -0.016799643635749817, -0.006605685222893953, 0.008381699211895466, 0.009015989489853382, -0.02803565189242363, 0.005803760141134262, -0.016754336655139923, -0.013519453816115856, -0.04690127074718475, 0.0005207413923926651, -0.016500620171427727, -0.010810126550495625, 0.0067325434647500515, 0.016953686252236366, 0.050525788217782974, 0.01035706140100956, 0.00951436161994934, 0.030772162601351738, -0.006293070502579212, 0.005468492396175861, 0.006863932125270367, -0.01928243786096573, -0.016038494184613228, -0.0035905386321246624, -0.012441160157322884, 0.027147643268108368, 0.015830084681510925, -0.002695735776796937, 0.0043607489205896854, 0.03504909574985504, 0.012531773187220097, -0.0008755477610975504, -0.020079832524061203, 0.030735917389392853, 0.005658779758960009, 0.011806868948042393, 0.004412851296365261, -0.06027574464678764, 0.005214775912463665, 0.020913472399115562, 0.011390049941837788, 0.0033685369417071342, -0.006605685222893953, 0.008368107490241528, -0.008671660907566547, -0.0364445336163044, -0.01902872323989868, 0.04450908675789833, 0.0345960296690464, 0.0009412421495653689, -0.007199199870228767, 0.03573775291442871, -0.032838139683008194, 0.015494816936552525, 0.058970917016267776, 0.013818477280437946, -0.019137458875775337, 0.035030972212553024, -0.02827124483883381, 0.015676042065024376, -0.003803479252383113, 0.034958481788635254, -0.0018643616931512952, -0.04922096058726311, 0.01072857528924942, -0.015694165602326393, -0.057086165994405746, -0.00015531628741882741 ]
Music can be represented in multiple forms, such as in the audio form as a recording of a performance, in the symbolic form as a computer readable score, or in the image form as a scan of the sheet music. Music synchronisation provides a way to navigate among multiple representations of music in a unified manner by generating an accurate mapping between them, lending itself applicable to a myriad of domains like music education, performance analysis, automatic accompaniment and music editing. Traditional synchronisation methods compute alignment using knowledge-driven and stochastic approaches, typically employing handcrafted features. These methods are often unable to generalise well to different instruments, acoustic environments and recording conditions, and normally assume complete structural agreement between the performances and the scores. This PhD furthers the development of performance-score synchronisation research by proposing data-driven, context-aware alignment approaches, on three fronts: Firstly, I replace the handcrafted features by employing a metric learning based approach that is adaptable to different acoustic settings and performs well in data-scarce conditions. Secondly, I address the handling of structural differences between the performances and scores, which is a common limitation of standard alignment methods. Finally, I eschew the reliance on both feature engineering and dynamic programming, and propose a completely data-driven synchronisation method that computes alignments using a neural framework, whilst also being robust to structural differences between the performances and scores.
[ 0.060127828270196915, -0.0030923676677048206, -0.03644279018044472, -0.005204792134463787, 0.006554524879902601, 0.004499880131334066, -0.07329234480857849, 0.031690988689661026, -0.06356687098741531, 0.020560314878821373, 0.03681257739663124, -0.020264483988285065, 0.026495441794395447, -0.018369311466813087, 0.005338841117918491, -0.01674223504960537, 0.04430082440376282, 0.0013531997101381421, -0.029786571860313416, -0.025219667702913284, -0.0010562122333794832, -0.029305845499038696, -0.030988389626145363, -0.005477512255311012, 0.010927289724349976, 0.009346438571810722, 0.02209494262933731, 0.03222718462347984, -0.042784683406353, -0.002861249027773738, 0.04197114706039429, 0.013552797958254814, -0.019894693046808243, -0.013432616367936134, -0.11441297829151154, -0.07125850021839142, 0.038310229778289795, -0.002182915573939681, -0.002919028513133526, -0.016279997304081917, -0.008999760262668133, 0.04385707527399063, 0.005052253603935242, -0.023259781301021576, -0.02962016686797142, -0.025219667702913284, -0.05901845917105675, 0.010169221088290215, 0.005306484177708626, -0.022316817194223404, 0.04925600811839104, 0.01807347871363163, -0.02876964956521988, -0.039308659732341766, -0.017731422558426857, -0.0030253431759774685, 0.05358254909515381, -0.020467868074774742, 0.05439608544111252, 0.009799431078135967, 0.025848310440778732, 0.050365377217531204, -0.013321679085493088, -0.03300374373793602, -0.029583187773823738, -0.06260541826486588, 0.012110617011785507, -0.041453443467617035, 0.045743003487586975, 0.05321275815367699, -0.01610434800386429, -0.029305845499038696, -0.0056670294143259525, 0.004969051107764244, 0.01542948093265295, -0.025829819962382317, 0.018535716459155083, 0.051178913563489914, 0.015882473438978195, -0.006947426591068506, 0.008139998652040958, 0.011639134958386421, -0.06349291652441025, 0.05247317999601364, -0.015632865950465202, -0.013654490001499653, -0.012406449764966965, -0.07369911670684814, -0.0014005789998918772, 0.011417261324822903, -0.06704290211200714, -0.0360175296664238, -0.027604812756180763, 0.04677841439843178, 0.0026694205589592457, -0.04881225898861885, 0.015115159563720226, -0.01937698759138584, -0.010816353373229504, -0.052547138184309006, 0.0023654995020478964, -0.009286347776651382, 0.007867278531193733, -0.05986897647380829, 0.022926971316337585, -0.0003409000055398792, 0.01130632497370243, -0.01855420507490635, 0.0016097414772957563, 0.10235782712697983, 0.015115159563720226, -0.0438200980424881, 0.03714539110660553, 0.008953536860644817, -0.061976779252290726, 0.004751799628138542, -0.07654649764299393, -0.08054022490978241, 0.004298807121813297, -0.018332332372665405, -0.029213398694992065, 0.05509868636727333, -0.039456576108932495, 0.07133246213197708, -0.05025444179773331, 0.06164396554231644, -0.03971542790532112, -0.05728044733405113, 0.010566744953393936, 0.0347602441906929, -0.044263843446969986, 0.041453443467617035, -0.0010943468660116196, -0.013247720897197723, 0.049736734479665756, 0.0058057005517184734, -0.0024891479406505823, -0.005514490883797407, 0.0009793653152883053, 0.02653242088854313, -0.02372201904654503, -0.020467868074774742, 0.0336138978600502, -0.04219302162528038, 0.014329356141388416, -0.010908800177276134, 0.007760964334011078, 0.0776558667421341, 0.01598416641354561, -0.00713232159614563, -0.056134097278118134, 0.020172035321593285, 0.004206359386444092, 0.0472591407597065, -0.01216608565300703, -0.011102939955890179, 0.03328108787536621, -0.03119177371263504, -0.019894693046808243, -0.006864224094897509, 0.05546847730875015, -0.011352548375725746, 0.020837657153606415, 0.05776117369532585, 0.07122152298688889, -0.01228626724332571, -0.02719804272055626, -0.08031835407018661, -0.0015045824693515897, 0.044744569808244705, -0.0028728048782795668, -0.013192253187298775, -0.026680337265133858, 0.005999840330332518, 0.020153546705842018, -0.01995016261935234, 0.0988818034529686, -0.02581133134663105, -0.058648668229579926, -0.026439974084496498, -0.07883919775485992, 0.01722296141088009, 0.04644560441374779, -0.0017172115622088313, 0.03333655372262001, 0.018628163263201714, 0.04097271338105202, -0.00714156636968255, 0.043413326144218445, -0.034834202378988266, 0.06330802291631699, 0.06896580755710602, 0.06541582196950912, 0.007372685242444277, 0.028603244572877884, -0.019894693046808243, -0.03494514152407646, -0.03649825602769852, 0.002845070557668805, 0.02947225049138069, -0.027493875473737717, -0.060793451964855194, 0.04348728433251381, 0.005787211004644632, -0.01464367751032114, 0.050032567232847214, 0.030082404613494873, 0.026791274547576904, -0.05935126915574074, -0.05924033373594284, 0.0007407352677546442, 0.025607947260141373, -0.02862173318862915, 0.014726880937814713, -0.005722498055547476, -0.02571888454258442, -0.007113832049071789, 0.005459022708237171, 0.04718518257141113, -0.0292503759264946, 0.011010492220520973, -0.004712509457021952, 0.05324973911046982, 0.008246313780546188, -0.01689939573407173, 0.01813819259405136, -0.011897988617420197, 0.02557096816599369, 0.0393456406891346, -0.016030389815568924, -0.021928537636995316, 0.010788618586957455, -0.02967563457787037, -0.02200249582529068, 0.016335466876626015, 0.01456972025334835, 0.030877452343702316, -0.03024880960583687, 0.02004260942339897, 0.012535875663161278, 0.002246473217383027, -0.03322561830282211, 0.010030549950897694, -0.027068616822361946, 0.01506893616169691, 0.017056556418538094, -0.00791812501847744, 0.05447004362940788, 0.049403924494981766, -0.0012919532600790262, -0.0201905257999897, -0.005181680433452129, 0.04222999885678291, 0.030396725982427597, -0.03625789284706116, 0.012822463177144527, -0.01879456825554371, -0.02166968584060669, 0.03109932690858841, -0.10516823083162308, 0.007026006933301687, -0.021262915804982185, -0.002544616349041462, 0.03213473781943321, -0.03156156465411186, 0.015762291848659515, 0.027512364089488983, -0.009055228903889656, 0.028584755957126617, -0.03784799203276634, 0.004821135196834803, 0.005782588850706816, -0.018988708034157753, -0.028825119137763977, -0.04404196888208389, -0.08956310153007507, 0.030063914135098457, -0.009919612668454647, 0.03335504233837128, -0.01228626724332571, 0.028973033651709557, -0.0031085459049791098, 0.03342900052666664, -0.01861891895532608, -0.04866434261202812, -0.005056876223534346, 0.018896261230111122, -0.034889671951532364, -0.03222718462347984, 0.03529644012451172, 0.005241771228611469, -0.05180755630135536, -0.046593520790338516, 0.026273569092154503, -0.0008100708946585655, 0.005759476684033871, -0.03228265419602394, -0.01088106632232666, 0.03524097055196762, -0.04504040256142616, -0.03209775686264038, -0.012129106558859348, 0.005227903835475445, 0.005361952818930149, -0.016178306192159653, 0.020153546705842018, 0.014578964561223984, 0.04337634891271591, -0.014541985467076302, -0.00569014111533761, -0.022705096751451492, 0.022409263998270035, 0.020061099901795387, -0.0032310388050973415, -0.030156362801790237, 0.06042366102337837, -0.009938102215528488, 0.04241489619016647, 0.013256966136395931, -0.02619961090385914, 0.009827164933085442, 0.013515818864107132, -0.11175049096345901, 0.015161383897066116, 0.005948994308710098, 0.0024452353827655315, 0.03485269472002983, 0.015207607299089432, 0.04418988525867462, -0.042747706174850464, -0.028159497305750847, 0.008454320020973682, 0.010391094721853733, 0.01100124791264534, 0.04825757443904877, 0.03200531005859375, -0.01076088473200798, 0.018822303041815758, 0.0019772201776504517, -0.05210338905453682, 0.015521928668022156, 0.015179873444139957, 0.011278590187430382, -0.03975240886211395, -0.01764822006225586, 0.023888424038887024, -0.051548704504966736, -0.0028982278890907764, -0.010539010167121887, -0.008246313780546188, 0.0010752795496955514, -0.05180755630135536, 0.01309980545192957, 0.0035638497211039066, -0.015420236624777317, -0.03318863734602928, -0.012905665673315525, -0.040787819772958755, -0.00917078834027052, 0.04319145530462265, 0.00983641017228365, -0.08601311594247818, 0.015447970479726791, 0.013377147726714611, -0.012563610449433327, -0.030803494155406952, -0.0438200980424881, -0.01828610710799694, 0.07044496387243271, 0.04367218166589737, -0.018323086202144623, 0.003965996205806732, 0.0022060275077819824, -0.00832489412277937, -0.06711685657501221, 0.06279031932353973, -0.005237148609012365, 0.0009758985252119601, -0.04877528175711632, 0.043265413492918015, -0.024258213117718697, 0.06404760479927063, 0.030969899147748947, 0.011398771777749062, -0.023444676771759987, 0.02176213264465332, 0.014736125245690346, -0.006110777147114277, -0.016215285286307335, 0.052879948168992996, -0.017934806644916534, 0.007807188201695681, -0.06685800105333328, -0.03834720700979233, -0.00832489412277937, -0.02991599775850773, -0.02780819684267044, 0.0035915838088840246, 0.00061188661493361, 0.007881145924329758, -0.041601356118917465, -0.0651569738984108, -0.024738941341638565, 0.035130035132169724, 0.022039474919438362, -0.01704731211066246, -0.019487924873828888, -0.02333373948931694, 0.06216167286038399, -0.01287793181836605, 0.0371084101498127, -0.013284699991345406, 0.01635395549237728, -0.06752362847328186, -0.0036054509691894054, 0.05461796000599861, -0.08187147229909897, 0.01991318352520466, -0.046075813472270966, -0.019321519881486893, -0.011824030429124832, -0.02009807899594307, 0.026587890461087227, 0.009207767434418201, 0.01517062820494175, 0.06371478736400604, -0.017093535512685776, -0.02004260942339897, 0.01335865817964077, -0.02462800405919552, 0.023555614054203033, -0.028325902298092842, 0.09045059978961945, -0.036553725600242615, 0.006873468868434429, -0.007058363873511553, 0.010104507207870483, -0.033077701926231384, -0.03964146971702576, 0.013562042266130447, -0.08238917589187622, -0.03875397518277168, 0.007525223307311535, -0.02091161534190178, 0.0013786227209493518, -0.0516226626932621, -0.02191004902124405, -0.009605291299521923, 0.008671571500599384, -0.02381446585059166, 0.0019286851165816188, -0.025515498593449593, -0.06367781013250351, -0.00496442848816514, 0.03749668970704079, -0.0032241051085293293, 0.026754295453429222, -0.011805540882050991, -0.030655577778816223, -0.04352426528930664, 0.01643715798854828, 0.0573544055223465, 0.012489652261137962, -0.0449664443731308, -0.013312434777617455, 0.009161543101072311, -0.04777684807777405, -0.0020974017679691315, -0.012748504988849163, 0.054507024586200714, 0.08823185414075851, -0.07451265305280685, 0.0018327708821743727, 0.02333373948931694, 0.008699306286871433, -0.028658712282776833, 0.001429468858987093, -0.02586679905653, 0.02529362589120865, -0.016853172332048416, 0.006799510680139065, -0.016548095270991325, 0.00920314434915781, 0.011167652904987335, 0.0035869614221155643, 0.006633105222135782, 0.026347527280449867, -0.0005705741932615638, -0.017638975754380226, -0.027345959097146988, 0.020800678059458733, 0.041601356118917465, -0.004197114612907171, 0.04167531430721283, 0.01924756169319153, 0.012119862250983715, 0.0002972763613797724, -0.02937980368733406, 0.045743003487586975, 0.008768641389906406, -0.027161063626408577, -0.039789386093616486, 0.04737007990479469, 0.005898147821426392, -0.0014364024391397834, 0.009448130615055561, 0.009577557444572449, -0.02610716223716736, 0.02629205770790577, 0.03191286325454712, 0.021743642166256905, 0.0235741026699543, 0.026791274547576904, 0.0037371886428445578, -0.018027255311608315, 0.021965516731142998, -0.010233934037387371, -0.033687856048345566, 0.03119177371263504, -0.014856306836009026, -0.004093111492693424, 0.004807267803698778, 0.020541826263070107, 0.04100969433784485, -0.009780941531062126, 0.05421119183301926, 0.050735168159008026, -0.017879338935017586, -0.0605715773999691, -0.048886217176914215, -0.0774339959025383, -0.007127699442207813, 0.02324129268527031, -0.05728044733405113, -0.002368966117501259, -0.007113832049071789, 0.0017333899158984423, 0.024609513580799103, -0.018600428476929665, -0.026643358170986176, -0.02810402773320675, 0.045743003487586975, -0.03568471968173981, 0.011555932462215424, -0.04289562255144119, 0.009045983664691448, 0.06715383380651474, -0.03219020739197731, 0.02233530580997467, 0.018156681209802628, 0.009267858229577541, 0.0037325662560760975, 0.005024519748985767, 0.0017865472473204136, -0.010770129039883614, 0.0012052837992087007, 0.022168900817632675, -0.045595087110996246, 0.004160135984420776, 0.008542145602405071, -0.010289402678608894, -0.0015207607066258788, -0.014615943655371666, 0.02148479036986828, 0.028880586847662926, 0.010705416090786457, 0.010908800177276134, 0.04481852799654007, 0.029879018664360046, -0.04197114706039429, 0.0008204712066799402, -0.04692633077502251, 0.01361751090735197, -0.010816353373229504, 0.004932072013616562, -0.008186222985386848, 0.01852647215127945, 0.00206966744735837, -0.01812894642353058, 0.02290848083794117, 0.019839225336909294, 0.00048506027087569237, -0.007465132512152195, -0.00011852053285110742, 0.02057880535721779, 0.002181760035455227, 0.010908800177276134, -0.03082198277115822, 0.011777807027101517, 0.00688271364197135, -0.008491299115121365, -0.0019067288376390934, 0.005357330199331045, -0.0065314131788909435, -0.03871699795126915, -0.0006217091577127576, 0.013922587968409061, -0.017999520525336266, 0.029879018664360046, -0.06345593929290771, -0.008329516276717186, 0.039604492485523224, -0.011934967711567879, 0.014819327741861343, -0.006489811930805445, -0.041416462510824203, 0.0426737479865551, -0.014033524319529533, -0.008629970252513885, 0.06759758293628693, -0.009156920947134495, 0.01943245716392994, 0.05106797814369202, -0.011352548375725746, 0.0047055757604539394, 0.02104104310274124, 0.03479722514748573, -0.021595727652311325, -0.006600748747587204, 0.025034772232174873, 0.03514852374792099, 0.04918204993009567, 0.011352548375725746, -0.07381005585193634, 0.0230563972145319, 0.027031637728214264, 0.031154794618487358, -0.015022712759673595, 0.0051169670186936855, -0.029065482318401337, -0.022113433107733727, -0.02762330137193203, -0.027993090450763702, -0.0032241051085293293, 0.05106797814369202, 0.0174078568816185, -0.04529925435781479, 0.03771856427192688, 0.022742075845599174, -0.054691918194293976, -0.034020666033029556, 0.021447811275720596, -0.023851444944739342, 0.052990883588790894, 0.004102356266230345, -0.00531110679730773, -0.03856908157467842, -0.012702281586825848, -0.004083866719156504, 0.050217460840940475, 0.004289562348276377, -0.001242262776941061, 0.04629768803715706, 0.05802002549171448, -0.02324129268527031, -0.009351060725748539, 0.010224688798189163, 0.014052013866603374, -0.03612846881151199, -0.007418908644467592, 0.05395234003663063, -0.0403810515999794, 0.0052741277031600475, -0.015521928668022156, 0.012230799533426762, 0.02876964956521988, 0.04467061161994934, -0.0190996453166008, 0.00080198171781376, 0.08985893428325653, 0.0006881557637825608, -0.07436473667621613, -0.012850197032094002, 0.008810242637991905, 0.039308659732341766, -0.03790345788002014, 0.013136784546077251, 0.016659032553434372, -0.006637727841734886, 0.0010007438249886036, -0.01855420507490635, -0.030156362801790237, -0.019987141713500023, 0.011056716553866863, 0.02142932079732418, -0.007913502864539623, 0.025497009977698326, 0.014162951149046421, -0.0685960128903389, 0.039604492485523224, -0.006938181817531586, 0.004779533948749304, 0.02115197852253914, 0.05842679738998413, -0.0008996293763630092, 0.02324129268527031, -0.025922268629074097, -0.007492866832762957, -0.011740827932953835, 0.014098238199949265, -0.019561883062124252, -0.014209174551069736, 0.007405041716992855, -0.01045580767095089, 0.002405945211648941, 0.052990883588790894, 0.007335706148296595, -0.0031339689157903194, -0.03927168250083923, -0.034815713763237, 0.0014260021271184087, 0.002701777033507824, -0.0043612089939415455, 0.00914305355399847, -0.02499779313802719, 0.052029430866241455, 0.033262595534324646, -0.04008521884679794, -0.05018048360943794, 0.032837338745594025, -0.005292617250233889, -0.005676274187862873, 0.028880586847662926, -0.04289562255144119, -0.03348447009921074, 0.009161543101072311, 0.005694763734936714, -0.03551831468939781, -0.025589456781744957, -0.016067368909716606, 0.035795658826828, -0.02257567085325718, -0.004065377172082663, 0.00936955027282238, -0.0008297159802168608, 0.006064553279429674, 0.030415214598178864, 0.020837657153606415, -0.00446521257981658, 0.01517062820494175, 0.016030389815568924, 0.016843928024172783, 0.04289562255144119, -0.018230639398097992, -0.014329356141388416, 0.04437478259205818, -0.009147676639258862, -0.034261029213666916, -0.0058241900987923145, 0.02309337630867958, 0.0675606057047844, -0.00011989280028501526, 0.020708231255412102, -0.05221432447433472, -0.024350661784410477, 0.030544640496373177, 0.01934000849723816, -0.023352228105068207, -0.003395132953301072, 0.008602236397564411, -0.006508301477879286, -0.008334138430655003, 0.013044336810708046, -0.011075206100940704, 0.0516226626932621, 0.028640223667025566, -0.04296958073973656, 0.016058124601840973, 0.0051955473609268665, 0.01635395549237728, 0.023037906736135483, -0.02557096816599369, 0.08298084139823914, -0.010372605174779892, 0.008777886629104614, 0.003300374373793602, -0.019173603504896164, -0.013062826357781887, 0.01592869684100151, -0.02523815631866455, -0.0007343795150518417, -0.0035338043235242367, 0.007784076035022736, 0.009032117202877998, 0.054691918194293976, 0.024443108588457108, 0.011204631999135017, -0.009706983342766762, -0.025774352252483368, 0.02514570951461792, 0.0021089576184749603, 0.005546847824007273, -0.009217011742293835, -0.02557096816599369, 0.06656217575073242, -0.013543552719056606, -0.029971467331051826, -0.019876204431056976, -0.03953053429722786, -0.036220915615558624, -0.005676274187862873, -0.004412055015563965, 0.02505326271057129, -0.009364928118884563, 0.0019113512244075537, -0.008620725944638252, 0.0168069489300251, -0.011056716553866863, -0.043561242520809174, -0.015115159563720226, -0.04004824161529541, -0.008431208319962025, 0.045077383518218994, -0.033502958714962006, 0.055320560932159424, 0.011195387691259384, -0.01045580767095089, 0.05173359811306, -0.0006534879794344306, -0.008301782421767712, -0.014301622286438942, -0.019839225336909294, 0.010233934037387371, -0.016122836619615555, 0.029416782781481743, -0.02729049138724804, 0.015919452533125877, -0.00191944045946002, 0.061126261949539185, -0.005861169192939997, 0.019062666222453117, 0.00920314434915781, -0.049403924494981766, 0.022705096751451492, -0.03037823550403118, -0.0008586057811044157, 0.03289280831813812, 0.00020771789422724396, -0.05709555372595787, 0.012064393609762192, -0.00575023191049695, -0.021078020334243774, 0.016058124601840973, -0.041268546134233475, 0.008916557766497135, 0.012203064747154713, -0.012295512482523918, -0.03941959887742996, 0.01900719851255417, -0.004541481379419565, 0.026014715433120728, 0.01861891895532608, 0.060682512819767, -0.008602236397564411, -0.02705012634396553, 0.02100406400859356, 0.01271152589470148, 0.009013627655804157, 0.016585074365139008, -0.012471162714064121, 0.06759758293628693, -0.01361751090735197, 0.004275694955140352, -0.014052013866603374, 0.0008297159802168608, -0.013377147726714611, -0.00967000424861908, -0.06796737015247345, -0.026828253641724586, -0.025164198130369186, -0.01943245716392994, 0.008500544354319572, 0.017999520525336266, 0.005126211792230606, -0.005875036120414734, 0.040602926164865494, -0.017907073721289635, -0.003469090908765793, -0.0224832221865654, -0.031062347814440727, 0.016483383253216743, 0.00979018583893776, 0.038273248821496964, -0.003311930224299431, 0.04799872264266014, -0.0020361554343253374, -0.014847062528133392, -0.016307732090353966, 0.033743321895599365, -0.05328671634197235, -0.009512843564152718, 0.025367584079504013, -0.009096830151975155, -0.01283170748502016, 0.05576431006193161, 0.03875397518277168, -0.027660280466079712, -0.0162892434746027, -0.000833182770293206, -0.005130833946168423, -0.006272560451179743, -0.04315447434782982, -0.031117815524339676, -0.009485109709203243, -0.04929298534989357, 0.019155114889144897, -0.008301782421767712, -0.005472889635711908, 0.02653242088854313, -0.02133687399327755, -0.003915150184184313, -0.008213956840336323, -0.010298646986484528, -0.03542586788535118, 0.024128787219524384, -0.03666466474533081, -0.04847944900393486, 0.03424254059791565, 0.002353943418711424, -0.02218739129602909, 0.08468187600374222, 0.013922587968409061, -0.04200812801718712, 0.06696894019842148, -0.014320111833512783, 0.0059027704410254955, -0.03964146971702576, -0.045410193502902985, 0.01970979943871498, -0.037552159279584885, -0.003473713295534253, 0.033669363707304, -0.0002841314999386668, 0.001774991280399263, 0.0269576795399189, 0.04681539535522461, -0.0013890231493860483, 0.03353993967175484, -0.03437196463346481, 0.006887335795909166, -0.006568392273038626, -0.006559147499501705, 0.01140801701694727, -0.014763860031962395, 0.044263843446969986, -0.019506413489580154, 0.011842519976198673, -0.006249448284506798, -0.01831384189426899, 0.044892486184835434, -0.020412400364875793, -0.0038273248355835676, -0.014967244118452072, 0.00015196051390375942, -0.02723502181470394, -0.001399423461407423, -0.023370718583464622, -0.03024880960583687, -0.030840473249554634, 0.01776840165257454, -0.010076773352921009, 0.009605291299521923, -0.04918204993009567, -0.006092287600040436, -0.0241472776979208, 0.02523815631866455, -0.03701596334576607, 0.021743642166256905, -0.005435910541564226, 0.03191286325454712, 0.03010089322924614, -0.014153705909848213, 0.03209775686264038, 0.013441860675811768, 0.01943245716392994, 0.01128783542662859, -0.02157723717391491, -0.005445155315101147, 0.01577153615653515, -0.021873069927096367, 0.0033581540919840336, 0.011639134958386421, 0.06086741015315056, 0.004661663435399532, 0.011713093146681786, -0.0843120813369751, 0.0008528278558515012, 0.0157160684466362, -0.029583187773823738, 0.026846742257475853, -0.02686523273587227, -0.01257285475730896, -0.006397364195436239, -0.02780819684267044, -0.032559994608163834, -0.02666184864938259, 0.05986897647380829, -0.005172435659915209, 0.006365007720887661, 0.010021304711699486, -0.03329957649111748, -0.010206200182437897, -0.022039474919438362, 0.006323406472802162, -0.015845494344830513, 0.04186021164059639, 0.028418349102139473, 0.01529080979526043, 0.014745370484888554, 0.005634672939777374, 0.023537123575806618, -0.02529362589120865, -0.02142932079732418, -0.01904417760670185, -0.028362881392240524, -0.015605131164193153, -0.040418028831481934, -0.006651594769209623, 0.012609833851456642, -0.04019615799188614, 0.02705012634396553, -0.013913342729210854, 0.023980870842933655, -0.03575867787003517 ]
Applying reinforcement learning to autonomous driving entails particular challenges, primarily due to dynamically changing traffic flows. To address such challenges, it is necessary to quickly determine response strategies to the changing intentions of surrounding vehicles. This paper proposes a new policy optimization method for safe driving using graph-based interaction-aware constraints. In this framework, the motion prediction and control modules are trained simultaneously while sharing a latent representation that contains a social context. To reflect social interactions, we illustrate the movements of agents in graph form and filter the features with the graph convolution networks. This helps preserve the spatiotemporal locality of adjacent nodes. Furthermore, we create feedback loops to combine these two modules effectively. As a result, this approach encourages the learned controller to be safe from dynamic risks and renders the motion prediction robust to abnormal movements. In the experiment, we set up a navigation scenario comprising various situations with CARLA, an urban driving simulator. The experiments show state-of-the-art performance on navigation strategy and motion prediction compared to the baselines.
[ 0.019625958055257797, -0.033532749861478806, -0.029378095641732216, -0.020060546696186066, 0.013011541217565536, 0.013811182230710983, -0.05079455301165581, 0.0347495935857296, -0.11153246462345123, -0.015636447817087173, 0.015471304766833782, 0.02179889567196369, 0.01655777357518673, -0.03544493392109871, -0.003498427104204893, 0.03966912254691124, 0.027883116155862808, 0.00432848883792758, -0.02040821500122547, -0.04797843098640442, 0.031255513429641724, -0.029986517503857613, -0.014689047820866108, 0.038382742553949356, 0.021260006353259087, 0.01844388246536255, 0.05232430249452591, 0.02934332937002182, -0.09512244910001755, 0.050655487924814224, 0.031637948006391525, 0.015697291120886803, 0.03335891664028168, 0.005801739636808634, -0.00313337380066514, -0.013515662401914597, 0.05625297129154205, 0.04314582049846649, -0.0329938605427742, 0.020303914323449135, 0.0009381651761941612, 0.018808934837579727, -0.027344228699803352, -0.05823468789458275, -0.009925971738994122, -0.012072833254933357, -0.03401948884129524, -0.015584297478199005, -0.039251916110515594, -0.011794697493314743, 0.04092073440551758, -0.040712129324674606, 0.047387391328811646, -0.02179889567196369, -0.025014840066432953, 0.040712129324674606, 0.01976502686738968, -0.02178151160478592, 0.03984295576810837, 0.03342844918370247, 0.02247685194015503, -0.04258954897522926, -0.07725222408771515, -0.012463961727917194, 0.013359211385250092, -0.03633149340748787, 0.038765180855989456, 0.00508467061445117, -0.013863332569599152, -0.025849247351288795, -0.06150278449058533, 0.017904993146657944, -0.055940065532922745, -0.04943864047527313, 0.026787957176566124, 0.03078615851700306, -0.032263755798339844, 0.03292432799935341, 0.04005155712366104, -0.0015123635530471802, 0.02790050022304058, -0.007596584502607584, -0.04293721914291382, -0.020251763984560966, 0.06317159533500671, -0.037444036453962326, 0.10186724364757538, -0.06157231703400612, 0.030056051909923553, -0.0021425150334835052, -0.020130079239606857, 0.015036717988550663, -0.02670103870332241, 0.015088868327438831, -0.005228084046393633, -0.04578810930252075, 0.03991249203681946, -0.009708678349852562, -0.06344973295927048, 0.04314582049846649, 0.0010473552392795682, 0.031185979023575783, 0.0148541908711195, 0.0148541908711195, 0.05055118724703789, -0.017366105690598488, -0.061746153980493546, -0.0028921780176460743, 0.005454069469124079, 0.12947222590446472, -0.011594787240028381, -0.0003430522920098156, 0.011325342580676079, 0.05917339771986008, -0.09060274064540863, 0.006297168787568808, -0.04123363643884659, 0.008713473565876484, 0.054062649607658386, 0.008226736448705196, 0.020686352625489235, 0.03570568561553955, 0.00580608518794179, -0.06045977398753166, -0.0395648218691349, -0.021242624148726463, 0.003048629267141223, -0.02859583869576454, -0.011968531645834446, -0.010942906141281128, 0.026927024126052856, 0.027917882427573204, -0.016131877899169922, -0.010812530294060707, 0.02139907516539097, -0.014941108413040638, 0.005567062180489302, -0.02758759632706642, -0.02179889567196369, 0.021746745333075523, -0.04881283640861511, -0.02009531296789646, -0.047561224550008774, 0.036992065608501434, 0.022807138040661812, 0.05020351707935333, 0.010908138938248158, 0.06188521906733513, -0.02941286377608776, 0.0277614314109087, -0.04728309065103531, 0.032402824610471725, 0.022459467872977257, 0.05580100044608116, 0.049716778099536896, 0.008839503861963749, -0.0380350723862648, 0.006236326415091753, 0.011846847832202911, -0.0473526231944561, 0.07384505867958069, -0.007257606368511915, -0.021381691098213196, 0.05409741774201393, 0.03678346425294876, 0.025553729385137558, 0.03356751799583435, -0.0326114259660244, -0.044918935745954514, 0.038382742553949356, -0.01413277629762888, -0.01193376537412405, -0.018617715686559677, 0.020008396357297897, 0.025901397690176964, 0.03122074529528618, 0.03942575305700302, -0.016653383150696754, -0.0006486214115284383, 0.027187775820493698, -0.04999491572380066, -0.027413761243224144, 0.0030768774449825287, 0.0419289767742157, 0.04481463506817818, 0.04245048016309738, 0.04860423505306244, -0.032837409526109695, 0.04119886830449104, 0.010056348517537117, 0.022320399060845375, 0.03681822866201401, 0.057956550270318985, -0.04610101133584976, -0.032524507492780685, -0.03480174392461777, -0.015193169005215168, -0.01768770068883896, 0.0004177469527348876, 0.02310265600681305, 0.004541436675935984, -0.020947104319930077, -0.014089317992329597, -0.007088117767125368, 0.005080324597656727, 0.040955498814582825, 0.020356064662337303, 0.027222543954849243, 0.013924174942076206, -0.0535411462187767, 0.004997753072530031, -0.02185104601085186, -0.06428413838148117, -0.027570214122533798, -0.038000307977199554, -0.024163048714399338, 0.005710476078093052, 0.005297618452459574, 0.010734304785728455, -0.04210280999541283, 0.012759480625391006, 0.04088596627116203, 0.028178635984659195, 0.013437436893582344, -0.024771472439169884, 0.0035136376973241568, -0.004302413668483496, -0.010690845549106598, -0.04182467237114906, -0.056322503834962845, 0.0025249517057090998, -0.013672114349901676, 0.037930771708488464, 0.017609473317861557, 0.03935622051358223, 0.04074689745903015, 0.04950817674398422, -0.003830886445939541, 0.0020621162839233875, -0.02379799634218216, -0.04929957538843155, -0.03367181867361069, -0.02991698496043682, 0.008604827336966991, 0.041094567626714706, 0.016201412305235863, 0.006444928701967001, 0.05962536856532097, 0.02550157904624939, 0.023120040073990822, -0.05301964282989502, -0.048882368952035904, -0.03772217035293579, -0.021381691098213196, -0.037304967641830444, 0.04519706964492798, 0.030264653265476227, -0.034089021384716034, 0.012237976305186749, -0.022963589057326317, 0.06995116174221039, 0.03789600729942322, -0.0070142378099262714, 0.06000780314207077, -0.03174225240945816, -0.006740447599440813, 0.02424996718764305, 0.051594194024801254, 0.015001950785517693, -0.017461715266108513, -0.0003435955150052905, -0.04182467237114906, -0.017366105690598488, -0.0026401174254715443, -0.012516112066805363, -0.014723815023899078, 0.00012086956849088892, -0.02557111158967018, 0.04085119813680649, -0.022894054651260376, 0.019991012290120125, -0.035410165786743164, 0.040016792714595795, -0.037652637809515, -0.0985991507768631, -0.049890611320734024, -0.061050813645124435, -0.0073923286981880665, -0.06710026413202286, 0.01858294941484928, -0.02908257767558098, 0.00005503639840753749, -0.010238874703645706, 0.014245769008994102, 0.009821671061217785, 0.04717878997325897, -0.021312156692147255, -0.02115570567548275, 0.008817775174975395, -0.008005096577107906, -0.005684400908648968, -0.003407163778319955, 0.013724264688789845, 0.0021088344510644674, -0.01089075580239296, -0.014089317992329597, -0.0036396679934114218, 0.05020351707935333, -0.05736551433801651, -0.025136524811387062, 0.002568410476669669, 0.040781665593385696, -0.05740027874708176, 0.005832160357385874, -0.034906044602394104, 0.03297647833824158, 0.0277614314109087, -0.022876670584082603, -0.029882216826081276, -0.03130766376852989, -0.019678110256791115, -0.008478797040879726, -0.02254638448357582, 0.006405815482139587, 0.003830886445939541, 0.04596194624900818, 0.02929117903113365, -0.016340479254722595, -0.03615765646100044, 0.002494530752301216, -0.015410463325679302, 0.04217234253883362, -0.06348450481891632, -0.005766972433775663, 0.030612323433160782, 0.018739400431513786, -0.03695729747414589, 0.03587952256202698, -0.05322824418544769, -0.039703886955976486, -0.007301065139472485, -0.03443669155240059, 0.0014287055237218738, 0.026718422770500183, 0.010447476990520954, -0.04283291473984718, 0.018356963992118835, 0.027813581749796867, 0.010334484279155731, 0.00584085239097476, 0.0008371236617676914, 0.007674810476601124, 0.0035136376973241568, -0.016835909336805344, 0.06922104954719543, 0.00196650717407465, -0.030386338010430336, -0.029360713437199593, -0.04279815033078194, 0.01629702001810074, 0.05573146417737007, -0.029239028692245483, -0.05653110519051552, 0.023085273802280426, -0.06438843905925751, 0.026805339381098747, -0.01051701046526432, -0.00847010500729084, 0.02941286377608776, 0.007157651707530022, -0.04036446288228035, 0.018096212297677994, 0.02424996718764305, -0.019121836870908737, 0.0043067592196166515, -0.00824846513569355, 0.007800840772688389, -0.04613577947020531, -0.01618402823805809, 0.045058004558086395, 0.010151957161724567, -0.005680054891854525, -0.008313653990626335, 0.0011940284166485071, -0.05402788519859314, 0.08747371286153793, 0.012290126644074917, -0.04943864047527313, 0.05055118724703789, 0.025831865146756172, 0.03615765646100044, -0.03709636628627777, -0.017409564927220345, -0.012272743508219719, 0.010160649195313454, 0.012490036897361279, 0.07725222408771515, -0.034401923418045044, 0.020808035507798195, -0.04391069337725639, -0.003498427104204893, -0.020877569913864136, 0.04092073440551758, 0.00576262641698122, -0.014089317992329597, 0.007887758314609528, -0.04217234253883362, -0.048708535730838776, 0.0001736990816425532, 0.02492792345583439, 0.03890424966812134, -0.04290245100855827, -0.008839503861963749, -0.01844388246536255, 0.02903042547404766, 0.026092616841197014, -0.026475053280591965, -0.025970932096242905, 0.027570214122533798, 0.005719167646020651, -0.003013862296938896, 0.010960289277136326, 0.04557950794696808, 0.010968981310725212, -0.02626645192503929, 0.019104454666376114, 0.012307509779930115, 0.00033354570041410625, -0.0853876993060112, -0.028422003611922264, 0.04005155712366104, -0.026092616841197014, 0.03273310884833336, -0.019695492461323738, -0.01756601594388485, -0.008865579031407833, 0.01278555579483509, -0.004750038497149944, -0.029795300215482712, -0.002655328018590808, -0.03702683001756668, -0.0729411169886589, -0.03820890933275223, -0.023033123463392258, 0.03789600729942322, -0.03810460865497589, 0.04745692387223244, -0.031568415462970734, -0.00783560797572136, -0.030751392245292664, -0.07516620308160782, 0.017348721623420715, -0.01856556534767151, -0.08469235897064209, 0.018965385854244232, -0.010882063768804073, -0.026735804975032806, -0.02506699040532112, 0.009500076994299889, -0.0013602579711005092, 0.026283835992217064, 0.012246668338775635, -0.0076530808582901955, -0.0027639747131615877, 0.00021281192312017083, -0.009647835977375507, -0.03344583138823509, -0.007870374247431755, 0.008478797040879726, -0.025658030062913895, 0.011264501139521599, -0.048117496073246, 0.03782647103071213, 0.009682603180408478, -0.00022014559363014996, 0.033202461898326874, 0.0031529301777482033, -0.034662675112485886, -0.018965385854244232, 0.017270496115088463, 0.0007942081429064274, 0.04905620589852333, 0.07780849933624268, -0.04676158353686333, 0.002290274715051055, 0.013237526640295982, 0.060216404497623444, -0.011420952156186104, -0.02624906785786152, -0.03966912254691124, -0.0040612174198031425, -0.02600570023059845, -0.051663730293512344, -0.0026053504552692175, -0.025797097012400627, 0.03328938037157059, -0.003300689859315753, -0.014176235534250736, 0.028995659202337265, 0.05851282179355621, 0.04547520726919174, -0.038382742553949356, 0.037304967641830444, -0.03016035258769989, -0.018600333482027054, 0.018044061958789825, 0.04679635167121887, 0.008978571742773056, -0.018044061958789825, -0.0012885511387139559, 0.0018969732336699963, 0.0512465238571167, 0.004002548288553953, -0.005480144638568163, 0.00609291298314929, -0.012976774014532566, 0.05030781775712967, -0.0215381421148777, 0.025449426844716072, 0.04439743235707283, 0.0024988765362650156, 0.014584747143089771, -0.010343176312744617, 0.014810732565820217, -0.053749747574329376, 0.06609202176332474, 0.019886711612343788, -0.041477005928754807, 0.018165746703743935, 0.011038515716791153, -0.04797843098640442, 0.021572910249233246, -0.039460521191358566, -0.06393647193908691, -0.01894800364971161, -0.03243758901953697, 0.036748696118593216, 0.01085598859935999, -0.008213698863983154, -0.02845677174627781, -0.0314641147851944, 0.04279815033078194, -0.02072111889719963, 0.04766552522778511, 0.029882216826081276, -0.0024141320027410984, -0.012107600457966328, -0.02953454665839672, -0.022077031433582306, 0.021068789064884186, 0.0015449575148522854, 0.033219847828149796, 0.01756601594388485, 0.019486891105771065, -0.030195120722055435, -0.0011027650907635689, -0.006566612981259823, 0.008391879498958588, -0.02972576580941677, -0.026544587686657906, 0.013619963079690933, -0.048882368952035904, -0.019104454666376114, -0.009517460130155087, -0.008304961957037449, -0.028665373101830482, 0.011499177664518356, 0.03852181136608124, 0.01177731342613697, 0.016827216371893883, -0.017583398148417473, -0.034401923418045044, -0.0064536202698946, -0.026805339381098747, 0.048395633697509766, 0.006114642135798931, 0.02216394804418087, -0.028439387679100037, -0.02046036720275879, 0.011203658767044544, -0.028630606830120087, 0.015619064681231976, 0.02266806922852993, 0.015010642819106579, -0.007179380860179663, 0.0032181183341890574, -0.047943662852048874, -0.034714825451374054, 0.02079065330326557, -0.02739637903869152, 0.005184625741094351, 0.045683808624744415, -0.011890306137502193, 0.008674360811710358, -0.027552830055356026, -0.03601858764886856, 0.021520759910345078, 0.005619212985038757, -0.023902297019958496, -0.08211959898471832, -0.00206320290453732, 0.04258954897522926, -0.0005834333715029061, 0.0043002404272556305, -0.014610822312533855, -0.020634200423955917, 0.04450173303484917, 0.025797097012400627, -0.003207253757864237, 0.002903042593970895, 0.03205515444278717, 0.01913922093808651, 0.008995955809950829, -0.045058004558086395, 0.0562877357006073, -0.004391503985971212, 0.013576504774391651, 0.023398175835609436, 0.013333136215806007, -0.024597637355327606, 0.02946501411497593, 0.006631800904870033, 0.026805339381098747, 0.024788854643702507, -0.020755885168910027, 0.02374584600329399, -0.0032637501135468483, -0.004413233138620853, -0.011959840543568134, 0.0034049907699227333, -0.0036070740316063166, 0.0077573820017278194, -0.0019295673118904233, -0.014897650107741356, -0.011985915713012218, 0.001506931148469448, 0.008509217761456966, 0.06449274718761444, 0.024041365832090378, 0.0045588198117911816, -0.059521064162254333, -0.010464860126376152, -0.029690999537706375, 0.0361228883266449, 0.005619212985038757, 0.005706130061298609, -0.013089766725897789, -0.05510566011071205, 0.011812080629169941, 0.036748696118593216, 0.03349798172712326, 0.0055322954431176186, 0.013524354435503483, 0.039703886955976486, -0.00042834001942537725, -0.00468919612467289, 0.03626195713877678, -0.010916830971837044, -0.01080383826047182, 0.04425836354494095, -0.0003131744160782546, -0.008326691575348377, 0.0032246371265500784, -0.02374584600329399, 0.03177701681852341, 0.026927024126052856, 0.09943355619907379, -0.02159029245376587, 0.0016720743151381612, 0.047943662852048874, -0.031898703426122665, 0.0037700440734624863, -0.0025640646927058697, 0.01820051297545433, 0.03501034528017044, 0.0019534695893526077, 0.016827216371893883, 0.038313210010528564, 0.004463210701942444, -0.009334933944046497, 0.005597483366727829, -0.032959096133708954, -0.06278916448354721, 0.006084220949560404, -0.00969998724758625, -0.02190319634974003, 0.028873974457383156, -0.013046308420598507, -0.008774315938353539, 0.014845499768853188, -0.04846516624093056, -0.021451225504279137, -0.010065039619803429, 0.014558671973645687, 0.056635405868291855, 0.02192057855427265, -0.0041676913388073444, -0.018426498398184776, 0.054757989943027496, 0.004493631888180971, 0.004871722776442766, -0.024962689727544785, -0.005988611839711666, 0.023276491090655327, 0.037444036453962326, -0.0034766977187246084, -0.006162446923553944, 0.0316205658018589, -0.049021437764167786, 0.0010049829725176096, 0.005349768791347742, 0.0067665232345461845, 0.000730106548871845, 0.00884385034441948, 0.03401948884129524, 0.022007497027516365, 0.001745954155921936, -0.01510625146329403, -0.0067534856498241425, 0.027744047343730927, 0.01598411798477173, -0.034036871045827866, 0.03480174392461777, -0.022250866517424583, -0.03429762274026871, -0.024649787694215775, 0.019851943477988243, -0.005506220273673534, -0.016383938491344452, -0.002583621069788933, 0.039703886955976486, -0.022529002279043198, 0.016097109764814377, 0.0034745249431580305, 0.017174886539578438, -0.00023413386952597648, -0.006327589973807335, 0.010204107500612736, 0.006988162640482187, -0.03608812391757965, 0.03236805647611618, -0.04721355438232422, 0.05385404825210571, -0.015314853750169277, -0.01080383826047182, 0.0036070740316063166, -0.0023424250539392233, 0.05813038721680641, 0.015323545783758163, -0.0019512965809553862, 0.022024881094694138, 0.004567511845380068, 0.04495370388031006, -0.015975426882505417, -0.0620938204228878, 0.031707484275102615, 0.0026075232308357954, -0.01705320179462433, -0.011916381306946278, -0.020999254658818245, 0.02367631159722805, 0.027796199545264244, -0.022894054651260376, -0.000593754812143743, 0.0023467710707336664, -0.032402824610471725, 0.015419154427945614, -0.007096809335052967, -0.008917729370296001, -0.005649633705615997, 0.01369818951934576, 0.011090666055679321, 0.022459467872977257, -0.004849993623793125, 0.00241630501113832, 0.0029356367886066437, 0.01606234349310398, -0.0014102355344220996, -0.016601230949163437, 0.005254159681499004, -0.03681822866201401, -0.013706880621612072, -0.012768172658979893, 0.06605725735425949, -0.02732684463262558, 0.028196018189191818, -0.027744047343730927, -0.03335891664028168, 0.007674810476601124, -0.005684400908648968, 0.01001288928091526, -0.028752289712429047, 0.0010229096515104175, 0.041477005928754807, 0.030942609533667564, 0.02694440819323063, -0.020564667880535126, 0.0027335535269230604, 0.007705231662839651, -0.053367309272289276, -0.0051628961227834225, 0.0008170239743776619, -0.003652705578133464, 0.04220711067318916, 0.008900346234440804, -0.03153364732861519, -0.02984745055437088, -0.016453472897410393, -0.0060320706106722355, 0.0355144664645195, 0.005619212985038757, -0.0031094716396182775, -0.016470855101943016, -0.011951148509979248, 0.005093362182378769, -0.05169849470257759, 0.0001775017153704539, 0.01655777357518673, -0.02046036720275879, -0.03208991885185242, 0.016601230949163437, -0.030142970383167267, -0.04710925370454788, -0.00014775965246371925, 0.010456168092787266, -0.04898667335510254, 0.027848349884152412, -0.007301065139472485, 0.023502476513385773, -0.011942456476390362, 0.032715726643800735, 0.12446577847003937, -0.0512465238571167, 0.04182467237114906, -0.039251916110515594, 0.02058205008506775, 0.015818974003195763, -0.03426285833120346, 0.02682272344827652, 0.029256410896778107, 0.0044110603630542755, 0.021955346688628197, -0.004506669472903013, 0.0021501202136278152, -0.043980225920677185, -0.054757989943027496, -0.01856556534767151, -0.02355462685227394, 0.036296725273132324, -0.020808035507798195, -0.01189899817109108, 0.034401923418045044, 0.05357591435313225, -0.02871752344071865, -0.012802939862012863, 0.03928668424487114, 0.06181568652391434, 0.03695729747414589, -0.0018252662848681211, -0.023398175835609436, 0.024197816848754883, 0.019347822293639183, -0.013811182230710983, -0.020130079239606857, 0.005584445782005787, -0.015940658748149872, 0.010273641906678677, -0.04283291473984718, -0.03149888291954994, -0.04484939947724342, 0.02072111889719963, 0.015375696122646332, -0.040955498814582825, 0.05847805738449097, -0.013280985876917839, 0.012142366729676723, 0.05218523368239403, -0.019539041444659233, -0.015453921630978584, -0.05722644552588463, 0.00464573735371232, -0.0290999598801136, -0.0011201485758647323, -0.007583546917885542, 0.09178481996059418, -0.006192868109792471, -0.010821221396327019, -0.02449333667755127, -0.036922529339790344, -0.009578302502632141, -0.025970932096242905, 0.021764127537608147, -0.049577709287405014, -0.01863509975373745, 0.03546231612563133, 0.05778271704912186, -0.01744433119893074, -0.010178032331168652, -0.00818327721208334, 0.02506699040532112, -0.008161547593772411, -0.022807138040661812, 0.008113743737339973, 0.004467556718736887, 0.014106701128184795, 0.00878735352307558, -0.0032767876982688904, 0.029551930725574493, 0.02694440819323063, -0.028474153950810432, -0.009500076994299889, 0.014219693839550018, 0.015219244174659252, -0.024910539388656616, 0.02965623140335083, 0.023884912952780724, -0.030073435977101326, -0.07481853663921356, 0.015836358070373535, 0.00601468700915575, 0.022650685161352158, 0.024458568543195724, -0.05082932114601135, 0.01945212483406067, -0.02209441363811493, 0.028056951239705086, 0.010977673344314098, -0.026648888364434242, 0.012324893847107887, -0.022320399060845375, -0.019747642800211906, -0.00241630501113832, 0.011029823683202267, 0.023641545325517654, 0.03078615851700306, 0.007466208655387163, -0.03401948884129524, -0.05357591435313225, -0.02058205008506775, 0.02744852937757969, -0.029934367164969444, -0.04248524829745293, 0.0011244944762438536, 0.02141645736992359, 0.020616818219423294, -0.012064141221344471, 0.02713562548160553, 0.01328967697918415, 0.008600480854511261, 0.013924174942076206, -0.025084374472498894, -0.01127319224178791, -0.01344612892717123, -0.05969490110874176, -0.027796199545264244, 0.0007306497427634895, -0.027153009548783302, -0.01820051297545433, -0.0011516561498865485, 0.07050742954015732, 0.013506971299648285, 0.00011061602708650753, -0.031116444617509842, -0.028300320729613304, -0.05583576485514641, 0.045544739812612534, -0.0072880275547504425, 0.001201633713208139, -0.019625958055257797, 0.004467556718736887, 0.005023828241974115, -0.04314582049846649, 0.038626112043857574, 0.024441184476017952, -0.023137424141168594, 0.03820890933275223, -0.0355144664645195, -0.032454974949359894, -0.055766232311725616, -0.01294200774282217, 0.06619632244110107, 0.014802040532231331, 0.021990112960338593, -0.01479334942996502, -0.008018134161829948, -0.039321452379226685, 0.048639003187417984, 0.008474450558423996, -0.008856887929141521, 0.04293721914291382, -0.04151177033782005, 0.03448884189128876, -0.008869925513863564, -0.033776119351387024, -0.00044735323172062635, -0.004428443964570761, -0.007435787469148636, -0.028873974457383156, 0.06039024144411087, 0.010951598174870014, 0.025136524811387062, -0.010412709787487984, -0.0010462687350809574, 0.05993827059864998, 0.010056348517537117, -0.004602278582751751, 0.03904331475496292, 0.00991728063672781, 0.0003848813066724688, 0.017140120267868042, -0.026283835992217064, 0.010838605463504791, -0.0030442834831774235, -0.01546261366456747, -0.016288328915834427, -0.01136010978370905, -0.04189420863986015, 0.017018435522913933, 0.01756601594388485, -0.06529238075017929, 0.017548631876707077, -0.029812684282660484, 0.04728309065103531, -0.0044197519309818745 ]
A growing body of research runs human subject evaluations to study whether providing users with explanations of machine learning models can help them with practical real-world use cases. However, running user studies is challenging and costly, and consequently each study typically only evaluates a limited number of different settings, e.g., studies often only evaluate a few arbitrarily selected explanation methods. To address these challenges and aid user study design, we introduce Use-Case-Grounded Simulated Evaluations (SimEvals). SimEvals involve training algorithmic agents that take as input the information content (such as model explanations) that would be presented to each participant in a human subject study, to predict answers to the use case of interest. The algorithmic agent's test set accuracy provides a measure of the predictiveness of the information content for the downstream use case. We run a comprehensive evaluation on three real-world use cases (forward simulation, model debugging, and counterfactual reasoning) to demonstrate that Simevals can effectively identify which explanation methods will help humans for each use case. These results provide evidence that SimEvals can be used to efficiently screen an important set of user study design decisions, e.g. selecting which explanations should be presented to the user, before running a potentially costly user study.
[ -0.04803645610809326, -0.010915773920714855, -0.04623773694038391, -0.03135419264435768, 0.032853126525878906, 0.06475399434566498, -0.002338779391720891, 0.016391294077038765, -0.005978105124086142, 0.02701609767973423, -0.019750673323869705, -0.0543496198952198, -0.012352987192571163, -0.04958829656243324, 0.015209781005978584, 0.03562174737453461, 0.02401822805404663, -0.00046015100087970495, 0.018816042691469193, -0.022307679057121277, -0.016585273668169975, -0.013957729563117027, -0.045356009155511856, -0.01667344756424427, 0.01380783598870039, 0.0024952858220785856, 0.003216097131371498, 0.024176938459277153, -0.012494063936173916, 0.04154695197939873, -0.013331703841686249, 0.019750673323869705, -0.024952858686447144, -0.026099102571606636, -0.04394524544477463, -0.004479170311242342, 0.022678004577755928, -0.016391294077038765, -0.06094493344426155, 0.07709816098213196, -0.033823028206825256, -0.024723609909415245, 0.016629360616207123, -0.0010933408048003912, -0.03278258815407753, -0.06369592249393463, -0.07618116587400436, -0.05082271248102188, -0.00685101468116045, -0.0010068214032799006, -0.045602891594171524, -0.0016565435798838735, 0.06581206619739532, -0.01707022450864315, -0.027157174423336983, 0.013005465269088745, 0.014945263043045998, -0.02382424846291542, 0.06023954972624779, -0.01825173757970333, 0.004386588931083679, 0.014989349991083145, 0.013358156196773052, 0.030049238353967667, 0.004659924190491438, -0.00541820889338851, -0.022995425388216972, -0.008173604495823383, 0.022131333127617836, -0.00744618009775877, -0.02005046047270298, 0.0449327789247036, 0.008442530408501625, 0.0292027797549963, 0.004479170311242342, -0.03472238779067993, 0.04542654752731323, 0.009284579195082188, 0.004148522857576609, -0.02006809413433075, 0.048953451216220856, 0.0112331947311759, 0.005920792929828167, -0.0018395017832517624, 0.1108153834939003, -0.05523134395480156, 0.008499843068420887, -0.045179665088653564, 0.01559774111956358, -0.04193491116166115, -0.03507507964968681, -0.02698083035647869, 0.00923167634755373, -0.008045753464102745, -0.06267311424016953, 0.01301428209990263, -0.022766176611185074, 0.014054719358682632, 0.004593794699758291, -0.012573419138789177, 0.0036635734140872955, -0.0182693712413311, -0.0049068075604736805, -0.012273631989955902, 0.008526294492185116, -0.01987411454319954, -0.08810210973024368, 0.013843105174601078, 0.02340102009475231, 0.09663721919059753, -0.059463631361722946, 0.014971715398132801, -0.08083668351173401, -0.0354277677834034, -0.0276333075016737, 0.003813466988503933, -0.027298251166939735, -0.07462932914495468, 0.032094843685626984, -0.06510668247938156, 0.024335650727152824, 0.061297621577978134, 0.0408768393099308, -0.042393408715724945, -0.07156091928482056, 0.08767887949943542, -0.014416227117180824, 0.031689248979091644, 0.04052414745092392, -0.02082637883722782, -0.002803890034556389, 0.028955897316336632, -0.0042124479077756405, 0.03198903426527977, 0.014522034674882889, 0.00045767115079797804, 0.016012152656912804, 0.017546355724334717, 0.020403150469064713, -0.022536927834153175, -0.06023954972624779, -0.005554876755923033, -0.047189999371767044, -0.016417747363448143, -0.010757062584161758, -0.060909662395715714, -0.0009473048849031329, 0.07886161655187607, -0.03830219805240631, 0.0033571734093129635, -0.00913468562066555, -0.016117960214614868, -0.010677707381546497, 0.007472631521522999, 0.02922041527926922, -0.010148671455681324, 0.02260746620595455, -0.015015801414847374, 0.024688340723514557, 0.026328351348638535, 0.08584488928318024, -0.0304019283503294, 0.008729091845452785, 0.03936026990413666, 0.04525019973516464, 0.0012917292769998312, -0.026769215241074562, -0.04902398958802223, -0.02241348661482334, 0.04292244464159012, -0.0097342599183321, 0.030631177127361298, -0.038654886186122894, 0.02262509986758232, 0.04666096344590187, 0.050364214926958084, 0.01143599208444357, 0.040418341755867004, -0.046378809958696365, 0.007931129075586796, -0.06447184085845947, -0.03230645880103111, 0.023383386433124542, 0.010122220031917095, 0.02842686139047146, -0.027686210349202156, 0.03378775715827942, 0.0097342599183321, 0.01964486576616764, -0.022007891908288002, -0.013931278139352798, 0.023771345615386963, -0.004990571644157171, 0.03876069560647011, -0.01612677611410618, -0.027315884828567505, -0.055548764765262604, -0.03713831678032875, -0.008662962354719639, -0.02678684890270233, -0.06408388167619705, -0.0452149324119091, 0.004827452357858419, 0.007208113558590412, 0.022166602313518524, 0.0008216588175855577, -0.005885524209588766, 0.038020044565200806, -0.030825156718492508, -0.10298565030097961, 0.003998629283159971, -0.008257368579506874, -0.013146541081368923, -0.040629953145980835, -0.04228759929537773, -0.009831249713897705, -0.0009169955155812204, 0.013252348639070988, -0.04115898907184601, -0.00605305191129446, 0.02146122232079506, 0.033082377165555954, 0.018816042691469193, -0.046872578561306, 0.018410447984933853, 0.04323986545205116, 0.004390997812151909, 0.022501658648252487, 0.016937965527176857, -0.007992850616574287, 0.030666446313261986, 0.010510179214179516, 0.02821524627506733, -0.01825173757970333, 0.010765880346298218, -0.055548764765262604, 0.03310001268982887, -0.018745504319667816, -0.02287198416888714, -0.010228026658296585, 0.014442679472267628, -0.02997869998216629, 0.00934630073606968, -0.03468712046742439, 0.0543496198952198, -0.024529630318284035, 0.02504103071987629, 0.02207843028008938, 0.08013129979372025, 0.0040515330620110035, -0.049341414123773575, -0.01083641778677702, 0.006555636413395405, 0.04468589648604393, 0.004097823519259691, 0.04309878870844841, 0.058299753814935684, -0.03535722941160202, 0.0008988099289126694, -0.02498812787234783, 0.03615078330039978, 0.0075299437157809734, -0.03787896782159805, 0.031142577528953552, -0.052938856184482574, -0.0372793935239315, 0.07801515609025955, -0.03918392211198807, -0.02542899176478386, -0.02860320545732975, 0.002221950562670827, -0.021302511915564537, -0.06602367758750916, 0.03352323919534683, -0.03646820783615112, -0.07399448752403259, -0.007525535300374031, 0.023189404979348183, 0.020138632506132126, -0.011480078101158142, -0.03572755679488182, -0.02638125605881214, -0.001802028389647603, 0.01744936592876911, 0.01727302186191082, -0.048177532851696014, 0.0224663894623518, -0.0040228767320513725, -0.045356009155511856, -0.005246272310614586, 0.005753265228122473, -0.026927925646305084, 0.01200029719620943, 0.042217060923576355, 0.05741802603006363, 0.047366343438625336, -0.03872542455792427, 0.009910604916512966, 0.044968049973249435, -0.024282746016979218, -0.0381963886320591, 0.0013446328230202198, 0.041617490351200104, 0.1156119704246521, 0.019627230241894722, 0.015447847545146942, 0.008777586743235588, 0.06182665750384331, -0.06052170321345329, -0.023594999685883522, 0.052515625953674316, 0.009593184106051922, -0.0006546818767674267, -0.04433320462703705, 0.00664821732789278, -0.016214950010180473, 0.032059572637081146, -0.04323986545205116, 0.024265112355351448, 0.010360285639762878, 0.0010266602039337158, -0.014151709154248238, -0.10326780378818512, -0.02026207372546196, 0.030313756316900253, 0.023700807243585587, -0.015959247946739197, 0.026698676869273186, 0.021919719874858856, -0.03324108570814133, -0.05660683661699295, 0.010686524212360382, -0.05004679411649704, 0.0292027797549963, -0.009593184106051922, -0.03269441798329353, -0.00902887899428606, 0.03262387961149216, -0.04891818389296532, 0.006996499374508858, -0.038266927003860474, -0.047366343438625336, -0.051316481083631516, -0.0274040587246418, 0.01540376152843237, -0.00934630073606968, -0.030454831197857857, 0.004071372095495462, 0.011594702489674091, -0.009249310940504074, 0.0010773595422506332, -0.025922758504748344, 0.006621765438467264, -0.001418477389961481, 0.010589534416794777, -0.034263890236616135, 0.02204316109418869, 0.026328351348638535, -0.001950819743797183, 0.017361193895339966, 0.057135872542858124, -0.029678912833333015, -0.025869853794574738, 0.06115654855966568, -0.10580717772245407, 0.030930964276194572, -0.024670707061886787, -0.0023586181923747063, 0.006837788503617048, -0.005400574300438166, -0.012494063936173916, 0.04821280390024185, 0.03597443923354149, 0.04091210663318634, -0.004937668330967426, 0.009399203583598137, 0.0413353368639946, 0.010316199623048306, -0.06256730854511261, 0.04563816264271736, -0.04838914796710014, -0.0132170794531703, -0.006604131311178207, 0.04623773694038391, -0.04345148056745529, 0.012979013845324516, 0.029731815680861473, 0.07177253067493439, -0.0048539042472839355, 0.03280022367835045, 0.023912420496344566, -0.023506827652454376, -0.025111569091677666, -0.06309634447097778, 0.04112372174859047, 0.045779235661029816, 0.025340817868709564, -0.02916751056909561, 0.06052170321345329, 0.01358740497380495, 0.0002970315981656313, -0.015474298968911171, -0.0112331947311759, 0.04711946099996567, -0.003683412214741111, -0.005524016451090574, 0.007000908255577087, 0.00923167634755373, -0.0034784108866006136, -0.03511034697294235, 0.015112791210412979, 0.01784614287316799, -0.0016918126493692398, -0.04726053774356842, 0.03632713109254837, 0.05741802603006363, -0.08528058230876923, 0.0006006761686876416, 0.05322100967168808, -0.0024842643178999424, -0.024494361132383347, 0.02498812787234783, 0.038231659680604935, -0.0028457720763981342, -0.019609596580266953, -0.025869853794574738, -0.0916290134191513, 0.01041318941861391, -0.02558770217001438, -0.00803693663328886, 0.030648810788989067, 0.01222072821110487, -0.02703373320400715, -0.04651988670229912, 0.03318818286061287, 0.04256975278258324, 0.023577366024255753, 0.05420854315161705, -0.0015000371495261788, -0.03355851024389267, -0.01064243819564581, -0.028885358944535255, -0.005224229302257299, 0.006119181402027607, -0.035233788192272186, -0.04246394708752632, 0.0013589608715847135, -0.02144358679652214, 0.01242352556437254, -0.01311127282679081, -0.08457519859075546, -0.009072965011000633, -0.07007961720228195, -0.028356323018670082, 0.06478925794363022, -0.04112372174859047, 0.01943325065076351, -0.05364423617720604, -0.02401822805404663, -0.019415616989135742, -0.007847364991903305, 0.07766246795654297, 0.04334567114710808, -0.032659146934747696, 0.05297412350773811, 0.042781367897987366, -0.043169327080249786, -0.01061598677188158, 0.0177138838917017, 0.028497399762272835, 0.006657034624367952, -0.032659146934747696, -0.005360896699130535, -0.02262509986758232, -0.019785942509770393, -0.015518385916948318, -0.0036503474693745375, -0.029520202428102493, 0.06958585232496262, -0.011594702489674091, 0.01987411454319954, 0.01728183776140213, -0.005563694052398205, -0.004095619544386864, -0.01033383421599865, -0.010386737994849682, -0.010342651046812534, -0.004862721543759108, -0.02877955138683319, -0.06962112337350845, -0.06009847670793533, -0.024494361132383347, -0.0050963787361979485, 0.02206079661846161, -0.0061059556901454926, -0.02123197354376316, -0.0033505605533719063, -0.02167283557355404, 0.03759681433439255, 0.02682211808860302, -0.007014133967459202, -0.005281541496515274, -0.0636606514453888, -0.013155358843505383, 0.03745574131608009, -0.005334445275366306, 0.04073576256632805, 0.0031543762888759375, 0.02161993272602558, -0.018727870658040047, 0.006709938403218985, 0.0077371494844555855, 0.00022360032016877085, -0.02382424846291542, 0.05124594271183014, 0.036644551903009415, -0.020738206803798676, 0.013340521603822708, 0.05018787086009979, 0.02659286931157112, -0.016364842653274536, 0.004368954803794622, -0.00016794133989606053, 0.03717358782887459, -0.04606138914823532, 0.0276333075016737, 0.02481178194284439, 0.03138945996761322, 0.05456123128533363, -0.00019742405856959522, -0.0007571825990453362, 0.03720885515213013, -0.03140709549188614, -0.019151099026203156, -0.013067185878753662, -0.023700807243585587, 0.009522645734250546, -0.005171325523406267, -0.035480670630931854, -0.01746700145304203, -0.045990850776433945, 0.02227240987122059, 0.02068530209362507, 0.008812855929136276, -0.0009351811022497714, 0.04390997812151909, 0.040629953145980835, 0.024864686653017998, 0.017387645319104195, 0.02624017931520939, 0.03258860856294632, -0.0003400157729629427, -0.007961990311741829, -0.0264341589063406, 0.0077547840774059296, -0.023877153173089027, 0.02303069457411766, 0.02662813849747181, -0.0008651940734125674, 0.003954543266445398, -0.0075475783087313175, 0.014909994788467884, 0.023559730499982834, 0.007177253253757954, -0.021708104759454727, 0.0035577663220465183, 0.03535722941160202, 0.06013374403119087, -0.005775308236479759, 0.012802667915821075, -0.054279081523418427, 0.00685101468116045, -0.0022814671974629164, -0.016038604080677032, -0.0050522927194833755, 0.013728480786085129, 0.018498621881008148, -0.03518088534474373, -0.009857702068984509, -0.02800363302230835, 0.04563816264271736, 0.022748542949557304, -0.01072179339826107, 0.016567640006542206, -0.04902398958802223, 0.010686524212360382, -0.01627667061984539, -0.023965325206518173, 0.011771048419177532, 0.03988930583000183, 0.040030382573604584, 0.026698676869273186, -0.013252348639070988, 0.01358740497380495, 0.03731466457247734, 0.007494674995541573, -0.006335204467177391, 0.010695341974496841, 0.018145930022001266, -0.016241401433944702, 0.0026473836041986942, -0.022290045395493507, 0.0034960454795509577, 0.07293641567230225, 0.007979623973369598, 0.009804798290133476, -0.029432028532028198, 0.014239882118999958, 0.020508958026766777, 0.006432194262742996, 0.028444495052099228, -0.015324405394494534, 0.0076754288747906685, -0.04211125522851944, 0.011250829324126244, -0.054102733731269836, 0.0025614153128117323, -0.004942076746374369, -0.025781681761145592, -0.014786552637815475, 0.02306596376001835, -0.031054405495524406, 0.05043475329875946, 0.005325627978891134, -0.018710235133767128, 0.0389370396733284, -0.0262049101293087, -0.01869260147213936, 0.019345078617334366, 0.03410517796874046, -0.013534501194953918, 0.010316199623048306, -0.02738642320036888, 0.02047368884086609, 0.027139540761709213, 0.002365231281146407, -0.006661443505436182, 0.06496560573577881, 0.017996037378907204, -0.004256534390151501, 0.004946485627442598, 0.0018758730730041862, -0.04038307070732117, 0.09698990732431412, -0.01401063334196806, 0.05494919419288635, -0.003493841039016843, 0.01429278589785099, 0.020350245758891106, 0.03255334123969078, 0.035057444125413895, 0.05844083055853844, 0.02384188398718834, 0.0437336303293705, -0.0025702326092869043, -0.010633621364831924, 0.03475765511393547, -0.01809302717447281, 0.013393424451351166, 0.0011286098742857575, 0.02821524627506733, 0.007490266114473343, 0.00954028032720089, -0.0062161716632544994, 0.011550616472959518, -0.012564602307975292, 0.01828700676560402, 0.009460925124585629, -0.04510912671685219, 0.04870656877756119, 0.0070714461617171764, -0.0276333075016737, -0.017960768193006516, 0.0540674664080143, 0.044368475675582886, -0.016320757567882538, -0.0004551912716124207, 0.012873206287622452, 0.0013413263950496912, 0.023524461314082146, -0.007318329531699419, 0.017414096742868423, -0.011965028010308743, 0.009240493178367615, -0.016558822244405746, -0.0001938420464284718, -0.038055311888456345, 0.07286587357521057, 0.00482304347679019, 0.009002426639199257, -0.01968013495206833, -0.0006960128084756434, 0.017916681244969368, 0.0027509864885360003, -0.0044108363799750805, -0.01461020763963461, -0.052727241069078445, -0.02364790439605713, 0.019010022282600403, 0.01439859252423048, -0.03911338374018669, 0.019750673323869705, -0.026663407683372498, -0.005598962772637606, 0.047189999371767044, -0.02996106445789337, 0.013940094970166683, 0.008539521135389805, -0.014874725602567196, 0.007803278975188732, -0.014548486098647118, 0.012961379252374172, -0.006273483857512474, 0.01909819431602955, 0.02661050483584404, -0.00037363157025538385, 0.04165275767445564, -0.027474597096443176, -0.016223765909671783, 0.05382058396935463, 0.06880993396043777, 0.02883245423436165, 0.007693063467741013, -0.04165275767445564, -0.04789537936449051, 0.05755910277366638, 0.0020202556625008583, -0.03216538205742836, -0.00823091622442007, -0.0014339076587930322, 0.06563571840524673, -0.022730907425284386, 0.027686210349202156, 0.01749345287680626, 0.014442679472267628, -0.021743373945355415, -0.034422602504491806, 0.03001396916806698, 0.0021888858173042536, -0.0224663894623518, -0.005925201810896397, -0.04553235322237015, -0.010086950846016407, 0.004778957460075617, -0.005934019107371569, 0.02701609767973423, 0.007582847494632006, -0.006273483857512474, -0.017757970839738846, -0.013992998749017715, 0.07078500092029572, 0.035057444125413895, 0.041582219302654266, -0.05128121003508568, -0.06849250942468643, -0.007701880764216185, 0.00834554061293602, 0.00566068384796381, 0.009196407161653042, 0.010554265230894089, 0.017819691449403763, 0.044968049973249435, 0.018622063100337982, -0.0013611651957035065, 0.03876069560647011, 0.05523134395480156, -0.04532073810696602, 0.011577067896723747, 0.024265112355351448, -0.04006564989686012, 0.04549708589911461, 0.01688506081700325, 0.02345392294228077, -0.03562174737453461, -0.003998629283159971, 0.03851381316781044, 0.01927454024553299, -0.03731466457247734, -0.0452149324119091, 0.010889321565628052, 0.03897231072187424, -0.01727302186191082, -0.028656110167503357, 0.05163390189409256, -0.03142473101615906, 0.002442382276058197, -0.014513217844069004, -0.023118868470191956, -0.018322275951504707, 0.017555173486471176, -0.007177253253757954, -0.04726053774356842, 0.0020235623233020306, 0.05138701945543289, 0.022678004577755928, -0.036256592720746994, -0.03710304945707321, -0.014222247526049614, -0.015430212952196598, -0.0046378811821341515, 0.02680448442697525, 0.021708104759454727, 0.017228934913873672, 0.01460138987749815, -0.003321904456242919, 0.009011244401335716, -0.02525264583528042, -0.012802667915821075, 0.0318303257226944, 0.014019450172781944, 0.05378531292080879, 0.012467612512409687, -0.029132241383194923, 0.009602000936865807, 0.06746970862150192, -0.02738642320036888, -0.013966547325253487, 0.036644551903009415, 0.018569158390164375, 0.02027970924973488, -0.00032596325036138296, -0.01567709632217884, -0.004432879853993654, 0.024300381541252136, -0.05752383545041084, -0.0050434754230082035, -0.02860320545732975, -0.02260746620595455, 0.012934926897287369, -0.02405349723994732, 0.04006564989686012, 0.033029474318027496, -0.029678912833333015, 0.00806338805705309, 0.03713831678032875, 0.028550302609801292, -0.004483579192310572, -0.030066872015595436, -0.0024930816143751144, 0.0007952070445753634, 0.00041937115020118654, -0.000031600939109921455, -0.031089674681425095, -0.012335353530943394, -0.012141373008489609, 0.010651255957782269, -0.014839456416666508, 0.0262049101293087, -0.029238048940896988, 0.021161435171961784, 0.007256608922034502, -0.003315291367471218, -0.01200029719620943, -0.0035489490255713463, -0.015324405394494534, -0.004091210663318634, 0.037667352706193924, -0.009214041754603386, -0.01704377308487892, -0.013534501194953918, -0.03611551597714424, 0.0357980951666832, 0.010113402269780636, 0.00045546682667918503, 0.007494674995541573, -0.011083301156759262, 0.022589832544326782, -0.028656110167503357, -0.029096972197294235, -0.04394524544477463, -0.026169640943408012, 0.024564899504184723, -0.017034955322742462, -0.015112791210412979, 0.003046364989131689, 0.03615078330039978, 0.020350245758891106, 0.0006387006142176688, -0.032888397574424744, 0.004809817764908075, 0.003295452566817403, 0.0021392886992543936, -0.027862556278705597, -0.013137724250555038, 0.0157299991697073, -0.011656424030661583, -0.017220117151737213, -0.057911794632673264, -0.012405890971422195, -0.05822921544313431, -0.010571899823844433, -0.018198834732174873, -0.00964608695358038, -0.03250043839216232, -0.004016263876110315, 0.010201575234532356, -0.008852533996105194, 0.024353284388780594, -0.0029096973594278097, 0.027086636051535606, -0.013631490990519524, -0.00942565593868494, -0.042816635221242905, -0.032059572637081146, -0.027686210349202156, 0.0007164027192629874, 0.019309809431433678, -0.04126479849219322, 0.0384785421192646, -0.01709667593240738, -0.016964416950941086, -0.012132556177675724, 0.008781995624303818, 0.026063833385705948, 0.03720885515213013, -0.036256592720746994, -0.04048888012766838, 0.021531760692596436, 0.0025217377115041018, -0.020350245758891106, 0.037843700498342514, -0.001765657216310501, 0.01690269634127617, 0.011074484325945377, -0.01183276902884245, 0.02819761261343956, -0.01805775798857212, 0.05509026721119881, 0.0014350097626447678, 0.03041956201195717, -0.036679819226264954, 0.011532981880009174, 0.021002724766731262, -0.013446328230202198, 0.019327443093061447, 0.0027730297297239304, -0.026557600125670433, -0.004681967664510012, -0.021496491506695747, -0.0065027326345443726, 0.013975364156067371, 0.009487376548349857, -0.005056701134890318, 0.004748097155243158, -0.011665240861475468, -0.011400722898542881, 0.030313756316900253, 0.05558403581380844, -0.02124960720539093, 0.0016333982348442078, -0.041441142559051514, -0.023118868470191956, -0.0004303927125874907, 0.008980384096503258, -0.04077102988958359, -0.01989174820482731, -0.0027884598821401596, -0.017123127356171608, 0.008817264810204506, 0.010192757472395897, -0.0030816339422017336, -0.027051366865634918, -0.020138632506132126, 0.0010768084321171045, -0.007922312244772911, -0.020914550870656967, -0.007534352596849203, -0.07702762633562088, -0.02583458460867405, 0.014354506507515907, -0.02082637883722782, 0.017202483490109444, 0.025305548682808876, -0.003892822191119194, 0.02123197354376316, -0.05188078433275223, -0.003630508668720722, -0.011347819119691849, -0.0062161716632544994, 0.03971295803785324, 0.015800537541508675, -0.032041940838098526, 0.034845829010009766, 0.01262632291764021, 0.006895100697875023, -0.025711143389344215, -0.005387348588556051, -0.08344659209251404, -0.021302511915564537, -0.027897825464606285, 0.008998018689453602, -0.02444145642220974, 0.0464140810072422, -0.021884450688958168, -0.014936446212232113, 0.006864240393042564, 0.01401063334196806, 0.04482697322964668, 0.007067037746310234, 0.007238974329084158, 0.016153229400515556, -0.0023916829377412796, -0.02937912568449974, 0.03830219805240631, 0.03116021305322647, -0.0050522927194833755, 0.05177497863769531, -0.03258860856294632, -0.042816635221242905, 0.009408021345734596, 0.006335204467177391, -0.0018692601006478071, -0.010968676768243313, 0.009355117566883564, -0.018569158390164375, 0.012652774341404438, -0.05833502113819122, -0.029255684465169907, 0.039430808275938034, -0.03343506529927254, 0.021161435171961784, -0.053326815366744995, -0.010898139327764511, -0.027562769129872322 ]
Differentiable physics enables efficient gradient-based optimizations of neural network (NN) controllers. However, existing work typically only delivers NN controllers with limited capability and generalizability. We present a practical learning framework that outputs unified NN controllers capable of tasks with significantly improved complexity and diversity. To systematically improve training robustness and efficiency, we investigated a suite of improvements over the baseline approach, including periodic activation functions, and tailored loss functions. In addition, we find our adoption of batching and an Adam optimizer effective in training complex locomotion tasks. We evaluate our framework on differentiable mass-spring and material point method (MPM) simulations, with challenging locomotion tasks and multiple robot designs. Experiments show that our learning framework, based on differentiable physics, delivers better results than reinforcement learning and converges much faster. We demonstrate that users can interactively control soft robot locomotion and switch among multiple goals with specified velocity, height, and direction instructions using a unified NN controller trained in our system. Code is available at https://github.com/erizmr/Complex-locomotion-skill-learning-via-differentiable-physics.
[ 0.011837221682071686, 0.010698692873120308, -0.02549956552684307, -0.05110342428088188, 0.02047613449394703, 0.03266099840402603, -0.026090558618307114, 0.028072118759155273, -0.09587975591421127, 0.052528757601976395, 0.04665360227227211, 0.01812954805791378, 0.03938787803053856, -0.0158351082354784, 0.01697363704442978, 0.01470527146011591, 0.001348200486972928, 0.026038412004709244, -0.028663111850619316, -0.03841447830200195, 0.03639815375208855, 0.012167481705546379, -0.022388167679309845, 0.017434263601899147, 0.03737155348062515, -0.000977200921624899, -0.031791891902685165, 0.002841976238414645, -0.06452242285013199, 0.059377312660217285, 0.03233073651790619, 0.010985498316586018, -0.0010852959239855409, 0.07029328495264053, -0.0014763935469090939, -0.0009109315578825772, 0.045784495770931244, 0.02716824971139431, -0.02941054292023182, 0.02329203672707081, 0.01985037885606289, -0.02435234561562538, -0.009733986109495163, -0.01264549046754837, 0.02654249407351017, 0.001165688270702958, -0.02581244334578514, 0.04196042940020561, 0.0058143180795013905, -0.02836761623620987, 0.017460336908698082, -0.007995774038136005, 0.015339718200266361, -0.02534312754869461, 0.00875189621001482, 0.02125832997262478, 0.07599461823701859, 0.05019955337047577, 0.02711610309779644, -0.009725295007228851, 0.017634158954024315, -0.061254583299160004, -0.0415780246257782, -0.010594400577247143, 0.014722653664648533, -0.04974761977791786, 0.061254583299160004, -0.010012099519371986, 0.027828769758343697, -0.01314088050276041, -0.04331623762845993, 0.018894361332058907, -0.06869412958621979, -0.03945740684866905, 0.036850087344646454, -0.0021227910183370113, 0.035876691341400146, 0.008221741765737534, 0.034764233976602554, -0.02862834744155407, 0.012497742660343647, 0.002757238456979394, -0.05186823755502701, -0.04780082404613495, 0.11166272312402725, 0.009073465131223202, 0.033304136246442795, -0.04477633535861969, 0.045541148632764816, -0.020510898903012276, -0.035389989614486694, 0.0014503204729408026, 0.007222269661724567, -0.028923843055963516, -0.003995714243501425, 0.02680322527885437, -0.02351800538599491, 0.0096123106777668, 0.010411888360977173, 0.0030505615286529064, 0.027550656348466873, 0.012454287149012089, -0.000018468499547452666, -0.043490055948495865, 0.00008351563883479685, -0.06681685894727707, -0.02941054292023182, 0.052111588418483734, -0.0285762008279562, 0.08190453797578812, 0.01901603676378727, -0.0473141223192215, -0.0114374328404665, 0.040256984531879425, -0.025673387572169304, -0.0035872345324605703, -0.05816056579351425, -0.08767540007829666, 0.06740785390138626, -0.08162642270326614, 0.0467231310904026, 0.07696801424026489, -0.001859886571764946, -0.020232785493135452, -0.029636509716510773, 0.0003356921370141208, -0.03165283426642418, -0.028350234031677246, 0.060211654752492905, 0.022770574316382408, 0.002368313493207097, 0.001378619228489697, -0.015174588188529015, -0.010020790621638298, 0.0004997358773835003, 0.004380293656140566, 0.006718188524246216, -0.012445596046745777, -0.019207239151000977, 0.0062314891256392, -0.0035980981774628162, -0.026837989687919617, -0.01645217463374138, 0.022179581224918365, -0.00414128927513957, -0.0005654619890265167, -0.00449327751994133, 0.015409247018396854, 0.0038914214819669724, -0.05155536159873009, -0.07780236005783081, -0.017790596932172775, -0.031531162559986115, 0.04707077518105507, 0.006878972984850407, -0.002405250445008278, -0.04720982909202576, -0.004541078116744757, 0.023865647614002228, -0.03156592324376106, 0.09226427972316742, 0.05437126383185387, 0.005362383089959621, 0.0608026459813118, 0.059585899114608765, 0.026368672028183937, 0.031635452061891556, 0.06938941031694412, -0.04974761977791786, 0.03384298086166382, -0.049191392958164215, -0.03302602469921112, -0.019137710332870483, 0.036224331706762314, 0.005731753073632717, 0.03956170007586479, 0.07961009442806244, -0.01927676796913147, -0.012784547172486782, -0.0001617351663298905, -0.053571686148643494, -0.008117448538541794, 0.027150867506861687, 0.042655717581510544, 0.05986401066184044, 0.05426697060465813, 0.061045996844768524, 0.04230807349085808, 0.039422642439603806, -0.011098481714725494, -0.00929943285882473, -0.04905233532190323, -0.012376067228615284, 0.010837750509381294, 0.0012428213376551867, -0.03768442943692207, -0.013940458185970783, -0.020458752289414406, 0.00045492261415347457, 0.06069835275411606, -0.01776452362537384, -0.06712973862886429, -0.011411360464990139, -0.011376596055924892, -0.006279289722442627, -0.015739507973194122, -0.007869753986597061, -0.037753958255052567, 0.03827542066574097, -0.05155536159873009, 0.04766176640987396, 0.016834581270813942, -0.04488062858581543, -0.043072886765003204, -0.0924033373594284, -0.052007295191287994, -0.011871986091136932, 0.002883258741348982, -0.0018468499183654785, -0.030853258445858955, -0.030279647558927536, -0.0031244356650859118, 0.0033960312139242887, -0.01807740144431591, -0.03394727408885956, -0.0009120179456658661, 0.02695966325700283, -0.015922019258141518, -0.010490107350051403, 0.008673676289618015, -0.014122970402240753, -0.029445307329297066, 0.0321916826069355, -0.020667336881160736, -0.043072886765003204, 0.04102179780602455, 0.025586476549506187, 0.004762700293213129, -0.008208705112338066, 0.0021499507129192352, -0.009681839495897293, -0.010194611735641956, 0.03862306475639343, -0.00046252727042883635, 0.01948535442352295, 0.003789301495999098, 0.008521582931280136, 0.046166904270648956, 0.005870810244232416, -0.025777680799365044, -0.03469470515847206, -0.020493516698479652, 0.02565600536763668, -0.015739507973194122, -0.015470084734261036, 0.02711610309779644, 0.03019273839890957, -0.03172236308455467, 0.01556568592786789, -0.03344319388270378, 0.021918850019574165, 0.030001534149050713, 0.04609737545251846, 0.04147373139858246, -0.019415825605392456, -0.011637327261269093, 0.031113989651203156, 0.07460404932498932, 0.0005244510830380023, 0.00041689921636134386, -0.003919667564332485, 0.008156558498740196, -0.0231008343398571, -0.004754009190946817, 0.0024508784990757704, -0.07050187140703201, 0.03764966502785683, -0.00916906725615263, 0.09087371081113815, 0.0007680723210796714, 0.02334418334066868, -0.014331555925309658, 0.04331623762845993, -0.0093515794724226, 0.02172764576971531, -0.0508948378264904, -0.021432150155305862, -0.042134251445531845, -0.03359963372349739, 0.03193094953894615, -0.01496600266546011, 0.025169305503368378, -0.019398443400859833, 0.023848265409469604, 0.0780109390616417, 0.0014177289558574557, -0.03394727408885956, -0.03886641561985016, 0.027081338688731194, 0.009021318517625332, -0.009316815063357353, 0.010490107350051403, 0.03180927410721779, -0.020493516698479652, -0.010915969498455524, -0.010324977338314056, 0.0011005053529515862, 0.01770368590950966, 0.0005160316359251738, 0.01792096346616745, 0.006757298018783331, 0.012784547172486782, -0.022892247885465622, -0.045680202543735504, -0.03876212239265442, 0.018355516716837883, 0.059585899114608765, 0.03914452716708183, -0.05204205960035324, -0.010907278396189213, 0.006618241313844919, 0.05617900192737579, -0.04995620623230934, 0.031531162559986115, 0.05576183274388313, 0.002844149013981223, 0.02852405421435833, -0.007035411894321442, -0.03422538936138153, 0.002218392677605152, -0.0028398034628480673, -0.036120038479566574, -0.05878632143139839, -0.016061076894402504, 0.010776912793517113, 0.01723437011241913, -0.03076634742319584, -0.006913737393915653, -0.04634072631597519, -0.036711033433675766, -0.007339599076658487, -0.0023813501466065645, -0.009681839495897293, 0.007383054122328758, -0.01493993028998375, -0.08600671589374542, -0.019502734765410423, 0.012549888342618942, 0.006683424115180969, 0.0033460576087236404, 0.0009533005068078637, 0.019398443400859833, 0.008656294085085392, -0.009933879598975182, 0.04818322882056236, -0.07710707187652588, 0.04373340681195259, -0.00034927192609757185, -0.06779025495052338, -0.03316507861018181, -0.00848681852221489, -0.049921441823244095, -0.025430038571357727, 0.01191544160246849, -0.07933198660612106, 0.0001856355811469257, -0.016052385792136192, -0.0561094731092453, 0.023796118795871735, 0.0894136130809784, -0.0020662990864366293, -0.009681839495897293, 0.028019974008202553, -0.020250165835022926, -0.01917247474193573, -0.023796118795871735, 0.01812954805791378, -0.021918850019574165, -0.050547197461128235, 0.032156918197870255, -0.01781667023897171, 0.05009526386857033, -0.033564869314432144, -0.014531450346112251, 0.03186142072081566, 0.07425640523433685, 0.005896883085370064, -0.01953749917447567, -0.010351050645112991, 0.03307816758751869, 0.04008316248655319, -0.01839027926325798, -0.047731295228004456, 0.0010972461896017194, 0.039109762758016586, -0.002242293208837509, 0.004749663639813662, -0.024108996614813805, -0.003939222544431686, 0.023743972182273865, -0.011646018363535404, -0.001953315455466509, -0.0009619915508665144, -0.020563045516610146, 0.023187745362520218, 0.006322745233774185, -0.031061843037605286, -0.05941207706928253, -0.0040022325702011585, -0.0075177657417953014, -0.026629403233528137, -0.01828598789870739, -0.008221741765737534, 0.0005328705301508307, 0.02094545215368271, -0.00329825677908957, -0.022892247885465622, 0.03055776283144951, -0.025204069912433624, -0.07196196913719177, 0.03820589557290077, 0.010872513987123966, 0.006622586864978075, 0.03719773143529892, -0.009586237370967865, 0.036954380571842194, 0.016625994816422462, -0.004286864772439003, -0.005944684147834778, -0.048252757638692856, 0.012767164967954159, 0.03563334047794342, 0.01917247474193573, -0.030157973989844322, -0.0011863295221701264, 0.005736098624765873, 0.028245940804481506, -0.003993541467934847, -0.059064432978630066, -0.026351289823651314, -0.027359452098608017, -0.0051537975668907166, 0.005205944180488586, -0.014244644902646542, 0.010829059407114983, -0.01434024702757597, -0.0032569742761552334, -0.013531978242099285, -0.022162199020385742, -0.026403436437249184, -0.03526831790804863, -0.014766108244657516, -0.020771630108356476, -0.0540236197412014, 0.02706395648419857, -0.0324871763586998, 0.019867759197950363, -0.012037116102874279, 0.013549360446631908, -0.051068659871816635, 0.045784495770931244, 0.004095661453902721, -0.00653133075684309, -0.03966599330306053, 0.05040813982486725, 0.012871458195149899, -0.01844242587685585, -0.017903581261634827, -0.003624171484261751, 0.012132718227803707, 0.05266781523823738, -0.05072101950645447, -0.010003408417105675, 0.026246996596455574, 0.05489272624254227, 0.02836761623620987, -0.05367597937583923, -0.1028326079249382, 0.0027507201302796602, -0.03285220265388489, 0.037858251482248306, -0.018772685900330544, 0.06267991662025452, -0.04661883786320686, -0.010681310668587685, -0.0035220514982938766, 0.06448765844106674, 0.02031969465315342, 0.02183193899691105, -0.006639968603849411, 0.02508239448070526, -0.04668836668133736, -0.03904023393988609, 0.021588589996099472, -0.008825769647955894, -0.017938345670700073, 0.02146691456437111, -0.014062132686376572, 0.0644528940320015, 0.018320752307772636, -0.0019967707339674234, -0.03024488501250744, 0.011559108272194862, 0.011741620488464832, -0.027133485302329063, 0.010620473884046078, 0.04467204213142395, 0.04241236671805382, -0.011585181578993797, -0.03782348707318306, 0.039109762758016586, -0.013392921537160873, 0.002494333777576685, -0.006153269670903683, -0.004606260918080807, -0.014140352606773376, 0.04095226898789406, 0.0018120857421308756, 0.03542475402355194, 0.05068625509738922, -0.010472726076841354, 0.03938787803053856, -0.010690001770853996, 0.02956698089838028, -0.04269048199057579, 0.019972052425146103, 0.02972342073917389, -0.04387246444821358, 0.003328675404191017, 0.02141476795077324, 0.0016241415869444609, 0.04800940677523613, -0.01703447476029396, -0.056039948016405106, -0.03615480288863182, -0.015652596950531006, -0.015218043699860573, 0.030018916353583336, 0.03384298086166382, 0.005466675851494074, -0.05120771750807762, 0.050651490688323975, -0.008430327288806438, 0.039318349212408066, -0.04116085544228554, -0.004436785355210304, 0.015061604790389538, -0.008760587312281132, -0.005019086413085461, 0.01958964578807354, -0.022579370066523552, 0.011567799374461174, 0.038588300347328186, 0.017694994807243347, -0.047835588455200195, -0.02094545215368271, -0.03140948712825775, -0.025482183322310448, -0.028037354350090027, -0.035285696387290955, -0.03099231608211994, 0.020076345652341843, -0.025795063003897667, -0.018564101308584213, 0.003387340111657977, -0.02183193899691105, -0.010637856088578701, 0.03432968258857727, 0.02888907864689827, 0.03782348707318306, -0.0056144241243600845, -0.025204069912433624, 0.014713962562382221, -0.004706208128482103, 0.04018745571374893, 0.007230960763990879, -0.0014622706221416593, -0.03865782916545868, -0.003789301495999098, -0.008995246142148972, -0.01651301234960556, -0.043594349175691605, 0.0035068420693278313, 0.05756957083940506, -0.014870401471853256, 0.02560385875403881, -0.041612789034843445, 0.011420050635933876, 0.04797464236617088, -0.025569094344973564, 0.03386036306619644, 0.04641025513410568, 0.016999710351228714, 0.035876691341400146, -0.02503024972975254, -0.0410565622150898, -0.012445596046745777, -0.005627460312098265, 0.02450878545641899, -0.053988855332136154, -0.039735518395900726, 0.0032482831738889217, 0.04995620623230934, -0.012758473865687847, -0.020232785493135452, -0.002133654896169901, 0.041821375489234924, 0.04946950450539589, -0.02303130552172661, -0.005792590789496899, -0.025464801117777824, 0.0436638779938221, 0.04654930904507637, 0.0032482831738889217, 0.015296263620257378, 0.015357100404798985, 0.04467204213142395, 0.04634072631597519, 0.028610965237021446, 0.024839045479893684, -0.02094545215368271, 0.0008777969051152468, 0.044011522084474564, -0.013210409320890903, 0.006466147489845753, 0.024439256638288498, 0.013531978242099285, -0.041612789034843445, 0.029167192056775093, 0.003906630910933018, -0.0007398263551294804, 0.05982924625277519, -0.009021318517625332, -0.03318246081471443, 0.016121914610266685, 0.01708662137389183, -0.010750839486718178, 0.026003647595643997, -0.00123087118845433, 0.012080571614205837, -0.033669162541627884, -0.008260851725935936, -0.0008424894767813385, 0.01974608562886715, -0.02183193899691105, 0.03681532293558121, -0.007117976900190115, 0.012106644921004772, 0.051903001964092255, 0.01021199394017458, 0.02177979238331318, 0.03464255854487419, 0.012184863910079002, 0.0628189742565155, -0.011663400568068027, 0.019155092537403107, 0.031270429491996765, -0.011298376135528088, 0.004180399235337973, 0.005762171931564808, 0.023796118795871735, -0.020180638879537582, 0.0319657139480114, 0.036224331706762314, -0.008812733925879002, 0.0028919498436152935, 0.04714030399918556, 0.03837971389293671, -0.027498509734869003, 0.04178661108016968, 0.011168010532855988, -0.02273580990731716, -0.00984696950763464, 0.03128781169652939, 0.02789829857647419, -0.021918850019574165, 0.04321194440126419, 0.027098720893263817, 0.020806394517421722, -0.011837221682071686, -0.056457117199897766, -0.026299143210053444, -0.019415825605392456, -0.027029192075133324, -0.0576738640666008, -0.00802184734493494, 0.019346296787261963, 0.002259675180539489, -0.036954380571842194, 0.0016708560287952423, -0.010351050645112991, -0.05329357087612152, 0.030210120603442192, 0.00989911612123251, 0.02303130552172661, 0.017521174624562263, 0.02914980985224247, -0.04425486922264099, 0.0561094731092453, 0.01217617280781269, 0.04425486922264099, -0.014296791516244411, 0.0019109465647488832, -0.001831640605814755, 0.06921558827161789, -0.025795063003897667, -0.0001781667087925598, 0.02297915890812874, -0.028437143191695213, -0.007139704655855894, -0.0016654240898787975, 0.032782673835754395, -0.001140701468102634, 0.027672329917550087, 0.007004993502050638, 0.021484296768903732, 0.022648898884654045, -0.03358225151896477, -0.01620013266801834, 0.03904023393988609, -0.005575314164161682, 0.011689473874866962, 0.0093515794724226, -0.05305022373795509, -0.02440449222922325, 0.03207000717520714, 0.021171418949961662, -0.03224382922053337, 0.026472965255379677, -0.015504848212003708, 0.02403946779668331, -0.028350234031677246, -0.015417938120663166, 0.0007246170425787568, -0.0049582491628825665, 0.028663111850619316, 0.02256198786199093, 0.06761643290519714, -0.009829587303102016, -0.012949677184224129, 0.01397522259503603, -0.03519878908991814, 0.053988855332136154, 0.023796118795871735, -0.014262027107179165, 0.007283107377588749, -0.006870281882584095, 0.027568038552999496, 0.028958607465028763, -0.016443483531475067, 0.07210101932287216, -0.01112455502152443, 0.017147459089756012, -0.031583305448293686, -0.022075289860367775, 0.027602802962064743, 0.0415780246257782, -0.03702390938997269, 0.0017773214494809508, 0.03316507861018181, 0.042029958218336105, 0.05423220619559288, -0.0028028665110468864, 0.028072118759155273, 0.017521174624562263, 0.021745027974247932, -0.03615480288863182, -0.006457456387579441, 0.005479712504893541, -0.034294918179512024, 0.06313184648752213, -0.020180638879537582, 0.038901180028915405, -0.01525280810892582, 0.014905165880918503, 0.01149827055633068, -0.019363678991794586, 0.0032156917732208967, -0.017216987907886505, 0.024265436455607414, -0.007356981281191111, -0.0073613268323242664, -0.02198837883770466, 0.01761677674949169, -0.021345240995287895, 0.013940458185970783, -0.023066069930791855, -0.008856188505887985, -0.010238067246973515, 0.007113631349056959, 0.0036784906405955553, 0.018685776740312576, -0.010298904962837696, 0.05548371747136116, 0.035024967044591904, -0.024960720911622047, -0.013679726049304008, 0.038796886801719666, -0.014774799346923828, -0.03191356733441353, 0.011446123942732811, 0.03591145575046539, -0.02346585877239704, 0.03146163374185562, 0.030905405059456825, 0.02591673657298088, -0.0316702164709568, 0.005279818084090948, 0.0074004363268613815, 0.014792181551456451, -0.0047279358841478825, -0.026837989687919617, 0.005549240857362747, -0.006092431955039501, 0.000030045261155464686, -0.003724118694663048, 0.03855353593826294, 0.009368961676955223, 0.0018533682450652122, 0.011063717305660248, -0.02125832997262478, -0.05993353947997093, 0.006418346893042326, 0.033043406903743744, -0.03667626902461052, -0.05019955337047577, -0.0051798708736896515, -0.0026507729198783636, -0.0003927272045984864, 0.03545951843261719, 0.02602102980017662, 0.03259146958589554, -0.02748112753033638, -0.006735570263117552, -0.011724238283932209, -0.018407661467790604, 0.05680476129055023, 0.0189638901501894, -0.013601507060229778, 0.028697876259684563, -0.016061076894402504, -0.02237078547477722, -0.0026594640221446753, -0.03834494948387146, -0.029792949557304382, 0.013236482627689838, -0.007165777962654829, 0.05030384659767151, -0.009855660609900951, -0.013888311572372913, -0.010064246132969856, 0.012315230444073677, 0.02204052545130253, -0.004176053684204817, -0.03851877152919769, 0.004126080311834812, 0.07105809450149536, 0.05805627256631851, -0.04901757091283798, -0.038171131163835526, -0.018216459080576897, -0.029427925124764442, 0.029845096170902252, 0.017990492284297943, 0.019346296787261963, -0.04571496695280075, 0.038588300347328186, -0.024995485320687294, -0.023170363157987595, -0.0675816684961319, 0.030853258445858955, 0.024282818660140038, -0.023118216544389725, 0.012341303750872612, 0.007717660162597895, -0.015922019258141518, -0.06076788157224655, -0.05433649942278862, 0.02334418334066868, -0.019937288016080856, -0.015078986994922161, 0.009699221700429916, -0.009873042814433575, -0.03485114499926567, 0.06434860080480576, 0.0236222967505455, -0.004945212509483099, 0.00462364312261343, -0.03201786056160927, -0.055205605924129486, -0.006735570263117552, 0.013053970411419868, -0.05092960223555565, -0.01332339271903038, 0.019189856946468353, 0.020041581243276596, -0.027203014120459557, 0.0017577665857970715, -0.050130024552345276, 0.010837750509381294, -0.0061576152220368385, 0.0047757369466125965, -0.016834581270813942, -0.03292173147201538, -0.028750022873282433, 0.04654930904507637, 0.025986265391111374, -0.010820368304848671, 0.07046710699796677, 0.0002605959598440677, -0.02873264066874981, -0.012654181569814682, 0.0016045867232605815, 0.03535522520542145, 0.012002351693809032, 0.026837989687919617, -0.013549360446631908, -0.028193794190883636, 0.04634072631597519, 0.03365178033709526, 0.0022151335142552853, -0.02372658997774124, 0.007569911889731884, 0.02555171214044094, -0.02946268953382969, 0.00997733511030674, 0.021918850019574165, 0.011411360464990139, 0.013314701616764069, 0.029636509716510773, 0.0041847447864711285, 0.0012221800861880183, 0.01818169467151165, 0.010915969498455524, 0.02602102980017662, 0.030105827376246452, -0.020337076857686043, -0.004154325928539038, -0.008717131800949574, 0.021240947768092155, -0.027098720893263817, -0.03530307859182358, 0.015009458176791668, 0.024526167660951614, 0.03076634742319584, -0.018772685900330544, 0.023222507908940315, 0.03535522520542145, 0.004528041463345289, 0.03417324274778366, 0.006670387461781502, -0.002587762661278248, 0.010950733907520771, 0.0008636739803478122, -0.05061672627925873, 0.011315758340060711, -0.025586476549506187, 0.01666075922548771, -0.025325745344161987, 0.007565566338598728, 0.04126514494419098, 0.013627580367028713, -0.03605050966143608, -0.014444539323449135, -0.02315298095345497, 0.01912032999098301, -0.04766176640987396, -0.021849321201443672, -0.02711610309779644, 0.02214481681585312, -0.01703447476029396, 0.014375011436641216, 0.013271247036755085, 0.004143462050706148, 0.006526985205709934, 0.021397385746240616, -0.008360798470675945, -0.036120038479566574, -0.0462016686797142, -0.02198837883770466, 0.040674153715372086, -0.01168078277260065, 0.026403436437249184, -0.026507729664444923, -0.0011086531449109316, 0.027759240940213203, -0.002496506553143263, 0.0015795999206602573, -0.022475076839327812, 0.01671290583908558, -0.013471140526235104, 0.007061485201120377, 0.011950206011533737, -0.057812921702861786, -0.016287043690681458, 0.007934936322271824, 0.019033418968319893, -0.04821799322962761, 0.015843799337744713, 0.002572553465142846, -0.030105827376246452, 0.006070704665035009, -0.028384998440742493, 0.05847344174981117, 0.026107940822839737, 0.040361277759075165, 0.07974915206432343, 0.002731165150180459, -0.011828530579805374, 0.03678055852651596, -0.0061749969609081745, 0.00013960013166069984, 0.008339070715010166, -0.029740802943706512, -0.026090558618307114, 0.029897240921854973, -0.01587856374680996, -0.014227262698113918, -0.017668921500444412, -0.02539527416229248, 0.06528723239898682, -0.034972820430994034, 0.08294746279716492, -0.037128202617168427 ]
Variational autoencoders (VAEs) are a popular framework for modeling complex data distributions; they can be efficiently trained via variational inference by maximizing the evidence lower bound (ELBO), at the expense of a gap to the exact (log-)marginal likelihood. While VAEs are commonly used for representation learning, it is unclear why ELBO maximization would yield useful representations, since unregularized maximum likelihood estimation cannot invert the data-generating process. Yet, VAEs often succeed at this task. We seek to elucidate this apparent paradox by studying nonlinear VAEs in the limit of near-deterministic decoders. We first prove that, in this regime, the optimal encoder approximately inverts the decoder -- a commonly used but unproven conjecture -- which we refer to as {\em self-consistency}. Leveraging self-consistency, we show that the ELBO converges to a regularized log-likelihood. This allows VAEs to perform what has recently been termed independent mechanism analysis (IMA): it adds an inductive bias towards decoders with column-orthogonal Jacobians, which helps recovering the true latent factors. The gap between ELBO and log-likelihood is therefore welcome, since it bears unanticipated benefits for nonlinear representation learning. In experiments on synthetic and image data, we show that VAEs uncover the true latent factors when the data generating process satisfies the IMA assumption.
[ 0.014277355745434761, 0.012821939773857594, -0.042394548654556274, -0.0552879199385643, 0.02637605182826519, 0.06910990178585052, -0.011295093223452568, 0.027501096948981285, -0.03509068489074707, 0.04232311621308327, -0.010187906213104725, -0.01608099788427353, 0.02100083790719509, -0.01846502162516117, -0.0074913701973855495, -0.0024934031534940004, 0.017447125166654587, 0.02112584374845028, -0.026965361088514328, -0.03300131857395172, -0.04318029433488846, -0.010812931694090366, -0.07357436418533325, -0.02498313970863819, 0.05060916393995285, 0.02412596344947815, 0.01760784536600113, -0.013446965254843235, -0.06853844970464706, 0.007192251272499561, 0.02482241950929165, -0.005986846052110195, -0.00827711634337902, 0.002257902640849352, -0.03219771385192871, 0.03735863417387009, 0.022554472088813782, 0.014804162085056305, -0.07764595746994019, 0.058145176619291306, 0.005044844001531601, -0.03850153461098671, 0.004852872341871262, 0.010598637163639069, 0.010518277063965797, 0.0001582094409968704, 0.00085327064152807, -0.03330489993095398, -0.05085917189717293, 0.004768047481775284, -0.002195400185883045, -0.05164491757750511, 0.03260844573378563, 0.022715192288160324, -0.02135799452662468, 0.037894368171691895, 0.0501091405749321, -0.0199115090072155, 0.059252362698316574, 0.03141196817159653, 0.01691138930618763, 0.029679754748940468, -0.09536094963550568, -0.034894250333309174, -0.008098537102341652, -0.028179695829749107, 0.048216208815574646, -0.00631721643730998, 0.01828644424676895, 0.012705864384770393, -0.03914441913366318, 0.017956074327230453, 0.0029197593685239553, 0.030715512111783028, 0.032412007451057434, -0.0017545343143865466, 0.011295093223452568, 0.07750309258699417, 0.030608363449573517, -0.00751815689727664, 0.06335967034101486, -0.006268107332289219, 0.03134053573012352, 0.013241599313914776, 0.040537331253290176, 0.01939363032579422, 0.028376132249832153, -0.0482519268989563, 0.02301877550780773, -0.02435811422765255, -0.061323873698711395, 0.02446526102721691, -0.020643681287765503, -0.021965162828564644, 0.011991550214588642, 0.024161677807569504, -0.020607965067029, -0.008486946113407612, -0.03989445045590401, 0.05282353609800339, -0.001048590987920761, -0.0075315507128834724, 0.0018661458743736148, 0.029965480789542198, -0.011839757673442364, -0.10657568275928497, -0.022429466247558594, -0.0001456531317671761, 0.01096472330391407, 0.15900634229183197, 0.0017679276643320918, 0.011830829083919525, -0.06678838282823563, -0.019465062767267227, -0.017965001985430717, -0.001200940809212625, -0.06714553385972977, -0.0510377511382103, 0.045394670218229294, -0.03664432093501091, 0.008294973522424698, 0.037608642131090164, 0.035590704530477524, -0.023358074948191643, -0.042394548654556274, 0.08493196219205856, -0.019875792786478996, -0.024375973269343376, 0.062359631061553955, -0.0008666640496812761, -0.004665364511311054, 0.016956033185124397, -0.01626850664615631, 0.010071830824017525, 0.00423454400151968, -0.016464943066239357, 0.044644638895988464, 0.006178818177431822, 0.02487599290907383, -0.02764395996928215, -0.0016674771904945374, -0.05910950154066086, -0.025590306147933006, -0.019465062767267227, -0.0006456730770878494, 0.022465182468295097, -0.022483039647340775, 0.09293227642774582, -0.002482241950929165, -0.02325092814862728, -0.0097236018627882, 0.06493116170167923, -0.051966357976198196, 0.07096711546182632, 0.08093179762363434, 0.04160880297422409, 0.025233149528503418, -0.006906525697559118, 0.013179097324609756, -0.029019014909863472, 0.06885989010334015, 0.00533949863165617, -0.017411408945918083, 0.04535895213484764, 0.011982620693743229, 0.002103878650814295, 0.026393910869956017, 0.013143381103873253, -0.03134053573012352, 0.039965879172086716, 0.028608284890651703, -0.014786303974688053, -0.009277155622839928, -0.06768127530813217, -0.023768804967403412, 0.013500538654625416, 0.03928728029131889, -0.0609310008585453, -0.03496567904949188, 0.0008515964727848768, -0.0339834988117218, -0.011562961153686047, 0.037037193775177, 0.047287601977586746, 0.06021668761968613, 0.03532283753156662, 0.07600302994251251, 0.0056966557167470455, 0.006058277562260628, -0.04860908165574074, -0.006174353417009115, 0.007830669172108173, 0.032519154250621796, -0.007254753727465868, 0.018607884645462036, -0.035930003970861435, -0.018081078305840492, -0.020072229206562042, -0.03291202709078789, 0.005665404722094536, 0.028751147910952568, -0.04171594977378845, 0.00827711634337902, 0.04218025505542755, 0.03416207805275917, 0.0014409057330340147, -0.024500977247953415, -0.0025692989584058523, 0.0008097421377897263, -0.019947225227952003, 0.029215451329946518, -0.060002394020557404, -0.03519783169031143, -0.07189572602510452, -0.012437996454536915, -0.015598836354911327, -0.05868091434240341, -0.023983100429177284, -0.043823178857564926, -0.06757412105798721, -0.054395027458667755, -0.0046341135166585445, 0.035412129014730453, 0.0026608204934746027, 0.04853764921426773, -0.010464703664183617, 0.04471607133746147, -0.029804760590195656, 0.029858333989977837, 0.03778722137212753, 0.002477777423337102, 0.021840156987309456, 0.019590066745877266, -0.007089568767696619, -0.013250528834760189, -0.0580737441778183, 0.015143461525440216, 0.009482521563768387, 0.049144819378852844, -0.047001875936985016, -0.03814437985420227, 0.006156495772302151, -0.04189452901482582, 0.02100083790719509, -0.03046550042927265, -0.0009258181671611965, 0.017447125166654587, 0.02567959576845169, 0.03871583193540573, -0.0011674573179334402, 0.03509068489074707, -0.04518037289381027, 0.014143421314656734, -0.004852872341871262, -0.07364579290151596, 0.052609242498874664, 0.027143940329551697, -0.03989445045590401, -0.05085917189717293, -0.000717104529030621, 0.0153488265350461, 0.06400255113840103, 0.020000798627734184, 0.05596651881933212, 0.002196516143158078, -0.041180215775966644, 0.04425176605582237, 0.03221557289361954, 0.0008153226808644831, 0.07471726834774017, 0.032804880291223526, -0.020232949405908585, -0.03671574965119362, -0.02850113809108734, 0.013670188374817371, -0.0008884283015504479, 0.017759637907147408, 0.027804680168628693, 0.01600956730544567, -0.02071511186659336, 0.03110838495194912, -0.0375014953315258, -0.024340257048606873, 0.07150284945964813, -0.02723322995007038, -0.034429945051670074, 0.010768286883831024, -0.001687567331828177, -0.029072588309645653, -0.02684035710990429, -0.007415474392473698, 0.06757412105798721, -0.06285965442657471, 0.0011562961153686047, 0.008232471533119678, -0.0339834988117218, -0.03605500981211662, -0.0341799333691597, 0.08271758258342743, -0.04350173473358154, -0.018036434426903725, 0.020643681287765503, 0.007477976847440004, 0.04589468985795975, -0.007656555622816086, 0.001593813649378717, -0.03342990577220917, 0.051859211176633835, -0.0049287681467831135, 0.00565647566691041, -0.03553713113069534, 0.08843210339546204, 0.00016072069411166012, -0.0463947094976902, -0.02100083790719509, -0.0008705704240128398, 0.0538950078189373, -0.06339538842439651, 0.008866425603628159, 0.00831283163279295, 0.019661499187350273, 0.006960099097341299, -0.022036593407392502, -0.050930604338645935, -0.014732730574905872, 0.008044963702559471, 0.05268067494034767, 0.022090166807174683, -0.009777176193892956, -0.021483000367879868, -0.003098337911069393, -0.03746578097343445, -0.024268824607133865, 0.01587563380599022, 0.015964923426508904, -0.00011000718222931027, -0.004794834181666374, 0.008482481352984905, -0.07664591819047928, -0.06914561241865158, 0.015759557485580444, -0.013929126784205437, -0.024215251207351685, -0.05460932105779648, 0.016438156366348267, -0.03173340857028961, -0.07521728426218033, -0.014679157175123692, 0.015732770785689354, 0.004982341546565294, 0.0009805078152567148, -0.022590186446905136, -0.03289416804909706, -0.010946865193545818, -0.010080759413540363, -0.03746578097343445, -0.040608763694763184, 0.03457280620932579, 0.010714713484048843, 0.05796659737825394, 0.03530497848987579, -0.044751785695552826, -0.059823814779520035, -0.034251365810632706, -0.04114449769258499, -0.0185185968875885, -0.04921624809503555, -0.02192944660782814, 0.04725188389420509, -0.018965043127536774, 0.015938136726617813, 0.03530497848987579, 0.0009414438391104341, -0.015089888125658035, 0.04368031397461891, 0.03146554157137871, -0.002228883560746908, -0.016839956864714622, -0.04007302597165108, 0.05153777077794075, -0.016250647604465485, 0.011375454254448414, -0.03718005493283272, 0.035644277930259705, -0.001916371053084731, 0.014848806895315647, -0.04021589085459709, 0.004714473616331816, 0.03814437985420227, 0.005107346456497908, -0.0004057081532664597, -0.08671774715185165, -0.026001038029789925, -0.05193064361810684, 0.05225208401679993, 0.031769122928380966, 0.004839478991925716, 0.00799139030277729, 0.033037032932043076, 0.02117941714823246, -0.020054372027516365, 0.011446884833276272, -0.023411648347973824, -0.03498353809118271, -0.0057279071770608425, 0.031072668731212616, -0.02182229980826378, 0.04957340657711029, 0.027322519570589066, -0.0199115090072155, -0.02267947606742382, -0.03421565145254135, -0.05564507842063904, -0.014321999624371529, 0.0238938108086586, 0.009455734863877296, -0.03323346748948097, 0.0013281779829412699, 0.041644517332315445, -0.0013705904129892588, 0.025197433307766914, -0.006393112242221832, 0.016197074204683304, -0.000936979369726032, -0.015205963514745235, 0.02221517264842987, 0.004455534741282463, -0.009196795523166656, -0.0033729025162756443, 0.01730426214635372, 0.04346602037549019, 0.007857456803321838, 0.024947423487901688, -0.015357756055891514, -0.015911350026726723, -0.050073426216840744, -0.013455893844366074, 0.020447244867682457, 0.0007996970671229064, 0.004084984306246042, 0.01650065928697586, 0.005348427686840296, 0.02769753336906433, -0.0019264161819592118, -0.04893052205443382, -0.03553713113069534, -0.021858014166355133, -0.056645117700099945, -0.020857974886894226, 0.004884123336523771, -0.07196715474128723, -0.005134133622050285, -0.07721737027168274, -0.06807414442300797, 0.037251487374305725, -0.02810826525092125, 0.027554670348763466, 0.00014579264097847044, 0.015107745304703712, -0.05489504709839821, 0.016750669106841087, 0.03925156593322754, 0.02694750390946865, -0.04757332801818848, 0.011446884833276272, 0.04893052205443382, 0.00013749153004027903, -0.022197313606739044, -0.02003651298582554, -0.005402001086622477, 0.012920157983899117, -0.04410890117287636, -0.008768207393586636, 0.029054731130599976, 0.024608124047517776, 0.08486052602529526, -0.006683302577584982, -0.038358673453330994, 0.04664471745491028, -0.05557364597916603, 0.013536253944039345, -0.02984047681093216, 0.04496607929468155, -0.0010100849904119968, -0.021608004346489906, 0.03128696233034134, 0.0365728884935379, 0.059538088738918304, 0.02226874604821205, -0.003589428961277008, -0.03291202709078789, -0.01755427196621895, -0.016714952886104584, 0.008933392353355885, 0.021393710747361183, -0.04571611061692238, 0.0003669231082312763, 0.018732890486717224, 0.06164531782269478, 0.06821700930595398, -0.03480495885014534, -0.011464742943644524, -0.004924303852021694, -0.008991430513560772, 0.026590347290039062, 0.03501925617456436, 0.008259258233010769, 0.0020916012581437826, 0.000040354567317990586, -0.04035875201225281, 0.02301877550780773, -0.010464703664183617, -0.001102722599171102, 0.004321600776165724, 0.048109062016010284, -0.03764436021447182, 0.03235843405127525, -0.018090007826685905, 0.016206003725528717, 0.004430980421602726, -0.008361941203474998, -0.0017188185593113303, 0.02378666400909424, 0.03276916593313217, -0.030840516090393066, 0.043608881533145905, -0.003609518986195326, -0.022429466247558594, 0.04843050241470337, 0.038751546293497086, -0.0037836330011487007, 0.04589468985795975, -0.011804042384028435, -0.0482519268989563, 0.030429786071181297, -0.02625104784965515, 0.022554472088813782, 0.027626102790236473, 0.00663419347256422, -0.019893649965524673, 0.025143859907984734, 0.02500099688768387, 0.01226834673434496, 0.004955554846674204, -0.01973292976617813, -0.046716149896383286, 0.018116794526576996, -0.018840037286281586, 0.0010084108216688037, -0.006294894032180309, 0.01828644424676895, -0.04903767257928848, -0.01825965754687786, -0.006312751676887274, -0.02619747444987297, 0.030269064009189606, -0.015438116155564785, 0.020625822246074677, -0.028090406209230423, -0.04018017277121544, 0.009268227033317089, 0.011321879923343658, -0.0013069717679172754, 0.00533949863165617, 0.0035871968138962984, -0.0346442386507988, 0.011375454254448414, 0.031876273453235626, -0.027108224108815193, -0.03253701329231262, -0.05885948985815048, 0.010741500183939934, -0.02500099688768387, -0.012357636354863644, 0.02648319862782955, 0.008062821812927723, 0.03839438781142235, 0.005433252546936274, 0.015464902855455875, 0.009777176193892956, -0.018090007826685905, -0.0097236018627882, 0.01693817600607872, 0.05246637761592865, -0.019875792786478996, 0.02834041602909565, -0.03410850465297699, -0.012536214664578438, 0.011795113794505596, 0.0024934031534940004, -0.005058237351477146, 0.06678838282823563, 0.004986806306988001, 0.000818112981505692, 0.009759318083524704, 0.002005660440772772, 0.009330729022622108, 0.025483159348368645, 0.00014955953520257026, -0.05478790029883385, -0.020911548286676407, -0.04403747245669365, 0.0074244034476578236, 0.013670188374817371, 0.008205684833228588, 0.009339658543467522, 0.012705864384770393, -0.01670602336525917, 0.04468035325407982, 0.04478750005364418, 0.0060448842123150826, 0.007812811993062496, 0.009116435423493385, -0.005143062211573124, 0.06078813970088959, -0.02407238818705082, 0.018893610686063766, -0.014321999624371529, -0.014991669915616512, -0.008924462832510471, 0.04471607133746147, 0.0014967115130275488, 0.008705704472959042, -0.030501216650009155, -0.009964683093130589, 0.016563160344958305, -0.015116674825549126, -0.011455814354121685, -0.002875114791095257, -0.024090247228741646, 0.013384462334215641, 0.03550141677260399, -0.02653677389025688, -0.01361661497503519, 0.027768965810537338, 0.035572849214076996, -0.0651097372174263, 0.0072368960827589035, 0.030911948531866074, -0.046609003096818924, -0.008000318892300129, 0.03432279825210571, 0.009830749593675137, -0.0013103201054036617, -0.01835787482559681, 0.03619787469506264, 0.0076878066174685955, -0.004893052391707897, 0.022465182468295097, 0.027483239769935608, 0.00865213107317686, 0.01776856556534767, -0.004294814076274633, 0.040894489735364914, -0.049251966178417206, 0.020732970908284187, 0.036269303411245346, -0.012973732315003872, 0.03693004325032234, 0.0003323235141579062, 0.02326878532767296, 0.012330848723649979, 0.0018761908868327737, 0.005875234492123127, 0.019250767305493355, -0.03700147569179535, 0.047180455178022385, 0.03407278656959534, -0.010804002173244953, 0.016482800245285034, -0.00039259379263967276, 0.013214812614023685, -0.03664432093501091, -0.004915374796837568, 0.04385889321565628, -0.03532283753156662, 0.02009008638560772, 0.0031853949185460806, 0.05050201341509819, 0.018018575385212898, 0.011991550214588642, 0.012509427964687347, 0.004906445741653442, 0.0016306453617289662, 0.030840516090393066, -0.01295587420463562, 0.039322998374700546, 0.020072229206562042, -0.029822617769241333, -0.0002288037649122998, -0.04507322609424591, -0.015411329455673695, 0.04078734293580055, -0.037537213414907455, -0.0074913701973855495, -0.019536493346095085, 0.008821780793368816, -0.03378706052899361, -0.01234870683401823, 0.027376092970371246, -0.040894489735364914, 0.014063061214983463, -0.004538127686828375, 0.023572368547320366, 0.04968055337667465, -0.02844756282866001, 0.020572248846292496, -0.04843050241470337, 0.010741500183939934, 0.008049428462982178, -0.0031385181937366724, 0.04232311621308327, 0.02244732342660427, 0.04432319849729538, 0.023518795147538185, 0.011527245864272118, 0.03721576929092407, 0.0038684578612446785, -0.006558297201991081, -0.005777016282081604, 0.09193223714828491, 0.014750588685274124, -0.0007065014215186238, -0.04928768053650856, 0.015545262955129147, 0.04200167581439018, -0.009116435423493385, 0.02285805530846119, 0.030054770410060883, 0.011000438593327999, 0.009973612613976002, -0.02994762361049652, 0.001070355181582272, 0.01675959676504135, 0.01471487246453762, -0.004741260781884193, -0.037037193775177, 0.05003771185874939, -0.03255486860871315, -0.04571611061692238, 0.013491610065102577, -0.025840315967798233, 0.01038434263318777, 0.01569705456495285, -0.03012620285153389, 0.01910790614783764, 0.02221517264842987, 0.03225128725171089, 0.003707737196236849, 0.014777375385165215, 0.04403747245669365, 0.0010435684816911817, -0.011304022744297981, -0.035179976373910904, -0.02585817500948906, 0.016223860904574394, 0.013946984894573689, -0.027804680168628693, 0.019715072587132454, -0.019661499187350273, 0.04107306897640228, 0.025983178988099098, 0.005290389526635408, 0.00008349942800123245, 0.04064447805285454, -0.01789357140660286, 0.015947064384818077, 0.022840196266770363, 0.0025692989584058523, -0.010161119513213634, 0.016491729766130447, 0.013973771594464779, 0.0001999242667807266, -0.022090166807174683, -0.02653677389025688, -0.013348747044801712, -0.01825965754687786, 0.0027612708508968353, 0.0012511659879237413, 0.018482880666851997, -0.02746538072824478, -0.014018416404724121, 0.015741700306534767, 0.026876071467995644, -0.037144340574741364, -0.000082104277680628, -0.0031161957886070013, -0.0033662058413028717, 0.006049348507076502, 0.010527205653488636, -0.02394738420844078, -0.04271598905324936, 0.03480495885014534, -0.02500099688768387, 0.02712608315050602, 0.028661858290433884, -0.06660979986190796, -0.023822378367185593, -0.0002387092972639948, -0.05950237438082695, 0.012464783154428005, -0.01636672392487526, -0.0010223622666671872, -0.008937856182456017, -0.07786025106906891, -0.009884322993457317, 0.010696855373680592, 0.020393671467900276, 0.001593813649378717, -0.018554311245679855, -0.002511260798200965, 0.020965121686458588, 0.015545262955129147, 0.012473711743950844, 0.0003532507107593119, -0.01393805630505085, -0.007366365287452936, -0.030090486630797386, -0.008701239712536335, -0.021340137347579002, -0.0505734458565712, 0.008299438282847404, 0.011143301613628864, -0.026626061648130417, -0.013821979984641075, -0.061216726899147034, -0.012429066933691502, -0.00932180043309927, 0.03594786301255226, -0.005678798072040081, 0.07536014914512634, 0.0341799333691597, -0.019786503165960312, -0.012866584584116936, -0.02332235872745514, 0.0231973547488451, -0.003549248678609729, -0.0036028223112225533, 0.055502213537693024, 0.04864479973912239, -0.015393471345305443, 0.013884482905268669, -0.009482521563768387, -0.02989405021071434, 0.02089369110763073, 0.0071431421674788, 0.02003651298582554, 0.005723442416638136, -0.015795273706316948, -0.0393587127327919, 0.0037523817736655474, 0.0234295055270195, 0.058430902659893036, -0.041930243372917175, -0.011134373024106026, -0.022072309628129005, 0.006531510502099991, 0.002977797295898199, -0.021715153008699417, -0.02637605182826519, -0.00416980916634202, 0.032751306891441345, 0.021947303786873817, -0.04957340657711029, 0.03871583193540573, -0.026108184829354286, 0.041644517332315445, -0.03230486065149307, -0.0031385181937366724, -0.08700346946716309, 0.00536628533154726, -0.007254753727465868, 0.005933272652328014, 0.037715788930654526, -0.03516211733222008, 0.038180094212293625, -0.0044153546914458275, 0.0393587127327919, 0.005866305436939001, -0.01503631379455328, 0.026643920689821243, -0.008853032253682613, 0.05414501577615738, -0.027429666370153427, 0.000426635320764035, -0.036787182092666626, -0.01298266090452671, -0.06053812801837921, 0.014411289244890213, -0.015223821625113487, -0.003743452951312065, 0.005361821036785841, -0.019179336726665497, 0.04471607133746147, 0.03757292777299881, 0.037537213414907455, 0.0034063858911395073, 0.03230486065149307, 0.006660980172455311, 0.035287123173475266, -0.005299318581819534, 0.008705704472959042, -0.03591214865446091, -0.0074333325028419495, 0.01035755593329668, -0.034483518451452255, 0.025072429329156876, -0.03618001565337181, -0.01001825649291277, 0.000920795660931617, -0.0393587127327919, -0.0185185968875885, 0.010527205653488636, -0.01621493324637413, 0.007870850153267384, 0.020447244867682457, -0.022822339087724686, -0.009098577313125134, 0.03455495089292526, 0.05028771981596947, -0.02723322995007038, 0.03825152665376663, 0.03410850465297699, 0.029697613790631294, -0.016902459785342216, -0.00014230477972887456, -0.03596572205424309, 0.022983059287071228, -0.01841144822537899, 0.030429786071181297, -0.05764515697956085, 0.01882218010723591, -0.002884043613448739, 0.021572289988398552, 0.03092980571091175, -0.008629808202385902, -0.03671574965119362, -0.011375454254448414, 0.019715072587132454, -0.00937537383288145, -0.03582285717129707, -0.004279188811779022, 0.018393591046333313, 0.01859002746641636, -0.017188185825943947, 0.008219078183174133, 0.0012690238654613495, 0.012991589494049549, 0.018536454066634178, -0.03728720173239708, -0.016482800245285034, 0.019947225227952003, -0.03689432889223099, -0.011670108884572983, 0.02526886574923992, -0.00600023940205574, -0.00293538486585021, 0.004294814076274633, -0.04775190353393555, 0.024143820628523827, 0.021679436787962914, -0.012545143254101276, -0.029983339831233025, -0.028929725289344788, -0.0034711207263171673, 0.0035626422613859177, 0.018340017646551132, -0.041215930134058, -0.010982581414282322, 0.0007717941771261394, -0.003609518986195326, -0.0034443337935954332, -0.03643002361059189, 0.016402440145611763, 0.08407478034496307, -0.008544983342289925, -0.004946625791490078, -0.016429226845502853, -0.021911589428782463, 0.020054372027516365, 0.03710862249135971, -0.023750947788357735, 0.029858333989977837, 0.04800191521644592, -0.04357316717505455, -0.008705704472959042, 0.027054650709033012, -0.008960179053246975, -0.0323227196931839, 0.017134612426161766, -0.006576155312359333, 0.020518675446510315, 0.03046550042927265, -0.015277395024895668, 0.003897476941347122, 0.006977957207709551, 0.008299438282847404, -0.00809407327324152, 0.045680392533540726, -0.006393112242221832, -0.03364419937133789, 0.0126433614641428, 0.023393791168928146, 0.019429346546530724, -0.007527085952460766, 0.03728720173239708, 0.04496607929468155, -0.020625822246074677, -0.015304181724786758, -0.03082265891134739, 0.001598278060555458, -0.025483159348368645, -0.013696975074708462, -0.0011228126240894198, -0.05500219389796257, 0.02378666400909424, -0.04232311621308327, -0.05060916393995285, -0.0017366764368489385, 0.004401961341500282, 0.04893052205443382, -0.035644277930259705, 0.007768167182803154, -0.013098737224936485 ]
In order to enhance levels of engagement with conversational systems, our long term research goal seeks to monitor the confusion state of a user and adapt dialogue policies in response to such user confusion states. To this end, in this paper, we present our initial research centred on a user-avatar dialogue scenario that we have developed to study the manifestation of confusion and in the long term its mitigation. We present a new definition of confusion that is particularly tailored to the requirements of intelligent conversational system development for task-oriented dialogue. We also present the details of our Wizard-of-Oz based data collection scenario wherein users interacted with a conversational avatar and were presented with stimuli that were in some cases designed to invoke a confused state in the user. Post study analysis of this data is also presented. Here, three pre-trained deep learning models were deployed to estimate base emotion, head pose and eye gaze. Despite a small pilot study group, our analysis demonstrates a significant relationship between these indicators and confusion states. We understand this as a useful step forward in the automated analysis of the pragmatics of dialogue.
[ -0.012870153412222862, 0.04662097245454788, -0.021631339564919472, -0.0487939827144146, 0.03405701369047165, 0.029375161975622177, -0.02088066376745701, 0.017650779336690903, -0.046107351779937744, 0.00857845600694418, 0.030738232657313347, -0.0782284066081047, -0.04749017581343651, -0.004948539659380913, 0.029375161975622177, 0.009200727567076683, 0.002407597843557596, 0.043539244681596756, 0.03158768266439438, -0.02350803278386593, 0.045001089572906494, -0.011358923278748989, -0.05930345505475998, 0.033721186220645905, 0.048517417162656784, 0.025542760267853737, 0.015783963724970818, -0.006079493090510368, -0.06009364128112793, 0.032200079411268234, -0.020426306873559952, 0.0016322279116138816, 0.03223958611488342, -0.023804351687431335, -0.027123132720589638, -0.04843840003013611, 0.027616998180747032, -0.02718239650130272, 0.03820548951625824, 0.07961123436689377, -0.03344462066888809, -0.032042041420936584, -0.04101065173745155, -0.03352363780140877, 0.013986291363835335, -0.06123941019177437, -0.029276389628648758, -0.02514766715466976, -0.018292805179953575, -0.009457537904381752, 0.0361114963889122, -0.049110058695077896, 0.05420675501227379, 0.02854546718299389, -0.021493058651685715, 0.017887834459543228, 0.011477450840175152, -0.061753030866384506, 0.07731969654560089, 0.028782524168491364, 0.06151597574353218, -0.02410067245364189, -0.04160328954458237, 0.006291855592280626, 0.001540862605907023, -0.0326346792280674, 0.03680291026830673, -0.02019912749528885, -0.002058187499642372, -0.00031792637309990823, 0.008588333614170551, 0.030678968876600266, -0.0008148792549036443, -0.021769622340798378, -0.019547225907444954, -0.05926394462585449, 0.03709923103451729, 0.08186326175928116, 0.018727406859397888, -0.03709923103451729, 0.008346338756382465, 0.009625452570617199, -0.03018510341644287, 0.0032471704762429, 0.07645048946142197, -0.06044922396540642, 0.015270343981683254, -0.09466427564620972, -0.004605302587151527, 0.010302049107849598, -0.030718479305505753, 0.018490351736545563, -0.007808024995028973, -0.03160743787884712, -0.02030777931213379, -0.012899785302579403, -0.009353825822472572, -0.024495763704180717, -0.025839081034064293, -0.0028446693904697895, 0.04251200333237648, 0.01821378618478775, 0.03488671034574509, -0.015349362045526505, 0.024890856817364693, -0.007121550850570202, -0.04357875511050224, -0.016672924160957336, 0.03783015161752701, 0.18521958589553833, -0.07439600676298141, 0.022065943107008934, -0.0005219548474997282, -0.01083542499691248, -0.02577981725335121, 0.029671482741832733, 0.006005413364619017, -0.04417139291763306, 0.00020865847181994468, 0.014993778429925442, 0.030718479305505753, 0.02645147405564785, -0.03144939988851547, -0.019557101652026176, -0.0033286584075540304, 0.047727230936288834, 0.023606805130839348, 0.013561566360294819, 0.02309318445622921, -0.000877847196534276, -0.011645365506410599, 0.021710358560085297, -0.03589419648051262, 0.02980976551771164, -0.008366093970835209, 0.016603782773017883, 0.0013766520423814654, 0.0005944914883002639, 0.012425674125552177, 0.058710817247629166, 0.002449576510116458, -0.009546433575451374, -0.021295512095093727, 0.045593731105327606, -0.0019050888950005174, -0.028644241392612457, 0.0006451127701438963, 0.027834299951791763, -0.05215227231383324, -0.010855179280042648, -0.03389897570014, 0.0487939827144146, -0.022243734449148178, 0.010064993984997272, -0.0034694101195782423, -0.0706426277756691, 0.03684242069721222, -0.051085520535707474, 0.009778550826013088, -0.011783648282289505, 0.021295512095093727, -0.049307603389024734, 0.02287588268518448, 0.010450209490954876, 0.034294068813323975, -0.0026718161534518003, -0.02135477587580681, -0.0076006012968719006, -0.029059087857604027, 0.04270955175161362, -0.037968434393405914, 0.04342071712017059, -0.00038058566860854626, 0.018934831023216248, 0.02639221027493477, -0.0005370795261114836, 0.002131032757461071, 0.02429821714758873, -0.06139744818210602, 0.01910274475812912, -0.035617630928754807, -0.025384724140167236, 0.050097789615392685, 0.012060212902724743, 0.03725726902484894, -0.03028387576341629, 0.04413188621401787, -0.06131843104958534, 0.0038990736939013004, 0.008479682728648186, 0.02483159303665161, 0.03464965522289276, 0.057288482785224915, 0.024436499923467636, 0.0072005693800747395, -0.036506589502096176, -0.053772155195474625, 0.013670217245817184, -0.00373362866230309, -0.020169496536254883, -0.04812232404947281, -0.03401750698685646, -0.012613343074917793, -0.006020229309797287, -0.05705142393708229, 0.04440845176577568, 0.007368484046310186, 0.03893641382455826, -0.016781574115157127, -0.020920172333717346, 0.02955295518040657, -0.04089212417602539, -0.005412773694843054, 0.0021347366273403168, -0.013008436188101768, -0.004094150848686695, 0.0010426751105114818, -0.012850399129092693, 0.10683313757181168, -0.014331997372210026, 0.008420418947935104, 0.01217874139547348, 0.05997511371970177, -0.013867763802409172, -0.03559787571430206, -0.017561882734298706, -0.04334169998764992, 0.07099820673465729, -0.039864882826805115, 0.011171254329383373, -0.03022461198270321, 0.044210903346538544, 0.04172181710600853, -0.03790917247533798, 0.05436479300260544, -0.007699374575167894, 0.05262638255953789, 0.0017519904067739844, -0.010637878440320492, 0.009783489629626274, -0.03012583963572979, -0.045475199818611145, -0.004234903026372194, -0.04361826553940773, 0.0734872967004776, -0.013146718963980675, 0.02204618789255619, -0.0011210762895643711, -0.003101479960605502, -0.018282927572727203, -0.014331997372210026, 0.04302562400698662, -0.047845758497714996, 0.012208373285830021, 0.013808499090373516, 0.04808281362056732, 0.0665336549282074, -0.023389503359794617, 0.029098598286509514, -0.03599296882748604, -0.004232433624565601, -0.027478717267513275, 0.03559787571430206, 0.03223958611488342, -0.036447327584028244, -0.0497422069311142, 0.07218348979949951, -0.007625294383615255, 0.06135793775320053, -0.05140159651637077, 0.037770889699459076, -0.03474842756986618, 0.028486203402280807, 0.0007698139525018632, 0.0032298851292580366, 0.005318939220160246, 0.05993560329079628, -0.010272417217493057, 0.01794709824025631, -0.03696094825863838, 0.02414018101990223, -0.047727230936288834, 0.019171886146068573, -0.04476403445005417, 0.013936905190348625, -0.012978804297745228, -0.021532567217946053, 0.00400278577581048, -0.06977342069149017, 0.01706801727414131, -0.02739969827234745, -0.023863615468144417, -0.0008451285539194942, 0.0386400930583477, 0.024535274133086205, 0.004501590505242348, 0.019013850018382072, 0.014825863763689995, 0.005225104745477438, -0.04365777224302292, -0.00014491887122858316, 0.003234823700040579, 0.0013840601313859224, 0.035558369010686874, 0.044487468898296356, 0.06281978636980057, 0.05199423432350159, 0.04136623442173004, 0.00043954094871878624, -0.003916359040886164, 0.04508011043071747, -0.008183362893760204, -0.019932441413402557, 0.016870470717549324, -0.024910612031817436, -0.011773770675063133, 0.020268268883228302, 0.0003605223319027573, 0.014450525864958763, -0.021236248314380646, -0.025127913802862167, -0.0021162168122828007, -0.08889591693878174, -0.0021557260770350695, 0.019902808591723442, 0.015132061205804348, -0.031093817204236984, -0.03767211362719536, -0.0198830533772707, 0.012050336226820946, -0.007709251716732979, -0.006864740513265133, -0.014786354266107082, 0.015527154318988323, 0.02866399474442005, -0.012158986181020737, 0.040279727429151535, 0.03097528964281082, -0.0020446062553673983, 0.018855812028050423, -0.0007451206329278648, -0.014756722375750542, -0.053614117205142975, -0.011121867224574089, -0.011082357726991177, -0.006321487482637167, -0.020129987969994545, 0.04120819643139839, -0.00556587241590023, -0.0364275723695755, 0.0010445270454511046, 0.002286600647494197, -0.04934711381793022, 0.03536082059144974, 0.012603466399013996, 0.01579384133219719, 0.004763339646160603, -0.04247249662876129, -0.0127516258507967, 0.04215642064809799, 0.015448135323822498, -0.032930999994277954, 0.009482230991125107, 0.00800557155162096, -0.039133958518505096, -0.040971141308546066, 0.025424232706427574, -0.042432986199855804, 0.007422809489071369, -0.01674206554889679, 0.023448769003152847, 0.03127161040902138, -0.028328167274594307, 0.010213153436779976, -0.03322732076048851, -0.01113174483180046, -0.018026117235422134, -0.04187985509634018, -0.03338535502552986, 0.05468086898326874, -0.041919365525245667, -0.04997926205396652, -0.01382825430482626, 0.035933706909418106, 0.00013874554133508354, 0.03512376546859741, 0.01199107151478529, 0.017650779336690903, -0.013126963749527931, 0.05333755165338516, 0.046423424035310745, -0.01110211294144392, -0.03385946899652481, -0.04606784135103226, 0.037810396403074265, -0.002716264221817255, 0.023132693022489548, 0.011092235334217548, 0.02062385343015194, 0.04820134490728378, -0.010153889656066895, 0.04184034466743469, 0.016811206936836243, -0.03269394487142563, 0.009250114671885967, -0.032358113676309586, -0.013482547365128994, 0.02178937755525112, 0.008603149093687534, 0.0018310090526938438, -0.04725312069058418, 0.015546908602118492, -0.03824499994516373, -0.00169889978133142, 0.0021297980565577745, 0.021236248314380646, -0.06775844842195511, 0.013028190471231937, -0.001944598276168108, 0.004116374999284744, -0.011270027607679367, 0.008489560335874557, 0.100748710334301, 0.02892080508172512, -0.04990024119615555, 0.023587049916386604, -0.07941368967294693, 0.008104344829916954, 0.020031213760375977, -0.015517276711761951, 0.022737599909305573, -0.03654609993100166, 0.03658561035990715, -0.08115209639072418, 0.020821399986743927, -0.014895005151629448, 0.024258708581328392, 0.01878667064011097, -0.0161593034863472, 0.011586101725697517, -0.0674818828701973, -0.04614685848355293, 0.035044748336076736, -0.024555029347538948, -0.016722310334444046, 0.022895637899637222, 0.025068650022149086, 0.0022335099056363106, -0.022737599909305573, 0.05341656878590584, -0.06791648268699646, 0.0551154688000679, -0.06771893799304962, -0.04440845176577568, -0.014549299143254757, -0.01758163794875145, 0.06910175830125809, -0.04634440690279007, 0.04413188621401787, -0.10501570999622345, 0.0006256667547859251, 0.041642799973487854, 0.02587858960032463, -0.008701922371983528, 0.03972660005092621, -0.038501810282468796, -0.016732187941670418, -0.038126472383737564, 0.003560775425285101, 0.05736749991774559, -0.03391873091459274, -0.01973489485681057, -0.03447186201810837, -0.022125206887722015, -0.02534521371126175, -0.03152842074632645, -0.030046820640563965, 0.017275439575314522, 0.009166156873106956, 0.035084255039691925, 0.04187985509634018, -0.041287217289209366, -0.016929734498262405, -0.0047213612124323845, -0.06598052382469177, -0.018875567242503166, 0.01441101636737585, -0.015201202593743801, -0.031212344765663147, -0.03075798787176609, -0.0557476207613945, -0.07542324811220169, 0.04302562400698662, -0.0194780845195055, -0.019725017249584198, -0.03221983090043068, -0.019033603370189667, -0.01493451464921236, 0.05389068275690079, -0.006993145681917667, 0.005743664223700762, -0.06645464152097702, -0.019339801743626595, 0.028881296515464783, -0.029572708532214165, 0.011309536173939705, 0.0315086655318737, 0.007640110328793526, -0.015971632674336433, 0.04016119986772537, 0.015714822337031364, -0.011961439624428749, 0.02182888612151146, -0.018826181069016457, -0.006844985764473677, 0.017235931009054184, 0.0329507552087307, 0.012356532737612724, 0.02949369139969349, -0.006973390933126211, -0.014549299143254757, 0.00039601896423846483, 0.005585627164691687, 0.02167084999382496, -0.01842121034860611, 0.035143520683050156, 0.037612851709127426, -0.0048571741208434105, -0.04768772050738335, 0.0288220327347517, -0.03792892396450043, 0.03630904480814934, -0.005294245667755604, -0.03808696195483208, -0.010015606880187988, 0.0034126155078411102, -0.003563244827091694, 0.006617807317525148, 0.04618636891245842, -0.04575176537036896, -0.01580371893942356, 0.027577489614486694, -0.03328658267855644, -0.013689971528947353, 0.004071927163749933, -0.01710752584040165, 0.015813596546649933, -0.011319413781166077, 0.030145594850182533, -0.03662511706352234, 0.013601075857877731, 0.006025168113410473, 0.011141621507704258, 0.030461668968200684, -0.01580371893942356, -0.0021433793008327484, 0.012336778454482555, -0.006242468953132629, 0.007827779278159142, -0.025858834385871887, 0.02214496210217476, 0.008405603468418121, -0.024476010352373123, 0.06546690315008163, 0.02530570514500141, -0.010005729272961617, -0.000573502155020833, 0.08210031688213348, 0.021117718890309334, 0.026056380942463875, -0.022283243015408516, -0.03233835846185684, -0.04409237578511238, -0.004486774560064077, 0.01773967407643795, 0.00849943794310093, 0.07747773081064224, -0.06447917222976685, 0.0007846299558877945, 0.05389068275690079, 0.041958872228860855, 0.014006045646965504, -0.0016964304959401488, 0.0039015430957078934, -0.023764843121170998, -0.028644241392612457, 0.008771063759922981, -0.04093163087964058, -0.02540447749197483, -0.0006895607220940292, 0.030362894758582115, 0.027044113725423813, 0.004200332332402468, -0.0006833873922005296, 0.006183205172419548, -0.017305072396993637, 0.03139013797044754, 0.03196302056312561, 0.018806425854563713, -0.03632880002260208, -0.05310049653053284, -0.007758638355880976, 0.02178937755525112, 0.09608661383390427, -0.03291124477982521, -0.0021581954788416624, -0.012415796518325806, -0.018361946567893028, 0.007170937489718199, 0.017255686223506927, -0.00038243766175583005, 0.006622746121138334, 0.03496572747826576, -0.02828865684568882, -0.014855495654046535, -0.05740701034665108, 0.012959050014615059, -0.05551056191325188, 0.01441101636737585, -0.0324568897485733, -0.005422651302069426, -0.011566346511244774, 0.05898738279938698, 0.002475504530593753, 0.0582762137055397, 0.024890856817364693, 0.017018629238009453, -0.04219593107700348, 0.010030423291027546, -0.00679559912532568, -0.03186424821615219, 0.02182888612151146, 0.001017364440485835, 0.023389503359794617, 0.0380079448223114, 0.03022461198270321, -0.006543727591633797, 0.022796865552663803, 0.05306098610162735, -0.05179668962955475, -0.02739969827234745, 0.018391577526926994, -0.03275320678949356, 0.029691237956285477, -0.01548764482140541, -0.00571897067129612, 0.015408625826239586, -0.013482547365128994, 0.028624486178159714, -0.0074376254342496395, 0.021552322432398796, -0.023863615468144417, -0.010756406001746655, 0.015655558556318283, -0.02319195680320263, -0.018361946567893028, 0.021018946543335915, -0.012000949122011662, -0.0006519033922813833, 0.0004969529109075665, 0.0354793481528759, -0.00257304310798645, 0.021453548222780228, -0.035143520683050156, 0.0316864550113678, 0.03154817596077919, 0.018026117235422134, 0.010430454276502132, 0.03196302056312561, 0.0395883172750473, 0.014213469810783863, -0.002221163362264633, -0.049149565398693085, 0.00018643449584487826, -0.01563580520451069, -0.0024878510739654303, -0.0015161692863330245, 0.029118351638317108, -0.017552005127072334, -0.02088066376745701, -0.01553703099489212, -0.05736749991774559, 0.01978428103029728, 0.028644241392612457, -0.012484937906265259, -0.016811206936836243, 0.0010531697189435363, 0.026846567168831825, -0.03142964467406273, -0.045475199818611145, -0.02607613615691662, -0.013778867200016975, -0.04828036203980446, -0.034096524119377136, -0.03352363780140877, 0.001680379849858582, -0.0403982549905777, 0.003834871109575033, -0.001012425753287971, 0.016880348324775696, -0.0023989551700651646, 0.01034155860543251, -0.012613343074917793, 0.050729937851428986, 0.015418503433465958, 0.005091760773211718, 0.007091918960213661, 0.005585627164691687, -0.04168231040239334, -0.02901957929134369, -0.0019347209017723799, -0.010440331883728504, 0.0033632288686931133, 0.029039334505796432, 0.0326346792280674, 0.05562908947467804, 0.041958872228860855, -0.012386164627969265, -0.0019804034382104874, 0.011773770675063133, 0.03909445181488991, 0.021749868988990784, 0.02775528095662594, -0.01951759308576584, -0.040437765419483185, 0.04555422067642212, 0.0028051601257175207, 0.002211285987868905, -0.021651094779372215, -0.005052251275628805, 0.002371792448684573, -0.043697282671928406, -0.03646708279848099, 0.009378519840538502, 0.017818693071603775, -0.009457537904381752, -0.0014210999943315983, 0.011121867224574089, 0.00913158617913723, 0.02666877582669258, 0.020169496536254883, -0.04519863799214363, 0.04187985509634018, 0.004420102573931217, 0.0007580846431665123, 0.02119673788547516, -0.020228760316967964, 0.032042041420936584, -0.03352363780140877, 0.015517276711761951, 0.0725390687584877, -0.00162358523812145, 0.03528180345892906, -0.022164715453982353, 0.0061930823139846325, -0.008603149093687534, -0.002916279947385192, -0.017670532688498497, -0.009047629311680794, -0.022164715453982353, -0.020139863714575768, -0.01984354481101036, 0.018589124083518982, 0.02356729656457901, 0.015102429315447807, 0.007249956019222736, 0.010904566384851933, 0.0032397625036537647, 0.02334999479353428, -0.008469806052744389, 0.016080284491181374, -0.0029064028058201075, 0.05337706208229065, -0.04567274823784828, -0.00826238188892603, -0.033622413873672485, 0.01243555173277855, -0.05013730004429817, -0.05594516545534134, -0.013087455183267593, -0.09126647561788559, 0.02410067245364189, -0.036881931126117706, 0.003617570037022233, -0.04583078622817993, 0.007684558164328337, -0.0001652908540563658, -0.02603662759065628, 0.0055609336122870445, 0.06357046216726303, 0.0003296557115390897, -0.009763735346496105, 0.015161693096160889, 0.02394263446331024, 0.017245808616280556, -0.035400331020355225, -0.040240220725536346, 0.052823930978775024, -0.04235396534204483, 0.005911578424274921, 0.008766124956309795, 0.02676755003631115, 0.007580846548080444, 0.027636753395199776, -0.036881931126117706, -0.05515497922897339, -0.004375654738396406, -0.032516151666641235, 0.0004750375810544938, 0.04108966886997223, 0.032614924013614655, -0.0076499879360198975, -0.0021865926682949066, 0.019250905141234398, 0.004523814655840397, -0.011813280172646046, -0.058868855237960815, 0.010173643939197063, -0.0003247170534450561, -0.049623679369688034, 0.009852631017565727, 0.011398432776331902, 0.023843860253691673, 0.0039706844836473465, -0.0313703827559948, -0.02230299822986126, -0.007561091799288988, 0.006133818533271551, -0.002310059266164899, -0.010667510330677032, -0.007971000857651234, 0.01773967407643795, -0.03992414474487305, 0.005723909474909306, -0.008074712939560413, 0.029928293079137802, -0.02252030000090599, -0.03490646556019783, -0.011882421560585499, 0.04298611730337143, -0.027439206838607788, 0.01706801727414131, 0.034037258476018906, -0.009650145657360554, 0.04741115868091583, -0.01219849567860365, 0.015783963724970818, 0.017186544835567474, 0.008484621532261372, -0.02350803278386593, 0.010499595664441586, 0.0005457221996039152, 0.10438356548547745, 0.022322753444314003, 0.019636120647192, 0.004780624993145466, -0.012119476683437824, 0.06404457241296768, 0.0484779067337513, -0.01899409480392933, 0.009220482781529427, 0.007086980156600475, -0.03591395169496536, 0.0053041232749819756, 0.012415796518325806, -0.0028076295275241137, 0.0011408309219405055, -0.044645506888628006, -0.0018557023722678423, -0.013838131912052631, -0.005427589640021324, 0.0056547680869698524, -0.024594537913799286, 0.007477134466171265, -0.03166670352220535, 0.019932441413402557, -0.00721538532525301, -0.009931650012731552, 0.007398115936666727, 0.03208154812455177, 0.03494597226381302, 0.01173426117748022, 0.004010193515568972, -0.02508840337395668, 0.010746529325842857, -0.014401138760149479, -0.032772962003946304, -0.04918907582759857, 0.014341874979436398, -0.006593114230781794, -0.00039601896423846483, -0.009106893092393875, 0.007664803881198168, -0.01191205345094204, 0.011931807734072208, 0.015517276711761951, -0.018085381016135216, -0.018174277618527412, 0.018144644796848297, 0.029256634414196014, -0.004992987494915724, -0.04666047915816307, 0.025226686149835587, -0.013413406908512115, -0.03206179663538933, -0.037237513810396194, 0.03640781715512276, -0.05483890324831009, -0.01811501383781433, -0.03656585514545441, -0.0315086655318737, -0.011191008612513542, 0.009719287045300007, -0.054720375686883926, 0.04654195159673691, -0.06364947557449341, -0.03380020335316658, 0.029671482741832733, 0.044013358652591705, 0.01637660339474678, 0.04606784135103226, 0.012307146564126015, 0.005348571110516787, 0.0027458961121737957, -0.029375161975622177, 0.0017285317881032825, -0.00033922435250133276, -0.003827463136985898, 0.0022791926749050617, 0.0077833314426243305, -0.0180557481944561, 0.034353334456682205, 0.00902787409722805, -0.005758480168879032, 0.008336462080478668, -0.0129886819049716, -0.040121693164110184, 0.013601075857877731, -0.01059836894273758, -0.01113174483180046, 0.011457696557044983, -0.06254322081804276, 0.02093992754817009, -0.01816440001130104, -0.006454831454902887, -0.006202959921211004, 0.02886154130101204, 0.012998558580875397, -0.0040595801547169685, 0.010440331883728504, 0.0073635452426970005, -0.03946978971362114, -0.015922246500849724, 0.009171095676720142, -0.03480768948793411, 0.004783094394952059, -0.011892298236489296, -0.0013902334030717611, 0.0025360030122101307, 0.05626124143600464, -0.020643608644604683, -0.019399065524339676, -0.020821399986743927, -0.02366606891155243, -0.02030777931213379, 0.017927343025803566, -0.029039334505796432, -0.018776793032884598, 0.021275756880640984, 0.02477232925593853, 0.03518303111195564, -0.01664329133927822, -0.005669584032148123, 0.022638827562332153, 0.017038384452462196, -0.025127913802862167, -0.053140006959438324, 0.001137126935645938, -0.01669267751276493, -0.00046639490756206214, 0.04958416894078255, -0.046107351779937744, 0.018727406859397888, -0.013522056862711906, -0.008479682728648186, -0.020080599933862686, 0.014085064642131329, -0.03152842074632645, -0.023962389677762985, 0.020663361996412277, -0.02388337068259716, -0.02467355690896511, -0.012603466399013996, -0.004066988360136747, -0.0017742144409567118, -0.019586734473705292, 0.020505325868725777, 0.014391262084245682, 0.03512376546859741, -0.013186228461563587, -0.02325122244656086, -0.054246265441179276, 0.029355408623814583, 0.06961537897586823, -0.00027733674505725503, 0.04630489647388458, 0.02986902929842472, -0.0161593034863472, -0.002164368750527501, -0.012771380133926868, -0.019586734473705292, 0.01637660339474678, -0.022638827562332153, 0.008731555193662643, -0.030777743086218834, 0.008366093970835209, -0.013848008587956429, -0.04342071712017059, 0.015033287927508354, -0.03648683801293373, 0.005822682753205299, 0.019754648208618164, 0.009087138809263706, -0.009205666370689869 ]
Column Generation (CG) is an iterative algorithm for solving linear programs (LPs) with an extremely large number of variables (columns). CG is the workhorse for tackling large-scale \textit{integer} linear programs, which rely on CG to solve LP relaxations within a branch and price algorithm. Two canonical applications are the Cutting Stock Problem (CSP) and Vehicle Routing Problem with Time Windows (VRPTW). In VRPTW, for example, each binary variable represents the decision to include or exclude a \textit{route}, of which there are exponentially many; CG incrementally grows the subset of columns being used, ultimately converging to an optimal solution. We propose RLCG, the first Reinforcement Learning (RL) approach for CG. Unlike typical column selection rules which myopically select a column based on local information at each iteration, we treat CG as a sequential decision-making problem: the column selected in a given iteration affects subsequent column selections. This perspective lends itself to a Deep Reinforcement Learning approach that uses Graph Neural Networks (GNNs) to represent the variable-constraint structure in the LP of interest. We perform an extensive set of experiments using the publicly available BPPLIB benchmark for CSP and Solomon benchmark for VRPTW. RLCG converges faster and reduces the number of CG iterations by 22.4\% for CSP and 40.9\% for VRPTW on average compared to a commonly used greedy policy. Our code is available at https://github.com/chichengmessi/reinforcement-learning-for-column-generation.git.
[ 0.005188404582440853, -0.012188918888568878, -0.043851256370544434, 0.030796853825449944, -0.018968554213643074, 0.01182829961180687, -0.007649628445506096, 0.024377837777137756, -0.03948776796460152, 0.0609806552529335, 0.020753618329763412, -0.03974020108580589, 0.03305072337388992, -0.04294971004128456, -0.015398426912724972, 0.036765094846487045, 0.008524129167199135, 0.014569003134965897, 0.019275080412626266, -0.03595370426774025, -0.0003203309897799045, 0.010512040928006172, 0.037828922271728516, 0.05030633509159088, 0.012531506828963757, 0.013775642029941082, 0.031157473102211952, -0.001249769818969071, -0.08741401880979538, 0.05470588803291321, 0.061413396149873734, 0.03278025612235069, 0.027875840663909912, -0.01510993205010891, 0.0029953906778246164, -0.007956154644489288, 0.04460855573415756, 0.05351584404706955, -0.03638644516468048, 0.025495756417512894, -0.005959227215498686, 0.030075615271925926, -0.04006475955247879, -0.0073881796561181545, 0.02661367505788803, -0.05228973925113678, -0.014109213836491108, 0.012720831669867039, -0.05362403020262718, -0.00891630258411169, -0.01918492466211319, -0.010989860631525517, 0.07911978662014008, 0.012567568570375443, -0.01701219566166401, -0.040677811950445175, 0.011043953709304333, 0.012883109971880913, 0.01669665426015854, 0.04287758842110634, -0.014010043814778328, -0.025441663339734077, -0.09491489082574844, -0.03667494282126427, 0.02432374469935894, -0.058600571006536484, 0.02780371718108654, 0.028110243380069733, 0.04785412922501564, -0.049657221883535385, -0.11027725785970688, -0.01605655625462532, -0.02060936950147152, -0.00781190674751997, 0.02273702062666416, 0.011098046787083149, 0.012423320673406124, -0.012720831669867039, 0.024107372388243675, -0.024071311578154564, 0.026036683470010757, 0.03104928694665432, -0.033753927797079086, -0.014208384789526463, 0.05924968421459198, -0.028885573148727417, 0.024576177820563316, -0.057807207107543945, -0.005932180676609278, -0.014623096212744713, -0.013703517615795135, 0.04875567555427551, 0.0021141283214092255, -0.034745629876852036, 0.018130114302039146, -0.02107817493379116, -0.003504764987155795, -0.030868977308273315, -0.028020087629556656, 0.0349620021879673, -0.05055876821279526, -0.026451395824551582, -0.004532528575509787, 0.014523926191031933, 0.03966807946562767, 0.015804123133420944, -0.026271086186170578, 0.03357362002134323, 0.00015692556917201728, 0.1130179613828659, -0.031301721930503845, -0.00292777456343174, 0.03177052363753319, 0.006004304625093937, -0.049296602606773376, 0.006364923436194658, -0.043995507061481476, -0.05961030349135399, 0.03707162290811539, -0.03880259394645691, -0.009285936132073402, 0.06094459444284439, 0.02183547429740429, -0.047565631568431854, -0.041002366691827774, 0.013992013409733772, -0.018021930009126663, 0.0039217304438352585, -0.0003516034339554608, 0.01799488253891468, -0.054958321154117584, -0.03793710842728615, -0.02143879421055317, -0.02028481289744377, 0.06083640828728676, 0.02475648745894432, 0.0487196110188961, -0.01224301103502512, -0.03725193068385124, 0.043454576283693314, -0.002481508767232299, -0.05398464947938919, 0.029047852382063866, 0.014460817910730839, 0.011467681266367435, -0.01858990453183651, -0.03254585713148117, 0.07154678553342819, -0.03732405602931976, 0.011377526447176933, -0.03128368780016899, 0.031662337481975555, 0.01974388398230076, 0.05358796939253807, -0.01473128143697977, 0.0001286817860091105, -0.006423524115234613, -0.013387976214289665, 0.052902791649103165, -0.07309745252132416, 0.06451471894979477, 0.01657945290207863, -0.009493292309343815, 0.0073250713758170605, -0.002519824542105198, 0.029931368306279182, 0.054128896445035934, -0.01141358818858862, -0.06242313235998154, 0.031157473102211952, -0.00008268878445960581, -0.006901344284415245, 0.0015968655934557319, 0.004467166494578123, 0.015813138335943222, 0.0001510091678937897, 0.02179941162467003, 0.002600963693112135, 0.003029198618605733, 0.03029198758304119, -0.017309706658124924, -0.06170189380645752, 0.03665691241621971, 0.03173446282744408, 0.041939977556467056, 0.029949398711323738, 0.07825429737567902, -0.007383672054857016, 0.007627089507877827, -0.008276203647255898, -0.0230255164206028, -0.0028195888735353947, 0.07331382483243942, -0.034547291696071625, -0.0025220783427357674, -0.052073366940021515, -0.05279460549354553, 0.00478721596300602, -0.012134825810790062, 0.043454576283693314, -0.0526864193379879, -0.018057990819215775, -0.0000018048552874461166, 0.007415226195007563, 0.044716741889715195, -0.020789679139852524, 0.014902575872838497, -0.010917737148702145, 0.008889256045222282, -0.06689480692148209, -0.027893871068954468, 0.024395868182182312, -0.06545232981443405, 0.0158221535384655, -0.004478435963392258, -0.00214117462746799, 0.02416146546602249, -0.009087596088647842, -0.03429485857486725, -0.049224480986595154, 0.023079609498381615, 0.08525030314922333, 0.05856451019644737, -0.06815697252750397, -0.009267905727028847, -0.009745725430548191, -0.010295669548213482, -0.006693988107144833, -0.02594652958214283, 0.007924600504338741, 0.012666738592088223, 0.01345108449459076, 0.016795825213193893, 0.0306526068598032, 0.018220270052552223, 0.016471268609166145, 0.02210593782365322, -0.007239424157887697, 0.029805151745676994, -0.01925704814493656, -0.0019383265171200037, -0.011566851288080215, -0.09130870550870895, -0.03611598163843155, 0.05315522477030754, -0.002242598682641983, -0.021853504702448845, 0.012224980629980564, 0.08525030314922333, 0.025063013657927513, -0.05975455045700073, -0.020933926105499268, -0.006031351163983345, -0.0725925862789154, -0.03301465883851051, 0.008546668104827404, 0.04731319844722748, -0.029354378581047058, -0.03600779548287392, 0.02214200049638748, 0.013541239313781261, 0.015533658675849438, -0.02329597994685173, 0.004509990103542805, -0.012369228526949883, 0.020032379776239395, 0.021546978503465652, 0.022484587505459785, -0.02048315294086933, 0.02167319506406784, -0.05265035852789879, -0.0457264743745327, -0.007865999825298786, -0.012684769928455353, -0.036458570510149, -0.038622282445430756, 0.023782815784215927, -0.04035325348377228, 0.04619527980685234, 0.00943018402904272, 0.034709569066762924, -0.015218117274343967, 0.0159032940864563, 0.02571212686598301, -0.036404479295015335, -0.01902264729142189, -0.022322310134768486, -0.026253055781126022, -0.04323820397257805, -0.005431822035461664, -0.020158596336841583, 0.022448526695370674, 0.011593897826969624, 0.03948776796460152, 0.012089748866856098, 0.03761254996061325, -0.007050099316984415, -0.046375591307878494, 0.019870100542902946, -0.02879541926085949, 0.016164742410182953, -0.005174881312996149, -0.01335191447287798, -0.008005739189684391, -0.04947691410779953, -0.0132527444511652, -0.026757922023534775, -0.024612240493297577, -0.011125093325972557, 0.015957385301589966, 0.028488893061876297, -0.03690934553742409, -0.004408565815538168, -0.005512961186468601, -0.028308583423495293, 0.052073366940021515, 0.08366358280181885, -0.033681806176900864, 0.0015979924937710166, -0.004586621653288603, 0.024197528138756752, -0.0032590932678431273, -0.09924232214689255, 0.02140273153781891, 0.016858933493494987, 0.05773508548736572, -0.0013951443834230304, 0.050486646592617035, -0.007636105176061392, 0.03142793849110603, -0.02472042478621006, -0.004976540803909302, 0.0007381418254226446, -0.0022403448820114136, -0.020717555657029152, -0.00816801842302084, -0.025694096460938454, 0.032563887536525726, -0.046808332204818726, -0.026793984696269035, -0.020320875570178032, -0.004117817152291536, 0.007717244327068329, 0.009763756766915321, -0.006590310484170914, -0.049188416451215744, 0.006608341354876757, -0.006739065516740084, 0.03321300074458122, -0.03631432354450226, 0.0009432437946088612, 0.03472759947180748, 0.020861802622675896, -0.0037098668981343508, 0.059393931180238724, 0.017336754128336906, -0.03357362002134323, 0.012405290268361568, -0.0112693402916193, 0.020753618329763412, 0.03184264898300171, -0.029949398711323738, -0.046411652117967606, 0.017769496887922287, -0.05063089355826378, 0.036566756665706635, -0.007050099316984415, -0.007176315877586603, -0.013333884067833424, -0.019239017739892006, -0.0271726343780756, 0.054922256618738174, 0.035340651869773865, -0.02902982197701931, 0.015876246616244316, 0.004216987174004316, 0.012991296127438545, -0.03761254996061325, -0.07006825506687164, 0.03177052363753319, -0.02206987701356411, 0.011206232011318207, -0.032563887536525726, -0.015957385301589966, 0.005436329636722803, 0.07435961812734604, -0.013144558295607567, -0.029805151745676994, 0.023476289585232735, 0.01216187234967947, 0.07082555443048477, -0.08308659493923187, 0.023350073024630547, -0.009520338848233223, 0.019761916249990463, 0.02392706461250782, 0.017354784533381462, 0.01814814656972885, 0.02764143794775009, -0.013099481351673603, 0.0020127042662352324, 0.007631597574800253, -0.053768277168273926, 0.03598976507782936, -0.03808135539293289, 0.014785374514758587, -0.018337471410632133, -0.041903916746377945, -0.02495482750236988, 0.010494009591639042, 0.004189940635114908, -0.043959442526102066, -0.05430920422077179, -0.01684991829097271, 0.02167319506406784, 0.016976134851574898, -0.07645120471715927, -0.009200289845466614, -0.009908003732562065, -0.011016907170414925, 0.010989860631525517, -0.003975823521614075, 0.04644771292805672, 0.016038525849580765, -0.020068442448973656, -0.020104503259062767, 0.002470239531248808, 0.022556710988283157, -0.030959133058786392, 0.02124045230448246, 0.01811208389699459, 0.0576629601418972, -0.007582012098282576, -0.03674706444144249, 0.005147834774106741, -0.0015134724089875817, -0.01958160661160946, 0.015795107930898666, -0.008091386407613754, -0.009484277106821537, 0.03485381603240967, -0.027551284059882164, -0.05138819292187691, -0.04569041356444359, -0.006459585856646299, -0.021528948098421097, -0.03624219819903374, -0.016480283811688423, -0.0025806790217757225, 0.009385107085108757, -0.07948040217161179, -0.00587358046323061, -0.0685897171497345, -0.01022354606539011, 0.0037031052634119987, -0.0017490016762167215, 0.010566134005784988, -0.011936485767364502, 0.023999188095331192, -0.013631394132971764, -0.004534782376140356, 0.0073431022465229034, -0.013712533749639988, -0.07399899512529373, 0.010557117871940136, 0.050126027315855026, -0.030995193868875504, -0.05607623979449272, -0.005774409975856543, -0.02372872270643711, -0.03651266172528267, -0.04327426850795746, 0.032329484820365906, 0.003822560189291835, -0.024017218500375748, -0.03797316923737526, 0.026126839220523834, -0.07078948616981506, -0.0026189947966486216, -0.022773083299398422, 0.04139905050396919, -0.02107817493379116, 0.026433365419507027, -0.029642872512340546, -0.027479160577058792, -0.00672554224729538, 0.0042891111224889755, -0.042661216109991074, 0.006175598595291376, 0.0025874406564980745, 0.007965169847011566, 0.06599325686693192, -0.05852844566106796, -0.01520910207182169, 0.017093336209654808, 0.024666331708431244, 0.009583447128534317, -0.041939977556467056, 0.010674319230020046, -0.012621661648154259, 0.028651170432567596, -0.014226415194571018, -0.000977615243755281, 0.0026437873020768166, -0.002344022737815976, -0.023872971534729004, 0.0493687279522419, 0.017499031499028206, -0.009466245770454407, 0.01315357442945242, -0.02574818953871727, 0.09073171764612198, -0.07140254229307175, 0.0018662028014659882, 0.026830045506358147, -0.00531912874430418, -0.021132268011569977, -0.007162792608141899, 0.0028736817184835672, 0.015713969245553017, 0.01335191447287798, -0.035142309963703156, -0.027695531025528908, -0.008650345727801323, -0.036134012043476105, 0.052073366940021515, 0.04323820397257805, -0.013009326532483101, 0.054922256618738174, 0.021384701132774353, 0.020627399906516075, 0.03626022860407829, -0.024846641346812248, -0.020392999053001404, -0.028416769579052925, -0.027316881343722343, 0.0487196110188961, -0.03883865475654602, -0.03191477060317993, 0.018103068694472313, -0.02942650206387043, 0.06945519894361496, -0.0351242795586586, -0.0203749667853117, 0.057013846933841705, -0.022051844745874405, -0.014109213836491108, -0.017147429287433624, -0.0001727026392472908, 0.024576177820563316, -0.03833378851413727, 0.023512352257966995, 0.029156038537621498, -0.014514910988509655, -0.07154678553342819, -0.022971423342823982, 0.0072935172356665134, -0.05593198910355568, -0.022610804066061974, -0.04835899546742439, 0.026793984696269035, -0.03894684091210365, 0.006869790144264698, 0.01593935489654541, -0.030129708349704742, -0.03369983658194542, 0.05099151283502579, 0.02499089017510414, -0.02179941162467003, 0.01602049358189106, -0.016831886023283005, -0.002499539637938142, -0.030273957177996635, -0.0238549392670393, -0.007784860208630562, 0.018021930009126663, -0.016245881095528603, 0.01748100109398365, -0.05225367844104767, 0.015245163813233376, -0.028020087629556656, -0.022051844745874405, 0.015010761097073555, 0.020122533664107323, 0.002312468597665429, -0.01665157824754715, -0.016426190733909607, 0.005129803903400898, -0.023620538413524628, -0.009592462331056595, -0.05200124531984329, 0.046808332204818726, 0.0007364514167420566, -0.02432374469935894, -0.04576253890991211, 0.00023412055452354252, -0.009953081607818604, -0.018968554213643074, -0.009998158551752567, -0.038982901722192764, -0.0043206652626395226, 0.014397709630429745, 0.026433365419507027, -0.04522160813212395, -0.021366668865084648, -0.03728799521923065, 0.04864748939871788, 0.0035566037986427546, 0.025099074468016624, -0.015840185806155205, -0.00039921639836393297, 0.03609795123338699, 0.023782815784215927, -0.03966807946562767, -0.0021242706570774317, -0.00826268084347248, 0.01629095897078514, 0.03483578562736511, -0.010016189888119698, -0.05773508548736572, 0.05409283563494682, -0.033122844994068146, 0.01965373009443283, -0.03353755548596382, 0.010827582329511642, 0.03618810698390007, -0.020465122535824776, -0.037396177649497986, -0.014172323048114777, 0.0028466354124248028, -0.014722266234457493, -0.0029908830765634775, -0.055787742137908936, -0.005449852906167507, 0.017345769330859184, 0.0002135539980372414, -0.047205012291669846, 0.044356122612953186, -0.01153078954666853, 0.021222421899437904, -0.0778936818242073, -0.005625654943287373, -0.0020476391073316336, 0.05712203308939934, -0.02724475786089897, -0.01443377137184143, -0.006996006704866886, 0.0038653837982565165, 0.021330608054995537, 0.02574818953871727, 0.03602582588791847, 0.04583466053009033, 0.05221761763095856, 0.03840591385960579, -0.016345052048563957, -0.02720869518816471, -0.01633603684604168, 0.013144558295607567, -0.0048728627152740955, 0.00618912186473608, -0.012684769928455353, 0.00008078708196990192, -0.005476899445056915, -0.00406372407451272, 0.00391496904194355, 0.003800021717324853, -0.0015495342668145895, 0.020302843302488327, -0.00987194199115038, 0.01346911583095789, -0.04579859972000122, 0.021546978503465652, -0.03005758486688137, -0.0027001339476555586, -0.014929622411727905, -0.031932804733514786, -0.02270095981657505, 0.026649735867977142, -0.01834648661315441, 0.023782815784215927, -0.058997251093387604, -0.051712751388549805, 0.0003020183357875794, 0.005147834774106741, -0.022160030901432037, -0.03393423929810524, -0.03869440779089928, -0.038982901722192764, -0.008835162967443466, 0.028218427672982216, -0.06307224184274673, -0.004196702502667904, 0.007478334475308657, -0.04172360524535179, 0.020988019183278084, 0.04688045755028725, -0.03638644516468048, 0.014037090353667736, 0.012747878208756447, -0.029282255098223686, 0.012270057573914528, -0.007005021907389164, 0.0025220783427357674, 0.01834648661315441, -0.0195455439388752, 0.010827582329511642, -0.016543392091989517, 0.012937203049659729, -0.06094459444284439, 0.011440634727478027, -0.003351501887664199, 0.009700648486614227, -0.0037594519089907408, 0.022881269454956055, 0.04749350994825363, -0.024179497733712196, 0.022592773661017418, 0.010881675407290459, 0.02491876482963562, 0.002779019298031926, -0.020356936380267143, 0.05146031454205513, 0.02194366045296192, -0.09664586186408997, -0.03384408354759216, 0.02024875022470951, 0.03317693993449211, -0.022196093574166298, 0.01720152050256729, -0.010034221224486828, -0.010917737148702145, -0.03503412753343582, -0.042769402265548706, 0.002646041102707386, 0.04298577085137367, -0.013324867933988571, -0.003842845093458891, 0.04320214316248894, -0.005814979784190655, -0.002368815476074815, 0.013460100628435612, -0.0036850743927061558, 0.003894684137776494, -0.023999188095331192, 0.027984026819467545, 0.001874091336503625, 0.011395556852221489, -0.0031238612718880177, 0.014298539608716965, -0.01335191447287798, 0.07486448436975479, 0.00478721596300602, 0.0699240043759346, 0.0035949195735156536, -0.048106562346220016, 0.014280508272349834, -0.000491343264002353, -0.0012430083006620407, 0.005738348234444857, -0.013045388273894787, 0.02143879421055317, 0.04327426850795746, 0.013333884067833424, -0.028272520750761032, 0.005981766153126955, 0.05106363445520401, 0.01194550096988678, -0.03200492635369301, 0.003754944307729602, -0.04320214316248894, 0.011007891967892647, -0.01040385477244854, 0.05679747462272644, -0.018535811454057693, 0.01247741375118494, 0.0031531613785773516, 0.020122533664107323, 0.02704641781747341, 0.005224466323852539, -0.0032027466222643852, -0.04327426850795746, 0.010602195747196674, 0.027298850938677788, 0.01759820245206356, -0.01767934113740921, 0.02107817493379116, 0.002954821102321148, -0.03018380142748356, 0.006910359486937523, -0.016399145126342773, 0.015948370099067688, 0.02017662674188614, -0.021186359226703644, 0.03380802273750305, 0.013811703771352768, -0.011161155067384243, 0.029913337901234627, 0.025135137140750885, -0.0417596697807312, -0.041831791400909424, 0.02472042478621006, -0.0026956263463944197, -0.00009522592881694436, 0.025928499177098274, 0.03424076363444328, 0.0004727488267235458, -0.019563574343919754, 0.00034371489891782403, -0.019509483128786087, 0.03440304100513458, 0.04248090460896492, 0.02365659922361374, -0.016949087381362915, 0.020988019183278084, 0.01161192823201418, -0.02634320966899395, -0.009448215365409851, 0.016354067251086235, -0.03714374452829361, -0.027785686776041985, -0.032419636845588684, -0.049044169485569, 0.03384408354759216, 0.020735586062073708, -0.047241076827049255, -0.026884138584136963, -0.017183490097522736, -0.04125479981303215, 0.0454019196331501, 0.014866514131426811, 0.025874406099319458, 0.05686959996819496, -0.049188416451215744, 0.009610493667423725, -0.014758327975869179, 0.0596463643014431, -0.0467362105846405, 0.033555589616298676, 0.019437357783317566, 0.015182055532932281, -0.03214917331933975, 0.0035520961973816156, -0.01259461510926485, -0.03717980906367302, -0.05517468973994255, 0.0016475776210427284, -0.006441554985940456, -0.023692661896348, -0.012702800333499908, 0.026487458497285843, -0.006008812226355076, 0.0217092577368021, 0.010557117871940136, -0.001389509649015963, -0.04713289067149162, -0.017354784533381462, 0.014343616552650928, 0.035340651869773865, -0.04244484379887581, -0.02262883633375168, 0.04294971004128456, 0.021745318546891212, 0.0017850635340437293, -0.014253461733460426, 0.05517468973994255, 0.010358777828514576, 0.0054994383826851845, -0.033753927797079086, 0.008222110569477081, -0.021781381219625473, 0.0072935172356665134, 0.03717980906367302, -0.016480283811688423, 0.04363488778471947, -0.02017662674188614, -0.011161155067384243, 0.04121873900294304, -0.036566756665706635, -0.028290553018450737, -0.03305072337388992, 0.0016025002114474773, -0.015569720417261124, -0.009448215365409851, -0.02701035514473915, 0.024648301303386688, -0.039920512586832047, -0.03883865475654602, -0.024017218500375748, -0.0015382650308310986, -0.0417596697807312, 0.00694191362708807, 0.08243747800588608, -0.0011201724410057068, -0.01085462886840105, 0.02448602207005024, 0.04388732090592384, -0.01965373009443283, 0.023151732981204987, -0.028615109622478485, 0.010412870906293392, -0.014037090353667736, -0.004099786281585693, -0.014406724832952023, 0.002238091081380844, 0.04377913475036621, -0.019058708101511, 0.025225291028618813, -0.04500523954629898, 0.052433986216783524, -0.018806274980306625, -0.012901141308248043, -0.005323636345565319, 0.03231145441532135, -0.025225291028618813, 0.036963436752557755, 0.03624219819903374, -0.02028481289744377, -0.04136298596858978, 0.03692737594246864, 0.008717961609363556, 0.021132268011569977, 0.027515221387147903, 0.011819284409284592, 0.008754023350775242, -0.042769402265548706, 0.008645838126540184, -0.001955230487510562, 0.01249544508755207, 0.0031283688731491566, -0.007144761737436056, -0.04489705339074135, 0.0013557017082348466, 0.05286673083901405, 0.01728266105055809, 0.03344740346074104, 0.00657678721472621, -0.023800846189260483, -0.03195083513855934, -0.024540115147829056, 0.013973982073366642, -0.06285587698221207, 0.019906163215637207, -0.009727695025503635, -0.01618277281522751, 0.035340651869773865, 0.021024081856012344, 0.003655774053186178, 0.009763756766915321, 0.0047060768119990826, 0.0467362105846405, 0.004537036642432213, -0.047601692378520966, -0.012008609250187874, -0.03160824626684189, -0.023404166102409363, -0.04327426850795746, -0.014091183431446552, -0.017895713448524475, 0.0015979924937710166, 0.05503044277429581, -0.0034889879170805216, 0.004782707896083593, -0.026361241936683655, -0.020392999053001404, -0.006283784285187721, 0.041543297469615936, -0.008285218849778175, -0.01803094521164894, 0.007041084114462137, 0.004228256642818451, 0.030905039981007576, -0.00889827124774456, -0.056545041501522064, 0.05019814893603325, 0.008037293329834938, 0.04900810867547989, -0.03963201493024826, 0.0008029405144043267, -0.04954903572797775, 0.016777794808149338, 0.035899609327316284, 0.012756893411278725, -0.035737331956624985, 0.022989453747868538, 0.032455701380968094, -0.039055027067661285, 0.023602506145834923, -0.017057273536920547, 0.0008485813159495592, -0.009980128146708012, -0.023782815784215927, 0.045113421976566315, -0.0013038626639172435, -0.03764861449599266, -0.03157218545675278, 0.013117512688040733, 0.011350479908287525, 0.016840903088450432, 0.010376809164881706, 0.011107061989605427, -0.0036264737136662006, -0.050450582057237625, -0.017228567972779274, 0.059033311903476715, 0.015650860965251923, -0.016561422497034073, 0.031157473102211952, 0.0366208478808403, -0.03393423929810524, 0.06620962917804718, -0.02107817493379116, -0.027298850938677788, -0.004602398723363876, -0.02416146546602249, 0.0115127582103014, -0.015677906572818756, -0.03797316923737526, 0.04165148362517357, 0.02939043939113617, -0.012973264791071415, 0.013342899270355701, -0.023043546825647354, -0.031139440834522247, -0.0010018444154411554 ]
Modeling time-evolving preferences of users with their sequential item interactions, has attracted increasing attention in many online applications. Hence, sequential recommender systems have been developed to learn the dynamic user interests from the historical interactions for suggesting items. However, the interaction pattern encoding functions in most existing sequential recommender systems have focused on single type of user-item interactions. In many real-life online platforms, user-item interactive behaviors are often multi-typed (e.g., click, add-to-favorite, purchase) with complex cross-type behavior inter-dependencies. Learning from informative representations of users and items based on their multi-typed interaction data, is of great importance to accurately characterize the time-evolving user preference. In this work, we tackle the dynamic user-item relation learning with the awareness of multi-behavior interactive patterns. Towards this end, we propose a new Temporal Graph Transformer (TGT) recommendation framework to jointly capture dynamic short-term and long-range user-item interactive patterns, by exploring the evolving correlations across different types of behaviors. The new TGT method endows the sequential recommendation architecture to distill dedicated knowledge for type-specific behavior relational context and the implicit behavior dependencies. Experiments on the real-world datasets indicate that our method TGT consistently outperforms various state-of-the-art recommendation methods. Our model implementation codes are available at https://github.com/akaxlh/TGT.
[ -0.0020748113747686148, -0.011305523104965687, -0.024402020499110222, -0.03482804819941521, 0.008051387965679169, -0.02000454068183899, -0.03182176873087883, 0.002498568734154105, -0.03617127984762192, 0.018549373373389244, 0.018309511244297028, -0.008315236307680607, -0.0007685596938244998, -0.0327332466840744, -0.02839973010122776, 0.019332924857735634, 0.024370038881897926, -0.007103930227458477, -0.042887430638074875, -0.009402613155543804, 0.008802956901490688, -0.0032041643280535936, -0.007959440350532532, 0.0320136584341526, 0.04240770637989044, 0.021475696936249733, 0.0009654469322413206, -0.007947446778416634, -0.05900619551539421, 0.02932719886302948, -0.03095826506614685, 0.015399178490042686, 0.05599991977214813, -0.013696153648197651, -0.05587199330329895, -0.019316934049129486, 0.07963437587022781, 0.04941169172525406, -0.014647608622908592, 0.010154183022677898, -0.002506564138457179, 0.017270106822252274, -0.03367670625448227, -0.04029691591858864, -0.0015551091637462378, 0.011337504722177982, 0.011897183954715729, -0.008051387965679169, -0.012632763013243675, -0.009266691282391548, 0.011705294251441956, 0.02497769147157669, -0.03241343051195145, 0.0484202615916729, 0.013704149052500725, 0.024114185944199562, 0.03553164377808571, 0.0012632763246074319, 0.04432660713791847, 0.07080743461847305, -0.038186125457286835, 0.03524380922317505, -0.05884628742933273, -0.016190724447369576, 0.05260986089706421, -0.06095707789063454, 0.04144825413823128, -0.008435167372226715, 0.010777825489640236, -0.027951987460255623, -0.09025229513645172, -0.014071938581764698, 0.03191771358251572, -0.05999762937426567, 0.023826351389288902, 0.008818947710096836, 0.06511469930410385, 0.014679590240120888, 0.007267836481332779, -0.029599042609333992, -0.03169384226202965, 0.08641449362039566, -0.016318650916218758, 0.04563785344362259, 0.011185592040419579, -0.039401426911354065, 0.0067721204832196236, -0.03936944529414177, 0.00857908558100462, 0.00612049363553524, -0.05497650429606438, 0.009338649921119213, -0.025457415729761124, -0.05097879469394684, -0.04918782040476799, -0.01957278698682785, 0.01714218035340309, 0.00522900465875864, -0.0968405231833458, 0.048516206443309784, 0.008667035028338432, -0.006456301547586918, -0.014455718919634819, -0.017398033291101456, 0.056191809475421906, -0.0334528349339962, -0.011417458765208721, 0.07694792002439499, -0.03383661434054375, 0.058622416108846664, -0.013760116882622242, -0.0015800948021933436, -0.00900284294039011, 0.01423984207212925, -0.06319579482078552, 0.030206695199012756, -0.05568010360002518, -0.07003987580537796, 0.028015950694680214, -0.0519702285528183, -0.01821356639266014, 0.03174181655049324, -0.015383187681436539, -0.030558492988348007, -0.023170726373791695, 0.040680695325136185, -0.009346645325422287, -0.0001286762853851542, 0.03751450777053833, 0.0064842854626476765, -0.04384688287973404, 0.04084060341119766, -0.00011306023225188255, -0.05379318445920944, 0.03374066948890686, -0.016598490998148918, 0.028591619804501534, -0.0038737808354198933, -0.025937141850590706, -0.006004560273140669, -0.026944564655423164, -0.0051210662350058556, -0.021475696936249733, -0.03172582387924194, -0.020404310896992683, 0.012696726247668266, -0.006828088313341141, 0.039753224700689316, -0.013032534159719944, 0.044742368161678314, -0.015295237302780151, -0.023506533354520798, -0.013864058069884777, 0.01224098727107048, -0.01822955720126629, 0.021731549873948097, -0.026224976405501366, -0.019956568256020546, 0.010609921999275684, -0.03751450777053833, 0.044806331396102905, 0.009834365919232368, -0.0003665400145109743, 0.04525407403707504, 0.014959430322051048, -0.001216303207911551, 0.09588107466697693, -0.010945729911327362, -0.0327332466840744, 0.04144825413823128, -0.015703003853559494, 0.03260532021522522, 0.01872527226805687, 0.05606388300657272, -0.014711571857333183, 0.0070719486102461815, 0.06786511838436127, -0.023474551737308502, -0.012656749226152897, 0.0021067929919809103, -0.013192442245781422, 0.03089430183172226, -0.015463141724467278, 0.055776048451662064, 0.0648268610239029, 0.031278081238269806, 0.0483882799744606, 0.006720150355249643, 0.03183776140213013, 0.011217573657631874, 0.015351206064224243, 0.04112843796610832, 0.07381371408700943, -0.04774864763021469, -0.004037687089294195, 0.04522209241986275, -0.04762071743607521, -0.037258654832839966, -0.005288970191031694, -0.0035139869432896376, -0.04112843796610832, -0.024609901010990143, 0.025953132659196854, -0.04646937921643257, 0.05443281680345535, -0.00007108427962521091, 0.016470564529299736, -0.01701425388455391, -0.03457219526171684, -0.04496623948216438, 0.036395151168107986, -0.016190724447369576, -0.0761803612112999, -0.036842893809080124, 0.02975895255804062, -0.025521378964185715, 0.028367748484015465, 0.028367748484015465, 0.04419868066906929, -0.007155900355428457, 0.01608678512275219, 0.025857187807559967, 0.06022150069475174, -0.0011713289422914386, 0.01555109117180109, -0.026320921257138252, -0.027664151042699814, -0.0038258081767708063, -0.021811503916978836, -0.023954277858138084, 0.042887430638074875, -0.0005441882531158626, -0.021603623405098915, -0.016902316361665726, -0.01579894870519638, 0.016838353127241135, 0.020596200600266457, -0.0484202615916729, 0.01516731083393097, 0.006004560273140669, 0.004825235810130835, 0.018485410138964653, -0.005884628742933273, -0.015191297046840191, 0.04787657409906387, 0.04087258502840996, 0.016214711591601372, 0.05894223228096962, 0.012856634333729744, 0.024817783385515213, -0.015703003853559494, -0.03908161073923111, 0.008411181159317493, 0.009530540555715561, -0.007495705969631672, 0.05635171756148338, 0.03706676512956619, -0.027168435975909233, -0.0055128419771790504, -0.08705412596464157, 0.03613929823040962, 0.03431634232401848, -0.019620759412646294, 0.08762980252504349, 0.034412287175655365, 0.014471709728240967, 0.09652070701122284, -0.045158129185438156, 0.010801811702549458, -0.002320670522749424, 0.03780234232544899, -0.05615982785820961, -0.014391755685210228, -0.05027519911527634, -0.04256761446595192, -0.00910678319633007, 0.009874342940747738, -0.028351757675409317, 0.05772693082690239, -0.004657331854104996, -0.020404310896992683, 0.026432856917381287, -0.0016780387377366424, 0.004105648025870323, 0.007263838779181242, -0.014543668366968632, -0.02248311974108219, -0.014071938581764698, -0.051426537334918976, -0.025969123467803, -0.010897756554186344, 0.003300109412521124, -0.00635236082598567, -0.010617917403578758, 0.10617917031049728, 0.036619022488594055, 0.01679038070142269, 0.015279246494174004, 0.0704876184463501, -0.0576309859752655, 0.014399751089513302, 0.01124955527484417, 0.027888024225831032, -0.01587890274822712, -0.03252536803483963, 0.014319796115159988, 0.05721522122621536, 0.05324949324131012, 0.006264411378651857, -0.08551900833845139, 0.0040916558355093, -0.0013092500157654285, -0.000730581465177238, 0.04148023575544357, -0.018565364181995392, 0.01213704701513052, 0.02576124295592308, 0.002462589181959629, -0.0031062206253409386, -0.05993366613984108, -0.029503097757697105, 0.00045448963646776974, -0.061948511749506, -0.0019189007580280304, -0.029343189671635628, 0.07247048616409302, 0.021811503916978836, -0.024801792576909065, 0.02449796535074711, 0.02712046355009079, -0.02540944330394268, -0.018165593966841698, -0.019956568256020546, 0.012840643525123596, -0.0128086619079113, 0.026608755812048912, 0.008978855796158314, 0.009066806174814701, -0.04976349323987961, -0.04029691591858864, -0.021475696936249733, 0.011369486339390278, 0.022898882627487183, -0.004905189853161573, -0.01074584387242794, -0.022866901010274887, -0.00904281996190548, 0.047364864498376846, 0.02406621351838112, 0.03396454080939293, 0.0008575087413191795, -0.03610731661319733, 0.023938287049531937, 0.03124609962105751, 0.08225687593221664, -0.024673864245414734, 0.014871480874717236, -0.0036299205385148525, 0.013416314497590065, 0.027136454358696938, 0.027216408401727676, -0.04467840492725372, -0.038186125457286835, 0.04471038654446602, -0.06645792722702026, -0.008151330053806305, -0.07151103019714355, -0.022547082975506783, 0.005536828190088272, -0.016262684017419815, -0.03473210334777832, 0.005248993169516325, 0.022786945104599, 0.014391755685210228, -0.002918328158557415, 0.04816440865397453, 0.01609477959573269, -0.015599063597619534, 0.0043135290034115314, 0.05187428370118141, -0.029487106949090958, -0.030222686007618904, -0.01615074835717678, -0.0045334030874073505, -0.015766967087984085, 0.0491238571703434, 0.02497769147157669, -0.029375171288847923, -0.0024825776927173138, -0.0043055335991084576, 0.0533774197101593, 0.0034400292206555605, -0.02720041759312153, -0.030990246683359146, 0.030510520562529564, -0.050211235880851746, 0.046309471130371094, 0.03297311067581177, 0.007235854864120483, -0.0167264174669981, -0.02911931835114956, -0.019412878900766373, -0.00380781851708889, 0.036970820277929306, -0.034476250410079956, -0.04080862179398537, -0.01622270606458187, 0.00019788663485087454, 0.0854550451040268, -0.0067721204832196236, 0.01217702403664589, -0.01527125108987093, -0.06527460366487503, -0.041672125458717346, 0.005624777637422085, 0.02042030170559883, -0.03895368427038193, 0.016350632533431053, 0.03190172463655472, -0.02748825214803219, 0.027072491124272346, 0.03460417687892914, 0.02683262899518013, -0.019045090302824974, -0.013280391693115234, 0.04742882773280144, 0.00179697060957551, -0.005452875979244709, -0.03709874674677849, -0.0711912140250206, 0.055903974920511246, 0.010529967956244946, 0.05609586462378502, -0.06220436468720436, -0.012448868714272976, -0.00542489206418395, 0.03244541212916374, 0.018101630732417107, -0.008103357627987862, -0.023602478206157684, -0.04378291964530945, -0.027088481932878494, -0.04087258502840996, 0.026640737429261208, 0.023602478206157684, 0.018533382564783096, -0.010633908212184906, -0.050499070435762405, -0.007531685288995504, -0.033133018761873245, -0.03802621737122536, 0.02540944330394268, 0.002182749565690756, -0.030926283448934555, -0.0009129769750870764, -0.03674694895744324, 0.03738658130168915, -0.014023966155946255, 0.05935799703001976, -0.03139001876115799, -0.030350612476468086, 0.0512666292488575, 0.018261538818478584, -0.02056421898305416, -0.01695028878748417, 0.024162158370018005, -0.023794367909431458, -0.008059383369982243, -0.016246693208813667, -0.016070794314146042, 0.011873197741806507, -0.016998261213302612, 0.015143324621021748, 0.019892603158950806, 0.018565364181995392, 0.003420040709897876, -0.009098787792026997, -0.07176688313484192, 0.0006736140931025147, 0.012736703269183636, 0.0147675396874547, 0.02056421898305416, 0.08014608919620514, -0.004301535896956921, 0.0065482486970722675, -0.006104502826929092, 0.021683577448129654, 0.00019751185027416795, -0.014351778663694859, 0.016102775931358337, -0.04717297479510307, 0.022323211655020714, -0.024034231901168823, 0.051778338849544525, 0.027504242956638336, -0.03645911440253258, -0.010673885233700275, -0.03361274302005768, 0.057694949209690094, -0.01893315277993679, -0.014599636197090149, -0.0019308938644826412, 0.042887430638074875, 0.00803939439356327, 0.03693883866071701, 0.0006761126569472253, -0.010913747362792492, 0.021747540682554245, -0.024817783385515213, -0.0013342356542125344, -0.040168989449739456, 0.010410035960376263, -0.00006564988871105015, -0.01651853695511818, -0.015918880701065063, 0.0029243247117847204, -0.013112488202750683, -0.03428436070680618, 0.023938287049531937, 0.017318079248070717, 0.002174754161387682, 0.0006766123697161674, -0.023074781522154808, 0.032637301832437515, -0.07131914049386978, 0.0035519651137292385, 0.0006671178271062672, 0.02184348553419113, 0.05472065135836601, 0.006664182059466839, -0.041320327669382095, -0.02078809030354023, -0.03161389008164406, -0.008938878774642944, 0.0455419085919857, -0.041544198989868164, 0.02371441386640072, 0.0062524182721972466, 0.00783151388168335, -0.03831405192613602, -0.04148023575544357, 0.006316381506621838, -0.03438030555844307, 0.03495597466826439, -0.002552537713199854, 0.003557961666956544, 0.00882694311439991, -0.044518496841192245, -0.03110218234360218, 0.009730425663292408, -0.0018629328114911914, 0.020900027826428413, 0.025505388155579567, -0.022515101358294487, -0.027392307296395302, 0.0024426006712019444, -0.03537173569202423, -0.014615627005696297, -0.00727982958778739, -0.01978066749870777, 0.021971413865685463, 0.011025683954358101, -0.0033500809222459793, -0.014487700536847115, 0.018341492861509323, 0.004917182959616184, 0.020116476342082024, 0.045669835060834885, 0.061884548515081406, 0.013248410075902939, -0.027008527889847755, -0.018117621541023254, -0.013088501989841461, 0.012448868714272976, -0.007399760652333498, 0.010410035960376263, 0.00008776222239248455, -0.050211235880851746, 0.012105065397918224, 0.003769840346649289, -0.008443162776529789, -0.029774943366646767, 0.048356298357248306, 0.03738658130168915, -0.02134777046740055, -0.020836062729358673, -0.049155838787555695, -0.04371895268559456, -0.015399178490042686, -0.01930094324052334, 0.022163303568959236, 0.0633237212896347, 0.01730208843946457, -0.0008590078796260059, -0.033996522426605225, -0.014655604027211666, -0.02120385318994522, -0.018101630732417107, 0.07195878028869629, -0.06671378016471863, 0.04953961819410324, 0.03230149671435356, 0.037482526153326035, 0.03501993790268898, -0.051554467529058456, -0.0377383790910244, 0.07074347138404846, -0.02611304074525833, 0.013240414671599865, 0.03386859595775604, -0.011033679358661175, -0.008691021241247654, 0.05817467346787453, -0.03681091219186783, 0.062396254390478134, -0.01224098727107048, 0.06028546392917633, 0.03869783133268356, -0.04234374314546585, -0.08775772899389267, 0.05254589766263962, -0.030990246683359146, 0.10713862627744675, 0.013408319093286991, -0.021187862381339073, -0.0003330592007841915, 0.04685315862298012, -0.02449796535074711, -0.02070813626050949, -0.01049798633903265, -0.0008934881188906729, 0.02150767855346203, -0.0327332466840744, -0.05248193442821503, -0.008874915540218353, -0.005081089213490486, 0.02177952229976654, 0.03162987902760506, 0.02405022270977497, 0.06322778016328812, -0.041320327669382095, -0.024162158370018005, 0.0012732705799862742, 0.05414498224854469, -0.0129845617339015, 0.01835748367011547, -0.013560231775045395, -0.01779780350625515, 0.02513759955763817, 0.00893088337033987, 0.014695581048727036, 0.034348323941230774, 0.015031388960778713, 0.04691712185740471, -0.02449796535074711, -0.024929719045758247, -0.004121638834476471, -0.023074781522154808, 0.03126209229230881, -0.0034180418588221073, -0.003064244519919157, 0.010729853063821793, 0.05376120284199715, -0.03658704087138176, 0.015599063597619534, -0.005700733978301287, -0.013800093904137611, -0.01608678512275219, -0.008691021241247654, 0.03380463272333145, 0.008371204137802124, -0.014343783259391785, -0.0704876184463501, 0.02056421898305416, 0.028671573847532272, -0.03329292684793472, 0.027935996651649475, 0.02590516023337841, 0.0030662433709949255, -0.04122438281774521, -0.01594286598265171, -0.029007382690906525, -0.05779089406132698, -0.011305523104965687, 0.008802956901490688, -0.023730404675006866, 0.0028703557327389717, -0.026576774194836617, -0.03553164377808571, 0.0448383130133152, -0.008547103963792324, -0.013728135265409946, 0.017925729975104332, 0.0040716673247516155, 0.0018489407375454903, 0.02000454068183899, -0.011969143524765968, -0.01053796336054802, 0.011481422930955887, 0.012520827353000641, 0.010258123278617859, 0.0022147311829030514, 0.010705866850912571, 0.017829785123467445, -0.0004582374822348356, 0.029806924983859062, 0.006732143461704254, -0.022451138123869896, -0.07003987580537796, -0.03383661434054375, 0.0005701733753085136, -0.022163303568959236, -0.009922315366566181, 0.004413471557199955, -0.00864304881542921, 0.02142772451043129, 0.008071376010775566, 0.016566509380936623, -0.029599042609333992, 0.018677299842238426, 0.01483949925750494, 0.012352922931313515, 0.07035969197750092, -0.03872981294989586, -0.009722430258989334, 0.01405594777315855, 0.028079913929104805, 0.03172582387924194, -0.007359783630818129, -0.004545396193861961, 0.041544198989868164, -0.038761794567108154, -0.00700798537582159, -0.013696153648197651, -0.0029203270096331835, 0.027008527889847755, -0.03943340852856636, 0.02518557198345661, -0.03578749671578407, -0.020468274131417274, 0.02086804434657097, -0.0047652702778577805, -0.03188573196530342, -0.02955107018351555, 0.02641686610877514, 0.0398491695523262, 0.008547103963792324, 0.040552768856287, -0.0024465983733534813, -0.04605361819267273, 0.032845184206962585, -0.008195305243134499, 0.043175265192985535, 0.0008904898422770202, -0.06677774339914322, 0.009426599368453026, 0.013512259349226952, -0.00836320873349905, 0.032781220972537994, -0.048004500567913055, 0.02233920246362686, 0.010050242766737938, -0.05948592349886894, 0.016254687681794167, 0.02056421898305416, 0.02406621351838112, -0.05759900435805321, 0.02911931835114956, -0.004063671920448542, -0.03706676512956619, 0.0055048465728759766, 0.03297311067581177, 0.034987956285476685, -0.0006676175398752093, -0.0033420855179429054, 0.0025605331175029278, 0.0370347835123539, 0.0019538807682693005, -0.019029099494218826, 0.003985716495662928, -0.010857779532670975, 0.016838353127241135, -0.002104794140905142, 0.025809215381741524, -0.019524814561009407, 0.012792671099305153, -0.007555671501904726, -0.02548939734697342, 0.017461996525526047, 0.031198127195239067, -0.004229576792567968, -0.02548939734697342, 0.020404310896992683, 0.039177555590867996, 0.018917161971330643, 0.02726438082754612, 0.0009199729538522661, -0.01377610769122839, 0.00021437718532979488, -0.017701858654618263, 0.013288387097418308, 0.01185720693320036, 0.009850356727838516, 0.030222686007618904, -0.008275259286165237, 0.008491135202348232, -0.04662928730249405, -0.010921742767095566, 0.016918307170271873, 0.01288062147796154, -0.004845224320888519, 0.007027973886579275, -0.0011693300912156701, -0.022371184080839157, 0.02569727785885334, 0.00999427493661642, -0.016126761212944984, -0.006088512018322945, -0.040744658559560776, -0.029359180480241776, -0.00025860185269266367, -0.040968529880046844, -0.015351206064224243, -0.021379752084612846, 0.006292395293712616, -0.010673885233700275, 0.008691021241247654, 0.013096497394144535, 0.009138764813542366, -0.020180439576506615, 0.016694435849785805, 0.037834323942661285, -0.040968529880046844, -0.03908161073923111, -0.04733288288116455, 0.041608162224292755, -0.01915702596306801, -0.026528801769018173, 0.006472292356193066, 0.04455047845840454, -0.005600791424512863, 0.024370038881897926, -0.018469419330358505, -0.009154755622148514, -0.02548939734697342, 0.01880522631108761, -0.02513759955763817, 0.0074517312459647655, 0.029423143714666367, 0.022738972678780556, 0.012328936718404293, 0.03479606658220291, 0.06431515514850616, -0.026592765003442764, 0.00038802772178314626, 0.027376316487789154, -0.0017959711840376258, 0.047588735818862915, 0.03450823202729225, -0.02910332754254341, 0.06601018458604813, 0.027888024225831032, -0.027392307296395302, -0.015063370577991009, 0.026464838534593582, 0.02598511427640915, 0.019045090302824974, -0.058686379343271255, -0.009170746430754662, -0.015367196872830391, -0.010905751958489418, -0.009442590177059174, -0.03815414384007454, 0.06856872141361237, 0.006104502826929092, 0.04541398212313652, 0.03924151882529259, -0.0348920114338398, 0.024737827479839325, -0.039465390145778656, 0.05312156677246094, -0.016918307170271873, 0.018181584775447845, 0.0002685961371753365, 0.02512160874903202, -0.011921171098947525, -0.039881154894828796, 0.0131684560328722, -0.020772099494934082, -0.024673864245414734, -0.012217001058161259, 0.01779780350625515, -0.0462774895131588, -0.05568010360002518, -0.00001820831857912708, -0.0031961689237505198, 0.012568799778819084, 0.0056447661481797695, -0.005264983978122473, 0.027152445167303085, 0.00747171975672245, -0.020548228174448013, 0.0288314837962389, -0.033420853316783905, 0.06453903019428253, 0.000545687391422689, 0.030414575710892677, -0.012057092972099781, 0.024753818288445473, -0.004023694898933172, 0.020116476342082024, 0.011849211528897285, 0.04969953000545502, -0.05273778736591339, -0.008595076389610767, -0.014215855859220028, -0.013520254753530025, -0.010985706932842731, 0.01714218035340309, 0.01695028878748417, 0.0024306075647473335, 0.0348920114338398, 0.02697654627263546, 0.043463099747896194, -0.028527656570076942, 0.01650254614651203, -0.0038997658994048834, 0.03537173569202423, 0.006156472954899073, 0.028447702527046204, -0.041320327669382095, -0.003785831155255437, -0.030846329405903816, -0.006060528103262186, 0.015255260281264782, 0.006136484444141388, -0.03546768054366112, 0.01092973817139864, -0.0005951590719632804, 0.0024825776927173138, -0.005356931127607822, 0.017477987334132195, -0.02796797826886177, 0.01872527226805687, 0.0028703557327389717, -0.04640541598200798, 0.00882694311439991, 0.008095362223684788, 0.0061684660613536835, -0.008107355795800686, -0.026081059128046036, 0.0017739837057888508, -0.05257787927985191, -0.03642713278532028, -0.03607533499598503, -0.004645338747650385, -0.019940577447414398, -0.000662120699416846, -0.03126209229230881, 0.04205590859055519, -0.006180459167808294, 0.04976349323987961, -0.01564703695476055, -0.003605934325605631, -0.0860946774482727, 0.019828639924526215, -0.011705294251441956, 0.025601333007216454, -0.02768014185130596, 0.008043392561376095, -0.022051367908716202, -0.023106763139367104, 0.02297883667051792, -0.013544240966439247, -0.010569944977760315, 0.04250365123152733, -0.030926283448934555, -0.017461996525526047, -0.018197575584053993, 0.008874915540218353, 0.013608204200863838, 0.021971413865685463, -0.011401467956602573, 0.019332924857735634, 0.04314328357577324, -0.027072491124272346, 0.02334662526845932, 0.007883483543992043, -0.03466814011335373, -0.01288062147796154, -0.016838353127241135, 0.0026165011804550886, 0.023746395483613014, -0.022227266803383827, -0.046437397599220276, 0.0167264174669981, -0.025393452495336533, -0.014743553474545479, -0.007171891629695892, 0.011497413739562035, -0.04899593070149422, -0.015199292451143265, -0.01508735679090023, 0.06844079494476318, -0.005081089213490486, 0.010234137065708637, 0.05452876165509224, 0.0043774922378361225, -0.027376316487789154, 0.03553164377808571, 0.0131684560328722, -0.006904044654220343, -0.049571599811315536, -0.023858333006501198, -0.016182729974389076, -0.015615054406225681, 0.010913747362792492, 0.0295350793749094, 0.049091875553131104, -0.019700713455677032, 0.026528801769018173, -0.009554526768624783, 0.05248193442821503, -0.037834323942661285 ]
In this paper, we introduce the first learning-based planner to drive a car in dense, urban traffic using Inverse Reinforcement Learning (IRL). Our planner, DriveIRL, generates a diverse set of trajectory proposals, filters these trajectories with a lightweight and interpretable safety filter, and then uses a learned model to score each remaining trajectory. The best trajectory is then tracked by the low-level controller of our self-driving vehicle. We train our trajectory scoring model on a 500+ hour real-world dataset of expert driving demonstrations in Las Vegas within the maximum entropy IRL framework. DriveIRL's benefits include: a simple design due to only learning the trajectory scoring function, relatively interpretable features, and strong real-world performance. We validated DriveIRL on the Las Vegas Strip and demonstrated fully autonomous driving in heavy traffic, including scenarios involving cut-ins, abrupt braking by the lead vehicle, and hotel pickup/dropoff zones. Our dataset will be made public to help further research in this area.
[ 0.014246417209506035, -0.011835484765470028, -0.02535131573677063, -0.06882115453481674, -0.05110445246100426, 0.034008752554655075, -0.008447394706308842, 0.03552471846342087, -0.09059260040521622, 0.03302246332168579, -0.016027219593524933, 0.021022597327828407, 0.023342205211520195, -0.050593044608831406, 0.0029109264723956585, -0.028529362753033638, 0.003652927465736866, -0.00033846654696390033, -0.03651100769639015, -0.044127363711595535, 0.024237172678112984, -0.004609537776559591, -0.06242853030562401, 0.04157031327486038, 0.02151574194431305, -0.01675780490040779, 0.022063681855797768, 0.01747012510895729, -0.05662037432193756, 0.017762359231710434, 0.03055673837661743, 0.0322188176214695, -0.012209909968078136, -0.006735085044056177, -0.02991747483611107, 0.01373500656336546, 0.022228064015507698, 0.0227394737303257, -0.018958693370223045, 0.043433304876089096, 0.022593356668949127, -0.021954093128442764, 0.0021791995968669653, -0.013305787928402424, 0.023323941975831985, -0.03446536883711815, -0.05888519063591957, -0.0030182311311364174, -0.03464801609516144, -0.00738804554566741, 0.0020159592386335135, -0.05187156796455383, 0.04244701564311981, -0.06206323578953743, -0.007433707360178232, 0.02832845225930214, 0.013972447253763676, 0.02357964590191841, 0.017369668930768967, 0.012346894480288029, 0.02168012410402298, -0.03340601921081543, -0.0850401520729065, -0.019689278677105904, -0.018922163173556328, -0.02971656434237957, 0.07130514085292816, 0.012155115604400635, 0.023159559816122055, 0.012712187133729458, 0.0004666043969336897, -0.004146072547882795, -0.07364301383495331, -0.01311400905251503, 0.0014440478989854455, -0.02551569789648056, -0.024949494749307632, 0.0070866793394088745, 0.01624639518558979, 0.02257509157061577, -0.008945105597376823, -0.024730319157242775, -0.00803187396377325, -0.009881168603897095, 0.027543071657419205, -0.009990756399929523, 0.05088527873158455, -0.07956075668334961, 0.03325990214943886, -0.04215478152036667, -0.021406155079603195, -0.0066939895041286945, -0.024565936997532845, -0.024346761405467987, -0.03970732167363167, 0.028766803443431854, 0.03824615105986595, 0.017177890986204147, -0.0583372488617897, -0.04178949072957039, 0.011424530297517776, 0.0013333185343071818, 0.008616342209279537, -0.02357964590191841, 0.03373478353023529, -0.038574911653995514, -0.03755209222435951, 0.05625507980585098, 0.016483834013342857, 0.06925950199365616, -0.006862937472760677, -0.017360538244247437, 0.02606363594532013, 0.003589001251384616, -0.03649274632334709, -0.016337716951966286, -0.03656580299139023, -0.0668850988149643, 0.06586228311061859, -0.03112294152379036, 0.027305632829666138, 0.03357040137052536, 0.015351427718997002, -0.03194484859704971, -0.031141206622123718, 0.017534051090478897, -0.0037762136198580265, -0.018922163173556328, 0.019707543775439262, 0.001891531515866518, -0.008789856918156147, -0.009543272666633129, 0.002657504752278328, 0.012118586339056492, 0.030136650428175926, 0.001457746373489499, 0.016520364210009575, -0.02728736773133278, 0.05450167506933212, 0.011735029518604279, -0.005799022037535906, -0.019999777898192406, -0.0015445033786818385, 0.028036218136548996, -0.01990845426917076, 0.047122761607170105, -0.04891269654035568, 0.024182379245758057, -0.03077591396868229, 0.007945116609334946, -0.024036262184381485, 0.08832778036594391, 0.006324130576103926, 0.03780779987573624, 0.05194462835788727, -0.0023150427732616663, -0.04401777312159538, 0.006027330178767443, -0.01004554983228445, -0.08314062654972076, 0.04073014110326767, -0.007935984991490841, -0.0499720461666584, 0.01903175190091133, 0.05190809816122055, 0.051469746977090836, 0.05256562680006027, -0.004785334691405296, -0.05581672862172127, 0.033460814505815506, -0.04825517162680626, -0.0073332516476511955, 0.023013442754745483, -0.017945006489753723, 0.03919591009616852, 0.009515875950455666, 0.04164337366819382, 0.00882638618350029, -0.028620686382055283, -0.03503157198429108, -0.03316858038306236, -0.0016164203407242894, 0.0020467808935791254, 0.029406065121293068, 0.029990533366799355, 0.053953737020492554, 0.06480292975902557, -0.011753293685615063, 0.056583844125270844, -0.023999731987714767, 0.019689278677105904, 0.054428618401288986, -0.0061003887094557285, 0.021534007042646408, -0.008214520290493965, -0.016913054510951042, -0.023835351690649986, -0.0038926508277654648, -0.0013755554100498557, 0.004353832919150591, -0.026355871930718422, -0.03461148589849472, -0.016648216173052788, 0.033826109021902084, 0.04040137678384781, 0.01872125267982483, 0.014995266683399677, 0.009762448258697987, 0.0009560395847074687, -0.04668441042304039, -0.024894699454307556, -0.028748538345098495, -0.08394426852464676, -0.012602599337697029, -0.06246505677700043, -0.03369825333356857, -0.02308650128543377, -0.016894789412617683, 0.006127785891294479, -0.060419417917728424, 0.00446342071518302, 0.031396910548210144, 0.02029201202094555, -0.016776068136096, -0.057789310812950134, -0.018776046112179756, 0.005817286670207977, 0.0303923562169075, -0.02745174989104271, -0.012465614825487137, -0.03583521768450737, -0.038209620863199234, -0.00037299812538549304, 0.017890211194753647, 0.021278301253914833, -0.017570581287145615, 0.016675613820552826, -0.0007477085455320776, 0.05157933384180069, -0.04460224509239197, -0.0033652593847364187, -0.025899255648255348, -0.04865699261426926, 0.0008025025017559528, 0.07707677036523819, 0.010639150626957417, -0.0014908509328961372, 0.029826151207089424, 0.04847434535622597, -0.02743348479270935, -0.05782584100961685, 0.011999865993857384, -0.013652816414833069, -0.030666325241327286, -0.030374091118574142, 0.07532336562871933, 0.05647425726056099, -0.04843781888484955, 0.026008842512965202, -0.02814580500125885, 0.06122306361794472, 0.02531478740274906, 0.04613647237420082, 0.07364301383495331, -0.004995378199964762, -0.00037870582309551537, -0.005031907465308905, 0.050921808928251266, -0.0018230390269309282, 0.002222578041255474, -0.025296522304415703, -0.08350592106580734, -0.01820984296500683, 0.033972226083278656, 0.0031438006553798914, -0.06352441012859344, 0.013241861946880817, 0.0023789689876139164, -0.011241883970797062, 0.007054715882986784, -0.009561537764966488, -0.0244746133685112, 0.030173180624842644, -0.0018161898478865623, -0.08978895843029022, -0.06593533605337143, 0.004776202607899904, -0.01171676442027092, 0.0007551285671070218, 0.012383423745632172, -0.012465614825487137, -0.003196311416104436, -0.002289928961545229, 0.016328586265444756, 0.054611265659332275, 0.02326914668083191, -0.00038298661820590496, -0.05494002625346184, -0.03280328959226608, 0.058446839451789856, -0.030081856995821, 0.031908322125673294, 0.03265717253088951, -0.004817298147827387, 0.018620796501636505, 0.010438240133225918, -0.05051998421549797, -0.009027296677231789, -0.038684502243995667, -0.037698209285736084, -0.030593266710639, 0.03430098667740822, -0.012356027029454708, -0.04157031327486038, 0.03128732368350029, 0.020328540354967117, 0.07758817821741104, -0.037332918494939804, -0.017871947959065437, -0.003620964242145419, 0.058812130242586136, -0.04474836215376854, -0.03831920772790909, 0.019524896517395973, 0.003182613058015704, 0.03128732368350029, 0.004442872945219278, 0.015232707373797894, -0.006515908986330032, -0.01145192701369524, -0.010922253131866455, 0.008027307689189911, -0.08430956304073334, 0.015497544780373573, 0.019999777898192406, 0.013972447253763676, -0.06001759693026543, 0.026629840955138206, -0.003974841441959143, -0.06209976598620415, -0.001728291274048388, 0.006415453739464283, 0.01224643923342228, -0.03481239825487137, 0.0061962781473994255, -0.05256562680006027, 0.013433640822768211, 0.00029737112345173955, -0.027524808421730995, -0.015798911452293396, 0.001049645827151835, 0.00023059104569256306, 0.016136806458234787, -0.035579513758420944, 0.05786237120628357, -0.0031460837926715612, -0.043250661343336105, -0.04244701564311981, -0.04756111279129982, 0.04960675537586212, 0.043433304876089096, -0.015862837433815002, -0.04332371801137924, 0.009027296677231789, -0.045552004128694534, 0.062282413244247437, -0.036967623978853226, 0.009123186580836773, 0.028949448838829994, 0.023013442754745483, -0.01867559179663658, 0.02536958083510399, 0.008529585786163807, -0.02480337768793106, 0.0006580976769328117, -0.02794489450752735, 0.004620952997356653, -0.04317760095000267, -0.0016814881237223744, 0.03271196410059929, 0.039780378341674805, -0.004922319669276476, -0.052529096603393555, -0.0008424563566222787, 0.008730496279895306, 0.08657437562942505, -0.020365070551633835, -0.028237128630280495, 0.009671125560998917, -0.0021426703315228224, 0.07360648363828659, -0.06578922271728516, -0.025935783982276917, -0.009671125560998917, 0.01362541876733303, 0.035725630819797516, 0.03864797204732895, -0.033552136272192, 0.022465502843260765, -0.0019029468530789018, 0.012675657868385315, 0.0687480941414833, 0.017223551869392395, -0.00820082239806652, -0.05501308664679527, 0.02252029813826084, -0.030867235735058784, -0.016894789412617683, 0.02272120863199234, 0.011013575829565525, -0.010620886459946632, -0.025789666920900345, -0.014913075603544712, -0.006630063056945801, 0.06483945995569229, -0.03795391693711281, 0.0018104821210727096, 0.01888563483953476, 0.011086634360253811, 0.0045958394184708595, -0.015150516293942928, 0.05431903153657913, -0.022666415199637413, 0.027908364310860634, -0.04051096364855766, 0.0919807106256485, 0.004684879444539547, 0.025132140144705772, -0.04032832011580467, -0.020200688391923904, 0.00019063714717049152, 0.006721386220306158, 0.022611619904637337, -0.04208172485232353, 0.03022797405719757, -0.003326446982100606, 0.0426296629011631, 0.042593132704496384, -0.03744250535964966, 0.023707497864961624, -0.03831920772790909, -0.05000857636332512, -0.03620050847530365, -0.014620841480791569, 0.003559321165084839, -0.002769375452771783, 0.008502188138663769, -0.006369791924953461, 0.005123230628669262, -0.011378868483006954, -0.09044647961854935, 0.06619104743003845, -0.05501308664679527, -0.06315911561250687, 0.03546992316842079, -0.025588756427168846, -0.0552687905728817, -0.014365136623382568, -0.005356104578822851, -0.026355871930718422, 0.04734193906188011, 0.02622801810503006, 0.01695871539413929, -0.026702899485826492, -0.007808132097125053, 0.002922341926023364, -0.043798599392175674, -0.019890189170837402, -0.006922297179698944, 0.003881235374137759, 0.0049497163854539394, -0.013826330192387104, 0.006803577300161123, 0.008018175140023232, -0.039597731083631516, 0.06279382109642029, -0.024894699454307556, -0.06315911561250687, -0.0031780467834323645, -0.06034636124968529, -0.00031791883520781994, 0.01546101551502943, 0.050410397350788116, -0.06871156394481659, 0.022465502843260765, 0.04127807915210724, 0.06224588304758072, -0.01328752376139164, -0.04409083351492882, 0.022264592349529266, -0.00764375040307641, -0.029132096096873283, -0.04215478152036667, 0.0034314687363803387, -0.050775691866874695, -0.05333273857831955, -0.01851120963692665, 0.0063743581995368, -0.005748794414103031, 0.01431947574019432, -0.014922208152711391, -0.03061153180897236, 0.0387575589120388, -0.03831920772790909, -0.015534074045717716, 0.023999731987714767, 0.027524808421730995, 0.02147921361029148, -0.00725562684237957, -0.059140894562006, 0.04178949072957039, 0.046246059238910675, 0.010191667824983597, -0.04924146085977554, 0.047962937504053116, -0.025771401822566986, 0.03285808116197586, -0.039049793034791946, 0.03232840821146965, 0.01109576690942049, 0.0027054492384195328, 0.028364980593323708, -0.008525019511580467, -0.010821796953678131, -0.021716652438044548, 0.061076946556568146, 0.009269303642213345, -0.047634173184633255, 0.040437906980514526, 0.03532380610704422, 0.01658429019153118, 0.040474437177181244, 0.0003721419780049473, -0.07641924172639847, 0.0037328351754695177, 0.0005710552795790136, 0.02374402806162834, 0.06407234817743301, 0.020712098106741905, 0.015954161062836647, -0.0288581270724535, 0.03674845024943352, -0.022666415199637413, 0.02620975486934185, 0.042410485446453094, -0.02935127168893814, -0.003986257128417492, -0.007922286167740822, -0.00918254628777504, 0.030374091118574142, 0.052163802087306976, 0.010009020566940308, -0.03267543390393257, 0.016748672351241112, -0.04208172485232353, -0.005552449729293585, 0.003963426221162081, -0.06224588304758072, -0.034355781972408295, -0.04164337366819382, 0.009935962036252022, -0.057606663554906845, 0.005593545269221067, -0.009155149571597576, -0.006456549279391766, -0.03598133474588394, -0.014273813925683498, 0.06480292975902557, -0.024401554837822914, 0.02973482944071293, -0.04109543189406395, -0.03185352683067322, -0.011022708378732204, -0.014821752905845642, 0.025734873488545418, -0.000030215131118893623, -0.021753182634711266, -0.053223151713609695, -0.016173336654901505, -0.011040972545742989, -0.007885756902396679, -0.005876646842807531, -0.0072282301262021065, 0.04109543189406395, -0.012840040028095245, 0.010967914015054703, -0.04876657947897911, -0.02113218419253826, 0.043104544281959534, 0.0010376597056165338, -0.040474437177181244, 0.046757470816373825, 0.04113196209073067, 0.03132385388016701, -0.026355871930718422, -0.01005468238145113, 0.020748628303408623, 0.014054638333618641, -0.010438240133225918, -0.07583477348089218, 0.009388023056089878, 0.031543027609586716, -0.008378902450203896, 0.046246059238910675, -0.006018197629600763, -0.012045527808368206, 0.0381365604698658, 0.00585838221013546, -0.0020239499863237143, -0.019817130640149117, -0.032437995076179504, 0.0345749594271183, 0.0016540911747142673, 0.0038652538787573576, 0.06575269252061844, 0.012575202621519566, 0.02463899552822113, 0.0014109432231634855, 0.002531935228034854, -0.030100122094154358, 0.00908665731549263, -0.0034679980017244816, 0.04087625816464424, 0.0015113987028598785, -0.0256983432918787, 0.020584246143698692, 0.010712209157645702, -0.00901816412806511, -0.01746099255979061, -0.030118385329842567, 0.017524918541312218, -0.006725952494889498, -0.003716853680089116, -0.028730273246765137, -0.00995422713458538, -0.0034520162735134363, -0.05399026721715927, 0.012986157089471817, 0.01622813008725643, -0.009415420703589916, -0.02657504752278328, 0.01136973686516285, -0.026611575856804848, 0.08043745905160904, -0.011187090538442135, -0.01336971390992403, -0.020182423293590546, -0.05157933384180069, 0.02012762986123562, 0.021077390760183334, 0.0117258969694376, 0.027141250669956207, -0.0049634152092039585, 0.0254974327981472, 0.0017671036766842008, 0.00003845562241622247, 0.038209620863199234, -0.04463877156376839, 0.00033532732049934566, -0.018419886007905006, 0.0020125347655266523, 0.012374291196465492, 0.016666481271386147, -0.034501899033784866, 0.039561204612255096, 0.026465458795428276, 0.055305320769548416, 0.011990734376013279, -0.0009252179879695177, 0.05749707669019699, -0.024164114147424698, 0.00787662435323, -0.04357942193746567, -0.0059451390989124775, -0.0005202567554078996, 0.014885678887367249, 0.01779888942837715, 0.04803599417209625, 0.008086668327450752, -0.005867514759302139, -0.0288581270724535, -0.028054481372237206, 0.02080342173576355, 0.020876480266451836, -0.02412758581340313, -0.05647425726056099, -0.004776202607899904, 0.05121404305100441, -0.023287411779165268, -0.010858326219022274, -0.049935515969991684, -0.04496753588318825, -0.009945094585418701, 0.034337516874074936, 0.02098606713116169, -0.0288581270724535, 0.015351427718997002, -0.017771491780877113, 0.02135135978460312, -0.02847456932067871, -0.02027374692261219, -0.011433662846684456, 0.004958848934620619, 0.01354322861880064, 0.03663886338472366, -0.001295647700317204, 0.0059908009134233, 0.006954260636121035, 0.0007579824305139482, -0.028255393728613853, 0.006086690351366997, 0.01057522464543581, 0.018584268167614937, 0.006333262659609318, 0.05559755489230156, 0.03512289747595787, 0.039780378341674805, -0.011534118093550205, -0.010556960478425026, 0.037332918494939804, 0.05249256640672684, -0.0010290981736034155, 0.04182601720094681, -0.06469334661960602, -0.034848928451538086, -0.005620941985398531, -0.0342644602060318, -0.004470269661396742, 0.0004897205508314073, -0.0006255637854337692, 0.025935783982276917, -0.05826419219374657, 0.0031460837926715612, 0.020913008600473404, 0.021917564794421196, 0.0014600293943658471, 0.009643727913498878, -0.004381229635328054, -0.009826374240219593, -0.016346849501132965, 0.014109431765973568, -0.05431903153657913, 0.04460224509239197, 0.015141383744776249, -0.012438218109309673, 0.05238297954201698, 0.009908565320074558, 0.06925950199365616, 0.033807843923568726, -0.006981657352298498, 0.04967981204390526, -0.008945105597376823, 0.013141406700015068, -0.032529316842556, -0.06030983105301857, 0.02586272545158863, 0.022629885002970695, 0.011798955500125885, 0.03707721456885338, -0.0038447061087936163, 0.05399026721715927, 0.038173090666532516, 0.018492944538593292, -0.01765277236700058, 0.04208172485232353, -0.052894387394189835, 0.027159515768289566, -0.009661993011832237, 0.016648216173052788, 0.02116871438920498, 0.030629796907305717, 0.002824169583618641, 0.0058994777500629425, 0.010894855484366417, -0.006488512270152569, -0.023488322272896767, 0.008798988536000252, -0.006657460238784552, -0.03499504551291466, -0.050410397350788116, -0.01925092749297619, -0.006620930973440409, 0.017022641375660896, 0.010748738422989845, -0.010538695380091667, 0.035049837082624435, 0.012082057073712349, 0.00959806703031063, -0.0006672299932688475, 0.011488456279039383, 0.0073332516476511955, -0.003461148589849472, -0.014054638333618641, 0.03024623915553093, 0.029606975615024567, -0.0004594697675202042, -0.03736944869160652, 0.000010282776202075183, -0.054099854081869125, 0.007579824421554804, 0.035725630819797516, 0.051652394235134125, -0.011305809952318668, 0.015524941496551037, -0.026794223114848137, -0.026100166141986847, -0.00459127314388752, -0.03548818826675415, -0.01259346678853035, -0.009680257178843021, -0.01939704455435276, 0.014821752905845642, -0.031908322125673294, 0.04288536682724953, 0.01084006205201149, -0.03163434937596321, 0.0003527358057908714, 0.02060251124203205, -0.031743939965963364, -0.03194484859704971, -0.003700871951878071, -0.0499720461666584, 0.0023401565849781036, -0.006406321190297604, -0.005214553792029619, -0.0019668731838464737, 0.03280328959226608, -0.00677161430940032, 0.031707409769296646, -0.0009309257147833705, 0.0005365237011574209, 0.0742274820804596, -0.02761613018810749, -0.015324030071496964, -0.03461148589849472, 0.02357964590191841, -0.015524941496551037, 0.0185568705201149, 0.0066939895041286945, 0.041862547397613525, 0.02920515462756157, 0.017945006489753723, 0.02062077447772026, -0.04376206919550896, 0.00011072936467826366, -0.04054749384522438, -0.026154959574341774, -0.015351427718997002, 0.0032511053141206503, -0.008538717404007912, 0.004381229635328054, 0.04248354583978653, 0.008990767411887646, -0.04493100568652153, -0.024383289739489555, 0.03623703867197037, 0.0244746133685112, -0.0009080949239432812, -0.020748628303408623, -0.007059282157570124, 0.02010936476290226, -0.030593266710639, -0.006155182607471943, -0.014639106579124928, 0.04175296053290367, -0.019671013578772545, 0.0028173201717436314, -0.046246059238910675, -0.03758862242102623, -0.029314741492271423, 0.03897673636674881, 0.0015844572335481644, -0.03305899351835251, 0.02606363594532013, -0.00901359785348177, 0.027378691360354424, 0.04032832011580467, 0.02551569789648056, -0.014666503295302391, -0.02619148977100849, 0.00573052978143096, -0.061442237347364426, 0.0035182256251573563, 0.02182624116539955, 0.03693109750747681, -0.0020878762006759644, -0.014721297658979893, -0.03285808116197586, 0.009780713357031345, 0.03799044340848923, -0.010082080028951168, 0.02445634827017784, -0.06104041635990143, -0.00279905553907156, 0.02887639030814171, 0.001764820539392531, -0.03448363393545151, 0.01974407210946083, -0.007063848432153463, 0.027579601854085922, -0.0013652816414833069, 0.01693131774663925, -0.005333274137228727, 0.002321891952306032, 0.022483767941594124, -0.0057579269632697105, -0.009164281189441681, -0.004527346696704626, 0.020913008600473404, -0.016566025093197823, -0.04785334691405296, 0.03777126967906952, 0.041716430336236954, 0.014502122066915035, 0.04759764298796654, -0.006018197629600763, -0.029680034145712852, -0.043615952134132385, 0.03342428430914879, -0.01493134070187807, -0.02147921361029148, 0.04032832011580467, 0.020492922514677048, 0.0053058769553899765, -0.007269325666129589, -0.03963426128029823, 0.029095565900206566, -0.03371651843190193, 0.01073960680514574, 0.0026712031103670597, -0.04087625816464424, 0.04178949072957039, -0.02080342173576355, 0.013598022051155567, 0.06578922271728516, 0.024218909442424774, 0.01625552773475647, -0.040474437177181244, -0.011543250642716885, 0.01870298758149147, -0.01276698149740696, -0.011114032007753849, -0.014383401721715927, 0.019123075529932976, 0.013570625334978104, -0.0014782940270379186, 0.021022597327828407, 0.02323261834681034, -0.021771447733044624, 0.0019520330242812634, -0.029643505811691284, -0.04814558103680611, -0.02270294353365898, -0.0004962844541296363, -0.016319453716278076, -0.004830996505916119, -0.006534173619002104, -0.052529096603393555, 0.020876480266451836, 0.08051051944494247, -0.007009054534137249, 0.02989920973777771, -0.04094931483268738, -0.013945050537586212, -0.009063825942575932, 0.03590827435255051, -0.031159469857811928, -0.008072969503700733, -0.04737846925854683, 0.007556993514299393, -0.007328685373067856, -0.021205242723226547, 0.04562506452202797, -0.013415375724434853, 0.015808044001460075, 0.04661135375499725, -0.030209708958864212, -0.03251105546951294, -0.03758862242102623, 0.0035479057114571333, 0.00459355628117919, -0.005675735883414745, -0.006840106565505266, 0.02604537270963192, 0.00699992198497057, 0.0007865209481678903, 0.009040995500981808, -0.006168880965560675, 0.026684634387493134, 0.01941530965268612, 0.007483934983611107, 0.006904032547026873, -0.011671102605760098, -0.05121404305100441, 0.0015810326440259814, -0.027908364310860634, 0.03755209222435951, -0.008862915448844433, 0.049022287130355835, 0.0469035878777504, -0.01031951978802681, 0.007579824421554804, 0.015972424298524857, 0.02235591597855091, 0.04387165606021881, 0.002694034017622471, 0.04354289546608925, 0.0166208203881979, 0.008127763867378235, -0.0009223641827702522, 0.009109487757086754, -0.025113875046372414, -0.004744239617139101, -0.010018153116106987, -0.006369791924953461, 0.028748538345098495, -0.0037716475781053305, 0.007109509781002998, -0.0011295536532998085, -0.026849016547203064, 0.011552383191883564, -0.010082080028951168, 0.000966884195804596, -0.03163434937596321 ]
Designing accurate deep learning models for molecular property prediction plays an increasingly essential role in drug and material discovery. Recently, due to the scarcity of labeled molecules, self-supervised learning methods for learning generalizable and transferable representations of molecular graphs have attracted lots of attention. In this paper, we argue that there exist two major issues hindering current self-supervised learning methods from obtaining desired performance on molecular property prediction, that is, the ill-defined pre-training tasks and the limited model capacity. To this end, we introduce Knowledge-guided Pre-training of Graph Transformer (KPGT), a novel self-supervised learning framework for molecular graph representation learning, to alleviate the aforementioned issues and improve the performance on the downstream molecular property prediction tasks. More specifically, we first introduce a high-capacity model, named Line Graph Transformer (LiGhT), which emphasizes the importance of chemical bonds and is mainly designed to model the structural information of molecular graphs. Then, a knowledge-guided pre-training strategy is proposed to exploit the additional knowledge of molecules to guide the model to capture the abundant structural and semantic information from large-scale unlabeled molecular graphs. Extensive computational tests demonstrated that KPGT can offer superior performance over current state-of-the-art methods on several molecular property prediction tasks.
[ 0.02071979269385338, -0.024086128920316696, -0.02538216859102249, 0.008462125435471535, 0.04039602354168892, -0.018009893596172333, -0.01878415048122406, -0.00042105489410459995, -0.0569920539855957, 0.0011824253015220165, 0.003046533325687051, -0.006564353592693806, 0.037130676209926605, -0.028108898550271988, -0.038611866533756256, 0.018397022038698196, -0.006442324258387089, -0.014155440032482147, -0.06900987029075623, -0.04813859239220619, 0.0156534593552351, -0.08624550700187683, -0.01962573453783989, 0.017471279948949814, 0.053087107837200165, -0.032569292932748795, 0.025701969861984253, 0.020601971074938774, -0.04759997874498367, 0.062142547219991684, 0.043392062187194824, 0.031441573053598404, 0.031727708876132965, 0.03777028247714043, -0.051942553371191025, -0.022318802773952484, 0.03548117354512215, 0.0368950329720974, -0.024052465334534645, -0.0061603933572769165, -0.01901979371905327, 0.002333291107788682, -0.02388414926826954, 0.01769009232521057, 0.028698008507490158, -0.04672473296523094, -0.013473756611347198, -0.03388216346502304, -0.004380443599075079, -0.022150486707687378, -0.00844529364258051, -0.016999993473291397, 0.05561186000704765, 0.030095037072896957, -0.009148015640676022, 0.09277620166540146, 0.02196533791720867, 0.04719601944088936, 0.05527522414922714, 0.06914452463388443, -0.03014553152024746, -0.015165340155363083, -0.08873659372329712, 0.001215036609210074, 0.04012671485543251, -0.04325740784406662, -0.004029082600027323, 0.0034294540528208017, 0.04184354841709137, 0.03218216449022293, -0.03198018670082092, 0.0227900892496109, 0.02307622879743576, -0.01690741814672947, 0.047128692269325256, -0.03103761188685894, 0.01620890386402607, 0.01824553683400154, 0.05584750324487686, -0.022588109597563744, 0.026425732299685478, 0.07769501954317093, -0.0049779680557549, 0.012202965095639229, 0.02959008701145649, -0.016629695892333984, 0.03928513079881668, -0.03324256092309952, -0.02849602699279785, -0.006387621164321899, -0.03669305518269539, 0.007755194790661335, -0.07237620651721954, -0.007376482244580984, -0.028883157297968864, 0.024271277710795403, 0.01608266681432724, 0.004447770304977894, -0.03447127342224121, -0.0024448009207844734, 0.0007016704767011106, -0.037164341658353806, 0.0076415808871388435, 0.0655425488948822, 0.01237128209322691, -0.05379403755068779, 0.0028866324573755264, 0.03334354981780052, -0.003244305495172739, 0.10085540264844894, 0.01876731961965561, -0.001490655355155468, 0.02221781201660633, 0.020416824147105217, -0.03908315300941467, -0.03307424485683441, -0.07789699733257294, -0.02962375059723854, 0.04877819865942001, -0.0342019647359848, 0.007595293689519167, 0.026392068713903427, -0.02677919715642929, -0.05783363804221153, -0.053087107837200165, 0.047398000955581665, -0.025213850662112236, -0.03793859854340553, -0.030852463096380234, 0.05379403755068779, -0.023850485682487488, 0.05376037582755089, 0.05197621509432793, -0.012590093538165092, 0.040025725960731506, 0.019002962857484818, 0.0035872510634362698, 0.03167721629142761, -0.03803958743810654, -0.009678213857114315, 0.031104937195777893, -0.010772272944450378, -0.0023417070042341948, -0.044839587062597275, 0.04591681435704231, 0.03019602783024311, -0.0030254938174039125, 0.047364335507154465, 0.03904948756098747, 0.02590394951403141, -0.04665740579366684, 0.02450692094862461, 0.020585140213370323, -0.0024069296196103096, -0.006850492209196091, 0.04722968488931656, -0.021746525540947914, -0.001579021685756743, -0.0092658381909132, -0.0483405739068985, 0.029657414183020592, -0.034134641289711, 0.007212373428046703, 0.06746135652065277, 0.02386731654405594, 0.06732670217752457, 0.036255430430173874, 0.0015821775887161493, -0.08893857896327972, 0.04813859239220619, 0.03538018465042114, 0.022857416421175003, 0.06392670422792435, 0.00698514562100172, -0.04016038030385971, 0.001314974739216268, 0.00024984520860016346, 0.0032022264786064625, 0.014618311077356339, 0.0005964725278317928, 0.003168563125655055, 0.002968686865642667, 0.004531928803771734, 0.017201973125338554, 0.030044542625546455, 0.020399991422891617, 0.04319008067250252, 0.043425723910331726, 0.06409502029418945, 0.05473661050200462, 0.004834899213165045, 0.025718800723552704, 0.02103959582746029, -0.045950476080179214, 0.020383160561323166, -0.01731979474425316, -0.03357919305562973, -0.014887617900967598, 0.010157916694879532, -0.045108892023563385, -0.026577217504382133, 0.02075345627963543, 0.009307917207479477, 0.017488110810518265, 0.015190587379038334, -0.015039103105664253, 0.00489801773801446, 0.017302963882684708, 0.00912276841700077, -0.0030170779209583998, -0.013928212225437164, -0.034269291907548904, -0.049417801201343536, -0.06301779299974442, 0.02418711967766285, -0.011689599603414536, -0.014458409510552883, 0.00209764763712883, -0.015291578136384487, -0.0049947998486459255, -0.016309894621372223, 0.03723166882991791, 0.10139402002096176, -0.0030044543091207743, 0.032333649694919586, -0.010166332125663757, 0.03243463858962059, -0.04416631907224655, 0.007115591317415237, -0.0020734521094709635, 0.03958810120820999, 0.000032282630854751915, -0.0022827961947768927, 0.0035725233610719442, 0.00005723427238990553, 0.01907029002904892, -0.019827714189887047, -0.029202958568930626, -0.011681183241307735, 0.015678705647587776, 0.05887720361351967, -0.0427861213684082, -0.0025247514713555574, -0.04100196436047554, 0.0370970144867897, 0.037972260266542435, -0.02757028490304947, 0.05524156242609024, 0.04689304903149605, 0.04500790312886238, 0.026122761890292168, -0.02189801074564457, 0.043998003005981445, -0.018632665276527405, 0.0009620354976505041, -0.000010421174920338672, 0.028664344921708107, -0.04012671485543251, -0.014332172460854053, -0.05944947898387909, 0.06332076340913773, -0.03891483694314957, 0.0199287049472332, 0.049956414848566055, 0.006122522056102753, 0.0007863548817113042, 0.038308896124362946, 0.0017483903793618083, 0.0019188111182302237, 0.04177622124552727, 0.0041889832355082035, -0.0397900827229023, -0.023480188101530075, 0.04157423973083496, -0.02898414619266987, -0.08402372896671295, 0.01039355993270874, 0.00682103680446744, 0.026897018775343895, -0.027486126869916916, -0.021443555131554604, -0.0739920511841774, -0.0021544545888900757, 0.03046533465385437, 0.06365740299224854, -0.046253446489572525, -0.007405937649309635, -0.025971276685595512, -0.06584551930427551, -0.04446928948163986, 0.008870293386280537, -0.010949005372822285, -0.030532659962773323, -0.033764343708753586, 0.021477218717336655, 0.016983160749077797, -0.02538216859102249, -0.024086128920316696, 0.006926234811544418, -0.02252078242599964, -0.07574254274368286, -0.010334649123251438, -0.0030823007691651583, 0.03834255784749985, -0.019575240090489388, 0.04531087353825569, 0.05147126689553261, 0.10947322100400925, -0.01719355769455433, -0.04009305313229561, 0.042011864483356476, 0.002815097803249955, 0.000203558083740063, -0.029724739491939545, 0.012901480309665203, -0.011336133815348148, 0.00023551196500193328, -0.05342373996973038, -0.017488110810518265, -0.027486126869916916, -0.03070097789168358, -0.023446524515748024, -0.06853858381509781, 0.014593062922358513, 0.009652966633439064, 0.04069899395108223, 0.024288108572363853, 0.021207911893725395, -0.06116631254553795, 0.013229697942733765, -0.019440585747361183, 0.011908411048352718, -0.06284947693347931, 0.009156432002782822, -0.006396037060767412, -0.02450692094862461, -0.07486729323863983, 0.051908887922763824, -0.06709106266498566, -0.016394052654504776, -0.014298508875072002, -0.035750482231378555, -0.003439973806962371, 0.009148015640676022, 0.02252078242599964, -0.04298810288310051, 0.003987003117799759, 0.027738602831959724, 0.038611866533756256, 0.0213762279599905, 0.0007574254414066672, 0.03477424383163452, -0.051706910133361816, 0.029691077768802643, 0.012135638855397701, -0.031071273609995842, 0.021510882303118706, -0.05002374202013016, -0.0008620974258519709, 0.011765341274440289, 0.017875241115689278, -0.06793264299631119, 0.0020240091253072023, 0.03297325223684311, -0.07910887897014618, 0.02502870187163353, -0.00533143337816, -0.011925242841243744, -0.001913551241159439, -0.012160886079072952, 0.013877716846764088, 0.01959207095205784, 0.02166236750781536, 0.017740586772561073, 0.006816829089075327, 0.01180742122232914, -0.024910880252718925, 0.04096829891204834, -0.058203935623168945, 0.03368018567562103, 0.0004323636821936816, 0.0018851477652788162, 0.008575739338994026, -0.005647027399390936, -0.03783760964870453, 0.03867919370532036, 0.010334649123251438, -0.028883157297968864, -0.01960890367627144, -0.0025731425266712904, 0.00966979842633009, -0.04076632112264633, 0.014349004253745079, -0.03494255989789963, 0.005731185898184776, -0.02252078242599964, 0.02443959377706051, 0.03669305518269539, 0.025752464309334755, -0.017471279948949814, -0.007187125738710165, 0.015619795769453049, -0.023783158510923386, -0.01510642934590578, -0.026526721194386482, -0.0054366313852369785, -0.011681183241307735, -0.054197996854782104, 0.04241582378745079, -0.02908513695001602, 0.0008021345711313188, -0.06099799647927284, 0.006842076312750578, -0.047398000955581665, 0.03847721219062805, 0.028310880064964294, -0.023480188101530075, 0.018901972100138664, 0.014357419684529305, 0.05015839636325836, 0.02928711660206318, 0.00067694898461923, 0.01579652726650238, -0.00305915717035532, -0.011134154163300991, 0.00454455241560936, 0.053625721484422684, -0.04473859444260597, -0.034875232726335526, -0.030616819858551025, 0.044233646243810654, 0.0023606426548212767, -0.00953514501452446, -0.03157622367143631, -0.06177225336432457, -0.04978809878230095, 0.02475939504802227, 0.001707363175228238, 0.011706430464982986, 0.04218018054962158, -0.029741572216153145, -0.020955437794327736, -0.06769700348377228, -0.002265964401885867, 0.0326702818274498, 0.02647622674703598, -0.036322757601737976, -0.01397029124200344, -0.03467325493693352, -0.06456630676984787, -0.027115831151604652, 0.0025899740867316723, -0.03662572801113129, -0.05810294672846794, 0.008895540609955788, -0.003107548225671053, 0.030599987134337425, -0.0030318056233227253, 0.07769501954317093, -0.05147126689553261, -0.020652467384934425, -0.004325740970671177, 0.016789596527814865, -0.030886126682162285, -0.031441573053598404, 0.057093046605587006, -0.02245345525443554, -0.011681183241307735, 0.029539592564105988, 0.027166325598955154, 0.06086334213614464, -0.015013854950666428, 0.011723262257874012, -0.009021778590977192, 0.026105929166078568, -0.0005691210390068591, 0.008571530692279339, -0.05857423320412636, 0.0006480195443145931, 0.01009058952331543, 0.022604940459132195, -0.002100803656503558, -0.003139107720926404, 0.019255436956882477, 0.011925242841243744, 0.031761374324560165, 0.03925146907567978, -0.04234849661588669, 0.022285139188170433, 0.013465341180562973, -0.039689093828201294, 0.013490588404238224, -0.047061365097761154, 0.012707915157079697, 0.04382968321442604, -0.03157622367143631, -0.0005875307251699269, -0.01454256847500801, 0.060459382832050323, 0.013322271406650543, 0.030835630372166634, -0.04975443333387375, 0.011352965608239174, 0.04729701206088066, 0.016503458842635155, 0.04093463718891144, -0.02016434818506241, 0.017555437982082367, -0.016301479190587997, 0.0036419539246708155, -0.004468810278922319, -0.005777473095804453, -0.03075147233903408, -0.025247514247894287, -0.02332870289683342, 0.016107914969325066, 0.005857423413544893, 0.00016003241762518883, -0.01817820966243744, 0.022655436769127846, -0.005743809510022402, -0.012724746949970722, -0.0228069219738245, -0.01660444773733616, -0.051403939723968506, 0.018009893596172333, -0.0011782173532992601, -0.019575240090489388, 0.04642176255583763, -0.00852524396032095, -0.02253761515021324, -0.006509650964289904, -0.01905345730483532, -0.0028087859973311424, -0.010174748487770557, 0.015712369233369827, -0.0008773511508479714, -0.003256929339841008, -0.002032425021752715, -0.002785642398521304, -0.04726334661245346, 0.0017483903793618083, -0.010974252596497536, 0.038847509771585464, 0.0270148403942585, -0.0026446771807968616, 0.028899988159537315, -0.013726231642067432, 0.004599255509674549, 0.023715831339359283, -0.022554446011781693, 0.0052472748793661594, -0.0008300120243802667, 0.00547029497101903, 0.04329106956720352, -0.04978809878230095, 0.006648512091487646, -0.05561186000704765, -0.026274247094988823, -0.016436131671071053, 0.01012425310909748, 0.04036235809326172, -0.035144541412591934, -0.015560884959995747, -0.010502966120839119, -0.05615047365427017, 0.04073265567421913, 0.034572262316942215, 0.01068811397999525, 0.025247514247894287, -0.007111383136361837, -0.009240590035915375, -0.04322374612092972, 0.023699000477790833, -0.0009078585426323116, 0.03011186793446541, 0.01280890591442585, -0.028108898550271988, -0.01196732185781002, 0.006539106369018555, 0.017420785501599312, -0.012421777471899986, 0.0368950329720974, 0.007208165246993303, -0.02082078345119953, -0.03362968936562538, -0.06672076135873795, -0.035144541412591934, -0.023699000477790833, -0.015140092931687832, -0.0242039505392313, 0.052784137427806854, -0.02071979269385338, -0.04093463718891144, -0.03251880034804344, -0.016015339642763138, 0.010881679132580757, -0.011756925843656063, 0.09816233813762665, -0.058776214718818665, -0.00589950243011117, 0.031205927953124046, 0.035178203135728836, 0.02221781201660633, -0.041102953255176544, 0.0061646015383303165, 0.041944537311792374, 0.03304057940840721, 0.019507912918925285, -0.015325240790843964, 0.032922759652137756, 0.007418561261147261, -0.007010393310338259, -0.06180591508746147, 0.05301978066563606, 0.013389598578214645, 0.018296031281352043, -0.0017210389487445354, -0.020433655008673668, -0.052817799150943756, 0.05473661050200462, -0.028327710926532745, 0.02450692094862461, -0.01584702357649803, -0.015468310564756393, 0.04921581968665123, 0.01035989634692669, -0.0007185021531768143, -0.020046526566147804, -0.015594547614455223, -0.022689100354909897, 0.0012476480333134532, -0.07823362946510315, -0.036322757601737976, 0.025197019800543785, -0.05244750156998634, -0.0270821675658226, 0.04359403997659683, 0.041170280426740646, -0.0035346520598977804, -0.07284749299287796, 0.020366327837109566, 0.01735345833003521, 0.024675237014889717, -0.0021186871454119682, 0.02018117904663086, 0.005293562076985836, 0.025954443961381912, 0.02366533689200878, 0.027183156460523605, 0.0040080430917441845, 0.01817820966243744, 0.03354553133249283, 0.05325542390346527, -0.005907918326556683, 0.012160886079072952, -0.027486126869916916, 0.001314974739216268, 0.027452463284134865, 0.04759997874498367, 0.0008415838237851858, 0.062479183077812195, -0.016141576692461967, -0.0067326705902814865, 0.020837614312767982, -0.0001737081620376557, -0.037702955305576324, 0.04611879214644432, 0.006219304166734219, 0.02563464269042015, -0.017269300296902657, -0.062142547219991684, -0.05517423525452614, 0.01590593345463276, 0.038813844323158264, -0.014559400267899036, 0.02048414945602417, -0.0050915819592773914, -0.039655428379774094, -0.008845046162605286, -0.03103761188685894, -0.018733656033873558, -0.019238606095314026, -0.01721038855612278, -0.004691829904913902, -0.007729947101324797, -0.014382666908204556, -0.0013517939951270819, -0.031273253262043, 0.04877819865942001, -0.004439354408532381, -0.0213425662368536, -0.020904941484332085, 0.008260144852101803, -0.005461879074573517, 0.03817424178123474, -0.011285639367997646, -0.014340587891638279, 0.027166325598955154, -0.02592078223824501, -0.01907029002904892, -0.008079204708337784, -0.010385144501924515, 0.022285139188170433, 0.007418561261147261, 0.025146523490548134, 0.02053464576601982, -0.01996236853301525, -0.005360888782888651, -0.003589354921132326, -0.0034294540528208017, 0.043998003005981445, -0.004096409305930138, 0.04090097174048424, 0.026089098304510117, 0.015333657152950764, -0.002008229261264205, 0.003772399388253689, 0.009838114492595196, 0.039756420999765396, -0.03325939178466797, -0.00913118477910757, 0.01912078447639942, -0.04248315095901489, 0.010747025720775127, 0.004243686329573393, 0.007191333454102278, 0.011479203589260578, 0.020315833389759064, -0.013499004766345024, 0.04628710821270943, -0.06295046955347061, -0.025971276685595512, 0.021999001502990723, 0.0398237444460392, -0.005482918582856655, -0.03847721219062805, 0.04921581968665123, 0.006257175467908382, -0.0797148197889328, 0.0370970144867897, 0.03078513592481613, 0.022419793531298637, -0.02331187203526497, 0.007448016665875912, 0.057665321975946426, 0.008802967146039009, 0.003608290571719408, 0.03837622329592705, -0.002510023768991232, -0.009745540097355843, -0.0540633425116539, 0.005558661185204983, -0.01026732288300991, -0.04871087148785591, 0.03925146907567978, 0.012312371283769608, -0.029169294983148575, -0.01903662644326687, -0.06096433103084564, -0.001823080936446786, -0.0022827961947768927, -0.03928513079881668, 0.02704850398004055, 0.03209800645709038, 0.01967622898519039, -0.06749501824378967, 0.00625296775251627, -0.021999001502990723, -0.04803760349750519, 0.02785642445087433, -0.006619056686758995, 0.07648313790559769, -0.02674553357064724, 0.062546506524086, 0.027991076931357384, -0.004775987938046455, 0.010780688375234604, -0.019996032118797302, 0.06066136062145233, -0.03463958948850632, 0.01380197424441576, 0.0028256175573915243, 0.03871285542845726, 0.015257914550602436, 0.03494255989789963, 0.018380191177129745, -0.007342818658798933, -0.042213842272758484, -0.021005932241678238, 0.002528959419578314, -0.004035394173115492, 0.007498511578887701, 0.007317571435123682, 0.021746525540947914, 0.026324741542339325, -0.018094051629304886, 0.00041316504939459264, 0.011083658784627914, -0.004130072426050901, 0.023564346134662628, -0.03558216243982315, 0.03224949166178703, 0.05887720361351967, -0.02815939486026764, -0.05672274902462959, -0.008584154769778252, -0.015131676569581032, 0.026089098304510117, 0.010199995711445808, 0.011108906008303165, 0.032821767032146454, 0.006299254950135946, 0.034067314118146896, 0.020399991422891617, -0.01738712191581726, -0.023699000477790833, -0.0370970144867897, -0.029371274635195732, -0.0227900892496109, -0.019861377775669098, 0.027199989184737206, 0.0099559361115098, -0.004125864710658789, -0.008428461849689484, -0.031778205186128616, 0.0327712744474411, -0.002242820803076029, 0.0028487611562013626, -0.047364335507154465, 0.01875048689544201, 0.030852463096380234, -0.029808899387717247, 0.011563361622393131, -0.061065319925546646, 0.037433646619319916, -0.0006480195443145931, -0.009450986050069332, 0.001302350894547999, -0.027149494737386703, -0.06180591508746147, -0.008007669821381569, -0.05487126484513283, 0.0056806905195117, -0.04992275312542915, 0.01821187324821949, 0.0012592198327183723, -0.03453860059380531, -0.010620787739753723, 0.06039205566048622, -0.011597025208175182, -0.027772266417741776, -0.020955437794327736, 0.012068311683833599, 0.0035136123187839985, 0.007595293689519167, -0.007721531670540571, 0.054803937673568726, -0.004456186201423407, -0.004226854536682367, 0.006614848971366882, -0.012707915157079697, 0.004464602097868919, 0.02019801177084446, 0.02613959275186062, 0.014862369745969772, 0.028883157297968864, -0.017875241115689278, 0.00690519530326128, -0.03265345096588135, -0.0025920781772583723, -0.01937325857579708, -0.013414845801889896, 0.026105929166078568, 0.007098759524524212, 0.03531285747885704, -0.0011740094050765038, -0.03049899823963642, -0.03179503604769707, -0.04716235771775246, 0.015098013915121555, -0.016697023063898087, 0.015451478771865368, 0.018329694867134094, -0.005949997343122959, 0.012649004347622395, 0.0024384891148656607, -0.03810691460967064, -0.033478204160928726, -0.032283153384923935, -0.015535636804997921, 0.022301971912384033, -0.026998009532690048, 0.006635888479650021, 0.024540584534406662, 0.01576286554336548, 0.014500489458441734, -0.03470691666007042, -0.016166824847459793, -0.003343191696330905, 0.007805689703673124, -0.02760394848883152, -0.024641573429107666, 0.002604701789095998, 0.07217422872781754, -0.008058165200054646, 0.014525736682116985, -0.014012370258569717, 0.04393067583441734, 0.012000985443592072, 0.011992569081485271, -0.00489801773801446, 0.01905345730483532, -0.03337721526622772, -0.006429700180888176, 0.043089091777801514, 0.04891285300254822, -0.011445540003478527, 0.026358405128121376, 0.02622375078499317, -0.026846524327993393, 0.04096829891204834, 0.0019303829176351428, 0.04749898985028267, -0.03524553030729294, -0.0025920781772583723, -0.03531285747885704, 0.04894651472568512, -0.00476336432620883, 0.022133653983473778, -0.02930394746363163, 0.005356681067496538, 0.0009946469217538834, 0.002303835703060031, 0.04433463513851166, -0.033410876989364624, -0.01166435144841671, -0.02026533894240856, 0.005760641302913427, -0.023833652958273888, -0.02417028695344925, -0.011125737801194191, -0.022874247282743454, -0.018363358452916145, 0.024052465334534645, -0.023177217692136765, 0.028630681335926056, 0.06685541570186615, -0.024422762915492058, -0.013128707185387611, 0.0056891064159572124, -0.012337618507444859, 0.02984256111085415, -0.025836622342467308, -0.01794256642460823, -0.0017525983275845647, 0.004569800104945898, 0.026122761890292168, -0.018043557181954384, 0.04016038030385971, 0.00038975849747657776, 0.0369623601436615, -0.014744548127055168, -0.01590593345463276, -0.05093265324831009, 0.005554453004151583, -0.0005028463201597333, -0.029674245044589043, -0.018346527591347694, 0.00008698557940078899, -0.0013581059174612164, -0.02275642566382885, 0.047095030546188354, 0.023732664063572884, -0.0024868801701813936, -0.01719355769455433, 0.007889848202466965, 0.004176359623670578, 0.017605934292078018, -0.021797019988298416, 0.05099998041987419, 0.01849801279604435, 0.006244551856070757, -0.0006211940781213343, -0.024591078981757164, -0.039958398789167404, 0.02878216654062271, -0.023530682548880577, -0.04988908767700195, 0.013263360597193241, 0.024843554943799973, -0.0006059403531253338, 0.01903662644326687, -0.026880187913775444, -0.04329106956720352, 0.012893063947558403, -0.010183163918554783, 0.015165340155363083, 0.02479305863380432, -0.007288116030395031, 0.00011335081944707781, -0.04813859239220619, 0.018110884353518486, 0.03817424178123474, 0.024136623367667198, -0.01679801382124424, 0.04063166677951813, 0.012068311683833599, -0.031121769919991493, 0.03901582583785057, 0.03962176665663719, -0.0025710384361445904, -0.018279200419783592, -0.0026720284949988127, 0.023766327649354935, -0.030818799510598183, 0.0015527221839874983, 0.0050915819592773914, -0.021258406341075897, -0.043358396738767624, 0.027267316356301308, -0.05379403755068779, 0.019575240090489388, -0.016326725482940674 ]
Transfer learning improves the performance of the target task by leveraging the data of a specific source task: the closer the relationship between the source and the target tasks, the greater the performance improvement by transfer learning. In neuroscience, the relationship between cognitive tasks is usually represented by similarity of activated brain regions or neural representation. However, no study has linked transfer learning and neuroscience to reveal the relationship between cognitive tasks. In this study, we propose a transfer learning framework to reflect the relationship between cognitive tasks, and compare the task relations reflected by transfer learning and by the overlaps of brain regions (e.g., neurosynth). Our results of transfer learning create cognitive taskonomy to reflect the relationship between cognitive tasks which is well in line with the task relations derived from neurosynth. Transfer learning performs better in task decoding with fMRI data if the source and target cognitive tasks activate similar brain regions. Our study uncovers the relationship of multiple cognitive tasks and provides guidance for source task selection in transfer learning for neural decoding based on small-sample data.
[ 0.001149800606071949, 0.022648589685559273, -0.02498127892613411, -0.004301412031054497, -0.027363598346710205, 0.018942756578326225, 0.047282446175813675, -0.003956058528274298, -0.009578914381563663, 0.027098895981907845, 0.01486468780785799, -0.04215383902192116, -0.01770196482539177, 0.007366168312728405, 0.05241105332970619, -0.024782750755548477, 0.002642886945977807, -0.002702858531847596, 0.014136756770312786, -0.018860038369894028, 0.031003255397081375, 0.016618341207504272, -0.0035155771765857935, -0.0673336461186409, -0.014988766983151436, 0.015708426013588905, 0.05839994177222252, -0.014947406947612762, -0.05247722938656807, 0.04231927916407585, 0.031317587941884995, 0.029249602928757668, 0.013872054405510426, -0.0634954646229744, 0.005298181902617216, -0.06405795365571976, -0.00589376175776124, 0.04678612947463989, -0.04609128460288048, 0.029944445937871933, 0.06031903252005577, 0.01137392595410347, -0.004677785560488701, -0.016709331423044205, -0.0011363585945218801, -0.06471970677375793, -0.04347734898328781, -0.03527158126235008, 0.000042619911255314946, 0.005968209356069565, 0.022234991192817688, -0.06601013243198395, 0.03983769565820694, 0.0018756638746708632, -0.024269890040159225, 0.039109762758016586, 0.038580358028411865, -0.003370818216353655, 0.06994757801294327, 0.028753286227583885, -0.012399647384881973, 0.028753286227583885, -0.009612001478672028, -0.03527158126235008, 0.07246225327253342, -0.06058373674750328, 0.027628300711512566, 0.008726903237402439, 0.050955191254615784, -0.057638924568891525, -0.034113507717847824, 0.00785834901034832, -0.015518171712756157, 0.018992388620972633, -0.02556031383574009, 0.018115563318133354, 0.046719953417778015, -0.003985010087490082, -0.0006467628409154713, 0.007601918652653694, -0.009214947931468487, 0.03318705037236214, 0.021722130477428436, 0.023475784808397293, 0.05896243453025818, 0.020315900444984436, -0.004590930417180061, -0.03444438427686691, 0.003559004981070757, 0.03798477724194527, -0.030374586582183838, -0.006692004855722189, 0.02607317455112934, 0.0526757538318634, -0.04718318209052086, -0.0008483915007673204, 0.028736742213368416, 0.01823136955499649, -0.03360064700245857, -0.025692665949463844, 0.029282690957188606, 0.011274662800133228, -0.04354352504014969, -0.038613446056842804, 0.07921215891838074, -0.011117495596408844, 0.004661242011934519, -0.0341796837747097, -0.019025476649403572, 0.10991762578487396, -0.005244413856416941, -0.009620273485779762, -0.0442383699119091, -0.006563789676874876, 0.016287462785840034, -0.022598957642912865, -0.020067742094397545, -0.005798634607344866, 0.005839994177222252, -0.0331539623439312, 0.05270884186029434, 0.07630043476819992, -0.015203837305307388, 0.005736595019698143, -0.03278999403119087, 0.07570485025644302, -0.02387283742427826, 0.012986956164240837, 0.006518293637782335, 0.05558748170733452, 0.05648085102438927, 0.07689601182937622, -0.013656983152031898, 0.0000446555859525688, 0.055951446294784546, -0.031019799411296844, 0.03811712935566902, 0.0375877246260643, -0.026635667309165, -0.04969785362482071, 0.01206876989454031, -0.03642965108156204, 0.04152517020702362, -0.015650521963834763, 0.050392698496580124, -0.006005432922393084, -0.0179832112044096, 0.08066802471876144, 0.012010865844786167, 0.017751596868038177, -0.002564303344115615, 0.0669035017490387, -0.036032598465681076, 0.015485083684325218, 0.0030999118462204933, -0.009463106282055378, 0.00981880072504282, -0.02246660739183426, 0.04016857221722603, -0.002525011543184519, 0.06270135194063187, 0.012622990645468235, 0.03642965108156204, 0.044734686613082886, 0.09185169637203217, 0.014260835945606232, 0.036297302693128586, -0.0005516353994607925, -0.07411663979291916, 0.04552879184484482, -0.07232990115880966, 0.022665133699774742, 0.013243386521935463, 0.03221096098423004, -0.00646039005368948, 0.0027814419008791447, 0.004640561994165182, -0.08013861626386642, -0.0716019719839096, -0.004963167943060398, -0.039407551288604736, -0.009339027106761932, 0.03540392965078354, 0.017519982531666756, 0.0494331531226635, 0.008069283328950405, 0.07113873958587646, 0.05747348442673683, 0.028703654184937477, -0.02104383148252964, 0.0024505641777068377, 0.0347752645611763, 0.05972345173358917, 0.0034866253845393658, 0.0538669154047966, -0.023922469466924667, -0.021473972126841545, 0.06005433201789856, 0.02021663635969162, 0.004921807907521725, 0.003195039229467511, -0.04129355773329735, 0.008040332235395908, 0.04566114395856857, -0.010637722909450531, -0.011423557996749878, 0.03398115560412407, -0.051815472543239594, -0.012895964086055756, -0.047811850905418396, -0.008412569761276245, -0.012556814588606358, -0.03287271410226822, -0.022234991192817688, -0.05982271581888199, 0.010232397355139256, 0.03755463659763336, -0.004462715238332748, -0.007229681126773357, 0.03871271014213562, -0.006216367706656456, 0.021937202662229538, 0.06336311250925064, -0.041988398879766464, -0.03666126728057861, 0.01333437766879797, -0.028720198199152946, -0.034113507717847824, -0.004739825148135424, -0.03470908850431442, 0.021804850548505783, 0.016634885221719742, 0.038613446056842804, -0.00984361581504345, -0.029117250815033913, -0.04688539355993271, 0.034609824419021606, -0.06564616411924362, -0.01617165468633175, 0.009736080653965473, 0.018611880019307137, -0.005281637888401747, 0.009893247857689857, -0.035503193736076355, 0.04741479828953743, 0.0020793606527149677, -0.05270884186029434, 0.09257962554693222, 0.00011083115532528609, -0.007974156178534031, 0.010381292551755905, -0.03148302808403969, -0.006315631326287985, 0.04016857221722603, -0.003370818216353655, 0.027347054332494736, 0.03815021738409996, 0.019405987113714218, 0.007337216287851334, -0.040036220103502274, 0.03444438427686691, 0.007490247488021851, 0.0008551124483346939, 0.031549204140901566, -0.00646039005368948, 0.0058234501630067825, 0.04605819657444954, -0.0343451201915741, -0.0026635667309165, -0.03907667472958565, -0.05704334378242493, -0.011456646025180817, -0.031334131956100464, -0.06402486562728882, -0.03259146958589554, -0.01937289908528328, 0.06438883394002914, -0.013963045552372932, 0.002525011543184519, 0.0510544516146183, -0.011316022835671902, 0.023508870974183083, -0.006898803170770407, 0.05975653976202011, -0.04351043701171875, -0.0010577751090750098, 0.0012873216765001416, 0.011820611543953419, 0.0020741906482726336, -0.0005074322107248008, -0.024501506239175797, -0.018198281526565552, -0.01876077428460121, -0.03444438427686691, -0.006902939174324274, -0.04817581549286842, -0.024236803874373436, -0.003949854522943497, 0.026437141001224518, -0.029812095686793327, -0.05588527023792267, -0.010265485383570194, -0.014955678954720497, 0.011754435487091541, -0.03054002672433853, 0.046984657645225525, 0.02157323621213436, 0.04830816760659218, -0.03533775359392166, -0.04092958942055702, -0.006265999283641577, 0.016006216406822205, 0.026238614693284035, -0.011969506740570068, 0.005103791132569313, 0.03035804256796837, 0.01274706982076168, 0.006836763583123684, -0.011878514662384987, -0.04172369837760925, -0.05241105332970619, 0.014690976589918137, -0.08688852190971375, 0.034642912447452545, -0.01988575980067253, 0.021258901804685593, 0.03953990340232849, 0.027115439996123314, -0.013797606341540813, 0.01824791356921196, -0.0022913292050361633, -0.06657262146472931, -0.035238493233919144, 0.0015768398297950625, 0.028984900563955307, 0.06005433201789856, -0.03004371002316475, -0.013623896054923534, -0.03712449595332146, -0.007581239100545645, 0.009339027106761932, 0.033551014959812164, -0.03752154856920242, -0.006220503710210323, -0.0015189361292868853, -0.054594848304986954, -0.025080541148781776, 0.008263674564659595, -0.03894432261586189, 0.04265015572309494, 0.000713455374352634, 0.0008933701901696622, 0.014128484763205051, -0.011092680506408215, -0.020994199439883232, -0.024617312476038933, -0.0136156240478158, 0.023459240794181824, 0.03335248678922653, 0.03728993609547615, -0.024534592404961586, -0.06362780928611755, -0.012225937098264694, -0.029960989952087402, -0.07219754904508591, 0.011034776456654072, -0.0071262819692492485, -0.016709331423044205, 0.04900301247835159, -0.010612906888127327, -0.012101857922971249, 0.049532413482666016, 0.04102885350584984, -0.029001444578170776, 0.00037146208342164755, 0.02079567313194275, 0.018413353711366653, -0.007750813849270344, -0.01932326704263687, 0.05873081833124161, 0.00667546084150672, -0.04377514123916626, -0.02274785190820694, 0.07001375406980515, -0.01738763228058815, 0.0325583815574646, 0.040797241032123566, -0.015195565298199654, -0.08252093940973282, 0.0633300244808197, 0.03712449595332146, -0.05442940816283226, -0.016767235472798347, -0.07795482128858566, 0.04691848158836365, 0.05115371569991112, -0.019290179014205933, 0.02355850301682949, 0.00735789630562067, 0.013243386521935463, -0.0588962584733963, -0.018132107332348824, 0.0008028958109207451, -0.05333751067519188, -0.015617434866726398, -0.00441308319568634, 0.0036107045598328114, 0.0002820216759573668, -0.012176305055618286, 0.050458874553442, -0.017850860953330994, 0.029646655544638634, -0.006150192115455866, -0.0022499694023281336, 0.027843371033668518, 0.010579819791018963, -0.029911357909440994, 0.015981400385499, -0.04228619113564491, 0.014178115874528885, -0.04228619113564491, -0.007730133831501007, 0.030440762639045715, -0.020547514781355858, -0.013226842507719994, -0.0067912680096924305, -0.0014817124465480447, 0.013929957523941994, -0.01236656028777361, -0.03897741064429283, 0.0739842876791954, -0.0002634098054841161, 0.04847360774874687, 0.01712292991578579, 0.012358288280665874, 0.010273757390677929, 0.016097208485007286, 0.006948435213416815, -0.032144784927368164, -0.05442940816283226, 0.024071363732218742, -0.017850860953330994, 0.014484178274869919, -0.027396686375141144, -0.02584156021475792, -0.040267836302518845, 0.03669435530900955, 0.003035804256796837, 0.0387788861989975, -0.021440885961055756, -0.055984534323215485, 0.026222070679068565, -0.09046200662851334, -0.02297946810722351, 0.02977900765836239, 0.03457673639059067, 0.002824869705364108, -0.056844815611839294, 0.02387283742427826, -0.03851418197154999, 0.0007827329100109637, 0.01193641871213913, -0.033286310732364655, -0.04873830825090408, -0.012383103370666504, -0.03087090328335762, -0.04030092433094978, -0.061609458178281784, -0.009926335886120796, 0.013549447990953922, 0.007597782649099827, -0.001104304799810052, -0.014823327772319317, 0.03194625675678253, 0.011994322761893272, 0.027032721787691116, 0.026602579280734062, -0.03695905581116676, -0.0007842839113436639, -0.006423166487365961, 0.004764641169458628, -0.008408433757722378, 0.017867404967546463, -0.03191316872835159, 0.028157705441117287, -0.025626489892601967, -0.011440102010965347, 0.051815472543239594, 0.039109762758016586, -0.06687041372060776, 0.006902939174324274, -0.04122738167643547, 0.03781934082508087, -0.03363373503088951, 0.005050023086369038, -0.0787489265203476, -0.019554881379008293, -0.01743726246058941, 0.07319018244743347, -0.01624610275030136, 0.02271476574242115, -0.028786374256014824, 0.029944445937871933, 0.0233103446662426, -0.01824791356921196, 0.08278564363718033, 0.0009218050399795175, -0.03762081265449524, 0.005575291812419891, -0.01995193399488926, -0.0036499963607639074, -0.0358009859919548, 0.012292112223803997, -0.013532903976738453, 0.004971439950168133, 0.035205405205488205, 0.022896748036146164, -0.026883825659751892, -0.007829396985471249, -0.004003622103482485, 0.0035755487624555826, -0.01766887679696083, 0.025725753977894783, 0.022880204021930695, -0.022847115993499756, -0.0055008442141115665, 0.028852548450231552, 0.016055848449468613, 0.021275445818901062, -0.0689549446105957, -0.03305469825863838, 0.0001238853292306885, 0.008768263272941113, -0.04033401235938072, 0.010513643734157085, 0.0420214869081974, 0.08781498670578003, -0.019587969407439232, -0.013996133580803871, -0.033517926931381226, -0.043940577656030655, 0.027677932754158974, -0.011713076382875443, 0.011696532368659973, 0.0043220920488238335, 0.012821516953408718, 0.05327133461833, -0.052047088742256165, -0.021490516141057014, -0.006294951308518648, -0.005273365881294012, 0.010530187748372555, -0.002845549490302801, -0.012846332974731922, -0.011837155558168888, -0.06700276583433151, 0.01965414546430111, -0.04413910582661629, -0.045594967901706696, 0.02297946810722351, 0.019488705322146416, 0.002702858531847596, -0.01562570594251156, 0.0012325199786573648, -0.007663958240300417, -0.013938229531049728, -0.027859915047883987, 0.042749419808387756, 0.013541175983846188, -0.00031433397089131176, 0.007064242381602526, 0.005868946202099323, -0.007556423079222441, 0.026437141001224518, 0.02079567313194275, 0.06888876855373383, -0.03623112663626671, -0.025411419570446014, 0.00815613940358162, 0.006952571216970682, 0.007957612164318562, -0.016916129738092422, -0.005132742691785097, 0.034907612949609756, -0.0004466850950848311, -0.043345000594854355, -0.05896243453025818, -0.04526409134268761, 0.02043170854449272, -0.02503090910613537, 0.003985010087490082, 0.0275290384888649, 0.03201243281364441, -0.02192065864801407, 0.010348205454647541, -0.004533026833087206, -0.01988575980067253, -0.025427963584661484, 0.025626489892601967, -0.05499190092086792, -0.01403749268501997, 0.03507305309176445, 0.023508870974183083, 0.03566863387823105, 0.00843738578259945, -0.021159639582037926, -0.005070703104138374, -0.01110095251351595, 0.006795404013246298, 0.007055970374494791, 0.04073106497526169, -0.017519982531666756, 0.012027409859001637, 0.005141014698892832, 0.012507183477282524, 0.019405987113714218, 0.01824791356921196, 0.011729620397090912, 0.0025518955662846565, -0.023657767102122307, 0.013475000858306885, 0.0306392889469862, 0.02580847218632698, -0.014020949602127075, -0.006216367706656456, 0.0005221666069701314, 0.018711142241954803, -0.05085592716932297, -0.013714887201786041, -0.03695905581116676, -0.020051198080182076, 0.01715601608157158, -0.0006984624778851867, 0.004301412031054497, 0.022797483950853348, -0.02187102660536766, 0.012507183477282524, 0.011779251508414745, 0.018363721668720245, 0.03593333438038826, -0.032111696898937225, -0.003532121190801263, -0.03927520290017128, 0.040565624833106995, 0.011961234733462334, 0.026867281645536423, 0.0006126410444267094, -0.029696287587285042, 0.04354352504014969, -0.0133178336545825, -0.029233058914542198, 0.009736080653965473, -0.04804346337914467, 0.025196349248290062, -0.023723943158984184, -0.0018880717689171433, -0.014020949602127075, -0.03963916748762131, -0.022069552913308144, -0.010703898966312408, 0.03778625279664993, 0.04797729104757309, -0.017917035147547722, -0.009454835206270218, 0.06653954088687897, -0.029001444578170776, 0.011440102010965347, -0.01740417443215847, 0.014236019924283028, 0.025196349248290062, 0.00770531827583909, -0.037488460540771484, -0.02691691368818283, 0.02441878616809845, 0.003807163331657648, 0.009049509651958942, 0.023442696779966354, 0.050359610468149185, 0.018975844606757164, -0.04357661306858063, -0.027429774403572083, -0.038845062255859375, -0.020630234852433205, -0.03983769565820694, 0.05495881289243698, -0.004992119502276182, -0.007552287075668573, 0.0008607994532212615, -0.05750657245516777, 0.003786483546718955, -0.011630356311798096, -0.03705831989645958, 0.035734809935092926, -0.009024693630635738, 0.029911357909440994, 0.01738763228058815, -0.02838931977748871, -0.01263126265257597, 0.05866464599967003, 0.007304128725081682, -0.030076798051595688, 0.0007915218593552709, -0.007899709045886993, 0.0126147186383605, 0.0393744632601738, 0.030374586582183838, 0.017553070560097694, -0.033220138400793076, -0.03695905581116676, 0.011514549143612385, 0.018462983891367912, -0.011762707494199276, 0.02832314372062683, 0.033534470945596695, -0.016270918771624565, 0.00722554512321949, 0.023806661367416382, 0.015336188487708569, 0.009603729471564293, 0.043311912566423416, -0.04741479828953743, 0.050094906240701675, 0.02830660156905651, 0.012424463406205177, -0.039738431572914124, 0.042749419808387756, 0.02888563647866249, -0.028505127876996994, -0.008611096069216728, -0.008933702483773232, 0.01932326704263687, -0.02077912911772728, -0.007974156178534031, 0.008520104922354221, 0.015402364544570446, -0.006857443600893021, -0.04347734898328781, 0.027330510318279266, -0.02613935060799122, -0.05535586550831795, -0.004574386402964592, -0.002636682940647006, -0.015559530816972256, 0.01909165270626545, 0.02329380065202713, 0.011531093157827854, -0.06094770133495331, -0.009901519864797592, -0.02499782294034958, -0.01208531390875578, 0.04777876287698746, -0.03164846822619438, 0.04678612947463989, -0.012929052114486694, 0.0004841673653572798, 0.03586715832352638, -0.005397445056587458, -0.026718387380242348, 0.03930829092860222, 0.01626264676451683, -0.02269822172820568, -0.021970288828015327, 0.0014300127513706684, 0.02470003254711628, 0.019025476649403572, -0.015493355691432953, -0.04490012675523758, -0.0006302189431153238, 0.04016857221722603, -0.022863660007715225, -0.019207458943128586, 0.0015995876165106893, 0.0837782770395279, -0.03391497954726219, 0.004450307227671146, 0.010348205454647541, 0.012821516953408718, 0.004442035220563412, -0.06233738735318184, 0.035172317177057266, 0.048407431691884995, 0.03533775359392166, 0.03679361939430237, -0.02580847218632698, -0.012225937098264694, -0.011514549143612385, 0.029233058914542198, 0.005575291812419891, 0.0028331417124718428, -0.01937289908528328, -0.01388032641261816, -0.05274192988872528, -0.01766887679696083, -0.01852915994822979, -0.003658268367871642, -0.03054002672433853, -0.02608971856534481, -0.007039426360279322, -0.012259024195373058, -0.017486894503235817, 0.017784684896469116, -0.016684515401721, -0.01763579063117504, 0.007535743061453104, -0.01651080511510372, -0.012531998567283154, -0.03676053136587143, -0.022003376856446266, -0.0020007770508527756, 0.04860595613718033, 0.01651080511510372, 0.011646900326013565, -0.01012486219406128, 0.03503996506333351, 0.03798477724194527, 0.0009538588346913457, -0.0020607486367225647, -0.019141284748911858, -0.04681921750307083, -0.0882120355963707, -0.009752624668180943, -0.011282934807240963, 0.02642059698700905, 0.011382197961211205, -0.0763666108250618, -0.02440224215388298, -0.0044916667975485325, -0.02211918495595455, 0.0482419915497303, 0.03027532435953617, 0.013127579353749752, 0.0017381428042426705, -0.034609824419021606, -0.018181737512350082, -0.02838931977748871, 0.0944325402379036, -0.006365262903273106, -0.006911211181432009, -0.010149678215384483, 0.04734862223267555, 0.012308656238019466, -0.02415408380329609, -0.01220112107694149, 0.0006664086831733584, -0.01263126265257597, 0.023988645523786545, 0.024766206741333008, 0.047580234706401825, 0.020663322880864143, 0.049565501511096954, -0.0035569369792938232, 0.03864653408527374, 0.015518171712756157, 0.009463106282055378, -0.002442292170599103, 0.014798511750996113, 0.018330633640289307, 0.050657398998737335, 0.010745258070528507, -0.00637353491038084, 0.02579192817211151, 0.024336066097021103, 0.02296292409300804, -0.02106037549674511, -0.008276082575321198, -0.028819462284445763, -0.009860159829258919, -0.00035000673960894346, -0.013152394443750381, 0.021540148183703423, -0.0076060546562075615, -0.00008963429718278348, -0.027611756697297096, 0.015981400385499, -0.01637018285691738, 0.005165830720216036, -0.0011249847011640668, -0.004925943911075592, 0.02470003254711628, -0.02278093993663788, -0.003573480760678649, -0.01680859550833702, 0.04049944877624512, -0.025692665949463844, 0.005889625754207373, 0.02999407798051834, -0.020878393203020096, -0.024187171831727028, 0.009281123988330364, -0.03527158126235008, -0.005447076633572578, 0.01849607191979885, -0.014327011071145535, -0.06915347278118134, -0.0020018110517412424, -0.0008649353985674679, -0.0008049638126976788, -0.012780156917870045, 0.007883165031671524, 0.035470105707645416, -0.002537419553846121, -0.013656983152031898, -0.02862093411386013, -0.05734113231301308, -0.04877139627933502, -0.03260801360011101, -0.018893126398324966, 0.006005432922393084, 0.0025932551361620426, -0.015592618845403194, 0.007047698367387056, -0.002979968674480915, 0.019720319658517838, -0.07570485025644302, -0.02043170854449272, 0.02465040050446987, -0.0073082647286355495, -0.03527158126235008, 0.01933981105685234, 0.016767235472798347, 0.015071486122906208, 0.017834316939115524, 0.005757274571806192, 0.038282569497823715, 0.01558434683829546, 0.010439196601510048, 0.009992511011660099, -0.004396539647132158, 0.02048133872449398, -0.03897741064429283, -0.047282446175813675, 0.05605071038007736, 0.03566863387823105, 0.023161450400948524, 0.009380387142300606, -0.027264336124062538, -0.018992388620972633, 0.01962105743587017, -0.04086341708898544, -0.022284623235464096, -0.04317956045269966, -0.020001566037535667, 0.010207582265138626, 0.023111818358302116, 0.021705588325858116, -0.007118009962141514, 0.039109762758016586, 0.011828883551061153, -0.022268079221248627, -0.011671716347336769, -0.0000435569672845304, 0.017238736152648926, -0.010794890113174915, -0.044172193855047226, -0.013739703223109245, 0.05251031741499901, -0.025957368314266205, 0.027727564796805382, -0.017503438517451286, 0.023922469466924667, 0.04539644345641136, 0.048109639436006546, -0.016444629058241844, -0.02471657656133175, -0.02249969355762005, 0.03642965108156204, -0.0472162701189518, -0.03781934082508087, -0.0163867250084877, 0.00412770127877593, -0.0003996384039055556, 0.013772791251540184, -0.004512346815317869, -0.010339933447539806, 0.01852915994822979, -0.011299478821456432, 0.0018622219795361161, 0.016568709164857864, 0.014707520604133606, 0.022582413628697395, 0.026470229029655457, -0.013640440069139004, 0.032442573457956314, 0.004096681252121925, -0.03864653408527374, -0.0013565992703661323, 0.01685822755098343, 0.00868554413318634, -0.0365620031952858, -0.02276439592242241, -0.006377670913934708, -0.021225813776254654, 0.050028733909130096, 0.02163941226899624, -0.045032475143671036, -0.02782682701945305, 0.002113482216373086, 0.03742228448390961, -0.008242994546890259, 0.0021631140261888504, -0.06121240183711052, -0.00700633879750967, -0.020415164530277252, 0.03272382169961929, -0.013632168062031269, 0.052874282002449036, 0.04258397966623306, 0.011870243586599827, -0.0028207337018102407, 0.010728714987635612, 0.02832314372062683, 0.011415285989642143, -0.011903330683708191, -0.03480834886431694, 0.02747940644621849, 0.01582423411309719, 0.005769682582467794, -0.002953084884211421, -0.021523604169487953, -0.03815021738409996, -0.02269822172820568, -0.048672132194042206, 0.011779251508414745, -0.007850077003240585 ]
Federated learning has been proposed as a privacy-preserving machine learning framework that enables multiple clients to collaborate without sharing raw data. However, client privacy protection is not guaranteed by design in this framework. Prior work has shown that the gradient sharing strategies in federated learning can be vulnerable to data reconstruction attacks. In practice, though, clients may not transmit raw gradients considering the high communication cost or due to privacy enhancement requirements. Empirical studies have demonstrated that gradient obfuscation, including intentional obfuscation via gradient noise injection and unintentional obfuscation via gradient compression, can provide more privacy protection against reconstruction attacks. In this work, we present a new data reconstruction attack framework targeting the image classification task in federated learning. We show that commonly adopted gradient postprocessing procedures, such as gradient quantization, gradient sparsification, and gradient perturbation, may give a false sense of security in federated learning. Contrary to prior studies, we argue that privacy enhancement should not be treated as a byproduct of gradient compression. Additionally, we design a new method under the proposed framework to reconstruct the image at the semantic level. We quantify the semantic privacy leakage and compare with conventional based on image similarity scores. Our comparisons challenge the image data leakage evaluation schemes in the literature. The results emphasize the importance of revisiting and redesigning the privacy protection mechanisms for client data in existing federated learning algorithms.
[ -0.044936951249837875, 0.006197269540280104, -0.02282825857400894, -0.05580241233110428, 0.05170087888836861, 0.01601935736835003, 0.028746696189045906, 0.0070157768204808235, -0.061343077570199966, 0.0369497574865818, -0.012268614955246449, -0.008652791380882263, 0.011387146078050137, -0.038029108196496964, -0.01613628678023815, 0.04695173725485802, 0.01948227360844612, -0.07087733596563339, 0.012871252372860909, -0.08382953703403473, 0.011369156651198864, -0.08282214403152466, -0.0013019662583246827, -0.01933836005628109, 0.016568027436733246, 0.061738837510347366, 0.03867672011256218, 0.0002151673543266952, -0.022774292156100273, 0.09001781791448593, 0.03401752561330795, 0.008936121128499508, -0.014886039309203625, -0.04069150611758232, -0.007744338363409042, 0.028135064989328384, 0.027325551956892014, 0.030365722253918648, 0.012115707620978355, 0.027739303186535835, -0.03741747885942459, -0.058392852544784546, 0.012160680256783962, 0.042670316994190216, 0.004414093215018511, -0.028117075562477112, -0.026929790154099464, -0.015515660867094994, -0.03698573634028435, 0.009561244398355484, -0.047203585505485535, -0.08217453956604004, 0.015776503831148148, -0.02000395953655243, -0.016226232051849365, -0.008468402549624443, 0.09268021583557129, -0.027739303186535835, 0.05616219341754913, -0.021029341965913773, 0.002356581389904022, 0.03986400365829468, -0.03950422257184982, 0.008319991640746593, -0.020453687757253647, 0.042994119226932526, 0.03806508705019951, -0.01860080286860466, -0.023907609283924103, -0.02086743898689747, -0.05569447576999664, 0.0006633506854996085, 0.03065354935824871, -0.02135314606130123, -0.03687780350446701, 0.0025904406793415546, 0.03889258950948715, 0.03225458413362503, -0.0034471750259399414, 0.013806689530611038, 0.002858029678463936, 0.044397275894880295, -0.02689381130039692, 0.020381731912493706, 0.06458112597465515, -0.003926136530935764, -0.04929032921791077, -0.06537265330553055, 0.03518681973218918, 0.030563602223992348, -0.033963557332754135, 0.024339349940419197, 0.009786109440028667, -0.03153501823544502, 0.032668337225914, 0.005900448188185692, -0.021910810843110085, -0.04015183076262474, -0.0738995149731636, 0.0168288704007864, -0.0599399209022522, 0.004686179105192423, -0.042022705078125, 0.048426851630210876, 0.02630016952753067, -0.06584037095308304, -0.006907842122018337, 0.021856844425201416, 0.019284391775727272, 0.1804673671722412, -0.028800664469599724, 0.009858066216111183, -0.07461908459663391, 0.037381500005722046, -0.009624206461012363, 0.06681178510189056, -0.06900646537542343, -0.02115526609122753, 0.003552861511707306, -0.02757740020751953, 0.05760132893919945, 0.038029108196496964, 0.014697153121232986, 0.024501251056790352, -0.054507192224264145, 0.06548058241605759, 0.02308010682463646, -0.0016988524002954364, -0.008733742870390415, 0.03914443776011467, 0.02263037860393524, 0.004328644368797541, 0.022324562072753906, -0.03538469970226288, 0.01643310859799385, 0.013231036253273487, 0.05331990495324135, 0.025130873546004295, -0.002293619327247143, 0.01921243593096733, 0.05335588380694389, 0.016406124457716942, 0.029754091054201126, 0.023008150979876518, -0.00017159983690362424, 0.027001745998859406, 0.020057925954461098, 0.051377072930336, -0.0009849071502685547, 0.03644606098532677, -0.052492402493953705, 0.06076742336153984, 0.053032077848911285, 0.026587996631860733, 0.05680980533361435, 0.0019034792203456163, 0.05983198434114456, -0.021263200789690018, 0.023853641003370285, -0.00711022038012743, 0.04184281453490257, -0.007375560235232115, 0.05709763243794441, 0.044397275894880295, 0.054039470851421356, 0.017278598621487617, 0.052096642553806305, 0.03781323879957199, -0.07073342055082321, 0.04705967381596565, 0.007258630823343992, 0.024141468107700348, -0.003251542802900076, 0.0011659231968224049, -0.017476480454206467, 0.037237584590911865, 0.02187483198940754, -0.07134505361318588, -0.05558653920888901, 0.015281801111996174, -0.002218289766460657, 0.03986400365829468, 0.0015774255152791739, 0.03398154675960541, 0.03378366306424141, 0.0050054872408509254, 0.005895950831472874, -0.008000683970749378, 0.016550038009881973, -0.016810880973935127, 0.02302614040672779, 0.028728706762194633, 0.015983378514647484, -0.041590966284275055, 0.0332619771361351, -0.04040367901325226, -0.006377161480486393, -0.04195074737071991, 0.053032077848911285, 0.0025094894226640463, -0.038568783551454544, -0.06641602516174316, -0.004726654849946499, 0.014661175198853016, -0.0007212533382698894, 0.018223030492663383, 0.006129810120910406, -0.0024397813249379396, -0.014724137261509895, -0.060263726860284805, -0.06137905269861221, -0.01535375788807869, -0.0599399209022522, -0.04490097239613533, 0.005850978195667267, -0.0056710862554609776, -0.005868967156857252, 0.007285614497959614, -0.01914047822356224, 0.005666588898748159, 0.010082930326461792, -0.01796218752861023, 0.010316790081560612, 0.0023633274249732494, -0.04702369496226311, -0.033351924270391464, -0.0332619771361351, 0.030563602223992348, -0.005212362390011549, 0.024609187617897987, -0.015434709377586842, -0.002745597390457988, 0.04648401960730553, -0.008387451060116291, 0.007613916881382465, -0.03160697594285011, 0.021569017320871353, 0.016550038009881973, -0.03592437505722046, -0.0063546751625835896, -0.026282180100679398, 0.0048750657588243484, -0.012403533793985844, -0.04349781572818756, 0.024069512262940407, 0.041590966284275055, -0.07447516918182373, 0.04295814037322998, 0.0208134725689888, 0.017800284549593925, -0.007195668760687113, 0.00669197179377079, -0.03446725383400917, -0.0010141395032405853, -0.0817427933216095, -0.04731152206659317, -0.012907230295240879, -0.03351382538676262, -0.015344763174653053, -0.03495296090841293, 0.08411736786365509, -0.015002969652414322, -0.05774524062871933, 0.04371368885040283, 0.02871071733534336, 0.00219580321572721, 0.04644804075360298, 0.029556209221482277, 0.03166094049811363, 0.017260611057281494, -0.044001515954732895, 0.011504075489938259, -0.06468906253576279, -0.053823601454496384, -0.05292414501309395, -0.019014554098248482, -0.012529457919299603, -0.008679775521159172, 0.04007987305521965, -0.015362752601504326, 0.03372969850897789, -0.014247423969209194, -0.03401752561330795, -0.03290219604969025, 0.005806005094200373, -0.014004570432007313, -0.05044163763523102, -0.01572253555059433, -0.021712930873036385, 0.013509867712855339, -0.04504488781094551, 0.011333177797496319, -0.06709960848093033, -0.02128119021654129, 0.021982768550515175, -0.003908147569745779, 0.011800896376371384, 0.042454443871974945, 0.03896454721689224, 0.006309702061116695, -0.0642213448882103, -0.06504884362220764, -0.013644786551594734, -0.01087445393204689, -0.03741747885942459, -0.00423869863152504, 0.00158979301340878, 0.057925134897232056, -0.03292018547654152, -0.03220061585307121, 0.02957419864833355, -0.015200850553810596, -0.020057925954461098, -0.03142708167433739, -0.03781323879957199, 0.056773826479911804, -0.007380057591944933, 0.029520230367779732, -0.029484253376722336, -0.04795913025736809, 0.03090539760887623, 0.04130313917994499, -0.07476300001144409, -0.004974006209522486, -0.017503464594483376, -0.026983758434653282, 0.00824353750795126, 0.06411340832710266, -0.0320746935904026, 0.021335158497095108, -0.009633201174438, -0.040187809616327286, -0.036841824650764465, -0.03578046336770058, -0.013249024748802185, 0.04274227097630501, -0.07461908459663391, 0.03234453126788139, -0.01131518930196762, -0.02876468561589718, -0.029592188075184822, -0.024986959993839264, -0.027919193729758263, 0.03230855241417885, 0.011018367484211922, 0.03466513380408287, -0.026462072506546974, 0.004481552634388208, 0.018420912325382233, -0.009282412938773632, 0.0009191342396661639, 0.020021948963403702, -0.05040565878152847, 0.01377970539033413, 0.0012997176963835955, -0.022846248000860214, 0.03795715421438217, -0.019284391775727272, -0.0003215564356651157, -0.027523431926965714, 0.06763928383588791, -0.04141107201576233, 0.006669485475867987, 0.016568027436733246, -0.026821855455636978, -0.05860872194170952, -0.008302003145217896, -0.024789078161120415, -0.014832071959972382, 0.048678699880838394, -0.02108331024646759, 0.028404902666807175, -0.022756302729249, 0.03644606098532677, -0.01572253555059433, -0.03158898651599884, -0.059040460735559464, -0.02871071733534336, -0.007348576560616493, 0.05421936511993408, 0.01093741599470377, 0.027469465509057045, 0.07562647759914398, 0.03025778755545616, 0.017188653349876404, 0.04263433814048767, -0.021029341965913773, -0.029556209221482277, -0.010964400134980679, 0.0101099144667387, 0.013293998315930367, 0.03124719113111496, 0.012115707620978355, 0.00896760169416666, 0.04249042272567749, 0.01334796566516161, -0.025004949420690536, -0.027199627831578255, 0.018151074647903442, -0.029070502147078514, -0.02964615449309349, 0.04605228081345558, -0.02576049417257309, -0.016819875687360764, -0.013087122701108456, 0.011306194588541985, 0.0071866740472614765, -0.013563835062086582, 0.022000757977366447, 0.024735111743211746, -0.004987497813999653, -0.06634406745433807, -0.0014762363862246275, 0.010046952404081821, 0.016523053869605064, 0.008445915766060352, -0.027217617258429527, 0.019860045984387398, -0.03459317609667778, 0.021928800269961357, 0.04101531207561493, -0.011486086063086987, 0.06091133505105972, 0.03946824371814728, -0.04076346382498741, 0.049542177468538284, 0.010883448645472527, 0.023242009803652763, -0.00018607550009619445, -0.030005939304828644, 0.03169691935181618, -0.01946428418159485, 0.00947129912674427, -0.0532839260995388, -0.057709261775016785, -0.02014787308871746, 0.01933836005628109, -0.020183850079774857, -0.021533038467168808, 0.0019540737848728895, 0.01756642572581768, -0.00044326443457975984, -0.0010079557541757822, 0.027541421353816986, -0.029880015179514885, -0.024465274065732956, 0.002275630133226514, -0.036032311618328094, -0.03748943284153938, -0.017674360424280167, -0.049758050590753555, 0.02809908613562584, -0.07519473880529404, -0.0646171048283577, 0.03518681973218918, -0.04770728200674057, 0.0017550685442984104, -0.044001515954732895, 0.025112884119153023, -0.03632013872265816, -0.007380057591944933, 0.03171490877866745, 0.00729460921138525, -0.008423429913818836, 0.008693267591297626, 0.024501251056790352, -0.030617570504546165, -0.04479303956031799, 0.013968591578304768, 0.004546763375401497, -0.020561622455716133, -0.03495296090841293, -0.002968213288113475, 0.0060533564537763596, -0.03104931116104126, 0.03468312323093414, 0.0018236523028463125, -0.07591430842876434, -0.008805699646472931, -0.02989800274372101, 0.01382467895746231, 0.028260989114642143, -0.01789023168385029, -0.07231646776199341, 0.005743043031543493, 0.005063951946794987, 0.067711241543293, -0.006269226316362619, 0.007083236239850521, -0.03137311711907387, 0.0032088186126202345, -0.022756302729249, -0.0037844721227884293, -0.012934214435517788, -0.00015108093793969601, -0.025670548900961876, -0.009075537323951721, 0.01382467895746231, 0.07605821639299393, 0.023367933928966522, 0.040907375514507294, -0.023062117397785187, 0.011854864656925201, 0.00996600091457367, 0.014661175198853016, -0.03788519650697708, -0.046124234795570374, -0.025148862972855568, 0.015209844335913658, 0.04846283048391342, 0.044325318187475204, 0.02442929521203041, 0.006152296904474497, -0.04184281453490257, -0.021856844425201416, -0.008310996927320957, 0.004659195430576801, -0.010847470723092556, -0.035708505660295486, 0.03065354935824871, 0.00823004636913538, -0.0008713505230844021, 0.011522064916789532, 0.04885859042406082, 0.0016583767719566822, 0.03705769404768944, 0.02824299968779087, 0.018393928185105324, 0.011369156651198864, -0.040583573281764984, -0.016846859827637672, 0.02423141524195671, -0.052564360201358795, -0.001288474421016872, 0.034359317272901535, 0.03270431607961655, 0.009030564688146114, 0.005585637874901295, -0.0007206911686807871, -0.023529836907982826, -0.007667884696274996, 0.050225768238306046, -0.006462609861046076, 0.01552465558052063, 0.005513681098818779, 0.0015740524977445602, 0.032812248915433884, -0.05587436631321907, -0.007712857332080603, -0.025256797671318054, 0.04263433814048767, 0.0012581177288666368, -0.008670780807733536, 0.03653600811958313, -0.015551638789474964, 0.010019968263804913, 0.044864993542432785, 0.021065320819616318, -0.015641584992408752, -0.014769109897315502, -0.005162892397493124, -0.0081176133826375, -0.019104501232504845, 0.006512080319225788, 0.026282180100679398, -0.06170285865664482, 0.0027590892277657986, 0.07249636203050613, -0.037237584590911865, 0.019086511805653572, 0.01854683645069599, -0.011126303113996983, -0.0540754497051239, -0.029286371544003487, 0.0018956089625135064, 0.0216049961745739, 0.01786324754357338, 0.013500872999429703, 0.03110327757894993, 0.013069133274257183, -0.007744338363409042, -0.04231053218245506, -0.04094335436820984, 0.03158898651599884, 0.005306805483996868, 0.03358578309416771, 0.008216554298996925, -0.012367555871605873, 0.028692729771137238, -0.05666588991880417, -0.007694868370890617, 0.02401554398238659, 0.016316179186105728, 0.023601792752742767, -0.012295599095523357, 0.0021845600567758083, 0.046340107917785645, 0.020255807787179947, 0.028854630887508392, -0.017953192815184593, -0.020705536007881165, 0.024861035868525505, 0.047887176275253296, 0.02401554398238659, -0.004812103230506182, 0.011863858439028263, 0.033819641917943954, 0.003370721125975251, 0.007681376300752163, -0.011009372770786285, 0.05227653309702873, 0.016253216192126274, 0.02923240326344967, -0.044397275894880295, 0.017359551042318344, 0.03720160573720932, 0.009714152663946152, 0.007330587599426508, -0.03838889300823212, -0.016864849254488945, 0.03191279247403145, -0.0063231936655938625, 0.023367933928966522, 0.04450521245598793, -0.02201874554157257, 0.03874867781996727, -0.019842056557536125, -0.015308785252273083, 0.008409937843680382, 0.042022705078125, -0.04695173725485802, -0.008751732297241688, -0.015740524977445602, 0.007474500685930252, -0.061990685760974884, -0.00886866170912981, 0.007969203405082226, 0.01854683645069599, 0.013069133274257183, 0.03151702880859375, 0.0006043237517587841, -0.01860080286860466, 0.0014256418216973543, 0.03838889300823212, -0.005131411366164684, -0.014616201631724834, 0.023997554555535316, -0.0024825057480484247, 0.021964779123663902, 0.03157099708914757, -0.005846480838954449, 0.02556261233985424, -0.010892443358898163, 0.022990161553025246, 0.010127903893589973, -0.05641404166817665, 0.03139110654592514, 0.010964400134980679, 0.003739499021321535, 0.0365539975464344, 0.049074459820985794, -0.014490277506411076, -0.021928800269961357, 0.025148862972855568, 0.011468096636235714, -0.033028118312358856, 0.049542177468538284, 0.008113116025924683, -0.00538775697350502, 0.04695173725485802, -0.009786109440028667, 0.014058537781238556, -0.005792513489723206, 0.034233395010232925, 0.019104501232504845, -0.019626187160611153, 0.011243232525885105, 0.012052745558321476, 0.020435698330402374, -0.01921243593096733, -0.037849217653274536, 0.02408750168979168, 0.002696127165108919, 0.030671538785099983, -0.06972602754831314, -0.003258288837969303, -0.004567001014947891, 0.0010383125627413392, 0.0006150047993287444, -0.035024918615818024, -0.00623774528503418, -0.023655761033296585, -0.013105111196637154, -0.028458869084715843, 0.018654771149158478, -0.013905629515647888, 0.01672993041574955, -0.022180648520588875, -0.027397507801651955, 0.034970950335264206, 0.017827268689870834, 0.020489666610956192, -0.027595389634370804, 0.019446294754743576, 0.009084532037377357, -0.005446221679449081, -0.002412797650322318, 0.02442929521203041, -0.0032830238342285156, 0.031139256432652473, 0.008405440486967564, 0.02448326349258423, -0.0006099453312344849, 0.02388961985707283, 0.007083236239850521, -0.045512605458498, -0.02194678969681263, 0.00490204943343997, 0.01237655058503151, 0.01241252850741148, 0.0007015776936896145, 0.010019968263804913, -0.0005835237680003047, -0.06706362962722778, -0.006813399028033018, 0.03025778755545616, -0.0013638040982186794, 0.006525571923702955, 0.0035281262826174498, 0.02905251272022724, 0.047203585505485535, -0.037381500005722046, -0.025940386578440666, 0.01365378126502037, -0.007631906308233738, -0.004164493177086115, -0.0123495664447546, 0.010028962977230549, -0.0009865936590358615, -0.022702334448695183, 0.00911601260304451, 0.0081670843064785, -0.006197269540280104, -0.039792049676179886, 0.019122488796710968, 0.019572218880057335, 0.022504454478621483, 0.0049650114960968494, -0.026282180100679398, 0.04069150611758232, 0.03184083476662636, -0.05688176304101944, 0.051628921180963516, -0.02248646505177021, -0.03200273588299751, -0.004292665980756283, 0.017944198101758957, -0.012061739340424538, 0.022432496771216393, -0.02448326349258423, 0.012439512647688389, 0.04036770015954971, -0.01334796566516161, 0.04119520261883736, 0.04303009808063507, -0.0029457269702106714, -0.00242404080927372, 0.0025881920009851456, 0.01120725367218256, -0.05950818210840225, 0.020057925954461098, 0.014391337521374226, 0.03358578309416771, -0.05634208768606186, -0.01919444650411606, 0.05562251806259155, 0.030473656952381134, -0.016541043296456337, -0.02342190220952034, 0.019572218880057335, 0.003107629483565688, 0.010541655123233795, 0.026857834309339523, 0.027919193729758263, -0.0274334866553545, 0.007523971144109964, 0.01840292289853096, -0.02588641829788685, -0.028458869084715843, 0.03975607082247734, -0.004567001014947891, 0.012367555871605873, 0.02728957310318947, -0.04569249600172043, 0.043389882892370224, -0.006844880059361458, -0.015038947574794292, 0.043785642832517624, -0.015596612356603146, -0.0637536272406578, 0.07116516679525375, -0.01628919504582882, -0.0008735991432331502, 0.01127021573483944, -0.05515480041503906, -0.022450486198067665, 0.00789724662899971, -0.01914047822356224, -0.0436057522892952, -0.010163881815969944, 0.032560400664806366, 0.030671538785099983, -0.01438234280794859, 0.006763928569853306, -0.04015183076262474, -0.03498893976211548, 0.011629999615252018, 0.04957815632224083, 0.011117308400571346, -0.048750653862953186, -0.014436310157179832, -0.008634802885353565, -0.017143679782748222, -0.0026061811950057745, 0.01322204153984785, -0.02167695201933384, -0.005963410250842571, -0.020507656037807465, 0.008715753443539143, -0.015641584992408752, 0.00378222344443202, -0.002504992065951228, -0.03360377252101898, 0.005617118906229734, -0.035492636263370514, 0.002936732256785035, -0.019050532951951027, 0.03946824371814728, 0.0016347659984603524, -0.0017696847207844257, 0.0016595011111348867, -0.0034539210610091686, 0.009426325559616089, -0.030797462910413742, -0.0013154582120478153, -0.004722157493233681, -0.013069133274257183, -0.000458723894553259, 0.02334994450211525, 0.007892749272286892, 0.0202198289334774, 0.02871071733534336, 0.008009678684175014, 0.004310655407607555, -0.002826548647135496, -0.0020046683494001627, -0.02093939669430256, 0.052636317908763885, -0.006530069280415773, -0.013060138560831547, -0.016577022150158882, 0.04997391998767853, -0.03254241123795509, -0.01023583859205246, 0.0210113525390625, -0.03119322471320629, 0.0091384993866086, -0.04335390403866768, -0.040583573281764984, -0.06101927161216736, 0.0070967283099889755, -0.044469233602285385, -0.021227221935987473, 0.03741747885942459, 0.0190685223788023, -0.0064446208998560905, -0.009187969379127026, -0.022666355594992638, -0.006251237355172634, -0.03860476240515709, -0.005230351816862822, 0.030635559931397438, -0.006736944895237684, -0.0184748787432909, 0.01722463220357895, -0.00650758296251297, 0.020021948963403702, -0.029322350397706032, -0.018438901752233505, -0.020129883661866188, -0.03139110654592514, 0.009390347637236118, -0.019050532951951027, -0.003928385209292173, 0.04777923971414566, 0.014814082533121109, -0.011054346337914467, 0.008270521648228168, -0.004544514697045088, 0.014778104610741138, -0.003510137088596821, 0.003624818054959178, -0.00027222675271332264, -0.004209466278553009, 0.02851283736526966, 0.005455216392874718, 0.00620626425370574, -0.03914443776011467, -0.003552861511707306, 0.02576049417257309, 0.005814999807626009, -0.028135064989328384, 0.0031885807402431965, -0.01860080286860466, 0.01498498022556305, 0.00433089304715395, -0.034359317272901535, 0.029070502147078514, 0.03110327757894993, 0.01241252850741148, 0.028027130290865898, 0.052420444786548615, -0.008387451060116291, 0.003085142932832241, 0.010361762717366219, -0.019967980682849884, 0.012223642319440842, 0.035492636263370514, -0.035690516233444214, 0.027991151437163353, -0.027181638404726982, 0.004247693344950676, 0.031624965369701385, 0.012151685543358326, -0.010586627759039402, 0.038316935300827026, -0.04407346993684769, 0.04310205578804016, -0.021245211362838745, 0.010163881815969944, -0.005216859746724367, -0.02383565343916416, 0.01626221090555191, 0.02167695201933384, 0.015137888491153717, -0.007865765132009983, 0.05569447576999664, -0.0002644970372784883, -0.007825289852917194, -0.0003552861453499645, -0.04608825966715813, -0.020849449560046196, 0.009345375001430511, 0.009543255902826786, -0.019518250599503517, 0.014616201631724834, -0.017008762806653976, 0.030275776982307434, -0.07343179732561111, 0.048606742173433304, 0.016406124457716942, 0.005446221679449081, -0.0043623740784823895, -0.017008762806653976, 0.00032380508491769433, 0.02728957310318947, -0.04795913025736809, -0.040043897926807404, -0.02950224094092846, -0.002198051894083619, -0.027721313759684563, 0.02227059379220009, 0.03238051012158394, -0.00037524287472479045, 0.04691575840115547, -0.028225010260939598, 0.012610409408807755, -0.015497671440243721, -0.005320297554135323, 0.04878663271665573, -0.008090630173683167, -0.02288222685456276, 0.017800284549593925, 0.03828095644712448, -0.06853874772787094, -0.0509813129901886, -0.020777493715286255, 0.04508086293935776, -0.05569447576999664, -0.012799295596778393, 0.03961215540766716, -0.014139489270746708, 0.050081852823495865, -0.02322402037680149, -0.026659952476620674, -0.010433719493448734, -0.056306108832359314, -0.012034756131470203, -0.022252606227993965, 0.023673750460147858, -0.021461082622408867, 0.01980607770383358, 0.008373959921300411, 0.027811259031295776, -0.002099111443385482, -0.006296209990978241, 0.049146417528390884, 0.01763838343322277, -0.039792049676179886, 0.016307184472680092, -0.03137311711907387, 0.012466495856642723, 0.04831891506910324, 0.05587436631321907, -0.05666588991880417, -0.014886039309203625, -0.05508284270763397, 0.024915002286434174, 0.011504075489938259, -0.005000989884138107, 0.011908832006156445, -0.039108458906412125, 0.028692729771137238, -0.02147907018661499 ]
Intelligent agents need to select long sequences of actions to solve complex tasks. While humans easily break down tasks into subgoals and reach them through millions of muscle commands, current artificial intelligence is limited to tasks with horizons of a few hundred decisions, despite large compute budgets. Research on hierarchical reinforcement learning aims to overcome this limitation but has proven to be challenging, current methods rely on manually specified goal spaces or subtasks, and no general solution exists. We introduce Director, a practical method for learning hierarchical behaviors directly from pixels by planning inside the latent space of a learned world model. The high-level policy maximizes task and exploration rewards by selecting latent goals and the low-level policy learns to achieve the goals. Despite operating in latent space, the decisions are interpretable because the world model can decode goals into images for visualization. Director outperforms exploration methods on tasks with sparse rewards, including 3D maze traversal with a quadruped robot from an egocentric camera and proprioception, without access to the global position or top-down view that was used by prior work. Director also learns successful behaviors across a wide range of environments, including visual control, Atari games, and DMLab levels.
[ 0.03453228250145912, -0.014474376104772091, -0.023657044395804405, -0.06182737648487091, 0.018822524696588516, 0.03924034535884857, 0.013268178328871727, 0.04023253917694092, -0.058520056307315826, 0.025427432730793953, 0.006410358939319849, 0.002589921001344919, 0.020875006914138794, -0.024960516020655632, -0.029065480455756187, 0.021750474348664284, 0.01656576804816723, 0.03338444605469704, -0.019104620441794395, -0.06069899722933769, 0.05245015770196915, -0.012071707285940647, -0.02497997134923935, 0.053345080465078354, 0.053345080465078354, -0.003720731707289815, 0.021264104172587395, -0.004163328558206558, -0.04972648620605469, 0.04922065883874893, 0.011867431923747063, 0.02881256863474846, -0.019055983051657677, -0.0038277332205325365, -0.011381061747670174, 0.024435237050056458, 0.03529101982712746, -0.027509097009897232, -0.019513171166181564, 0.08015380054712296, -0.029065480455756187, 0.012441348284482956, -0.050154492259025574, -0.08194364607334137, -0.01280126255005598, -0.02114737406373024, -0.02097228169441223, -0.0026798995677381754, -0.01790814846754074, 0.008642797358334064, -0.03768396005034447, -0.05245015770196915, 0.02408505044877529, -0.027100544422864914, -0.05011558160185814, 0.00949394516646862, 0.06112700328230858, -0.012567805126309395, 0.018773887306451797, 0.05992080271244049, 0.006210946943610907, -0.016507403925061226, -0.0657961517572403, 0.01662413217127323, 0.05758622661232948, -0.0660296157002449, 0.03056350164115429, -0.003244088962674141, 0.03462955355644226, -0.05778077617287636, -0.022159025073051453, -0.03758668527007103, -0.06937584280967712, -0.05128287151455879, 0.0024513055104762316, -0.017616327852010727, 0.019590990617871284, -0.009192395955324173, -0.004408945329487324, -0.04715844988822937, 0.014338192529976368, 0.011361607350409031, -0.03787850961089134, -0.024123959243297577, 0.10241010040044785, -0.061555009335279465, 0.030621865764260292, -0.07517337054014206, 0.006711908150464296, 0.012519167736172676, -0.007378235459327698, 0.03737268224358559, -0.008783845230937004, -0.054862555116415024, -0.008657388389110565, -0.013336270116269588, -0.01120596844702959, 0.008774117566645145, -0.012480258010327816, -0.03890961408615112, 0.01744123362004757, -0.017810875549912453, -0.02408505044877529, -0.020466456189751625, 0.010242955759167671, -0.04789773374795914, -0.03723650053143501, -0.021886657923460007, -0.006877274252474308, 0.10419994592666626, -0.003514024429023266, -0.023365221917629242, -0.045602064579725266, 0.06529033184051514, -0.03585520759224892, -0.0044624460861086845, -0.042255841195583344, -0.05855896696448326, 0.01991199515759945, -0.06244992837309837, 0.05610766261816025, -0.021089009940624237, 0.013355724513530731, -0.034843556582927704, -0.028851477429270744, 0.05233342945575714, -0.009844131767749786, 0.004491628613322973, 0.0413220077753067, 0.004545129369944334, -0.05081595480442047, 0.027625825256109238, -0.005709985736757517, 0.06630197912454605, 0.025271793827414513, 0.04832573980093002, -0.01328763272613287, -0.01600157842040062, -0.010233228094875813, -0.01690622605383396, -0.02009681425988674, -0.03104987181723118, -0.06887001544237137, -0.02400723099708557, 0.015612482093274593, 0.01180906780064106, 0.017198048532009125, 0.07805268466472626, -0.05132177844643593, 0.039843443781137466, -0.0434231273829937, 0.07276097685098648, -0.007553328759968281, 0.025096699595451355, 0.018326427787542343, 0.015291477553546429, -0.03188642859458923, 0.006857819389551878, -0.026361262425780296, -0.01978553831577301, 0.07198278605937958, -0.005359799135476351, -0.00345079624094069, 0.05606875196099281, 0.08202146738767624, 0.04532969743013382, -0.011419971473515034, -0.0049293613992631435, -0.04427913948893547, 0.04817010089755058, -0.03414318710565567, 0.031944792717695236, -0.01844315603375435, 0.005875351373106241, 0.011760430410504341, -0.03437664359807968, 0.09844131767749786, 0.031010961160063744, -0.050310131162405014, -0.01340436190366745, -0.018024878576397896, -0.00322220241650939, 0.01950344257056713, 0.05171087384223938, 0.04762536659836769, 0.04556315764784813, 0.04501842334866524, 0.016808953136205673, 0.038267605006694794, -0.018151333555579185, 0.0002348255948163569, 0.049026113003492355, 0.022839942947030067, -0.04046599566936493, 0.02704218029975891, -0.04797555133700371, 0.005461936816573143, 0.017120229080319405, -0.03318990021944046, 0.02799546718597412, -0.027081090956926346, -0.02881256863474846, 0.001747284783050418, 0.028987661004066467, 0.010554232634603977, 0.0038082783576101065, 0.0008073744829744101, 0.004513515159487724, -0.008550387807190418, -0.07330571115016937, 0.048792652785778046, -0.03758668527007103, -0.033715181052684784, -0.04459041729569435, -0.056457847356796265, -0.028754204511642456, -0.0257581640034914, 0.01767469197511673, 0.01726614125072956, -0.05120505020022392, -0.00006258216308197007, 0.008584433235228062, 0.04361767694354057, 0.007149641402065754, -0.027800917625427246, 0.029804764315485954, -0.018151333555579185, 0.01718832179903984, 0.03071913868188858, 0.003740186570212245, -0.027431277558207512, 0.002107198815792799, 0.034901924431324005, -0.011857704259455204, 0.019873084500432014, -0.027100544422864914, 0.03764504939317703, 0.01120596844702959, 0.015087202191352844, -0.012110617011785507, 0.026691993698477745, -0.024513056501746178, 0.006094218231737614, 0.00842393096536398, 0.09657365828752518, 0.020388636738061905, 0.001445735339075327, 0.04459041729569435, 0.024610329419374466, 0.008798436261713505, 0.0038836656603962183, -0.0013861549086868763, -0.012694261036813259, 0.004669153597205877, -0.01973690092563629, 0.046574804931879044, 0.0572749488055706, -0.017129957675933838, 0.009814949706196785, 0.024299053475260735, 0.018744705244898796, 0.02793710120022297, 0.06439541280269623, 0.01574866659939289, -0.04680826514959335, 0.0307969581335783, 0.033462267369031906, 0.0015551685355603695, 0.026205623522400856, 0.0027650143019855022, -0.042411476373672485, -0.06696344166994095, -0.001522338599897921, 0.012577532790601254, -0.015028838068246841, -0.0405438169836998, 0.011225422844290733, 0.01112814899533987, 0.06778054684400558, 0.04108855128288269, 0.05307271331548691, -0.06213865056633949, -0.012091162614524364, 0.020544275641441345, -0.02855965495109558, -0.009284806437790394, 0.0006040109437890351, 0.010495868511497974, -0.05521273985505104, 0.02632235363125801, -0.01220789086073637, 0.04365658387541771, -0.018092969432473183, -0.04435695707798004, 0.06494014710187912, 0.005953170824795961, -0.040504906326532364, 0.0046156528405845165, 0.017869239673018456, -0.01672140695154667, -0.013024993240833282, 0.02713945508003235, 0.013073629699647427, -0.02042754739522934, 0.015174749307334423, 0.03015494905412197, -0.05521273985505104, 0.058442238718271255, 0.0045767431147396564, 0.03025222383439541, 0.011595064774155617, 0.0034143184311687946, 0.0128498999401927, -0.04638025909662247, -0.029143299907445908, 0.0264196265488863, 0.08225492388010025, -0.04680826514959335, -0.037217043340206146, -0.018209699541330338, 0.01017486397176981, 0.04291730374097824, -0.06548488140106201, 0.01216898113489151, 0.0002738871844485402, 0.015233113430440426, 0.0037353227380663157, -0.01795678585767746, -0.038267605006694794, -0.00849202275276184, -0.05385090410709381, -0.04844246804714203, -0.008292611688375473, -0.034668464213609695, 0.02472705952823162, -0.044395867735147476, -0.044006772339344025, 0.024629784747958183, -0.011925796046853065, -0.04906501993536949, -0.02377377264201641, -0.012626169249415398, 0.005252797622233629, -0.0006766624865122139, -0.03525210916996002, -0.06326702982187271, -0.056457847356796265, 0.02505779080092907, 0.01867661438882351, 0.02210066094994545, 0.0011678963201120496, -0.026361262425780296, -0.03663340210914612, -0.028345653787255287, 0.05097159370779991, -0.024123959243297577, 0.0009161998168565333, 0.012256528250873089, -0.04194456338882446, 0.00038879213389009237, 0.04139982908964157, -0.07423954457044601, -0.06859764456748962, -0.010447231121361256, -0.07836396247148514, -0.011818794533610344, 0.005709985736757517, -0.04883156344294548, -0.0035505022387951612, 0.04268384352326393, 0.01220789086073637, 0.0069648209027945995, 0.009625265374779701, 0.0016001578187569976, -0.017995696514844894, -0.034999195486307144, -0.007305279839783907, -0.03324826434254646, -0.04922065883874893, 0.0391041599214077, -0.02616671472787857, 0.03727540746331215, -0.034979742020368576, 0.040349267423152924, -0.012742898426949978, 0.07521228492259979, 0.008769254200160503, -0.06128263846039772, 0.0007775842677801847, 0.03350117802619934, 0.04532969743013382, -0.033481720834970474, -0.037625595927238464, 0.0009903712198138237, 0.05042685940861702, -0.008560114540159702, 0.03708086162805557, -0.05256688594818115, -0.01432846486568451, -0.026944907382130623, -0.014260373078286648, 0.016089124605059624, 0.01970771886408329, 0.03437664359807968, 0.00016202205733861774, -0.009853859432041645, 0.03774232417345047, 0.00022129842545837164, -0.005690530873835087, 0.004311671480536461, -0.008754663169384003, -0.07844177633523941, -0.046963904052972794, 0.007451191078871489, 0.016497675329446793, 0.04003799334168434, 0.030213315039873123, -0.01844315603375435, -0.0061331274919211864, -0.043928951025009155, 0.008375294506549835, 0.05832551047205925, 0.00369154941290617, 0.015914032235741615, -0.05960952863097191, 0.0026385581586509943, 0.06423977017402649, 0.02034972794353962, -0.02529124915599823, -0.04159437492489815, 0.04964866489171982, 0.005987216718494892, 0.03188642859458923, -0.09680711477994919, -0.04027144983410835, -0.006682726088911295, -0.027703644707798958, 0.0738893523812294, -0.027431277558207512, -0.00213516503572464, -0.02210066094994545, -0.06295575201511383, 0.003027654252946377, -0.02848183736205101, 0.008467704057693481, 0.0035918436478823423, -0.022956671193242073, -0.022995581850409508, 0.003200315637513995, -0.02225629799067974, -0.09276051819324493, 0.012947173789143562, -0.030524590983986855, -0.04676935449242592, 0.049765393137931824, -0.01626421883702278, -0.00788406003266573, -0.026789268478751183, -0.05011558160185814, -0.040504906326532364, 0.016779771074652672, -0.012703988701105118, 0.008029971271753311, -0.03231443464756012, 0.04116636887192726, 0.02009681425988674, -0.05591311305761337, -0.024143414571881294, 0.007903515361249447, 0.02706163562834263, 0.050543587654829025, -0.030680229887366295, 0.04069945588707924, -0.017168866470456123, 0.03408481925725937, 0.06451214104890823, -0.02801492065191269, -0.041360918432474136, 0.04571879655122757, -0.014202008955180645, 0.017810875549912453, -0.01380318496376276, 0.026147259399294853, -0.03369572386145592, 0.011643701232969761, 0.01399773359298706, 0.08069853484630585, 0.024610329419374466, -0.011711793020367622, -0.01906570978462696, -0.0019515602616593242, -0.037139225751161575, -0.0019868221133947372, -0.003655071835964918, 0.0077235582284629345, -0.04163328558206558, -0.037314318120479584, -0.04155546799302101, 0.014250645413994789, 0.04077727347612381, -0.031088780611753464, -0.02433796226978302, -0.006011534947901964, 0.0051020230166614056, 0.010865509510040283, 0.05766404792666435, 0.0009611890418455005, 0.027742553502321243, -0.013112539425492287, -0.019639626145362854, -0.011526972986757755, 0.037450503557920456, 0.007271233946084976, -0.047586455941200256, 0.0007386746583506465, 0.004995021503418684, 0.0015576004516333342, 0.028034375980496407, 0.029979856684803963, -0.008530932478606701, -0.009391807951033115, -0.01273317076265812, 0.018024878576397896, -0.00242212344892323, -0.04346203804016113, 0.035466112196445465, 0.03636103495955467, -0.024143414571881294, 0.019493715837597847, 0.011886886321008205, -0.008881119079887867, 0.04307294264435768, 0.010028952732682228, -0.020330272614955902, -0.0070815496146678925, 0.013686456717550755, 0.023890502750873566, 0.030699685215950012, 0.05711930990219116, -0.012412166222929955, -0.00482479203492403, 0.05443454906344414, 0.018637703731656075, 0.03807305544614792, -0.002281076041981578, -0.024629784747958183, 0.03159460425376892, -0.017305050045251846, 0.01121569611132145, 0.008647661656141281, 0.006113673094660044, -0.01564166508615017, 0.004228988662362099, -0.013618364930152893, -0.03215879574418068, -0.04058272764086723, -0.010165136307477951, 0.009625265374779701, -0.0039566210471093655, -0.04069945588707924, 0.027800917625427246, 0.01005813479423523, -0.002799060195684433, 0.029960401356220245, 0.010408321395516396, 0.0061477189883589745, 0.026477990671992302, 0.04167219623923302, 0.018744705244898796, 0.0163420382887125, -0.023579224944114685, -0.008302338421344757, 0.007246915251016617, -0.002932812087237835, 0.019231075420975685, 0.018871162086725235, -0.010359684005379677, -0.011079512536525726, -0.02282048761844635, 0.004102532286196947, 0.027022726833820343, -0.03717813640832901, 0.022217389196157455, 0.014182553626596928, -0.0018615818116813898, -0.047197360545396805, -0.03733377531170845, -0.017664963379502296, 0.04474605619907379, -0.030505135655403137, -0.012674806639552116, 0.03429882228374481, 0.030621865764260292, 0.020797187462449074, 0.008224518969655037, 0.010525050573050976, 0.00686268275603652, -0.004793177824467421, 0.017684418708086014, -0.042489297688007355, -0.012042525224387646, 0.01994117721915245, -0.015447116456925869, 0.005335480440407991, -0.01277208048850298, 0.01772332936525345, 0.07536792010068893, -0.004197374451905489, 0.00022996189363766462, -0.008419067598879337, 0.00132171087898314, 0.014270100742578506, -0.010456958785653114, -0.011517245322465897, 0.030621865764260292, -0.011108694598078728, -0.0064589958637952805, 0.0012621305650100112, -0.035232655704021454, -0.042644936591386795, -0.0024610329419374466, 0.020232997834682465, 0.04213910922408104, 0.03040786273777485, -0.01795678585767746, -0.0070815496146678925, 0.0022701327688992023, -0.014591104350984097, 0.007251779083162546, -0.0026239671278744936, 0.042878393083810806, -0.005802396219223738, -0.02106955461204052, -0.01372536551207304, -0.046886082738637924, -0.016711678355932236, 0.027431277558207512, 0.02449360117316246, 0.04085509479045868, 0.011585337109863758, -0.04556315764784813, -0.020369181409478188, 0.04175001382827759, 0.035641204565763474, -0.016633858904242516, 0.01121569611132145, 0.03529101982712746, 0.0027066499460488558, 0.03025222383439541, -0.013268178328871727, 0.012995810247957706, 0.030933141708374023, 0.008312066085636616, 0.05248906835913658, -0.000969092536251992, -0.050699226558208466, 0.02161429077386856, -0.020388636738061905, -0.006128264125436544, 0.009425853379070759, 0.045757703483104706, -0.0311860553920269, -0.0012706420384347439, 0.014104735106229782, 0.04338421672582626, 0.002808787627145648, 0.045368608087301254, 0.0023588952608406544, -0.018044332042336464, 0.06622415781021118, 0.005262525286525488, -0.008506613783538342, -0.01567084714770317, 0.03071913868188858, 0.024123959243297577, 0.02322903834283352, 0.029824217781424522, 0.03320935368537903, -0.019075438380241394, 0.01662413217127323, -0.030991505831480026, -0.010641778819262981, -0.013589181937277317, -0.01129351556301117, -0.008190473541617393, -0.01862797699868679, -0.0022543256636708975, -0.009834405034780502, -0.018024878576397896, 0.032119885087013245, -0.047586455941200256, 0.02250921167433262, -0.004177919588983059, -0.02935730293393135, 0.015427661128342152, 0.009469627402722836, -0.027431277558207512, -0.022839942947030067, 0.04155546799302101, 0.0026069439481943846, -0.02408505044877529, 0.016604676842689514, -0.026691993698477745, 0.012470531277358532, 0.06941474974155426, -0.034104276448488235, -0.010126226581633091, 0.01793733239173889, -0.00009461419540457428, -0.020466456189751625, 0.017587145790457726, 0.04984321445226669, 0.007995925843715668, 0.033481720834970474, 0.023676499724388123, 0.052061062306165695, -0.002465896774083376, -0.06494014710187912, -0.030466226860880852, -0.0024671126157045364, 0.027976011857390404, 0.004681312944740057, 0.02951294183731079, -0.028987661004066467, -0.0005711809499189258, -0.01125460583716631, 0.028073284775018692, 0.024843787774443626, 0.012548349797725677, -0.008073744364082813, 0.04326748847961426, -0.0477420948445797, 0.013637819327414036, 0.00010206174192717299, -0.013676729053258896, 0.006643816363066435, -0.009435581043362617, 0.010408321395516396, -0.007752740290015936, -0.0256997998803854, 0.009990043006837368, -0.05241124704480171, 0.06972602754831314, -0.017820602282881737, 0.017567690461874008, 0.03704195097088814, -0.015505480580031872, 0.027470186352729797, 0.01711050234735012, -0.006852955557405949, 0.0842004045844078, 0.012149526737630367, 0.038656700402498245, -0.024532509967684746, -0.020855551585555077, 0.021478107199072838, 0.04532969743013382, -0.03867615386843681, 0.026944907382130623, -0.02009681425988674, 0.007738149259239435, 0.02793710120022297, -0.00784515030682087, 0.04108855128288269, 0.06805291026830673, -0.0019722310826182365, -0.03324826434254646, -0.017052138224244118, 0.026283442974090576, -0.03492137789726257, 0.029979856684803963, -0.029396211728453636, 0.03149733319878578, -0.0601542629301548, -0.011702066287398338, -0.058597877621650696, -0.0023759182076901197, 0.022606484591960907, -0.042333658784627914, -0.0018761728424578905, -0.032664619386196136, -0.010311047546565533, -0.00738309882581234, 0.06330593675374985, -0.009348034858703613, 0.013705911114811897, 0.015116384252905846, -0.02433796226978302, 0.021964475512504578, 0.008652525022625923, 0.0012372040655463934, -0.01072932593524456, -0.013618364930152893, 0.0021789383608847857, 0.018851706758141518, -0.020330272614955902, -0.05855896696448326, -0.03056350164115429, 0.04381222277879715, -0.045057330280542374, 0.04517406225204468, -0.0039566210471093655, -0.013929641805589199, 0.02418232522904873, -0.0044429912231862545, -0.018540430814027786, 0.012256528250873089, 0.027470186352729797, 0.029746398329734802, -0.010797417722642422, 0.011954978108406067, 0.027878737077116966, -0.010563960298895836, 0.045602064579725266, -0.013472453691065311, -0.013676729053258896, 0.007139913737773895, 0.04890938475728035, -0.029551850631833076, -0.07957015931606293, -0.0376645065844059, 0.006716771982610226, 0.0020609935745596886, 0.014454920776188374, -0.04501842334866524, -0.004185215104371309, 0.008968666195869446, -0.016273945569992065, 0.017353687435388565, -0.008146700449287891, 0.011993887834250927, 0.04797555133700371, -0.0253690667450428, -0.0033219081815332174, -0.04159437492489815, 0.030271679162979126, -0.020466456189751625, 0.0015503049362450838, -0.000854795565828681, 0.03597193583846092, -0.005471664480865002, 0.00006584996299352497, 0.005607848055660725, -0.018968436866998672, -0.014056097716093063, 0.0024646806996315718, -0.006541678681969643, 0.010301319882273674, -0.010953055694699287, 0.017849784344434738, 0.014211735688149929, -0.01636149175465107, 0.02521342970430851, 0.006935638375580311, -0.029960401356220245, 0.023734863847494125, 0.005189569666981697, 0.06918129324913025, -0.025252338498830795, -0.028053831309080124, -0.01718832179903984, -0.012528895400464535, -0.03120550885796547, -0.05245015770196915, 0.022275753319263458, -0.025835983455181122, 0.019746627658605576, -0.02976585365831852, -0.013715638779103756, -0.03733377531170845, -0.004674017429351807, -0.0008049426251091063, -0.048092279583215714, 0.022392481565475464, -0.019055983051657677, 0.023326313123106956, -0.029551850631833076, -0.038325969129800797, 0.007028048858046532, -0.0485202856361866, -0.005252797622233629, -0.009420990012586117, 0.0558352954685688, -0.030855322256684303, 0.03104987181723118, -0.014737015590071678, 0.02608889527618885, -0.015631936490535736, 0.004970702808350325, -0.04556315764784813, -0.011789612472057343, 0.023287402465939522, -0.04062163457274437, -0.008190473541617393, 0.02649744600057602, 0.038423243910074234, -0.010719598270952702, -0.006600043270736933, 0.005987216718494892, 0.040971823036670685, 0.026049986481666565, -0.004579175263643265, -0.027411822229623795, -0.00036964131868444383, -0.005495982710272074, 0.025874892249703407, 0.02457142062485218, -0.00017630918591748923, 0.03756723180413246, -0.04797555133700371, -0.00807860866189003, -0.04221693053841591, 0.014513285830616951, 0.013832367025315762, 0.009527991525828838, -0.03305371478199959, -0.03130278363823891, -0.0478588230907917, 0.014863472431898117, 0.01759687252342701, -0.024046139791607857, -0.009873313829302788, -0.0020889597944915295, 0.038092512637376785, -0.019406169652938843, -0.015807030722498894, -0.01891007274389267, 0.011274060234427452, 0.024532509967684746, -0.007767331320792437, -0.05315053090453148, 0.026769813150167465, 0.009241033345460892, 0.020310817286372185, -0.00793756078928709, -0.014056097716093063, -0.022275753319263458, 0.00187495700083673, 0.0085163414478302, 0.02402668632566929, -0.006288766395300627, 0.017275867983698845, 0.003990666940808296, 0.04182783514261246, 0.012577532790601254, -0.022373028099536896, 0.03727540746331215, 0.0224313922226429, 0.0066146343015134335, -0.003504296997562051, -0.012937446124851704, 0.0036210259422659874, -0.01803460530936718, 0.00532575324177742, -0.014727288857102394, 0.013268178328871727, -0.019766082987189293, -0.0002263141213916242, 0.004737245384603739, 0.06396740674972534, 0.00904162134975195, 0.029454577714204788, -0.027489641681313515, -0.018686341121792793, -0.02817055955529213, 0.042800575494766235, -0.025797072798013687, 0.0032051794696599245, -0.032431162893772125, -0.006765408907085657, 0.00476642744615674, -0.053734175860881805, 0.007762467954307795, 0.020719368010759354, 0.017052138224244118, 0.0170035008341074, -0.03795632719993591, -0.009644720703363419, -0.031555697321891785, -0.024629784747958183, 0.016507403925061226, -0.01994117721915245, 0.037936873733997345, -0.015427661128342152, -0.0031006098724901676, 0.013015265576541424, 0.0016755452379584312, -0.008662252686917782, -0.004571879282593727, -0.04190565273165703, -0.04626353085041046, 0.00029850969440303743, 0.024123959243297577, -0.022625939920544624, -0.030991505831480026, -0.00530629837885499, -0.02130301296710968, -0.04781991243362427, 0.025388522073626518, 0.016449037939310074, -0.019279712811112404, -0.031808607280254364, -0.012713716365396976, 0.0347851924598217, 0.03455173596739769, 0.057236041873693466, 0.036750130355358124, 0.01117678638547659, -0.0019053551368415356, 0.03009658493101597, 0.013579455204308033, -0.013988005928695202, -0.02322903834283352, 0.0066389525309205055, 0.0023747023660689592, 0.02297612652182579, -0.009722539223730564, 0.015622209757566452, -0.045679885894060135, -0.024143414571881294, 0.043539855629205704, -0.03359844908118248, 0.0464191697537899, 0.019717445597052574 ]
Recent techniques for approximating Nash equilibria in very large games leverage neural networks to learn approximately optimal policies (strategies). One promising line of research uses neural networks to approximate counterfactual regret minimization (CFR) or its modern variants. DREAM, the only current CFR-based neural method that is model free and therefore scalable to very large games, trains a neural network on an estimated regret target that can have extremely high variance due to an importance sampling term inherited from Monte Carlo CFR (MCCFR). In this paper we propose an unbiased model-free method that does not require any importance sampling. Our method, ESCHER, is principled and is guaranteed to converge to an approximate Nash equilibrium with high probability. We show that the variance of the estimated regret of ESCHER is orders of magnitude lower than DREAM and other baselines. We then show that ESCHER outperforms the prior state of the art -- DREAM and neural fictitious self play (NFSP) -- on a number of games and the difference becomes dramatic as game size increases. In the very large game of dark chess, ESCHER is able to beat DREAM and NFSP in a head-to-head competition over $90\%$ of the time.
[ -0.004210364073514938, -0.010058463551104069, -0.04630284756422043, -0.00855906493961811, 0.0205988772213459, 0.04337545111775398, 0.011593561619520187, 0.012985859997570515, -0.04901604354381561, 0.06329602748155594, -0.02152707614004612, 0.006350130308419466, -0.005587043706327677, -0.030951865017414093, 0.014512033201754093, 0.03321881219744682, -0.0024967659264802933, -0.016163157299160957, -0.02475792169570923, -0.052621740847826004, 0.03300461173057556, -0.006042218301445246, 0.04223305359482765, -0.006640192586928606, -0.007166767027229071, 0.035860609263181686, 0.059618931263685226, -0.004230445250868797, -0.09460489451885223, 0.05197913944721222, 0.04330405220389366, 0.035575009882450104, -0.006903479807078838, -0.04330405220389366, -0.021794825792312622, -0.027631768956780434, 0.025739671662449837, -0.025293421000242233, 0.020081227645277977, 0.05008704215288162, 0.0308090653270483, 0.030130766332149506, -0.010522563010454178, -0.033486563712358475, 0.03282611444592476, -0.02152707614004612, -0.03926995396614075, -0.004051945172250271, 0.005533493589609861, -0.0699005201458931, 0.050479743629693985, -0.049301642924547195, 0.019974127411842346, -0.025436220690608025, -0.04412515088915825, 0.01241466123610735, 0.05169354006648064, -0.030130766332149506, 0.07189971953630447, -0.005881568416953087, 0.059690333902835846, 0.0224909745156765, -0.07011471688747406, -0.008875902742147446, -0.008184215985238552, -0.052478939294815063, 0.025471920147538185, -0.00508278189226985, 0.03380786255002022, -0.031112514436244965, -0.022151824086904526, 0.03848455473780632, -0.04187605157494545, -0.020938025787472725, 0.02047392725944519, -0.008246690966188908, -0.0016533543821424246, 0.053728438913822174, -0.015654431656003, 0.059547532349824905, -0.008679552935063839, 0.02159847505390644, 0.01302156038582325, 0.012245086021721363, 0.05022984370589256, -0.02961311675608158, 0.03073766455054283, -0.059440433979034424, -0.011763136833906174, 0.020866626873612404, -0.036842357367277145, 0.008318090811371803, -0.01815342903137207, 0.012575310654938221, -0.015618732199072838, 0.0308090653270483, -0.016912855207920074, 0.005765543319284916, -0.030844764783978462, 0.027631768956780434, 0.017376955598592758, 0.01527958270162344, 0.007782591041177511, -0.009326614439487457, -0.016154231503605843, -0.030844764783978462, -0.08453750610351562, 0.02957741729915142, 0.03393281251192093, 0.12787725031375885, 0.008443040773272514, 0.01303048525005579, -0.029934415593743324, 0.03887725621461868, -0.059190534055233, -0.005533493589609861, -0.03507521003484726, -0.026864219456911087, 0.060725629329681396, -0.03727075830101967, -0.033557962626218796, 0.014931508339941502, 0.051622141152620316, 0.001597573165781796, -0.047052547335624695, 0.035753510892391205, -0.02140212617814541, 0.021794825792312622, 0.030327115207910538, 0.03593200817704201, -0.00004413686474435963, -0.022455275058746338, 0.024204572662711143, -0.0033892649225890636, -0.017278781160712242, 0.010388688184320927, 0.026792818680405617, -0.06661612540483475, 0.011183012276887894, -0.05472803860902786, -0.017296630889177322, -0.013298234902322292, -0.012950160540640354, 0.0224909745156765, 0.003799814498052001, -0.02498997189104557, 0.016091756522655487, 0.03639610856771469, -0.05205054208636284, -0.006818692199885845, -0.04323264956474304, 0.0861797034740448, 0.009835339151322842, 0.0018095417181029916, 0.03157661482691765, 0.00510955648496747, -0.05533493682742119, 0.01715383119881153, 0.002371815964579582, -0.015493782237172127, 0.05101524293422699, -9.238759162144561e-7, -0.046909745782613754, 0.00509616918861866, 0.003652552142739296, 0.07075732201337814, -0.0038533643819391727, 0.03632470965385437, -0.020884476602077484, 0.049265943467617035, -0.03498595952987671, 0.00910349003970623, 0.001339864102192223, 0.026471519842743874, 0.040233854204416275, 0.03371861204504967, 0.024222422391176224, -0.04012675583362579, -0.015565182082355022, 0.05633453652262688, -0.04566024988889694, -0.05237184092402458, 0.0038779079914093018, 0.04541034996509552, 0.053942639380693436, 0.06265342980623245, 0.04962294176220894, -0.008389490656554699, 0.06483112275600433, -0.03255836293101311, -0.03252266347408295, 0.09474769234657288, 0.023347772657871246, -0.06390292942523956, 0.03505735844373703, -0.05180064216256142, -0.026489369571208954, -0.0026284095365554094, 0.02595387026667595, 0.046981148421764374, -0.05894063413143158, -0.017359105870127678, 0.03425411134958267, -0.006983804516494274, 0.006162705365568399, 0.0013186672003939748, 0.04530324786901474, -0.022026874125003815, 0.024686522781848907, -0.02481147088110447, -0.03071981482207775, 0.0005056564696133137, -0.0430898517370224, -0.04430364817380905, -0.073399119079113, -0.038091856986284256, -0.0014715077122673392, 0.014012234285473824, 0.02732831984758377, -0.04448214918375015, -0.040376655757427216, 0.05797673389315605, 0.004317463841289282, -0.0501941442489624, 0.02929181605577469, 0.014949358068406582, 0.03371861204504967, -0.02024187706410885, -0.02934536710381508, -0.07989650964736938, -0.03418271243572235, 0.005020306911319494, 0.03780625760555267, 0.03200501203536987, 0.031183915212750435, -0.040412355214357376, 0.006974879652261734, -0.0030545778572559357, -0.011879161931574345, -0.009888888336718082, -0.04898034408688545, -0.06011873111128807, -0.004636532161384821, 0.03755635768175125, 0.002405284671112895, -0.024704372510313988, -0.015538407489657402, 0.0564059354364872, 0.05422823876142502, 0.027596069499850273, -0.051764942705631256, -0.06758002191781998, 0.014297833666205406, 0.09189169853925705, -0.006055605597794056, 0.026417970657348633, -0.01253961119800806, -0.0009917895076796412, 0.046981148421764374, -0.013351785019040108, 0.004712394438683987, 0.011495387181639671, 0.017019955441355705, 0.05540633574128151, -0.03646750748157501, 0.028060168027877808, -0.006439380347728729, 0.02506137080490589, -0.03179081529378891, 0.02854211814701557, -0.02502567134797573, -0.06111833080649376, -0.03196931257843971, -0.03068411536514759, 0.01908162795007229, -0.049230244010686874, -0.014485258609056473, -0.01409255899488926, 0.03884155675768852, 0.038127556443214417, 0.039091456681489944, 0.010388688184320927, 0.038020458072423935, 0.006470617838203907, -0.05454953759908676, -0.04805214703083038, -0.029077617451548576, -0.011111612431704998, -0.03321881219744682, -0.011156237684190273, -0.015493782237172127, -0.03277256339788437, -0.02729261852800846, 0.02268732339143753, 0.025525471195578575, 0.021116526797413826, -0.024151021614670753, 0.0543353371322155, 0.038020458072423935, 0.003043421544134617, -0.031380265951156616, 0.021098675206303596, 0.015154632739722729, -0.01641305722296238, -0.041483353823423386, 0.007269404362887144, 0.0008456427603960037, 0.08210990577936172, -0.03596770763397217, 0.04116205498576164, 0.006631267257034779, -0.009273064322769642, -0.03887725621461868, -0.017296630889177322, -0.03752065822482109, -0.017109205946326256, 0.052693139761686325, 0.005604893434792757, -0.061689529567956924, -0.01683253049850464, 0.01182561181485653, -0.033415161073207855, -0.04323264956474304, 0.05308584123849869, 0.02156277559697628, 0.0015284045366570354, 0.012227236293256283, 0.02836361713707447, -0.009228439070284367, 0.011075912043452263, -0.0065732551738619804, -0.01138828694820404, -0.017037805169820786, -0.013235759921371937, 0.007144454400986433, 0.07193541526794434, -0.0027488968335092068, 0.02963096648454666, -0.002369584748521447, -0.031219614669680595, -0.0035967708099633455, -0.004176895134150982, 0.012611011043190956, -0.007376504130661488, -0.02379402332007885, -0.006934717297554016, -0.07143561542034149, -0.022258924320340157, -0.003688252065330744, -0.013985458761453629, 0.0009995988802984357, -0.004694544710218906, 0.041447654366493225, -0.02609666995704174, 0.063688725233078, -0.04744524508714676, -0.001991388387978077, 0.010522563010454178, 0.009299839846789837, 0.033308062702417374, 0.029791615903377533, -0.013360709883272648, -0.018439028412103653, 0.05544203519821167, -0.011022362858057022, -0.0472310446202755, -0.0204203762114048, 0.004685619845986366, 0.0015194795560091734, 0.057119935750961304, -0.0031192840542644262, -0.014842257834970951, -0.03061271458864212, 0.0067963795736432076, 0.011709586717188358, -0.026578620076179504, 0.03079121559858322, 0.008956227451562881, -0.06561652570962906, 0.024650821462273598, 0.006644655019044876, 0.04069795459508896, -0.011290112510323524, 0.059369031339883804, 0.06051143258810043, 0.04990854486823082, 0.014378158375620842, -0.027524668723344803, 0.007296179421246052, 0.019974127411842346, 0.03057701513171196, -0.0519077405333519, -0.007903078570961952, 0.03644965961575508, -0.0027667467948049307, -0.03264761343598366, 0.008773265406489372, -0.021759124472737312, -0.02165202610194683, -0.021277176216244698, -0.04462495073676109, 0.05454953759908676, -0.03516446053981781, 0.006434917915612459, -0.035717807710170746, -0.0084341149777174, -0.03887725621461868, -0.042411550879478455, 0.0023138036485761404, 0.008701865561306477, -0.022241074591875076, -0.010745687410235405, 0.01608283258974552, -0.015118932351469994, 0.029220417141914368, -0.006497392430901527, -0.01525280810892582, -0.0035900771617889404, 0.049194544553756714, -0.07632651180028915, 0.004051945172250271, 0.01934937760233879, 0.08018210530281067, -0.011522161774337292, -0.016984255984425545, 0.02145567536354065, -0.004640994593501091, 0.01909947767853737, -0.01697533018887043, -0.04269715026021004, 0.02141997590661049, -0.030916165560483932, -0.02838146686553955, 0.00021210795966908336, -0.037841957062482834, -0.04451784864068031, 0.01660940609872341, 0.0260431207716465, -0.009018702432513237, -0.06215362995862961, 0.020081227645277977, -0.02738186903297901, 0.024383071810007095, -0.002345041139051318, 0.004980144556611776, 0.040198154747486115, -0.04330405220389366, -0.006711592432111502, 0.025257721543312073, 0.0026127907913178205, -0.0726851150393486, -0.00825115293264389, -0.06458123028278351, -0.016145307570695877, 0.07739751040935516, -0.0005349415587261319, -0.040305253118276596, -0.049373045563697815, 0.012959085404872894, 0.025828920304775238, -0.021241476759314537, 0.004997994285076857, 0.03428981080651283, -0.045803047716617584, -0.024293823167681694, 0.054977938532829285, -0.012334335595369339, -0.03477175906300545, -0.01926012896001339, 0.020938025787472725, -0.0032620837446302176, -0.05537063628435135, -0.017287705093622208, 0.01917087845504284, 0.033593662083148956, 0.016457680612802505, -0.0037574206944555044, -0.0993172898888588, 0.013075110502541065, 0.0024454472586512566, 0.043589651584625244, 0.04155475273728371, 0.0500156432390213, 0.003652552142739296, -0.050479743629693985, 0.01938507705926895, 0.04155475273728371, -0.03387926146388054, -0.01029051374644041, -0.04391095042228699, -0.004192513879388571, 0.012655635364353657, 0.01528850756585598, -0.0406622551381588, -0.009746088646352291, 0.020099077373743057, 0.01300371065735817, -0.05869073420763016, 0.02727476879954338, 0.04109065234661102, 0.004551745019853115, -0.013494584709405899, 0.013851583935320377, 0.013173284940421581, 0.0052077313885092735, 0.0102101881057024, 0.031255315989255905, 0.036735258996486664, -0.021919775754213333, 0.017805354669690132, 0.015752607956528664, 0.05915483459830284, -0.01806418038904667, -0.002568165771663189, 0.014628058299422264, 0.009192739613354206, 0.006492929998785257, 0.010272663086652756, 0.004085414111614227, 0.01577938161790371, 0.004011782817542553, -0.005542418919503689, -0.02955956570804119, -0.0032799337059259415, -0.033468712121248245, 0.051407940685749054, 0.010397613048553467, -0.03759205713868141, 0.03630685806274414, -0.011013437062501907, -0.004948907066136599, 0.06668752431869507, -0.0013766796328127384, -0.06890092045068741, -0.03182651475071907, -0.018831728026270866, 0.04915884509682655, -0.0004666096356231719, -0.020955875515937805, 0.025775371119379997, -0.005649518687278032, 0.04876614362001419, 0.012530685402452946, 0.006051143165677786, -0.032344162464141846, -0.0007123257382772863, 0.020938025787472725, -0.0472310446202755, 0.029184717684984207, 0.037984758615493774, -0.003474052296951413, -0.026257319375872612, -0.03050561621785164, -0.029809465631842613, 0.010576113127171993, -0.0152706578373909, 0.003672633320093155, -0.0102101881057024, 0.02270517498254776, -0.032362014055252075, 0.03195146471261978, -0.02507922239601612, -0.012146911583840847, -0.03430766239762306, -0.01660940609872341, 0.004069795366376638, 0.04034095257520676, 0.06715162098407745, -0.018903128802776337, 0.006724979728460312, -0.03277256339788437, -0.0010486863320693374, 0.01768040470778942, -0.02259807474911213, 0.018599679693579674, 0.0541568398475647, -0.0387701541185379, 0.026935620233416557, 0.03136241436004639, 0.0010927534895017743, 0.032272763550281525, -0.009978138841688633, 0.014279983937740326, 0.043839551508426666, 0.025596870109438896, -0.010995587334036827, -0.01913517899811268, -0.012325410731136799, 0.027399718761444092, -0.06401002407073975, -0.00855014007538557, 0.019010229036211967, -0.016600480303168297, -0.0153152821585536, -0.008086040616035461, 0.02034897729754448, 0.009871038608253002, -0.02156277559697628, 0.04416085034608841, -0.08503730595111847, 0.026882069185376167, 0.011031287722289562, 0.005118481814861298, -0.0102101881057024, 0.0203311275690794, 0.025239871814846992, 0.04298274964094162, 0.05872643366456032, -0.038056157529354095, -0.029041916131973267, 0.02843501791357994, 0.021901926025748253, 0.03987685590982437, -0.052621740847826004, 0.05297873914241791, -0.009344464167952538, -0.02161632478237152, -0.006997191812843084, -0.0385916568338871, -0.010308363474905491, 0.04401804879307747, 0.007791516371071339, 0.05351423844695091, -0.02388327196240425, -0.0014670451637357473, 0.025757521390914917, 0.01305725984275341, -0.017252005636692047, 0.005595968570560217, -0.002554778242483735, 0.002237941138446331, -0.020884476602077484, -0.026650018990039825, 0.004107726737856865, 0.023276373744010925, -0.032379861921072006, 0.006225180346518755, 0.03709225729107857, 0.036628156900405884, -0.020813075825572014, -0.0182605292648077, 0.02166987583041191, 0.025507621467113495, 0.004165738821029663, 0.008991926908493042, -0.003672633320093155, 0.018938828259706497, -0.02281227335333824, 0.01913517899811268, 0.014886883087456226, 0.02627517096698284, 0.02393682301044464, 0.008800039999186993, 0.039198555052280426, 0.0006119196186773479, -0.0010531487641856074, 0.051586441695690155, -0.00841626524925232, -0.007229242008179426, 0.013735559768974781, -0.00735419150441885, -0.019617127254605293, -0.0037440331652760506, -0.023133574053645134, 0.07104291766881943, -0.004667769651859999, 0.05022984370589256, 0.01945647783577442, 0.000055432552471756935, 0.03077336587011814, -0.02493642084300518, -0.00045322213554754853, -0.005180956795811653, 0.03951985388994217, 0.032486964017152786, -0.05562053620815277, 0.04676694795489311, 0.08189570903778076, 0.029238266870379448, -0.027399718761444092, -0.007233704440295696, 0.024615122005343437, 0.0012383423745632172, -0.052728839218616486, -0.049444444477558136, -0.006948104593902826, -0.02584677003324032, -0.007912003435194492, -0.00825115293264389, 0.00478825718164444, 0.024186722934246063, -0.07022181898355484, 0.017617929726839066, -0.013449959456920624, 0.04555314779281616, 0.03643180802464485, -0.0010682097636163235, -0.009871038608253002, 0.004491501022130251, -0.018001705408096313, -0.023169273510575294, -0.01305725984275341, -0.007394354324787855, -0.005555806215852499, 0.03705655783414841, 0.01695748046040535, 0.006907942239195108, 0.03366506099700928, -0.017332330346107483, 0.025775371119379997, 0.026971319690346718, 0.009281989187002182, 0.02964881621301174, 0.02279442362487316, 0.04530324786901474, -0.01586863212287426, 0.03862735629081726, -0.042447250336408615, 0.012182611040771008, 0.005578118842095137, 0.022223224863409996, 0.013789108954370022, -0.0003787542518693954, -0.005957430694252253, -0.02497212216258049, 0.018617529422044754, 0.034593261778354645, -0.0036034646909683943, 0.000011827354683191516, -0.012120136059820652, 0.01029943861067295, -0.026489369571208954, -0.05094384029507637, 0.0019467633683234453, -0.007220316678285599, -0.03625330701470375, 0.005234506446868181, 0.033200960606336594, -0.006885629612952471, 0.0072470917366445065, 0.0024119785521179438, -0.0040541766211390495, 0.07111431658267975, 0.0018407792085781693, -0.013753409497439861, -0.007876303978264332, -0.025222022086381912, 0.019510027021169662, 0.00970146432518959, 0.004395557567477226, 0.019688528031110764, -0.0051541817374527454, 0.044803448021411896, 0.01597573235630989, -0.06715162098407745, 0.008826814591884613, 0.03546791151165962, 0.018724627792835236, 0.004152351524680853, -0.0036123895552009344, 0.012325410731136799, 0.050301242619752884, -0.03163016587495804, 0.000055397689720848575, 0.011914861388504505, -0.015716906636953354, -0.05422823876142502, 0.022383874282240868, 0.011682812124490738, -0.009487263858318329, 0.011504312045872211, 0.02366907335817814, 0.01827837899327278, -0.038056157529354095, -0.021295025944709778, 0.004596369806677103, 0.00783614069223404, -0.002989871660247445, 0.004491501022130251, 0.025543320924043655, -0.02495427243411541, 0.016198856756091118, 0.059333331882953644, 0.03380786255002022, -0.03769915550947189, 0.015645507723093033, -0.012682410888373852, -0.007822753861546516, 0.032344162464141846, 0.04462495073676109, -0.033379461616277695, -0.020848777145147324, -0.01918872818350792, 0.016761131584644318, 0.02945246733725071, 0.025222022086381912, -0.03418271243572235, -0.026346569880843163, -0.021830525249242783, -0.026774968951940536, -0.001502745202742517, 0.023115724325180054, 0.017403731122612953, -0.0028916967567056417, 0.01768040470778942, -0.04751664772629738, 0.017725029960274696, -0.008019103668630123, 0.016350582242012024, 0.034575410187244415, 0.015636581927537918, 0.007447903975844383, -0.004056408070027828, 0.008862514980137348, 0.011914861388504505, -0.00804141629487276, -0.03421841189265251, 0.052764538675546646, -0.022276774048805237, -0.04644564539194107, -0.024043923243880272, -0.01420858409255743, -0.0028180654626339674, -0.014369233511388302, -0.05412113666534424, -0.024240272119641304, 0.035699959844350815, -0.005042619071900845, 0.03855595737695694, -0.0070864418521523476, -0.0365210585296154, 0.08596549928188324, -0.03414701297879219, -0.006492929998785257, -0.07432731240987778, 0.039198555052280426, -0.018599679693579674, 0.025454070419073105, -0.007978941313922405, 0.04619574919342995, 0.023276373744010925, 0.033522263169288635, 0.011343661695718765, 0.0012227236293256283, -0.004685619845986366, -0.021223625168204308, 0.001185907982289791, -0.005042619071900845, -0.03361150994896889, -0.005845868494361639, 0.004154582973569632, 0.03596770763397217, 0.041376251727342606, -0.0008277927991002798, -0.009790713898837566, -0.03432551026344299, 0.06233213096857071, 0.03744925558567047, -0.03866305574774742, 0.0073318793438375, -0.014993983320891857, 0.03264761343598366, 0.04662414640188217, -0.01195056177675724, 0.03762775659561157, 0.002208935096859932, 0.011897011660039425, -0.057191334664821625, 0.0036123895552009344, -0.05679863691329956, 0.016770055517554283, 0.031005414202809334, -0.00402070814743638, 0.03370076045393944, 0.020973725244402885, 0.034682512283325195, 0.009987063705921173, -0.03066626563668251, 0.00479718204587698, -0.022312475368380547, 0.024686522781848907, 0.04405374825000763, 0.007068592123687267, -0.03537866100668907, 0.0517292395234108, -0.01755545474588871, 0.015377757139503956, -0.038091856986284256, -0.019884876906871796, -0.025168471038341522, -0.0147083830088377, 0.019670678302645683, -0.039162855595350266, 0.016475530341267586, 0.018073104321956635, 0.037949055433273315, -0.022026874125003815, -0.045874446630477905, 0.056084636598825455, -0.0011167393531650305, -0.005506718531250954, -0.043482549488544464, -0.008295778185129166, -0.03941275551915169, 0.023169273510575294, -0.019581427797675133, 0.026632169261574745, -0.007581778801977634, 0.02040252648293972, -0.004886432085186243, 0.013271460309624672, -0.031058965250849724, 0.040198154747486115, -0.03959125652909279, 0.00060076336376369, 0.04080505296587944, -0.01422643382102251, -0.012325410731136799, -0.0005129080382175744, -0.011879161931574345, 0.013244684785604477, 0.0037038708105683327, -0.027863819152116776, 0.024347372353076935, -0.008376102894544601, 0.007996791042387486, -0.035807058215141296, -0.0010631894692778587, 0.012959085404872894, -0.00020555367518682033, -0.03653891012072563, 0.04858764633536339, 0.060440029948949814, -0.01423535868525505, 0.035878460854291916, 0.005863718222826719, -0.013699859380722046, -0.0003656456829048693, 0.002387434709817171, -0.0016410824609920382, -0.03852025792002678, 0.0014871264575049281, 0.02943461574614048, 0.03186221420764923, -0.005060469266027212, -0.004721319768577814, 0.025721820071339607, -0.0224909745156765, 0.006997191812843084, 0.03146951273083687, 0.022151824086904526, -0.0004295151447877288, 0.06690172106027603, -0.009808563627302647, -0.0562274344265461, -0.03384356200695038, -0.02140212617814541, -0.029791615903377533, 0.0029207030311226845, 0.06008303165435791, 0.017787504941225052, 0.019777776673436165, -0.04898034408688545, -0.018813878297805786, -0.02027757652103901, 0.025757521390914917, -0.0012316486099734902, -0.025614721700549126, -0.028006618842482567, 0.041126351803541183, 0.0018530510133132339, -0.0006147086969576776, 0.01681468077003956, 0.013815884478390217, 0.01420858409255743, 0.02836361713707447, 0.002690884517505765, -0.012173686176538467, -0.029095467180013657, 0.011022362858057022, 0.015056458301842213, -0.0007234819931909442, 0.013914058916270733, 0.006434917915612459, 0.017287705093622208, -0.01824267953634262, 0.034468311816453934, -0.01017448864877224, -0.009496189653873444, 0.02040252648293972, -0.033522263169288635, 0.034575410187244415, -0.009246289730072021, -0.0113793620839715, -0.03844885528087616, 0.043732449412345886, -0.028827717527747154, -0.031130364164710045, 0.03395066037774086, -0.0007636444643139839, 0.005778931081295013, -0.007804903667420149, -0.0018485885811969638, 0.02379402332007885, 0.00882235262542963, 0.01594003103673458, -0.01306618470698595, -0.005930655635893345, -0.03639610856771469, 0.013806959614157677, 0.0075862412340939045, 0.0066223423928022385, 0.0011513236677274108, -0.023329922929406166, -0.06097552925348282, 0.0018017323454841971, -0.030112916603684425, 0.01690393127501011, -0.0203311275690794, -0.016216706484556198, -0.03493240848183632, -0.005582581274211407, 0.006443842779844999, -0.0258646197617054 ]
Collaborative filtering algorithms capture underlying consumption patterns, including the ones specific to particular demographics or protected information of users, e.g. gender, race, and location. These encoded biases can influence the decision of a recommendation system (RS) towards further separation of the contents provided to various demographic subgroups, and raise privacy concerns regarding the disclosure of users' protected attributes. In this work, we investigate the possibility and challenges of removing specific protected information of users from the learned interaction representations of a RS algorithm, while maintaining its effectiveness. Specifically, we incorporate adversarial training into the state-of-the-art MultVAE architecture, resulting in a novel model, Adversarial Variational Auto-Encoder with Multinomial Likelihood (Adv-MultVAE), which aims at removing the implicit information of protected attributes while preserving recommendation performance. We conduct experiments on the MovieLens-1M and LFM-2b-DemoBias datasets, and evaluate the effectiveness of the bias mitigation method based on the inability of external attackers in revealing the users' gender information from the model. Comparing with baseline MultVAE, the results show that Adv-MultVAE, with marginal deterioration in performance (w.r.t. NDCG and recall), largely mitigates inherent biases in the model on both datasets.
[ -0.002842961810529232, -0.03173418343067169, -0.028593551367521286, -0.012657435610890388, -0.0014624643372371793, 0.031181983649730682, -0.03454694524407387, -0.006639329716563225, -0.021949907764792442, 0.011587549932301044, -0.038308802992105484, -0.0392061248421669, -0.010457267053425312, -0.02483169548213482, -0.004089723341166973, 0.02122514694929123, 0.016082793474197388, -0.02659182995557785, 0.02552194520831108, -0.050008516758680344, 0.029111238196492195, -0.014486594125628471, 0.004100508522242308, 0.034046515822410583, 0.036617692559957504, 0.08710938692092896, -0.028645319864153862, 0.0024913663510233164, -0.02990502491593361, 0.0012920591980218887, 0.04255383089184761, 0.0001962894748430699, -0.002683341735973954, -0.04203614592552185, -0.051837675273418427, 0.008287298493087292, 0.027230311185121536, 0.061294082552194595, 0.00692405691370368, 0.07012926787137985, -0.013062955811619759, -0.024227729067206383, -0.0696115791797638, -0.01454699132591486, 0.017998233437538147, -0.030992165207862854, -0.0075841075740754604, -0.0023792008869349957, 0.022778205573558807, -0.018015490844845772, 0.021104352548718452, -0.029801486060023308, -0.009007745422422886, -0.02357199229300022, -0.06301970779895782, 0.044486526399850845, 0.0194995254278183, -0.0038481364026665688, 0.038412339985370636, 0.010440011508762836, -0.012545269913971424, 0.048386432230472565, 0.011225169524550438, 0.009352869354188442, -0.001472171046771109, -0.00540550984442234, 0.00580240273848176, 0.039413198828697205, -0.04804130643606186, 0.026678111404180527, -0.1007072851061821, 0.03979283571243286, 0.009697994217276573, -0.024521084502339363, -0.014426197856664658, 0.010112143121659756, 0.060155171900987625, 0.022605644538998604, -0.00020168203627690673, 0.0182053092867136, 0.021087097004055977, 0.038964539766311646, -0.015841206535696983, 0.045107752084732056, 0.06774790585041046, -0.0322173573076725, 0.006022419780492783, -0.0647798404097557, 0.010310589335858822, -0.05442610755562782, -0.04024149850010872, 0.02174283377826214, 0.010974953882396221, -0.06405507773160934, -0.08144934475421906, 0.0010558647336438298, -0.01053492072969675, -0.03792916610836983, -0.08738548308610916, 0.029404593631625175, -0.010897301137447357, -0.008852439001202583, 0.0030392513144761324, -0.008572026155889034, 0.03439164161682129, -0.06039676070213318, -0.036721229553222656, -0.011216540820896626, -0.0351509153842926, 0.14867956936359406, -0.015573736280202866, -0.01618633233010769, -0.023934373632073402, 0.03751501441001892, -0.00235763075761497, 0.009361498057842255, -0.04151845723390579, -0.050112053751945496, 0.01989641785621643, -0.057877350598573685, 0.016393406316637993, 0.02331314980983734, 0.024883465841412544, -0.029732462018728256, -0.02899044379591942, 0.07385660707950592, 0.008861067704856396, 0.01691972091794014, 0.03446066379547119, 0.027506409212946892, -0.03130277618765831, 0.03152710944414139, -0.02272643707692623, -0.05811893939971924, 0.005547873675823212, 0.039551250636577606, 0.0675063207745552, 0.008727331645786762, 0.022450339049100876, -0.027834277600049973, -0.03259699419140816, -0.010897301137447357, -0.08648815751075745, 0.012096608057618141, -0.03989637270569801, 0.011138888075947762, -0.011363218538463116, 0.01905086450278759, -0.025004258379340172, 0.03475401923060417, -0.031199241057038307, 0.06595326215028763, 0.00679463567212224, 0.02453834004700184, 0.06795497983694077, 0.02339942939579487, 0.04821386933326721, -0.006846404168754816, -0.0012737244833260775, -0.05594465509057045, 0.06664351373910904, -0.019672086462378502, 0.0334080345928669, 0.05439159646630287, 0.06046578288078308, 0.025729019194841385, 0.01614319160580635, 0.02181185781955719, -0.08448643982410431, 0.06412409991025925, -0.025401150807738304, 0.0012607823591679335, -0.043899815529584885, 0.0014872702304273844, -0.04697142168879509, 0.03523719683289528, 0.06612582504749298, -0.05335622280836105, -0.03616902977228165, 0.003388689598068595, -0.04976693168282509, 0.03737696632742882, 0.025366639718413353, 0.029801486060023308, 0.017860185354948044, 0.01101809460669756, 0.0446590892970562, -0.028593551367521286, -0.0005252361297607422, -0.030940396711230278, 0.022519363090395927, 0.04189809411764145, 0.04855899512767792, 0.0023511594627052546, 0.023589247837662697, 0.02093179151415825, -0.03332175686955452, -0.07482295483350754, 0.04182906821370125, -0.0084382900968194, 0.01355475839227438, -0.062398482114076614, 0.05815345048904419, -0.0033433919306844473, 0.034081026911735535, 0.027903303503990173, 0.030094843357801437, 0.04027600958943367, -0.03578939288854599, -0.04345115274190903, -0.03490932658314705, -0.00700602401047945, -0.05252792313694954, 0.007730785291641951, 0.0006638250779360533, 0.000643872597720474, -0.0154270576313138, 0.007601363584399223, 0.02350296825170517, -0.01566864550113678, -0.008602224290370941, 0.001307158381678164, 0.0181707963347435, 0.004728203639388084, -0.006643643602728844, -0.02467638999223709, 0.006160469260066748, 0.052942074835300446, -0.023951629176735878, 0.01162206195294857, 0.008451232686638832, 0.007333892397582531, 0.0030198378954082727, -0.041656509041786194, 0.07213098555803299, 0.0008439368684776127, -0.013908511027693748, -0.015444314107298851, -0.00005604900070466101, -0.05528891831636429, -0.06250201910734177, -0.005129410419613123, -0.007381347008049488, -0.042243219912052155, 0.06633289903402328, -0.005892998073250055, -0.04704044759273529, 0.04348566755652428, 0.05049169063568115, 0.05922333523631096, -0.003869706764817238, -0.01791195385158062, -0.03150985389947891, 0.0334770604968071, -0.01768762245774269, 0.02125965990126133, 0.01243310421705246, -0.06584972143173218, -0.04686788469552994, -0.03789465129375458, -0.019430499523878098, 0.009275216609239578, -0.025194076821208, 0.033011142164468765, 0.036721229553222656, -0.0013761833542957902, 0.05314914882183075, -0.015798065811395645, 0.04013796150684357, 0.010258820839226246, -0.009050886146724224, -0.042139682918787, -0.025090539827942848, 0.001921911141835153, 0.012916278094053268, 0.016117306426167488, -0.0223295446485281, -0.05528891831636429, 0.04921473190188408, -0.026160424575209618, 0.03454694524407387, -0.019292451441287994, 0.008157876320183277, -0.009577200748026371, 0.036065492779016495, -0.008886951953172684, -0.0022109528072178364, 0.004542699083685875, -0.02357199229300022, -0.028006840497255325, -0.008973232470452785, -0.011527152732014656, -0.034771278500556946, -0.01875750720500946, 0.06536655128002167, 0.027230311185121536, -0.027420129626989365, 0.017169935628771782, 0.046695321798324585, -0.06557362526655197, -0.039344172924757004, -0.027092261239886284, 0.033269986510276794, 0.02817940153181553, -0.02584981359541416, 0.022502107545733452, 0.008041396737098694, 0.08842085301876068, -0.018774764612317085, -0.0730973333120346, 0.03130277618765831, 0.033045656979084015, -0.04414140433073044, -0.0012025425676256418, -0.014883487485349178, 0.043830789625644684, 0.029577156528830528, -0.007605677470564842, -0.0007042693323455751, -0.03259699419140816, -0.05363232269883156, 0.029559899121522903, -0.015496082603931427, -0.022484850138425827, -0.03806721419095993, -0.034150052815675735, -0.033891208469867706, 0.05335622280836105, -0.017385639250278473, -0.010129399597644806, -0.048317406326532364, -0.0016177702927961946, 0.0293528251349926, 0.00671266857534647, 0.00428385566920042, 0.013917138800024986, -0.023899860680103302, 0.038826487958431244, -0.032493457198143005, -0.07337343692779541, -0.032355405390262604, -0.006419312674552202, -0.004702318925410509, 0.028196658939123154, 0.014408941380679607, -0.02077648602426052, 0.003515954129397869, 0.021432220935821533, 0.01905086450278759, -0.015513339079916477, 0.0010617965599521995, -0.01735975407063961, -0.0030004247091710567, 0.022519363090395927, 0.04072467237710953, -0.0027976641431450844, 0.015038792975246906, -0.012053467333316803, -0.028938675299286842, 0.030043072998523712, 0.008481430821120739, -0.014322659932076931, -0.042174194008111954, 0.0334080345928669, -0.041104309260845184, -0.05936138704419136, -0.03958576172590256, -0.0014732495183125138, 0.04742008447647095, -0.03152710944414139, -0.04379627853631973, -0.018257077783346176, 0.007873148657381535, -0.023295892402529716, -0.06081090867519379, -0.014736809767782688, 0.008062967099249363, -0.011276938021183014, -0.009775646962225437, 0.04414140433073044, -0.016022397205233574, -0.002487052232027054, -0.0728212371468544, -0.013908511027693748, 0.02331314980983734, 0.0025194077752530575, 0.038964539766311646, 0.037273429334163666, -0.006492651533335447, -0.004065996035933495, 0.01761859841644764, -0.010905928909778595, 0.00652716401964426, -0.08269178867340088, 0.01765310950577259, -0.01713542267680168, 0.006169097498059273, -0.006358915939927101, 0.03114747256040573, -0.03097490966320038, 0.006962883751839399, 0.0042407154105603695, -0.04628117382526398, 0.030957654118537903, -0.03644512966275215, 0.036100007593631744, 0.00031627409043721855, -0.043313104659318924, 0.08855890482664108, -0.006742866709828377, 0.029525388032197952, -0.01261429488658905, -0.04127687215805054, 0.01794646494090557, 0.0017331712879240513, 0.012036211788654327, -0.01599651388823986, 0.02483169548213482, 0.011009466834366322, -0.020569410175085068, 0.016634993255138397, 0.043899815529584885, 0.07606540620326996, -0.019361475482583046, -0.0065616765059530735, 0.05097486451268196, -0.02990502491593361, -0.020017212256789207, 0.04300249367952347, -0.023002536967396736, 0.04469360038638115, 0.028403732925653458, -0.02132868394255638, -0.04707495868206024, 0.00017067477165255696, 0.023692786693572998, 0.03982735052704811, -0.022450339049100876, 0.0060267336666584015, -0.03406377136707306, -0.01006037462502718, -0.018636714667081833, -0.030905883759260178, 0.0391370989382267, -0.021397709846496582, -0.022674668580293655, 0.031578876078128815, -0.036652203649282455, -0.04800679534673691, -0.02438303455710411, -0.07958567142486572, 0.04079369828104973, -0.05798088759183884, -0.0783432275056839, 0.05214828625321388, -0.013710064813494682, 0.02828294038772583, -0.030992165207862854, 0.02015526220202446, -0.013062955811619759, -0.04987046867609024, 0.027299335226416588, -0.003410259960219264, 0.0040444256737828255, -0.025194076821208, 0.021138865500688553, -0.04748911038041115, 0.009033629670739174, 0.008679877035319805, -0.033632367849349976, -0.011121631599962711, 0.056738439947366714, -0.01290765032172203, -0.016928348690271378, -0.012976675294339657, 0.07503002882003784, -0.032648760825395584, -0.11133711040019989, 0.025936095044016838, -0.011906789615750313, 0.03026740439236164, 0.02861080691218376, 0.011320078745484352, -0.03485755994915962, 0.007320950273424387, -0.003362805349752307, 0.008930092677474022, 0.023088818415999413, -0.08144934475421906, -0.06388251483440399, -0.026091400533914566, 0.016531456261873245, 0.010940441861748695, -0.007031908258795738, -0.0037122436333447695, 0.002676870673894882, 0.016160447150468826, 0.01340808067470789, 0.051872190088033676, 0.00029119866667315364, 0.0024244985543191433, 0.07061243802309036, -0.04942180588841438, -0.010172540321946144, 0.055012818425893784, -0.037135377526283264, -0.013080212287604809, -0.029766974970698357, 0.008701447397470474, -0.030578017234802246, 0.010138027369976044, 0.06212238222360611, 0.0033002514392137527, -0.035996466875076294, -0.008537513203918934, 0.002789036137983203, 0.013986163772642612, -0.038860999047756195, -0.01371869258582592, 0.014124213717877865, -0.010716110467910767, 0.022743694484233856, -0.024555597454309464, 0.030681554228067398, -0.04144943505525589, 0.0320793092250824, 0.034374386072158813, 0.006997395772486925, 0.009370125830173492, 0.025021513924002647, 0.010448639281094074, 0.028886906802654266, -0.029922280460596085, -0.05425354465842247, 0.061432134360075, -0.03280406817793846, 0.03325273096561432, -0.004818798508495092, 0.0059361387975513935, -0.018412383273243904, -0.008239843882620335, 0.05559953302145004, 0.0021699692588299513, 0.01035373006016016, -0.011898161843419075, -0.014564246870577335, 0.015332148410379887, -0.08096616715192795, -0.003108276054263115, -0.012864509597420692, -0.004124235827475786, -0.0181707963347435, -0.028006840497255325, -0.02795507200062275, -0.027523666620254517, -0.006604817230254412, -0.024434803053736687, 0.036030981689691544, -0.005181179381906986, -0.010595316998660564, -0.00924933236092329, -0.013675551861524582, 0.012260542251169682, -0.0013794188853353262, -0.0008331517456099391, 0.0012057782150804996, -0.0012575468281283975, 0.05321817472577095, 0.005836915224790573, -0.02710951678454876, -0.04037954658269882, -0.0048921373672783375, -0.010707482695579529, -0.0336151123046875, -0.03796367719769478, -0.009188935160636902, -0.015314892865717411, 0.010621201246976852, 0.004792914260178804, 0.021104352548718452, -0.027316590771079063, -0.0503191277384758, 0.019482269883155823, 0.029042212292551994, -0.00290120136924088, 0.008705761283636093, -0.02622945047914982, -0.038860999047756195, -0.008213959634304047, -0.002088002162054181, 0.005772204603999853, 0.06809303164482117, -0.00812767818570137, 0.02200167626142502, -0.02971520647406578, -0.013002559542655945, 0.007955116219818592, -0.010103515349328518, 0.03197576850652695, -0.042139682918787, -0.016634993255138397, 0.014262263663113117, 0.03130277618765831, 0.02132868394255638, -0.008800670504570007, -0.030077585950493813, 0.013295914977788925, -0.000145060068462044, -0.004628980066627264, -0.0026337301824241877, -0.01629849709570408, 0.018222564831376076, 0.047903258353471756, -0.0320793092250824, 0.021449478343129158, -0.020327823236584663, 0.04134589433670044, -0.014167354442179203, -0.011880905367434025, -0.0210008155554533, -0.015875719487667084, -0.005517675541341305, 0.06812754273414612, 0.04534933716058731, 0.018015490844845772, 0.050698764622211456, -0.002937871031463146, -0.00042035066871903837, 0.012864509597420692, 0.0090681416913867, -0.03484030067920685, 0.014124213717877865, -0.04196712002158165, -0.019482269883155823, -0.021207891404628754, 0.005319228861480951, 0.025867069140076637, 0.012571154162287712, 0.04524580016732216, -0.013839486055076122, 0.008679877035319805, -0.012493501417338848, -0.015012908726930618, 0.05925785005092621, -0.000531437573954463, 0.004350723698735237, 0.021639296784996986, -0.003175143850967288, 0.018032746389508247, 0.008265728130936623, -0.024521084502339363, 0.009585828520357609, 0.02350296825170517, 0.01592748798429966, 0.029473619535565376, -0.010491780005395412, -0.0006212238222360611, -0.007959430105984211, 0.038895513862371445, -0.034995608031749725, 0.0030263089574873447, 0.01717856340110302, 0.0054011959582567215, -0.00812767818570137, 0.00814493466168642, 0.008304554037749767, 0.03197576850652695, -0.006691098213195801, 0.050733279436826706, 0.05242438614368439, 0.01548745483160019, 0.02736835926771164, -0.04807582125067711, 0.03817075118422508, 0.0838652178645134, -0.030181122943758965, 0.0016080636996775866, 0.01103535108268261, -0.02129417099058628, -0.006194981746375561, -0.018740251660346985, 0.011207913048565388, -0.05670392885804176, 0.022864487022161484, -0.02552194520831108, -0.01666087843477726, 0.010983582586050034, 0.016755785793066025, -0.031837720423936844, 0.00511215440928936, -0.05411549657583237, -0.04859350621700287, 0.048317406326532364, -0.010448639281094074, 0.025176821276545525, -0.02740287221968174, -0.004236401058733463, -0.014771321788430214, -0.011742855422198772, 0.001475406577810645, -0.012571154162287712, 0.02125965990126133, -0.017497804015874863, 0.050077542662620544, -0.00987918395549059, -0.009490919299423695, 0.004935278091579676, -0.010603945702314377, -0.004538385197520256, 0.01022430881857872, -0.02552194520831108, 0.045107752084732056, -0.03730794042348862, 0.0223985705524683, -0.010362358763813972, 0.02578078769147396, 0.030871372669935226, 0.0006999553297646344, -0.00031276894151233137, 0.009516803547739983, 0.02688518539071083, 0.048455458134412766, 0.05270048603415489, -0.06277811527252197, -0.009603084996342659, -0.007592735346406698, 0.0003933878324460238, 0.035582318902015686, -0.008050025440752506, 0.012528013437986374, 0.0023123330902308226, 0.0007474098820239305, -0.015263124369084835, -0.015012908726930618, 0.01827433332800865, -0.009853299707174301, -0.034667741507291794, 0.01989641785621643, 0.003203185275197029, 0.011173400096595287, -0.0028731601778417826, -0.039482224732637405, -0.005155294667929411, -0.024262242019176483, 0.015185470692813396, 0.04524580016732216, -0.01449522189795971, 0.051216453313827515, -0.03765306621789932, 0.008563397452235222, 0.02666085585951805, 0.007230354938656092, 0.0391370989382267, -0.03204479441046715, -0.02736835926771164, -0.0011162615846842527, 0.001297451788559556, -0.01087141688913107, 0.030612528324127197, -0.061811767518520355, 0.0160051416605711, 0.031872231513261795, -0.01436580065637827, 0.013494362123310566, 0.0335460864007473, -0.015314892865717411, -0.01449522189795971, 0.006264006718993187, -0.0013028443790972233, -0.04541836306452751, 0.00039096115506254137, 0.002597060753032565, 0.025280358269810677, -0.034477923065423965, -0.025004258379340172, 0.007929231971502304, 0.028369219973683357, -0.005845543462783098, -0.033925723284482956, 0.05087132751941681, -0.006565990392118692, 0.015375289134681225, -0.015496082603931427, -0.0039279465563595295, -0.014037932269275188, -0.01180325262248516, 0.0002347115078009665, -0.03658318147063255, 0.015539223328232765, 0.02067294716835022, -0.003095333930104971, 0.022226007655262947, 0.031026678159832954, -0.028162145987153053, 0.01703188568353653, -0.0010051745921373367, 0.02074197307229042, 0.02412419207394123, -0.003757541300728917, -0.029853254556655884, 0.040034424513578415, -0.00275452365167439, -0.01452973484992981, 0.0012489187065511942, -0.04983595386147499, -0.002601374639198184, 0.013925767503678799, 0.042139682918787, 0.020759228616952896, 0.000710740452632308, -0.013597899116575718, 0.043830789625644684, -0.00016973106539808214, -0.0182398222386837, -0.004042268730700016, -0.01618633233010769, -0.01465915609151125, 0.0011119474656879902, -0.0012640178902074695, -0.04141492024064064, 0.04586702585220337, -0.01033647358417511, -0.02795507200062275, -0.01894732564687729, -0.024745415896177292, -0.012597038410604, -0.009404637850821018, 0.01655733957886696, 0.03520268201828003, 0.003509483067318797, 0.03861941397190094, 0.002063196385279298, -0.0210008155554533, 0.011518524959683418, -0.010854160413146019, 0.02119063399732113, -0.0160051416605711, -0.007446057628840208, 0.008649678900837898, 0.00580240273848176, 0.005815345328301191, 0.027489153668284416, -0.014486594125628471, -0.03910258784890175, -0.00775235565379262, 0.019775625318288803, -0.007208784576505423, 0.026453780010342598, 0.01618633233010769, 0.004693691153079271, -0.012528013437986374, 0.060672860592603683, 0.009654853492975235, -0.0531836599111557, 0.02581530064344406, 0.014063816517591476, -0.008446917869150639, -0.05049169063568115, -0.0008250628598034382, -0.015064677223563194, -0.0003462028398644179, -0.0010127242421731353, -0.03865392506122589, -0.004654864314943552, 0.033304497599601746, 0.002780407899990678, 0.025694506242871284, -0.05442610755562782, -0.023123331367969513, -0.04586702585220337, -0.01116477232426405, 0.023692786693572998, -0.03865392506122589, 0.040068935602903366, -0.021087097004055977, -0.005271774251013994, 0.045694462954998016, -0.03534073382616043, 0.027609948068857193, -0.01150989718735218, 0.02243308164179325, -0.01927519403398037, 0.02243308164179325, 0.004659178666770458, 0.02077648602426052, -0.0645727664232254, -0.038895513862371445, -0.05777381360530853, 0.011647946201264858, -0.01261429488658905, -0.014408941380679607, -0.011259681545197964, 0.02743738517165184, -0.008632422424852848, 0.02438303455710411, -0.026436524465680122, 0.006203609984368086, 0.010612573474645615, -0.030025817453861237, 0.02850726991891861, -0.004577211569994688, 0.00331535073928535, -0.00272216834127903, 0.016867952421307564, -0.014063816517591476, 0.0532526858150959, 0.027903303503990173, -0.01438305713236332, 0.03989637270569801, 0.03744599223136902, -0.008213959634304047, -0.04037954658269882, -0.02629847452044487, 0.007204470690339804, 0.047385573387145996, -0.01176873967051506, 0.002370572881773114, 0.0223985705524683, 0.03209656476974487, 0.011630690656602383, -0.022243263199925423, 0.03423633426427841, -0.015038792975246906, 0.03578939288854599, -0.0037467561196535826, 0.004012070596218109, -0.0018604359356686473, 0.038308802992105484, 0.011147515848279, 0.007385660894215107, -0.05943041294813156, 0.00830886885523796, -0.007243297062814236, 0.003054350381717086, 0.05632429197430611, 0.03851587697863579, -0.06529752165079117, 0.019844649359583855, -0.006570304743945599, 0.007769611664116383, -0.009982721880078316, -0.007653132081031799, 0.01212249230593443, 0.020500386133790016, -0.010724739171564579, -0.015081933699548244, 0.016686761751770973, -0.029887767508625984, -0.015651388093829155, -0.013546130619943142, -0.08103519678115845, 0.001090377219952643, -0.031423572450876236, -0.0028257055673748255, -0.02916300669312477, 0.042829930782318115, -0.038860999047756195, -0.030353685840964317, -0.012691947631537914, 0.005099212285131216, -0.007480570115149021, 0.02129417099058628, -0.017998233437538147, -0.028386477380990982, -0.08110421895980835, -0.022519363090395927, -0.00991369690746069, -0.007346834521740675, -0.04189809411764145, 0.02314058691263199, -0.0419326089322567, -0.030888628214597702, 0.020793741568922997, -0.0002626180648803711, 0.016212215647101402, -0.015047421678900719, -0.005172551143914461, -0.02453834004700184, -0.010345102287828922, 0.04973241686820984, -0.013106096535921097, 0.010940441861748695, 0.032200101763010025, 0.009922324679791927, -0.006885230541229248, -0.012320938520133495, 0.017161307856440544, 0.001150773954577744, -0.026936953887343407, -0.0009151187841780484, -0.030474478378891945, 0.001034833723679185, 0.021829115226864815, -0.03458146005868912, -0.027126772329211235, 0.013433964923024178, 0.01213974878191948, 0.008485744707286358, 0.01561687607318163, 0.015245867893099785, -0.045694462954998016, 0.027161285281181335, 0.05242438614368439, 0.04928375408053398, -0.013433964923024178, 0.028490014374256134, 0.06194981932640076, -0.01768762245774269, -0.04421042650938034, 0.04662629961967468, -0.004935278091579676, -0.02398614212870598, 0.018377870321273804, 0.007044850382953882, -0.05487477034330368, -0.0034275162033736706, -0.05480574443936348, -0.009974093176424503, 0.007251925300806761, -0.00339731783606112, 0.06533204019069672, 0.0049180216155946255, 0.048524484038352966, -0.015219983644783497 ]
Hardware-based acceleration is an extensive attempt to facilitate many computationally-intensive mathematics operations. This paper proposes an FPGA-based architecture to accelerate the convolution operation - a complex and expensive computing step that appears in many Convolutional Neural Network models. We target the design to the standard convolution operation, intending to launch the product as an edge-AI solution. The project's purpose is to produce an FPGA IP core that can process a convolutional layer at a time. System developers can deploy the IP core with various FPGA families by using Verilog HDL as the primary design language for the architecture. The experimental results show that our single computing core synthesized on a simple edge computing FPGA board can offer 0.224 GOPS. When the board is fully utilized, 4.48 GOPS can be achieved.
[ -0.04416070505976677, 0.02006835676729679, -0.026224717497825623, -0.003705853596329689, 0.018898993730545044, 0.019569657742977142, -0.0348745733499527, 0.04168440401554108, -0.049078915268182755, 0.049078915268182755, 0.009208745323121548, -0.0333440825343132, 0.10689366608858109, -0.021942779421806335, -0.012751231901347637, 0.05017949268221855, 0.015571463853120804, -0.012252531945705414, -0.004028288647532463, -0.048769377171993256, 0.0326562225818634, -0.006212248466908932, -0.010249135084450245, -0.05330926179885864, -0.02648266591131687, 0.014427893795073032, -0.004961200524121523, 0.016345307230949402, -0.04006792977452278, 0.0011134757660329342, 0.02352486178278923, 0.0345306433737278, -0.05427226796746254, -0.02381720207631588, -0.0168955959379673, -0.048872556537389755, -0.019518068060278893, 0.018658241257071495, -0.028632232919335365, -0.014161347411572933, 0.0656907707452774, 0.0031835087575018406, -0.03669740632176399, 0.02041228860616684, 0.022665034979581833, -0.02042948454618454, 0.012286924757063389, -0.01349928043782711, -0.025003762915730476, 0.011203543283045292, 0.03097096085548401, -0.018520670011639595, 0.042097121477127075, 0.028494659811258316, -0.01982760615646839, -0.01190000306814909, 0.007235442753881216, 0.06479654461145401, 0.04409191757440567, -0.008374713361263275, -0.005554480943828821, -0.015657445415854454, -0.019019369035959244, 0.009458094835281372, -0.011143355630338192, -0.0077814324758946896, 0.0169987753033638, 0.0671352744102478, 0.008847617544233799, 0.007880312390625477, -0.059534408152103424, -0.05723007023334503, 0.006001591216772795, -0.02376561239361763, 0.007845919579267502, -0.003383418545126915, 0.09251736104488373, 0.02753165364265442, 0.03024870716035366, 0.032570239156484604, 0.018795814365148544, 0.022922983393073082, -0.042234692722558975, -0.0327937938272953, 0.062423426657915115, -0.021581653505563736, 0.0019109650747850537, -0.059293657541275024, -0.06273296475410461, -0.029440470039844513, -0.04938845336437225, 0.05692053586244583, -0.022252317517995834, -0.002534339437261224, 0.05650781840085983, 0.02388598769903183, -0.01190000306814909, -0.0342726968228817, -0.05052342265844345, -0.014255928806960583, -0.0343414843082428, 0.04938845336437225, 0.011401303112506866, 0.0338771753013134, 0.04519249498844147, -0.021065756678581238, 0.012673847377300262, 0.02754885144531727, 0.062182676047086716, 0.09203585982322693, -0.005098773166537285, -0.04766879975795746, 0.0657939463853836, -0.02042948454618454, -0.0012338514206930995, 0.0052406443282961845, -0.025347694754600525, -0.014574063941836357, -0.015717633068561554, -0.0024182628840208054, 0.05808989703655243, 0.026345092803239822, -0.0086627546697855, -0.011409902013838291, -0.02670622058212757, 0.07827863097190857, -0.009165753610432148, -0.021839600056409836, -0.018761420622467995, -0.04419509693980217, -0.016018573194742203, 0.007209647912532091, 0.01513295155018568, 0.0016530170105397701, 0.011151953600347042, -0.06056620180606842, 0.03017992153763771, 0.07456418126821518, 0.010601664893329144, 0.017918789759278297, 0.002542937872931361, 0.010936996899545193, 0.00830592680722475, -0.009354915469884872, 0.05881215259432793, 0.04195954650640488, -0.031194515526294708, 0.021547259762883186, -0.006986092776060104, -0.003938006702810526, -0.04065261036157608, 0.069302037358284, 0.001823907601647079, 0.027823995798826218, 0.04037746787071228, 0.007682552561163902, 0.029285700991749763, 0.004471099469810724, 0.05072978138923645, -0.042544230818748474, 0.0038111822213977575, -0.01031792163848877, -0.015003977343440056, 0.04808151349425316, -0.00511167012155056, 0.055304061621427536, 0.03962082043290138, 0.045983538031578064, -0.02395477518439293, 0.024522259831428528, 0.0334472618997097, 0.004028288647532463, 0.004539885558187962, 0.04154683277010918, -0.004720448981970549, 0.024573849514126778, -0.0031684618443250656, -0.0020334904547780752, -0.06128845363855362, -0.029492059722542763, -0.0348401814699173, -0.03993035852909088, 0.04839105159044266, -0.0045355865731835365, 0.04147804528474808, 0.0003350637562107295, 0.019053762778639793, -0.010919800028204918, 0.002172137377783656, -0.018004773184657097, 0.0338083915412426, 0.019088154658675194, 0.03097096085548401, -0.039242494851350784, 0.0048881154507398605, -0.07532082498073578, -0.02362804114818573, -0.004195954650640488, 0.007080673705786467, 0.03951764106750488, -0.04687775671482086, 0.008967993780970573, -0.002697706688195467, -0.004400163888931274, -0.01004277728497982, -0.04859741032123566, 0.012811419554054737, -0.07855377346277237, 0.013997980393469334, -0.02371402271091938, -0.015640249475836754, 0.017574859783053398, -0.028649428859353065, -0.0686829686164856, 0.02338728867471218, 0.01686980202794075, 0.0069645969197154045, -0.05334365367889404, -0.013791621662676334, 0.009965392760932446, 0.00009834268712438643, 0.028718214482069016, -0.025915179401636124, -0.05440983921289444, 0.021014166995882988, -0.025640035048127174, -0.02717052772641182, -0.014135552570223808, -0.04048064723610878, 0.010876809246838093, -0.056232672184705734, 0.01981041021645069, -0.021805208176374435, 0.0028094840236008167, 0.004673158749938011, -0.056129492819309235, 0.003989596385508776, -0.03009393811225891, -0.05499452352523804, 0.03700694441795349, -0.032725006341934204, 0.014384902082383633, -0.03724769875407219, -0.0033447262831032276, -0.03095376491546631, 0.0335676372051239, -0.006306829396635294, 0.07360117137432098, -0.04092775657773018, -0.014806217513978481, 0.00291051366366446, -0.013026376254856586, -0.022303907200694084, 0.03625029698014259, -0.006311128847301006, 0.03064422681927681, 0.00010714247764553875, -0.021186131983995438, -0.04357602074742317, -0.01742009073495865, 0.02758324332535267, -0.021873993799090385, -0.04680897295475006, 0.00988800823688507, -0.03676619380712509, -0.02330130711197853, 0.01695578545331955, 0.04144365340471268, -0.052380647510290146, -0.028701018542051315, 0.055579204112291336, -0.009380710311233997, -0.039070531725883484, -0.015597257763147354, 0.05440983921289444, -0.012398702092468739, -0.006534683518111706, 0.07518325746059418, 0.059912730008363724, 0.053137294948101044, 0.0036263195797801018, 0.04116850718855858, 0.027858387678861618, 0.013396102003753185, 0.01752327010035515, -0.04044625163078308, -0.048975735902786255, -0.0686829686164856, -0.05004192143678665, -0.025863589718937874, -0.01343909278512001, 0.02314653806388378, -0.032398272305727005, 0.05052342265844345, 0.014548269100487232, -0.07642140984535217, -0.045777179300785065, -0.07655897736549377, 0.05317169055342674, -0.022389890626072884, -0.03986157104372978, -0.013086563907563686, 0.019690033048391342, -0.0008544528973288834, -0.069921113550663, 0.001953956438228488, -0.009208745323121548, 0.045777179300785065, 0.02347327210009098, -0.0681326761841774, 0.022613445296883583, 0.042165905237197876, 0.029474861919879913, 0.013009179383516312, -0.03045506589114666, 0.018795814365148544, 0.019105352461338043, -0.004832226783037186, -0.015485480427742004, -0.04354162886738777, 0.022630641236901283, -0.018451882526278496, -0.09244857728481293, 0.04687775671482086, 0.013576664961874485, 0.0346854142844677, 0.011487286537885666, 0.005373917520046234, -0.09286129474639893, 0.022922983393073082, -0.028872983530163765, -0.023129340261220932, -0.00766965514048934, 0.0340835340321064, -0.01205477211624384, -0.0167408287525177, -0.032501451671123505, 0.03735087811946869, -0.0016175492201000452, 0.004806431941688061, 0.035063736140728, 0.002998645883053541, 0.015829412266612053, 0.019156940281391144, -0.03081619180738926, -0.033223707228899, -0.036009546369314194, -0.032105933874845505, -0.0330517441034317, -0.08625782281160355, 0.0011446444550529122, 0.021650439128279686, 0.00207970617339015, 0.003035188652575016, 0.0327765978872776, -0.025124140083789825, -0.012596462853252888, -0.00844779796898365, -0.02402356080710888, -0.016405494883656502, 0.0343070887029171, -0.01529631856828928, 0.007686851546168327, 0.022613445296883583, -0.05881215259432793, 0.031951162964105606, -0.05454741418361664, -0.0685453936457634, 0.0040777288377285, 0.02748006395995617, -0.02061864733695984, 0.07005868852138519, 0.007188152056187391, -0.024264313280582428, -0.009655854664742947, -0.04037746787071228, 0.00987941026687622, -0.03941446170210838, -0.05121128261089325, 0.026310700923204422, -0.012553471140563488, -0.008976591750979424, 0.02674061432480812, -0.015528472140431404, 0.07366996258497238, 0.012364309281110764, 0.04109971970319748, -0.04010232165455818, -0.0170589629560709, 0.023008964955806732, 0.00043098817695863545, -0.048528626561164856, -0.021409686654806137, -0.07442660629749298, -0.024539457634091377, -0.0329829566180706, -0.0024096646811813116, -0.01375722885131836, 0.011771028861403465, -0.002067883498966694, -0.0681670680642128, -0.006216547917574644, 0.01180542167276144, 0.008495088666677475, -0.0344790555536747, 0.025106942281126976, -0.02730809897184372, -0.018297113478183746, 0.008202747441828251, 0.002841727575287223, 0.06293932348489761, -0.02005116082727909, -0.024591047316789627, -0.022269513458013535, -0.0066077690571546555, -0.022579051554203033, -0.02392038144171238, 0.004557081963866949, -0.015657445415854454, 0.0018540015444159508, -0.07470175623893738, 0.03659422695636749, 0.006835623178631067, -0.02072182670235634, 0.042165905237197876, -0.02036069892346859, 0.045708391815423965, -0.015631651505827904, 0.01490079890936613, 0.05128007009625435, 0.01180542167276144, -0.025433676317334175, 0.014230133965611458, -0.052655793726444244, -0.03138367831707001, 0.005704951006919146, 0.05698931962251663, 0.04436706379055977, -0.06149481236934662, 0.014660047367215157, -0.031572841107845306, -0.039586424827575684, -0.0169987753033638, -0.012364309281110764, -0.034461859613657, -0.022922983393073082, -0.045983538031578064, -0.0170589629560709, 0.021031362935900688, -0.07607747614383698, -0.0671696662902832, 0.024728618562221527, -0.055304061621427536, -0.06287053227424622, 0.028958966955542564, 0.019380496814846992, 0.025038156658411026, -0.013095161877572536, 0.04044625163078308, -0.03738526999950409, -0.008538080379366875, 0.07449539750814438, 0.03979278355836868, -0.01680961437523365, 0.005313729867339134, 0.04034307226538658, -0.04763440415263176, -0.07057458162307739, 0.006629264447838068, 0.031160123646259308, -0.012648052535951138, 0.014290321618318558, 0.02367963083088398, 0.02672341652214527, 0.0337739959359169, 0.008172653615474701, -0.0011371209984645247, 0.008976591750979424, -0.05781475454568863, -0.01676662266254425, 0.028374284505844116, -0.05076417326927185, 0.01043829694390297, -0.014909396879374981, -0.015984179452061653, 0.004406612366437912, 0.03005954436957836, 0.0333956740796566, 0.058880940079689026, -0.014075364917516708, 0.0328797772526741, 0.008890609256923199, -0.01365404948592186, 0.0029191120993345976, -0.025055352598428726, -0.038210704922676086, -0.02723931334912777, 0.00493970513343811, 0.025691624730825424, 0.0010925173992291093, -0.03755723312497139, -0.029560845345258713, 0.010455493815243244, -0.009664453566074371, -0.008757336065173149, 0.005326626822352409, 0.017764022573828697, 0.035803187638521194, -0.007532082963734865, 0.012252531945705414, 0.0169385876506567, 0.025244515389204025, 0.011487286537885666, -0.04467660188674927, -0.009544077329337597, -0.012278326787054539, -0.017815612256526947, -0.03852023929357529, 0.017445886507630348, 0.05038585141301155, 0.009019583463668823, -0.045880358666181564, -0.024539457634091377, 0.04099654033780098, 0.022579051554203033, 0.056060709059238434, -0.015365105122327805, -0.021478474140167236, 0.017850004136562347, 0.0012768427841365337, -0.002534339437261224, -0.00750628812238574, -0.04825348034501076, -0.012510480359196663, 0.015382301062345505, -0.002347327070310712, -0.009716043248772621, 0.0085208835080266, -0.004109972156584263, -0.02058425359427929, -0.0347370021045208, 0.017506074160337448, -0.0014681542525067925, 0.019260119646787643, -0.03628469258546829, 0.006917306687682867, 0.0349261648952961, -0.04374798759818077, -0.029664024710655212, 0.0018421788699924946, -0.011917199939489365, -0.016216333955526352, -0.012175147421658039, -0.04481417313218117, 0.00023175019305199385, 0.010988586582243443, 0.00660347007215023, -0.035768795758485794, 0.012527676299214363, -0.0006932353717274964, -0.02092818357050419, -0.04116850718855858, 0.017953183501958847, -0.025760410353541374, -0.012286924757063389, -0.025674428790807724, 0.04990434646606445, 0.03711012378334999, -0.024487867951393127, 0.021770814433693886, -0.006895810831338167, 0.0175920557230711, -0.028752608224749565, 0.016164744272828102, -0.0005986543837934732, -0.003222201019525528, -0.02985318750143051, -0.021478474140167236, -0.03810752555727959, 0.05894972383975983, 0.00772984279319644, -0.026431076228618622, 0.011323918588459492, -0.01517594326287508, 0.019363299012184143, 0.003791836090385914, -0.02037789486348629, -0.04137486591935158, -0.0347026102244854, -0.04653382673859596, -0.006414307747036219, 0.00871434435248375, -0.031968358904123306, 0.010713442228734493, -0.02042948454618454, -0.017626449465751648, -0.005704951006919146, 0.02369682677090168, -0.02761763706803322, -0.0330345444381237, 0.0003678446519188583, 0.045673999935388565, 0.052208684384822845, -0.04285376891493797, -0.029784400016069412, 0.007364416494965553, -0.015743428841233253, -0.006882913410663605, 0.005541583523154259, 0.005326626822352409, 0.031555645167827606, -0.03040347620844841, 0.0666193813085556, 0.02015434019267559, 0.007575074210762978, 0.03748844936490059, -0.002082930412143469, 0.012940393760800362, 0.0083145247772336, -0.027652030810713768, 0.03655983507633209, -0.03841705992817879, 0.006474495865404606, 0.066034696996212, -0.0167580246925354, 0.04629307612776756, -0.00016551665612496436, 0.02075621858239174, -0.03048945777118206, -0.041993942111730576, -0.014840610325336456, -0.018761420622467995, -0.07951678335666656, 0.010790826752781868, -0.0037810883950442076, -0.013954988680779934, -0.018331507220864296, 0.02993916906416416, -0.024264313280582428, -0.0328969731926918, -0.009793426841497421, 0.021409686654806137, -0.01650007627904415, 0.018727026879787445, -0.002239848719909787, 0.04639625549316406, -0.026327896863222122, -0.05320608243346214, 0.02058425359427929, 0.006238043308258057, 0.05870897322893143, 0.015657445415854454, 0.024917781352996826, 0.032346684485673904, 0.017987577244639397, -0.015726232901215553, 0.038485847413539886, 0.02350766398012638, 0.0027213518042117357, 0.025485266000032425, -0.014823414385318756, 0.04429827630519867, 0.0016562413657084107, -0.005709249991923571, -0.014608457684516907, -0.018331507220864296, -0.0050643798895180225, 0.007084972690790892, -0.014126954600214958, 0.05506330728530884, -0.029371684417128563, -0.055854350328445435, 0.019311709329485893, 0.012501881457865238, 0.022527461871504784, -0.021908387541770935, 0.04677457734942436, 0.059087298810482025, 0.02067023701965809, 0.022510265931487083, -0.029440470039844513, -0.006981793791055679, -0.07532082498073578, -0.04068700596690178, -0.05640463903546333, -0.009397907182574272, -0.0026891082525253296, 0.011667849496006966, -0.021134542301297188, -0.022321103140711784, -0.004935405682772398, 0.018400292843580246, -0.010894005186855793, 0.019449282437562943, 0.04020550101995468, 0.1018722802400589, -0.022303907200694084, 0.002010919852182269, 0.04670579358935356, -0.021444080397486687, 0.010679048486053944, 0.009690248407423496, 0.02006835676729679, -0.034049142152071, -0.01977601647377014, 0.05853701010346413, 0.008950796909630299, -0.03145246580243111, -0.07538961619138718, 0.014092560857534409, -0.019586853682994843, 0.04054943099617958, -0.017566261813044548, 0.028271105140447617, 0.0341695174574852, -0.02742847427725792, 0.013954988680779934, -0.011212141253054142, -0.019019369035959244, 0.02668902464210987, 0.012656650505959988, 0.035063736140728, 0.004406612366437912, -0.067891925573349, -0.010851014405488968, 0.046258680522441864, -0.0038133319467306137, 0.005679156165570021, -0.031779199838638306, -0.010171751491725445, 0.01036091335117817, 0.011392705142498016, -0.005107371136546135, -0.011237936094403267, -0.00999978557229042, -0.024539457634091377, 0.025743214413523674, 0.04116850718855858, -0.018211131915450096, 0.00865415669977665, 0.017643645405769348, -0.032621830701828, 0.008228542283177376, -0.02029191330075264, 0.025244515389204025, -0.08845898509025574, -0.005223447922617197, 0.012716838158667088, -0.006513188127428293, -0.025278907269239426, 0.032570239156484604, -0.019208529964089394, 0.02342168241739273, 0.0037273492198437452, -0.042131513357162476, -0.01338750310242176, -0.035768795758485794, -0.0011704391799867153, -0.031142927706241608, -0.005752241238951683, 0.010644655674695969, 0.015863804146647453, -0.028391480445861816, 0.008146858774125576, 0.0343242846429348, -0.05086735263466835, -0.02324971742928028, 0.006070377305150032, 0.01989639177918434, 0.0040605319663882256, 0.055854350328445435, 0.0349433608353138, 0.0174716804176569, 0.0014025925192981958, -0.005232045892626047, 0.017901593819260597, 0.04381677508354187, 0.014789020642638206, 0.02980159781873226, -0.007385912351310253, -0.04447024315595627, 0.0036929561756551266, -0.024848993867635727, 0.04140925779938698, -0.0025278907269239426, -0.03004234842956066, -0.019449282437562943, -0.03762602061033249, -0.02682659588754177, 0.05100492760539055, 0.018916189670562744, 0.016035769134759903, 0.007884611375629902, -0.006306829396635294, 0.0335332453250885, 0.011212141253054142, 0.004935405682772398, 0.003454354126006365, 0.035700008273124695, -0.025347694754600525, 0.08653297275304794, 0.0023838698398321867, -0.03045506589114666, 0.035700008273124695, 0.012983384542167187, -0.0011424948461353779, -0.019260119646787643, -0.0166290495544672, -0.009208745323121548, -0.00042319600470364094, 0.04422949254512787, 0.0038391267880797386, -0.0015638100448995829, 0.0331721194088459, -0.005623267497867346, -0.02739408239722252, -0.06118527427315712, -0.029199717566370964, -0.04804712161421776, -0.03759162873029709, -0.0066421618685126305, -0.005864018574357033, -0.01982760615646839, -0.0013789472868666053, -0.0008141485159285367, -0.04381677508354187, 0.0037961353082209826, 0.032553043216466904, 0.021788010373711586, 0.020893791690468788, 0.05420348048210144, 0.0042432453483343124, -0.03965521231293678, -0.005932805128395557, -0.019242923706769943, 0.05145203694701195, -0.012708240188658237, 0.022080352529883385, -0.02041228860616684, 0.0044238087721168995, 0.0008447798318229616, 0.004574278369545937, 0.009096967987716198, 0.017549065873026848, -0.04863180220127106, -0.028958966955542564, 0.011108961887657642, 0.02385159581899643, 0.024814601987600327, -0.03666301444172859, 0.00024384151038248092, 0.05341244116425514, 0.019483676180243492, -0.018090756610035896, -0.04760001227259636, 0.014720235019922256, 0.0018507771892473102, -0.04330087825655937, -0.002852475503459573, -0.015571463853120804, 0.01754046604037285, 0.011263730935752392, 0.006220846902579069, 0.0015681091463193297, 0.007501988671720028, -0.009053976275026798, 0.00034742377465590835, 0.006710948422551155, -0.008310225792229176, 0.011100363917648792, 0.001481051673181355, -0.003383418545126915, -0.012940393760800362, 0.045536428689956665, -0.02742847427725792, -0.014531073160469532, -0.01512435358017683, -0.03724769875407219, 0.013086563907563686, 0.018589455634355545, -0.0005148213240318, 0.004591475240886211, 0.03611272573471069, 0.016018573194742203, 0.059293657541275024, -0.004514090716838837, -0.01528772059828043, -0.014273124746978283, 0.0009775155922397971, -0.02345607429742813, -0.03621590510010719, 0.02349046804010868, 0.00763956131413579, -0.029027752578258514, 0.004995593801140785, -0.019741622731089592, -0.0033038845285773277, -0.012338514439761639, 0.05705810710787773, 0.0003433933306951076, 0.013980783522129059, -0.05881215259432793, 0.002914812881499529, -0.029578041285276413, 0.0078115263022482395, -0.009165753610432148, 0.0046000732108950615, -0.0329485647380352, -0.039483245462179184, 0.0012327766744419932, 0.0066077690571546555, 0.01360245980322361, -0.01740289479494095, -0.03783237934112549, 0.03989596292376518, -0.006491692271083593, -0.0009850390488281846, -0.03968960419297218, 0.04825348034501076, -0.027995960786938667, 0.03128049895167351, 0.011280927807092667, 0.003106124233454466, -0.004548483993858099, -0.012794222682714462, 0.012089164927601814, -0.03690376505255699, 0.010283528827130795, -0.014488081447780132, 0.002783689182251692, -0.014161347411572933, 0.04089336097240448, 0.05788354203104973, 0.0018583006458356977, -0.0016712883953005075, -0.01183981541544199, -0.027978764846920967, -0.021478474140167236, -0.04794394224882126, 0.031933967024087906, -0.0025644334964454174, -0.009612863883376122, 0.02758324332535267, 0.0166978370398283, 0.007609467022120953, -0.059018511325120926, 0.05808989703655243, 0.02362804114818573, 0.014823414385318756, 0.028443070128560066, -0.0014251628890633583, 0.03707573190331459, -0.004069130402058363, -0.035218507051467896, 0.0002641280589159578, -0.0344274640083313, -0.017566261813044548, -0.045777179300785065, -0.018331507220864296, 0.02075621858239174, 0.028615035116672516, 0.01719653606414795, -0.0003181359206791967, 0.007308527827262878, 0.03143526613712311, 0.0026353690773248672, -0.0005717847961932421, -0.007609467022120953, -0.04010232165455818, -0.011384107172489166, 0.0033791193272918463, -0.05062660202383995, -0.002145267790183425, 0.014926593750715256, -0.009071173146367073, -0.0016841856995597482, 0.02392038144171238, -0.014281723648309708, -0.016104556620121002, -0.015356507152318954, 0.04010232165455818, -0.011091765947639942, 0.00816405564546585, 0.011306722648441792, -0.021788010373711586, 0.014625653624534607, -0.022063156589865685, -0.03697255253791809, -0.09746996313333511, 0.042922552675008774, -0.04687775671482086, 0.01737709902226925, 0.018211131915450096, -0.032535847276449203, 0.011994583532214165, -0.011237936094403267, 0.009664453566074371, -0.04323209077119827, 0.018400292843580246, -0.03659422695636749, -0.008353217504918575, -0.028735412284731865, -0.035459257662296295, 0.03028310090303421, -0.04649943485856056, 0.07951678335666656, 0.009045378305017948, 0.04529567435383797, 0.0004729047359433025, 0.0168612040579319, -0.008189850486814976, -0.025210121646523476, 0.022045958787202835, -0.0029642528388649225, 0.014058168046176434, 0.0036435159854590893, 0.007166656199842691, 0.005687754135578871, 0.004716149996966124, -0.002306485315784812, 0.004320629872381687, -0.03621590510010719, -0.0025751811917871237, -0.02696416899561882 ]
Black-box nature of Artificial Intelligence (AI) models do not allow users to comprehend and sometimes trust the output created by such model. In AI applications, where not only the results but also the decision paths to the results are critical, such black-box AI models are not sufficient. Explainable Artificial Intelligence (XAI) addresses this problem and defines a set of AI models that are interpretable by the users. Recently, several number of XAI models have been to address the issues surrounding by lack of interpretability and explainability of black-box models in various application areas such as healthcare, military, energy, financial and industrial domains. Although the concept of XAI has gained great deal of attention recently, its integration into the IoT domain has not yet been fully defined. In this paper, we provide an in-depth and systematic review of recent studies using XAI models in the scope of IoT domain. We categorize the studies according to their methodology and applications areas. In addition, we aim to focus on the challenging problems and open issues and give future directions to guide the developers and researchers for prospective future investigations.
[ -0.030436374247074127, 0.03512679412961006, -0.028125401586294174, -0.018504904583096504, 0.06624790281057358, -0.0060256486758589745, 0.009603377431631088, -0.0075834160670638084, 0.013532032258808613, 0.019600477069616318, 0.0031904270872473717, -0.04772587865591049, 0.04081007465720177, 0.014139733277261257, -0.01877879723906517, 0.009834474883973598, 0.043001219630241394, -0.018522022292017937, -0.016382232308387756, -0.03382579982280731, 0.008935763500630856, 0.02869030460715294, -0.020730286836624146, 0.005999971181154251, 0.0560111440718174, 0.014293797314167023, 0.0013748151250183582, -0.003984289243817329, -0.07415656745433807, 0.056524693965911865, 0.04276156425476074, -0.021654674783349037, -0.025848664343357086, -0.04053618386387825, -0.06768584251403809, -0.0019322304287925363, -0.010219637304544449, 0.06368014961481094, -0.017135439440608025, 0.06094122305512428, -0.02023385465145111, -0.029066909104585648, 0.01263332087546587, -0.006068444810807705, -0.03824232891201973, -0.017092643305659294, -0.05142343416810036, -0.052998319268226624, -0.023845819756388664, 0.023092614486813545, -0.03197702392935753, -0.08476992696523666, 0.03718099370598793, 0.002922953339293599, -0.026088319718837738, 0.0169899333268404, 0.049951259046792984, -0.009363721124827862, 0.037215229123830795, -0.009988539852201939, 0.03351767361164093, 0.03683862462639809, -0.029135381802916527, -0.0038152458146214485, 0.003318814327940345, -0.015260983258485794, 0.013343730941414833, 0.007198253646492958, -0.012658998370170593, -0.013155429624021053, -0.003671879880130291, 0.052827138453722, -0.001938649802468717, -0.01840219460427761, -0.008875849656760693, -0.03998839855194092, 0.0013726752949878573, 0.032028377056121826, -0.002764608711004257, 0.018059827387332916, 0.016125457361340523, 0.054847098886966705, 0.011400801129639149, 0.016099780797958374, 0.03803690895438194, 0.012316632084548473, -0.0015684660756960511, -0.07456740736961365, 0.017683224752545357, -0.043480534106492996, -0.05005396902561188, 0.03526373952627182, -0.02115824446082115, -0.01041649840772152, 0.02679017186164856, -0.025540534406900406, 0.01763186976313591, 0.0002163862664019689, -0.028793014585971832, -0.02655051462352276, 0.04639064893126488, 0.03283293917775154, 0.00012798618990927935, 0.037591833621263504, -0.012453578412532806, -0.05916091427206993, 0.0023302314803004265, -0.03882434964179993, -0.02601984702050686, 0.11667847633361816, -0.009355162270367146, 0.028810134157538414, -0.05792839825153351, -0.023229561746120453, -0.025437824428081512, 0.032319389283657074, -0.021654674783349037, -0.06765159964561462, 0.005362313706427813, 0.04611675441265106, -0.04563744366168976, 0.06237915903329849, 0.07744327932596207, -0.022253816947340965, -0.029375039041042328, 0.10976266860961914, 0.054230839014053345, -0.03611965477466583, 0.0470411442220211, 0.021329427137970924, 0.03755759447813034, 0.08360587805509567, 0.045226603746414185, -0.0036954174283891916, 0.007309522945433855, -0.016733158379793167, 0.039337899535894394, -0.0006349827162921429, -0.016134018078446388, -0.042932748794555664, -0.04039923846721649, -0.010750304907560349, -0.039337899535894394, 0.017974236980080605, 0.008610514923930168, 0.028056927025318146, -0.006038487423211336, 0.02305837720632553, -0.029717404395341873, 0.0050156679935753345, -0.020952824503183365, 0.026601869612932205, 0.002053128555417061, -0.021945687010884285, 0.06994545459747314, 0.00635517667979002, 0.057825688272714615, -0.02389717474579811, 0.00637229485437274, 0.027115419507026672, 0.05008820444345474, -0.021089771762490273, 0.018367957323789597, 0.05717518925666809, 0.05518946424126625, -0.018111182376742363, -0.007065586745738983, -0.019720304757356644, -0.055531833320856094, 0.032781582325696945, -0.0008751741261221468, -0.04365171864628792, -0.051491908729076385, 0.02122671715915203, -0.017289504408836365, 0.011358005926012993, 0.034014102071523666, 0.003470739582553506, -0.048273663967847824, 0.002800985239446163, -0.05412812903523445, -0.01763186976313591, 0.016211049631237984, -0.02932368405163288, 0.009243893437087536, 0.015106918290257454, 0.07525213807821274, -0.03182295709848404, 0.016801631078124046, -0.00022735269158147275, -0.015748854726552963, 0.01144359726458788, 0.047143854200839996, -0.028519121930003166, 0.022424999624490738, -0.04580862447619438, 0.02160331979393959, -0.025163931772112846, -0.016630448400974274, -0.04005686938762665, -0.008747462183237076, 0.007874427363276482, -0.037591833621263504, -0.015432165935635567, 0.03338072448968887, 0.00830666534602642, 0.0016797352582216263, -0.03772877901792526, 0.0000628897687420249, -0.008049890398979187, -0.004994269926100969, 0.07107526808977127, -0.0560111440718174, -0.035982709378004074, -0.008833053521811962, -0.001674385741353035, 0.004328795243054628, -0.05597690865397453, -0.05892125889658928, -0.022989904507994652, 0.01641646958887577, 0.013557709753513336, 0.019942844286561012, -0.016887223348021507, 0.0413578636944294, -0.034835781902074814, -0.003475019009783864, -0.0063851336017251015, -0.008430772460997105, 0.028279466554522514, -0.013309494592249393, 0.03023095428943634, 0.06189984828233719, -0.035537634044885635, 0.0016422888729721308, -0.011058434844017029, 0.01328381709754467, 0.00999709963798523, -0.024753091856837273, -0.041186679154634476, -0.042487673461437225, 0.007403673604130745, -0.006470725405961275, -0.0627557635307312, 0.07401961833238602, -0.03153194487094879, 0.01393431331962347, 0.06255034357309341, 0.0033594705164432526, 0.033089712262153625, 0.011974264867603779, 0.01235942728817463, 0.02374311164021492, -0.0019985639955848455, -0.045979809015989304, 0.041255153715610504, 0.056832823902368546, -0.000712015142198652, 0.018367957323789597, 0.0048273662105202675, 0.058750078082084656, 0.06532350927591324, 0.06898683309555054, 0.0476231686770916, -0.057517558336257935, -0.012427900917828083, 0.1098996177315712, -0.0007398324087262154, 0.014824465848505497, -0.023623282089829445, 0.03177160397171974, -0.021654674783349037, -0.018213892355561256, 0.013369408436119556, -0.0031904270872473717, 0.011726049706339836, -0.002514253370463848, 0.006667586043477058, -0.0012828041799366474, 0.001171535113826394, -0.015038444660604, -0.04854755848646164, 0.03841350972652435, -0.0014069119933992624, -0.0008473568595945835, -0.03199414163827896, -0.05084141343832016, 0.015920037403702736, -0.06368014961481094, -0.001407981850206852, 0.0008248890517279506, -0.00007850355177652091, 0.0007901174831204116, -0.028382176533341408, 0.035845763981342316, -0.01369465608149767, -0.012025619857013226, -0.005880143027752638, 0.03594847396016121, -0.04344629868865013, -0.03731793910264969, -0.04310392960906029, -0.018299484625458717, 0.061180878430604935, 0.007078425493091345, 0.013677538372576237, 0.009012795984745026, 0.09086404740810394, -0.0032289433293044567, -0.02862183190882206, 0.014636164531111717, -0.0015845145098865032, -0.02976875938475132, -0.06207102909684181, -0.0021269512362778187, 0.04009110853075981, 0.03587999939918518, -0.019069809466600418, 0.01977165974676609, -0.013343730941414833, 0.02557477168738842, -0.016930019482970238, -0.11428190767765045, 0.015962833538651466, -0.08312656730413437, -0.016673244535923004, 0.03305547684431076, -0.011452156119048595, 0.0028330821078270674, -0.02220246195793152, -0.02754337713122368, 0.03466460108757019, -0.03329513221979141, -0.00528528168797493, 0.016587652266025543, -0.005032786168158054, -0.03083009459078312, 0.03642778471112251, -0.030710266903042793, 0.0016208910383284092, 0.01412261463701725, -0.06203679367899895, -0.08278419822454453, -0.01110123097896576, -0.028056927025318146, -0.04159751906991005, -0.026242384687066078, 0.01816253736615181, 0.03230227157473564, -0.00976600218564272, 0.0009404377196915448, -0.03632507473230362, -0.03642778471112251, 0.01198282465338707, -0.02518104948103428, 0.005152614321559668, -0.017803054302930832, -0.009081268683075905, 0.053785763680934906, -0.0019397196592763066, 0.04841060936450958, -0.020353682339191437, -0.031121106818318367, 0.019206754863262177, -0.07148610800504684, -0.016741717234253883, -0.029974179342389107, -0.017666107043623924, -0.04296698421239853, 0.023554809391498566, -0.04769163951277733, 0.07956595718860626, -0.022236699238419533, 0.04176870360970497, 0.03913247957825661, -0.012308072298765182, 0.0007976067718118429, -0.050875648856163025, -0.00919253844767809, 0.07525213807821274, -0.01650206185877323, -0.0206789318472147, -0.05741484835743904, 0.05104683339595795, -0.08696106821298599, 0.056764353066682816, 0.04207683354616165, -0.001446498092263937, 0.06504961848258972, 0.04861602932214737, -0.010253873653709888, 0.00041993381455540657, -0.014978530816733837, -0.1004503071308136, 0.06436488777399063, 0.0005114098312333226, -0.0042731608264148235, 0.025591889396309853, 0.024547671899199486, -0.007562017999589443, 0.003070598701015115, 0.005820229183882475, -0.004917237441986799, 0.04098125919699669, -0.024444961920380592, 0.012487814761698246, -0.03707828372716904, 0.04067312926054001, 0.03047061152756214, -0.03516102954745293, -0.023092614486813545, -0.003761750878766179, -0.01932658441364765, -0.0245819091796875, -0.02947774901986122, 0.00020675722043961287, -0.036153893917798996, 0.03158330172300339, 0.050738703459501266, -0.04710961878299713, -0.03632507473230362, 0.03546915948390961, 0.007989976555109024, -0.04341205954551697, -0.011666135862469673, -0.01064759586006403, -0.009295248426496983, -0.0277145616710186, 0.019651832059025764, 0.019823014736175537, 0.029203854501247406, -0.005995691753923893, 0.012068415991961956, -0.029426394030451775, -0.0010319137945771217, -0.035914234817028046, -0.01665612682700157, 0.032781582325696945, 0.00999709963798523, 0.016159694641828537, -0.05142343416810036, 0.03177160397171974, 0.013900076039135456, 0.044473398476839066, -0.031018396839499474, -0.006504961755126715, 0.017246708273887634, -0.005161173641681671, -0.020593339577317238, -0.03687286376953125, -0.02420530468225479, 0.00627814419567585, -0.04967736825346947, -0.019668949767947197, -0.00028405713965184987, -0.023024141788482666, 0.00769040547311306, -0.040707364678382874, 0.022630419582128525, -0.04211106896400452, -0.026516279205679893, 0.08976847678422928, -0.0028587596025317907, 0.023315152153372765, 0.05666164308786392, 0.0269442368298769, -0.03353479132056236, -0.017161116003990173, -0.008858731016516685, 0.036290839314460754, 0.010091249831020832, 0.013540592044591904, -0.013480677269399166, -0.004219666123390198, 0.001548138097859919, 0.039269428700208664, 0.034476298838853836, -0.009646173566579819, 0.04457610845565796, -0.04539778456091881, 0.05443625897169113, 0.00742507167160511, 0.0060641649179160595, 0.01985725201666355, -0.011700372211635113, 0.047897059470415115, -0.009586259722709656, 0.04539778456091881, -0.04799976944923401, -0.05998259410262108, -0.03341496363282204, -0.011529188603162766, -0.01848778687417507, -0.029443511739373207, -0.025814427062869072, -0.06730923801660538, -0.07230778783559799, 0.0277145616710186, 0.03841350972652435, 0.023931412026286125, -0.0167502760887146, -0.022698892280459404, -0.0012282395036891103, 0.011058434844017029, 0.02021673694252968, 0.0078444704413414, -0.02405123971402645, 0.018504904583096504, 0.02634509466588497, 0.0025420705787837505, -0.0037938477471470833, -0.04351476952433586, 0.01946352981030941, -0.027885744348168373, 0.035537634044885635, 0.019583359360694885, -0.00675745727494359, 0.0009538114536553621, 0.02656763419508934, 0.051183778792619705, -0.001342718256637454, -0.041323624551296234, 0.047897059470415115, 0.010296669788658619, -0.04368595406413078, 0.014644723385572433, 0.004506397992372513, 0.018984217196702957, 0.02091858722269535, 0.036598969250917435, -0.014473539777100086, -0.005199689883738756, -0.018076946958899498, -0.04067312926054001, 0.031942784786224365, 0.021243836730718613, 0.05868160352110863, 0.02939215674996376, -0.0033701693173497915, -0.02709830179810524, -0.04673301428556442, 0.04817095398902893, 0.0418371744453907, 0.021500609815120697, 0.029066909104585648, 0.023315152153372765, 0.03329513221979141, -0.02199704200029373, -0.013104074634611607, 0.03594847396016121, -0.0022596183698624372, -0.005691841710358858, -0.019634714350104332, -0.006397972349077463, 0.02105553448200226, -0.005315238609910011, -0.008499246090650558, 0.0012870837235823274, -0.0523478239774704, 0.016202490776777267, 0.02083299681544304, -0.012907213531434536, 0.021945687010884285, -0.004853043705224991, -0.0020702469628304243, -0.040262289345264435, 0.012196803465485573, 0.0853177085518837, 0.025454942137002945, 0.01271035335958004, -0.05474438890814781, 0.00778455613180995, -0.039646029472351074, 0.01469607837498188, 0.0019825154449790716, 0.020559102296829224, 0.04252190887928009, -0.029888587072491646, -0.026054084300994873, 0.01853914186358452, -0.01469607837498188, 0.028347939252853394, -0.0037339336704462767, 0.014867261052131653, -0.022784484550356865, -0.005516378674656153, -0.03343208134174347, -0.007467867340892553, -0.005982853006571531, -0.02114112675189972, -0.002850200282409787, 0.01342932227998972, -0.04734927415847778, 0.011589103378355503, 0.00022427675139624625, 0.002141929930076003, 0.023263797163963318, 0.0013983527896925807, 0.03341496363282204, -0.050190914422273636, 0.04228225350379944, 0.010844456031918526, 0.06587129831314087, 0.050259388983249664, 0.023332271724939346, 0.043788664042949677, -0.020781641826033592, 0.018813034519553185, 0.01064759586006403, -0.007771717384457588, 0.009646173566579819, -0.037899963557720184, 0.017905764281749725, -0.02213398925960064, 0.036907099187374115, -0.013412204571068287, 0.03389427438378334, 0.01580020971596241, -0.003594847396016121, 0.014148292131721973, 0.014987089671194553, -0.025215286761522293, 0.04091278463602066, -0.007566297892481089, -0.005178291816264391, 0.0037360733840614557, 0.011135467328131199, 0.005764594301581383, -0.01603986695408821, 0.012034179642796516, 0.00926957093179226, -0.009295248426496983, -0.027218129485845566, -0.00976600218564272, 0.020559102296829224, -0.010305228643119335, 0.011392242275178432, 0.0261739119887352, -0.0059657348319888115, 0.0106047997251153, 0.009235333651304245, 0.0006809881888329983, 0.01985725201666355, 0.08819358795881271, -0.022253816947340965, 0.05381999909877777, 0.009064150974154472, -0.005713239312171936, 0.009723206050693989, 0.04991702362895012, 0.03127517178654671, 0.04036499932408333, 0.009945744648575783, 0.014978530816733837, 0.024102594703435898, -0.01443074457347393, 0.02268177457153797, 0.028296584263443947, 0.0586131289601326, 0.02489003911614418, 0.018898626789450645, 0.0050755818374454975, 0.07059595733880997, 0.03351767361164093, -0.005897261667996645, -0.01968606933951378, 0.006410811096429825, 0.013865839689970016, 0.002078806050121784, 0.025609007105231285, -0.015817327424883842, -0.01749492436647415, -0.03261040151119232, 0.03670167922973633, 0.020422156900167465, 0.010818778537213802, 0.02001131698489189, 0.021637557074427605, -0.00041966632124967873, -0.04841060936450958, -0.023914294317364693, -0.0028330821078270674, -0.03000841662287712, 0.021774504333734512, -0.008666150271892548, -0.0169899333268404, 0.0014229604275897145, -0.0025335114914923906, -0.00662051048129797, 0.010253873653709888, -0.0049001192674040794, 0.03947484865784645, 0.012813063338398933, 0.0017835149774327874, -0.04632217437028885, 0.008910086005926132, -0.03444205969572067, -0.018658969551324844, 0.0381738543510437, 0.00868326798081398, -0.03411681205034256, 0.007540620397776365, -0.01075886469334364, 0.027509141713380814, -0.006162595469504595, 0.010733187198638916, 0.03442494198679924, -0.042179543524980545, -0.03885858878493309, -0.02312685176730156, 0.010998521000146866, 0.02221957966685295, 0.05477862432599068, 0.03885858878493309, 0.0685417577624321, -0.008323783054947853, 0.013300934806466103, -0.01347211841493845, -0.00020969942852389067, 0.016322318464517593, 0.03267887234687805, 0.014114055782556534, -0.017734579741954803, -0.03848198428750038, 0.011280973441898823, 0.04276156425476074, -0.04954041913151741, -0.02343498170375824, 0.00829810556024313, 0.0033637499436736107, 0.026773054152727127, -0.012470696121454239, -0.044849999248981476, 0.04091278463602066, 0.043309349566698074, 0.011272414587438107, 0.03738641366362572, 0.020935706794261932, -0.02672169916331768, 0.024410724639892578, -0.0258829016238451, -0.01939505711197853, -0.021551964804530144, -0.011811641044914722, 0.010673273354768753, -0.0029935662169009447, -0.0005723938229493797, 0.014601927250623703, -0.04943770915269852, -0.004669021815061569, 0.028570476919412613, -0.005657604895532131, 0.025249522179365158, -0.05334068834781647, 0.017648989334702492, -0.0041233752854168415, 0.011888673529028893, -0.006902962923049927, 0.049163818359375, 0.01228239480406046, -0.0009281339589506388, 0.07703243941068649, -0.0009024564642459154, 0.05895549803972244, 0.04235072433948517, -0.011049875989556313, 0.012231039814651012, -0.019480649381875992, 0.01734085939824581, 0.016014188528060913, 0.006932919844985008, 0.019138282164931297, 0.032918531447649, -0.05104683339595795, 0.007035629823803902, -0.04060465469956398, 0.024770209565758705, -0.004243203904479742, 0.0014925035648047924, -0.002105553401634097, 0.01953200437128544, 0.010425057262182236, -0.004523516166955233, 0.008738902397453785, -0.06813091784715652, -0.00488300109282136, 0.01778593473136425, -0.07977137714624405, 0.002848060568794608, 0.011589103378355503, -0.010853014886379242, -0.009791679680347443, 0.024153949692845345, 0.0005245160427875817, 0.024325134232640266, -0.019634714350104332, -0.01289865467697382, -0.0012753148330375552, 0.0685417577624321, -0.001965397270396352, 0.05351186916232109, -0.009868712164461613, 0.020199619233608246, -0.036153893917798996, -0.035606108605861664, -0.009218215942382812, -0.028947079554200172, -0.019959961995482445, 0.037215229123830795, 0.03358614444732666, 0.07888121902942657, 0.0350925587117672, -0.0018658969784155488, 0.03360326215624809, -0.02405123971402645, -0.017614752054214478, -0.030213836580514908, -0.017315180972218513, -0.030812976881861687, -0.06100969389081001, -0.030573321506381035, -0.038139618933200836, 0.008987118490040302, -0.01714399829506874, -0.04954041913151741, -0.0075491792522370815, 0.02610543929040432, 0.01932658441364765, -0.010236755944788456, -0.04043347388505936, -0.0021012737415730953, 0.006299541797488928, -0.027218129485845566, -0.010099809616804123, -0.022579064592719078, 0.02846776694059372, -0.032850056886672974, 0.014216764830052853, 0.010467853397130966, -0.008807376027107239, 0.010296669788658619, 0.018367957323789597, -0.0008591256919316947, -0.016852986067533493, -0.01668180339038372, -0.01465328224003315, 0.007831631228327751, 0.007840191014111042, 0.029580457136034966, 0.033106833696365356, -0.009012795984745026, -0.03837927430868149, 0.010741746053099632, 0.0018872948130592704, 0.01538081094622612, 0.028210991993546486, 0.012684675864875317, 0.015449284575879574, 0.030111126601696014, -0.03327801451086998, 0.004238924011588097, 0.005726078059524298, -0.0230412594974041, 0.031035514548420906, -0.019600477069616318, -0.07025358825922012, 0.009868712164461613, 0.007048468571156263, -0.0303165465593338, -0.04098125919699669, -0.01736653596162796, -0.009226774796843529, -0.006248186808079481, 0.02007978968322277, 0.011571984738111496, 0.06053038313984871, 0.006248186808079481, 0.03228515386581421, 0.04344629868865013, 0.004917237441986799, -0.027286602184176445, 0.011683253571391106, 0.0016123318346217275, -0.018727442249655724, -0.005174012389034033, 0.012470696121454239, -0.035537634044885635, -0.030504846945405006, 0.011298091150820255, -0.012179684825241566, 0.00342580396682024, 0.018145419657230377, 0.04303545877337456, 0.02016538195312023, 0.03175448626279831, -0.0008115153759717941, -0.007159737404435873, 0.033774446696043015, 0.0018926443299278617, 0.005293840542435646, 0.0175206009298563, -0.013412204571068287, -0.02061045728623867, -0.020593339577317238, -0.0006210740539245307, 0.021620439365506172, 0.012025619857013226, -0.041255153715610504, -0.021551964804530144, -0.05635351315140724, -0.007095544133335352, -0.031942784786224365, 0.003806686494499445, -0.0026319418102502823, 0.01816253736615181, -0.05734637379646301, -0.0481024794280529, -0.009201097302138805, -0.01285585854202509, 0.0029464908875524998, 0.034852899610996246, 0.06809668242931366, -0.03276446461677551, 0.0020103328861296177, 0.011306650936603546, -0.007476426661014557, -0.03718099370598793, 0.02085011452436447, -0.0049771517515182495, -0.011623339727520943, -0.02288719452917576, 0.02778303436934948, 0.001033518579788506, 0.010887252166867256, 0.008238191716372967, -0.005640486720949411, -0.055155228823423386, 0.032096851617097855, -0.016382232308387756, -0.03611965477466583, 0.010433616116642952, 0.017229590564966202, 0.01064759586006403, 0.006115519907325506, -0.00435875216498971, 0.008139761164784431, 0.016690362244844437, 0.03978297859430313, 0.01953200437128544, 0.01900133676826954, -0.03428799659013748, 0.014319474808871746, 0.001493573421612382, -0.03326089680194855, -0.03372308984398842, -0.03855045884847641, -0.012051297351717949, -0.05474438890814781, 0.007874427363276482, 0.012992805801331997, 0.02831370197236538, -0.00432451581582427, -0.0142681198194623, 0.004566311836242676, 0.0044464836828410625, -0.029974179342389107, 0.0068687261082232, -0.02054198458790779, -0.06984274834394455, -0.011888673529028893, -0.024444961920380592, -0.042179543524980545, -0.020182499662041664, 0.023571927100419998, 0.003956472035497427, -0.06713805347681046, -0.012265277095139027, -0.029118264093995094, -0.006303821690380573, -0.006659026723355055, 0.04437068849802017, -0.01687866449356079, 0.013540592044591904, -0.018059827387332916, -0.051936984062194824, 0.005362313706427813, 0.02762896940112114, -0.01477311085909605, -0.037215229123830795, 0.034698836505413055, 0.029375039041042328, 0.008349460549652576, 0.009397958405315876, -0.010176841169595718, -0.011803082190454006, -0.006196832284331322, 0.003926514647901058, 0.02235652692615986, -0.02228805422782898, -0.013420763425529003, 0.013300934806466103, -0.00852920301258564, 0.028895724564790726, 0.04368595406413078, -0.03314106911420822, -0.0031519108451902866, 0.029289446771144867, -0.030248071998357773, -0.022014159709215164, -0.013001364655792713, 0.03772877901792526, 0.03807114437222481, -0.00864903163164854, 0.03882434964179993, 0.017024170607328415, 0.041631754487752914, -0.0306075569242239, 0.0049001192674040794, 0.0065605961717665195, -0.0314292348921299, 0.03807114437222481, -0.0005536706885322928, -0.004917237441986799, 0.010356583632528782 ]
Node classification and graph classification are two graph learning problems that predict the class label of a node and the class label of a graph respectively. A node of a graph usually represents a real-world entity, e.g., a user in a social network, or a document in a document citation network. In this work, we consider a more challenging but practically useful setting, in which a node itself is a graph instance. This leads to a hierarchical graph perspective which arises in many domains such as social network, biological network and document collection. We study the node classification problem in the hierarchical graph where a 'node' is a graph instance. As labels are usually limited, we design a novel semi-supervised solution named SEAL-CI. SEAL-CI adopts an iterative framework that takes turns to update two modules, one working at the graph instance level and the other at the hierarchical graph level. To enforce a consistency among different levels of hierarchical graph, we propose the Hierarchical Graph Mutual Information (HGMI) and further present a way to compute HGMI with theoretical guarantee. We demonstrate the effectiveness of this hierarchical graph modeling and the proposed SEAL-CI method on text and social network data.
[ -0.058188583701848984, 0.041461486369371414, -0.03752569854259491, 0.02356383204460144, 0.06836734712123871, 0.02142629213631153, -0.02578619495034218, 0.007561971433460712, -0.046958018094301224, -0.001877769362181425, 0.022562921047210693, -0.03296222165226936, -0.0011811604490503669, -0.06412619352340698, -0.03219881281256676, 0.008092114701867104, 0.04064718633890152, -0.024971894919872284, 0.05954575166106224, -0.08176938444375992, 0.01274889800697565, -0.053676001727581024, 0.025175468996167183, 0.018491415306925774, 0.051809895783662796, -0.002300824038684368, 0.05676355957984924, -0.0034480553586035967, -0.09276244044303894, 0.06449941545724869, 0.005471084266901016, 0.026702282950282097, 0.04227578639984131, -0.01613333635032177, 0.02656656689941883, 0.006561059970408678, 0.047433026134967804, 0.053438495844602585, 0.000945246429182589, 0.011968526989221573, 0.024734389036893845, 0.015785561874508858, -0.008503506891429424, -0.011060920543968678, 0.02213880605995655, -0.032792575657367706, -0.0320122055709362, -0.005199650302529335, -0.0168034378439188, 0.00441927881911397, -0.03021395578980446, 0.004775535315275192, 0.02047627419233322, -0.037152476608753204, -0.037457842379808426, 0.04000253230333328, 0.04634729400277138, 0.0001766704226611182, 0.022070948034524918, 0.05045272782444954, -0.02537904493510723, 0.016506558284163475, -0.04492226615548134, 0.026634424924850464, 0.04241150617599487, -0.04295437037944794, -0.00441927881911397, -0.02878892980515957, 0.061377931386232376, -0.029518406838178635, -0.03593102842569351, -0.03462475165724754, 0.02412366308271885, -0.006442307494580746, 0.03772927448153496, 0.01854231022298336, 0.022630779072642326, -0.06276902556419373, 0.017032461240887642, -0.014267230406403542, 0.06456727534532547, 0.025311186909675598, 0.007337190210819244, 0.01842355728149414, 0.02439509704709053, -0.05038486793637276, 0.02760140784084797, -0.061581503599882126, 0.0316220186650753, 0.049163416028022766, -0.03542209044098854, 0.027703195810317993, 0.009585000574588776, -0.020628955215215683, 0.0032932532485574484, -0.012799791991710663, 0.0379667803645134, -0.03223274275660515, -0.05479566380381584, 0.016260571777820587, 0.010882792063057423, 0.04210614040493965, 0.013385070487856865, -0.02424241602420807, -0.007595900446176529, 0.005449878517538309, -0.05045272782444954, -0.0014547145692631602, -0.02882285788655281, 0.11895579099655151, -0.013427482917904854, 0.00808363314718008, -0.002052716910839081, 0.040273964405059814, -0.03728819638490677, -0.0015957328723743558, -0.04729731008410454, -0.028161238878965378, 0.04047754034399986, -0.008923380635678768, -0.01617574878036976, -0.0004805753706023097, 0.01486947387456894, -0.02629513293504715, -0.10891274362802505, 0.037457842379808426, -0.03233453258872032, -0.022749532014131546, 0.0046440595760941505, 0.0021301177330315113, -0.012409606017172337, -0.005568630527704954, 0.010908239521086216, -0.001206607325002551, 0.047500886023044586, -0.003704644972458482, 0.05577960982918739, 0.012901579961180687, -0.03606674447655678, -0.037389982491731644, -0.009585000574588776, 0.009186332114040852, -0.03197827562689781, -0.01949232816696167, 0.04709373414516449, 0.022121841087937355, 0.0015225730603560805, 0.04977414384484291, -0.051775965839624405, 0.04800982400774956, -0.02858535386621952, 0.09350888431072235, 0.018593203276395798, 0.048925913870334625, -0.007235402707010508, 0.00824055541306734, 0.02225755713880062, -0.025005823001265526, -0.04091861844062805, -0.0059036812745034695, 0.08828379213809967, -0.06242973357439041, -0.03136754781007767, 0.03895072638988495, -0.05425279587507248, 0.07722286880016327, -0.010136350058019161, 0.007277814205735922, -0.05598318576812744, 0.036677468568086624, 0.026430848985910416, 0.023241505026817322, 0.041461486369371414, -0.022240594029426575, 0.009093026630580425, -0.018169088289141655, 0.06796019524335861, -0.027974627912044525, -0.0057806880213320255, 0.028415707871317863, -0.008066668175160885, -0.011043955571949482, 0.046245504170656204, 0.034573860466480255, 0.008520470932126045, -0.0013667107559740543, 0.06368511915206909, 0.05289562791585922, 0.0008556520915590227, -0.009618929587304592, 0.04502405226230621, 0.03660961240530014, 0.08000506460666656, -0.06290474534034729, -0.01759229227900505, -0.048688407987356186, -0.0018194535514339805, 0.04526155814528465, 0.005360814277082682, -0.017744973301887512, -0.024208486080169678, -0.02392008900642395, -0.016591381281614304, 0.03511672466993332, 0.03328454867005348, -0.013113637454807758, 0.011968526989221573, -0.04200435429811478, 0.0006303410045802593, -0.021714691072702408, -0.014004278928041458, -0.022240594029426575, -0.02870410680770874, -0.05842608958482742, 0.01755836233496666, 0.006361725740134716, 0.04733124002814293, -0.02692282386124134, -0.001058697234839201, 0.0043153706938028336, 0.06351546943187714, -0.022783460095524788, 0.08305869251489639, 0.0018205138621851802, -0.02308882400393486, 0.022393275052309036, 0.027329973876476288, -0.026736212894320488, -0.010365371592342854, -0.009534106589853764, 0.00877918116748333, 0.004226306453347206, 0.005131792277097702, -0.0072396439500153065, -0.0035456018522381783, -0.015174836851656437, 0.030943434685468674, -0.02870410680770874, 0.010730111040174961, -0.004209341946989298, -0.014903402887284756, 0.019933408126235008, -0.01688826084136963, -0.01821998320519924, 0.03262292966246605, 0.000897533493116498, 0.021460222080349922, -0.00042358491919003427, 0.04376867413520813, 0.05469387769699097, -0.03996860235929489, -0.023428115993738174, 0.0171936247497797, 0.010348407551646233, -0.02183344215154648, 0.018236946314573288, 0.0177958682179451, 0.01091672107577324, 0.04122398421168327, -0.016820402815937996, 0.0470598042011261, 0.00530992029234767, -0.044107966125011444, 0.03328454867005348, 0.009534106589853764, -0.014996708370745182, 0.04258115217089653, -0.007277814205735922, 0.043836530297994614, -0.023462044075131416, -0.004754329565912485, -0.04614371806383133, -0.03969717025756836, 0.06874056905508041, -0.06582265347242355, -0.04512584209442139, 0.04454904422163963, 0.012647110968828201, -0.043904390186071396, -0.009449283592402935, -0.02427634596824646, -0.02799159288406372, -0.020425381138920784, -0.004245391581207514, -0.015191800892353058, -0.05469387769699097, -0.03854357451200485, -0.010076973587274551, -0.04119005426764488, -0.03309793770313263, -0.03372563049197197, 0.015827974304556847, 0.014530181884765625, -0.009746164083480835, 0.005721312016248703, -0.009126955643296242, -0.05238668993115425, -0.02412366308271885, 0.030061274766921997, -0.03613460063934326, -0.006213285494595766, -0.02953537181019783, -0.003342026611790061, 0.038645364344120026, -0.030892539769411087, 0.015963690355420113, 0.01369891595095396, 0.09099812805652618, 0.02151111513376236, -0.052488479763269424, -0.07559426873922348, 0.02861928381025791, -0.02107003517448902, -0.010212690569460392, -0.018762849271297455, -0.04000253230333328, 0.05184382200241089, -0.01913607120513916, 0.04214007034897804, -0.05024915188550949, 0.010840380564332008, -0.0010072732111439109, -0.06938522309064865, 0.04441332817077637, -0.020900389179587364, 0.04638122022151947, -0.012986402958631516, 0.032605964690446854, -0.01913607120513916, -0.03800070658326149, -0.0024068530183285475, -0.024921000003814697, 0.009457765147089958, -0.03664353862404823, -0.013800703920423985, -0.0723370611667633, -0.038611434400081635, 0.027550512924790382, -0.02297007106244564, 0.006603471469134092, -0.020747708156704903, -0.05913860350847244, -0.022291487082839012, 0.04404010623693466, 0.03040056675672531, 0.00522933853790164, -0.004639818798750639, -0.010568946599960327, 0.05717070773243904, 0.03901858627796173, 0.0008121803402900696, 0.026227274909615517, -0.0070912037044763565, -0.026006733998656273, 0.021816479042172432, -0.039832886308431625, -0.023428115993738174, -0.024055805057287216, 0.013156048953533173, 0.010305996052920818, 0.03146933764219284, -0.0909302681684494, -0.03976502642035484, -0.03542209044098854, -0.06066541746258736, -0.0363721065223217, 0.030230920761823654, 0.04495619609951973, -0.028025522828102112, 0.005407467018812895, -0.036677468568086624, -0.01901731826364994, -0.006883387453854084, -0.021612903103232384, -0.0027652301359921694, 0.03301311656832695, 0.003895496716722846, 0.004012128338217735, 0.02356383204460144, 0.023614725098013878, -0.007498354185372591, 0.011934597045183182, 0.007820681668817997, -0.02795766480267048, -0.029518406838178635, 0.0020537772215902805, 0.011697093024849892, -0.03416670858860016, -0.02882285788655281, -0.02688889391720295, 0.06378690153360367, -0.03221577778458595, -0.008444130420684814, -0.0328095406293869, 0.02186737209558487, 0.018915530294179916, -0.015743151307106018, -0.063277967274189, 0.06673874706029892, 0.022885248064994812, -0.0013995796907693148, -0.03542209044098854, 0.01984858512878418, 0.017965514212846756, 0.012248442508280277, -0.022410240024328232, 0.01253684051334858, -0.05622069165110588, -0.0395275242626667, -0.013588646426796913, 0.04855269193649292, -0.044582974165678024, 0.001185401575639844, -0.011790398508310318, -0.023394186049699783, 0.026312097907066345, -0.03248721361160278, 0.014097584411501884, 0.034777432680130005, 0.014793133363127708, -0.006497442722320557, -0.014284194447100163, 0.09968400001525879, -0.033267583698034286, -0.0573403537273407, 0.038882866501808167, 0.02359776198863983, 0.023258469998836517, -0.006531371735036373, -0.010017597116529942, 0.009542588144540787, -0.015073048882186413, 0.0016423854976892471, 0.009245707653462887, -0.04132577031850815, -0.02831391990184784, 0.026821035891771317, -0.009559553116559982, 0.004533790051937103, -0.023699548095464706, -0.019746797159314156, 0.004065142944455147, -0.018084265291690826, -0.028653211891651154, 0.027584442868828773, -0.018406592309474945, 0.004241150338202715, -0.054422441869974136, -0.027686230838298798, -0.025005823001265526, -0.0454651340842247, 0.019322682172060013, -0.10402693599462509, -0.06144578754901886, 0.07891932874917984, 0.00027912072255276144, -0.013834632933139801, -0.02502278797328472, 0.03735605254769325, 0.006387172732502222, -0.05425279587507248, 0.06066541746258736, -0.04444725811481476, -0.07837646454572678, -0.02412366308271885, 0.02724515087902546, -0.031774699687957764, -0.00943231862038374, 0.003630424849689007, 0.016548968851566315, 0.020764673128724098, -0.0711834728717804, 0.058935027569532394, 0.020493239164352417, -0.043191876262426376, -0.04207221418619156, 0.03711855039000511, -0.07308350503444672, 0.00956803560256958, 0.01969590224325657, -0.0006552577251568437, 0.04156327620148659, 0.03735605254769325, 0.08875879645347595, 0.01142565906047821, -0.02956930175423622, 0.026430848985910416, -0.018576238304376602, 0.011256013065576553, -0.04502405226230621, 0.005284473299980164, 0.046245504170656204, -0.023343292996287346, -0.056322477757930756, 0.04977414384484291, -0.025599583983421326, 0.011866739019751549, -0.007629829924553633, 0.0656190812587738, 0.035489946603775024, -0.004007887095212936, -0.006013951264321804, 0.006777358707040548, 0.023614725098013878, 0.024140628054738045, 0.008143008686602116, 0.03762748837471008, 0.006166632752865553, -0.013427482917904854, 0.04180077835917473, -0.004014248959720135, 0.0028076416347175837, -0.01570073887705803, -0.040545400232076645, -0.006438066251575947, 0.017846761271357536, 0.012782827951014042, -0.0007003200007602572, 0.011103332042694092, 0.05544031783938408, 0.021697726100683212, -0.021697726100683212, 0.014496251940727234, -0.02632906287908554, -0.034064922481775284, -0.009797058068215847, 0.00684945797547698, 0.015149389393627644, -0.012418088503181934, -0.034455105662345886, 0.0032699271105229855, -0.011866739019751549, -0.007990327663719654, 0.0013932179426774383, 0.006056362763047218, -0.016319947317242622, -0.02656656689941883, -0.022478098049759865, -0.019543221220374107, -0.02566744200885296, -0.0040290928445756435, 0.03284347057342529, -0.039154302328825, 0.010704663582146168, -0.0008651947136968374, 0.02929786778986454, 0.0379667803645134, -0.003829758847132325, -0.03051931969821453, -0.002928514499217272, -0.023987947031855583, -0.018847672268748283, 0.0514027439057827, -0.013011849485337734, -0.02285131812095642, -0.0024089734070003033, -0.004245391581207514, -0.005857028998434544, 0.03274168074131012, -0.007460183929651976, 0.030773788690567017, 0.026956751942634583, 0.0446847602725029, -0.0077316174283623695, -0.006438066251575947, -0.028687141835689545, 0.01095065101981163, 0.03969717025756836, 0.0254977960139513, 0.011086367070674896, -0.008469577878713608, -0.022053983062505722, -0.040511470288038254, -0.05594925582408905, 0.01415695995092392, 0.02047627419233322, 0.033148832619190216, 0.024208486080169678, 0.056797485798597336, 0.01464893389493227, -0.02644781395792961, 0.015649845823645592, 0.020136982202529907, -0.0019721349235624075, -0.004101192578673363, 0.01194307953119278, -0.011476553045213223, -0.038136426359415054, 0.0403418242931366, -0.005250544287264347, 0.027329973876476288, 0.019475363194942474, -0.013300247490406036, -0.008588329888880253, 0.0466526560485363, 0.02902643382549286, -0.018644098192453384, 0.001691158744506538, 0.05476173385977745, -0.018762849271297455, 0.06354939937591553, -0.03450600057840347, 0.015344482846558094, 0.04285258427262306, 0.017108801752328873, -0.009423836134374142, 0.0355917364358902, -0.053676001727581024, 0.02573530189692974, 0.013054260984063148, 0.016031548380851746, 0.02716032788157463, 0.017253000289201736, -0.03328454867005348, -0.00022160011576488614, 0.03613460063934326, 0.029128221794962883, 0.006815528962761164, -0.02712639793753624, -0.06202258542180061, 0.06829948723316193, 0.008448371663689613, 0.04872233793139458, 0.050317008048295975, -0.06436370313167572, -0.006378690246492624, 0.011171190068125725, -0.026481743901968002, -0.002640116261318326, -0.013741327449679375, 0.006607712246477604, 0.0013836753787472844, -0.059647541493177414, -0.016023065894842148, -0.03728819638490677, -0.030027344822883606, 0.013826150447130203, 0.04756874218583107, -0.012927026487886906, -0.012655593454837799, -0.04346331208944321, 0.03223274275660515, 0.015556540340185165, 0.019526256248354912, -0.01747353933751583, 0.017812831327319145, -0.014996708370745182, -0.017210587859153748, 0.0050469692796468735, -0.004298406187444925, 0.02965412475168705, 0.015157871879637241, -0.008490783162415028, 0.03170683979988098, -0.004979110788553953, -0.024971894919872284, -0.03827214241027832, 0.01448777038604021, -0.03830607235431671, 0.018678026273846626, -0.008126044645905495, -0.017812831327319145, 0.018169088289141655, -0.010339925065636635, 0.002379285404458642, -0.012341747991740704, -0.04967235401272774, -0.003019699128344655, -0.005886716768145561, 0.01488643791526556, -0.009601964615285397, -0.019237859174609184, -0.02147718518972397, 0.018084265291690826, 0.021205753087997437, -0.03330151364207268, -0.01707487180829048, -0.03291132673621178, -0.026956751942634583, -0.028636248782277107, -0.04122398421168327, -0.030672000721096992, -0.035286370664834976, -0.01059439405798912, 0.00722692022100091, -0.005360814277082682, -0.025209398940205574, 0.03616853058338165, -0.009500176645815372, -0.03976502642035484, -0.01945839822292328, 0.005225097294896841, 0.022868283092975616, -0.028754999861121178, 0.04594014212489128, 0.01002607960253954, -0.0043768673203885555, -0.0034607788547873497, -0.004336576443165541, 0.020340558141469955, -0.038882866501808167, -0.00382551783695817, -0.003057869616895914, 0.03096039779484272, 0.004010007716715336, 0.05622069165110588, 0.005233579780906439, 0.015989137813448906, -0.017694080248475075, 0.004088468849658966, -0.011731022037565708, 0.00670101772993803, -0.01928875222802162, 0.04119005426764488, 0.033912237733602524, 0.004347179085016251, 0.008685876615345478, -0.01842355728149414, -0.008465336635708809, 0.031096115708351135, -0.006862181704491377, -0.003842482343316078, -0.0056873830035328865, -0.057509999722242355, -0.0403418242931366, -0.00010589622979750857, -0.003019699128344655, 0.019712867215275764, 0.010289031080901623, -0.00027647000388242304, 0.024887071922421455, -0.0019053368596360087, 0.015225729905068874, 0.00471615931019187, 0.006412619724869728, 0.01589583232998848, 0.007752823177725077, 0.028839822858572006, 0.017880691215395927, -0.03708462044596672, -0.010433230549097061, -0.024937964975833893, 0.0011143622687086463, -0.03725426644086838, 0.03487922251224518, 0.02926393784582615, 0.00956803560256958, -0.007523801177740097, -0.020391451194882393, 0.000958500022534281, 0.01257077045738697, -0.031011292710900307, 0.055372461676597595, -0.07301564514636993, -0.005475325509905815, 0.0020707417279481888, 0.024055805057287216, -0.054626017808914185, -0.019034283235669136, -0.018101230263710022, -0.041698992252349854, 0.0061539094895124435, 0.012825239449739456, -0.009313566610217094, 0.011510482057929039, 0.0168034378439188, -0.045770496129989624, -0.03854357451200485, -0.025090645998716354, -0.0034183673560619354, 0.013792221434414387, 0.025599583983421326, 0.09011596441268921, -0.03867929428815842, 0.033352408558130264, -0.008957309648394585, -0.034268494695425034, 0.015064566396176815, -0.008787663653492928, -0.016040030866861343, 0.01949232816696167, -0.008155732415616512, 0.007006380707025528, 0.01570073887705803, -0.011977008543908596, 0.02285131812095642, 0.03562566265463829, -0.023020964115858078, -0.009652858600020409, -0.0201709121465683, -0.002396250143647194, 0.007159062195569277, -0.010433230549097061, 0.063277967274189, 0.015157871879637241, 0.0024280587676912546, -0.013300247490406036, 0.003040904877707362, -0.02067985013127327, -0.025769229978322983, 0.057068921625614166, -0.014504734426736832, 0.03945966437458992, 0.01886463724076748, -0.033114902675151825, -0.021290576085448265, -0.02237631008028984, 0.009907327592372894, 0.002519243396818638, 0.0005868691951036453, 0.03847571834921837, 0.013503823429346085, -0.00039893321809358895, 0.0025213640183210373, 0.02300400100648403, -0.013486858457326889, -0.005505013279616833, -0.025803159922361374, -0.00501303980126977, -0.012341747991740704, 0.0039103408344089985, -0.03867929428815842, -0.03036663681268692, 0.00024558912264183164, -0.0680280551314354, -0.0005958816618658602, 0.037457842379808426, -0.021222716197371483, 0.040307894349098206, 0.018016407266259193, 0.03698283061385155, 0.027262115851044655, 0.027109434828162193, -0.0031660187523812056, -0.043157946318387985, 0.01969590224325657, 0.01925482414662838, -0.01059439405798912, 0.0355917364358902, 0.060835063457489014, -0.003045146120712161, 0.019186964258551598, -0.0050215222872793674, -0.00412027770653367, 0.0021110326051712036, -0.015327517874538898, -0.06222616136074066, -0.023479009047150612, 0.03732212260365486, -0.004694953560829163, -0.010170279070734978, 0.002667683642357588, 0.03474350646138191, 0.023479009047150612, 0.0018639856716617942, 0.010068491101264954, 0.01842355728149414, 0.0034968284890055656, 0.005259026773273945, -0.017965514212846756, 0.056288547813892365, -0.009101509116590023, -0.02237631008028984, 0.016777992248535156, 0.021562008187174797, -0.006667088717222214, 0.03823821246623993, -0.04617764800786972, -0.001900035422295332, -0.01368195191025734, -0.0249040350317955, -0.03901858627796173, -0.022427203133702278, 0.03732212260365486, 0.0466526560485363, 0.003032422624528408, 0.04085076227784157, 0.03633817657828331, -0.022664709016680717, -0.033471159636974335, -0.018253911286592484, -0.015149389393627644, -0.006913075223565102, -0.03235149756073952, 0.05974932760000229, -0.00617935648187995, 0.013639540411531925, -0.05998683348298073, -0.021171823143959045, -0.054659947752952576, -0.03850964829325676, -0.006586506497114897, -0.011391730047762394, 0.006493201479315758, -0.004665265325456858, 0.00861801765859127, 0.012256924994289875, 0.00736263720318675, 0.0013041538186371326, -0.004037575330585241, 0.026379955932497978, -0.07145490497350693, 0.006739187985658646, 0.022715602070093155, 0.014106066897511482, 0.017643185332417488, 0.027313008904457092, -0.03172380477190018, 0.010738592594861984, -0.031163973733782768, -0.006980933714658022, -0.009169367142021656, -0.03538816049695015, -0.06310831755399704, -0.009449283592402935, -0.0027206980157643557, -0.05445637181401253, -0.025039752945303917, -0.0011440503876656294, 0.02861928381025791, 0.011502000503242016, 0.04332759231328964, -0.031180938705801964, 0.04295437037944794, -0.011018509045243263, 0.0020410537254065275, 0.020730743184685707, 0.020018231123685837, 0.027618372812867165, 0.001765378867276013, -0.05469387769699097, 0.053200989961624146, 0.025565655902028084, -0.004294164944440126, 0.026871928945183754, -0.04678837209939957, -0.05045272782444954, -0.027414796873927116, -0.05710285156965256, -0.013427482917904854, -0.021680761128664017, 0.04376867413520813, -0.017863726243376732, 0.006802805233746767, 0.03922215849161148, 0.01510697789490223, -0.014598039910197258, -0.018559275195002556, 0.027737123891711235, 0.017643185332417488, -0.044345468282699585, -0.035014938563108444, 0.0011122417636215687, -0.009126955643296242, 0.003437452483922243, -0.006387172732502222, -0.020425381138920784, -0.0011514723300933838, -0.0042899237014353275, 0.009169367142021656, -0.006043639499694109, 0.0069427634589374065, -0.0029073087498545647, -0.006925798952579498, -0.0010783125180751085, -0.019305717200040817, -0.01782979629933834, -0.03221577778458595, 0.030298778787255287, 0.008138767443597317, 0.02558261901140213, 0.022987036034464836, 0.05214918777346611, 0.04967235401272774, -0.041698992252349854, 0.020391451194882393, 0.017049424350261688, -0.0026210309006273746, 0.010017597116529942, -0.024072770029306412, 0.01665075682103634, 0.017626222223043442, 0.029874663800001144, -0.023122752085328102, 0.03654175251722336, -0.017176659777760506, 0.040511470288038254, -0.007074239198118448, -0.022087911143898964, -0.00261466926895082, 0.0367792584002018, 0.036948904395103455, 0.004368384834378958, -0.02956930175423622, -0.036270320415496826, 0.005059692542999983, 0.012197548523545265, 0.0012956714490428567, -0.0399346724152565, 0.034455105662345886, 0.028992503881454468, -0.022155771031975746, 0.0038276382256299257, 0.015191800892353058, -0.002767350757494569, -0.013393552973866463, 0.022749532014131546, -0.006887628231197596, -0.007574694696813822, -0.009898845106363297, 0.041020408272743225, -0.012163619510829449, -0.04237757623195648, -0.026193344965577126, -0.010840380564332008, -0.05364207178354263, -0.044820480048656464, -0.007850369438529015, -0.0049663870595395565, -0.014199371449649334, -0.043395452201366425, -0.028738034889101982, -0.05289562791585922, -0.023020964115858078 ]
Membership inference attacks (MIAs) against machine learning models can lead to serious privacy risks for the training dataset used in the model training. In this paper, we propose a novel and effective Neuron-Guided Defense method named NeuGuard against membership inference attacks (MIAs). We identify a key weakness in existing defense mechanisms against MIAs wherein they cannot simultaneously defend against two commonly used neural network based MIAs, indicating that these two attacks should be separately evaluated to assure the defense effectiveness. We propose NeuGuard, a new defense approach that jointly controls the output and inner neurons' activation with the object to guide the model output of training set and testing set to have close distributions. NeuGuard consists of class-wise variance minimization targeting restricting the final output neurons and layer-wise balanced output control aiming to constrain the inner neurons in each layer. We evaluate NeuGuard and compare it with state-of-the-art defenses against two neural network based MIAs, five strongest metric based MIAs including the newly proposed label-only MIA on three benchmark datasets. Results show that NeuGuard outperforms the state-of-the-art defenses by offering much improved utility-privacy trade-off, generality, and overhead.
[ -0.01122415903955698, -0.012501484714448452, -0.035076629370450974, -0.03480485826730728, 0.05471664294600487, 0.023752819746732712, -0.02918824926018715, 0.008012726902961731, 0.030021680518984795, 0.04594748467206955, -0.05551384016871452, -0.024912377819418907, 0.058231551200151443, -0.0335184745490551, -0.010762147605419159, -0.021524295210838318, -0.010653438977897167, -0.041019365191459656, 0.015056136064231396, -0.010263900272548199, 0.03552957996726036, -0.04728822410106659, 0.012021355330944061, -0.022212782874703407, 0.018534809350967407, 0.05602114647626877, 0.0181090347468853, 0.012845728546380997, -0.031000057235360146, 0.05736188217997551, -0.00924022775143385, 0.029604963958263397, 0.005747965071350336, 0.007831545546650887, -0.032739393413066864, -0.02416953630745411, 0.018154330551624298, -0.005091184284538031, -0.00011741373600671068, 0.046454790979623795, 0.004638231825083494, -0.03250385820865631, -0.011269453912973404, -0.0261625275015831, 0.04120054468512535, -0.027630092576146126, -0.011514048092067242, -0.07942972332239151, -0.008828041143715382, 0.01940447837114334, 0.020908279344439507, -0.013615746982395649, 0.022049719467759132, -0.04420814663171768, -0.02714090421795845, 0.020980753004550934, 0.02509355917572975, 0.005390132777392864, 0.0241151824593544, -0.01155934389680624, 0.007745484821498394, 0.008936749771237373, 0.006377568934112787, 0.06069561466574669, 0.011061095632612705, -0.0421789214015007, 0.04583877697587013, 0.0010502832010388374, 0.024060828611254692, 0.005467134527862072, -0.05254247039556503, 0.029387546703219414, -0.054789114743471146, -0.026379944756627083, -0.02177794836461544, -0.02585451863706112, -0.0022828797809779644, 0.041417960077524185, 0.003342788200825453, 0.002817363478243351, 0.05236129090189934, 0.025637101382017136, 0.008968456648290157, 0.05156409367918968, 0.08218367397785187, 0.016242871060967445, 0.002445942722260952, -0.06109420955181122, -0.006522513460367918, -0.03353659063577652, -0.04232386499643326, 0.026216881349682808, 0.02712278626859188, 0.00988341961055994, 0.03844659402966499, 0.007070586085319519, -0.02784750983119011, -0.02650677040219307, -0.09080788493156433, 0.002654300769791007, -0.02377093769609928, -0.009321759454905987, -0.00704793818295002, 0.016668645665049553, -0.007396711502224207, -0.010209545493125916, 0.020292265340685844, 0.071312814950943, 0.06319590657949448, 0.13059522211551666, -0.0342613160610199, 0.0016487465472891927, -0.03558393567800522, 0.02917013131082058, 0.01274607889354229, 0.01175864227116108, -0.09704051166772842, -0.02715902216732502, -0.01578085869550705, -0.055876199156045914, 0.005689081270247698, 0.059862181544303894, 0.04714328050613403, 0.048484016209840775, -0.08116906136274338, 0.054499223828315735, 0.006726342253386974, -0.008506445214152336, -0.016260989010334015, 0.02987673692405224, 0.048121657222509384, 0.019621895626187325, 0.0374319814145565, -0.08182130753993988, 0.00014253843983169645, 0.005163656547665596, 0.04297611862421036, -0.003915772773325443, -0.011514048092067242, -0.007201942149549723, 0.02449566312134266, -0.01203947328031063, -0.03208714351058006, -0.013307739980518818, 0.006635751575231552, 0.03415260463953018, 0.05290483310818672, 0.04130925238132477, -0.04467921704053879, 0.027956217527389526, -0.04120054468512535, 0.07087798416614532, 0.08682190626859665, 0.023625994101166725, 0.0685226321220398, 0.017991267144680023, 0.01255583856254816, -0.025637101382017136, -0.018625400960445404, -0.034297551959753036, 0.04083818197250366, 0.007401240989565849, -0.007487302180379629, 0.0609855018556118, -0.00006638582999585196, 0.09689556062221527, 0.04964357614517212, -0.0041739558801054955, -0.041417960077524185, 0.053484611213207245, -0.027738800272345543, 0.0025093560107052326, -0.01982119493186474, 0.019585659727454185, -0.03764939680695534, 0.02210407331585884, 0.05739812180399895, -0.05801413580775261, 0.0005551496869884431, 0.0022772178053855896, -0.03641736879944801, 0.018607281148433685, -0.014014345593750477, -0.01609792560338974, 0.009974010288715363, 0.04062076658010483, 0.0376131609082222, -0.014068699441850185, 0.041381724178791046, -0.02308245189487934, 0.008130494505167007, 0.007596010807901621, 0.005358426366001368, -0.03384459763765335, 0.005648315418511629, -0.018317392095923424, -0.010128013789653778, -0.024531899020075798, 0.02788374572992325, 0.035765115171670914, -0.010617203079164028, -0.02953249216079712, 0.05431804433465004, -0.005426369141787291, 0.00293966056779027, 0.007247237488627434, -0.016578055918216705, 0.036997146904468536, -0.034043896943330765, 0.0071113514713943005, -0.034750502556562424, -0.008728391490876675, -0.06971842050552368, -0.04801294580101967, -0.014557887800037861, -0.01057190727442503, -0.004534052684903145, -0.03578323498368263, -0.021198170259594917, 0.03119935654103756, 0.01873410865664482, 0.00043681589886546135, 0.010762147605419159, 0.006825991906225681, -0.07142152637243271, 0.0056166090071201324, -0.04819412901997566, 0.043338481336832047, -0.04221515730023384, -0.031000057235360146, -0.04228762909770012, -0.010834620334208012, 0.03255821391940117, 0.0035194396041333675, 0.04522276297211647, -0.02246643602848053, 0.024912377819418907, -0.033717770129442215, -0.006930170580744743, -0.008148612454533577, -0.06493524461984634, -0.05536889284849167, -0.0024368835147470236, 0.01873410865664482, 0.0335184745490551, -0.012528661638498306, -0.04094688966870308, 0.01974872127175331, 0.04254128411412239, 0.028282344341278076, -0.01053567137569189, -0.0315617173910141, 0.005050418432801962, -0.0221584290266037, -0.06910240650177002, 0.0025048265233635902, 0.039026372134685516, -0.02380717545747757, 0.03953367844223976, 0.005892910063266754, 0.03324669972062111, -0.019205179065465927, -0.009267404675483704, 0.05304977670311928, 0.010010246187448502, 0.01877034455537796, 0.020727097988128662, 0.016967594623565674, 0.05475287884473801, 0.009684121236205101, -0.015572501346468925, -0.012818550691008568, -0.04855649173259735, -0.07877746969461441, 0.016333460807800293, 0.01172240637242794, 0.01357951108366251, 0.023046214133501053, -0.02181418426334858, -0.006767108105123043, 0.05196269229054451, -0.006332273595035076, -0.011514048092067242, -0.028717178851366043, 0.04134548828005791, -0.021560531109571457, -0.009394231252372265, -0.010934269055724144, -0.047723058611154556, -0.010354490019381046, -0.019640013575553894, 0.01648746430873871, -0.004724293015897274, -0.041381724178791046, 0.039026372134685516, 0.004044864326715469, 0.02310056984424591, -0.006164681166410446, -0.01682264916598797, -0.01239277608692646, -0.10117143392562866, -0.008298086933791637, 0.0012784579303115606, 0.022629499435424805, -0.02820987068116665, 0.029586846008896828, 0.011649933643639088, 0.07381311058998108, -0.04051205515861511, 0.0018865464953705668, 0.00012753439659718424, 0.009226638823747635, -0.045621357858181, -0.024658724665641785, -0.037359509617090225, -0.014304234646260738, -0.0077590737491846085, 0.020672744140028954, 0.015291671268641949, -0.009602589532732964, 0.0033269349951297045, 0.04156290739774704, -0.019005879759788513, 0.004531788174062967, -0.03627242147922516, -0.028572233393788338, -0.03252197802066803, 0.09588094800710678, -0.022720089182257652, -0.0037980054039508104, -0.06826897710561752, 0.0015728769358247519, -0.05359331890940666, -0.043374717235565186, -0.035420872271060944, -0.017837263643741608, -0.017538314685225487, 0.02978614531457424, -0.023970237001776695, 0.0027969807852059603, -0.03215961530804634, -0.03877272084355354, -0.06877627968788147, 0.021542413160204887, -0.032739393413066864, -0.00903639942407608, 0.0004379482998047024, -0.00552601832896471, 0.0030913997907191515, 0.015536265447735786, 0.001072930870577693, 0.0005483553977683187, 0.012483366765081882, 0.006608574651181698, 0.02987673692405224, 0.0575430653989315, 0.050078410655260086, -0.010734970681369305, -0.041780322790145874, -0.025238504633307457, 0.011604638770222664, -0.019694367423653603, -0.01877034455537796, 0.004513670224696398, -0.02880776859819889, -0.07044314593076706, -0.04464298114180565, 0.027394557371735573, 0.024984851479530334, 0.04464298114180565, 0.012963496148586273, 0.04029463976621628, -0.003055163426324725, -0.011803938075900078, 0.0261625275015831, -0.019187061116099358, 0.0382654145359993, 0.024006472900509834, 0.008633271791040897, 0.04870143532752991, -0.01023672241717577, 0.005530547816306353, -0.021035106852650642, -0.023915883153676987, 0.015527206473052502, 0.011033918708562851, 0.0023372340947389603, 0.02250267192721367, 0.03549334406852722, -0.026090053841471672, -0.05562254786491394, -0.0025297387037426233, 0.0007377461297437549, -0.040765710175037384, 0.02244831807911396, 0.032050907611846924, -0.009045458398759365, -0.040439583361148834, 0.0173661932349205, -0.046092428267002106, -0.03121747449040413, 0.04391825944185257, -0.009312700480222702, -0.056166090071201324, -0.019005879759788513, -0.007473713718354702, 0.01809997484087944, -0.039098843932151794, 0.017665140330791473, -0.054825350642204285, 0.05058571696281433, -0.04623737558722496, -0.03480485826730728, -0.007953843101859093, -0.008823511190712452, 0.003961068112403154, -0.03293869271874428, 0.004459315910935402, -0.021216288208961487, -0.0005755325546488166, 0.04652726277709007, -0.010381667874753475, 0.10320065915584564, -0.00012265100667718798, -0.01838986575603485, -0.003249933011829853, -0.030311569571495056, -0.007958372123539448, 0.07942972332239151, -0.024713080376386642, 0.04051205515861511, -0.005951793864369392, -0.015654033049941063, -0.05442675203084946, -0.01877034455537796, -0.04717951640486717, 0.007138528861105442, -0.05674586817622185, 0.00527689466252923, -0.002955514006316662, -0.004665409214794636, -0.009312700480222702, 0.017520196735858917, 0.011378162540495396, -0.010209545493125916, -0.05656468868255615, -0.009493880905210972, -0.02547403983771801, 0.009040928445756435, 0.009448586031794548, -0.055115241557359695, 0.013661042787134647, -0.03888142853975296, -0.0304927509278059, 0.06123915687203407, 0.004568024538457394, -0.010716852732002735, -0.04098312556743622, 0.023028096184134483, 0.0057977898977696896, -0.011350985616445541, 0.04029463976621628, -0.02447754517197609, -0.03656231239438057, -0.04047581925988197, 0.024984851479530334, -0.046092428267002106, -0.04482416436076164, 0.009638825431466103, -0.0035217043478041887, 0.06845016032457352, 0.0221584290266037, 0.014204584993422031, -0.0008317337487824261, 0.007790780160576105, 0.042070213705301285, -0.005118361208587885, -0.034080132842063904, -0.017239365726709366, 0.01713065803050995, 0.02047344483435154, 0.03520345687866211, -0.0037413863465189934, -0.013842223212122917, 0.0014041522517800331, -0.04533147066831589, 0.03692467510700226, 0.008180319331586361, -0.016677705571055412, -0.07406676560640335, -0.05768800899386406, 0.008316204883158207, 0.00853362213820219, -0.06808779388666153, 0.016886062920093536, -0.02851787954568863, 0.01774667203426361, -0.00854721013456583, 0.1105203703045845, 0.05054948106408119, 0.05029582604765892, -0.09175002574920654, -0.03583759069442749, 0.04460674524307251, 0.04094688966870308, -0.026253117248415947, -0.025999464094638824, -0.0009189270786009729, 0.05160032957792282, 0.029985444620251656, 0.009158696047961712, 0.046744681894779205, 0.034080132842063904, -0.022611381486058235, 0.015010840259492397, 0.0025591806042939425, -0.011586520820856094, -0.008764627389609814, 0.02947813831269741, 0.02005673013627529, -0.003607765305787325, 0.004359666258096695, -0.030311569571495056, 0.03116312064230442, -0.04330224171280861, 0.04489663615822792, 0.030909467488527298, 0.0025546511169523, 0.006708224304020405, -0.012284067459404469, -0.03607312589883804, 0.029586846008896828, -0.06718189269304276, 0.005208951886743307, 0.03047463297843933, -0.002213804516941309, -0.011668052524328232, -0.027702564373612404, -0.018498573452234268, -0.01270984299480915, -0.06475406885147095, 0.015219198539853096, 0.0045453766360878944, -0.008293556980788708, -0.037105854600667953, 0.006930170580744743, 0.024658724665641785, -0.06355827301740646, 0.01608886756002903, 0.00546260504052043, -0.01569932885468006, 0.004341548308730125, -0.012492425739765167, -0.06105797365307808, 0.021343113854527473, -0.018589163199067116, -0.03324669972062111, 0.05221634358167648, 0.008628741838037968, -0.04428062215447426, 0.0024232950527220964, -0.008619682863354683, 0.039388734847307205, 0.009856242686510086, -0.014258939772844315, -0.049752283841371536, -0.009511998854577541, 0.046092428267002106, 0.01506519503891468, 0.020274147391319275, -0.0007745485054329038, -0.05834026262164116, -0.0348229743540287, 0.010979564860463142, 0.02547403983771801, -0.022538907825946808, -0.0019035321893170476, 0.022538907825946808, 0.03194219991564751, 0.004192073829472065, -0.00822108518332243, -0.01640593446791172, 0.02112569659948349, 0.04659973457455635, 0.018172448500990868, 0.0015038017882034183, -0.02549215778708458, -0.0312355924397707, -0.04029463976621628, -0.031000057235360146, 0.016170399263501167, 0.015192021615803242, 0.002620329149067402, 0.002023564651608467, 0.018969643861055374, -0.005725317634642124, 0.03797552362084389, 0.014956486411392689, 0.06906617432832718, -0.04359213262796402, 0.024930495768785477, 0.02717714011669159, 0.05895627662539482, 0.0010474523296579719, -0.025347212329506874, -0.01848951354622841, -0.017683258280158043, -0.00041218663682229817, 0.018516691401600838, -0.03275751322507858, 0.034043896943330765, 0.004203397780656815, 0.05776048079133034, -0.013189972378313541, 0.0244413074105978, 0.004620113875716925, 0.016351578757166862, -0.030673932284116745, -0.015952982008457184, -0.05308601260185242, 0.047795530408620834, -0.01770137809216976, 0.040403347462415695, 0.024350717663764954, 0.0030642226338386536, 0.027340203523635864, -0.013969049789011478, 0.0020065789576619864, 0.005652845371514559, 0.015092371962964535, -0.006635751575231552, 0.030402161180973053, -0.03924379125237465, 0.01604357175529003, -0.02181418426334858, 0.026923486962914467, 0.021705476567149162, -0.023553522303700447, 0.01911458931863308, 0.02175983041524887, -0.01474812813103199, -0.011686170473694801, -0.026615479961037636, 0.020111083984375, -0.010698733851313591, -0.034678030759096146, -0.020527800545096397, -0.024314481765031815, 0.016559937968850136, 0.01842610165476799, -0.03348223492503166, -0.019259532913565636, 0.00019505260570440441, 0.0026407120749354362, -0.00957541260868311, 0.007754543796181679, 0.01140533946454525, 0.0003731194883584976, 0.018045620992779732, 0.0016000540927052498, -0.01938636042177677, -0.007351416628807783, -0.003970127087086439, 0.020020492374897003, 0.015336966142058372, -0.026398062705993652, 0.01609792560338974, 0.007487302180379629, -0.002056403551250696, 0.050078410655260086, -0.029333192855119705, -0.025890756398439407, -0.02710466831922531, 0.05471664294600487, 0.031670428812503815, -0.0336090624332428, 0.015980158001184464, 0.005915557499974966, -0.0035624701995402575, -0.04870143532752991, -0.004896414931863546, 0.009090753272175789, 0.003360906383022666, -0.024006472900509834, -0.05127420276403427, -0.003222755854949355, 0.0069754659198224545, 0.0735594630241394, -0.03768563270568848, -0.024205772206187248, -0.020237909629940987, -0.04938992112874985, 0.015934864059090614, 0.006676517426967621, 0.049063798040151596, -0.024531899020075798, -0.019060233607888222, 0.01003742404282093, -0.02820987068116665, 0.020980753004550934, -0.03583759069442749, 0.028445405885577202, -0.02849976159632206, 0.055115241557359695, -0.018299274146556854, 0.01605263166129589, 0.0001285252219531685, 0.038410358130931854, 0.04667221009731293, 0.01556344237178564, -0.001791426446288824, 0.048447780311107635, -0.02917013131082058, 0.02175983041524887, -0.01037260890007019, 0.022375846281647682, 0.032666921615600586, 0.00007339243165915832, -0.00471070408821106, 0.004887355491518974, 0.03551146388053894, 0.044353093951940536, 0.022665735334157944, -0.05863014981150627, -0.03949744254350662, -0.03114500269293785, -0.011015800759196281, -0.03310175612568855, -0.04457050934433937, 0.003777622478082776, 0.03616371378302574, -0.015916744247078896, -0.019023997709155083, 0.010762147605419159, 0.024568134918808937, -0.024296363815665245, 0.02282879687845707, 0.02877153269946575, 0.0026995958760380745, -0.02012920193374157, 0.012311244383454323, 0.026343706995248795, 0.005643785931169987, -0.02880776859819889, -0.01138722151517868, 0.005394662264734507, -0.03116312064230442, 0.010291077196598053, -0.038736484944820404, -0.0023802644573152065, 0.027249611914157867, -0.017909735441207886, 0.05877509340643883, -0.04464298114180565, -0.029931090772151947, -0.0010423565981909633, 0.033029284328222275, -0.011504989117383957, 0.01087085623294115, -0.06692823767662048, -0.004407226108014584, 0.016849827021360397, -0.02612629160284996, 0.02016543783247471, 0.04855649173259735, -0.035312164574861526, 0.00904998742043972, -0.019531304016709328, 0.004269075579941273, -0.04018593207001686, -0.014639419503509998, -0.008483797311782837, 0.018987761810421944, -0.019585659727454185, -0.057434357702732086, 0.014566946774721146, 0.025564629584550858, 0.006481748074293137, -0.01672299951314926, 0.012501484714448452, -0.0055486662313342094, 0.0061012678779661655, 0.03583759069442749, 0.021904775872826576, 0.0014279322931542993, -0.0016125102993100882, 0.008433972485363483, -0.028916476294398308, -0.023734701797366142, 0.004701645113527775, -0.021035106852650642, -0.033717770129442215, -0.0042101917788386345, -0.0033382587134838104, 0.008497386239469051, 0.012827610597014427, -0.025383448228240013, 0.03176101669669151, 0.010336372070014477, -0.015916744247078896, 0.06939230114221573, -0.0073921820148825645, -0.0022908065002411604, -0.04330224171280861, -0.05395568162202835, 0.014820600859820843, -0.049426160752773285, -0.007328768726438284, -0.015382261015474796, -0.011432517319917679, 0.010816501453518867, -0.013805987313389778, 0.0034039367455989122, 0.02210407331585884, 0.006178270094096661, 0.024296363815665245, -0.011088273487985134, -0.022049719467759132, 0.005929145961999893, -0.04159914329648018, -0.028554115444421768, -0.03382648155093193, -0.00654969085007906, -0.047759294509887695, -0.0019544893875718117, -0.027032194659113884, 0.026271235197782516, 0.006006148178130388, 0.042033977806568146, 0.01608886756002903, -0.008121435530483723, 0.009566353633999825, -0.032666921615600586, 0.01713065803050995, -0.03315611183643341, 0.06073185056447983, -0.020527800545096397, 0.03949744254350662, -0.01372445560991764, -0.0014086817391216755, 0.008823511190712452, 0.02849976159632206, -0.019929902628064156, -0.0355658158659935, 0.016514642164111137, -0.010019306093454361, 0.011459694243967533, 0.004919062368571758, 0.04362836852669716, -0.016550878062844276, -0.023245513439178467, 0.013199031352996826, 0.029224485158920288, 0.008311674930155277, 0.027050312608480453, -0.010617203079164028, 0.001250148401595652, -0.010816501453518867, -0.012836669571697712, -0.04250504821538925, -0.020002374425530434, 0.004635967314243317, -0.004495551809668541, 0.020256027579307556, 0.015373202040791512, 0.011586520820856094, 0.014313293620944023, -0.0315617173910141, 0.0100555419921875, -0.04420814663171768, -0.0014630360528826714, -0.03641736879944801, -0.02545592188835144, 0.05540512874722481, 0.0014653007965534925, -0.011441576294600964, -0.0005466568400152028, -0.023009978234767914, 0.006989054381847382, 0.0030279862694442272, -0.04112807288765907, -0.016342520713806152, 0.038337886333465576, -0.03315611183643341, 0.015608737245202065, -0.009756593033671379, 0.04264999181032181, -0.056129854172468185, -0.005915557499974966, -0.058159079402685165, -0.04359213262796402, -0.02279256097972393, -0.002156053204089403, -0.013769751414656639, 0.039026372134685516, 0.008302615955471992, -0.012773255817592144, 0.018571045249700546, -0.005095713771879673, 0.003983716014772654, 0.007623187731951475, -0.028554115444421768, 0.0009721489623188972, 0.030945703387260437, 0.015019899234175682, 0.041780322790145874, 0.03127183020114899, -0.03494980186223984, 0.025564629584550858, 0.006123915780335665, -0.027322085574269295, 0.03449685126543045, -0.023372340947389603, -0.005811378359794617, 0.020020492374897003, 0.030710168182849884, 0.0012807226739823818, 0.023354222998023033, 0.0244413074105978, 0.01873410865664482, -0.008764627389609814, 0.03594629839062691, -0.035076629370450974, 0.028644705191254616, 0.005258776713162661, -0.029405666515231133, -0.021306877955794334, 0.009000162594020367, -0.000348490197211504, 0.02442318946123123, -0.065913625061512, 0.006594986189156771, -0.005177245009690523, 0.03456932306289673, 0.042396340519189835, 0.003822917817160487, 0.0018038826528936625, 0.0415266714990139, -0.04996970295906067, 0.005204422399401665, -0.02652488835155964, -0.00822108518332243, -0.0100555419921875, 0.05696328729391098, 0.030239097774028778, -0.024948615580797195, -0.0037821519654244184, -0.044063203036785126, -0.021723594516515732, 0.01372445560991764, -0.032377034425735474, -0.03326481953263283, -0.016215693205595016, -0.023934001103043556, -0.07515385001897812, 0.03627242147922516, -0.022339608520269394, -0.023281749337911606, -0.0006647075642831624, 0.04707080498337746, -0.004334753844887018, -0.007487302180379629, -0.055477600544691086, -0.024912377819418907, -0.029423784464597702, 0.020618390291929245, -0.001139175146818161, -0.036652904003858566, -0.0013769750948995352, 0.006427393760532141, -0.021705476567149162, -0.016614291816949844, 0.03223208710551262, 0.01577180065214634, 0.0655512586236, -0.016360638663172722, 0.041744086891412735, -0.009820006787776947, 0.029007067903876305, 0.055151477456092834, 0.028554115444421768, -0.004615584388375282, 0.015989217907190323, 0.061855170875787735, -0.03511286526918411, -0.002513885498046875, -0.01138722151517868, -0.006776167079806328, -0.03717832639813423, -0.0030098683200776577, -0.024260127916932106, 0.0025614453479647636, -0.00986530166119337, -0.01976683922111988, -0.042070213705301285, 0.01945883221924305, -0.007288002874702215, -0.04580254107713699, -0.012130063958466053, 0.016333460807800293, -0.026017582044005394, -0.011876409873366356, 0.033282939344644547, 0.04949863255023956, -0.004164896905422211, -0.0041060131043195724, 0.07711060345172882, -0.02143370546400547, -0.008787275291979313, -0.007940254174172878, -0.059862181544303894, -0.006296037696301937, -0.0030098683200776577, 0.044135674834251404, -0.02750326506793499, -0.005598491057753563, -0.05366579443216324, 0.062181297689676285, -0.006540631875395775, -0.00012031546793878078, 0.04993346706032753, 0.0004846589872613549, -0.028101162984967232, -0.004400432109832764 ]
An in-depth understanding of uncertainty is the first step to making effective decisions under uncertainty. Deep/machine learning (ML/DL) has been hugely leveraged to solve complex problems involved with processing high-dimensional data. However, reasoning and quantifying different types of uncertainties to achieve effective decision-making have been much less explored in ML/DL than in other Artificial Intelligence (AI) domains. In particular, belief/evidence theories have been studied in KRR since the 1960s to reason and measure uncertainties to enhance decision-making effectiveness. We found that only a few studies have leveraged the mature uncertainty research in belief/evidence theories in ML/DL to tackle complex problems under different types of uncertainty. In this survey paper, we discuss several popular belief theories and their core ideas dealing with uncertainty causes and types and quantifying them, along with the discussions of their applicability in ML/DL. In addition, we discuss three main approaches that leverage belief theories in Deep Neural Networks (DNNs), including Evidential DNNs, Fuzzy DNNs, and Rough DNNs, in terms of their uncertainty causes, types, and quantification methods along with their applicability in diverse problem domains. Based on our in-depth survey, we discuss insights, lessons learned, limitations of the current state-of-the-art bridging belief theories and ML/DL, and finally, future research directions.
[ 0.02870049513876438, -0.0024360555689781904, -0.031122788786888123, -0.014074987731873989, 0.11105844378471375, 0.03158155456185341, -0.04525282606482506, -0.008390857838094234, -0.008702820166945457, 0.03093928098678589, 0.027544401586055756, -0.04147258400917053, 0.0006336726364679635, 0.046317167580127716, -0.07483416050672531, -0.0057391817681491375, 0.04800543189048767, 0.021543722599744797, 0.0004570471355691552, -0.032425686717033386, 0.05729088932275772, -0.0038398841861635447, 0.0015024635940790176, 0.028498638421297073, 0.010092885233461857, 0.003582974197342992, 0.025434071198105812, -0.008789985440671444, -0.09322156012058258, 0.0766325294971466, 0.0447390079498291, 0.0069503276608884335, -0.018708540126681328, -0.019121430814266205, -0.04903307184576988, -0.006197948940098286, -0.009395558387041092, 0.0013797433348372579, -0.022057542577385902, 0.010285567492246628, 0.02521386183798313, -0.022167647257447243, -0.013707973062992096, -0.013955707661807537, 0.034994784742593765, -0.023562299087643623, -0.039013590663671494, -0.005564849823713303, 0.0004759712901432067, -0.04837244749069214, 0.005844698287546635, -0.05787811055779457, 0.033214766532182693, 0.0013212504563853145, -0.024498185142874718, 0.04114226996898651, 0.06022699922323227, -0.04015133157372475, 0.02692047879099846, 0.01796533539891243, 0.01919483207166195, 0.019176481291651726, -0.043674666434526443, -0.01544211432337761, -0.008647767826914787, -0.034077249467372894, 0.0639338418841362, -0.041656091809272766, 0.04264703020453453, -0.027434296905994415, -0.025837786495685577, 0.007918327115476131, 0.02530561573803425, 0.007175123784691095, 0.004314708523452282, 0.041105568408966064, -0.023250337690114975, 0.05362074822187424, -0.015396238304674625, 0.02666356787085533, 0.0709805116057396, 0.05277661606669426, -0.03191186860203743, -0.03143475204706192, 0.051895782351493835, 0.05769460275769234, 0.018919572234153748, -0.06925554573535919, 0.00013039032637607306, 0.002309894422069192, 0.02842523530125618, 0.00603279285132885, 0.00019010179676115513, -0.04965699464082718, 0.03710511699318886, 0.02950792759656906, 0.013120750896632671, -0.010900315828621387, -0.016075214371085167, -0.03481128066778183, 0.002351183444261551, 0.05740099027752876, 0.0041885473765432835, 0.0188828706741333, 0.005574025213718414, -0.061107832938432693, 0.01683676801621914, 0.051565468311309814, -0.010900315828621387, 0.12845490872859955, -0.011716922745108604, 0.0322788842022419, 0.0037389553617686033, -0.0007248526671901345, -0.0281683262437582, 0.002612680895254016, -0.024791795760393143, -0.08096329122781754, 0.016607383266091347, -0.03539850190281868, -0.001526548876427114, 0.0895514190196991, 0.01770842634141445, -0.008198175579309464, -0.0598599873483181, 0.06327321380376816, -0.031067736446857452, -0.040665153414011, 0.00144855841062963, 0.016634909436106682, -0.03525169566273689, 0.02273651771247387, -0.03427910804748535, -0.012625281699001789, -0.010570003651082516, -0.009124886244535446, 0.024865198880434036, -0.020846396684646606, 0.02150702103972435, 0.0016171555034816265, -0.0003205637913197279, 0.007005380000919104, -0.010634231381118298, 0.0019245297880843282, 0.03620593249797821, -0.015102626755833626, -0.035526957362890244, 0.0779537782073021, -0.05600633844733238, 0.0031723773572593927, -0.007124659605324268, 0.06437426060438156, 0.007849512621760368, 0.009184525348246098, 0.053987760096788406, -0.009014781564474106, 0.00466795964166522, -0.0127904387190938, -0.002192908665165305, -0.035747166723012924, 0.0319669209420681, -0.006835636217147112, 0.0005665778880938888, 0.04205980524420738, 0.021323515102267265, 0.08580787479877472, -0.006762233097106218, -0.03824286162853241, -0.06323651224374771, 0.05013411492109299, -0.04833574593067169, -0.02365405298769474, -0.017524918541312218, 0.04892296716570854, -0.036389440298080444, 0.037618935108184814, 0.010716808959841728, 0.02156207337975502, 0.0001597084483364597, 0.02574603259563446, -0.06228227913379669, -0.005138196051120758, 0.03211372718214989, 0.04323425143957138, 0.07545807957649231, -0.0015930702211335301, 0.07259537279605865, 0.005193248391151428, 0.05431807413697243, 0.01287301629781723, -0.017469866201281548, 0.01635964959859848, 0.03222383186221123, -0.025452421978116035, 0.019213182851672173, -0.05391435697674751, -0.05791481211781502, 0.01581830345094204, -0.03084752708673477, -0.0060419682413339615, -0.002665439387783408, -0.06753057986497879, 0.03222383186221123, 0.043417759239673615, 0.03905029222369194, -0.03849976882338524, 0.016423877328634262, -0.027232440188527107, 0.04617036134004593, -0.021378565579652786, 0.018258947879076004, -0.005642840638756752, -0.04895966872572899, -0.012973945587873459, -0.054831892251968384, -0.004323883913457394, -0.021488670259714127, -0.003693078411743045, -0.023048480972647667, -0.0010867055971175432, -0.023048480972647667, 0.028278429061174393, 0.039710916578769684, 0.016708312556147575, 0.017882756888866425, -0.012304144911468029, 0.016809241846203804, 0.014864067547023296, 0.008620241656899452, -0.051345258951187134, -0.03358178213238716, 0.06286950409412384, 0.02203919179737568, -0.022167647257447243, 0.02376415766775608, -0.0031769650522619486, -0.02097485028207302, -0.000668653636239469, -0.0035279220901429653, 0.006519086193293333, 0.01871771551668644, 0.0076430668123066425, -0.047271404415369034, -0.008978080004453659, 0.0441884882748127, -0.02273651771247387, -0.028994107618927956, 0.007771521806716919, 0.0424635224044323, -0.004940926097333431, -0.0036380263045430183, 0.00018709112191572785, 0.036701399832963943, 0.01391900610178709, -0.021378565579652786, 0.04440869390964508, 0.023103531450033188, -0.015625622123479843, 0.012129813432693481, -0.09953419864177704, 0.07450384646654129, -0.014625508338212967, 0.055162206292152405, 0.022975077852606773, -0.00545474560931325, -0.015295309014618397, 0.0374537818133831, 0.05479519069194794, 0.016882644966244698, 0.008546838536858559, -0.0015758663648739457, -0.023892613127827644, -0.007629303727298975, -0.013441888615489006, -0.02145196869969368, -0.039821021258831024, 0.0006462887395173311, 0.026076344773173332, -0.011799500323832035, 0.04995060712099075, 0.023855911567807198, -0.012955594807863235, -0.009845150634646416, -0.008078895509243011, -0.02569098025560379, -0.004422518890351057, -0.02123176120221615, -0.027470998466014862, -0.095276840031147, -0.04297734051942825, -0.0241311714053154, -0.009271691553294659, -0.06474126875400543, -0.00422524893656373, 0.06286950409412384, 0.04228001460433006, -0.023617351427674294, -0.023342091590166092, 0.061217937618494034, -0.018625961616635323, 0.0020954206120222807, -0.012781263329088688, 0.03576551377773285, 0.04595015570521355, 0.023837560787796974, 0.024736745283007622, 0.023727456107735634, 0.015754075720906258, -0.02069959044456482, -0.026700269430875778, -0.02225939929485321, 0.03758223354816437, -0.04730810597538948, -0.035967372357845306, 0.02756275236606598, 0.0714576318860054, 0.06030040234327316, 0.004200016614049673, -0.011625168845057487, -0.03508653864264488, 0.01641470193862915, -0.0008429852896369994, -0.08081648498773575, 0.020314225926995277, -0.0038077703211456537, -0.01153341494500637, 0.004775770008563995, 0.012175689451396465, -0.04859265685081482, 0.01941504143178463, 0.00640898197889328, -0.022241048514842987, -0.04451879858970642, -0.0020162833388894796, -0.007684356067329645, -0.007560488767921925, 0.0031471452675759792, 0.0517122745513916, 0.000054335276217898354, -0.026535112410783768, -0.0177451279014349, -0.0184516292065382, -0.08066967874765396, -0.0575110949575901, 0.04081195965409279, -0.04767512157559395, -0.029966693371534348, -0.034939732402563095, -0.010092885233461857, 0.0004427106468938291, 0.0009657056070864201, 0.004560149274766445, -0.02767285704612732, -0.01625872030854225, 0.0357288159430027, -0.03383869305253029, -0.05347394198179245, 0.017185430973768234, -0.022699816152453423, 0.05982328578829765, -0.026094695553183556, -0.0369032584130764, -0.06874172389507294, 0.012148164212703705, -0.0511617548763752, -0.021268462762236595, 0.017506567761301994, 0.019855458289384842, -0.0009949520463123918, -0.015157679095864296, -0.017662549391388893, 0.01818554475903511, 0.044335294514894485, 0.005647428333759308, -0.019928861409425735, 0.02391096204519272, -0.04628046602010727, 0.02220434695482254, -0.04855595529079437, 0.049473490566015244, -0.02660851553082466, 0.026700269430875778, -0.015194379724562168, -0.016634909436106682, -0.009955255314707756, 0.0068172854371368885, 0.008730345405638218, -0.024956952780485153, 0.011368258856236935, 0.05240960046648979, 0.0012478476855903864, -0.033269818872213364, -0.02783801220357418, -0.039343900978565216, 0.054244671016931534, -0.0008601890876889229, -0.01678171567618847, 0.006133721675723791, -0.0040463292971253395, 0.0013843310298398137, -0.02750770002603531, 0.027048932388424873, 0.006418157368898392, -0.0628328025341034, 0.008840450085699558, 0.004899637307971716, 0.03266424685716629, 0.015276958234608173, 0.013285906985402107, 0.0030714485328644514, 0.05079473927617073, -0.005537324119359255, -0.014873242937028408, -0.05105165019631386, 0.02058948576450348, 0.0038788793608546257, -0.042023103684186935, 0.02295672707259655, -0.015744900330901146, -0.01502004824578762, 0.01059752982109785, 0.0117719741538167, 0.057364288717508316, -0.03319641575217247, -0.019433392211794853, 0.040848661214113235, -0.029269367456436157, -0.03883008286356926, -0.007367806509137154, -0.013038172386586666, 0.03266424685716629, 0.0022766338661313057, 0.017680900171399117, -0.001751345000229776, 0.027048932388424873, -0.050170816481113434, 0.01110217347741127, 0.05828182399272919, -0.025727681815624237, 0.018102966248989105, 0.02853533998131752, -0.011441661976277828, -0.01748821698129177, 0.0140841631218791, -0.037306975573301315, -0.04917987808585167, -0.004674841184169054, -0.03780244290828705, -0.06885182857513428, -0.006821873132139444, -0.032205481082201004, 0.04172949492931366, -0.08206433057785034, -0.010505775921046734, 0.040628451853990555, -0.02214929647743702, 0.004037154372781515, -0.034352511167526245, -0.006051143631339073, -0.03727027401328087, -0.005431807599961758, 0.07131082564592361, 0.029361121356487274, -0.006748470012098551, -0.004264243878424168, 0.014717262238264084, -0.02424127608537674, -0.005711655598133802, -0.019928861409425735, 0.023507246747612953, -0.01445117685943842, -0.05035432428121567, -0.015478815883398056, -0.027122335508465767, 0.013579518534243107, 0.0007305872859433293, 0.0035577421076595783, -0.04859265685081482, 0.025452421978116035, -0.007661417592316866, 0.049583591520786285, 0.056887172162532806, 0.0018832406494766474, 0.013285906985402107, -0.013469413854181767, 0.00799631793051958, 0.06419075280427933, 0.03249908983707428, -0.025342317298054695, -0.07410012930631638, -0.05916265770792961, -0.04973039776086807, -0.002787012606859207, -0.042610328644514084, 0.004007334355264902, -0.010459898971021175, -0.018681013956665993, -0.03444426506757736, 0.08969822525978088, 0.023782508447766304, -0.03618758171796799, 0.004690897651016712, -0.009946079924702644, 0.03716016933321953, -0.02231445163488388, 0.02591118961572647, -0.02627820335328579, 0.02959967963397503, -0.012194040231406689, 0.02047938108444214, 0.006363105494529009, 0.023855911567807198, 0.02976483665406704, -0.017405640333890915, 0.01866266317665577, 0.028388533741235733, 0.0459134541451931, -0.04000452905893326, 0.030021745711565018, 0.016130266711115837, 0.040298137813806534, -0.038646575063467026, 0.0004868670366704464, 0.07046668976545334, -0.043674666434526443, 0.03426075726747513, 0.007679768372327089, -0.015588920563459396, 0.006835636217147112, -0.022185998037457466, -0.01667161099612713, 0.04694109410047531, -0.03651789575815201, -0.033490028232336044, -0.01064340677112341, 0.005092319566756487, 0.0424635224044323, 0.03916039690375328, -0.003057685447856784, 0.00001085092662833631, -0.05626324936747551, 0.02981988899409771, 0.0002668019733391702, 0.033324871212244034, 0.010441549122333527, -0.008675293996930122, 0.051675572991371155, -0.018864519894123077, 0.030774125829339027, -0.0036311449948698282, -0.005395106039941311, -0.004876698832958937, -0.043637964874506, -0.019616898149251938, -0.039013590663671494, 0.011304032057523727, -0.02563592791557312, 0.0007965351105667651, 0.004729893058538437, -0.06562210619449615, 0.022222697734832764, -0.034627772867679596, -0.04297734051942825, 0.02187403477728367, 0.010386496782302856, -0.013790551573038101, -0.010313093662261963, 0.08881738781929016, 0.00047367747174575925, 0.033875394612550735, -0.025323966518044472, -0.007175123784691095, -0.023470547050237656, -0.0435645617544651, 0.006367693189531565, 0.01544211432337761, 0.035802215337753296, -0.025892838835716248, -0.00863400474190712, 0.014974171295762062, 0.02279157005250454, -0.010202989913523197, 0.020681239664554596, 0.02703058160841465, 0.028663793578743935, -0.05244630202651024, -0.054134566336870193, -0.03339827433228493, 0.04917987808585167, -0.015065925195813179, -0.010753510519862175, 0.026938827708363533, -0.055272310972213745, -0.009014781564474106, 0.010202989913523197, -0.014442001469433308, 0.06991616636514664, -0.009234989993274212, 0.015221905894577503, -0.03383869305253029, -0.006996204610913992, 0.0051565468311309814, 0.031141139566898346, 0.05519890785217285, 0.009349682368338108, 0.04026143625378609, -0.021543722599744797, -0.01305652316659689, -0.0012868428602814674, -0.00395457586273551, -0.060850922018289566, -0.04866605997085571, 0.05002401024103165, -0.02108495496213436, 0.02794811688363552, -0.02387426234781742, -0.02075464278459549, -0.010533302091062069, 0.006803522352129221, 0.02332374081015587, 0.006289702840149403, -0.027526050806045532, 0.019727002829313278, 0.005606139078736305, -0.021305164322257042, 0.023048480972647667, 0.013854779303073883, -0.009881852194666862, -0.006243825890123844, -0.02811327390372753, -0.04407838359475136, 0.02959967963397503, -0.007666005287319422, -0.01801121234893799, 0.004220661241561174, -0.02541572041809559, 0.03409560024738312, 0.024479834362864494, 0.07343950122594833, -0.04793202877044678, -0.021947437897324562, 0.001862596138380468, -0.017249658703804016, 0.05952967330813408, -0.01022134069353342, 0.022993428632616997, -0.02172723039984703, 0.028039870783686638, 0.030278656631708145, -0.026571813970804214, -0.026938827708363533, 0.0009404734009876847, -0.02038762904703617, 0.039343900978565216, -0.020259173586964607, -0.01716708019375801, -0.0036380263045430183, 0.0019187951693311334, 0.033067964017391205, 0.024094469845294952, 0.011322381906211376, 0.042720429599285126, -0.0024016478564590216, 0.02923266589641571, 0.01813049241900444, -0.0022112594451755285, 0.032370634377002716, 0.013469413854181767, 0.028076572343707085, 0.01673583872616291, 0.00981762446463108, 0.008170649409294128, 0.005211599171161652, 0.046207062900066376, 0.00810183398425579, -0.037196870893239975, 0.013616220094263554, 0.008028431795537472, 0.008973492309451103, -0.020901447162032127, -0.04334435611963272, -0.0001670200435910374, 0.0383896641433239, -0.011239804327487946, -0.032627545297145844, 0.004803295712918043, 0.03582056611776352, 0.027067283168435097, -0.029416173696517944, 0.033490028232336044, -0.013992409221827984, -0.01657985895872116, 0.03598572313785553, -0.05765790119767189, 0.04242682084441185, -0.008959729224443436, -0.0029796950984746218, -0.018580084666609764, 0.005170309916138649, 0.0020334869623184204, -0.016387175768613815, -0.01188207883387804, -0.022332802414894104, 0.0037274861242622137, 0.06760398298501968, 0.040041230618953705, 0.020020615309476852, 0.03734367713332176, -0.03536180034279823, 0.009221226908266544, 0.00281683262437582, 0.00691821426153183, 0.0027181976474821568, 0.012753737159073353, 0.03367353603243828, 0.014919119887053967, 0.02253466099500656, -0.024388080462813377, 0.005119845271110535, -0.010001132264733315, 0.030865877866744995, -0.007188886869698763, -0.0035049838479608297, -0.009542364627122879, -0.01855255849659443, 0.014286020770668983, -0.005555674433708191, 0.012973945587873459, -0.0325908437371254, 0.0011320088524371386, -0.0021263875532895327, 0.018102966248989105, -0.04007792845368385, 0.020681239664554596, 0.0010241984855383635, -0.05534571409225464, 0.030920930206775665, 0.03194857016205788, 0.00962494220584631, 0.013230855576694012, -0.042500223964452744, -0.016634909436106682, 0.01700192503631115, -0.030645670369267464, -0.006849398836493492, 0.012515177950263023, -0.012652807869017124, 0.044115085154771805, -0.007670592982321978, 0.030168551951646805, 0.023048480972647667, -0.05802491679787636, 0.047271404415369034, -0.047381509095430374, -0.052483003586530685, -0.00955154001712799, 0.020662888884544373, 0.01668078638613224, 0.011441661976277828, -0.026259852573275566, -0.02468169294297695, 0.04488581418991089, 0.017579970881342888, -0.026736970990896225, 0.08353239297866821, -0.02446148358285427, -0.021947437897324562, 0.020185770466923714, 0.019396690651774406, 0.014221793040633202, 0.0430140420794487, 0.009331331588327885, -0.005252887960523367, -0.05453828349709511, -0.021066604182124138, -0.03679315373301506, 0.027048932388424873, -0.029214315116405487, -0.010625055991113186, 0.011964656412601471, -0.027415946125984192, 0.018277298659086227, 0.020204121246933937, 0.02236950397491455, -0.03717852011322975, 0.02848028764128685, 0.005477684084326029, -0.067383773624897, 0.001526548876427114, 0.02134186401963234, -0.0369032584130764, -0.008601890876889229, -0.005574025213718414, 0.01040484756231308, 0.016001811251044273, -0.006684242747724056, -0.03015020117163658, 0.01684594340622425, -0.03139805048704147, -0.011377434246242046, 0.015056749805808067, -0.00536299217492342, 0.004133495502173901, 0.009404733777046204, -0.051565468311309814, -0.002720491262152791, 0.01823142170906067, -0.04484911262989044, 0.04371136799454689, 0.024222925305366516, 0.026516761630773544, 0.021360214799642563, -0.0188828706741333, 0.01850668154656887, 0.043087445199489594, -0.04580334946513176, -0.04268372803926468, 0.04000452905893326, -0.036279335618019104, -0.0025392782408744097, -0.008913853205740452, -0.039013590663671494, -0.013295082375407219, -0.01488241832703352, -0.05417126789689064, -0.0006766821024939418, -0.013313433155417442, -0.026131397113204002, 0.03356343135237694, -0.047271404415369034, 0.004626670386642218, 0.05622654780745506, -0.017313886433839798, -0.005541911814361811, -0.02178228087723255, 0.05402446165680885, -0.026847075670957565, -0.01126733049750328, 0.02044268138706684, 0.03967421501874924, -0.021965788677334785, 0.03207702562212944, -0.0034017611760646105, -0.00527123874053359, 0.02616809867322445, -0.006665891967713833, 0.0423901192843914, 0.007849512621760368, 0.000020572855646605603, 0.016176141798496246, 0.013616220094263554, -0.005752944853156805, 0.0078357495367527, 0.01432272233068943, 0.011790324933826923, -0.04253692552447319, -0.002484226133674383, 0.05791481211781502, -0.006175010930746794, 0.024039417505264282, 0.027103984728455544, -0.0061520724557340145, -0.005560262128710747, -0.029618030413985252, 0.012414248660206795, -0.0322788842022419, 0.004954689182341099, -0.032205481082201004, 0.02666356787085533, -0.03974761813879013, 0.05582283064723015, -0.0034636948257684708, 0.010634231381118298, 0.04264703020453453, -0.025030355900526047, 0.005771295167505741, 0.006450271233916283, 0.019543496891856194, 0.026681918650865555, -0.0296547319740057, -0.021103305742144585, 0.010845264419913292, 0.05035432428121567, -0.024901900440454483, -0.0021458850242197514, -0.05310692638158798, -0.01727718487381935, -0.02396601438522339, 0.013551992364227772, -0.02086474746465683, 0.01469891145825386, 0.011597642675042152, 0.018323173746466637, -0.06272269785404205, 0.02697552926838398, 0.007152185775339603, 0.01978205516934395, 0.009533189237117767, -0.00557861290872097, -0.012184864841401577, 0.0034017611760646105, -0.0049317507073283195, 0.04635386914014816, -0.012900542467832565, 0.06540189683437347, -0.02939782291650772, -0.005853873677551746, -0.011671045795083046, 0.013992409221827984, 0.014735613018274307, -0.046317167580127716, -0.045289527624845505, 0.026425009593367577, -0.032480739057064056, 0.039454005658626556, -0.015653148293495178, -0.044702306389808655, -0.054831892251968384, 0.02686542645096779, 0.042500223964452744, 0.005101494956761599, -0.020185770466923714, -0.0014955820515751839, 0.01048742514103651, -0.028939055278897285, -0.01850668154656887, -0.01882781833410263, 0.028682144358754158, 0.0007311607478186488, 0.016322948038578033, -0.011423311196267605, 0.03813275694847107, 0.026094695553183556, -0.001785752596333623, 0.004314708523452282, -0.005642840638756752, -0.038756679743528366, 0.03536180034279823, -0.022075893357396126, 0.013625395484268665, -0.049803800880908966, -0.005697892513126135, 0.0012948713265359402, 0.015570569783449173, -0.027746260166168213, 0.0035439790226519108, 0.014166740700602531, 0.027012230828404427, -0.01599263586103916, 0.03336157277226448, 0.016157791018486023, 0.00010085717076435685, 0.02493860200047493, -0.02044268138706684, 0.00436058547347784, 0.01737811416387558, -0.015845829620957375, -0.0374537818133831, -0.0030714485328644514, 0.026351606473326683, -0.0325174406170845, -0.034077249467372894, -0.04767512157559395, -0.01193713117390871, -0.02890235371887684, 0.039710916578769684, -0.0024979892186820507, -0.007977967150509357, -0.06756728142499924, -0.011992182582616806, 0.025819435715675354, -0.03791254758834839, -0.02242455631494522, -0.019598549231886864, 0.004154139664024115, 0.017313886433839798, 0.03191186860203743, -0.0029544627759605646, 0.003833002643659711, 0.003236604854464531, -0.012460125610232353, 0.03361848369240761, -0.01935998909175396, 0.013882305473089218, 0.009285454638302326, -0.008973492309451103, 0.051088351756334305, 0.00890467781573534, 0.022497959434986115, 0.014056636951863766, -0.021855683997273445, -0.027856362983584404, -0.0057391817681491375, 0.019818756729364395, -0.01346023939549923, 0.015148503705859184, -0.014799839816987514, 0.004922575317323208, 0.015240256674587727, 0.010386496782302856, -0.0018362170085310936, 0.027929766103625298, 0.027324194088578224, 0.014854892157018185, 0.01354281697422266, 0.044592201709747314, 0.07369641214609146, -0.011285681277513504, 0.009615766815841198, 0.05149206519126892, -0.0069778538309037685, -0.019543496891856194, -0.02387426234781742, 0.04437199607491493, -0.04734480753540993, 0.02365405298769474, -0.03938060253858566, 0.013845603913068771, 0.029618030413985252, -0.04723470285534859, 0.001932558137923479, -0.00007229172479128465, 0.036114178597927094, -0.017313886433839798 ]
Artificial intelligence (AI) has the potential to greatly improve society, but as with any powerful technology, it comes with heightened risks and responsibilities. Current AI research lacks a systematic discussion of how to manage long-tail risks from AI systems, including speculative long-term risks. Keeping in mind the potential benefits of AI, there is some concern that building ever more intelligent and powerful AI systems could eventually result in systems that are more powerful than us; some say this is like playing with fire and speculate that this could create existential risks (x-risks). To add precision and ground these discussions, we provide a guide for how to analyze AI x-risk, which consists of three parts: First, we review how systems can be made safer today, drawing on time-tested concepts from hazard analysis and systems safety that have been designed to steer large processes in safer directions. Next, we discuss strategies for having long-term impacts on the safety of future systems. Finally, we discuss a crucial concept in making AI systems safer by improving the balance between safety and general capabilities. We hope this document and the presented concepts and tools serve as a useful guide for understanding how to analyze AI x-risk.
[ -0.0226228516548872, -0.027493050321936607, -0.027689429000020027, -0.0184596199542284, 0.06500142812728882, -0.007280748803168535, -0.008532664738595486, 0.010044782422482967, 0.0020668881479650736, 0.00152684620115906, -0.0026879366487264633, 0.029162270948290825, 0.05082286521792412, 0.006721068639308214, -0.02780725620687008, 0.018253421410918236, 0.004774462431669235, -0.020305581390857697, -0.008719224482774734, -0.03927578404545784, -0.011488167569041252, 0.014217833988368511, -0.0721496194601059, 0.035250015556812286, 0.008940150961279869, -0.0018103682668879628, 0.010329531505703926, 0.00775205809623003, -0.07713764160871506, 0.0665331780910492, 0.016662752255797386, -0.012578070163726807, -0.04359612241387367, -0.042928434908390045, -0.03428776189684868, -0.005307140294462442, 0.056007269769907, 0.011920200660824776, -0.023369092494249344, 0.09371202439069748, 0.014296385459601879, -0.0039496710523962975, -0.03169555962085724, -0.04658108204603195, 0.0124111482873559, -0.017055509611964226, -0.023408368229866028, -0.04257494956254959, -0.03297202289104462, -0.008341195061802864, 0.004565809853374958, -0.027551963925361633, 0.04654180631041527, -0.038725923746824265, -0.0476808026432991, -0.008189001120626926, 0.0738384798169136, -0.0582067146897316, 0.07427050918340683, -0.0030757850036025047, 0.0379011332988739, 0.021405303850769997, -0.015877235680818558, 0.017978491261601448, -0.011714003048837185, -0.026668258011341095, -0.0005943530704826117, 0.015513935126364231, -0.031145697459578514, 0.0018852376379072666, -0.060681089758872986, -0.003684559604153037, -0.026668258011341095, -0.03208831697702408, 0.02782689407467842, -0.032343607395887375, 0.03312912583351135, 0.07768750190734863, -0.022897783666849136, 0.05710699036717415, 0.05294375866651535, 0.026354052126407623, -0.01445348933339119, 0.04536353051662445, 0.04008093848824501, 0.02291742153465748, 0.016122709959745407, -0.06888972967863083, 0.03091004304587841, -0.03242215886712074, -0.030183440074324608, 0.06515853106975555, -0.010879392735660076, -0.01215585507452488, 0.033836089074611664, -0.021562406793236732, -0.025588173419237137, 0.0138152576982975, -0.00476955296471715, -0.014532040804624557, 0.014384756796061993, -0.00700581818819046, 0.008002441376447678, -0.02702173963189125, -0.05671423301100731, -0.08562121540307999, -0.01899966038763523, 0.014787333086133003, 0.017497362568974495, 0.15003350377082825, -0.0048554688692092896, 0.013245758600533009, -0.07564516365528107, 0.004116593394428492, -0.0237225741147995, 0.008297009393572807, -0.03499472513794899, -0.0711677223443985, -0.01081066019833088, 0.01684931106865406, -0.06511925160884857, 0.020187754184007645, 0.05341506749391556, -0.008395198732614517, -0.03468051925301552, 0.04976242035627365, 0.006274306681007147, -0.05561451241374016, 0.006524689961224794, 0.04775935411453247, -0.006833986844867468, 0.1061231717467308, 0.014816789887845516, 0.018862195312976837, -0.0006910083466209471, -0.021405303850769997, 0.035937342792749405, -0.0037582016084343195, 0.005336597096174955, 0.0038883027154952288, -0.04984097182750702, -0.023251265287399292, -0.07321006059646606, 0.018381066620349884, -0.003122424939647317, -0.009740394540131092, -0.04257494956254959, 0.03744946047663689, -0.040728989988565445, -0.004045405890792608, -0.04815211147069931, 0.001431111479178071, -0.028180375695228577, -0.004521624650806189, 0.05640002712607384, -0.012764629907906055, -0.008080992847681046, 0.027630515396595, -0.03222578018903732, 0.07317078858613968, 0.03440558910369873, -0.04638470336794853, -0.020168116316199303, 0.07525240629911423, 0.06311618536710739, -0.007644049823284149, 0.06531563401222229, -0.001227981992997229, -0.09190534055233002, 0.05761757865548134, -0.02550962194800377, -0.08177218586206436, -0.05192258954048157, 0.008233186788856983, 0.004722913261502981, 0.005370963830500841, 0.02193552628159523, 0.059777744114398956, 0.0036722859367728233, 0.0012052756501361728, -0.05793178454041481, -0.020580511540174484, -0.00648541422560811, 0.017448266968131065, -0.0211500097066164, 0.03489653393626213, 0.07521312683820724, -0.004826012067496777, 0.027257394045591354, 0.007226744666695595, -0.007295477204024792, -0.036958515644073486, 0.020207392051815987, 0.006023923400789499, -0.0023602291475981474, -0.035446397960186005, -0.007997531443834305, -0.03432703763246536, 0.005601708777248859, -0.03367898613214493, -0.02594165690243244, -0.0077471486292779446, 0.0027370313182473183, 0.06877189874649048, 0.008459022268652916, 0.024763382971286774, 0.04516715183854103, -0.026648620143532753, 0.0015734861372038722, -0.016220899298787117, 0.03189193829894066, -0.02613803558051586, -0.00503711961209774, -0.039315059781074524, -0.03338441625237465, -0.015513935126364231, -0.002656024880707264, 0.050194453448057175, -0.04634542763233185, -0.04854486882686615, -0.0038122059777379036, -0.0009377093520015478, 0.02641296572983265, -0.02959430404007435, 0.03338441625237465, -0.03010488860309124, -0.025666724890470505, -0.018695274367928505, -0.010899030603468418, -0.016574380919337273, 0.002739486051723361, 0.00841483660042286, 0.004158323630690575, 0.013314491137862206, 0.05196186527609825, -0.011880924925208092, 0.03678177297115326, 0.004219692200422287, -0.014865884557366371, 0.0023418187629431486, -0.0369192399084568, -0.01714388094842434, 0.03807787224650383, -0.015042625367641449, 0.0709320679306984, 0.015435383655130863, -0.042417846620082855, 0.02014847844839096, -0.021699871867895126, 0.03939361125230789, -0.024449177086353302, 0.0297121312469244, 0.04080754145979881, 0.0021307114511728287, -0.0023209534119814634, 0.005915915127843618, 0.061662983149290085, 0.012087122537195683, 0.0007707873010076582, 0.03138135373592377, 0.05105851963162422, 0.000740103074349463, 0.03418957069516182, 0.05526103079319, -0.05604654550552368, -0.01696714013814926, 0.04493149742484093, 0.008787957020103931, 0.0369192399084568, -0.00475727953016758, 0.029869234189391136, 0.004276151303201914, 0.013569783419370651, -0.009686390869319439, -0.015317556448280811, -0.028690960258245468, 0.0569891631603241, 0.022210456430912018, -0.02902480587363243, 0.01684931106865406, -0.0016999050276353955, -0.006328310817480087, 0.06111312285065651, -0.047405872493982315, -0.03817606344819069, -0.07085351645946503, -0.04096464440226555, 0.0044700754806399345, -0.11971259117126465, -0.017968671396374702, -0.0020779345650225878, 0.018184687942266464, -0.009249447844922543, 0.020403770729899406, 0.02613803558051586, 0.007953346706926823, 0.026373689994215965, 0.026275500655174255, -0.04006130248308182, -0.028141099959611893, 0.0039496710523962975, -0.012636983767151833, -0.011831830255687237, 0.03898121789097786, -0.004607540555298328, 0.03548567369580269, 0.010702651925384998, 0.07552733272314072, -0.038627736270427704, 0.013127931393682957, 0.024900848045945168, -0.002788580721244216, -0.058481644839048386, -0.0009143893839791417, 0.04807355999946594, 0.026491517201066017, 0.00906288716942072, 0.015268461778759956, 0.014433851465582848, -0.018675636500120163, 0.050783589482307434, -0.050194453448057175, -0.09426188468933105, 0.044303085654973984, -0.07658778131008148, -0.01141943410038948, 0.02352619543671608, 0.03805823624134064, -0.05922788381576538, -0.022014077752828598, -0.016427097842097282, -0.012568251229822636, -0.022112267091870308, -0.02411533147096634, -0.014139282517135143, -0.01750718057155609, -0.0342288464307785, 0.010604461655020714, -0.0248222965747118, -0.03328622877597809, -0.004524079617112875, -0.032166868448257446, -0.05781395733356476, -0.056085821241140366, -0.03746910020709038, -0.05671423301100731, 0.014424032531678677, 0.01740899123251438, 0.01770356111228466, 0.01574959047138691, 0.0011371567379683256, -0.004438163712620735, 0.016613656654953957, 0.006804529577493668, 0.0036526480689644814, 0.01719297468662262, 0.015072082169353962, -0.015474659390747547, 0.03519110381603241, -0.0014568861806765199, 0.033168401569128036, -0.04665963351726532, -0.027669791132211685, 0.00867994874715805, -0.04575629159808159, -0.017674103379249573, -0.03609444573521614, -0.009234718978404999, -0.04925183579325676, 0.011154322884976864, -0.026471879333257675, 0.059070780873298645, 0.04516715183854103, 0.01141943410038948, 0.049016181379556656, -0.03061547502875328, 0.022406835108995438, -0.04100392013788223, -0.02582382969558239, 0.036938875913619995, 0.0006096952129155397, 0.0031764290761202574, 0.031086783856153488, 0.023899314925074577, -0.047405872493982315, 0.010997219942510128, 0.026255862787365913, -0.0379011332988739, 0.06394097954034805, 0.0540434792637825, -0.018695274367928505, 0.02421352081000805, -0.03120461106300354, -0.06311618536710739, 0.010643737390637398, -0.0029726859647780657, -0.0036501933354884386, -0.02623622491955757, 0.027866169810295105, -0.028278565034270287, 0.013029742054641247, -0.0028744966257363558, 0.031656283885240555, 0.026354052126407623, -0.004045405890792608, 0.006991089787334204, 0.020109202712774277, -0.015543391928076744, 0.02073761448264122, -0.002478056587278843, -0.010761565528810024, 0.013687611557543278, -0.030635112896561623, -0.03925614804029465, -0.006372496020048857, 0.036192636936903, 0.014041093178093433, 0.0032402523793280125, 0.003353170119225979, -0.03697815164923668, -0.038941942155361176, 0.010201885364949703, 0.04347829520702362, -0.03140098974108696, 0.00475727953016758, 0.007094188593327999, 0.014158920384943485, -0.0012764630373567343, -0.013471594080328941, -0.05781395733356476, 0.025882743299007416, -0.008247914724051952, -0.014345480129122734, -0.0265307929366827, -0.02839639224112034, -0.030026337131857872, -0.0033458059187978506, -0.004138685762882233, 0.007536041084676981, -0.018940746784210205, -0.028592770919203758, 0.022014077752828598, 0.009823855943977833, -0.00019530497957020998, -0.042221467941999435, -0.031067145988345146, -0.008125178515911102, -0.0033163491170853376, -0.0074820369482040405, -0.03898121789097786, -0.02423315867781639, 0.026196949183940887, -0.07073568552732468, -0.03542675822973251, 0.037842217832803726, -0.030949318781495094, 0.023565471172332764, -0.046109773218631744, 0.015317556448280811, -0.030124526470899582, 0.03670322149991989, 0.05251172557473183, 0.01785084418952465, -0.015828141942620277, 0.027571601793169975, 0.04936966300010681, -0.031184973195195198, -0.018665816634893417, 0.0163878221064806, 0.042614225298166275, -0.002815582789480686, -0.04508860036730766, -0.010604461655020714, -0.008640673011541367, -0.02132675051689148, -0.0029039534274488688, -0.014492765069007874, -0.0045510814525187016, -0.015739770606160164, -0.018174869939684868, 0.00668179290369153, 0.05585016682744026, 0.01205766573548317, -0.03279528021812439, -0.020207392051815987, 0.0039693089202046394, 0.005528066772967577, 0.015386288985610008, -0.0012936461716890335, -0.03756728768348694, -0.0021699871867895126, -0.03729235753417015, 0.05361144617199898, -0.045913394540548325, -0.07057858258485794, -0.04618832468986511, -0.06229139491915703, -0.01890147104859352, 0.05211896821856499, 0.0308118537068367, -0.026157673448324203, -0.03381644934415817, -0.027866169810295105, 0.033541519194841385, 0.0038784837815910578, -0.008910694159567356, -0.01814541220664978, -0.029967423528432846, -0.01640745997428894, -0.04300698637962341, -0.015572848729789257, -0.05164765939116478, 0.01885237731039524, 0.012470061890780926, 0.01888183318078518, -0.01858726516366005, 0.05636075139045715, 0.008370651863515377, 0.053689997643232346, 0.014973892830312252, -0.01673148386180401, -0.0017428629798814654, 0.004779371898621321, 0.015818322077393532, -0.04508860036730766, 0.029378287494182587, 0.023958228528499603, -0.012430786155164242, 0.003618281800299883, -0.0013734251260757446, -0.0352107398211956, 0.026373689994215965, -0.05152982845902443, -0.028671322390437126, -0.032834555953741074, 0.007241473067551851, 0.029456838965415955, 0.05620364844799042, -0.016594018787145615, -0.024665193632245064, -0.061073847115039825, 0.05412203073501587, 0.03731199726462364, 0.046698909252882004, 0.005974828731268644, 0.0033875363878905773, 0.0672401413321495, -0.008154635317623615, -0.006568875163793564, 0.029339011758565903, -0.01770356111228466, -0.0454813577234745, -0.012882457114756107, 0.008925422094762325, 0.015857597813010216, -0.0077962432987987995, 0.013294853270053864, 0.0008057672530412674, -0.030831491574645042, -0.013638515956699848, -0.0027247576508671045, -0.026059484109282494, -0.034562692046165466, 0.053493618965148926, -0.007683325558900833, -0.0476808026432991, 0.05663568153977394, 0.07615574449300766, -0.015366651117801666, 0.0198048148304224, -0.013098474591970444, -0.020285943523049355, -0.012754810974001884, -0.0254310704767704, -0.029437201097607613, -0.0048039196990430355, -0.0145516786724329, -0.059581365436315536, -0.0347197949886322, 0.009730575606226921, -0.039138320833444595, 0.002384776482358575, -0.03128316253423691, 0.02621658705174923, -0.008026988245546818, -0.0014225197955965996, -0.02552925981581211, -0.023977866396307945, -0.014090187847614288, -0.0017097240779548883, -0.053100861608982086, 0.006411771755665541, -0.012362053617835045, 0.00513530895113945, -0.026157673448324203, 0.018007947131991386, 0.03079221583902836, -0.010908849537372589, 0.023153075948357582, -0.039629265666007996, 0.027473412454128265, 0.037351273000240326, 0.0410824716091156, 0.02162132039666176, -0.03365934640169144, 0.03491617366671562, 0.008252824656665325, 0.01750718057155609, -0.002206808188930154, 0.025195416063070297, 0.019844090566039085, -0.04485294595360756, 0.026098759844899178, -0.032461438328027725, 0.05561451241374016, -0.02007974497973919, -0.009190533310174942, -0.024174245074391365, -0.009431097656488419, 0.048112835735082626, -0.007084369659423828, 0.014296385459601879, 0.047798629850149155, 0.0018201872007921338, 0.006426500156521797, 0.0701858252286911, -0.016446735709905624, 0.036330100148916245, -0.0019502881914377213, 0.011841649189591408, -0.03079221583902836, -0.003029144834727049, 0.0008941377745941281, -0.03358079493045807, 0.022779954597353935, -0.028455305844545364, 0.046227600425481796, 0.07560588419437408, 0.023192351683974266, -0.04355684667825699, 0.005886458326131105, -0.017084967344999313, 0.022956697270274162, 0.09284795820713043, -0.007889523170888424, 0.01895056664943695, 0.03167591989040375, -0.01082047913223505, 0.03312912583351135, 0.009936773218214512, 0.05082286521792412, 0.024684831500053406, 0.02171950973570347, 0.03585879132151604, 0.029162270948290825, 0.003399810055270791, 0.020992906764149666, -0.0004930951981805265, 0.021699871867895126, 0.0420643649995327, 0.012794086709618568, 0.0015378925018012524, -0.006549237295985222, 0.02851421944797039, 0.024979399517178535, -0.0038637553807348013, 0.04905545711517334, -0.012116579338908195, 0.0005019936361350119, 0.018253421410918236, 0.00508130481466651, -0.043321192264556885, -0.05372927337884903, 0.03365934640169144, -0.008630854077637196, -0.00017827523697633296, -0.0015391198685392737, 0.03984528407454491, 0.02820001356303692, -0.006691611837595701, -0.016319088637828827, -0.004911927971988916, -0.01242096722126007, 0.004055224824696779, -0.024350987747311592, -0.004001220688223839, -0.005606618244200945, 0.006961632985621691, -0.007884614169597626, -0.0011156777618452907, -0.03089040517807007, -0.0028892250265926123, 0.005015026777982712, -0.006956723518669605, 0.003534820629283786, 0.014993530698120594, -0.05294375866651535, -0.021503493189811707, 0.004136231262236834, -0.0315384566783905, -0.006917447783052921, -0.008910694159567356, -0.004533898551017046, 0.009382002986967564, -0.016220899298787117, 0.008247914724051952, 0.006509961560368538, -0.01709478534758091, -0.018498895689845085, 0.026982463896274567, 0.02252466231584549, 0.03365934640169144, -0.009946592152118683, 0.020069926977157593, 0.047995008528232574, 0.027257394045591354, 0.03658539429306984, -0.008488479070365429, 0.005861910991370678, 0.021503493189811707, 0.020580511540174484, -0.01899966038763523, 0.0058275447227060795, -0.02700210176408291, -0.036428291350603104, 0.012695897370576859, -0.0020693428814411163, 0.021071458235383034, -0.0030708755366504192, -0.01804722286760807, 0.04807355999946594, 0.004718003794550896, -0.008719224482774734, 0.0030414185021072626, 0.01670202799141407, 0.032834555953741074, 0.017713379114866257, 0.005719536449760199, 0.005312049761414528, -0.013147569261491299, 0.0432819165289402, 0.0004906404647044837, 0.012450424022972584, -0.0315384566783905, 0.0084982980042696, -0.018547989428043365, -0.02651115506887436, 0.022563938051462173, -0.003191157476976514, 0.02533288113772869, 0.026452241465449333, -0.01628963276743889, 0.060052674263715744, -0.03572132810950279, -0.01873455010354519, -0.0034709975589066744, 0.008213548921048641, 0.008999064564704895, -0.007305296137928963, -0.00695181405171752, -0.005920824594795704, 0.09559725970029831, -0.002019020728766918, 0.02503831312060356, 0.04972314462065697, 0.016711845993995667, -0.01132124476134777, -0.005341506563127041, 0.01648601144552231, -0.0006474367692135274, 0.013235939666628838, -0.05533958226442337, 0.06072036549448967, -0.0381564237177372, 0.010417901910841465, -0.022387197241187096, 0.02741449885070324, -0.0105750048533082, -0.02929973602294922, -0.005130399484187365, 0.0044897133484482765, -0.009519468061625957, -0.03287383168935776, 0.01868545450270176, -0.02939792536199093, -0.0007529904250986874, -0.038117147982120514, -0.04728804528713226, 0.02533288113772869, 0.057460471987724304, -0.023094162344932556, -0.0007026683306321502, 0.02900516800582409, 0.0037115616723895073, -0.0011353156296536326, 0.006146660540252924, -0.026982463896274567, -0.015484478324651718, 0.00879286602139473, -0.022779954597353935, 0.05954208970069885, -0.0041656880639493465, 0.02431171014904976, -0.024488452821969986, 0.022269370034337044, 0.004239330068230629, 0.013854533433914185, 0.010476815514266491, 0.036958515644073486, 0.011095409281551838, 0.03627118840813637, 0.06637607514858246, 0.014581135474145412, 0.06460866332054138, 0.0005489404429681599, 0.021955164149403572, -0.017880301922559738, 0.05172621086239815, -0.02941756322979927, -0.02052159793674946, -0.005380782764405012, -0.034837622195482254, -0.020855441689491272, -0.008463931269943714, -0.01270571630448103, 0.007668597158044577, 0.05211896821856499, -0.00803189817816019, 0.0035863700322806835, -0.02743413671851158, -0.006460866890847683, 0.01306901779025793, -0.04878052696585655, 0.024390263482928276, -0.024802658706903458, -0.0005661236355081201, -0.03900085389614105, -0.03701742738485336, -0.00347590702585876, 0.04504932463169098, -0.0019392418907955289, -0.011822011321783066, -0.0051500373519957066, 0.0035937342327088118, -0.008925422094762325, -0.009043249301612377, 0.004752370063215494, -0.010133152827620506, 0.03218650445342064, -0.023270903155207634, 0.004938929807394743, -0.06142732873558998, -0.01865599863231182, 0.006372496020048857, 0.0052678645588457584, 0.015219367109239101, 0.02741449885070324, 0.048584144562482834, -0.0011150641366839409, -0.0008573167724534869, 0.009745304472744465, 0.04249639809131622, -0.055182479321956635, -0.007982803508639336, 0.0037508374080061913, -0.0028794060926884413, 0.0018189598340541124, -0.04984097182750702, -0.021582044661045074, -0.07450616359710693, -0.02949611470103264, 0.028533857315778732, -0.015258642844855785, 0.002276768209412694, 0.0007652641506865621, 0.03159736841917038, 0.03676213324069977, -0.00979439914226532, 0.01932368613779545, 0.027787618339061737, 0.0018520987359806895, 0.027591239660978317, 0.014885522425174713, 0.01305919885635376, -0.015239004977047443, -0.013520688749849796, -0.02892661653459072, -0.002438780851662159, -0.0019257408566772938, -0.025882743299007416, -0.0024731471203267574, -0.01621107943356037, 0.021915888413786888, -0.008994154632091522, 0.047013115137815475, 0.01890147104859352, 0.020875079557299614, 0.010771384462714195, -0.004443073179572821, -0.03147954121232033, 0.018282877281308174, -0.019755719229578972, -0.04186798632144928, -0.007310205604881048, 0.00857194047421217, -0.01743844896554947, 0.0052875024266541, -0.008071173913776875, 0.030242353677749634, -0.0430462621152401, -0.016662752255797386, -0.05553596094250679, 0.01611289009451866, -0.04567773640155792, 0.04897690564393997, -0.014316023327410221, -0.040120214223861694, -0.03200976550579071, -0.007536041084676981, 0.0081300875172019, 0.016662752255797386, 0.006902719382196665, -0.039825644344091415, -0.011655089445412159, -0.0297121312469244, 0.01221476960927248, -0.030576199293136597, 0.008002441376447678, -0.0188327394425869, -0.013599240221083164, -0.0049045635387301445, 0.024350987747311592, 0.024409901350736618, 0.00015242380322888494, 0.004624723922461271, -0.0027075745165348053, -0.020659063011407852, 0.021169647574424744, -0.027178842574357986, -0.00002857466824934818, -0.03212759271264076, 0.01655474305152893, 0.05423985794186592, 0.013569783419370651, 0.0020607514306902885, -0.020776890218257904, 0.044813670217990875, 0.03650684282183647, -0.01614234782755375, 0.057067714631557465, -0.0113114258274436, 0.02871059812605381, 0.019893184304237366, -0.033953916281461716, -0.04995879903435707, 0.003534820629283786, -0.018793463706970215, -0.04339974373579025, -0.02851421944797039, 0.04045405983924866, -0.011488167569041252, 0.04273205250501633, 0.0018717366037890315, -0.022897783666849136, -0.008817413821816444, 0.06460866332054138, -0.027689429000020027, -0.03167591989040375, -0.04068971425294876, 0.0016409914242103696, -0.03226505592465401, -0.0024240524508059025, -0.013383223675191402, -0.01995209977030754, 0.00272966711781919, 0.006941995117813349, 0.023310178890824318, -0.02113037183880806, 0.02692355029284954, -0.03477870672941208, 0.0005111988866701722, -0.016790397465229034, -0.009627477265894413, -0.06810421496629715, -0.04885907843708992, -0.02391895279288292, -0.0025431071408092976, 0.0006719841621816158, -0.06103457137942314, 0.018616722896695137, 0.007133464328944683, 0.020619787275791168, -0.022760316729545593, -0.015710314735770226, -0.018714912235736847, 0.012087122537195683, -0.010201885364949703, 0.009995687752962112, 0.002193307038396597, 0.007118735928088427, -0.038549184799194336, -0.004227056168019772, 0.008684857748448849, 0.0667688325047493, -0.028180375695228577, 0.002680572448298335, 0.006995999254286289, -0.010643737390637398, -0.022897783666849136, -0.005596799310296774, 0.032363247126340866, 0.005876639392226934, 0.002749304985627532, 0.005253136157989502, -0.013687611557543278, -0.004880016203969717, 0.015877235680818558, -0.037724390625953674, 0.017526818439364433, -0.0843643844127655, 0.0054838815703988075, 0.05027300491929054, 0.031754471361637115, 0.033168401569128036 ]
In order to develop effective sequential recommenders, a series of sequence representation learning (SRL) methods are proposed to model historical user behaviors. Most existing SRL methods rely on explicit item IDs for developing the sequence models to better capture user preference. Though effective to some extent, these methods are difficult to be transferred to new recommendation scenarios, due to the limitation by explicitly modeling item IDs. To tackle this issue, we present a novel universal sequence representation learning approach, named UniSRec. The proposed approach utilizes the associated description text of items to learn transferable representations across different recommendation scenarios. For learning universal item representations, we design a lightweight item encoding architecture based on parametric whitening and mixture-of-experts enhanced adaptor. For learning universal sequence representations, we introduce two contrastive pre-training tasks by sampling multi-domain negatives. With the pre-trained universal sequence representation model, our approach can be effectively transferred to new recommendation domains or platforms in a parameter-efficient way, under either inductive or transductive settings. Extensive experiments conducted on real-world datasets demonstrate the effectiveness of the proposed approach. Especially, our approach also leads to a performance improvement in a cross-platform setting, showing the strong transferability of the proposed universal SRL method. The code and pre-trained model are available at: https://github.com/RUCAIBox/UniSRec.
[ 0.024581702426075935, 0.010947727598249912, -0.03037656471133232, -0.01075343880802393, 0.02838299609720707, -0.004865656606853008, 0.01169109158217907, 0.02037493698298931, -0.04328406974673271, -0.01812794990837574, -0.01430131308734417, -0.02272329293191433, 0.0009988956153392792, -0.04203386604785919, 0.040614716708660126, 0.010913938283920288, 0.023399077355861664, 0.01684395782649517, -0.023872127756476402, -0.025240592658519745, 0.00865850318223238, -0.0004260617133695632, -0.019057154655456543, 0.038959041237831116, 0.008962607011198997, 0.02747068554162979, -0.010778781026601791, -0.00950323510915041, -0.06207090988755226, -0.00480652553960681, 0.03612074255943298, 0.008599372580647469, -0.02578122168779373, 0.014715231955051422, -0.058117564767599106, 0.007868679240345955, 0.06578773260116577, 0.05581989511847496, -0.03632347658276558, 0.00945255160331726, 0.03966861590743065, 0.00681276386603713, -0.06139512360095978, 0.02856883779168129, 0.0051951021887362, -0.04466943070292473, -0.023432867601513863, -0.0012438679113984108, -0.027082109823822975, -0.036830317229032516, -0.0114545663818717, -0.011201146990060806, 0.012637191452085972, -0.026372535154223442, -0.056022629141807556, 0.05345464497804642, 0.04304754361510277, -0.00961305107921362, 0.039702408015728, 0.02253745123744011, -0.054029062390327454, 0.008835896849632263, -0.0013621303951367736, -0.004595342557877302, 0.021794086322188377, -0.02584880031645298, 0.044331539422273636, -0.017114270478487015, 0.051866546273231506, -0.008113651536405087, -0.061901964247226715, 0.01540791243314743, 0.03997271880507469, 0.02647390216588974, -0.014504048973321915, 0.06281427294015884, 0.034836750477552414, 0.030832719057798386, 0.032049134373664856, 0.008096756413578987, 0.026237377896904945, 0.027555160224437714, 0.03346828371286392, 0.011167357675731182, 0.019496414810419083, -0.033806174993515015, 0.0005292774294503033, -0.05139349773526192, 0.002424380974844098, 0.005106405355036259, -0.007475878577679396, 0.011479908600449562, -0.014132367447018623, -0.03615453094244003, -0.05156244337558746, -0.011403882876038551, 0.012214825488626957, 0.01632867008447647, -0.05409663915634155, -0.010736544616520405, 0.02775789424777031, 0.003913221415132284, -0.02856883779168129, -0.0627804845571518, 0.016370907425880432, -0.024328282102942467, -0.016751036047935486, 0.02143929898738861, -0.05913124233484268, 0.08095911890268326, 0.016708800569176674, -0.026524586603045464, 0.005271127913147211, 0.02632185071706772, 0.006918355356901884, -0.017401481047272682, -0.09143379330635071, -0.07291726768016815, 0.0270990040153265, -0.044331539422273636, 0.039736196398735046, 0.009173789992928505, 0.01239221915602684, -0.02672732248902321, -0.024581702426075935, 0.03804673254489899, -0.005144418217241764, 0.00688456604257226, 0.02529127709567547, 0.04007408767938614, -0.02878846786916256, 0.05507652834057808, -0.04345301538705826, -0.041831132024526596, 0.02265571430325508, 0.02916014939546585, 0.007674390450119972, 0.04172976315021515, -0.027082109823822975, -0.023179447278380394, -0.03987135365605354, -0.0292277280241251, -0.019648468121886253, -0.0037843994796276093, -0.00026252688257955015, -0.016269538551568985, -0.01261184923350811, 0.062307436019182205, -0.0161090400069952, 0.041425660252571106, 0.0016345565672963858, 0.021979928016662598, -0.059367768466472626, 0.01044088788330555, 0.003767504822462797, 0.07953996956348419, 0.040986400097608566, -0.054434534162282944, 0.037708837538957596, 0.04044577106833458, 0.03922935575246811, 0.013465029187500477, 0.0048867748118937016, 0.06703793257474899, 0.06088828667998314, 0.002289223950356245, 0.07251179963350296, 0.01919231191277504, -0.07366063445806503, 0.03828325495123863, -0.05534684285521507, 0.043621961027383804, 0.004810749087482691, 0.019327469170093536, 0.04493974521756172, 0.0014634982217103243, 0.0873115062713623, -0.03865493834018707, -0.03341760113835335, -0.03103545494377613, -0.028636416420340538, 0.027115898206830025, 0.001458218670450151, 0.043554384261369705, 0.07501220703125, 0.028045104816555977, 0.07420126348733902, 0.02360181324183941, -0.024615492671728134, -0.012231719680130482, 0.04210144653916359, 0.024463439360260963, 0.0395672507584095, 0.05331948772072792, 0.010094547644257545, 0.004210989456623793, -0.010821017436683178, 0.0008574030362069607, -0.03000488318502903, 0.02419312670826912, -0.036458633840084076, -0.043520595878362656, 0.034769169986248016, -0.008540241047739983, 0.013946525752544403, -0.0014170380309224129, 0.0026017746422439814, 0.016683457419276237, -0.036458633840084076, -0.10048932582139969, 0.02456480823457241, -0.03912798687815666, -0.06338869035243988, -0.015281202271580696, -0.01448715478181839, -0.012012089602649212, -0.011184251867234707, -0.008282598108053207, -0.026761110872030258, 0.002485624048858881, -0.0005760016501881182, -0.06953833997249603, 0.05804998800158501, -0.009900259785354137, 0.002312453929334879, -0.028551943600177765, 0.019952571019530296, 0.002008350333198905, 0.04257449507713318, -0.009334289468824863, -0.013684659264981747, 0.000883272965438664, 0.0015828167088329792, -0.015830278396606445, 0.010331072844564915, 0.021016933023929596, 0.008717634715139866, -0.06311837583780289, -0.05389390513300896, -0.028653310611844063, 0.012510481290519238, 0.05372495949268341, 0.023551128804683685, 0.014529391191899776, 0.03456643596291542, 0.002724260790273547, 0.015686674043536186, 0.014850389212369919, 0.058185141533613205, 0.027453791350126266, -0.0344819612801075, 0.000677897478453815, -0.014309761114418507, 0.0072858138009905815, -0.03909419849514961, 0.01713961362838745, 0.06321974843740463, -0.06511194258928299, 0.008088309317827225, -0.046054791659116745, -0.005161312874406576, 0.044838376343250275, 0.0069563682191073895, 0.011834695935249329, 0.025561591610312462, 0.046561628580093384, 0.06771372258663177, -0.07575556635856628, 0.06626078486442566, 0.002156178466975689, 0.04037819057703018, -0.04798078164458275, -0.06115860119462013, -0.0025827682111412287, -0.03432990983128548, -0.04977161064743996, 0.03578285127878189, 0.006314372178167105, 0.05906366556882858, 0.022148873656988144, 0.015222071669995785, 0.005849769338965416, 0.0029924632981419563, 0.0051528653129935265, -0.053150542080402374, -0.05872577056288719, -0.041831132024526596, 0.01636246033012867, -0.03720200061798096, 0.03169434517621994, -0.013828263618052006, -0.0011572828516364098, -0.06700414419174194, 0.03632347658276558, 0.07122780382633209, 0.05321811884641647, 0.014351997524499893, 0.0562591552734375, 0.025325067341327667, -0.045210059732198715, 0.007699732668697834, -0.017638005316257477, 0.07224148511886597, 0.019614677876234055, -0.0355125367641449, 0.04953508824110031, -0.00018320126400794834, -0.010947727598249912, -0.04216902330517769, -0.05700251832604408, 0.023736970499157906, -0.013608633540570736, 0.0416959747672081, -0.018330685794353485, 0.0003270696906838566, 0.02037493698298931, 0.04037819057703018, 0.010897043161094189, -0.02993730455636978, -0.014884178526699543, -0.01599077694118023, -0.01292440015822649, -0.04669678583741188, -0.006770527455955744, 0.05240717530250549, 0.0024433874059468508, -0.005647033918648958, 0.016210408881306648, 0.04196628928184509, 0.011006858199834824, -0.030393458902835846, -0.045243848115205765, 0.0016873523127287626, 0.00719711696729064, 0.019057154655456543, 0.011800906620919704, -0.012290851213037968, 0.019614677876234055, -0.029430463910102844, -0.09454241394996643, 0.02900809794664383, 0.008928817696869373, 0.00968907680362463, 0.023179447278380394, 0.017072034999728203, 0.0015268531860783696, -0.03473538160324097, 0.05372495949268341, 0.0021097182761877775, 0.03500569611787796, 0.0008927761809900403, -0.0260346420109272, 0.03588421642780304, -0.020915566012263298, 0.03598558530211449, -0.054366953670978546, 0.0030494825914502144, -0.01384515780955553, 0.026355639100074768, 0.05666462704539299, -0.005021932069212198, -0.02466617524623871, -0.049805402755737305, 0.03419475257396698, -0.04466943070292473, -0.010804123245179653, 0.0017612662632018328, -0.0035478745121508837, 0.028805362060666084, 0.009553919546306133, -0.06805161386728287, 0.0047727362252771854, 0.00038435307214967906, -0.005718836095184088, -0.020949354395270348, 0.02728484570980072, 0.032420817762613297, -0.007239353843033314, 0.04210144653916359, 0.030106250196695328, -0.0059215715155005455, 0.007687061559408903, -0.009334289468824863, 0.0039913589134812355, 0.0068000927567481995, 0.027622736990451813, 0.020645251497626305, -0.001606046804226935, -0.06808540225028992, -0.03260665759444237, 0.02654148079454899, -0.020070834085345268, -0.045277636498212814, -0.03275870904326439, 0.004709381144493818, 0.04470321908593178, 0.03062998317182064, 0.008481109514832497, 0.020577672868967056, 0.028872940689325333, 0.00672829058021307, -0.009410315193235874, -0.005068392492830753, 0.011733327992260456, 0.00803340133279562, -0.03350207209587097, 0.01128561981022358, 0.003999806009232998, 0.056833572685718536, -0.0030346999410539865, 0.015796490013599396, -0.035647694021463394, -0.04929856210947037, 0.028366101905703545, 0.04885930195450783, 0.012476691976189613, -0.05078529193997383, 0.01191072165966034, 0.0050134845077991486, 0.007889796979725361, -0.0026397877372801304, 0.007708179764449596, 0.021523771807551384, 0.021168984472751617, -0.03307970613241196, 0.03628968819975853, -0.0025363080203533173, -0.004548882134258747, -0.049433719366788864, -0.047744255512952805, 0.044432904571294785, 0.03507327288389206, 0.05581989511847496, -0.01639624871313572, -0.008358623832464218, 0.02931220270693302, 0.001475113327614963, 0.022892238572239876, 0.0034486185759305954, -0.042675863951444626, -0.02875467948615551, -0.005431626923382282, -0.01354950200766325, 0.010271941311657429, 0.022334715351462364, -0.019462626427412033, 0.011125121265649796, 0.005397837609052658, -0.003480296116322279, -0.014098578132689, -0.03510706499218941, 0.005613244604319334, -0.03845220431685448, -0.05125834047794342, 0.048115938901901245, -0.04129050299525261, 0.007733521983027458, -0.018448946997523308, 0.008624713867902756, -0.01610059291124344, 0.007391405291855335, 0.03679652884602547, 0.03585042804479599, -0.04294617846608162, -0.028332313522696495, 0.01588096283376217, -0.02665974386036396, -0.040175456553697586, -0.011150462552905083, -0.03142403066158295, 0.01417460385710001, -0.04872414469718933, 0.01890510320663452, 0.019800519570708275, -0.007682838011533022, 0.016303328797221184, 0.015644436702132225, -0.0789993405342102, 0.01566977985203266, -0.022385399788618088, -0.016413142904639244, 0.008650056086480618, 0.033518966287374496, -0.0054865344427526, 0.04213523492217064, -0.03431301563978195, -0.0006657544290646911, 0.028011314570903778, -0.01702135056257248, 0.005820203572511673, -0.01676793023943901, 0.012214825488626957, -0.014816599898040295, 0.03191397711634636, -0.0012755453353747725, -0.09069043397903442, 0.007505444344133139, -0.024581702426075935, 0.044365327805280685, -0.003562657395377755, -0.012164141051471233, 0.02706521563231945, 0.014107025228440762, 0.002107606502249837, 0.026980740949511528, 0.01996946521103382, 0.04081745073199272, 0.043081335723400116, 0.0017274770652875304, 0.011479908600449562, -0.013439686968922615, 0.03041035309433937, -0.02297671139240265, 0.0055118766613304615, -0.0071295383386313915, 0.013633974827826023, -0.02040872536599636, -0.00533025898039341, 0.028653310611844063, 0.024699965491890907, 0.016894640401005745, 0.020020149648189545, -0.029650093987584114, 0.026237377896904945, -0.060212500393390656, 0.0006097909645177424, 0.041053976863622665, -0.02850125916302204, 0.04956887662410736, -0.014934862963855267, -0.00967218168079853, 0.0013156702043488622, 0.022233348339796066, -0.048994459211826324, 0.017857635393738747, -0.00788557343184948, 0.045277636498212814, 0.01790831983089447, 0.026997637003660202, -0.009900259785354137, -0.012899057939648628, 0.06399689614772797, -0.010778781026601791, 0.008979501202702522, -0.0012998314341530204, 0.023010501638054848, 0.01643848605453968, -0.02993730455636978, -0.011944510973989964, 0.036019373685121536, -0.008388189598917961, -0.007851784117519855, -0.036931686103343964, 0.003982911817729473, -0.026676638051867485, -0.03706684336066246, -0.03740473464131355, -0.030934087932109833, -0.0017676018178462982, -0.02828162908554077, -0.0054823108948767185, 0.05379253625869751, -0.013228503987193108, -0.02716658264398575, 0.055177897214889526, -0.0031487387605011463, 0.02547711879014969, 0.0542655847966671, 0.012071221135556698, -0.007015499752014875, -0.014123919419944286, 0.010964621789753437, 0.006069399882107973, 0.014199946075677872, -0.017181849107146263, 0.01757042668759823, -0.0036788079887628555, -0.037506103515625, 0.03422854095697403, -0.00853179395198822, 0.013076452538371086, -0.04419638216495514, -0.0321505032479763, 0.03387375548481941, -0.015940094366669655, 0.02143929898738861, -0.03875630721449852, -0.021794086322188377, 0.03269112855195999, 0.0014592745574191213, 0.03628968819975853, 0.021168984472751617, 0.01716495491564274, 0.0035520982928574085, -0.03500569611787796, 0.009587708860635757, 0.013887395150959492, -0.011251830495893955, 0.035647694021463394, -0.05115697160363197, 0.03184639662504196, 0.04304754361510277, 0.019276784732937813, 0.02287534438073635, -0.038925252854824066, -0.01426752470433712, 0.09785375744104385, 0.0009191740537062287, 0.049805402755737305, 0.004396830219775438, -0.03460022434592247, 0.021760297939181328, 0.044432904571294785, -0.05331948772072792, 0.03534358739852905, 0.007505444344133139, 0.07690440863370895, 0.0041877590119838715, 0.005756848957389593, -0.0034296121448278427, 0.014588522724807262, -0.027859263122081757, 0.11501871794462204, -0.005347153637558222, -0.026338744908571243, 0.05247475579380989, 0.0376412607729435, -0.058996085077524185, 0.004975471645593643, 0.02003704383969307, -0.0219461377710104, 0.031930871307849884, -0.014005657285451889, -0.04460185021162033, -0.03007245995104313, 0.020763514563441277, 0.027555160224437714, -0.01101530622690916, 0.031643662601709366, 0.0074420892633497715, -0.001068058074451983, 0.020526988431811333, -0.02047630399465561, 0.05717146396636963, 0.004172976128757, -0.029954198747873306, 0.005786414723843336, -0.005440074484795332, 0.019023366272449493, -0.0020738171879202127, -0.020510094240307808, 0.05470484867691994, 0.018550315871834755, 0.039432093501091, -0.002986127743497491, -0.010837912559509277, 0.02110140584409237, -0.02334839291870594, 0.015965435653924942, -0.030680667608976364, 0.015078467316925526, 0.014402681030333042, -0.011091331951320171, -0.019242996349930763, 0.0582527220249176, -0.017080482095479965, 0.0025151895824819803, -0.003737939288839698, 0.02147308923304081, 0.019293680787086487, 0.013270740397274494, -0.04037819057703018, -0.040614716708660126, 0.03588421642780304, 0.034110281616449356, -0.05166381224989891, -0.012544270604848862, 0.012552718631923199, 0.02209819108247757, -0.01636246033012867, -0.04892687872052193, 0.032454606145620346, -0.02569674886763096, -0.0010696419049054384, 0.030900297686457634, -0.012358429841697216, 0.018888209015130997, 0.0024623938370496035, -0.07859387248754501, 0.025798115879297256, -0.0355125367641449, -0.005879335105419159, 0.026828689500689507, 0.04254070669412613, 0.025831906124949455, 0.00875142402946949, -0.022452978417277336, -0.009477893821895123, 0.050278451293706894, 0.015213624574244022, -0.010567598044872284, -0.008498004637658596, 0.015154493041336536, 0.022115085273981094, 0.03323175758123398, -0.018043477088212967, 0.023956600576639175, 0.026000851765275, -0.05382632464170456, 0.033704809844493866, 0.03150850534439087, -0.023331498727202415, -0.03419475257396698, -0.0021297805942595005, 0.024699965491890907, -0.01084635965526104, 0.017671793699264526, -0.009460998699069023, 0.011167357675731182, 0.021489983424544334, 0.0065340022556483746, 0.044838376343250275, 0.03628968819975853, -0.058894719928503036, -0.044399116188287735, -0.030798930674791336, 0.005651257466524839, 0.008548688143491745, 0.01673414185643196, -0.015602201223373413, 0.04933235049247742, -0.027234161272644997, 0.008886581286787987, 0.013507265597581863, -0.018229316920042038, -0.021489983424544334, -0.05700251832604408, 0.008181230165064335, -0.028112681582570076, -0.0002385048137512058, 0.010618281550705433, -0.038519781082868576, 0.02610222063958645, 0.0078011006116867065, 0.01550083328038454, 0.0140816830098629, -0.005714612081646919, 0.041898708790540695, 0.009807338938117027, 0.01849963143467903, 0.06940318644046783, 0.005647033918648958, 0.026642849668860435, -0.017621111124753952, -0.08562204241752625, 0.007066183723509312, 0.008544464595615864, 0.0109730688855052, 0.003558433847501874, -0.03490432724356651, 0.03404270112514496, 0.04054713994264603, -0.007999612018465996, 0.0032648893538862467, 0.0373709462583065, -0.0017844964750111103, -0.05595505237579346, 0.015382570214569569, 0.004929011687636375, -0.039837561547756195, 0.032302554696798325, -0.027082109823822975, 0.030545510351657867, -0.013338319025933743, -0.02084798738360405, 0.0344819612801075, 0.030106250196695328, -0.017773162573575974, -0.03394133225083351, 0.029954198747873306, 0.016869299113750458, 0.014672995544970036, 0.027555160224437714, 0.0668352022767067, -0.012620296329259872, 0.02856883779168129, -0.01154748722910881, -0.00814321730285883, 0.033738598227500916, -0.0038646492175757885, -0.015272755175828934, -0.002667241496965289, -0.0007322771125473082, 0.02228403091430664, 0.042709652334451675, -0.019648468121886253, -0.009925602003932, -0.0480145700275898, -0.03328244388103485, -0.021743403747677803, 0.056495677679777145, -0.01248514000326395, -0.005279575474560261, 0.038080520927906036, -0.036830317229032516, 0.05119076371192932, 0.0073449453338980675, 0.018178634345531464, 0.0051824310794472694, 0.012932847253978252, -0.0023166777100414038, 0.04892687872052193, -0.004971248097717762, 0.004734722897410393, 0.020087728276848793, -0.04206765443086624, 0.018415158614516258, 0.0416959747672081, -0.05450211092829704, -0.012713217176496983, 0.005368272308260202, -0.00797849427908659, 0.002821404952555895, -0.021236563101410866, -0.049062035977840424, 0.006660712417215109, -0.011648855172097683, 0.01176711730659008, 0.011294067837297916, -0.004747394006699324, 0.00432925159111619, 0.007535009644925594, 0.0038139652460813522, -0.02475064806640148, -0.010322625748813152, 0.03740473464131355, 0.00976510252803564, 0.03672894835472107, 0.025831906124949455, 0.019327469170093536, 0.021489983424544334, 0.028433680534362793, -0.02669353224337101, -0.034583330154418945, -0.031018560752272606, 0.0067198434844613075, -0.01944573223590851, 0.02500406838953495, 0.013245398178696632, 0.031525399535894394, 0.03514085337519646, -0.012544270604848862, 0.020949354395270348, -0.0114545663818717, -0.023990390822291374, 0.0239734947681427, 0.016810167580842972, 0.00803340133279562, -0.004278567619621754, -0.017198745161294937, 0.09089317172765732, 0.006373503245413303, -0.030292091891169548, 0.023838337510824203, 0.011251830495893955, -0.002563761780038476, 0.020966248586773872, -0.03307970613241196, 0.020273569971323013, -0.006191886030137539, 0.03140713647007942, 0.019175417721271515, -0.05281264707446098, 0.019614677876234055, -0.03919556736946106, -0.008578253909945488, 0.006179214920848608, -0.020104622468352318, -0.024429650977253914, -0.018634788691997528, -0.0017971674678847194, -0.041831132024526596, 0.03612074255943298, -0.016016120091080666, 0.068963922560215, -0.05919882282614708, -0.000961410638410598, -0.04838625341653824, 0.010559150949120522, -0.048656564205884933, 0.0016525071114301682, 0.02878846786916256, -0.013101793825626373, -0.032555971294641495, 0.0061369785107672215, -0.017857635393738747, -0.019513310864567757, 0.05169760063290596, -0.002950226655229926, 0.02279086969792843, 0.0013621303951367736, -0.04260828346014023, -0.032522182911634445, -0.0666324645280838, 0.02606843039393425, 0.013397450558841228, 0.025426434352993965, -0.02265571430325508, 0.03912798687815666, 0.04385848715901375, 0.005832874681800604, 0.018111055716872215, -0.014596969820559025, -0.03438059613108635, 0.0521368607878685, -0.013836710713803768, 0.009604603052139282, 0.014943310059607029, 0.014461812563240528, -0.006255240645259619, 0.03142403066158295, -0.0037843994796276093, 0.029954198747873306, 0.02750447578728199, -0.011243383400142193, 0.05288022756576538, 0.0270990040153265, 0.009173789992928505, 0.005161312874406576, -0.008084085769951344, -0.06642972677946091, 0.02125345915555954, 0.021050723269581795, -0.006504436954855919, -0.0005221500177867711, 0.026169799268245697, -0.03438059613108635, 0.006014492362737656, 0.0068296585232019424, 0.012856821529567242, -0.024395860731601715, 0.028045104816555977, -0.025460224598646164, 0.04159460589289665, -0.010618281550705433, -0.02309497445821762, 0.004268008749932051, 0.005782190710306168, 0.009368078783154488, -0.011277172714471817, -0.059773240238428116, 0.014461812563240528, -0.055245473980903625, -0.01569512113928795, -0.0025341962464153767, -0.013220056891441345, -0.014723679982125759, 0.009562366642057896, -0.07122780382633209, 0.04379091039299965, -0.05247475579380989, 0.01790831983089447, -0.020949354395270348, 0.010880148969590664, -0.0627129077911377, 0.0024729531724005938, -0.04135807976126671, 0.035309799015522, -0.027403106912970543, 0.015526174567639828, -0.049062035977840424, -0.005723059643059969, 0.06947076320648193, -0.0045868949964642525, 0.023331498727202415, 0.009004843421280384, -0.016159724444150925, -0.015171387232840061, -0.0020558666437864304, 0.028011314570903778, 0.0031360676512122154, 0.011420777067542076, 0.036830317229032516, 0.03304591774940491, 0.023517340421676636, -0.028737783432006836, 0.007214011624455452, -0.0034655132330954075, -0.016649669036269188, -0.029903514310717583, 0.02165892906486988, 0.0005971199716441333, 0.030798930674791336, -0.02584880031645298, 0.0030494825914502144, 0.008248808793723583, -0.002041083760559559, 0.003780175931751728, -0.017333902418613434, 0.017038244754076004, -0.05923261120915413, 0.019428836181759834, 0.008793660439550877, 0.03514085337519646, 0.0219461377710104, 0.020324252545833588, 0.046933311969041824, 0.0067494092509150505, -0.04027682542800903, 0.02518991008400917, 0.016556747257709503, -0.009756655432283878, -0.03240391984581947, -0.018229316920042038, -0.02404107339680195, -0.012417561374604702, -0.004451737739145756, 0.0021878560073673725, 0.05554958060383797, -0.03247150033712387, 0.015855619683861732, 0.00027876158128492534, 0.06872739642858505, -0.04740636423230171 ]
To tackle the heterogeneous requirements of beyond 5G (B5G) and future 6G wireless networks, conventional medium access control (MAC) procedures need to evolve to enable base stations (BSs) and user equipments (UEs) to automatically learn innovative MAC protocols catering to extremely diverse services. This topic has received significant attention, and several reinforcement learning (RL) algorithms, in which BSs and UEs are cast as agents, are available with the aim of learning a communication policy based on agents' local observations. However, current approaches are typically overfitted to the environment they are trained in, and lack robustness against unseen conditions, failing to generalize in different environments. To overcome this problem, in this work, instead of learning a policy in the high dimensional and redundant observation space, we leverage the concept of observation abstraction (OA) rooted in extracting useful information from the environment. This in turn allows learning communication protocols that are more robust and with much better generalization capabilities than current baselines. To learn the abstracted information from observations, we propose an architecture based on autoencoder (AE) and imbue it into a multi-agent proximal policy optimization (MAPPO) framework. Simulation results corroborate the effectiveness of leveraging abstraction when learning protocols by generalizing across environments, in terms of number of UEs, number of data packets to transmit, and channel conditions.
[ -0.01657269522547722, -0.03316345438361168, -0.029189618304371834, -0.014387086033821106, 0.045373961329460144, 0.0755750983953476, -0.012463388964533806, 0.025540916249155998, -0.06560438871383667, 0.004813758190721273, -0.01538054458796978, -0.04262840375304222, 0.07492484152317047, -0.012138256803154945, 0.000872098549734801, -0.011235113255679607, 0.027256889268755913, 0.016563663259148598, -0.013348470441997051, -0.0188937745988369, -0.003786431858316064, -0.07550285011529922, -0.01521797850728035, 0.005048575811088085, 0.0024001055862754583, 0.010187465697526932, 0.017331335693597794, -0.00978105142712593, -0.11849251389503479, 0.08345051854848862, 0.04396505653858185, 0.048336274921894073, 0.013158810324966908, -0.027509771287441254, -0.05921012908220291, -0.01986917108297348, 0.06849445402622223, -0.020212365314364433, 0.015678582713007927, 0.006597468163818121, 0.003673538798466325, -0.016003714874386787, -0.0022985017858445644, -0.030815277248620987, 0.03861844167113304, 0.012806584127247334, -0.0201762393116951, -0.018442204222083092, -0.02124194987118244, -0.05848761275410652, -0.00917594414204359, -0.07658662647008896, 0.025920236483216286, -0.004836336709558964, -0.03307313844561577, 0.01325815636664629, 0.07600861042737961, -0.0069135683588683605, 0.03959383815526962, -0.014269676990807056, 0.03901582583785057, -0.027654273435473442, -0.01954403892159462, 0.024818401783704758, 0.033289894461631775, -0.01867702044546604, 0.01442321203649044, 0.015615361742675304, 0.01563342474400997, 0.0009861205471679568, -0.08308926224708557, 0.021928340196609497, -0.01809900812804699, 0.006696813739836216, 0.028557417914271355, 0.07084262371063232, 0.06264207512140274, 0.07185414433479309, 0.030544335022568703, -0.003998670727014542, -0.00352677796036005, 0.03948546200990677, -0.02129613794386387, 0.018360920250415802, 0.06119704619050026, 0.0355658158659935, 0.03757079690694809, -0.07991019636392593, 0.03804043307900429, 0.003962544724345207, -0.025938300415873528, 0.06358134746551514, -0.02707626111805439, 0.005044059827923775, -0.008643089793622494, 0.026895632967352867, -0.012201477773487568, -0.029984384775161743, -0.08121071755886078, 0.009835239499807358, -0.02227153442800045, 0.0036487022880464792, -0.00829086359590292, 0.044434692710638046, 0.014134205877780914, -0.04183363541960716, -0.004181557334959507, 0.00576657522469759, -0.023174678906798363, 0.13366533815860748, -0.0034409791696816683, 0.038257185369729996, -0.014612872153520584, 0.032477062195539474, -0.05350225791335106, -0.021729648113250732, -0.04168913513422012, -0.021729648113250732, -0.010539691895246506, 0.08019919693470001, 0.013375564478337765, 0.0010668389732018113, -0.007225153036415577, -0.06723005324602127, -0.05758447200059891, 0.03966609016060829, 0.03020114079117775, 0.022470226511359215, 0.044434692710638046, -0.014531589113175869, -0.04613260179758072, -0.021440641954541206, -0.015534079633653164, -0.030237264931201935, 0.00376385310664773, 0.03309120237827301, -0.021350327879190445, -0.0018954738043248653, 0.011253176257014275, -0.04573521763086319, 0.03789592906832695, -0.0069451783783733845, 0.017421649768948555, 0.010151339694857597, 0.030183076858520508, 0.023409496992826462, 0.06271433085203171, 0.06946984678506851, -0.0643761157989502, 0.012671112082898617, -0.06408710777759552, 0.019905297085642815, 0.003980607725679874, 0.004741506651043892, 0.007238700520247221, 0.021115509793162346, 0.007685756776481867, -0.008796623907983303, 0.005378223489969969, 0.03923258185386658, 0.05805410444736481, -0.033777590841054916, 0.044181812554597855, 0.05093732848763466, 0.03916032984852791, 0.009808145463466644, 0.03260350227355957, 0.012535640969872475, -0.03291057422757149, 0.052599113434553146, -0.023608187213540077, -0.011722810566425323, -0.04533783718943596, 0.050756700336933136, 0.022054780274629593, 0.015470859594643116, 0.03332601860165596, -0.009473982267081738, 0.02138645388185978, 0.010955138131976128, -0.030724963173270226, -0.0008986284374259412, 0.04887815937399864, 0.05368288606405258, 0.0496729277074337, 0.04006347432732582, 0.0334705226123333, -0.047938890755176544, -0.04382055252790451, -0.04060535877943039, 0.025613168254494667, 0.03430141508579254, 0.06264207512140274, -0.01642819121479988, 0.02675112895667553, -0.07304629683494568, -0.023535937070846558, 0.022957924753427505, -0.011343490332365036, -0.0014834142057225108, -0.019652416929602623, -0.03814880922436714, -0.0001464786910219118, 0.017286179587244987, 0.006854863837361336, -0.0410388708114624, 0.028647731989622116, 0.026462122797966003, 0.030869467183947563, 0.006389744579792023, -0.021187761798501015, -0.022488288581371307, -0.033759526908397675, 0.016961047425866127, 0.0501425638794899, 0.0028810298535972834, 0.009257227182388306, -0.055886559188365936, -0.01569664478302002, -0.0009573327843099833, 0.04349542036652565, 0.06144992634654045, 0.07337143272161484, 0.013529099524021149, 0.007270310539752245, -0.03901582583785057, 0.021530956029891968, 0.02676919288933277, -0.04107499495148659, -0.022325722500681877, -0.007699303794652224, 0.0851123034954071, 0.011930533684790134, 0.005373707506805658, 0.0007913800654932857, 0.0025062249042093754, 0.032567378133535385, 0.03170035779476166, -0.00512534286826849, -0.030472083017230034, -0.042086515575647354, 0.005075669847428799, -0.05072057619690895, -0.03861844167113304, 0.025288036093115807, -0.030706901103258133, -0.05743996798992157, 0.046999622136354446, 0.023283055052161217, 0.03854619339108467, -0.001909020938910544, -0.004373475443571806, 0.0014077759115025401, 0.01041325181722641, -0.041761383414268494, 0.0214587040245533, 0.039846718311309814, -0.0848955512046814, 0.001415678416378796, -0.011731842532753944, 0.06455674022436142, 0.036414772272109985, 0.005057607311755419, 0.0052472674287855625, -0.002228508237749338, 0.0038361046463251114, 0.042014267295598984, 0.029261870309710503, -0.03011082485318184, 0.014766406267881393, -0.04093049094080925, -0.007283857557922602, -0.0029284448828548193, 0.019507912918925285, 0.005337581969797611, -0.026624688878655434, -0.05949913710355759, 0.020645875483751297, 0.024312639608979225, 0.039051953703165054, 0.044326312839984894, -0.00036041095154359937, -0.001431483426131308, -0.005030512809753418, -0.02572154439985752, -0.026155054569244385, -0.03551162779331207, -0.004219940863549709, -0.05538079887628555, -0.00643038609996438, -0.010747415013611317, 0.005834311246871948, -0.024691961705684662, -0.0009274161420762539, -0.019092466682195663, -0.004872462712228298, 0.01021456066519022, -0.008634057827293873, 0.054260898381471634, -0.012210508808493614, 0.02539641410112381, 0.002691369503736496, -0.007292889058589935, -0.012707238085567951, -0.023933319374918938, -0.0031813252717256546, -0.03814880922436714, -0.006231694482266903, 0.0007225153385661542, -0.004468305502086878, 0.05086507648229599, -0.022632792592048645, -0.04349542036652565, -0.007545769214630127, -0.015904368832707405, 0.03338020667433739, 0.02868385799229145, -0.005644650664180517, -0.06723005324602127, -0.04074986279010773, 0.02611892856657505, 0.01939953677356243, -0.0557420551776886, 0.01818029209971428, -0.009943616576492786, 0.009799113497138023, 0.049636803567409515, 0.03386790677905083, -0.05046769604086876, 0.030743027105927467, -0.039774466305971146, 0.0033777591306716204, -0.01956210285425186, 0.010322937741875648, 0.02819615975022316, -0.036739904433488846, -0.023969445377588272, 0.06672428548336029, -0.0074419076554477215, -0.030092762783169746, 0.010539691895246506, -0.030472083017230034, 0.010747415013611317, -0.004140915814787149, -0.04179751127958298, 0.0028719983529299498, -0.062353070825338364, 0.00640780758112669, 0.0014755117008462548, 0.025829922407865524, 0.0010295843239873648, -0.033109262585639954, -0.002659759484231472, 0.008661151863634586, 0.039051953703165054, -0.009943616576492786, -0.022379912436008453, -0.004940198268741369, -0.03560194373130798, -0.025107407942414284, 0.0304359570145607, -0.050178688019514084, 0.001713715959340334, 0.0010493405861780047, -0.04736087843775749, 0.006263304501771927, -0.03175454959273338, -0.014459338039159775, 0.0070219459012150764, -0.00957332830876112, -0.03558387979865074, 0.0034206584095954895, 0.05599493533372879, -0.02330111898481846, -0.03451816737651825, 0.03757079690694809, 0.011993754655122757, -0.006218147464096546, -0.03643283620476723, 0.04916716739535332, 0.015886304900050163, 0.028412913903594017, -0.016762355342507362, 0.016527537256479263, 0.004998902790248394, 0.05144308879971504, -0.01610306091606617, -0.01905634067952633, 0.008638573810458183, 0.05328550562262535, 0.0003437592531554401, -0.032802194356918335, -0.03948546200990677, -0.0033122811000794172, 0.0306707751005888, 0.002440747106447816, 0.03186292573809624, -0.003779658116400242, -0.017990631982684135, -0.03771530091762543, -0.017204895615577698, -0.00462409807369113, 0.031140409409999847, 0.031104283407330513, -0.00480924267321825, 0.0013784237671643496, -0.03563806787133217, -0.013727790676057339, -0.004705381114035845, -0.018360920250415802, 0.026480186730623245, -0.027907153591513634, 0.02996632270514965, -0.021982528269290924, 0.004515720531344414, 0.057331591844558716, -0.0778871476650238, -0.0064168390817940235, -0.005012449808418751, -0.06639915704727173, -0.011668622493743896, 0.012779489159584045, 0.026299556717276573, -0.014080016873776913, 0.025775734335184097, 0.017999662086367607, 0.011424773372709751, -0.02971344254910946, -0.031194599345326424, -0.009284322150051594, 0.035782571882009506, 0.039449337869882584, 0.0027433002833276987, -0.030056636780500412, -0.01201181672513485, -0.020609749481081963, -0.01994142308831215, -0.018388014286756516, -0.02131420187652111, -0.02163933403789997, 0.010964170098304749, -0.018604768440127373, -0.007360624615103006, 0.017755813896656036, -0.004818274173885584, -0.02770846150815487, -0.007161932997405529, -0.0445430688560009, -0.010503566823899746, -0.022452162578701973, -0.0778871476650238, 0.018198354169726372, -0.069505974650383, 0.011713779531419277, 0.06029390171170235, -0.0645928680896759, -0.024168137460947037, -0.02852129191160202, 0.014513526111841202, -0.001185376662760973, 0.0047189281322062016, 0.04764988645911217, 0.0669410452246666, -0.02339143306016922, -0.01689782738685608, 0.019327284768223763, -0.07235991209745407, -0.032260309904813766, -0.00038778752787038684, 0.009510108269751072, 0.0011707006487995386, -0.05245461314916611, 0.01747583970427513, 0.03775142505764961, 0.005486600566655397, -0.00011663259647320956, -0.022054780274629593, -0.07470808178186417, -0.016220469027757645, -0.01501928735524416, 0.009699768386781216, -0.0057123866863548756, 0.023698503151535988, -0.02084456756711006, -0.023806879296898842, 0.029677316546440125, -0.01594952493906021, 0.022650854662060738, 0.030869467183947563, -0.0627504512667656, 0.017882253974676132, -0.015001224353909492, 0.034156911075115204, 0.02355399914085865, -0.00981717649847269, -0.05509179085493088, 0.04468757286667824, -0.009275290183722973, -0.010684194974601269, 0.054586030542850494, -0.024854525923728943, -0.01570567674934864, 0.04512108117341995, 0.034879427403211594, -0.006606499198824167, 0.003226482542231679, 0.05570593103766441, 0.04165300726890564, 0.007292889058589935, 0.022939860820770264, 0.019327284768223763, 0.07221540808677673, 0.006299430504441261, -0.003942224197089672, 0.019652416929602623, 0.03484329953789711, 0.008087655529379845, -0.03991897031664848, 0.0109009500592947, 0.04999805986881256, 0.025757670402526855, 0.01785515993833542, -0.001939502079039812, 0.0501425638794899, -0.03426528722047806, 0.013980671763420105, 0.0776703953742981, -0.008227643556892872, 0.03390403091907501, -0.031212661415338516, -0.03807655721902847, 0.02243410050868988, -0.018568644300103188, -0.06712166965007782, -0.029117366299033165, 0.004687318112701178, 0.047866638749837875, 0.07293792068958282, -0.020573623478412628, -0.010494534857571125, 0.03325376659631729, 0.04577134549617767, 0.02884642407298088, 0.017502933740615845, -0.0024475206155329943, 0.024059759452939034, 0.04168913513422012, -0.025667356327176094, -0.0034477526787668467, 0.012969150207936764, 0.02570348232984543, -0.020374931395053864, -0.005007934290915728, -0.00187741091940552, -0.02411394938826561, -0.003370985621586442, 0.004402827471494675, -0.030345642939209938, -0.052599113434553146, -0.014450306072831154, -0.0015026060864329338, 0.005464022047817707, 0.022416038438677788, 0.005093732848763466, -0.021169697865843773, 0.007161932997405529, 0.03583675995469093, 0.028774172067642212, 0.013005275279283524, 0.03291057422757149, 0.013691665604710579, -0.02124194987118244, -0.01721392758190632, 0.005296940449625254, 0.005441443528980017, 0.0010786927305161953, 0.0012858514674007893, 0.012120194733142853, -0.057150959968566895, -0.009157881140708923, 0.0007264665910042822, -0.011686685495078564, 0.03663152456283569, 0.03675796836614609, 0.02803359366953373, 0.009600422345101833, -0.012111162766814232, -0.019580164924263954, -0.0029126398731023073, -0.026389872655272484, -0.0146941551938653, -0.009044989012181759, -0.05953526124358177, -0.00045665225479751825, -0.010241654701530933, -0.010286811739206314, -0.01478446926921606, 0.010160371661186218, -0.0017803228693082929, -0.022470226511359215, -0.0012339206878095865, 0.04042473062872887, 0.015606330707669258, 0.02660662680864334, -0.042809031903743744, 0.0064168390817940235, 0.05303262546658516, 0.030887529253959656, 0.025667356327176094, 0.015434733591973782, -0.004113821778446436, 0.030472083017230034, 0.03515037149190903, -0.027654273435473442, -0.009898459538817406, 0.01042228378355503, 0.033362142741680145, -0.004452500492334366, 0.026227306574583054, -0.006931631360203028, 0.03861844167113304, -0.040171850472688675, -0.011189956218004227, 0.036324456334114075, -0.005671745166182518, 0.021115509793162346, -0.03583675995469093, -0.06582114845514297, 0.0022781810257583857, -0.01522701047360897, -0.04649386182427406, 0.04960067570209503, -0.018225448206067085, 0.004418632481247187, 0.010467440821230412, -0.0027523317839950323, -0.00860696379095316, 0.05393576994538307, 0.007035492919385433, 0.026642752811312675, -0.04038860648870468, 0.008304410614073277, -0.022650854662060738, 0.04862527921795845, -0.006443933583796024, 0.03153779357671738, 0.00881468690931797, 0.010964170098304749, 0.01810804009437561, 0.027347205206751823, -0.029659254476428032, 0.012770458124577999, -0.02868385799229145, 0.028394851833581924, -0.01542570162564516, 0.008733403868973255, 0.002245442010462284, -0.04905879124999046, -0.02581186033785343, 0.009988774545490742, 0.00224431324750185, -0.015407638624310493, -0.045229457318782806, 0.011361553333699703, 0.005378223489969969, -0.009383667260408401, 0.04515720531344414, 0.008561806753277779, 0.023915257304906845, 0.04118337109684944, -0.049781303852796555, -0.00546853756532073, -0.002558155683800578, 0.009627516381442547, -0.020411057397723198, -0.040244102478027344, 0.014152268879115582, 0.028719983994960785, -0.047938890755176544, -0.05520017072558403, -0.018803460523486137, -0.004479594994336367, 0.014567715115845203, 0.0038157838862389326, -0.037137288600206375, -0.013592319563031197, -0.03495167940855026, -0.00033077652915380895, -0.011831188574433327, -0.0022612472530454397, -0.018604768440127373, -0.026480186730623245, 0.014947035349905491, -0.058306984603405, -0.019652416929602623, 0.05252686142921448, -0.0045224945060908794, -0.0007925090030767024, 0.042411647737026215, -0.03742629289627075, -0.015561173669993877, -0.0005548691842705011, 0.00264395447447896, 0.01777387596666813, 0.0294966883957386, 0.04927554354071617, 0.017105549573898315, 0.006601983681321144, -0.009492045268416405, 0.008941126987338066, 0.006958725396543741, 0.01794547401368618, -0.009708799421787262, 0.04118337109684944, 0.034500107169151306, -0.033434394747018814, -0.01938147284090519, 0.008841780945658684, -0.03291057422757149, 0.054838910698890686, -0.002424942096695304, 0.014829627238214016, 0.00893209595233202, -0.061486054211854935, -0.00576657522469759, 0.024330703541636467, 0.02691369503736496, -0.0008201677701435983, -0.001881926553323865, -0.0021652879659086466, 0.018162228167057037, -0.03572838380932808, -0.05794572830200195, 0.030165014788508415, 0.07499708980321884, 0.02770846150815487, 0.0033687276300042868, 0.04349542036652565, 0.019887233152985573, -0.02642599679529667, 0.030887529253959656, -0.02306630089879036, 0.03356083482503891, -0.008801139891147614, -0.004768601153045893, 0.026859506964683533, 0.010359063744544983, -0.013077527284622192, -0.08243899792432785, -0.012102131731808186, 0.011289301328361034, -0.04421793669462204, 0.03451816737651825, -0.04284515976905823, -0.020483309403061867, 0.061630554497241974, 0.018080946058034897, 0.036739904433488846, -0.022723106667399406, 0.043387044221162796, 0.023030174896121025, 0.049709051847457886, 0.016780417412519455, 0.016229500994086266, 0.03162810951471329, -0.013149778358638287, -0.012102131731808186, 0.007017429918050766, 0.03383177891373634, -0.010955138131976128, 0.05350225791335106, 0.018532518297433853, 0.023770753294229507, -0.059788141399621964, 0.016075965017080307, 0.01325815636664629, -0.034391727298498154, -0.032332561910152435, -0.008751466870307922, 0.029207682237029076, -0.032007429748773575, 0.03562000393867493, -0.025649294257164, 0.029189618304371834, 0.0030345642007887363, 0.013158810324966908, -0.013492973521351814, -0.06744680553674698, -0.0011294946307316422, 0.02868385799229145, 0.012960118241608143, -0.035294871777296066, 0.022723106667399406, 0.004764085169881582, 0.05610331520438194, 0.00001748959766700864, 0.009672673419117928, 0.024475205689668655, -0.02348174713551998, -0.015461827628314495, 0.01421548891812563, 0.023120490834116936, -0.04764988645911217, 0.01069322694092989, -0.07889867573976517, -0.03262156620621681, -0.016364971175789833, -0.0419781394302845, -0.01008811965584755, 0.020772315561771393, 0.03220612183213234, 0.02754589542746544, -0.013402659446001053, 0.012436294928193092, 0.009735893458127975, 0.008516649715602398, 0.0039648027159273624, -0.022957924753427505, -0.011135767214000225, -0.03477105125784874, -0.03771530091762543, -0.03901582583785057, 0.027274953201413155, 0.0350961796939373, -0.02089875563979149, -0.009591390378773212, 0.0015195399755612016, 0.011632496491074562, 0.006231694482266903, 0.013086558319628239, 0.01666300930082798, 0.02250635251402855, -0.030706901103258133, 0.01762937381863594, -0.03155585750937462, 0.00610976992174983, -0.0008602447924204171, 0.041147246956825256, 0.003587740007787943, 0.02210896834731102, -0.006358134560286999, 0.01706039346754551, -0.0028652248438447714, -0.005197594407945871, -0.06372585147619247, -0.029984384775161743, 0.0001211483177030459, 0.031212661415338516, 0.004755054134875536, -0.014802532270550728, -0.00610976992174983, 0.031844861805438995, 0.028304537758231163, 0.06802481412887573, -0.024655835703015327, -0.029514750465750694, 0.0019112788140773773, 0.013312344439327717, 0.01851445436477661, -0.04158075526356697, 0.03422916308045387, 0.025288036093115807, 0.02828647382557392, -0.0205194354057312, 0.01085579302161932, -0.008340535685420036, -0.00578915374353528, -0.04801114276051521, -0.00013307265180628747, 0.003589997999370098, -0.0025920236948877573, -0.003066174453124404, -0.04624098166823387, 0.04230327159166336, -0.004723443649709225, -0.023427559062838554, 0.031844861805438995, 0.002198026981204748, 0.02339143306016922, -0.005007934290915728, 0.012896898202598095, 0.008945642970502377, -0.0025829921942204237, -0.0013818105217069387, 0.07738138735294342, -0.032802194356918335, -0.015100570395588875, -0.03948546200990677, -0.019760793074965477, -0.03926870599389076, 0.02084456756711006, 0.08417303115129471, 0.0016448512906208634, 0.02219928242266178, 0.04429018869996071, 0.028557417914271355, -0.02196446619927883, -0.00023072509793564677, 0.0063852290622889996, 0.06455674022436142, -0.01462190318852663, -0.025251910090446472, 0.0037299853283911943, -0.01843317225575447, 0.028467103838920593, -0.005039544310420752, -0.003908356186002493, 0.016148217022418976, -0.01261692401021719, -0.021260013803839684, -0.01570567674934864, -0.005518210586160421, 0.04486820101737976, -0.032260309904813766, 0.007469002157449722, 0.015814054757356644, 0.010160371661186218, -0.037859801203012466, 0.01826157420873642, 0.05501954257488251, 0.05794572830200195, -0.00797024741768837, 0.01650044322013855, 0.011921502649784088, -0.03742629289627075, 0.04797501862049103, 0.009483013302087784, 0.004423148464411497, 0.03222418203949928, -0.012887867167592049, -0.0065613421611487865, 0.008123781532049179, 0.008399240672588348, 0.002594281453639269, 0.03572838380932808, 0.0016459801699966192, -0.013529099524021149, -0.026787254959344864, -0.021025195717811584, 0.027347205206751823, -0.07058974355459213, -0.03995509818196297, 0.04107499495148659, 0.03242287412285805, -0.0033122811000794172, 0.005798185244202614, 0.021729648113250732, 0.04320641607046127, -0.010485503822565079, 0.05581430718302727, -0.02339143306016922, -0.020013675093650818, 0.00039681897033005953, -0.03764304891228676, 0.004840852692723274, 0.0029758599121123552, -0.018532518297433853, -0.03627026826143265, -0.026859506964683533, 0.061630554497241974, -0.0010668389732018113, 0.01691588945686817, -0.008909516967833042, -0.015299261547625065, 0.04606034979224205, 0.03491555154323578, 0.015317324548959732, -0.017656467854976654, -0.03699278458952904, 0.031844861805438995, 0.023734627291560173, -0.056609075516462326, -0.011632496491074562, 0.023698503151535988, 0.03887132555246353, -0.0012418231926858425, -0.04447081685066223, -0.018857650458812714, -0.019435662776231766, 0.0005709564429707825, 0.0466383621096611, -0.008218611590564251, 0.0643761157989502, 0.00204223464243114, -0.05664519965648651, -0.03645089641213417, -0.006005908362567425, -0.01771065592765808, 0.0017295210855081677, -0.01329428143799305, -0.0016042097704485059, 0.02940637245774269, -0.0068006752990186214, 0.026155054569244385, -0.03596320003271103, -0.005554336588829756, 0.010232622735202312, -0.024565519765019417, 0.020284617319703102, -0.025920236483216286, -0.021260013803839684, -0.009600422345101833, -0.020880691707134247, 0.061160922050476074, 0.0006677621859125793, 0.0034229164011776447, 0.015814054757356644, 0.010882887057960033, -0.034734923392534256, -0.008778560906648636, -0.010512597858905792, -0.045626841485500336, 0.002499451395124197, -0.009564296342432499, 0.01994142308831215, 0.0029758599121123552, -0.04895041137933731, 0.0057439967058598995, 0.031140409409999847, -0.016292721033096313, 0.00392641918733716, -0.05888499692082405, 0.02042912133038044, -0.026136990636587143 ]
It is crucial to consider the social and ethical consequences of AI and ML based decisions for the safe and acceptable use of these emerging technologies. Fairness, in particular, guarantees that the ML decisions do not result in discrimination against individuals or minorities. Identifying and measuring reliably fairness/discrimination is better achieved using causality which considers the causal relation, beyond mere association, between the sensitive attribute (e.g. gender, race, religion, etc.) and the decision (e.g. job hiring, loan granting, etc.). The big impediment to the use of causality to address fairness, however, is the unavailability of the causal model (typically represented as a causal graph). Existing causal approaches to fairness in the literature do not address this problem and assume that the causal model is available. In this paper, we do not make such assumption and we review the major algorithms to discover causal relations from observable data. This study focuses on causal discovery and its impact on fairness. In particular, we show how different causal discovery approaches may result in different causal models and, most importantly, how even slight differences between causal models can have significant impact on fairness/discrimination conclusions. These results are consolidated by empirical analysis using synthetic and standard fairness benchmark datasets. The main goal of this study is to highlight the importance of the causal discovery step to appropriately address fairness using causality.
[ -0.011625371873378754, -0.06040216237306595, -0.0248861163854599, 0.023357398808002472, -0.014878342859447002, 0.025081651285290718, -0.05656258761882782, -0.0178824532777071, -0.054891664534807205, 0.044475045055150986, -0.0004746693593915552, -0.030361061915755272, 0.00962559413164854, 0.020708804950118065, -0.026788126677274704, 0.01830907166004181, 0.05499831959605217, -0.02243305742740631, 0.035853784531354904, -0.01278968621045351, -0.028370173647999763, -0.02127763070166111, 0.010692141950130463, 0.03932006284594536, 0.013411839492619038, 0.021099871024489403, 0.003939561080187559, -0.013785131275653839, -0.04123985022306442, 0.04024440795183182, 0.042235296219587326, 0.01814020238816738, -0.030041098594665527, -0.07743137329816818, -0.06744137406349182, -0.023464053869247437, -0.006883677560836077, 0.030698802322149277, 0.006003775633871555, 0.061859775334596634, -0.016424836590886116, 0.0217575766146183, 0.009963334538042545, -0.03034328669309616, -0.025010546669363976, -0.023410726338624954, -0.06249970570206642, 0.006114874500781298, -0.04870568588376045, -0.0031685358844697475, 0.007750247605144978, -0.04209309071302414, 0.03309853374958038, -0.0294189453125, -0.026112647727131844, 0.018157977610826492, 0.012300851754844189, -0.04728362336754799, 0.05204753577709198, 0.0055238292552530766, -0.057593584060668945, 0.06239305064082146, -0.024939443916082382, 0.0045728241093456745, -0.006937005091458559, -0.02623707801103592, -0.03400510177016258, 0.02038883976638317, 0.02326851896941662, 0.0043684025295078754, -0.06779689341783524, 0.0361737497150898, -0.0044839452020823956, -0.0001238056574948132, -0.018237968906760216, 0.007576933596283197, 0.0461459718644619, 0.008279077708721161, -0.0624641515314579, -0.023890672251582146, 0.017589151859283447, -0.005639371927827597, -0.0033351839520037174, 0.03434284031391144, 0.08390176296234131, -0.0010193309281021357, 0.030218856409192085, -0.06150425970554352, -0.003986222669482231, -0.022468607872724533, -0.003832906484603882, -0.005710475146770477, -0.0008104652515612543, -0.01326074544340372, -0.025188304483890533, -0.021170975640416145, 0.012709695845842361, -0.02808576077222824, -0.03603154048323631, 0.03946227207779884, 0.018913449719548225, 0.02218419499695301, -0.03005887381732464, 0.0412042997777462, 0.020211081951856613, -0.06317518651485443, -0.044688355177640915, 0.03174757584929466, 0.0172247476875782, 0.20136423408985138, -0.03011220134794712, 0.05595821142196655, -0.04749692976474762, -0.015296073630452156, -0.015020549297332764, 0.019340068101882935, -0.06598376482725143, -0.0370803140103817, 0.01745583303272724, -0.0074924989603459835, -0.012283076532185078, 0.06676589697599411, 0.02557937242090702, -0.017589151859283447, -0.04010219871997833, 0.040813229978084564, -0.024815013632178307, -0.0194467231631279, 0.03144538775086403, 0.02876124158501625, 0.02102876827120781, 0.03258303552865982, -0.010958779603242874, 0.027463607490062714, 0.028636809438467026, -0.01096766721457243, 0.025063874199986458, 0.023943999782204628, 0.0031618699431419373, -0.023570707067847252, -0.01404288038611412, -0.03528495877981186, -0.06552159041166306, 0.011225416325032711, 0.006874789949506521, -0.025934888049960136, 0.006319296080619097, 0.027925778180360794, -0.029365617781877518, -0.00871014129370451, -0.0330452062189579, 0.04756803438067436, 0.011838681064546108, 0.016238192096352577, 0.07224084436893463, -0.05791354924440384, -0.00644372683018446, -0.043799564242362976, 0.006199309602379799, 0.0022464164067059755, 0.07814240455627441, -0.019748911261558533, 0.018291296437382698, 0.03514275327324867, 0.050803229212760925, 0.03167647123336792, -0.00995444692671299, 0.000051348448323551565, -0.06854347884654999, 0.06957447528839111, 0.020264409482479095, -0.0013509605778381228, -0.05858903005719185, -0.008314629085361958, -0.012540825642645359, 0.03548049181699753, 0.024708358570933342, 0.03185423091053963, -0.023588484153151512, -0.016798129305243492, -0.053540702909231186, 0.013207417912781239, -0.005714918952435255, 0.017722470685839653, 0.032511934638023376, 0.012185309082269669, 0.05898009613156319, 0.0026641476433724165, 0.06619706749916077, 0.029987771064043045, -0.0046839225105941296, 0.004510608501732349, 0.04056436941027641, -0.005603820085525513, 0.014629481360316277, -0.015233858488500118, -0.01950005069375038, -0.06534383445978165, -0.004268413409590721, 0.02284190058708191, -0.002646371955052018, -0.05414507910609245, 0.0023441833909600973, 0.020459942519664764, 0.044937215745449066, -0.05407397821545601, 0.047176968306303024, -0.036547038704156876, -0.024850565940141678, -0.01859348453581333, -0.03500054404139519, -0.0008743470534682274, 0.018015770241618156, -0.021313181146979332, -0.02600599266588688, -0.025863785296678543, 0.005470501724630594, 0.04529273137450218, -0.04294632747769356, -0.014211750589311123, 0.00424841558560729, 0.02289522811770439, 0.03571157902479172, -0.006737027317285538, 0.013242969289422035, 0.013429615646600723, 0.00452394038438797, -0.012531937099993229, -0.01942894607782364, 0.00768803246319294, -0.001242083846591413, -0.025437166914343834, -0.041097644716501236, 0.012709695845842361, 0.024032877758145332, 0.004657259210944176, 0.010336626321077347, -0.00645705871284008, -0.0029063429683446884, -0.016629258170723915, -0.026183750480413437, -0.040351059287786484, -0.021455388516187668, -0.02966780588030815, 0.06537938117980957, -0.02625485323369503, 0.0021086540073156357, 0.010469945147633553, 0.04074212908744812, 0.034022875130176544, -0.02378401719033718, 0.019837791100144386, 0.0001381096226396039, -0.03078768216073513, 0.000524386006873101, 0.05816240981221199, 0.00054466153960675, -0.03418285772204399, 0.002746360842138529, -0.05311408266425133, 0.038111310452222824, 0.003201865591108799, 0.007119207177311182, 0.020246634259819984, -0.03288522735238075, -0.039924442768096924, 0.012816349975764751, -0.0036818122025579214, 0.010132204741239548, -0.018451277166604996, -0.0309832151979208, -0.016380397602915764, -0.014798351563513279, -0.022521935403347015, -0.011047658510506153, -0.0317297987639904, -0.012185309082269669, 0.0525808110833168, 0.054002873599529266, 0.010149980895221233, -0.016824793070554733, -0.029330065473914146, 0.03492944315075874, -0.000527441268786788, 0.014576153829693794, -0.05414507910609245, -0.03622707724571228, -0.006590377073734999, -0.11532937735319138, -0.02486834116280079, -0.01381179504096508, -0.020691027864813805, -0.05993999168276787, 0.0430174320936203, 0.019606705754995346, -0.001207643304951489, -0.012487498112022877, -0.02399732731282711, 0.04056436941027641, 0.002841905690729618, 0.0002498332760296762, -0.06943226605653763, 0.04963002726435661, 0.042164191603660583, -0.005154981277883053, 0.030503269284963608, 0.0675835832953453, 0.05460724979639053, -0.03960447758436203, 0.00347516848705709, -0.007968001067638397, 0.02600599266588688, 0.030503269284963608, -0.03665369376540184, -0.010487720370292664, 0.03324074298143387, 0.0031063207425177097, -0.04369290918111801, -0.004603931680321693, -0.010158868506550789, 0.015936002135276794, -0.027214746922254562, -0.09662923961877823, 0.0017020326340571046, -0.04123985022306442, -0.034058429300785065, -0.045826006680727005, 0.0030218856409192085, -0.054216183722019196, -0.028867894783616066, -0.08063101768493652, 0.03843127563595772, -0.014122871682047844, -0.0041084312833845615, -0.02081546001136303, -0.031143197789788246, -0.0139273377135396, 0.05727361887693405, -0.03521385416388512, -0.05997554212808609, -0.015767132863402367, 0.03308076038956642, -0.08973222970962524, -0.0035196079406887293, 0.0237306896597147, -0.04689255356788635, 0.006901453249156475, 0.01427396573126316, 0.028334621340036392, 0.0020453277975320816, 0.0009582266211509705, -0.05140760540962219, -0.012300851754844189, 0.003737361403182149, 0.05706031247973442, -0.00479946518316865, 0.012549713253974915, -0.04689255356788635, -0.007234749849885702, -0.004032884258776903, 0.05087433382868767, -0.029703358188271523, -0.031320955604314804, 0.01514497958123684, -0.07650703191757202, -0.03229862451553345, 0.01050549652427435, -0.008336849510669708, -0.020939890295267105, -0.028121311217546463, -0.04906120151281357, 0.041062094271183014, 0.040635474026203156, -0.007839126512408257, -0.0018620147602632642, -0.007083655335009098, -0.03555159643292427, -0.0011854234617203474, -0.02104654535651207, 0.04123985022306442, -0.08439948409795761, 0.003259636927396059, -0.040422163903713226, 0.05773578956723213, -0.03786244988441467, -0.023428501561284065, 0.06975223124027252, 0.025028323754668236, -0.02396177500486374, 0.034520599991083145, -0.025294959545135498, -0.0194467231631279, -0.0029085648711770773, -0.09883343428373337, 0.007861346937716007, -0.0012898562708869576, 0.02917008474469185, 0.002428618259727955, 0.040351059287786484, -0.03907120227813721, 0.014780575409531593, -0.04095543920993805, -0.00361959682777524, 0.054393939673900604, -0.011705363169312477, 0.02762359008193016, -0.025614924728870392, 0.007496942766010761, 0.028121311217546463, 0.006817018613219261, -0.009127872064709663, 0.0016242634737864137, 0.020637700334191322, -0.0013731804210692644, 0.0076347049325704575, 0.0029130089096724987, -0.02085101045668125, -0.00458171172067523, 0.0417020209133625, -0.04326629266142845, -0.016184864565730095, 0.021864231675863266, 0.07113873958587646, -0.015544935129582882, 0.01587378792464733, -0.01745583303272724, -0.0011432060273364186, -0.0352671816945076, -0.02330407127737999, -0.0438351184129715, 0.046750348061323166, 0.055993761867284775, -0.008821239694952965, -0.01189200859516859, 0.0018020215211436152, 0.016593707725405693, 0.05041216313838959, -0.004923895932734013, -0.030965439975261688, -0.0009632260189391673, 0.0008410174050368369, -0.0221664197742939, -0.0028507935348898172, 0.06655258685350418, -0.05969112738966942, -0.02714364230632782, 0.009101208299398422, -0.0652727261185646, -0.037009209394454956, -0.06779689341783524, -0.06985888630151749, 0.04465280473232269, -0.06018885225057602, -0.06018885225057602, 0.01482501532882452, -0.017109205946326256, 0.036760348826646805, -0.030841009691357613, 0.037258073687553406, -0.014629481360316277, -0.01288745366036892, 0.08262190967798233, 0.004312852863222361, -0.01633595861494541, -0.01764247938990593, 0.027961330488324165, -0.024548375979065895, -0.018149089068174362, 0.0011220972519367933, 0.008270190097391605, 0.03786244988441467, -0.0040506599470973015, -0.03352515399456024, -0.026983661577105522, 0.006754803005605936, 0.0282635185867548, 0.03896454721689224, -0.020211081951856613, 0.0344494953751564, -0.05229639634490013, 0.036102645099163055, 0.08802574872970581, -0.042235296219587326, 0.0038551262114197016, 0.01255860086530447, 0.0057949102483689785, 0.02668147161602974, 0.010754358023405075, -0.024281740188598633, -0.051727570593357086, -0.027908002957701683, -0.018664587289094925, 0.006097098812460899, 0.001950893783941865, -0.00872791651636362, 0.010132204741239548, 0.011527604423463345, -0.017340291291475296, 0.002377512864768505, -0.02422841265797615, 0.036298178136348724, 0.008510163053870201, -0.02853015623986721, -0.018842345103621483, 0.03754248470067978, -0.013100762851536274, -0.03012997657060623, -0.00802132859826088, 0.013482942245900631, -0.01718030869960785, 0.05378956347703934, -0.010798797011375427, -0.017935780808329582, -0.006390399299561977, -0.024121757596731186, 0.017918003723025322, 0.055993761867284775, -0.01784690096974373, 0.004228417761623859, 0.0031196523923426867, 0.01762470416724682, -0.017695806920528412, -0.006008219439536333, 0.06655258685350418, -0.011003218591213226, 0.04273301735520363, 0.01762470416724682, -0.007185866124927998, 0.011109873652458191, -0.03414730727672577, 0.00858571007847786, 0.027783572673797607, 0.017358066514134407, -0.05517607554793358, 0.01766914315521717, -0.024566153064370155, 0.043337393552064896, 0.02150871604681015, -0.029134532436728477, -0.04618152230978012, -0.05005664750933647, 0.037258073687553406, 0.023428501561284065, 0.05119429901242256, -0.018291296437382698, 0.029063429683446884, 0.023570707067847252, -0.015153867192566395, 0.013634037226438522, 0.012389730662107468, 0.0264503862708807, 0.018789017572999, -0.017926892265677452, -0.02556159719824791, 0.014905006624758244, -0.01177646592259407, 0.004366180393844843, 0.010869900695979595, -0.022344177588820457, -0.007710252422839403, 0.025437166914343834, 0.01898455247282982, 0.02173980139195919, 0.01447838731110096, 0.015100540593266487, -0.02147316373884678, 0.05211864039301872, 0.10715250670909882, -0.012976332567632198, 0.018504604697227478, -0.030005546286702156, -0.03711586445569992, -0.0005410508601926267, -0.030947664752602577, 0.009216750971972942, 0.032440830022096634, 0.017775798216462135, -0.06381511688232422, -0.04095543920993805, -0.002588600618764758, -0.01268303208053112, 0.014638369902968407, 0.006852569989860058, 0.033827342092990875, 0.015882674604654312, 0.017011437565088272, -0.022717470303177834, -0.007621373515576124, 0.011020994745194912, 0.02534828707575798, -0.05066102370619774, 0.04187978059053421, -0.040386613458395004, 0.003650704398751259, -0.03103654272854328, 0.00651483004912734, 0.04003109782934189, 0.0056127081625163555, 0.024512825533747673, -0.04707031324505806, 0.03978223353624344, 0.0011520938714966178, 0.04803020507097244, 0.005034994799643755, -0.012389730662107468, 0.010025549679994583, -0.021810904145240784, 0.02127763070166111, -0.005297187715768814, 0.01877124235033989, 0.008901230990886688, -0.05204753577709198, 0.01482501532882452, -0.027570262551307678, 0.032014213502407074, -0.030698802322149277, 0.05204753577709198, 0.021188750863075256, -0.010292187333106995, 0.016815904527902603, 0.012629704549908638, -0.007843570783734322, 0.06697920709848404, 0.04863458126783371, 0.025952665135264397, 0.03892899677157402, 0.01290522888302803, -0.02492166869342327, 0.005537161137908697, -0.02534828707575798, -0.04145316034555435, -0.018735690042376518, -0.03151648864150047, 0.011723138391971588, 0.026965884491801262, -0.005057214293628931, -0.002308631781488657, 0.05492721498012543, 0.017082542181015015, -0.01560715027153492, 0.01233640406280756, 0.03885789215564728, -0.02083323523402214, 0.047603584825992584, -0.0033840674441307783, 0.03322296589612961, -0.013385175727307796, -0.01517164334654808, 0.026308180764317513, 0.004732806235551834, -0.016931448131799698, 0.03782689943909645, 0.016602594405412674, 0.043586257845163345, 0.0276058129966259, -0.010798797011375427, -0.004710586275905371, 0.01830907166004181, 0.008990109898149967, 0.03750693425536156, 0.0018264632672071457, 0.015420504845678806, 0.019642256200313568, 0.017020326107740402, 0.017073653638362885, 0.006243749056011438, 0.02218419499695301, 0.031160973012447357, -0.0009210085263475776, 0.02829907089471817, -0.027285849675536156, -0.03169424831867218, -0.04504387080669403, 0.053078532218933105, 0.03530273586511612, -0.021793128922581673, 0.018664587289094925, 0.05748692899942398, 0.007150314748287201, -0.0008782354998402297, -0.015073876827955246, -0.06360180675983429, -0.011696474626660347, 0.0020419948268681765, 0.014753912575542927, 0.015482719987630844, 0.011598708108067513, 0.006465946324169636, -0.011518716812133789, -0.019997771829366684, -0.015100540593266487, -0.06011774763464928, -0.00986556801944971, 0.02892122231423855, 0.0178824532777071, -0.013482942245900631, 0.015953779220581055, -0.01404288038611412, -0.02764136530458927, -0.01766914315521717, -0.011012107133865356, 0.010398841463029385, -0.007132539059966803, 0.047887999564409256, -0.034253962337970734, 0.04685700312256813, 0.017535824328660965, 0.043088532984256744, -0.008243526332080364, -0.02106432057917118, -0.0178824532777071, 0.009581155143678188, -0.017251411452889442, 0.08525272458791733, -0.00035829341504722834, 0.037578035145998, 0.037720244377851486, -0.019411170855164528, -0.0014076209627091885, -0.0049016764387488365, -0.025223856791853905, -0.011189864948391914, 0.00009248969581676647, -0.04159536585211754, 0.0016853677807375789, 0.019340068101882935, 0.024103982374072075, 0.02328629419207573, -0.008670145645737648, -0.0010621038964018226, 0.03126762807369232, -0.020477719604969025, 0.01694033481180668, -0.0017453611362725496, -0.002817463828250766, 0.009252302348613739, 0.01311853900551796, 0.016851456835865974, 0.017358066514134407, -0.011234303936362267, 0.021366508677601814, -0.013678476214408875, 0.0069236732088029385, -0.0008571267244406044, -0.00361959682777524, 0.0443328395485878, -0.002815241925418377, -0.009127872064709663, 0.002377512864768505, 0.029738910496234894, 0.054002873599529266, -0.04003109782934189, 0.05293632671236992, -0.015544935129582882, -0.02938339300453663, -0.017989106476306915, 0.006643704604357481, 0.02191755920648575, 0.0178824532777071, -0.03139206022024155, -0.018415726721286774, 0.02579268254339695, 0.029578927904367447, 0.016069320961833, 0.046714797616004944, -0.01859348453581333, -0.027996880933642387, 0.04319518804550171, 0.006043771281838417, -0.01325185690075159, 0.00995444692671299, -0.03599599003791809, 0.031107645481824875, -0.006074878852814436, -0.017926892265677452, 0.005754914600402117, 0.03055659681558609, -0.06353069841861725, 0.030254406854510307, 0.052616361528635025, 0.03219196945428848, -0.005341627169400454, -0.03252971172332764, 0.004728362429887056, -0.032263074070215225, 0.02266414277255535, -0.019393395632505417, -0.03080545738339424, -0.010478832758963108, 0.029241187497973442, -0.01628263108432293, -0.00926119089126587, 0.008101319894194603, -0.04980778694152832, 0.02602376788854599, -0.059406716376543045, -0.039711132645606995, -0.01967780850827694, 0.002699699252843857, -0.03892899677157402, 0.016620371490716934, -0.014718360267579556, 0.015882674604654312, -0.013642924837768078, -0.025508269667625427, -0.035658251494169235, -0.006461502518504858, -0.027499159798026085, 0.0035662695299834013, -0.025081651285290718, 0.07856902480125427, 0.04692810773849487, -0.00005926423182245344, -0.030876560136675835, 0.015367177315056324, -0.026165973395109177, -0.026148198172450066, 0.029561150819063187, -0.0005838238284923136, -0.04916785657405853, -0.012700807303190231, -0.08347514271736145, -0.013296296820044518, -0.04803020507097244, -0.03236972913146019, -0.009305629879236221, -0.0062126414850354195, -0.0046261511743068695, 0.06601931154727936, -0.014469499699771404, 0.023197416216135025, 0.05144315958023071, -0.03482278808951378, 0.004546160344034433, 0.0008837904315441847, 0.031783126294612885, 0.025170529261231422, -0.03638705983757973, 0.013874010182917118, -0.0023797350004315376, 0.036102645099163055, 0.0027419168036431074, -0.0278546754270792, -0.011572044342756271, -0.0016487052198499441, -0.0028374616522341967, -0.010167756117880344, -0.005248304456472397, -0.004723918158560991, -0.040351059287786484, 0.013767355121672153, 0.006874789949506521, -0.022113092243671417, 0.013651812449097633, -0.00047216963139362633, 0.019375620409846306, 0.05901565030217171, -0.01563381403684616, -0.01836239919066429, -0.03347182646393776, -0.011963112279772758, 0.01632707007229328, 0.007652481086552143, -0.016024881973862648, -0.001639817375689745, -0.021117648109793663, -0.008212418295443058, -0.07017885148525238, -0.028459051623940468, -0.029312290251255035, 0.026539266109466553, 0.0021219858899712563, -0.048279065638780594, 0.05002109333872795, -0.008514607325196266, 0.010798797011375427, 0.020886562764644623, -0.003172979922965169, -0.03711586445569992, -0.0014542824355885386, 0.03146316111087799, 0.012620816007256508, 0.014051767997443676, 0.002593044424429536, -0.03149871528148651, -0.03974668309092522, -0.020228857174515724, 0.0012987442314624786, -0.014842791482806206, -0.04340849816799164, -0.04511497542262077, 0.005474945530295372, 0.027285849675536156, 0.011020994745194912, 0.04547049105167389, 0.006843681912869215, 0.019322292879223824, -0.004168424755334854, -0.023357398808002472, -0.020939890295267105, -0.002724141115322709, -0.015544935129582882, -0.007963557727634907, 0.043372947722673416, 0.010789909400045872, 0.011812017299234867, 0.027232522144913673, 0.018504604697227478, 0.024139532819390297, 0.008985665626823902, 0.016664810478687286, -0.012363066896796227, -0.020317737013101578, -0.017286963760852814, 0.04593266174197197, -0.010061101987957954, -0.03487611562013626, 0.011945336125791073, -0.019108982756733894, -0.012647479772567749, 0.029241187497973442, 0.01743805781006813, 0.028832344338297844, 0.0030907667241990566, 0.012576377019286156, -0.019304515793919563, -0.0000011283465255473857, 0.06513052433729172, -0.013954001478850842, -0.016780352219939232, 0.0051016537472605705, 0.03715141862630844, 0.023837344720959663, 0.0061193183064460754, 0.007656924892216921, 0.028619034215807915, -0.049665577709674835, 0.027001436799764633, -0.02287745103240013, -0.008190198801457882, -0.014638369902968407, 0.03411175683140755, 0.007941337302327156, 0.013474054634571075, -0.00001637838431634009, 0.020282184705138206, 0.025846010074019432, 0.014718360267579556, -0.020922113209962845, 0.021170975640416145, -0.04870568588376045, 0.023232968524098396, 0.06761913746595383, -0.04411952942609787, -0.0034818344283849, 0.01720697246491909, -0.030183304101228714, -0.00020511604088824242, 0.01076324563473463, 0.006301520392298698, 0.0061770896427333355, -0.014745024032890797, -0.002755248686298728, -0.01582046039402485, -0.05201198533177376, 0.013545158319175243, 0.02673479914665222, -0.015936002135276794, -0.05627817660570145, 0.004455059301108122, 0.014425059780478477, -0.001054882537573576, -0.006465946324169636, 0.00317075802013278, -0.0011098763206973672, -0.04522163048386574, 0.006474834401160479, -0.0008971223141998053, -0.025081651285290718, -0.0072747450321912766, 0.008772356435656548, -0.008741248399019241, 0.02150871604681015, -0.01346516702324152, -0.011056546121835709, 0.02081546001136303, 0.011572044342756271, -0.018433501943945885, -0.009341181255877018, 0.021170975640416145, -0.010718805715441704, -0.01971335895359516, 0.005799354054033756, -0.03183645382523537, -0.031072095036506653, -0.008030216209590435, -0.018237968906760216, -0.019286740571260452, -0.03309853374958038, 0.01740250550210476, -0.018273519352078438, 0.01787356473505497, 0.03055659681558609, 0.004463947378098965, 0.04667924344539642, 0.031374283134937286, 0.030236631631851196, -0.032494157552719116, 0.004457281436771154, -0.0072525255382061005, 0.01992666907608509, -0.026094870641827583, -0.020051099359989166, 0.007025883998721838, -0.02129540592432022, -0.02033551223576069, -0.051016539335250854, -0.0070658796466887, 0.038786791265010834, -0.06555714458227158, 0.03900010138750076, -0.029258962720632553, 0.041559815406799316, -0.018931224942207336 ]
Data-driven models (DDM) based on machine learning and other AI techniques play an important role in the perception of increasingly autonomous systems. Due to the merely implicit definition of their behavior mainly based on the data used for training, DDM outputs are subject to uncertainty. This poses a challenge with respect to the realization of safety-critical perception tasks by means of DDMs. A promising approach to tackling this challenge is to estimate the uncertainty in the current situation during operation and adapt the system behavior accordingly. In previous work, we focused on runtime estimation of uncertainty and discussed approaches for handling uncertainty estimations. In this paper, we present additional architectural patterns for handling uncertainty. Furthermore, we evaluate the four patterns qualitatively and quantitatively with respect to safety and performance gains. For the quantitative evaluation, we consider a distance controller for vehicle platooning where performance gains are measured by considering how much the distance can be reduced in different operational situations. We conclude that the consideration of context information of the driving situation makes it possible to accept more or less uncertainty depending on the inherent risk of the situation, which results in performance gains.
[ -0.00863301008939743, 0.023323776200413704, -0.027085063979029655, -0.01973259449005127, 0.09427794814109802, 0.033908307552337646, -0.07609523087739944, 0.019392376765608788, -0.06891287118196487, -0.01792755350470543, 0.05023873224854469, 0.001650289399549365, 0.011746942065656185, 0.02094225585460663, -0.054850563406944275, -0.006766540929675102, 0.011075957678258419, -0.009752891026437283, -0.007711588405072689, -0.035874009132385254, 0.03957859426736832, 0.0009426850010640919, -0.050881363451480865, 0.030714048072695732, 0.003083217889070511, 0.019770396873354912, -0.0006739370874129236, -0.022718945518136024, -0.0998726338148117, 0.04974730685353279, 0.03158349171280861, 0.020110612735152245, -0.01943017914891243, -0.019751494750380516, -0.0326230451464653, -0.0004828602832276374, 0.018664689734578133, 0.012654188089072704, 0.02028072252869606, 0.008883447386324406, 0.030846353620290756, -0.010896398685872555, -0.04407702013850212, -0.023531686514616013, 0.0029745374340564013, -0.015886250883340836, -0.06811903417110443, 0.0073524704203009605, -0.04392581433057785, -0.028899556025862694, -0.009960802271962166, -0.07499898225069046, 0.025176068767905235, -0.031810302287340164, -0.01132167037576437, 0.011435076594352722, 0.004451174288988113, 0.044606246054172516, 0.012710890732705593, -0.005207212176173925, 0.04411482438445091, 0.008940150961279869, -0.056702855974435806, 0.020545335486531258, -0.025327276438474655, 0.0037423886824399233, 0.05417012795805931, -0.006483026780188084, 0.02052643522620201, -0.029806802049279213, -0.03659224510192871, -0.02364509180188179, -0.01453483197838068, -0.02430662512779236, 0.03835003077983856, 0.03186700493097305, -0.03337908163666725, 0.03957859426736832, 0.002556353807449341, 0.01922226883471012, 0.04211132228374481, 0.022057412192225456, -0.04880226030945778, -0.012777043506503105, 0.02821912243962288, -0.0009491821983829141, 0.061125680804252625, -0.07205042988061905, 0.06641794741153717, -0.019449079409241676, -0.031602393835783005, 0.00921421404927969, 0.061428096145391464, 0.01741722784936428, -0.0263668280094862, 0.05265805497765541, 0.022359827533364296, 0.0013939451891928911, -0.040939461439847946, -0.008174661546945572, -0.004285790957510471, 0.009181137196719646, 0.039124973118305206, 0.036516640335321426, 0.11325450986623764, -0.032963261008262634, 0.00525919022038579, 0.0637718141078949, 0.004817380104213953, 0.1400182545185089, -0.003331292886286974, -0.007782467175275087, 0.025365078821778297, 0.009374872781336308, -0.058517348021268845, 0.027897804975509644, -0.013088909909129143, -0.07639764994382858, 0.04203571751713753, -0.007659610826522112, 0.011425625532865524, 0.0471767783164978, 0.047025568783283234, 0.004408647306263447, -0.011368922889232635, 0.012644737027585506, 0.03744278848171234, -0.04403921961784363, 0.030714048072695732, -0.020696543157100677, -0.013873298652470112, 0.004711062181740999, -0.035817306488752365, 0.011028706096112728, 0.00974344089627266, 0.003699861466884613, 0.0003473050019238144, -0.012994404882192612, 0.014166263863444328, 0.02579979971051216, 0.001221474027261138, -0.028427032753825188, -0.02288905344903469, 0.016292620450258255, -0.007914774119853973, 0.02339937910437584, -0.017861399799585342, 0.07809873670339584, -0.03485335782170296, 0.00659170700237155, -0.019137214869260788, 0.0047370512038469315, 0.0029934383928775787, 0.009034655056893826, 0.08225694298744202, -0.0066342344507575035, -0.045815907418727875, 0.023361576721072197, -0.03353029116988182, -0.021830599755048752, 0.06101227551698685, -0.026574738323688507, 0.004633096046745777, 0.06766541302204132, 0.033662594854831696, -0.008193562738597393, 0.03141338378190994, -0.025572989135980606, -0.06490586698055267, 0.032150521874427795, -0.05167520418763161, -0.047819409519433975, 0.008618834428489208, 0.04785721004009247, 0.006322368513792753, 0.0346454456448555, 0.02173609472811222, 0.005641934461891651, -0.0005894734640605748, 0.05156179890036583, -0.06883727014064789, 0.013646488077938557, 0.0602562353014946, 0.015546033158898354, 0.043547794222831726, 0.05507737398147583, 0.06407422572374344, 0.02043193019926548, 0.07352470606565475, -0.01200210489332676, 0.022265322506427765, 0.02549738436937332, 0.05726988613605499, 0.004900071769952774, -0.004479525610804558, -0.04600491747260094, -0.06585092097520828, -0.03659224510192871, 0.015838997438549995, 0.0008794849272817373, -0.007295767776668072, -0.08611273765563965, 0.010480578057467937, 0.05640044063329697, 0.0022184993140399456, -0.02419321984052658, 0.03233952820301056, 0.03447533771395683, 0.04906687140464783, -0.056816261261701584, 0.019751494750380516, -0.008822019211947918, -0.06800562888383865, 0.026933856308460236, -0.03776410222053528, -0.012134411372244358, 0.008770042099058628, 0.020847750827670097, 0.0009515448473393917, -0.061125680804252625, 0.010962552390992641, -0.02364509180188179, -0.02615891769528389, -0.03946518898010254, -0.01876864582300186, 0.023928605020046234, -0.021849501878023148, 0.03254744037985802, -0.046118322759866714, -0.039389584213495255, -0.017398327589035034, 0.03685685619711876, 0.015933502465486526, -0.053149476647377014, 0.03976760432124138, 0.0038487063720822334, 0.011293319053947926, 0.021622689440846443, -0.001039552385918796, 0.010679038241505623, -0.013391325250267982, -0.05076795816421509, -0.010981453582644463, -0.07794752717018127, 0.06116348132491112, 0.003669147379696369, 0.006572806276381016, 0.0057080877013504505, 0.061125680804252625, -0.014015056192874908, -0.025043761357665062, -0.015224717557430267, 0.013013306073844433, -0.02264334075152874, -0.003390358295291662, 0.042451538145542145, 0.026442432776093483, -0.047063373029232025, 0.025081563740968704, -0.01453483197838068, 0.06815683096647263, 0.021773897111415863, -0.000015412397260661237, 0.06388521939516068, -0.053640902042388916, 0.008495978079736233, 0.020564235746860504, 0.06131469085812569, 0.024174317717552185, -0.05553099885582924, 0.008977952413260937, -0.04804622009396553, -0.019694792106747627, -0.03789640963077545, 0.00954025611281395, -0.00011931225890293717, 0.029334278777241707, 0.01642492786049843, -0.026536937803030014, 0.01582009717822075, -0.045853711664676666, 0.021169066429138184, 0.025535186752676964, -0.03931397944688797, -0.02852153778076172, -0.04373680427670479, -0.032112717628479004, -0.012351772747933865, -0.05114597827196121, 0.005793142132461071, -0.013665388338267803, -0.01882534846663475, -0.049482692033052444, -0.0010572720784693956, 0.052998270839452744, 0.011236616410315037, -0.009398498572409153, -0.046193927526474, -0.009081907570362091, -0.0708029642701149, -0.002321273321285844, -0.009190588258206844, 0.02118796855211258, 0.028956258669495583, 0.053451891988515854, -0.021849501878023148, 0.003468324663117528, 0.0010295112151652575, -0.010782993398606777, -0.021169066429138184, -0.03870914876461029, 0.014119011349976063, -0.055757809430360794, -0.013070008717477322, -0.022813448682427406, 0.037934210151433945, 0.016434378921985626, 0.023928605020046234, -0.01726602017879486, 0.04392581433057785, 0.014979004859924316, -0.000776120345108211, -0.07155900448560715, 0.011047606356441975, 0.011208265088498592, 0.003945573698729277, -0.03256634250283241, 0.005991601850837469, -0.07171021401882172, 0.02194400504231453, -0.05262025073170662, -0.009979702532291412, -0.08512988686561584, -0.035212475806474686, -0.002307097427546978, 0.013816596008837223, -0.028540438041090965, 0.04007001966238022, -0.012389574199914932, -0.04940709099173546, -0.008174661546945572, 0.016406027600169182, -0.06811903417110443, -0.04653414338827133, -0.01753063313663006, -0.052393440157175064, 0.017502281814813614, -0.003324205055832863, -0.04158209636807442, -0.005651384592056274, 0.0008977952529676259, -0.03143228217959404, -0.02079104818403721, 0.008656635880470276, 0.029712297022342682, -0.0034635995980352163, -0.025138266384601593, 0.010981453582644463, -0.006657860707491636, 0.03438083082437515, 0.059122178703546524, -0.020998958498239517, -0.04630733281373978, 0.004465349949896336, -0.052544645965099335, 0.01781414821743965, 0.020110612735152245, -0.03795311227440834, 0.007012253161519766, 0.03869025036692619, -0.032509639859199524, 0.05031433701515198, 0.07087857276201248, -0.0002492563216947019, -0.023380478844046593, 0.028805050998926163, 0.007220163941383362, -0.027727697044610977, -0.03152678906917572, 0.03751838952302933, -0.02043193019926548, -0.004297603853046894, -0.03139448165893555, -0.006105007603764534, -0.02188730239868164, 0.08565911650657654, 0.03379490226507187, 0.01295660249888897, 0.010707389563322067, 0.04729018360376358, 0.012124961242079735, -0.022832350805401802, -0.005656110122799873, -0.0331333689391613, 0.042678352445364, 0.016642289236187935, 0.03540148213505745, -0.04555129632353783, -0.013381874188780785, -0.032604143023490906, -0.015905151143670082, 0.004295241553336382, -0.011132661253213882, 0.017256569117307663, 0.0039006839506328106, 0.01937347650527954, 0.015101861208677292, 0.011227165348827839, 0.021169066429138184, 0.04112847149372101, 0.039691999554634094, -0.002435860224068165, -0.00848180241882801, -0.01312671136111021, 0.05662725493311882, -0.013646488077938557, 0.00024216844758484513, 0.05016312748193741, -0.044303830713033676, -0.023682894185185432, -0.0099135497584939, 0.051334988325834274, 0.04022122547030449, -0.028332527726888657, 0.012210015207529068, 0.05889536812901497, -0.03473994880914688, -0.0028351428918540478, -0.044152624905109406, 0.008203013800084591, 0.03483445569872856, -0.014789995737373829, -0.009114984422922134, -0.04653414338827133, 0.0007188268355093896, 0.01646273024380207, -0.011879248544573784, 0.05553099885582924, -0.024136515334248543, -0.009337070398032665, -0.03031712770462036, -0.023078063502907753, -0.005159960128366947, 0.04831083491444588, -0.014062308706343174, -0.025289474055171013, 0.011822545900940895, -0.05182640999555588, -0.07148340344429016, -0.018362274393439293, -0.05526638403534889, 0.05458595231175423, -0.053149476647377014, -0.03844453766942024, 0.04381240904331207, -0.013485829345881939, 0.003253326518461108, -0.06290236860513687, -0.014922302216291428, -0.043850209563970566, 0.03889815881848335, 0.0602562353014946, -0.0005631893291138113, 0.013098360039293766, -0.0018404802540317178, 0.004574030637741089, -0.02651803568005562, -0.026234522461891174, -0.011888698674738407, 0.021320274099707603, 0.02328597381711006, -0.06551069766283035, 0.026990560814738274, -0.01194540224969387, 0.002231493592262268, 0.021206868812441826, -0.04203571751713753, -0.01335352286696434, 0.0010011597769334912, -0.021925104781985283, 0.05197761952877045, 0.06078546121716499, 0.0223409254103899, -0.017294371500611305, -0.01508296001702547, 0.004297603853046894, 0.05477495864033699, 0.02063984051346779, -0.054548148065805435, -0.01565943844616413, -0.023304874077439308, -0.026499135419726372, 0.005963250529021025, -0.011803644709289074, -0.03984320908784866, -0.022662242874503136, -0.007253240328282118, -0.026744848117232323, 0.04698776826262474, 0.0677410140633583, -0.0223409254103899, -0.014676589518785477, 0.012408475391566753, -0.0059868767857551575, 0.0057411640882492065, -0.010782993398606777, 0.016651738435029984, -0.034626543521881104, -0.0074280742555856705, 0.03638433292508125, 0.0067051127552986145, 0.026442432776093483, 0.03097866103053093, -0.018693041056394577, 0.02449563518166542, 0.013674839399755001, 0.0411662757396698, 0.00495677487924695, 0.018844248726963997, 0.0038014540914446115, 0.0009190588025376201, -0.0013218853855505586, 0.00838729739189148, 0.04487086087465286, -0.007692687679082155, 0.03874695301055908, 0.03288765624165535, -0.03477775305509567, 0.019288422539830208, -0.04007001966238022, -0.03424852713942528, 0.02203851006925106, -0.06105007603764534, -0.05847954750061035, 0.0064688511192798615, -0.02052643522620201, -0.0017601512372493744, 0.0732978954911232, 0.0011541394051164389, 0.0010218326933681965, -0.03058174066245556, 0.018248869106173515, 0.01841897889971733, 0.024873653426766396, 0.00569863710552454, 0.01500735618174076, 0.011586284264922142, -0.006331819109618664, 0.004233813378959894, 0.012039906345307827, 0.007248515263199806, -0.0003836302785202861, -0.02300245873630047, 0.030846353620290756, -0.03031712770462036, 0.00503237871453166, -0.025270573794841766, -0.008051806129515171, 0.0015640538185834885, -0.01483724731951952, -0.007309943437576294, -0.05844174325466156, -0.031356681138277054, 0.034664347767829895, 0.02339937910437584, 0.016944704577326775, -0.0035203024744987488, 0.03485335782170296, -0.02249213308095932, 0.04044803977012634, -0.007092582527548075, -0.025289474055171013, -0.011189363896846771, -0.03674345090985298, 0.01441197656095028, -0.026782650500535965, 0.017861399799585342, -0.05904657393693924, -0.04161989688873291, 0.015271969139575958, -0.0067098382860422134, -0.002238581655547023, -0.006629508920013905, 0.05197761952877045, 0.030241524800658226, -0.014308021403849125, 0.011132661253213882, -0.019713694229722023, 0.015243617817759514, -0.02515716850757599, -0.0003644340031314641, 0.019307322800159454, -0.02485475316643715, 0.008047080598771572, -0.019940504804253578, 0.0036833230406045914, 0.04347218945622444, 0.025780899450182915, 0.006700387690216303, -0.07189922034740448, -0.0002553105296101421, 0.03332237899303436, -0.011236616410315037, 0.03585510700941086, 0.02606441266834736, 0.015479880385100842, 0.002277564723044634, -0.025743097066879272, 0.01508296001702547, -0.01282429601997137, 0.0015805921284481883, -0.03492895886301994, 0.04513547569513321, -0.020715443417429924, 0.008245540782809258, 0.006435774266719818, -0.0005182995810173452, 0.012474628165364265, -0.00659170700237155, 0.007928949780762196, 0.03007141500711441, -0.01200210489332676, 0.02343718148767948, 0.024344427511096, -0.023096963763237, 0.017436128109693527, -0.0071540107019245625, 0.00012278235226403922, 0.00029074979829601943, -0.020148415118455887, -0.041241876780986786, 0.009157511405646801, -0.01812601275742054, -0.03243403509259224, -0.0036360707599669695, -0.01746447943150997, -0.0039881011471152306, 0.019845999777317047, -0.008902348577976227, -0.004786666017025709, -0.03328457847237587, -0.02113126404583454, -0.0411662757396698, 0.01742667891085148, -0.005991601850837469, -0.00886454712599516, -0.008453451097011566, -0.025270573794841766, 0.031810302287340164, 0.015933502465486526, 0.0014565546298399568, -0.018144914880394936, 0.013854398392140865, 0.04725237935781479, -0.02992020733654499, -0.024590138345956802, 0.028597140684723854, 0.0036077192053198814, 0.032056014984846115, 0.024911455810070038, -0.028502635657787323, 0.013022756204009056, 0.008080157451331615, 0.020110612735152245, 0.040637046098709106, 0.013448027893900871, 0.036327630281448364, -0.01888205111026764, -0.002523277187719941, 0.09049776196479797, 0.010745191015303135, 0.0032391506247222424, -0.0441904254257679, 0.04143088683485985, 0.020413028076291084, -0.031904809176921844, 0.0022858339361846447, 0.0301281176507473, 0.008264441043138504, -0.00780609343200922, -0.0006136902957223356, -0.015791745856404305, 0.006804342847317457, 0.0263668280094862, -0.07515018433332443, -0.01051838044077158, -0.02500596083700657, 0.04592931270599365, -0.026499135419726372, 0.0035959063097834587, -0.05080575868487358, -0.017833048477768898, 0.0038794204592704773, 0.0013242480345070362, 0.04294296354055405, -0.003588818246498704, -0.046609748154878616, 0.005046554375439882, 0.01737942546606064, 0.00012005057942587882, -0.006695662625133991, -0.0183244738727808, -0.049974117428064346, -0.01868359185755253, 0.03439973294734955, -0.0038628822658210993, 0.009341795928776264, 0.022057412192225456, -0.04732798412442207, 0.004415735136717558, 0.007829719223082066, 0.018248869106173515, -0.029504386708140373, -0.004900071769952774, 0.03303886577486992, 0.035269178450107574, 0.00951190385967493, -0.020507533103227615, -0.048121824860572815, 0.01741722784936428, 0.012172213755548, -0.05095696821808815, 0.009634760208427906, -0.050125326961278915, 0.006407422944903374, 0.014430876821279526, -0.011104309931397438, 0.00014840200310572982, -0.007938399910926819, 0.00011539917613845319, 0.01662338711321354, -0.035571593791246414, -0.002357893856242299, 0.00042999666766263545, 0.0062609403394162655, -0.0163209717720747, 0.019959405064582825, 0.02109346352517605, -0.02424992248415947, -0.006738189607858658, 0.04196011275053024, -0.027179569005966187, 0.05481276288628578, -0.03449423983693123, -0.04426603019237518, 0.01943017914891243, -0.005656110122799873, 0.034267425537109375, -0.003626620164141059, 0.012947152368724346, 0.038935963064432144, -0.00577424094080925, 0.0627511590719223, -0.023380478844046593, -0.04173330217599869, -0.0030336028430610895, 0.04944489151239395, -0.023078063502907753, 0.013466928154230118, -0.026140017434954643, 0.005089081358164549, 0.02389080449938774, -0.009058281779289246, -0.005637208931148052, 0.05798812210559845, -0.058214932680130005, 0.010102558881044388, 0.01822996884584427, 0.021830599755048752, 0.07174801826477051, 0.05001192167401314, 0.03131887689232826, -0.018201617524027824, -0.03058174066245556, 0.006686212029308081, -0.03377600386738777, 0.003940848633646965, -0.005211937706917524, 0.027538686990737915, -0.008429824374616146, -0.04679875820875168, 0.01747393049299717, 0.010036406107246876, 0.007210713345557451, -0.017842499539256096, 0.03407841548323631, -0.025232771411538124, -0.026536937803030014, 0.008477076888084412, -0.008141585625708103, 0.0011505954898893833, 0.028880655765533447, 0.0256107896566391, 0.005415122956037521, 0.0401456244289875, -0.018352825194597244, -0.057307686656713486, 0.0034872256219387054, -0.006289292126893997, -0.030241524800658226, 0.02273784577846527, 0.007910048589110374, 0.03840673714876175, 0.02067764289677143, -0.027746597304940224, -0.047025568783283234, -0.006303467787802219, -0.048121824860572815, -0.002262207679450512, 0.02273784577846527, 0.025837602093815804, -0.0022421255707740784, 0.0041794730350375175, 0.0010643599089235067, 0.03583620488643646, -0.060672055929899216, -0.012162762694060802, 0.09072457253932953, -0.0391627736389637, -0.0014660051092505455, 0.014156813733279705, -0.04759259894490242, -0.007073681335896254, -0.04362339898943901, -0.04207352176308632, -0.07174801826477051, 0.007120933849364519, -0.005457649938762188, 0.024514535441994667, -0.028842853382229805, 0.015045158565044403, 0.05243124067783356, 0.007050055079162121, 0.014430876821279526, -0.035420384258031845, 0.013627586886286736, 0.0003369685437064618, -0.009875747375190258, -0.02500596083700657, 0.028748348355293274, -0.0009143335628323257, 0.04112847149372101, -0.0016408389201387763, 0.0003390358469914645, 0.005675010848790407, -0.01873084343969822, 0.018711943179368973, -0.003307666629552841, 0.0014931752812117338, -0.020167315378785133, 0.05526638403534889, 0.027236271649599075, 0.02319146879017353, 0.010773543268442154, 0.005400947295129299, 0.010112009942531586, 0.0023094601929187775, 0.04914247617125511, -0.016840748488903046, -0.003957387059926987, 0.02088555321097374, 0.008472352288663387, -0.003170634852722287, -0.014506480656564236, 0.03946518898010254, 0.027633192017674446, 0.003172997385263443, -0.0376506969332695, -0.012181663885712624, -0.05451034754514694, 0.045853711664676666, 0.049482692033052444, 0.01312671136111021, 0.027330776676535606, 0.005188311450183392, 0.021395878866314888, 0.04180890694260597, 0.017899202182888985, 0.013221216388046741, -0.01636822521686554, -0.019505782052874565, -0.008188837207853794, 0.010546731762588024, -0.0027406380977481604, 0.030543938279151917, -0.027122866362333298, 0.02665034309029579, -0.014005606062710285, -0.0035014015156775713, -0.002577617298811674, 0.0021228131372481585, 0.00023493292974308133, -0.018815897405147552, -0.05080575868487358, 0.04362339898943901, 0.0042172749526798725, -0.011406724341213703, 0.012181663885712624, -0.009752891026437283, 0.004703974351286888, 0.0026792099233716726, -0.010849147103726864, -0.0028162419330328703, 0.014903401024639606, 0.020053910091519356, -0.00397865055128932, 0.034116219729185104, 0.00983794592320919, 0.03107316605746746, -0.0021606150548905134, -0.006775991525501013, 0.009970252402126789, 0.013665388338267803, -0.009875747375190258, 0.06445224583148956, -0.004021177534013987, -0.03224502503871918, -0.03148898854851723, 0.02695275843143463, -0.022019609808921814, 0.025119366124272346, -0.023096963763237, -0.030846353620290756, 0.006171160843223333, -0.014232417568564415, -0.009677287191152573, 0.028408130630850792, -0.019089961424469948, 0.0033194797579199076, 0.019467981532216072, -0.02239762805402279, 0.01766294054687023, 0.02786000445485115, -0.004942599218338728, 0.021565986797213554, 0.037329379469156265, -0.05435913801193237, -0.030184820294380188, -0.04793281480669975, -0.00480792997404933, -0.028880655765533447, -0.042905163019895554, 0.0033950835932046175, 0.0361575223505497, -0.0066720363683998585, -0.011453976854681969, 0.026971658691763878, 0.006638959515839815, 0.0046165576204657555, 0.011813094839453697, -0.023134766146540642, -0.04914247617125511, 0.01857018657028675, -0.04320757836103439, 0.0007991559104993939, -0.011964302510023117, -0.013230666518211365, -0.03228282555937767, 0.004141671117395163, 0.0838446244597435, -0.03112986870110035, -0.002660308964550495, -0.017899202182888985, -0.02249213308095932, -0.014969554729759693, 0.02816241979598999, -0.040788255631923676, 0.02339937910437584, -0.04910467565059662, -0.003895958885550499, -0.029447684064507484, -0.058668557554483414, -0.0073524704203009605, -0.009752891026437283, 0.009856847114861012, 0.03950298950076103, 0.000821600784547627, -0.0481974296271801, -0.025591889396309853, -0.03644103556871414, 0.009053556248545647, -0.031999312341213226, 0.0032297002617269754, -0.020696543157100677, -0.0130511075258255, 0.009058281779289246, 0.04513547569513321, 0.002523277187719941, 0.014997906051576138, 0.04090166091918945, -0.00833532027900219, -0.02576199732720852, 0.02254883572459221, 0.0063932472839951515, -0.007584006991237402, 0.012162762694060802, -0.01706756092607975, -0.013892199844121933, 0.028653843328356743, 0.001152958138845861, -0.05556879937648773, 0.001853474648669362, 0.001152367447502911, 0.03850124031305313, 0.029561089351773262, 0.026442432776093483, 0.051486194133758545, -0.019146664068102837, -0.004106231965124607, 0.017351074144244194, -0.06569971144199371, -0.0371403731405735, 0.02916416898369789, 0.028597140684723854, -0.044606246054172516, 0.014893950894474983, -0.03782080486416817, 0.01717151515185833, 0.006081381347030401, -0.029806802049279213, 0.06093667075037956, 0.017256569117307663, 0.0053347940556705, 0.007229614537209272 ]
Recently, a considerable amount of works have been made to tackle the communication burden in federated learning (FL) (e.g., model quantization, data sparsification, and model compression). However, the existing methods, that boost the communication efficiency in FL, result in a considerable trade-off between communication efficiency and global convergence rate. We formulate an optimization problem for compression-aided FL, which captures the relationship between the distortion rate, number of participating IoT devices, and convergence rate. Following that, the objective function is to minimize the total transmission time for FL convergence. Because the problem is non-convex, we propose to decompose it into sub-problems. Based on the property of a FL model, we first determine the number of IoT devices participating in the FL process. Then, the communication between IoT devices and the server is optimized by efficiently allocating wireless resources based on a coalition game. Our theoretical analysis shows that, by actively controlling the number of participating IoT devices, we can avoid the training divergence of compression-aided FL while maintaining the communication efficiency.
[ -0.03237486630678177, 0.00351891340687871, -0.025393065065145493, -0.024427680298686028, 0.035408928990364075, 0.0028509015683084726, -0.014032555744051933, 0.04064958915114403, -0.051717035472393036, 0.053992584347724915, -0.013110268861055374, -0.028289219364523888, 0.04140810668468475, -0.04054615646600723, 0.00023137986136134714, 0.013929122127592564, 0.04495934396982193, -0.03678805008530617, 0.06492211669683456, -0.05195838212966919, 0.03864986449480057, -0.023393338546156883, 0.013170605525374413, 0.010171016678214073, -0.008304893970489502, 0.04289066046476364, 0.01892843469977379, 0.009300447069108486, -0.08660879731178284, 0.05037239193916321, 0.04440769553184509, -0.014196326024830341, -0.048579536378383636, -0.04195975512266159, -0.017135577276349068, -0.04551099240779877, 0.06954217702150345, -0.0015676727052778006, 0.009955529123544693, 0.0648876428604126, -0.0786098912358284, -0.018066484481096268, -0.05926772207021713, 0.009283208288252354, 0.04102884978055954, -0.006494797766208649, -0.026341211050748825, 0.005378571804612875, -0.0006825571181252599, 0.00214517954736948, -0.021566003561019897, -0.067232146859169, 0.04875192418694496, 0.03671909496188164, -0.0064646294340491295, -0.005516483914107084, 0.11329478770494461, 0.020497186109423637, 0.06481868773698807, 0.000022390513549908064, 0.014239423908293247, -0.03789134696125984, -0.044993821531534195, -0.0110760647803545, -0.025255152955651283, 0.044786952435970306, -0.014566965401172638, 0.05726799741387367, 0.005887122359126806, -0.023065797984600067, -0.05575096607208252, 0.030495811253786087, -0.043856047093868256, -0.005706112831830978, -0.02730659581720829, 0.0069861095398664474, 0.019428366795182228, 0.020928161218762398, 0.03418496251106262, -0.013929122127592564, 0.0054432181641459465, 0.019824864342808723, -0.0009088191436603665, 0.016471875831484795, 0.030426856130361557, 0.030823353677988052, -0.023134754970669746, -0.06933530420064926, 0.042994096875190735, 0.028409890830516815, -0.034926239401102066, 0.01587712951004505, -0.03585714474320412, -0.011593235656619072, -0.0027108346112072468, -0.015084135346114635, -0.02609986439347267, -0.011446704156696796, -0.04788997396826744, 0.002310027601197362, -0.014127369970083237, 0.07688599079847336, -0.012739629484713078, 0.00028740664129145443, 0.02085920423269272, -0.01930769346654415, 0.014213565737009048, -0.010834719054400921, 0.04844162240624428, 0.11115714907646179, 0.002363899489864707, 0.035064149647951126, -0.003594334004446864, 0.020135166123509407, -0.013394712470471859, 0.008339372463524342, -0.0031159513164311647, -0.040787503123283386, 0.013205083087086678, 0.03066820278763771, 0.010145158506929874, 0.02487589418888092, -0.023393338546156883, -0.024255290627479553, -0.06240522488951683, 0.034564219415187836, 0.004380864091217518, -0.0324438214302063, 0.020255839452147484, -0.012920639477670193, -0.00042585746268741786, 0.013954980298876762, -0.004417496733367443, -0.025892995297908783, 0.029409755021333694, -0.005632847081869841, 0.044062916189432144, -0.006214663852006197, -0.026996292173862457, 0.0017907023429870605, 0.05844024941325188, 0.021203985437750816, 0.007679979782551527, 0.021100550889968872, 0.016454637050628662, 0.06219835579395294, -0.04502829909324646, 0.03153015300631523, 0.0170062854886055, 0.038201648741960526, -0.02630673162639141, 0.057647254317998886, 0.011196738108992577, 0.057061128318309784, 0.050786130130290985, -0.025324108079075813, 0.05133777856826782, -0.014575584791600704, 0.047924451529979706, -0.019617995247244835, 0.023755358532071114, -0.0011657881550490856, 0.018600894138216972, 0.028547802940011024, 0.029116692021489143, 0.0004732647503260523, 0.02894430048763752, 0.03961525112390518, -0.07785137742757797, 0.04382156953215599, 0.03437459096312523, 0.017351064831018448, 0.015118613839149475, -0.0030276014003902674, 0.031633585691452026, 0.02703077159821987, 0.007050755899399519, -0.05240659788250923, -0.030461333692073822, 0.01573059894144535, -0.01659254916012287, 0.014385955408215523, 0.013230941258370876, 0.008240248076617718, 0.0617501400411129, 0.023048559203743935, -0.006188805215060711, 0.008834993466734886, 0.0013942051446065307, 0.016454637050628662, 0.0567508265376091, 0.06081923469901085, 0.05895742028951645, -0.04888983815908432, 0.028047872707247734, -0.06623228639364243, 0.021031593903899193, -0.001361881964839995, 0.04968283325433731, -0.015971943736076355, -0.02358296886086464, -0.019997254014015198, -0.026892859488725662, -0.0036374314222484827, 0.02223832532763481, -0.012980976141989231, 0.016618408262729645, -0.013954980298876762, 0.036477748304605484, -0.03882225602865219, 0.005960388574749231, -0.024686265736818314, -0.006762002594769001, 0.006990419235080481, 0.031168133020401, 0.01529100351035595, 0.014084273017942905, -0.03996003046631813, -0.03561579808592796, 0.006007795687764883, 0.026048146188259125, 0.027685852721333504, -0.01097263116389513, -0.038787778466939926, -0.027909960597753525, -0.03709835559129715, 0.0009314453927800059, 0.010696806944906712, -0.02044546790421009, 0.03689148649573326, 0.010989869944751263, 0.025996429845690727, 0.015135852620005608, 0.016385680064558983, 0.02530686929821968, -0.00836092047393322, 0.004264500457793474, 0.02144533023238182, -0.045131731778383255, -0.006615470629185438, -0.06168118491768837, 0.008003211580216885, -0.04709697887301445, -0.02530686929821968, 0.023324383422732353, -0.011610474437475204, -0.019531801342964172, 0.07005934417247772, -0.019600756466388702, 0.021255701780319214, -0.06795618683099747, -0.040063463151454926, 0.02565165050327778, 0.010231353342533112, -0.007856680080294609, 0.014894505962729454, 0.04782101884484291, -0.06561168283224106, -0.002016964368522167, -0.049269095063209534, 0.02609986439347267, 0.003811976406723261, 0.009162534959614277, 0.01300683431327343, 0.03159910812973976, -0.015747837722301483, 0.049131184816360474, 0.01773894391953945, 0.025755083188414574, 0.00394988851621747, -0.04551099240779877, 0.004745038226246834, -0.031116416677832603, 0.001817638287320733, 0.004100730177015066, -0.00789977703243494, -0.0655772015452385, -0.01504965778440237, -0.007860989309847355, 0.044200826436281204, 0.05575096607208252, 0.015566827729344368, 0.0033637622836977243, -0.03575371205806732, -0.05354437232017517, -0.05644052475690842, -0.03689148649573326, -0.004255881067365408, -0.06719766557216644, -0.012980976141989231, -0.03451250120997429, -0.009533173404633999, 0.0012950807576999068, -0.02201421745121479, 0.016256388276815414, 0.016316724941134453, -0.02165219932794571, 0.03435735031962395, 0.034995194524526596, 0.003958507906645536, -0.015894368290901184, 0.006615470629185438, 0.04582129418849945, -0.014179087243974209, -0.0020719137974083424, -0.014377336017787457, 0.008386779576539993, -0.006102610379457474, -0.01580817438662052, 0.0005742745706811547, 0.01548063289374113, -0.024772459641098976, -0.02609986439347267, -0.08509176224470139, -0.03235762566328049, 0.017170056700706482, 0.04640742018818855, -0.034478023648262024, -0.017239011824131012, -0.046131595969200134, 0.049924179911613464, 0.026634274050593376, -0.08467802405357361, 0.00917977374047041, -0.006132778711616993, -0.043338876217603683, 0.045993685722351074, 0.049924179911613464, -0.006137088406831026, -0.0029952782206237316, -0.045269645750522614, -0.009567651897668839, -0.031116416677832603, -0.0337195061147213, 0.0022281422279775143, 0.027116965502500534, -0.04375261068344116, 0.032547254115343094, -0.021841827780008316, -0.006822338793426752, -0.0036783742252737284, -0.0580265149474144, -0.02087644301354885, 0.007774794474244118, 0.010851957835257053, 0.014618681743741035, -0.05354437232017517, 0.007796342950314283, 0.058785032480955124, -0.0504758283495903, 0.000948145636357367, 0.013291277922689915, 0.004546789452433586, 0.04957939684391022, -0.005055340472608805, -0.04923461750149727, 0.010084821842610836, 0.048579536378383636, -0.0772307738661766, 0.007283482700586319, 0.01122259721159935, -0.017351064831018448, 0.00917977374047041, -0.005818166770040989, -0.0536133274435997, -0.032702405005693436, -0.022341759875416756, -0.01979038491845131, -0.015885749831795692, 0.03352987766265869, -0.02894430048763752, 0.04923461750149727, 0.0023962226696312428, 0.033426444977521896, -0.026530839502811432, 0.014523867517709732, -0.03016827069222927, -0.05030343681573868, -0.046131595969200134, 0.03554684296250343, 0.038787778466939926, 0.023324383422732353, 0.04382156953215599, -0.0265136007219553, 0.043925002217292786, 0.021393613889813423, -0.04530412331223488, -0.0653703361749649, -0.0021225532982498407, 0.0437181331217289, 0.02873743325471878, -0.04854505881667137, -0.006606851238757372, -0.025858517736196518, 0.04240797087550163, -0.016971807926893234, 0.027909960597753525, -0.016911471262574196, -0.006938702426850796, -0.012851683422923088, -0.05247555300593376, 0.05213077366352081, -0.0051070572808384895, -0.0032646378967911005, -0.000443096476374194, -0.01333437580615282, -0.00398221192881465, 0.017842376604676247, 0.0033680719789117575, -0.010171016678214073, -0.02444491907954216, -0.010912294499576092, 0.013463668525218964, -0.016178812831640244, 0.013618819415569305, 0.0001213464856846258, -0.06578406691551208, -0.03315062075853348, -0.016566690057516098, -0.05875055119395256, -0.023289905861020088, 0.022824451327323914, 0.07412774860858917, 0.018273353576660156, 0.021497048437595367, -0.022100413218140602, 0.05144121125340462, 0.010610612109303474, -0.002394067822024226, 0.025203434750437737, 0.01908358559012413, 0.026789424940943718, 0.003833525348454714, -0.086057148873806, -0.024134617298841476, 0.010395124554634094, 0.012144884094595909, 0.03609849140048027, -0.022565865889191628, 0.009886573068797588, -0.01550649106502533, -0.012343132868409157, 0.005460456945002079, -0.009671085514128208, -0.020497186109423637, -0.030633723363280296, -0.00340255000628531, -0.03575371205806732, 0.014860028401017189, 0.017488976940512657, -0.06957665085792542, 0.03609849140048027, -0.06309478729963303, -0.03609849140048027, -0.009326305240392685, -0.06357747316360474, 0.0022130580618977547, -0.04368365556001663, 0.008020450361073017, -0.07385192811489105, 0.03230590745806694, 0.006701665930449963, 0.008080787025392056, 0.001287538674660027, -0.020479945465922356, 0.01979038491845131, 0.0149720823392272, -0.05995728448033333, -0.01815268024802208, -0.014179087243974209, -0.05933668091893196, -0.05519931763410568, 0.029340798035264015, 0.023203710094094276, 0.027323834598064423, 0.002521205460652709, 0.004602816421538591, -0.08460906893014908, 0.005904361605644226, -0.016118476167321205, -0.014842789620161057, -0.01885947957634926, 0.04730384796857834, -0.031495675444602966, 0.002818578388541937, 0.046993546187877655, 0.0022410715464502573, -0.00520187197253108, 0.05768173560500145, 0.00036040309350937605, 0.008701391518115997, -0.04868296906352043, 0.014523867517709732, -0.00015474707470275462, -0.03103022091090679, -0.04447665065526962, -0.02609986439347267, -0.006727524567395449, -0.009731422178447247, 0.001656022621318698, -0.017032144591212273, -0.01801476813852787, -0.00416537607088685, 0.036270882934331894, -0.008136813528835773, -0.06716319173574448, 0.026117103174328804, -0.006339646875858307, -0.009714183397591114, -0.0033896206878125668, 0.049786265939474106, 0.06209491938352585, 0.024272529408335686, -0.05644052475690842, 0.0076153334230184555, 0.01951456069946289, -0.008869471959769726, -0.046786677092313766, -0.00020323178614489734, 0.036132968962192535, -0.014204945415258408, 0.016127096489071846, 0.029185647144913673, 0.035202063620090485, -0.02122122421860695, 0.05444080010056496, 0.01944560557603836, 0.009084959514439106, 0.022134890779852867, 0.0028013393748551607, -0.014747974462807178, 0.04061511158943176, -0.07043860107660294, -0.0530272014439106, -0.020824726670980453, 0.00968832429498434, -0.019324932247400284, 0.013308517634868622, -0.02087644301354885, 0.001449154457077384, -0.024324245750904083, 0.022134890779852867, -0.011981112882494926, 0.03103022091090679, 0.0056543960236012936, 0.015385817736387253, -0.004234332125633955, -0.06561168283224106, -0.014308379963040352, 0.02158324234187603, 0.04689011350274086, -0.030857831239700317, 0.011558757163584232, 0.04354574531316757, -0.03937390446662903, -0.05264794081449509, 0.07323132455348969, -0.034977953881025314, -0.057716213166713715, 0.019031869247555733, 0.010981250554323196, 0.012618957087397575, 0.04509725421667099, -0.017704464495182037, 0.007623952813446522, -0.040063463151454926, 0.007167119067162275, 0.031771499663591385, -0.01709248125553131, 0.04061511158943176, 0.004221403039991856, -0.049717310816049576, -0.033271294087171555, -0.020255839452147484, -0.03135776147246361, -0.016920089721679688, -0.0001263969752471894, 0.0536133274435997, 0.012989595532417297, 0.02894430048763752, 0.007464492227882147, -0.029254604130983353, 0.018531937152147293, 0.015980564057826996, 0.02101435512304306, 0.0296510998159647, -0.0042989784851670265, -0.012834444642066956, -0.017316587269306183, -0.02687561884522438, 0.011455323547124863, -0.0005503015709109604, -0.026479123160243034, 0.0029629552736878395, 0.008524691686034203, -0.004053322598338127, 0.010283070616424084, -0.015532350167632103, 0.007391226477921009, -0.06826648861169815, -0.020566141232848167, 0.033409204334020615, 0.021462569013237953, 0.06081923469901085, -0.015713360160589218, 0.0165149737149477, -0.005615608301013708, 0.03321957588195801, 0.019462844356894493, 0.012420708313584328, 0.07750659435987473, 0.015411676838994026, 0.03709835559129715, -0.0076627410016953945, 0.0015762922121211886, 0.012136264704167843, -0.01572197861969471, 0.012799966149032116, 0.005051030311733484, 0.0005478773382492363, 0.0455799475312233, -0.0037861180026084185, 0.018238874152302742, 0.04440769553184509, 0.009360783733427525, 0.02478969842195511, -0.03115089423954487, -0.05082060769200325, -0.008356611244380474, -0.05064821615815163, 0.028134066611528397, 0.016127096489071846, -0.043338876217603683, -0.025341346859931946, -0.019842103123664856, -0.021962501108646393, 0.024100137874484062, -0.0034650415182113647, -0.029771773144602776, 0.0012207375839352608, -0.07426566630601883, -0.0012282795505598187, -0.01637706160545349, 0.03961525112390518, -0.007710148114711046, 0.028271978721022606, -0.01029169000685215, -0.023324383422732353, 0.025255152955651283, 0.036857008934020996, 0.03101298213005066, 0.028047872707247734, 0.03144395723938942, 0.04826923459768295, -0.03316785767674446, -0.07323132455348969, 0.050441350787878036, -0.030271705240011215, 0.017058001831173897, 0.05461319163441658, 0.04030480980873108, 0.03328853100538254, 0.009421120397746563, 0.016032280400395393, 0.012256937101483345, -0.030478572472929955, 0.031633585691452026, 0.051130909472703934, 0.024893132969737053, 0.06609436869621277, -0.029392516240477562, 0.02130741812288761, -0.0026461882516741753, 0.008507451973855495, 0.034495264291763306, -0.0040878006257116795, 0.012274176813662052, 0.03844299539923668, -0.004167531151324511, -0.03830508515238762, -0.019686952233314514, 0.010834719054400921, 0.0032603282015770674, -0.00882637407630682, -0.018100962042808533, -0.005361332558095455, 0.020393751561641693, 0.006404292769730091, -0.044304259121418, -0.006507726851850748, 0.020997116342186928, -0.015351340174674988, 0.00655944412574172, -0.02628949284553528, -0.012455185875296593, 0.035202063620090485, 0.029426993802189827, 0.006456010043621063, 0.01730796881020069, -0.0019178400980308652, 0.017687225714325905, 0.026565317064523697, 0.01736830547451973, 0.02758242003619671, 0.002381138503551483, 0.0012810741318389773, -0.00041589117608964443, 0.01268791314214468, -0.01290340069681406, 0.011524279601871967, 0.010231353342533112, 0.025255152955651283, 0.0018510388908907771, 0.002965110121294856, 0.06543929129838943, -0.04651085287332535, -0.014498009346425533, 0.02666875161230564, -0.019824864342808723, 0.0023208020720630884, 0.0009384487057104707, 0.016601167619228363, 0.010989869944751263, -0.029547667130827904, -0.00026626192266121507, -0.0048139942809939384, 0.0038593837525695562, -0.02630673162639141, -0.03325405344367027, 0.015739217400550842, 0.003751639975234866, -0.027754809707403183, -0.07171428948640823, 0.003796892473474145, 0.02315199375152588, 0.018997391685843468, 0.02001449279487133, 0.06040549650788307, 0.017049383372068405, 0.005529412999749184, 0.031564630568027496, -0.015834031626582146, -0.00655944412574172, 0.02023860067129135, -0.009498695842921734, -0.0016657195519655943, 0.03409876674413681, 0.04209766536951065, -0.0448903888463974, -0.018428504467010498, 0.008585028350353241, -0.03682253137230873, 0.023479534313082695, -0.008024760521948338, -0.015851272270083427, 0.03015103191137314, 0.00801183097064495, -0.018032006919384003, 0.03003035858273506, 0.036270882934331894, 0.009636607952415943, 0.006395673379302025, 0.02301408164203167, 0.03658118471503258, -0.012101786211133003, 0.009550412185490131, 0.001963092479854822, -0.04202871024608612, 0.009653846733272076, -0.016902850940823555, 0.04640742018818855, 0.0022259873803704977, 0.01304131280630827, -0.09626264125108719, -0.03446078673005104, 0.014437672682106495, 0.010739904828369617, -0.0055251033045351505, -0.03325405344367027, 0.010834719054400921, -0.011722528375685215, 0.06285344064235687, 0.005098437890410423, 0.014213565737009048, -0.012489664368331432, -0.010360646061599255, 0.036857008934020996, -0.029720056802034378, 0.013532624579966068, 0.06826648861169815, -0.013730873353779316, 0.0008468664600513875, -0.0026591175701469183, 0.008675532415509224, 0.05681978166103363, 0.01143808476626873, 0.007417085114866495, 0.013748112134635448, -0.003469351213425398, -0.04602816328406334, 0.048131320625543594, -0.00893842801451683, 0.012196601368486881, -0.009817617014050484, -0.05133777856826782, -0.004251571372151375, -0.02601366862654686, -0.06909395754337311, 0.0013834306737408042, -0.0008220853633247316, 0.08081648498773575, -0.02129017934203148, 0.027185922488570213, 0.016704602167010307, -0.0047105601988732815, -0.026530839502811432, -0.033702269196510315, 0.001444844645448029, -0.047338325530290604, -0.07040412724018097, 0.008481593802571297, 0.015092754736542702, 0.02944423258304596, 0.027927199378609657, -0.05323407053947449, -0.04523516818881035, 0.009274588897824287, 0.027323834598064423, 0.023910509422421455, 0.00384214473888278, 0.0010865965159609914, 0.0004880795313511044, -0.04933805391192436, 0.019393889233469963, -0.055716488510370255, 0.0063353367149829865, -0.018187157809734344, 0.02001449279487133, -0.007313651032745838, 0.02615158073604107, -0.014989321120083332, -0.010007246397435665, -0.009929670952260494, 0.013394712470471859, -0.029771773144602776, -0.007671360392123461, -0.008296274580061436, 0.023358860984444618, 0.02172115445137024, 0.002579387277364731, 0.022548627108335495, 0.014523867517709732, 0.07964423298835754, -0.01614433526992798, -0.03623640164732933, -0.009084959514439106, 0.0007639037212356925, 0.013299897313117981, -0.015678880736231804, -0.0019016785081475973, -0.021048832684755325, 0.009197012521326542, 0.013946360908448696, -0.029358036816120148, 0.014558346010744572, -0.022893408313393593, -0.03144395723938942, -0.04309752956032753, -0.02351401187479496, -0.002206593519076705, 0.03130604699254036, -0.0655772015452385, 0.018411265686154366, 0.07888571918010712, 0.004077026154845953, 0.02323818765580654, 0.0030362210236489773, 0.031116416677832603, 0.031840454787015915, -0.01780789904296398, 0.009059100411832333, -0.00226046540774405, -0.0003784501750487834, -0.018756045028567314, 0.04809684306383133, -0.0140153169631958, -0.016963187605142593, -0.04523516818881035, -0.027858244255185127, -0.05457871034741402, 0.0025061212945729494, 0.05640604719519615, -0.0018941364251077175, 0.02185906656086445, 0.01851469837129116, -0.0066758072935044765, -0.005762139800935984, -0.026496361941099167, 0.04947596415877342, 0.00017669987573754042, 0.0016226220177486539, -0.05523379519581795, 0.008852232247591019, -0.035133104771375656, 0.030650964006781578, 0.0249448511749506, -0.020928161218762398, -0.012774107977747917, -0.022772734984755516, -0.034840043634176254, -0.022203847765922546, 0.007585165090858936, -0.020910922437906265, -0.006460319738835096, 0.01815268024802208, 0.011248455382883549, -0.05895742028951645, -0.00248457258567214, 0.02230728231370449, 0.0386153869330883, 0.006766312289983034, -0.02451387420296669, 0.014532486908137798, 0.040339287370443344, -0.02515171840786934, -0.004255881067365408, 0.02637568861246109, -0.014928984455764294, 0.001109761418774724, 0.014351477846503258, -0.004230022430419922, 0.049786265939474106, 0.054992448538541794, -0.025272391736507416, 0.03702939674258232, 0.029392516240477562, 0.006714595016092062, 0.009240110404789448, -0.01830783113837242, 0.0029780392069369555, -0.05340645834803581, -0.019100824370980263, 0.04516621306538582, 0.024548353627324104, 0.03294375166296959, -0.027530701830983162, 0.048786405473947525, 0.008921188302338123, 0.015894368290901184, 0.04837266728281975, -0.017963049933314323, 0.017187295481562614, 0.012541381642222404, -0.026255015283823013, -0.014394574798643589, -0.03466765210032463, -0.024496635422110558, 0.02287616953253746, -0.0155840665102005, 0.055130358785390854, 0.05716456472873688, 0.012282796204090118, -0.025772321969270706, -0.009921051561832428, -0.012274176813662052, 0.044304259121418, -0.024031182751059532, -0.030978504568338394, -0.026927337050437927, 0.02278997376561165, 0.022324521094560623, -0.055647529661655426, 0.02973729558289051, -0.033978093415498734, 0.018962912261486053, 0.012498283758759499, -0.030202748253941536, -0.022048696875572205, -0.02187630534172058, 0.0017605341272428632, 0.03094402700662613, -0.00986071489751339, 0.00814974308013916, -0.005602678749710321, -0.07364506274461746, 0.006447390653192997, 0.008429876528680325, 0.0014965616865083575, -0.028289219364523888, 0.03123709000647068, -0.03809821605682373, 0.02408289909362793, 0.042132146656513214, -0.0011248455848544836, -0.02716868370771408, -0.004732108674943447, 0.021324656903743744, -0.028858106583356857, 0.00961074884980917, 0.0020298936869949102, -0.03442630544304848, 0.03768448159098625, -0.010877816937863827, 0.05109643191099167, -0.016196051612496376, -0.0028961540665477514, 0.02551373839378357, 0.04161497578024864, -0.027323834598064423, 0.04351126775145531, -0.023462295532226562, -0.020479945465922356, 0.019980015233159065, 0.011696669273078442, -0.027996154502034187, -0.006964561063796282, -0.02365192398428917, 0.023289905861020088, -0.004322682041674852, -0.03203008323907852, 0.006369814742356539, -0.013282658532261848, 0.013411951251327991, -0.003656825516372919 ]
Deep Reinforcement Learning (DRL) is regarded as a potential method for car-following control and has been mostly studied to support a single following vehicle. However, it is more challenging to learn a stable and efficient car-following policy when there are multiple following vehicles in a platoon, especially with unpredictable leading vehicle behavior. In this context, we adopt an integrated DRL and Dynamic Programming (DP) approach to learn autonomous platoon control policies, which embeds the Deep Deterministic Policy Gradient (DDPG) algorithm into a finite-horizon value iteration framework. Although the DP framework can improve the stability and performance of DDPG, it has the limitations of lower sampling and training efficiency. In this paper, we propose an algorithm, namely Finite-Horizon-DDPG with Sweeping through reduced state space using Stationary approximation (FH-DDPG-SS), which uses three key ideas to overcome the above limitations, i.e., transferring network weights backward in time, stationary policy approximation for earlier time steps, and sweeping through reduced state space. In order to verify the effectiveness of FH-DDPG-SS, simulation using real driving data is performed, where the performance of FH-DDPG-SS is compared with those of the benchmark algorithms. Finally, platoon safety and string stability for FH-DDPG-SS are demonstrated.
[ -0.024497639387845993, -0.006472439039498568, -0.024859227240085602, -0.03422437608242035, 0.010757265612483025, 0.011860111728310585, -0.036014240235090256, 0.02881862409412861, -0.10138949006795883, 0.011534681543707848, 0.022129232063889503, 0.02494962513446808, 0.03536337986588478, -0.012791202403604984, -0.05861353874206543, 0.04704269766807556, 0.012700805440545082, 0.03905158489942551, 0.007168497424572706, -0.07983879745006561, 0.03015650250017643, 0.002361626597121358, -0.048018988221883774, 0.03785834461450577, -0.010766305029392242, 0.023213999345898628, 0.026215186342597008, 0.013803650625050068, -0.08569654077291489, 0.06309723854064941, -0.00732217263430357, 0.02332247607409954, -0.0034170139115303755, -0.03109663352370262, -0.015195767395198345, 0.006965103559195995, 0.017898643389344215, 0.020809432491660118, 0.0002565020404290408, 0.07398106157779694, 0.0024113450199365616, 0.019688507542014122, -0.07521045953035355, 0.00836625974625349, 0.017220664769411087, 0.02881862409412861, -0.04946534335613251, 0.03275994211435318, -0.014400272630155087, -0.02932484820485115, 0.02305128425359726, -0.005306315142661333, 0.024443401023745537, 0.008189985528588295, -0.03760522976517677, 0.002779713599011302, 0.05206878110766411, 0.03362775593996048, 0.0042012096382677555, -0.02005009725689888, 0.008284902200102806, -0.028746306896209717, -0.07882635295391083, -0.009247632697224617, -0.024371081963181496, 0.002128853928297758, 0.05008004233241081, -0.014852258376777172, 0.025275055319070816, -0.06262717396020889, -0.06085538864135742, -0.005518748424947262, -0.040787212550640106, -0.003588768420740962, 0.023467110469937325, -0.030933918431401253, -0.04610256850719452, 0.0803450271487236, 0.008895083330571651, 0.04646415635943413, -0.03198252618312836, -0.013297426514327526, -0.06042148172855377, -0.021731484681367874, 0.03599616140127182, -0.0024429841432720423, 0.05434679239988327, -0.06378425657749176, 0.003342436160892248, -0.010305279865860939, -0.02588975615799427, 0.048127464950084686, 0.04429462179541588, -0.0004228893667459488, -0.024027572944760323, 0.012366335839033127, 0.012673686258494854, 0.011362927034497261, -0.025564325973391533, -0.004809130448848009, -0.025003863498568535, 0.0462472029030323, -0.018567582592368126, 0.03089776076376438, 0.055467717349529266, -0.007968512363731861, -0.019959699362516403, 0.029216371476650238, -0.0064588794484734535, 0.1120925173163414, -0.03543569892644882, -0.0241179708391428, -0.016307653859257698, 0.070437490940094, -0.040751054883003235, 0.018359670415520668, -0.04357144609093666, -0.08056197315454483, 0.07969416677951813, 0.001448614988476038, 0.046355679631233215, 0.07441496849060059, 0.007860035635530949, -0.0375690720975399, -0.01945347525179386, -0.013071433641016483, 0.0036972451489418745, -0.004621556494385004, 0.013523419387638569, -0.04107648506760597, -0.018097518011927605, -0.03406166285276413, -0.027770016342401505, 0.0170489102602005, -0.01934499852359295, -0.015150569379329681, -0.012619447894394398, -0.01716642640531063, 0.002696096198633313, 0.028005050495266914, -0.05203262344002724, -0.03916006162762642, -0.01677771843969822, 0.051960304379463196, 0.03059040941298008, 0.04299290478229523, 0.012628487311303616, 0.06024068966507912, -0.0016520086210221052, 0.0048859682865440845, -0.024009494110941887, 0.04038946330547333, 0.002533381339162588, 0.029812993481755257, 0.0219484381377697, 0.004976365249603987, -0.01139004621654749, 0.008104108273983002, -0.0096092214807868, -0.09365148842334747, 0.045053958892822266, -0.016994671896100044, -0.0017864744877442718, 0.04183581843972206, 0.02278009243309498, 0.046355679631233215, 0.05391288548707962, -0.006910865195095539, -0.06092770770192146, 0.035580333322286606, -0.025130419060587883, -0.0009062318131327629, 0.03082544170320034, 0.05120096728205681, 0.03912390395998955, 0.00034944163053296506, 0.048489052802324295, -0.03209100291132927, -0.027046838775277138, 0.03429669514298439, -0.08150210976600647, -0.018070397898554802, 0.00009053843677975237, 0.01732010208070278, 0.0760059580206871, 0.03999171778559685, 0.05991525948047638, 0.05615473538637161, 0.02822200395166874, -0.0410403236746788, 0.0018452326767146587, 0.032778020948171616, 0.07991112023591995, -0.006115369964390993, 0.013152791187167168, -0.023430952802300453, -0.04198045656085014, -0.020502083003520966, 0.037243641912937164, 0.04960997775197029, -0.021767644211649895, -0.03046385385096073, -0.053189706057310104, 0.02782425470650196, 0.021134862676262856, -0.004696134012192488, 0.02388293854892254, 0.06208479031920433, 0.04082337021827698, -0.09950922429561615, -0.032741863280534744, -0.02688412554562092, -0.06917192786931992, 0.005211398005485535, -0.07206463813781738, -0.01152564212679863, 0.013839810155332088, -0.007078099995851517, 0.03916006162762642, -0.03482099622488022, 0.01874837651848793, 0.0142285181209445, -0.05438295006752014, -0.03012034483253956, -0.034477487206459045, 0.000028761138310073875, -0.008551574312150478, 0.0436437651515007, -0.06570068001747131, -0.05807115510106087, -0.018531424924731255, -0.0297587551176548, -0.014716662466526031, 0.016822917386889458, 0.014336994849145412, 0.011950508691370487, 0.003032825654372573, 0.024063732475042343, 0.003550349734723568, -0.018965329974889755, 0.01097421906888485, -0.047621238976716995, -0.0059797740541398525, 0.03482099622488022, 0.017989041283726692, 0.05637168884277344, 0.020032018423080444, 0.01934499852359295, 0.04212509095668793, 0.0036068479530513287, -0.05051394924521446, -0.02024897001683712, -0.01614493876695633, -0.0525750070810318, -0.009374188259243965, 0.05264732241630554, 0.009012600407004356, -0.04212509095668793, 0.010368557646870613, -0.04993540793657303, 0.04172734171152115, 0.0015480519505217671, -0.01945347525179386, 0.032380275428295135, -0.017356261610984802, -0.0054012322798371315, 0.033808548003435135, 0.060529958456754684, 0.04693422093987465, -0.0009508654475212097, -0.019760826602578163, -0.06555604189634323, -0.04198045656085014, -0.010847662575542927, -0.023593666031956673, -0.020935989916324615, -0.03547185659408569, -0.04498164355754852, 0.02869206853210926, 0.04183581843972206, -0.009044239297509193, -0.023141680285334587, 0.04270363226532936, -0.04527091234922409, -0.08764911442995071, -0.04989925026893616, -0.026179026812314987, -0.023340554907917976, -0.012429613620042801, 0.025835517793893814, -0.036683179438114166, -0.032470669597387314, -0.019833143800497055, -0.04613872617483139, 0.07372795045375824, 0.03738828003406525, -0.02455187775194645, 0.03256106749176979, -0.005740221589803696, -0.035544175654649734, -0.019236521795392036, -0.019001489505171776, 0.06725551187992096, -0.021604929119348526, -0.01014256477355957, -0.0006977533339522779, -0.029867231845855713, -0.008944801986217499, -0.048055145889520645, -0.002152583096176386, -0.0038938589859753847, 0.0017243264010176063, -0.05300891399383545, -0.03295881673693657, -0.02151453122496605, -0.02505810186266899, 0.03923238068819046, 0.022129232063889503, -0.04646415635943413, -0.02131565846502781, 0.025275055319070816, 0.014255637302994728, -0.013821730390191078, 0.022942807525396347, 0.053695932030677795, -0.000437296403106302, 0.03482099622488022, -0.03411589935421944, -0.06852106750011444, -0.012321136891841888, 0.0026915762573480606, -0.030337296426296234, -0.1008109450340271, -0.008962881751358509, -0.02625134401023388, 0.019995858892798424, -0.055323079228401184, -0.01696755364537239, 0.0006813688087277114, -0.032506830990314484, -0.02111678384244442, -0.004700653720647097, -0.0033582556061446667, -0.02305128425359726, 0.004492740612477064, -0.010567431338131428, 0.023033203557133675, -0.018874933943152428, -0.0008406938868574798, -0.03212716057896614, 0.0008570783538743854, -0.004235108382999897, -0.005808019544929266, 0.008239704184234142, 0.057058706879615784, -0.050188519060611725, 0.007408049888908863, 0.01107365544885397, -0.024027572944760323, -0.014635304920375347, 0.027408428490161896, -0.02084559202194214, -0.07289629429578781, 0.0020260270684957504, -0.04913991317152977, 0.029939549043774605, -0.00854705460369587, -0.031711336225271225, 0.00783291645348072, 0.04454773664474487, -0.012655606493353844, 0.04541555047035217, 0.05394904315471649, -0.023467110469937325, -0.004262227565050125, 0.009672499261796474, 0.02988531067967415, -0.050224680453538895, -0.012339216656982899, 0.03196444734930992, 0.03650238737463951, 0.024262605234980583, -0.022671615704894066, 0.0043435851112008095, 0.011652197688817978, 0.0523218959569931, -0.012773123569786549, -0.010486073791980743, 0.016316693276166916, -0.011561800725758076, 0.04440309852361679, -0.02344903163611889, -0.011453323997557163, 0.007896194234490395, -0.0026667171623557806, 0.03905158489942551, -0.016443248838186264, 0.01095613930374384, -0.006847587414085865, -0.07148610055446625, 0.0033333965111523867, 0.012538090348243713, 0.014273716136813164, -0.009717698208987713, -0.028276242315769196, 0.008669090457260609, -0.05554003268480301, -0.015132489614188671, 0.02948756329715252, 0.06432664394378662, -0.013270307332277298, -0.030445773154497147, -0.011932428926229477, -0.021333737298846245, 0.03342888131737709, 0.006522157229483128, -0.02285240963101387, 0.022725854068994522, -0.043318334966897964, -0.05998757481575012, -0.0189110916107893, 0.05188798904418945, 0.020737115293741226, 0.008687170222401619, 0.006124409846961498, 0.04310138151049614, 0.017980001866817474, 0.01099229883402586, -0.04653647541999817, -0.0016825177008286119, 0.048525210469961166, 0.005622705444693565, 0.01531328447163105, -0.025871675461530685, -0.00797303207218647, -0.02258121781051159, 0.022834330797195435, -0.010865742340683937, -0.042052771896123886, 0.024642273783683777, -0.01579238846898079, -0.042052771896123886, -0.013939246535301208, 0.025202736258506775, 0.007561725098639727, 0.004533418919891119, 0.019363079220056534, -0.024660354480147362, 0.01176067441701889, 0.015927985310554504, -0.06418200582265854, 0.005360553506761789, -0.06197631359100342, -0.01257424894720316, 0.021207181736826897, -0.03219947963953018, -0.011932428926229477, -0.06168704479932785, -0.003950357437133789, -0.013451102189719677, 0.0445115752518177, 0.01668732240796089, -0.005297275260090828, -0.01622629538178444, 0.03789450228214264, 0.0003121528134215623, -0.00810862798243761, -0.061470091342926025, -0.005310834851115942, -0.019326919689774513, 0.03966628760099411, -0.011923389509320259, 0.054093677550554276, -0.00542835146188736, 0.017862485721707344, 0.05438295006752014, 0.00004357426951173693, -0.05528692156076431, -0.016804838553071022, 0.01057647168636322, 0.03829225152730942, 0.03176557272672653, 0.03243451192975044, -0.007489407435059547, 0.005473549943417311, 0.007484887260943651, 0.03219947963953018, -0.023738302290439606, -0.015186727978289127, -0.007340251933783293, 0.03445940837264061, 0.004316465929150581, -0.030301138758659363, 0.0003118703025393188, -0.024226447567343712, 0.0427759513258934, 0.013315506279468536, -0.028077367693185806, 0.055467717349529266, -0.004336805082857609, 0.02605247125029564, -0.008212585002183914, 0.043282173573970795, -0.03610463812947273, -0.03256106749176979, 0.03306729346513748, 0.007340251933783293, -0.05597393959760666, -0.06338650733232498, -0.012221700511872768, 0.011127893812954426, 0.060168370604515076, -0.01148948259651661, 0.0010604721028357744, 0.013360705226659775, 0.030138423666357994, -0.004363924264907837, 0.023467110469937325, -0.0031684215646237135, 0.027336111292243004, 0.0019683989230543375, 0.03690013289451599, -0.035417620092630386, -0.006635153666138649, -0.027209553867578506, 0.02838471718132496, 0.015141529962420464, -0.05159871652722359, 0.056660957634449005, -0.01720258593559265, -0.03652046620845795, 0.02632366120815277, -0.0395578108727932, -0.014309875667095184, -0.015421761199831963, -0.02561856433749199, -0.03172941505908966, 0.04349912703037262, -0.011435244232416153, 0.009319950826466084, -0.014590106904506683, 0.0430290624499321, 0.008727848529815674, 0.019905460998415947, 0.015720071271061897, 0.017076028510928154, 0.004433982074260712, -0.015882786363363266, 0.010052167810499668, -0.011236370541155338, 0.002942428458482027, 0.009681539610028267, -0.04668110981583595, 0.03905158489942551, -0.03286841884255409, -0.025962073355913162, -0.02652253583073616, -0.025962073355913162, -0.007344771642237902, -0.05376825109124184, -0.039810921996831894, -0.03406166285276413, 0.004133411683142185, -0.009012600407004356, 0.010449915193021297, 0.036719340831041336, -0.002341287210583687, 0.03829225152730942, -0.004583137575536966, 0.0262875035405159, -0.026540614664554596, -0.008185465820133686, -0.03872615844011307, -0.04212509095668793, 0.006300684064626694, 0.004571837838739157, 0.0029469483997672796, -0.015141529962420464, -0.014581066556274891, -0.0028113527223467827, -0.0026192585937678814, -0.022129232063889503, -0.003062204923480749, 0.02498578280210495, -0.017473777756094933, 0.0005276935989968479, -0.03720748424530029, -0.009170794859528542, 0.028963260352611542, -0.03738828003406525, -0.015123450197279453, 0.023358633741736412, -0.006621594075113535, 0.0029966668225824833, -0.06754478067159653, -0.017076028510928154, 0.014147160574793816, 0.0015299724182114005, -0.008045350201427937, -0.05206878110766411, -0.0019796984270215034, 0.05214110016822815, 0.01981506496667862, -0.0045921774581074715, 0.02288856916129589, 0.018088478595018387, 0.008343661203980446, 0.021098705008625984, 0.03590576350688934, -0.023467110469937325, 0.020809432491660118, 0.013758452609181404, 0.024569956585764885, -0.03201868385076523, 0.02719147503376007, 0.02928869053721428, 0.037243641912937164, 0.019977780058979988, -0.0029469483997672796, -0.021695325151085854, 0.03138590604066849, -0.04404151067137718, 0.036140795797109604, -0.030445773154497147, -0.012086104601621628, 0.0033695553429424763, 0.0033311364240944386, -0.00494472635909915, -0.0200862567871809, -0.024226447567343712, -0.008284902200102806, 0.013640936464071274, 0.005740221589803696, -0.02455187775194645, -0.02722763456404209, -0.026142867282032967, -0.0164613276720047, 0.002492702566087246, -0.0035865085665136576, 0.011679316870868206, -0.011173092760145664, -0.015141529962420464, -0.0072905332781374454, 0.04320985823869705, -0.007453248370438814, -0.005197838414460421, 0.028312399983406067, -0.04740428552031517, 0.03543569892644882, 0.018621820956468582, 0.03586960583925247, 0.0023774460423737764, 0.04411382973194122, 0.039847083389759064, 0.00919339433312416, -0.03590576350688934, 0.052358053624629974, 0.014264676719903946, 0.0029288691002875566, 0.05373208969831467, -0.010178723372519016, -0.02955988235771656, 0.0024949624203145504, 0.019796984270215034, 0.03330232575535774, 0.0329226553440094, 0.05962598696351051, 0.004664495121687651, 0.01501497346907854, 0.05293659493327141, -0.03592384234070778, -0.004465621430426836, -0.002009077463299036, 0.02332247607409954, 0.04877832531929016, -0.02221962995827198, 0.04136575385928154, 0.0742703303694725, 0.039087746292352676, -0.006124409846961498, -0.009116556495428085, -0.02225578762590885, -0.04020867124199867, 0.03438709303736687, -0.04924838989973068, -0.004895007703453302, 0.012104183435440063, 0.009699618443846703, -0.05781804397702217, 0.004176350310444832, -0.032380275428295135, -0.03413397818803787, 0.009853294119238853, -0.0006892785895615816, 0.04494548216462135, 0.031476300209760666, -0.038653839379549026, -0.0003274073242209852, 0.004259967710822821, 0.008171905763447285, 0.0037560032214969397, -0.019363079220056534, -0.025998232886195183, -0.01055839192122221, 0.06280796974897385, -0.028402797877788544, -0.009672499261796474, 0.0003237349446862936, -0.019073806703090668, -0.020068176090717316, 0.018730297684669495, 0.055467717349529266, 0.005708582699298859, 0.016714440658688545, 0.053623612970113754, 0.029162133112549782, 0.014807060360908508, -0.028782466426491737, -0.008443097583949566, 0.007299573160707951, -0.0011627338826656342, -0.030102264136075974, -0.006834027823060751, -0.03422437608242035, -0.04740428552031517, -0.01071206759661436, 0.006314243655651808, -0.003609107807278633, -0.02522081695497036, -0.005798979662358761, 0.034748680889606476, -0.0375690720975399, -0.028673989698290825, 0.005473549943417311, -0.015882786363363266, 0.00028743481379933655, 0.01365901529788971, 0.02091790921986103, -0.027932731434702873, -0.014318915084004402, 0.04646415635943413, -0.006318763829767704, 0.035417620092630386, 0.0051390803419053555, -0.031711336225271225, 0.014427391812205315, -0.013405903242528439, 0.04827209934592247, 0.00614700885489583, -0.004585397429764271, 0.04993540793657303, -0.029469484463334084, 0.03442325070500374, -0.0030034466180950403, -0.06736398488283157, 0.028746306896209717, 0.021930359303951263, -0.017121227458119392, 0.026594853028655052, -0.024569956585764885, -0.012809282168745995, 0.03480291739106178, 0.004519859328866005, -0.004239628091454506, 0.04877832531929016, -0.05651632323861122, 0.002212471328675747, 0.0066939122043550014, 0.017934802919626236, -0.003066724631935358, 0.03382663056254387, 0.009672499261796474, -0.02341287210583687, -0.02588975615799427, -0.0395578108727932, 0.0155302369967103, 0.010223922319710255, 0.004953766241669655, 0.03366391360759735, 0.000985894352197647, -0.015819508582353592, -0.011634118854999542, -0.03545377776026726, 0.010748226195573807, 0.010603590868413448, 0.01961619034409523, -0.00852897483855486, 0.01079342421144247, 0.001671218080446124, 0.012122263200581074, 0.009428426623344421, 0.04863368719816208, -0.0447646901011467, 0.030915839597582817, 0.08772143721580505, -0.000020851382942055352, -0.042920585721731186, 0.026233265176415443, -0.0022147311829030514, -0.03134974464774132, -0.013387824408710003, 0.007394490297883749, -0.006092770490795374, 0.029144054278731346, 0.0057311817072331905, 0.00136951741296798, 0.00852897483855486, -0.056660957634449005, -0.009564022533595562, 0.02191227860748768, -0.010169683955609798, 0.0042012096382677555, -0.006540236994624138, 0.03934085741639137, 0.003249779110774398, -0.05850506201386452, -0.015937024727463722, 0.05029699578881264, -0.0517071932554245, -0.02071903645992279, 0.0005988813936710358, -0.02462419494986534, -0.00787359569221735, 0.0029153095092624426, -0.034911394119262695, -0.07014822214841843, -0.013532459735870361, -0.015132489614188671, 0.02805928885936737, 0.02202075533568859, 0.04480084776878357, 0.06537524610757828, -0.0210806243121624, 0.019308840855956078, -0.03623119369149208, 0.03256106749176979, -0.008980960585176945, 0.006806908641010523, -0.009934651665389538, 0.03436901047825813, 0.009053278714418411, -0.002648637630045414, -0.03454980626702309, -0.012095144018530846, -0.03690013289451599, -0.0421612486243248, -0.009274751879274845, -0.0019616191275417805, 0.017934802919626236, -0.017220664769411087, 0.03847304359078407, -0.0057131024077534676, 0.026938362047076225, 0.016153978183865547, -0.011155012995004654, 0.051490239799022675, 0.03596000373363495, 0.024009494110941887, -0.010287200100719929, -0.020700957626104355, 0.011362927034497261, 0.01910996623337269, 0.01085670292377472, -0.010016009211540222, 0.01925460249185562, -0.0003158251929562539, -0.013225109316408634, -0.024208366870880127, -0.027697699144482613, -0.04530707374215126, 0.030048025771975517, 0.03876231610774994, -0.01649748720228672, 0.01871221885085106, -0.014969774521887302, -0.0323621928691864, 0.021333737298846245, -0.010151604190468788, 0.005708582699298859, -0.048091307282447815, 0.006639673840254545, -0.04621104523539543, -0.018287351354956627, -0.012113223783671856, 0.06450743228197098, -0.0007265674066729844, 0.008605812676250935, -0.016524607315659523, -0.01081150397658348, -0.03713516518473625, 0.010603590868413448, 0.004474660847336054, -0.02475075051188469, -0.03821993246674538, 0.0436437651515007, 0.0623740628361702, -0.04219741001725197, -0.010205842554569244, -0.007841955870389938, 0.0003969001700170338, -0.012248819693922997, -0.026811806485056877, 0.017003711313009262, 0.011796833015978336, 0.030572330579161644, 0.007032901514321566, 0.00441138306632638, 0.02088175155222416, 0.03512834757566452, -0.007448728661984205, -0.006580915302038193, 0.04324601590633392, -0.00522043788805604, -0.04613872617483139, 0.051056332886219025, -0.009527863934636116, -0.03887079283595085, -0.016705401241779327, 0.017265863716602325, -0.02664909139275551, -0.018007120117545128, -0.03606848046183586, -0.023973334580659866, 0.005369592923671007, -0.017500896006822586, -0.00513004045933485, 0.01085670292377472, -0.06266333162784576, 0.00704646110534668, 0.02021281234920025, 0.014264676719903946, 0.0226896945387125, 0.026142867282032967, 0.005817059427499771, 0.045632503926754, 0.033338483422994614, -0.048922959715127945, -0.011796833015978336, -0.03326616808772087, 0.006861147005110979, -0.03590576350688934, -0.032542988657951355, -0.018332550302147865, -0.004174090456217527, 0.02455187775194645, -0.0644712746143341, -0.0025040023028850555, -0.013604776933789253, 0.03288649767637253, 0.003093843813985586, -0.023539427667856216, -0.046789586544036865, -0.004302906338125467, -0.04574097692966461, 0.011263489723205566, -0.007697321008890867, -0.02829432114958763, -0.04527091234922409, 0.018224073573946953, 0.05980678275227547, -0.0007469067932106555, -0.007882635109126568, -0.03418821841478348, -0.006436279974877834, -0.02818584442138672, 0.0401725135743618, 0.004727772902697325, -0.010865742340683937, -0.037243641912937164, 0.013586698099970818, -0.013478221371769905, -0.04349912703037262, 0.013505340553820133, -0.0020260270684957504, -0.015566396526992321, 0.05836042761802673, -0.06588147580623627, -0.043716080486774445, -0.04534323140978813, 0.014960735104978085, 0.03272378444671631, 0.014237557537853718, -0.001325448858551681, -0.013595737516880035, -0.028131606057286263, -0.0120589854195714, 0.020972147583961487, 0.014020604081451893, 0.044149987399578094, 0.00864649098366499, -0.015033053234219551, -0.00003541733531164937, 0.011905309744179249, -0.02041168510913849, -0.00836625974625349, 0.008623892441391945, -0.014888416975736618, -0.03140398487448692, 0.04049794003367424, 0.02778809703886509, 0.014309875667095184, 0.023358633741736412, -0.0102600809186697, 0.017437618225812912, 0.020158573985099792, -0.014065803028643131, 0.012999116443097591, 0.050188519060611725, -0.009500744752585888, 0.016488447785377502, -0.007701840717345476, -0.032344114035367966, 0.0049221268855035305, -0.028348559513688087, -0.01846814528107643, 0.005758300889283419, -0.02798696979880333, 0.01462626550346613, -0.01807943731546402, -0.017862485721707344, 0.03778602555394173, 0.015304244123399258, 0.0436437651515007, -0.011751635000109673 ]
Pre-trained Generative Language models (e.g. PLBART, CodeT5, SPT-Code) for source code yielded strong results on several tasks in the past few years, including code generation and translation. These models have adopted varying pre-training objectives to learn statistics of code construction from very large-scale corpora in a self-supervised fashion; the success of pre-trained models largely hinges on these pre-training objectives. This paper proposes a new pre-training objective, "Naturalizing" of source code, exploiting code's bimodal, dual-channel (formal & natural channels) nature. Unlike natural language, code's bimodal, dual-channel nature allows us to generate semantically equivalent code at scale. We introduce six classes of semantic preserving transformations to introduce un-natural forms of code, and then force our model to produce more natural original programs written by developers. Learning to generate equivalent, but more natural code, at scale, over large corpora of open-source code, without explicit manual supervision, helps the model learn to both ingest & generate code. We fine-tune our model in three generative Software Engineering tasks: code generation, code translation, and code refinement with limited human-curated labeled data and achieve state-of-the-art performance rivaling CodeT5. We show that our pre-trained model is especially competitive at zero-shot and few-shot learning, and better at learning code properties (e.g., syntax, data flow).
[ 0.03017493151128292, -0.009095771238207817, -0.02580896206200123, -0.01549274567514658, 0.014065055176615715, 0.0421859547495842, -0.02273251861333847, 0.006000906229019165, -0.03997533768415451, 0.015032201074063778, 0.008276000618934631, -0.026306351646780968, 0.0025422105100005865, -0.032238174229860306, 0.016515156254172325, 0.009427363984286785, -0.0026826767716556787, -0.009344465099275112, -0.002326905494555831, -0.037451550364494324, 0.010758339427411556, 0.013890048488974571, -0.02477734163403511, 0.04410182312130928, 0.01991398073732853, 0.020835071802139282, -0.010003045201301575, -0.0019757396075874567, -0.026103710755705833, 0.002595173195004463, 0.0008422223618254066, 0.013309760950505733, 0.010832026600837708, -0.0268221627920866, -0.015032201074063778, -0.011357048526406288, 0.044580791145563126, 0.06816071271896362, -0.04483869671821594, 0.01932448334991932, -0.018431026488542557, -0.02149825729429722, 0.03699100390076637, 0.007668080274015665, 0.021995646879076958, -0.009966202080249786, 0.02731955051422119, -0.04601769149303436, -0.014507179148495197, -0.0874667763710022, 0.05983405560255051, 0.04660719260573387, 0.04749143868684769, 0.004540977533906698, -0.004522555507719517, 0.05559703707695007, 0.004128789063543081, 0.005945640616118908, 0.05471279099583626, 0.008082571439445019, 0.015548011288046837, 0.08326660096645355, -0.029640700668096542, -0.007308855187147856, 0.056333910673856735, -0.011863648891448975, 0.0012503806501626968, 0.007069371175020933, 0.052428483963012695, 0.015898026525974274, -0.031114444136619568, -0.02531157247722149, -0.05290745198726654, 0.03606991469860077, 0.040491148829460144, 0.04627559706568718, 0.026030024513602257, 0.044212356209754944, 0.015603276900947094, -0.014562444761395454, 0.0011421524686738849, -0.006226573139429092, -0.005609442479908466, -0.011762328445911407, 0.03901740163564682, -0.017602043226361275, 0.04531766474246979, -0.053791698068380356, 0.01497693546116352, -0.01086887065321207, -0.01687438227236271, 0.002011431846767664, -0.03839106112718582, -0.015621698461472988, -0.015308528207242489, 0.053386420011520386, -0.058912962675094604, -0.011642586439847946, -0.07685580849647522, 0.06252364069223404, -0.0013252192875370383, 0.004996917210519314, 0.005858137272298336, -0.012388670817017555, -0.03135392814874649, -0.043438639491796494, -0.0012584401993080974, 0.023469392210245132, -0.0035231721121817827, 0.1386057287454605, -0.023764140903949738, -0.021848272532224655, -0.03711995482444763, 0.016119087114930153, -0.0252747293561697, 0.005793660879135132, -0.03820684179663658, -0.09218276292085648, 0.056739188730716705, -0.006406186148524284, 0.011679430492222309, 0.027209021151065826, 0.013834782876074314, -0.06609746813774109, -0.012324194423854351, 0.013125542551279068, -0.007612815126776695, -0.009381309151649475, 0.01937974989414215, 0.042259640991687775, -0.004511042032390833, 0.01268341951072216, 0.0673133134841919, -0.0002544513263273984, 0.058286622166633606, -0.0019078091718256474, -0.0011692096013575792, -0.01631251722574234, -0.03210922330617905, -0.030377572402358055, 0.02350623533129692, 0.0007570214220322669, -0.006710146088153124, -0.02580896206200123, 0.022437769919633865, -0.00332283484749496, 0.0003258358337916434, 0.12519465386867523, -0.024519436061382294, -0.018937624990940094, 0.006940418854355812, 0.037322595715522766, -0.011412314139306545, 0.01982187293469906, 0.01240709237754345, 0.043807074427604675, -0.00748846773058176, 0.03170394152402878, -0.004460381809622049, -0.004386694636195898, 0.034725122153759, -0.01796126924455166, 0.0016890501137822866, -0.0012377157108858228, 0.053054824471473694, 0.019545545801520348, 0.018182331696152687, 0.02927226386964321, -0.059060338884592056, 0.04133855178952217, 0.014617710374295712, 0.02282462827861309, -0.0056508914567530155, -0.015861181542277336, -0.001543978345580399, -0.021479835733771324, 0.03853843733668327, -0.018292861059308052, 0.014682185836136341, -0.0011939638061448932, 0.008211524225771427, -0.013475557789206505, 0.03258819133043289, -0.00415642186999321, 0.013466346077620983, 0.02354307845234871, 0.08348766714334488, 0.012876848690211773, 0.0384647473692894, -0.027301128953695297, -0.03048810362815857, -0.014940091408789158, -0.04822831228375435, -0.04038061946630478, 0.018117854371666908, -0.0009032445959746838, -0.03573831915855408, -0.03820684179663658, -0.03140919283032417, 0.0924038216471672, -0.030230198055505753, -0.049702055752277374, -0.021442992612719536, -0.020816650241613388, -0.00566010270267725, 0.020853493362665176, -0.05858137086033821, 0.05445488542318344, 0.02378256246447563, -0.003995230887085199, 0.0505494587123394, -0.03444879502058029, -0.06735015660524368, -0.0322565957903862, -0.01510588824748993, -0.046349287033081055, -0.008441796526312828, 0.006152885966002941, -0.03157499060034752, -0.027927471324801445, 0.00013427775411400944, 0.00764505285769701, 0.03404351323843002, -0.04130170866847038, -0.04211226850748062, -0.010887292213737965, 0.010924136266112328, -0.009929358027875423, 0.054381195455789566, 0.01324528455734253, 0.013107120990753174, 0.038722652941942215, 0.020153464749455452, -0.06344472616910934, 0.03465143218636513, -0.022382505238056183, 0.053386420011520386, -0.014396647922694683, -0.007138452958315611, 0.006843704264611006, -0.026195820420980453, 0.008626014925539494, -0.043807074427604675, -0.047933559864759445, 0.042259640991687775, -0.05040208622813225, -0.037138380110263824, 0.05452857166528702, 0.030617056414484978, 0.023064112290740013, 0.0018479382852092385, 0.0027770886663347483, 0.02545894868671894, -0.008750362321734428, -0.06300260871648788, 0.018191542476415634, 0.019250797107815742, -0.03675151988863945, 0.0443597286939621, -0.029051201418042183, -0.010813605040311813, 0.02518262155354023, 0.020208731293678284, 0.05902349576354027, -0.035683054476976395, 0.03798578307032585, 0.007626631297171116, -0.004188660066574812, 0.015898026525974274, 0.048928339034318924, 0.03135392814874649, -0.025164198130369186, -0.0035761347971856594, 0.02499840222299099, 0.00950565654784441, 0.00858917087316513, 0.01708623394370079, -0.01240709237754345, 0.010251739993691444, 0.0005273244460113347, 0.015197996981441975, -0.017684942111372948, 0.021000869572162628, 0.045759785920381546, -0.03879634290933609, -0.058876119554042816, -0.049112558364868164, -0.024740496650338173, -0.05276007577776909, -0.00815625861287117, 0.008464823476970196, 0.030727587640285492, -0.021977225318551064, 0.032956626266241074, 0.005821293219923973, -0.0008387682610191405, -0.03135392814874649, 0.020227152854204178, 0.018992891535162926, 0.00993856880813837, -0.0533495768904686, -0.050438929349184036, 0.022806206718087196, 0.020392948761582375, -0.07707687467336655, 0.012922902591526508, -0.0042162928730249405, 0.05824977904558182, -0.05508122593164444, -0.004432749003171921, 0.0008094084914773703, -0.02186669409275055, -0.01091492548584938, -0.05136001855134964, -0.006793044041842222, 0.04450710490345955, 0.023487813770771027, -0.0073779369704425335, -0.03404351323843002, 0.021719319745898247, -0.014921669848263264, -0.01882709376513958, -0.10876239091157913, 0.04723353311419487, 0.04015955701470375, 0.025016823783516884, 0.02685900591313839, 0.06705540418624878, 0.04207542538642883, -0.06550797075033188, -0.04664403572678566, -0.026914270594716072, -0.02182985097169876, -0.013982157222926617, 0.01003067847341299, 0.0003304413112346083, -0.04995996132493019, 0.05239164084196091, 0.004766644444316626, -0.018292861059308052, -0.012554466724395752, 0.008966818451881409, -0.017067810520529747, 0.01331897173076868, 0.04078589752316475, -0.056923408061265945, -0.045575570315122604, 0.024851027876138687, -0.02967754378914833, 0.02450101263821125, 0.0009953536791726947, 0.01692964695394039, 0.032735563814640045, -0.04701247066259384, 0.03268029913306236, -0.010214895941317081, -0.0022486126981675625, -0.0212403517216444, 0.03682520613074303, 0.05032839626073837, 0.03385929390788078, -0.032956626266241074, 0.014516389928758144, -0.016634898260235786, -0.017077021300792694, -0.02195880375802517, 0.006502900738269091, 0.024574700742959976, 0.04060167819261551, 0.004068918526172638, -0.017629677429795265, 0.04730721935629845, -0.00817007478326559, 0.009404336102306843, 0.03957005962729454, -0.01869814097881317, 0.021111398935317993, 0.016975702717900276, -0.013549244962632656, 0.05802871659398079, -0.0030695348978042603, 0.041854362934827805, 0.00577523885294795, 0.0028185376431792974, -0.0010972493328154087, 0.023432549089193344, 0.0252747293561697, -0.020540323108434677, -0.06381316483020782, -0.008584565483033657, 0.027337972074747086, -0.04715984687209129, -0.04447026178240776, -0.04314389079809189, 0.036143600940704346, 0.07236088812351227, -0.04587031900882721, -0.0028945275116711855, 0.0009423909359611571, -0.02636161632835865, -0.03374876454472542, -0.031224975362420082, -0.005710762459784746, 0.03126182034611702, -0.04365970194339752, -0.038501594215631485, -0.012287350371479988, -0.04148592799901962, 0.01003067847341299, -0.045170288532972336, -0.01231498271226883, -0.03496460244059563, 0.010574121959507465, 0.044396571815013885, 0.03557252511382103, -0.021516678854823112, -0.03157499060034752, -0.01746387965977192, 0.028019580990076065, -0.008708912879228592, 0.0207798071205616, 0.026122132316231728, -0.0017051692120730877, 0.015934869647026062, -0.010767550207674503, -0.015686174854636192, 0.05585494264960289, 0.06882389634847641, -0.023082533851265907, -0.012324194423854351, 0.03842790424823761, 0.01937974989414215, 0.027430081740021706, -0.022806206718087196, -0.024611543864011765, -0.053975917398929596, 0.001747769652865827, 0.00006926170317456126, -0.020337684080004692, 0.021700898185372353, 0.005443646106868982, -0.058691900223493576, 0.02831432968378067, -0.026011602953076363, -0.02490629255771637, -0.020485058426856995, -0.04925993084907532, -0.030138088390231133, -0.01746387965977192, -0.03748839348554611, -0.06112357974052429, 0.01851392351090908, -0.08098229765892029, 0.023893093690276146, 0.04605453833937645, -0.04999680444598198, -0.05784449726343155, -0.0011686338111758232, 0.04377023130655289, -0.05327588692307472, -0.0015923356404528022, -0.0077970330603420734, 0.0056508914567530155, -0.0474545955657959, -0.02741166017949581, 0.002530696801841259, -0.020816650241613388, -0.037691034376621246, 0.009828038513660431, 0.026803741231560707, -0.004798882640898228, -0.049112558364868164, -0.007295038551092148, -0.035590946674346924, 0.025422103703022003, 0.0421859547495842, 0.020245574414730072, -0.04914940148591995, -0.02087191678583622, -0.018477080389857292, 0.026011602953076363, -0.03982796147465706, 0.020337684080004692, -0.048154622316360474, 0.03363823518157005, 0.00856153853237629, 0.017390193417668343, 0.009837249293923378, 0.06281838566064835, -0.018744196742773056, -0.03234870731830597, -0.01329133938997984, 0.007423991337418556, -0.0234141256660223, 0.031224975362420082, -0.03238555043935776, -0.029309106990695, -0.04767565801739693, 0.04443341866135597, -0.018937624990940094, -0.008105598390102386, -0.024482591077685356, -0.017095444723963737, 0.031096022576093674, 0.012950535863637924, -0.004388997331261635, -0.006595009472221136, 0.06882389634847641, -0.014672975055873394, 0.02571685239672661, -0.006332498975098133, -0.02118508704006672, -0.014341382309794426, -0.035185664892196655, -0.04623875394463539, 0.04119117930531502, 0.012701841071248055, -0.03408035635948181, 0.025827383622527122, -0.00008181876182788983, 0.0366041474044323, -0.007193718571215868, -0.0010448623215779662, 0.017473090440034866, -0.02304569073021412, 0.04959152638912201, 0.04903887212276459, -0.005489700939506292, 0.013051855377852917, -0.031556569039821625, -0.025164198130369186, 0.05143370479345322, -0.01978502981364727, -0.0393858402967453, -0.026914270594716072, -0.04690194129943848, 0.0048771752044558525, 0.009335254319012165, -0.008902342058718204, 0.009450390934944153, -0.00784769281744957, 0.01914026588201523, 0.02750376984477043, 0.02142457105219364, 0.02890382707118988, -0.008584565483033657, 0.02300884574651718, -0.004490317311137915, 0.024611543864011765, 0.011135987006127834, -0.06598693877458572, 0.028774874284863472, -0.007152269594371319, 0.03920162096619606, -0.04999680444598198, -0.0648079439997673, -0.0366041474044323, -0.03734101727604866, -0.007925985381007195, -0.05390223115682602, -0.013807150535285473, 0.03376718610525131, 0.013788728043437004, -0.0204666368663311, 0.009058927185833454, -0.006981867831200361, 0.03682520613074303, 0.008796416223049164, 0.0016533578746020794, -0.01549274567514658, -0.014387437142431736, 0.026435304433107376, -0.021479835733771324, 0.04804409295320511, -0.0031363139860332012, 0.03601464629173279, 0.007995067164301872, -0.019619232043623924, -0.012029444798827171, -0.05095474049448967, -0.07346619665622711, -0.06075514480471611, -0.004720590077340603, 0.03017493151128292, 0.007106215227395296, 0.04100695997476578, -0.02754061296582222, -0.011891281232237816, 0.028111688792705536, -0.031224975362420082, -0.0007316914270631969, 0.029161732643842697, 0.0308565404266119, -0.028461704030632973, 0.006360131315886974, 0.014636131934821606, -0.0010368027724325657, 0.02831432968378067, 0.0170585997402668, -0.055560193955898285, -0.024077311158180237, -0.006673302501440048, 0.03887002915143967, -0.016165142878890038, -0.01851392351090908, -0.01978502981364727, 0.044212356209754944, -0.047933559864759445, -0.0035853455774486065, 0.022124599665403366, -0.007649658713489771, -0.018403392285108566, 0.041228022426366806, -0.037543658167123795, 0.009215513244271278, -0.019269218668341637, 0.000375632313080132, -0.006378553342074156, -0.015317738987505436, 0.01288605947047472, 0.032827675342559814, 0.0008151652873493731, 0.0019032037816941738, -0.01746387965977192, -0.01585197076201439, 0.050844207406044006, -0.0032767802476882935, -0.08216129243373871, -0.012222873978316784, -0.021111398935317993, -0.04214911162853241, -0.013668986037373543, -0.04944415017962456, -0.011246518231928349, 0.0134110813960433, 0.011624164879322052, 0.0115504777058959, 0.04487553983926773, -0.00902668945491314, -0.011642586439847946, 0.004725195467472076, -0.003829434746876359, -0.008695096708834171, 0.059502460062503815, -0.011900492012500763, -0.00535614276304841, -0.010942557826638222, 0.026195820420980453, 0.08319291472434998, 0.03957005962729454, -0.014801927842199802, 0.00670554069802165, 0.034688275307416916, 0.06782912462949753, -0.02658267877995968, 0.02908804453909397, 0.0319434255361557, -0.03548041358590126, -0.004301493521779776, 0.018753407523036003, 0.035683054476976395, 0.008953002281486988, 0.0028507758397608995, -0.01817312091588974, 0.054565414786338806, -0.05412328988313675, -0.009206301532685757, 0.015170364640653133, -0.005567993503063917, 0.020724540576338768, -0.005738395266234875, -0.006249600555747747, -0.036733098328113556, 0.0006672150921076536, 0.03483565151691437, -0.012167608365416527, 0.012757106684148312, 0.0319434255361557, -0.0072213513776659966, 0.011808383278548717, -0.03702784702181816, -0.00462157279253006, 0.03376718610525131, -0.02391151525080204, -0.026306351646780968, -0.008257578127086163, 0.043401796370744705, 0.01867050863802433, -0.05917086824774742, -0.009514867328107357, -0.022161442786455154, -0.034725122153759, -0.0207798071205616, -0.0103899035602808, 0.04981258511543274, 0.009321438148617744, -0.02241934835910797, -0.016459891572594643, 0.02921699732542038, -0.02545894868671894, 0.01352161169052124, -0.01356766652315855, -0.04697562754154205, -0.02555105648934841, 0.0462019108235836, 0.04251754656434059, 0.013899259269237518, 0.011403103359043598, 0.034282997250556946, 0.011964968405663967, 0.0015232538571581244, 0.06583956629037857, -0.010555699467658997, 0.023487813770771027, -0.004771249834448099, 0.026011602953076363, 0.05051261559128761, -0.008547722361981869, -0.027393238618969917, 0.04074905440211296, -0.019858716055750847, -0.010150419548153877, 0.010205685161054134, -0.055339131504297256, -0.008570749312639236, -0.0029659122228622437, -0.01143073569983244, -0.0316302552819252, 0.04078589752316475, -0.027006380259990692, 0.027282707393169403, -0.061860453337430954, -0.043622858822345734, 0.002332662232220173, 0.005217979196459055, -0.023119376972317696, -0.021258773282170296, 0.012830793857574463, -0.004554793704301119, -0.028830140829086304, 0.008612198755145073, -0.009344465099275112, 0.037414707243442535, 0.03345401585102081, -0.015253262594342232, 0.03465143218636513, 0.0072213513776659966, 0.004881781060248613, -0.018716564401984215, 0.03406193479895592, 0.08223497867584229, 0.004246228374540806, -0.018771829083561897, -0.01969292014837265, -0.050438929349184036, 0.022308817133307457, -0.014792717061936855, -0.006668697111308575, 0.03129866346716881, -0.03455932438373566, 0.029198575764894485, 0.024022046476602554, 0.003435668535530567, 0.005287060979753733, 0.03334348276257515, -0.019306061789393425, -0.0212403517216444, 0.028185376897454262, 0.009422758594155312, -0.007143058814108372, 0.03172236308455467, -0.0034080357290804386, 0.08238235861063004, -0.011099142953753471, 0.03466985374689102, 0.018956046551465988, -0.018900781869888306, -0.019619232043623924, -0.002463917713612318, 0.01715070940554142, -0.01502299029380083, 0.01313475426286459, -0.002018340164795518, 0.01776784099638462, -0.021719319745898247, 0.016478313133120537, -0.024666810408234596, -0.01336502656340599, 0.008317449130117893, 0.031022336333990097, -0.02031926065683365, -0.0924038216471672, -0.002954398514702916, 0.03653045743703842, 0.03711995482444763, -0.020227152854204178, 0.013107120990753174, 0.007750978693366051, -0.03334348276257515, -0.04034377261996269, 0.02803800255060196, -0.012093921191990376, 0.00231078639626503, -0.018458658829331398, -0.008985240012407303, -0.06812386959791183, -0.03454090282320976, -0.037359438836574554, 0.03776472061872482, 0.02912488952279091, -0.01172548532485962, 0.031556569039821625, -0.002362597733736038, 0.008004278875887394, 0.006682513281702995, -0.03820684179663658, 0.017906004562973976, 0.019342904910445213, 0.0021116004791110754, -0.01687438227236271, -0.04196489229798317, -0.0009141825721599162, 0.04119117930531502, 0.0028208403382450342, -0.02006135694682598, -0.010997823439538479, 0.009634609334170818, 0.00846942886710167, 0.025882650166749954, 0.03004598058760166, -0.01268341951072216, -0.0036705464590340853, 0.0058074770495295525, -0.005858137272298336, -0.045575570315122604, 0.03452248126268387, -0.012545255944132805, 0.009763562120497227, 0.01987713761627674, 0.0021242655348032713, -0.04918624460697174, 0.022087756544351578, 0.040896426886320114, -0.03649361431598663, -0.0030349940061569214, 0.0409332737326622, -0.023966779932379723, 0.017694152891635895, -0.023156220093369484, -0.030285462737083435, 0.03142761439085007, 0.010951768606901169, 0.03868580982089043, 0.029659122228622437, -0.06174992397427559, 0.02431679517030716, -0.0025974758900702, 0.02903277985751629, -0.014396647922694683, -0.017657309770584106, -0.015197996981441975, -0.0474545955657959, 0.037691034376621246, 0.012701841071248055, 0.01928764022886753, -0.008409558795392513, -0.0015197996981441975, -0.044986072927713394, -0.007654264103621244, -0.04170698672533035, -0.02245619148015976, 0.019453436136245728, -0.029253842309117317, 0.04211226850748062, -0.0008007732685655355, 0.00670554069802165, -0.01919553056359291, -0.009689874947071075, 0.0070555550046265125, 0.007774005644023418, 0.005245611537247896, 0.02540368214249611, 0.007396358530968428, -0.01529010571539402, 0.0027425475418567657, 0.0022969699930399656, 0.024150999262928963, -0.06440266221761703, -0.031685519963502884, -0.059686679393053055, 0.0124807795509696, 0.026527412235736847, -0.04395445063710213, 0.005687735043466091, 0.06930286437273026, 0.039717432111501694, -0.004803488031029701, -0.005729184485971928, -0.01272947434335947, -0.007723345886915922, -0.004642297513782978, -0.037322595715522766, -0.035775162279605865, -0.015612487681210041, 0.013659775257110596, 0.0207798071205616, 0.02654583565890789, 0.021700898185372353, 0.03384087234735489, -0.0030165722128003836, 0.015400636941194534, 0.029972292482852936, -0.009551710449159145, -0.04944415017962456, 0.025569478049874306, 0.008750362321734428, 0.012545255944132805, 0.026693210005760193, 0.03104075789451599, 0.010960979387164116, 0.024243108928203583, 0.0769294947385788, 0.016828328371047974, 0.014267695136368275, -0.028424860909581184, 0.05231795459985733, 0.039901651442050934, -0.007879931479692459, 0.02159036695957184, -0.0067239622585475445, -0.037322595715522766, 0.0007616269285790622, -0.013595298863947392, 0.018071800470352173, 0.01190970279276371, 0.023893093690276146, 0.02803800255060196, -0.03610675781965256, -0.03923846408724785, 0.004794277250766754, -0.06502900272607803, 0.01401900127530098, 0.014194007962942123, 0.019563967362046242, -0.014120320789515972, 0.005968668032437563, 0.028572235256433487, -0.00022912131680641323, -0.024445747956633568, 0.04937046393752098, 0.005540360696613789, 0.0023902305401861668, 0.017730996012687683, -0.025035245344042778, -0.037359438836574554, 0.05441804230213165, -0.002673465758562088, 0.009579343721270561, -0.058286622166633606, 0.022806206718087196, 0.03209080174565315, 0.012471568770706654, 0.004045891109853983, -0.014682185836136341, -0.0026711630634963512, -0.007248984184116125, 0.0017546778544783592, -0.05710762366652489, -0.017049388960003853, -0.00044039651402272284, 0.004596242681145668, -0.02809326723217964, -0.01572301797568798, 0.023929936811327934, 0.05080736428499222, -0.022714097052812576, 0.03485407307744026, -0.010629386641085148, 0.011366259306669235, -0.01594408042728901, 0.06963445991277695, -0.06219204515218735, -0.00035749832750298083, 0.037359438836574554, -0.018283650279045105, -0.045944005250930786, -0.0017777051543816924, 0.03159341216087341, -0.04727037623524666, -0.01897446997463703, 0.0124807795509696, 0.013963735662400723, 0.01867050863802433, -0.000735145527869463, -0.014765084721148014, 0.010988612659275532, 0.011974179185926914, -0.0033850085455924273, 0.018182331696152687, -0.00939973071217537, -0.01864287629723549, -0.01150442287325859, -0.026785317808389664, 0.05640759691596031, 0.011145197786390781, 0.012020234018564224, 0.028111688792705536, 0.026969537138938904, -0.058507684618234634, 0.005084421020001173, 0.006263417191803455, -0.028793295845389366, 0.0103899035602808, -0.03590411692857742, 0.031206553801894188, 0.014940091408789158, -0.06491847336292267, -0.011255729012191296, -0.011587321758270264, 0.002431679517030716, 0.019950825721025467, -0.08326660096645355, 0.019950825721025467, -0.03979111835360527 ]
This paper systematically investigates the effectiveness of various augmentations for contrastive self-supervised learning of electrocardiogram (ECG) signals and identifies the best parameters. The baseline of our proposed self-supervised framework consists of two main parts: the contrastive learning and the downstream task. In the first stage, we train an encoder using a number of augmentations to extract generalizable ECG signal representations. We then freeze the encoder and finetune a few linear layers with different amounts of labelled data for downstream arrhythmia detection. We then experiment with various augmentations techniques and explore a range of parameters. Our experiments are done on PTB-XL, a large and publicly available 12-lead ECG dataset. The results show that applying augmentations in a specific range of complexities works better for self-supervised contrastive learning. For instance, when adding Gaussian noise, a sigma in the range of 0.1 to 0.2 achieves better results, while poor training occurs when the added noise is too small or too large (outside of the specified range). A similar trend is observed with other augmentations, demonstrating the importance of selecting the optimum level of difficulty for the added augmentations, as augmentations that are too simple will not result in effective training, while augmentations that are too difficult will also prevent the model from effective learning of generalized representations. Our work can influence future research on self-supervised contrastive learning on bio-signals and aid in selecting optimum parameters for different augmentations.
[ 0.03415779024362564, 0.06969305872917175, -0.024627115577459335, -0.02686086669564247, 0.019917622208595276, 0.037471190094947815, -0.050892315804958344, 0.013355975039303303, -0.013933028094470501, -0.026749180629849434, -0.020736664533615112, -0.03946295008063316, 0.01551526878029108, -0.012034338898956776, 0.02447819896042347, -0.017907245084643364, -0.026302428916096687, -0.03964909911155701, -0.005216741468757391, -0.0023314785212278366, 0.022579509764909744, -0.043632622808218, -0.03348766639828682, 0.004437255207449198, -0.004695532843470573, 0.0433720164000988, 0.044563353061676025, 0.014584538526833057, -0.03393441438674927, 0.04675987362861633, 0.04471226781606674, 0.008302111178636551, -0.01889381930232048, 0.027698524296283722, -0.04783952236175537, -0.036763835698366165, 0.05591825768351555, 0.03802962601184845, -0.051190149039030075, 0.007655254099518061, 0.0022849421948194504, -0.02794051356613636, 0.024924948811531067, -0.024887720122933388, -0.03278030827641487, -0.08190423995256424, -0.08927562087774277, -0.008483603596687317, -0.016725217923521996, 0.012136719189584255, -0.023082103580236435, -0.020289912819862366, 0.024794647470116615, 0.03581449016928673, -0.036466002464294434, 0.05193473398685455, 0.01880074478685856, 0.038048241287469864, 0.10692226141691208, 0.013188444077968597, 0.010870926082134247, 0.041138265281915665, -0.0675709992647171, 0.016902055591344833, 0.02068082056939602, -0.06433205306529999, 0.014026100747287273, 0.008781437762081623, 0.017162660136818886, 0.04519624635577202, -0.062284450978040695, -0.01876351609826088, -0.015589727088809013, 0.06373638659715652, 0.027047013863921165, -0.0008062448468990624, 0.012657927349209785, 0.042515747249126434, 0.0031807697378098965, 0.032463863492012024, 0.059715636074543, 0.030918849632143974, -0.02555784583091736, 0.0370616689324379, 0.05584380030632019, 0.0039253537543118, -0.005654184613376856, -0.05681175738573074, -0.04415383189916611, 0.03426947817206383, -0.016492534428834915, 0.03553527221083641, -0.040803201496601105, 0.04173393175005913, 0.007236425764858723, 0.02572537586092949, 0.003743861336261034, -0.018344687297940254, -0.07818131893873215, -0.04657372832298279, -0.007329498417675495, -0.03469761461019516, -0.015394274145364761, 0.00454661576077342, 0.007050279527902603, -0.017060279846191406, -0.009102539159357548, -0.0022221177350729704, 0.022672582417726517, 0.12151610851287842, -0.04471226781606674, -0.021071726456284523, -0.005747257731854916, 0.013700345531105995, -0.08860549330711365, -0.03756426274776459, -0.007455147337168455, -0.054019566625356674, -0.020122382789850235, -0.012025031261146069, 0.030416255816817284, 0.08570161461830139, -0.0063801538199186325, 0.04821181297302246, -0.04891916736960411, 0.06600736826658249, -0.004937522578984499, 0.0014612460508942604, 0.03497683256864548, 0.03990970179438591, 0.022002456709742546, 0.030807161703705788, 0.005123668350279331, -0.011792348697781563, 0.03257554769515991, 0.04277634993195534, 0.006775714457035065, 0.03583310544490814, 0.0022977397311478853, -0.020587747916579247, -0.0328175388276577, -0.015571112744510174, -0.017190583050251007, 0.00400213897228241, 0.011252525262534618, -0.011001228354871273, 0.0018602965865284204, 0.09590242058038712, -0.036801062524318695, 0.016566993668675423, -0.02326824888586998, 0.004590825643390417, -0.027512378990650177, -0.013151214458048344, 0.05550873652100563, -0.003932334017008543, 0.028201118111610413, -0.04657372832298279, 0.012657927349209785, -0.05078062787652016, 0.07211296260356903, 0.018679751083254814, 0.01960117369890213, 0.009418987669050694, 0.052158109843730927, 0.03261277824640274, -0.014389085583388805, -0.012583469040691853, -0.05420571565628052, 0.04828627035021782, 0.0051376293413341045, -0.02585567906498909, 0.03164482116699219, 0.039425723254680634, -0.013960950076580048, 0.04653649777173996, 0.01171789038926363, -0.010554477572441101, -0.032966457307338715, 0.03335736319422722, -0.08078736066818237, 0.005877560004591942, 0.01163412444293499, -0.01171789038926363, 0.04966375231742859, 0.02660026215016842, 0.07598479837179184, -0.030509328469634056, 0.018810052424669266, -0.0008091533672995865, -0.020624976605176926, 0.00855806190520525, 0.053945109248161316, -0.007943780161440372, 0.007227118127048016, -0.025334469974040985, -0.02293318696320057, -0.02660026215016842, 0.0284431092441082, -0.03639154136180878, -0.04173393175005913, -0.03547942638397217, 0.03652184456586838, -0.047690603882074356, 0.02969028614461422, 0.011261832900345325, 0.07404887676239014, 0.000758544949349016, -0.019545329734683037, 0.003578656818717718, -0.017292963340878487, 0.030714089050889015, -0.03607509285211563, -0.027847440913319588, -0.04333478957414627, -0.02494356408715248, 0.07255970686674118, 0.004404679872095585, 0.043967682868242264, 0.04746722802519798, 0.049812667071819305, 0.017525644972920418, 0.07602202147245407, -0.03531189635396004, -0.0010947711998596787, 0.040728744119405746, 0.008111312054097652, 0.002045279135927558, 0.04445166513323784, 0.01657630130648613, -0.00555645814165473, -0.015915483236312866, -0.005979940295219421, 0.012146025896072388, 0.01161551009863615, -0.017609411850571632, 0.012927839532494545, 0.03935126215219498, -0.007534258998930454, -0.024087291210889816, -0.012099489569664001, -0.00198361836373806, 0.005398233886808157, -0.03039764054119587, 0.05107846111059189, -0.03160759061574936, -0.013253594748675823, 0.09538120776414871, 0.0647415742278099, -0.004148728679865599, -0.06604459881782532, 0.0016089994460344315, 0.008292804472148418, -0.003427413059398532, -0.06250782310962677, -0.027251774445176125, 0.03946295008063316, -0.057779718190431595, 0.012229791842401028, -0.03207295387983322, 0.06946968287229538, 0.0142215546220541, -0.02915046364068985, 0.05651392415165901, -0.02222583256661892, -0.005165551323443651, 0.054280173033475876, 0.05528536066412926, -0.0033413206692785025, -0.02447819896042347, -0.009595826268196106, -0.0004444235819391906, -0.043967682868242264, -0.026116283610463142, 0.01338389702141285, -0.0055424971505999565, 0.026991169899702072, -0.0490308552980423, -0.01442631520330906, 0.010331102646887302, -0.026544420048594475, 0.004558250308036804, 0.06544893234968185, 0.06302903592586517, 0.007194542791694403, -0.03587033227086067, -0.017693176865577698, 0.001550828805193305, -0.05562042444944382, -0.024180365726351738, 0.05249316990375519, -0.07453285902738571, -0.04642480984330177, -0.022169988602399826, 0.007250386755913496, -0.029969505965709686, -0.03923957794904709, -0.04683433100581169, -0.006915323901921511, 0.0011849355651065707, -0.023956989869475365, 0.0024897027760744095, -0.020718049257993698, 0.05037110671401024, -0.04098934680223465, -0.046685416251420975, 0.006515109911561012, 0.042143452912569046, -0.04102657735347748, -0.029224921017885208, 0.05308884009718895, -0.012899917550384998, -0.018335381522774696, -0.030472099781036377, -0.001063940697349608, -0.00470716692507267, 0.009288685396313667, -0.012927839532494545, 0.03819715976715088, 0.004111499525606632, 0.018074776977300644, -0.0002159584400942549, -0.0966470018029213, 0.008213692344725132, -0.00036502067814581096, -0.04653649777173996, 0.03289199620485306, 0.00023006481933407485, -0.033338747918605804, 0.020327143371105194, -0.041510555893182755, 0.025129709392786026, -0.023249635472893715, 0.01976870559155941, 0.024906333535909653, 0.025241397321224213, -0.05375896394252777, -0.007003743201494217, -0.06600736826658249, -0.014528695493936539, -0.03240801766514778, 0.013207058422267437, -0.07140560448169708, -0.03594479337334633, 0.012518318369984627, -0.00008383841486647725, -0.041808389127254486, 0.013104678131639957, -0.02094142511487007, -0.03157036006450653, 0.0010552151361480355, 0.008106658235192299, 0.02285872772336006, -0.00707820151001215, -0.0208483524620533, 0.011969187296926975, -0.006319656502455473, -0.037508416920900345, -0.001072084647603333, -0.029504140838980675, 0.0002638037840370089, -0.0696186050772667, -0.025595074519515038, 0.004032387863844633, -0.059864550828933716, -0.009130461141467094, 0.023417165502905846, 0.00870697945356369, 0.03534912317991257, -0.019005505368113518, -0.03990970179438591, 0.015412888489663601, 0.02030852809548378, -0.021667394787073135, 0.04448889195919037, 0.013616579584777355, -0.00860925205051899, 0.019787319004535675, -0.03220325708389282, 0.039425723254680634, -0.10066775232553482, -0.021239258348941803, 0.0014054023195058107, 0.03581449016928673, 0.038104087114334106, 0.057072363793849945, -0.008027546107769012, 0.011857500299811363, -0.01747910864651203, 0.044228289276361465, -0.03789932653307915, -0.0611303448677063, 0.00157409708481282, -0.009744742885231972, 0.005579726304858923, 0.0142215546220541, 0.0504455640912056, 0.06641688942909241, 0.05528536066412926, 0.014249475672841072, -0.010833697393536568, -0.012657927349209785, 0.0036158859729766846, -0.014686918817460537, 0.02915046364068985, -0.004486118443310261, -0.05822646617889404, -0.0018091064412146807, 0.023082103580236435, -0.03728504478931427, 0.04154778644442558, -0.04165947437286377, -0.0022640007082372904, -0.027828825637698174, -0.014584538526833057, 0.05148798227310181, -0.0698792040348053, 0.006589568220078945, 0.02138817496597767, -0.03760148957371712, -0.02652580477297306, 0.019619788974523544, 0.05629054829478264, -0.029076004400849342, 0.03211018443107605, -0.009660976938903332, 0.03987247124314308, 0.018847282975912094, 0.015487346798181534, 0.036130938678979874, 0.013737574219703674, 0.052381481975317, -0.008250921033322811, -0.028089430183172226, 0.000476417422760278, -0.003464642446488142, -0.004555923398584127, 0.00458849873393774, -0.04229237139225006, 0.012350786477327347, -0.052902691066265106, -0.0013006951194256544, -0.014538002200424671, -0.0344928540289402, -0.01151312980800867, -0.04244128614664078, -0.020922809839248657, 0.0768410712480545, -0.048770252615213394, -0.0010290383361279964, -0.08465919643640518, -0.023137947544455528, -0.09255179017782211, -0.01163412444293499, 0.015850331634283066, -0.011829578317701817, 0.02485049143433571, -0.027884669601917267, 0.026953941211104393, -0.014444929547607899, 0.007678522262722254, 0.03691275045275688, -0.010442790575325489, -0.03916511684656143, 0.03378549963235855, 0.023175176233053207, -0.04370708018541336, -0.05204642191529274, -0.00994950346648693, 0.05789140611886978, 0.0007643619901500642, -0.007762288209050894, -0.04098934680223465, 0.008362608961760998, 0.03227771446108818, 0.0509667731821537, -0.03648461401462555, -0.06515109539031982, 0.02723315916955471, -0.018046854063868523, 0.015729336068034172, -0.019024120643734932, -0.022486437112092972, 0.026469960808753967, 0.002850360469892621, -0.0034972180146723986, 0.023137947544455528, -0.013625887222588062, 0.00020301547192502767, -0.013355975039303303, -0.024161750450730324, -0.0008172972593456507, -0.013849262148141861, 0.007180581800639629, 0.050855085253715515, -0.011243218556046486, 0.0312725268304348, -0.029001547023653984, 0.08830766379833221, -0.0012064587790519, -0.005151590332388878, 0.02081112191081047, -0.005844984203577042, -0.015524576418101788, -0.001286734244786203, -0.017339499667286873, -0.047690603882074356, -0.012704464606940746, -0.004714147187769413, -0.029913662001490593, 0.04586637392640114, 0.014007486402988434, 0.002566487994045019, 0.006398768629878759, -0.023286864161491394, 0.015757258981466293, -0.023621926084160805, 0.006575607229024172, -0.00388347078114748, 0.04307418316602707, 0.03343182057142258, -0.021574320271611214, -0.024534042924642563, 0.025334469974040985, -0.06142817810177803, 0.015338430181145668, 0.03291061148047447, 0.0186611358076334, 0.04474949836730957, 0.045010101050138474, -0.026953941211104393, -0.013570043258368969, -0.031458672136068344, -0.024180365726351738, 0.006798982620239258, -0.012136719189584255, 0.026879481971263885, 0.026823638007044792, -0.01687413454055786, -0.0019242842681705952, -0.040058620274066925, 0.07609648257493973, 0.014919601380825043, 0.007227118127048016, 0.007352767046540976, -0.00550526799634099, 0.06046022102236748, -0.03946295008063316, -0.017367420718073845, 0.051860272884368896, 0.017227811738848686, -0.009996039792895317, -0.031793735921382904, 0.024161750450730324, -0.04162224382162094, -0.04024476557970047, -0.03207295387983322, 0.01240663044154644, -0.024701572954654694, -0.03540496900677681, -0.02319379150867462, 0.0014821875374764204, -0.0010930260177701712, 0.004567557480186224, -0.00857202336192131, -0.041101034730672836, 0.03147728741168976, 0.06265674531459808, -0.023528853431344032, 0.004886332433670759, -0.04404214397072792, 0.033841341733932495, -0.02756822295486927, -0.016687989234924316, -0.0038904512766748667, 0.004658303689211607, 0.038104087114334106, -0.027791596949100494, 0.03620539605617523, 0.03056517243385315, 0.04370708018541336, 0.01943364180624485, -0.008190424181520939, 0.019191652536392212, -0.022951802238821983, -0.013048834167420864, -0.004106846172362566, -0.059119969606399536, -0.021499862894415855, 0.000815552135463804, 0.03445562347769737, 0.026972554624080658, 0.020494673401117325, 0.009698206558823586, -0.0481373555958271, -0.0029271456878632307, -0.006198661867529154, 0.017907245084643364, 0.04489841312170029, -0.04795121029019356, -0.00994950346648693, 0.02794051356613636, 0.015208127908408642, 0.03469761461019516, -0.001157595426775515, -0.0292807649821043, 0.033636581152677536, -0.0020650571677833796, 0.0014554290100932121, 0.003262208541855216, -0.03566557168960571, -0.004197592381387949, -0.022039685398340225, -0.025911523029208183, 0.037005823105573654, 0.0018789111636579037, 0.003911392763257027, -0.03168204799294472, -0.00474904989823699, -0.03136559948325157, 0.0642203688621521, -0.025111094117164612, 0.034008875489234924, -0.018307458609342575, 0.01906134933233261, 0.06842727214097977, -0.015319815836846828, -0.031588975340127945, 0.004479138180613518, -0.044302746653556824, -0.05554596707224846, -0.010852311737835407, -0.024906333535909653, -0.016380848363041878, 0.03361796587705612, 0.02155570685863495, -0.05230702459812164, 0.03549804165959358, 0.030509328469634056, 0.026209356263279915, -0.022542281076312065, 0.014528695493936539, -0.003774109994992614, 0.005342389922589064, -0.01403540838509798, 0.0171812754124403, -0.016483228653669357, 0.00009496354323346168, 0.043930456042289734, 0.014705534093081951, 0.018605291843414307, 0.04340924695134163, 0.042813580483198166, 0.026916710659861565, -0.03289199620485306, 0.014500773511826992, 0.044302746653556824, 0.022169988602399826, 0.008041506633162498, 0.014575231820344925, 0.012937147170305252, -0.028219733387231827, 0.039388492703437805, -0.03598202019929886, 0.005393580067902803, 0.017963089048862457, 0.01640876941382885, -0.0013193096965551376, -0.010768545791506767, 0.03737811744213104, -0.0045303283259272575, -0.05588102713227272, -0.02669333666563034, 0.01745118759572506, 0.03315260261297226, -0.025408929213881493, 0.043520934879779816, 0.0029550676699727774, -0.02269119769334793, -0.01819577068090439, -0.01257416233420372, -0.011336291208863258, -0.032836154103279114, -0.016604222357273102, -0.0033157255966216326, 0.003103984519839287, 0.042143452912569046, 0.027828825637698174, -0.018940355628728867, -0.03557249903678894, -0.00394396809861064, -0.00153803126886487, -0.008511525578796864, -0.0400213897228241, 0.026786409318447113, 0.024385126307606697, -0.025129709392786026, 0.01967563107609749, -0.014528695493936539, 0.03566557168960571, -0.043595392256975174, 0.01720919832587242, 0.0031784428283572197, -0.0039625829085707664, 0.0005241173203103244, 0.0036112323869019747, 0.006552339065819979, -0.002288432326167822, 0.004339528735727072, 0.0019138135248795152, -0.0268980972468853, -0.0033459742553532124, 0.017339499667286873, 0.06153986603021622, 0.0005465130088850856, -0.012369401752948761, -0.01240663044154644, -0.012164641171693802, 0.004218533635139465, 0.05033387616276741, -0.011336291208863258, 0.027847440913319588, -0.009977425448596478, -0.04623866453766823, 0.025632303208112717, 0.060869742184877396, 0.021834924817085266, 0.013476970605552197, -0.00717127462849021, 0.0076738689094781876, 0.02948552556335926, 0.016129551455378532, -0.03583310544490814, 0.015142977237701416, 0.04642480984330177, -0.013570043258368969, -0.007538912817835808, 0.04783952236175537, 0.007436532527208328, -0.007585449144244194, 0.008925700560212135, -0.006068359594792128, 0.022616738453507423, 0.009288685396313667, 0.008874510414898396, 0.05316329747438431, 0.04471226781606674, 0.02302625961601734, -0.04616420716047287, -0.047392770648002625, 0.028461722657084465, -0.01413778867572546, 0.05107846111059189, -0.012099489569664001, -0.016120243817567825, 0.005868252366781235, -0.010107727721333504, -0.026469960808753967, -0.00954928994178772, -0.020718049257993698, 0.018205078318715096, -0.0003772364871110767, -0.016418077051639557, -0.001040672417730093, -0.009223533794283867, 0.07907482236623764, -0.06209830567240715, 0.03356212377548218, 0.019154423847794533, -0.012769615277647972, 0.02965305745601654, 0.01906134933233261, 0.06462989002466202, -0.0636991634964943, 0.02306348830461502, 0.0030900235287845135, -0.005965979304164648, 0.001496148412115872, 0.012602084316313267, 0.0054587312042713165, 0.017693176865577698, 0.01795378141105175, -0.06392253190279007, -0.015682799741625786, -0.0051795123144984245, -0.005677452776581049, -0.026581648737192154, -0.057779718190431595, -0.0238080732524395, 0.009386411868035793, 0.014714840799570084, -0.026265200227499008, 0.015989940613508224, 0.005993901286274195, -0.0043814112432301044, -0.022840114310383797, -0.014817221090197563, 0.02518555335700512, -0.043223101645708084, -0.03553527221083641, 0.016697295010089874, -0.017423264682292938, -0.0035902909003198147, 0.012788229621946812, 0.021872155368328094, 0.0020476060453802347, -0.04374431073665619, 0.0111315306276083, -0.011224603280425072, 0.008814012631773949, -0.03523743897676468, 0.017711792141199112, 0.03765733540058136, 0.006221930030733347, -0.012564854696393013, 0.004046348389238119, -0.03453008085489273, 0.03197988122701645, -0.014007486402988434, -0.043260328471660614, -0.045307934284210205, -0.03332013264298439, -0.042180683463811874, -0.005295853596180677, 0.00060322938952595, -0.03302229940891266, 0.038383305072784424, -0.00310165761038661, -0.014593846164643764, -0.0020022329408675432, -0.0022337520495057106, -0.02514832466840744, 0.002053423086181283, 0.008264882490038872, -0.042217910289764404, 0.05528536066412926, 0.03103053756058216, 0.03795516863465309, -0.0038718366995453835, 0.013132600113749504, -0.035256050527095795, -0.0017160334391519427, -0.04240405932068825, -0.017507031559944153, -0.04299972578883171, -0.002348929876461625, -0.0031132916919887066, 0.008060121908783913, -0.007241079118102789, -0.038346074521541595, 0.02589290775358677, -0.011205988936126232, -0.019619788974523544, -0.026916710659861565, 0.0057798330672085285, -0.0044395821169018745, -0.006356885656714439, 0.01976870559155941, -0.012006416916847229, 0.002622331725433469, 0.004651322960853577, -0.01025664433836937, -0.002415244234725833, -0.0023826686665415764, 0.009251455776393414, 0.016892749816179276, 0.008576677180826664, -0.0027875362429767847, 0.0028806093614548445, -0.08994574844837189, -0.031253911554813385, 0.043260328471660614, -0.00017436644702684134, -0.012685849331319332, -0.010694087482988834, 0.024050062522292137, -0.036224011331796646, 0.002640946302562952, -0.027828825637698174, 0.0023396224714815617, 0.004793259315192699, 0.04489841312170029, 0.03186819329857826, 0.007846053689718246, 0.013011605478823185, 0.027158701792359352, -0.016362233087420464, -0.03760148957371712, -0.02719593048095703, -0.01610162854194641, 0.026469960808753967, 0.011289754882454872, 0.019619788974523544, 0.01317913644015789, 0.02669333666563034, 0.0012111123651266098, 0.007371381390839815, -0.048025667667388916, 0.001186099019832909, 0.02319379150867462, -0.01785140112042427, -0.012285635806620121, -0.028387265279889107, -0.024627115577459335, 0.016585608944296837, -0.012816151604056358, 0.005021288059651852, -0.0027386730071157217, 0.02293318696320057, -0.04850964620709419, -0.025092480704188347, -0.045642998069524765, 0.019861778244376183, -0.004239474888890982, 0.05066893994808197, -0.010452097281813622, 0.018782131373882294, 0.00033360853558406234, 0.03015565127134323, 0.010182186029851437, 0.00010812464461196214, 0.027047013863921165, -0.018670443445444107, 0.03778763860464096, -0.04314864054322243, -0.010870926082134247, -0.017367420718073845, 0.029634442180395126, 0.0005534935044124722, 0.03302229940891266, 0.012741693295538425, 0.013877184130251408, -0.009921581484377384, 0.008478949777781963, 0.04400491341948509, 0.021090341731905937, -0.01424016896635294, 0.024794647470116615, -0.04850964620709419, -0.01818646304309368, 0.0022256080992519855, -0.005323775578290224, -0.04299972578883171, 0.007762288209050894, 0.025408929213881493, -0.003029526211321354, 0.029076004400849342, -0.022002456709742546, -0.0035484081599861383, -0.0010715029202401638, -0.03601925075054169, -0.024794647470116615, -0.005291199777275324, -0.017776941880583763, 0.017702484503388405, 0.009214227087795734, -0.02356608398258686, -0.015505961142480373, 0.021295102313160896, -0.008613905869424343, -0.05889659374952316, -0.0038253001403063536, -0.046275895088911057, 0.004344182088971138, 0.010312488302588463, -0.004048675298690796, 0.012415938079357147, -0.032054342329502106, -0.009139768779277802, 0.025669533759355545, 0.013635193929076195, -0.030993308871984482, -0.01963840238749981, 0.0074830688536167145, 0.0067850216291844845, -0.026805022731423378, -0.00017989265325013548, 0.01153174415230751, -0.03076993301510811, 0.007599410135298967, -0.020289912819862366, -0.013737574219703674, 0.016231931746006012, 0.004416313953697681, 0.0012018050765618682, -0.018837975338101387, -0.0123880160972476, -0.012713771313428879, -0.03957463800907135, 0.013328053057193756, 0.014612460508942604, 0.013151214458048344, 0.05308884009718895, -0.019508101046085358, -0.035051289945840836, 0.012090182863175869, 0.020457444712519646, -0.03566557168960571, 0.04869579151272774, 0.018065469339489937, 0.03473484143614769, -0.010889540426433086, 0.037471190094947815, 0.01617608778178692, -0.021406790241599083, 0.045307934284210205, 0.03324567526578903, 0.0032947841100394726, -0.03441839665174484, 0.006543031893670559, 0.03583310544490814, -0.013839954510331154, 0.026805022731423378, 0.020252684131264687, 0.002522278344258666, 0.02030852809548378, 0.0019824549090117216, -0.02276565507054329, 0.04795121029019356, -0.026805022731423378, 0.022169988602399826, -0.022989030927419662, 0.036466002464294434, -0.01841914653778076 ]
Machine learning (ML) models are increasingly being used in application domains that often involve working together with human experts. In this context, it can be advantageous to defer certain instances to a single human expert when they are difficult to predict for the ML model. While previous work has focused on scenarios with one distinct human expert, in many real-world situations several human experts with varying capabilities may be available. In this work, we propose an approach that trains a classification model to complement the capabilities of multiple human experts. By jointly training the classifier together with an allocation system, the classifier learns to accurately predict those instances that are difficult for the human experts, while the allocation system learns to pass each instance to the most suitable team member -- either the classifier or one of the human experts. We evaluate our proposed approach in multiple experiments on public datasets with "synthetic" experts and a real-world medical dataset annotated by multiple radiologists. Our approach outperforms prior work and is more accurate than the best human expert or a classifier. Furthermore, it is flexibly adaptable to teams of varying sizes and different levels of expert diversity.
[ -0.007000000216066837, 0.003774937940761447, -0.03990523889660835, -0.027074813842773438, 0.04877306893467903, 0.007615337148308754, -0.06423940509557724, 0.028384041041135788, -0.006506858393549919, 0.003572007641196251, -0.024561097845435143, -0.06382045149803162, -0.018748130649328232, -0.033970076590776443, -0.044548630714416504, -0.0063148383051157, 0.005450748372823, 0.039800502359867096, -0.009478803724050522, -0.036728180944919586, 0.018643392249941826, -0.041685789823532104, -0.031194515526294708, 0.047236911952495575, 0.015056110918521881, 0.028645886108279228, 0.03290523961186409, -0.025241896510124207, -0.12261347472667694, 0.043047383427619934, 0.04444389417767525, -0.004804863128811121, -0.002225685864686966, -0.0476558618247509, -0.05620947852730751, -0.031054865568876266, 0.05778055265545845, 0.045281797647476196, 0.02147132344543934, 0.05554613843560219, 0.003174875397235155, -0.018399003893136978, -0.03686783090233803, -0.013912718743085861, 0.03297506272792816, -0.04137157276272774, -0.08036908507347107, 0.017386535182595253, 0.00624937703832984, -0.02154114842414856, 0.008217581547796726, -0.01041271910071373, -0.028052370995283127, -0.02127930335700512, -0.04720199853181839, 0.039591025561094284, 0.001696540042757988, 0.011014963500201702, 0.051810476928949356, 0.06898753345012665, 0.004156795796006918, -0.003041770774871111, -0.040324192494153976, 0.007933915592730045, 0.014096010476350784, -0.07034913450479507, 0.03760100156068802, 0.016024937853217125, 0.025835413485765457, -0.027668330818414688, -0.004591022618114948, 0.00018520107551012188, -0.0023326061200350523, 0.0024831672199070454, -0.03185785561800003, 0.006327930372208357, 0.01853865385055542, 0.034301746636629105, -0.016985038295388222, 0.024456361308693886, 0.005874065216630697, 0.04433915391564369, 0.003805486485362053, 0.051286786794662476, 0.05945636332035065, 0.021663343533873558, -0.0029675811529159546, -0.06228429451584816, -0.04119700938463211, -0.024927683174610138, -0.0586184561252594, 0.018433915451169014, 0.03150872886180878, 0.024369079619646072, -0.014096010476350784, 0.004093516618013382, -0.006546135060489178, -0.019952619448304176, -0.08064838498830795, -0.029344141483306885, -0.009618454612791538, 0.009321696124970913, 0.0077680801041424274, -0.010683292523026466, 0.031892769038677216, -0.0543241910636425, 0.010377805680036545, -0.022623442113399506, -0.00269264355301857, 0.11912219971418381, 0.0028170200530439615, -0.048738159239292145, -0.03589027747511864, -0.0395561121404171, -0.023408979177474976, -0.030827932059764862, -0.05058853328227997, -0.06710224598646164, 0.014174564741551876, -0.02480548806488514, 0.016950124874711037, 0.031177058815956116, -0.04158104956150055, 0.024177059531211853, -0.0395561121404171, 0.035488780587911606, -0.016836659982800484, 0.012507482431828976, 0.03623940423130989, 0.02950124815106392, 0.008824190124869347, -0.0011619389988481998, -0.033254366368055344, -0.03721696138381958, -0.010403990745544434, 0.0517057403922081, 0.087211973965168, 0.004700125195086002, -0.012673317454755306, 0.012786784209311008, -0.0069956365041434765, -0.02175062522292137, -0.006834165193140507, 0.013293018564581871, -0.017569826915860176, -0.008741272613406181, 0.023583542555570602, 0.10012967884540558, -0.033917706459760666, -0.005380922928452492, -0.03554115071892738, 0.04392020031809807, -0.014864090830087662, 0.014314215630292892, 0.016697008162736893, -0.007628429215401411, -0.02527680993080139, 0.02806982770562172, -0.0005007793079130352, -0.0025879053864628077, -0.0036701997742056847, 0.0006022443994879723, -0.01827680878341198, 0.0767381563782692, 0.032154615968465805, 0.03473815694451332, -0.026865338906645775, -0.010726933367550373, -0.10711222887039185, 0.03924189880490303, -0.030077308416366577, -0.020598504692316055, 0.003257793141528964, 0.0077593522146344185, -0.011442644521594048, 0.07212968170642853, -0.013903990387916565, -0.011329177767038345, -0.01080548670142889, 0.014000000432133675, -0.07499252259731293, 0.015736907720565796, 0.014837905764579773, 0.009417706169188023, 0.07310723513364792, -0.003674563718959689, 0.0609925240278244, 0.016635911539196968, 0.042733170092105865, 0.003971321973949671, -0.00045031955232843757, 0.02670823037624359, 0.05285785719752312, -0.03030424192547798, 0.019219452515244484, -0.01393890380859375, 0.00907730683684349, -0.004887780640274286, 0.049715712666511536, -0.054149627685546875, -0.040184542536735535, -0.07925187796354294, -0.001347412820905447, -0.017194515094161034, 0.03445885330438614, 0.0016321697039529681, 0.004213528707623482, -0.009487532079219818, 0.007794264703989029, -0.07541147619485855, -0.002841022564098239, 0.006790523882955313, -0.024770574644207954, 0.019620949402451515, -0.0071178306825459, -0.005372195038944483, 0.05044887959957123, 0.0048834169283509254, 0.0319276824593544, 0.00538528710603714, 0.04172069951891899, 0.048074815422296524, 0.01610349304974079, -0.016688279807567596, 0.03760100156068802, 0.053905241191387177, 0.015649626031517982, 0.019376559183001518, 0.038159601390361786, -0.0028715713415294886, -0.011163342744112015, 0.000053528292482951656, 0.019306734204292297, 0.01625187136232853, 0.039206985384225845, -0.05320698395371437, 0.015422694385051727, -0.0210872832685709, 0.00830486323684454, -0.011975063011050224, -0.00809975154697895, -0.06137656047940254, -0.03609975427389145, -0.028628431260585785, 0.09265835583209991, 0.015291771851480007, 0.01615586131811142, 0.0366932675242424, 0.006362843327224255, 0.002993765752762556, -0.008448878303170204, -0.01567581109702587, -0.007807357236742973, -0.0029348505195230246, -0.0018700126092880964, 0.05118204653263092, 0.021453866735100746, -0.0750623494386673, 0.009112220257520676, -0.023321697488427162, 0.05013466626405716, 0.0366932675242424, -0.00913840439170599, 0.018521199002861977, -0.013554863631725311, -0.02670823037624359, 0.057675812393426895, -0.014706983231008053, 0.01866084896028042, 0.0006529769743792713, -0.039800502359867096, -0.047167085111141205, -0.04315212368965149, -0.03578553721308708, 0.030653368681669235, -0.08036908507347107, -0.022832918912172318, -0.024299252778291702, 0.019341647624969482, 0.06259850412607193, 0.01615586131811142, 0.01906234584748745, 0.04870324581861496, -0.004495012573897839, -0.011058604344725609, -0.04748129844665527, -0.025433916598558426, -0.01820698380470276, -0.016304239630699158, -0.0009420979185961187, 0.0013943267986178398, -0.048144642263650894, 0.03725187107920647, -0.00009491895616520196, 0.0917506292462349, -0.012900250032544136, -0.022029927000403404, -0.008405237458646297, -0.00014428772556129843, -0.001231764443218708, -0.001993298064917326, -0.005551122594624758, -0.0008913654019124806, 0.016810474917292595, -0.004582294728606939, 0.008479426614940166, -0.017002495005726814, 0.0809975117444992, -0.01086658425629139, -0.00778553681448102, -0.0259750634431839, 0.03304488956928253, -0.021366585046052933, -0.010552369989454746, -0.022379053756594658, 0.07603990286588669, -0.00858852919191122, -0.014061097986996174, 0.045665837824344635, -0.03292269632220268, -0.03341147303581238, 0.013144639320671558, -0.07296758890151978, 0.005105985328555107, -0.024124689400196075, -0.03040897846221924, -0.007205112837255001, 0.055266834795475006, -0.04301247000694275, 0.004796134773641825, -0.05463840812444687, -0.013397756032645702, -0.05296259745955467, 0.0017150873318314552, -0.0008346321992576122, 0.01963840425014496, 0.02356608584523201, 0.01672319322824478, -0.032800499349832535, 0.0203715730458498, -0.015335412696003914, -0.0005771509022451937, -0.026603491976857185, 0.013450125232338905, -0.0007380767492577434, -0.026847882196307182, -0.01727306842803955, 0.0030352245084941387, 0.011844140477478504, -0.007353491615504026, 0.001015741960145533, -0.00018179161997977644, 0.0032163343857973814, 0.02278055064380169, -0.07122194766998291, -0.022885289043188095, -0.038753118366003036, 0.00809975154697895, 0.022553617134690285, -0.029990026727318764, 0.024403991177678108, -0.07129177451133728, -0.0900748148560524, -0.022815462201833725, -0.06657855957746506, 0.031299252063035965, -0.02897755801677704, 0.019481297582387924, -0.019603492692112923, 0.011870324611663818, -0.01689775660634041, 0.043571073561906815, 0.08190523833036423, 0.061795514076948166, -0.031159602105617523, 0.012088529765605927, 0.0017390898428857327, -0.031822945922613144, -0.009487532079219818, 0.031159602105617523, -0.005908977705985308, 0.02670823037624359, 0.015588529407978058, -0.009548628702759743, 0.0024417084641754627, 0.0809975117444992, -0.005376558750867844, -0.023775562644004822, -0.027668330818414688, 0.04643391817808151, 0.01577182114124298, -0.0007713529048487544, 0.0033298006746917963, -0.0319276824593544, 0.007462593726813793, -0.020389027893543243, 0.07436409592628479, 0.02466583624482155, 0.031630925834178925, 0.02244887873530388, -0.01371197123080492, 0.02017955295741558, -0.016374066472053528, 0.009164589457213879, -0.020022444427013397, -0.07178055495023727, 0.012394015677273273, 0.008771820925176144, 0.01031670905649662, 0.0050667086616158485, -0.018311722204089165, 0.031124690547585487, -0.012577307410538197, -0.024002494290471077, 0.010430174879729748, 0.045596010982990265, 0.01099750678986311, -0.016304239630699158, -0.018102245405316353, -0.03374314308166504, 0.01236783154308796, 0.013423941098153591, 0.08658354729413986, -0.029728181660175323, 0.0202493779361248, 0.03767082467675209, -0.027458854019641876, -0.005638404283672571, -0.024980051442980766, -0.0006960723549127579, 0.024054864421486855, 0.03390024974942207, 0.014192020520567894, -0.045351624488830566, 0.06396010518074036, 0.021366585046052933, -0.010211970657110214, 0.02506733313202858, -0.04053366929292679, -0.04189526289701462, -0.010526184923946857, 0.0064239404164254665, -0.008898379281163216, -0.029920201748609543, -0.0041306111961603165, -0.05495262145996094, 0.02395012602210045, -0.015544888563454151, -0.02494513802230358, 0.01674937829375267, -0.0767381563782692, 0.025102246552705765, -0.08804988116025925, -0.029920201748609543, 0.03843890503048897, 0.026655862107872963, -0.023600999265909195, -0.026743143796920776, 0.016932670027017593, -0.0383690781891346, -0.02003990113735199, 0.03840399160981178, 0.04748129844665527, 0.00162780552636832, -0.05442893132567406, 0.016077307984232903, -0.1126982644200325, -0.038753118366003036, 0.02199501357972622, 0.0378803014755249, -0.010098503902554512, -0.026673318818211555, -0.011102245189249516, -0.025119701400399208, 0.0029523069970309734, -0.007562967948615551, 0.027144640684127808, -0.045980051159858704, -0.030251871794462204, -0.021261846646666527, 0.03948628529906273, 0.01243765652179718, -0.012917706742882729, -0.0009666459518484771, 0.06430923193693161, 0.00894638430327177, 0.027057358995079994, 0.022117208689451218, 0.0046521201729774475, -0.031194515526294708, 0.016827931627631187, -0.014366584829986095, 0.002690461464226246, -0.0003908588259946555, -0.00035485505941323936, -0.013650873675942421, -0.011905238032341003, -0.023670824244618416, 0.0814862921833992, -0.016670823097229004, -0.005690773483365774, -0.0277556125074625, 0.005821696016937494, 0.007968828082084656, 0.019219452515244484, 0.01211471389979124, 0.009382793679833412, -0.054219454526901245, -0.039730675518512726, -0.013738155364990234, 0.025346634909510612, 0.05952618643641472, 0.07282793521881104, -0.0018361909314990044, 0.013895262964069843, 0.05034414306282997, 0.015518704429268837, 0.0063584791496396065, 0.0014270574320107698, 0.02480548806488514, -0.010517456568777561, -0.031159602105617523, -0.0008728179964236915, 0.05425436794757843, -0.034563593566417694, 0.001479426515288651, 0.014872819185256958, -0.012882793322205544, 0.054743144661188126, -0.040044888854026794, -0.01413092389702797, 0.015588529407978058, -0.020336659625172615, -0.004213528707623482, -0.03623940423130989, -0.004591022618114948, 0.014602244831621647, 0.004340087529271841, 0.0030352245084941387, -0.05355611443519592, -0.026847882196307182, 0.07129177451133728, 0.049855366349220276, -0.02023192122578621, -0.01784912869334221, 0.020511223003268242, 0.02206483855843544, -0.07562094926834106, -0.009566085413098335, 0.03882294520735741, -0.0293092280626297, -0.02344389073550701, 0.0352618470788002, 0.005044888239353895, -0.06057357043027878, -0.04894763231277466, 0.02023192122578621, -0.048004988580942154, -0.007702618837356567, -0.013633416965603828, 0.017246883362531662, -0.0008389963186345994, 0.017718205228447914, -0.013144639320671558, -0.0010713840601965785, -0.03042643517255783, -0.03585536405444145, 0.06643890589475632, -0.0021722258534282446, 0.02944887988269329, 0.023077307268977165, -0.039137158542871475, -0.01796259544789791, 0.0042462595738470554, -0.012708229944109917, 0.007283666171133518, 0.02873316965997219, -0.01145137194544077, 0.025311721488833427, -0.010491272434592247, 0.009504987858235836, -0.006345387082546949, -0.01073566172271967, 0.011975063011050224, 0.0036505612079054117, -0.022082295268774033, -0.011320449411869049, -0.05083291977643967, -0.01224563643336296, -0.0071178306825459, -0.008235038258135319, -0.0038644017186015844, -0.007724439259618521, -0.004108790773898363, -0.0031814216636121273, -0.004447007551789284, 0.015422694385051727, 0.0025988155975937843, -0.005236907862126827, -0.06259850412607193, -0.010822943411767483, -0.0007249844493344426, 0.00824376568198204, 0.013790524564683437, 0.016574813053011894, 0.023915212601423264, 0.003159601241350174, -0.0033647133968770504, 0.00660723214969039, -0.009260599501430988, 0.04276808351278305, 0.008021197281777859, 0.045211974531412125, 0.001976932864636183, 0.040324192494153976, 0.018905237317085266, 0.023426435887813568, -0.010238154791295528, 0.018049877136945724, 0.006668329704552889, 0.04493267089128494, -0.019271820783615112, 0.04992518946528435, 0.007846633903682232, 0.04901745915412903, 0.008806733414530754, 0.007693890947848558, -0.026882793754339218, -0.0014674252597615123, -0.01887032575905323, -0.07024439424276352, -0.0006938903243280947, 0.01093640923500061, -0.006681421771645546, -0.026551123708486557, 0.008331048302352428, 0.010438903234899044, 0.05139152333140373, 0.037635911256074905, -0.0011401185765862465, -0.021663343533873558, 0.028244391083717346, -0.016644639894366264, 0.07352618873119354, -0.00031475999276153743, 0.012053616344928741, 0.04517706111073494, -0.018852869048714638, 0.06476309895515442, -0.015693267807364464, 0.01073566172271967, 0.02161097340285778, -0.014445138163864613, 0.02976309321820736, -0.018975064158439636, 0.0007686253520660102, -0.0005836970522068441, -0.0067730676382780075, 0.05596509203314781, -0.004385910462588072, 0.030321696773171425, 0.03924189880490303, 0.014366584829986095, 0.015597257763147354, 0.022099751979112625, 0.027301747351884842, -0.02461346797645092, 0.06392519176006317, -0.002446072408929467, -0.002117674797773361, -0.009557357057929039, -0.045596010982990265, -0.05854863300919533, 0.05268329381942749, 0.031630925834178925, -0.03393516317009926, 0.03278304263949394, 0.035558607429265976, -0.0424189567565918, -0.006336658727377653, -0.018241897225379944, -0.02702244557440281, -0.025503741577267647, -0.016312967985868454, 0.011564838699996471, -0.004150249529629946, -0.01211471389979124, 0.06905736029148102, -0.02599252015352249, -0.01742144674062729, -0.031124690547585487, 0.018032420426607132, 0.016234414651989937, -0.017831671983003616, 0.01970823109149933, -0.006210099905729294, -0.008867830969393253, -0.00017810941790230572, 0.016906484961509705, -0.007955736480653286, -0.010596010833978653, -0.007222569081932306, -0.036204490810632706, 0.029134664684534073, -0.021663343533873558, 0.0209650881588459, 0.00781608559191227, -0.013293018564581871, -0.02995511330664158, 0.01374688372015953, -0.014610973186790943, 0.028174566105008125, 0.027004988864064217, 0.0032010599970817566, 0.06357606500387192, 0.007322943303734064, 0.024526186287403107, -0.020266834646463394, 0.013013716787099838, 0.04517706111073494, 0.004198254551738501, 0.0019092893926426768, -0.006345387082546949, -0.033917706459760666, -0.04922693595290184, -0.007222569081932306, 0.04084788262844086, -0.0005624220939353108, 0.027895264327526093, -0.006223192438483238, 0.02971072494983673, -0.01550997607409954, -0.030461348593235016, 0.007414589170366526, 0.05397506430745125, -0.03753117471933365, 0.02702244557440281, 0.021960100159049034, -0.0041829803958535194, 0.002198410453274846, -0.025311721488833427, 0.016697008162736893, 0.016627183184027672, -0.02649875544011593, -0.022082295268774033, 0.0014728803653270006, 0.003307980252429843, -0.0178665854036808, -0.020877806469798088, -0.02070324309170246, 0.05006483942270279, -0.029413966462016106, 0.036204490810632706, 0.009784289635717869, -0.04996010288596153, 0.00644576083868742, -0.0021034914534538984, 0.0050667086616158485, -0.005634040106087923, -0.004372818395495415, -0.010438903234899044, 0.03791521489620209, 0.02995511330664158, 0.009644638746976852, 0.015134664252400398, 0.013266833499073982, -0.02147132344543934, -0.0011728492099791765, 0.011931422166526318, -0.005555486772209406, -0.005145261995494366, 0.0074189528822898865, 0.04151122272014618, -0.06018953025341034, 0.03028678521513939, -0.03634414076805115, 0.0035523693077266216, 0.028087282553315163, -0.032748132944107056, 0.025381548330187798, -0.016374066472053528, 0.01782294362783432, -0.0027341023087501526, -0.021174564957618713, 0.004975062794983387, 0.01742144674062729, -0.012524938210844994, -0.03641396760940552, -0.005459476727992296, 0.01410473883152008, -0.02244887873530388, 0.01031670905649662, -0.021907731890678406, 0.04151122272014618, 0.03524439036846161, 0.007466957904398441, 0.04137157276272774, 0.036134663969278336, -0.009478803724050522, -0.05394015461206436, 0.006838528905063868, -0.022082295268774033, 0.035418953746557236, 0.0009693735046312213, -0.04308229684829712, -0.03798503801226616, -0.009662095457315445, -0.016627183184027672, 0.020615961402654648, 0.01853865385055542, 0.00515835452824831, 0.008710723370313644, -0.0050754365511238575, 0.017980050295591354, 0.012673317454755306, -0.03250374272465706, -0.04727182164788246, 0.047167085111141205, -0.021523691713809967, -0.02951870486140251, -0.009670823812484741, -0.030566086992621422, -0.006738155148923397, 0.05236908048391342, 0.0023631546646356583, -0.021977556869387627, 0.017072319984436035, -0.011058604344725609, 0.03412718325853348, -0.03924189880490303, -0.011495012789964676, 0.004944514017552137, -0.03917207196354866, 0.009513716213405132, -0.0383690781891346, 0.0369376577436924, -0.0015154302818700671, 0.030600998550653458, 0.0020140274427831173, 0.06151621416211128, -0.03376059979200363, -0.00836159661412239, -0.056837908923625946, 0.004944514017552137, -0.013589776121079922, 0.027057358995079994, -0.029029926285147667, 0.03164838254451752, -0.014733168296515942, 0.030374066904187202, 0.012900250032544136, 0.03517456725239754, -0.021174564957618713, -0.005930798128247261, 0.00018547382205724716, 0.009426434524357319, 0.0024722570087760687, 0.03934663534164429, 0.030129676684737206, 0.009443891234695911, 0.021000001579523087, -0.014715711586177349, -0.012140898033976555, -0.014532419852912426, 0.006567955482751131, -0.03910224512219429, 0.02623690851032734, -0.036134663969278336, 0.010264339856803417, -0.03513965383172035, 0.010421447455883026, 0.07394514232873917, 0.010403990745544434, 0.026743143796920776, 0.003242518985643983, 0.0051932670176029205, -0.012804239988327026, -0.005581671372056007, 0.019533667713403702, -0.009574813768267632, 0.017927682027220726, 0.020336659625172615, 0.03795012831687927, -0.03997506573796272, 0.058932673186063766, -0.04570075124502182, -0.014610973186790943, -0.01253366656601429, -0.015536160208284855, -0.048807982355356216, -0.0041829803958535194, 0.013275561854243279, 0.006812344305217266, -0.04151122272014618, 0.011599751189351082, 0.0010342893656343222, -0.053102247416973114, 0.0030352245084941387, -0.014733168296515942, 0.04035910591483116, 0.022117208689451218, -0.07199002802371979, -0.009286783635616302, 0.00036985662882216275, 0.023024939000606537, 0.017779303714632988, 0.008937655948102474, -0.03997506573796272, 0.02070324309170246, -0.006790523882955313, 0.011774314567446709, 0.026586037129163742, 0.0091733168810606, -0.027825437486171722, 0.03180548921227455, 0.0016572631429880857, 0.002063123509287834, -0.023391522467136383, 0.019673317670822144, -0.005258728284388781, 0.004041147418320179, 0.02749376744031906, -0.014715711586177349, 0.0025639028754085302, -0.002308603608980775, -0.004665212240070105, 0.024962594732642174, -0.004835411906242371, 0.00999376643449068, -0.011442644521594048, -0.03421446681022644, 0.0638553649187088, 0.030985038727521896, 0.014192020520567894, 0.06298254430294037, 0.00836159661412239, 0.008492519147694111, -0.01086658425629139, -0.057815466076135635, -0.007222569081932306, -0.005267456639558077, 0.06898753345012665, 0.01648753136396408, 0.058862846344709396, 0.015335412696003914, -0.03302743285894394, -0.024840399622917175, 0.01063965167850256, -0.02793017588555813, 0.028942644596099854, -0.01122443936765194, 0.01497755665332079, 0.0010397444711998105, 0.02297257073223591, -0.03760100156068802, 0.057221949100494385, -0.007353491615504026, 0.035209476947784424, 0.006162095349282026, 0.025416459888219833, -0.03028678521513939, 0.0011193890823051333, -0.03040897846221924, -0.009051122702658176, -0.014532419852912426, 0.0007915368187241256, -0.0161995030939579, -0.03983541205525398, -0.06287781149148941, -0.025905238464474678, 0.04692269489169121, -0.005821696016937494, -0.0277556125074625, -0.000865726382471621, -0.02625436522066593, 0.0024177059531211853, -0.030216960236430168, -0.03152618557214737, 0.02382793091237545, 0.00913840439170599, 0.029850374907255173, -0.03857855498790741, 0.0013223192654550076, -0.005939526483416557, -0.0014281484764069319, -0.013703242875635624, 0.029431423172354698, -0.04563092440366745, -0.01801496371626854, 0.016470076516270638, 0.038159601390361786, 0.004700125195086002, 0.011486285366117954, -0.01887032575905323, -0.04405985400080681, -0.005900249816477299, -0.00936533696949482, -0.030251871794462204, 0.02990274503827095, 0.015387781895697117, -0.005040524061769247, 0.019673317670822144, 0.009347881190478802, 0.05645386874675751, -0.020022444427013397, 0.046189527958631516, 0.029623443260788918, 0.0048834169283509254, -0.044478803873062134, 0.021925188601017, 0.003227244596928358, 0.0424189567565918, -0.0005171446828171611, 0.027371572330594063, -0.013738155364990234, 0.0312119722366333, -0.06326185166835785, 0.02447381615638733, 0.010692020878195763, -0.0693366602063179, 0.03400499001145363, 0.016312967985868454, -0.02826184779405594, -0.013354115188121796 ]
Shared-account Cross-domain Sequential Recommendation (SCSR) task aims to recommend the next item via leveraging the mixed user behaviors in multiple domains. It is gaining immense research attention as more and more users tend to sign up on different platforms and share accounts with others to access domain-specific services. Existing works on SCSR mainly rely on mining sequential patterns via Recurrent Neural Network (RNN)-based models, which suffer from the following limitations: 1) RNN-based methods overwhelmingly target discovering sequential dependencies in single-user behaviors. They are not expressive enough to capture the relationships among multiple entities in SCSR. 2) All existing methods bridge two domains via knowledge transfer in the latent space, and ignore the explicit cross-domain graph structure. 3) None existing studies consider the time interval information among items, which is essential in the sequential recommendation for characterizing different items and learning discriminative representations for them. In this work, we propose a new graph-based solution, namely TiDA-GCN, to address the above challenges. Specifically, we first link users and items in each domain as a graph. Then, we devise a domain-aware graph convolution network to learn userspecific node representations. To fully account for users' domainspecific preferences on items, two effective attention mechanisms are further developed to selectively guide the message passing process. Moreover, to further enhance item- and account-level representation learning, we incorporate the time interval into the message passing, and design an account-aware self-attention module for learning items' interactive characteristics. Experiments demonstrate the superiority of our proposed method from various aspects.
[ 0.0014965496957302094, -0.021573493257164955, -0.036871060729026794, -0.03446410223841667, -0.00026925079873763025, -0.030274206772446632, -0.006948982365429401, 0.021983567625284195, -0.03819043189287186, -0.0019066242966800928, 0.011196820996701717, -0.01733011193573475, 0.005339885130524635, -0.05470039322972298, -0.014914236962795258, 0.03501680865883827, 0.02825949341058731, -0.03744160011410713, -0.0029841845389455557, -0.05395156145095825, 0.02825949341058731, 0.02139519900083542, 0.0381191149353981, 0.024729285389184952, 0.04061521962285042, 0.030470330268144608, 0.01825723610818386, -0.004662370774894953, -0.06967703253030777, 0.016322754323482513, -0.012088287621736526, 0.01757972314953804, 0.01905955746769905, -0.03084474615752697, -0.04532216489315033, -0.028919178992509842, 0.07866301387548447, 0.053523655980825424, 0.00598174100741744, 0.017829332500696182, 0.0003186993417330086, 0.031575750559568405, -0.043788842856884, 0.005723216105252504, -0.0002710615808609873, -0.002964126644656062, -0.0034366040490567684, -0.019933193922042847, -0.00723870936781168, 0.005166049115359783, 0.001073660096153617, -0.024925407022237778, -0.024515332654118538, 0.014218892902135849, -0.015440202318131924, 0.038760971277952194, 0.031040869653224945, -0.01746383123099804, 0.015065786428749561, 0.040650878101587296, -0.025478117167949677, 0.014218892902135849, -0.03359046205878258, 0.0215021762996912, 0.05880114063620567, -0.05330970510840416, 0.019451802596449852, 0.020182805135846138, 0.03202148154377937, -0.05416551232337952, -0.07110337913036346, 0.006650341209024191, 0.024176575243473053, -0.039723753929138184, 0.016839804127812386, -0.006472047884017229, 0.05869416519999504, 0.033073414117097855, 0.02139519900083542, -0.02476494386792183, -0.00774684501811862, 0.06450652331113815, -0.000046384124289033934, 0.04435938224196434, 0.040650878101587296, -0.07145996391773224, -0.001251396257430315, -0.047033779323101044, 0.05805230885744095, -0.003935825079679489, -0.03344782814383507, -0.01612663082778454, -0.04175629839301109, -0.04856710135936737, -0.07035455107688904, -0.01468245591968298, 0.036068741232156754, -0.002284383401274681, -0.06653907150030136, 0.03421448916196823, -0.014111917465925217, -0.008807690814137459, -0.004294640384614468, -0.002462676726281643, 0.006489877123385668, -0.035765640437603, -0.027653295546770096, 0.030916063115000725, -0.05855153128504753, 0.09506600350141525, 0.003610439831390977, 0.02879437245428562, -0.011954567395150661, 0.03384007513523102, -0.06514838337898254, 0.0023779873736202717, -0.0595499724149704, -0.020468074828386307, -0.02667268179357052, -0.08172966539859772, 0.019166532903909683, 0.010501476936042309, -0.007809247821569443, -0.022126201540231705, -0.0013561436207965016, 0.06311584264039993, 0.00490306643769145, -0.023088986054062843, -0.010314268991351128, 0.01879211701452732, -0.019273508340120316, 0.010929381474852562, -0.024782773107290268, -0.03583696112036705, 0.014834005385637283, 0.028437785804271698, 0.041043125092983246, -0.027439342811703682, -0.0043280706740915775, -0.013211536221206188, -0.004557623062282801, 0.0005894823116250336, -0.026440901681780815, -0.035890448838472366, -0.028241664171218872, 0.046463243663311005, -0.008188121020793915, 0.07523978501558304, -0.037548575550317764, 0.057410452514886856, -0.0107510881498456, 0.04974383860826492, -0.01718747615814209, 0.01550260465592146, -0.04204156622290611, 0.04029429331421852, -0.012391386553645134, -0.048602763563394547, 0.009494120255112648, 0.011945652775466442, 0.05149111524224281, 0.00879431888461113, 0.011901079677045345, 0.018310725688934326, -0.021270394325256348, 0.010661941021680832, 0.06136856600642204, 0.019665753468871117, -0.053095754235982895, 0.046070996671915054, 0.006926695816218853, 0.021947909146547318, 0.014548735693097115, 0.027510661631822586, 0.031736213713884354, 0.03819043189287186, 0.0648987740278244, -0.041471026837825775, -0.021609151735901833, 0.0433252789080143, -0.048888031393289566, 0.02868739701807499, -0.0058970521204173565, 0.04924461618065834, 0.0565546452999115, 0.04981515556573868, 0.038475699722766876, 0.004319156054407358, -0.0033630579710006714, -0.04164932295680046, 0.02961452305316925, -0.010376672260463238, 0.0731002688407898, -0.013897964730858803, -0.0009510834934189916, -0.01461113803088665, -0.045536115765571594, -0.017945224419236183, 0.036175716668367386, -0.030274206772446632, -0.05117018520832062, 0.03269899636507034, 0.04528650641441345, 0.0021027468610554934, 0.0105549655854702, 0.021609151735901833, -0.01399602647870779, -0.017642125487327576, -0.03478502854704857, -0.010447989217936993, 0.007568551693111658, 0.0009984426433220506, -0.05897943302989006, -0.055805813521146774, 0.012204178608953953, 0.004294640384614468, 0.031450942158699036, 0.023570377379655838, 0.004319156054407358, -0.005268567707389593, -0.01568089798092842, 0.02216186188161373, 0.059728264808654785, 0.014058428816497326, 0.03195016458630562, -0.06297320127487183, 0.038618333637714386, 0.04393147677183151, -0.03961677849292755, -0.00279029062949121, 0.007662155665457249, 0.03059513494372368, -0.027635466307401657, -0.028081199154257774, -0.019416144117712975, -0.012070458382368088, 0.01747274585068226, -0.06432823091745377, -0.02893700823187828, -0.01088480744510889, -0.03986638784408569, 0.0148874931037426, -0.00456208037212491, 0.022839374840259552, 0.02934708259999752, 0.0043837870471179485, 0.00892803817987442, 0.020218463614583015, 0.06297320127487183, 0.017383599653840065, 0.012783631682395935, -0.03844004124403, -0.006940067745745182, 0.007951882667839527, -0.015529349446296692, 0.04763997718691826, 0.03275248408317566, -0.0006602425128221512, 0.008847806602716446, -0.055948447436094284, 0.045785728842020035, 0.017089415341615677, -0.04207722470164299, 0.020236292853951454, 0.012801460921764374, 0.046998120844364166, 0.05031437799334526, -0.03004242666065693, 0.05384458601474762, 0.0020024569239467382, -0.018720800057053566, -0.07331421971321106, -0.04842446744441986, -0.06447086483240128, -0.04361054673790932, -0.015324311330914497, 0.03786950185894966, -0.020610708743333817, 0.0524538978934288, 0.00006877526175230742, 0.02324945107102394, -0.002676628530025482, -0.009797218255698681, -0.022001396864652634, -0.047675635665655136, -0.060655392706394196, -0.06807239353656769, -0.02595950849354267, -0.03203931078314781, -0.02948971651494503, -0.04731905087828636, -0.01049256231635809, -0.014334783889353275, -0.005152677185833454, 0.06165383383631706, 0.01593942381441593, 0.01420106366276741, -0.0056741852313280106, 0.014735943637788296, -0.08893271535634995, -0.03202148154377937, 0.0201649758964777, 0.025210676714777946, 0.04575007036328316, 0.000161856907652691, 0.0011767359683290124, 0.029133129864931107, 0.03911755606532097, 0.020860319957137108, -0.0179987121373415, -0.0008279496687464416, -0.028241664171218872, -0.020182805135846138, 0.0037151873111724854, -0.05220428854227066, -0.039830729365348816, 0.04913764074444771, -0.012115031480789185, -0.0026587992906570435, -0.05751742795109749, 0.05084925889968872, 0.008553622290492058, -0.08208625018596649, -0.024390527978539467, -0.024283550679683685, 0.03250287473201752, -0.023302938789129257, -0.023641696199774742, 0.02216186188161373, -0.01895258016884327, -0.0050590732134878635, 0.005968369077891111, -0.04585704579949379, -0.002061516745015979, -0.021145589649677277, 0.024550991132855415, -0.006547822616994381, 0.042683422565460205, -0.05042135342955589, -0.039188873022794724, 0.009690242819488049, 0.04585704579949379, 0.031575750559568405, 0.017758015543222427, -0.011446432210505009, 0.003971484024077654, -0.02706492692232132, 0.048888031393289566, 0.011187906377017498, -0.004178749863058329, 0.0009159820037893951, -0.018096772953867912, 0.010349927470088005, 0.033055584877729416, 0.06800107657909393, -0.03531990945339203, -0.02053939178586006, -0.041043125092983246, 0.03243155777454376, 0.011544493027031422, -0.00893695279955864, -0.08893271535634995, -0.034178830683231354, 0.012311154045164585, -0.04275473952293396, -0.02501455508172512, -0.037156328558921814, -0.0003855593386106193, 0.002037001308053732, 0.006498791743069887, -0.08950325101613998, 0.017481660470366478, -0.013265023939311504, 0.012810375541448593, -0.040116000920534134, 0.03840438276529312, 0.010447989217936993, -0.01096503995358944, -0.009743730537593365, 0.03533773869276047, -0.002460448071360588, -0.013265023939311504, 0.007942968048155308, -0.017258794978260994, -0.03679974377155304, 0.0049298107624053955, 0.056732937693595886, 0.012525106780230999, -0.02423006296157837, 0.013853391632437706, -0.013033242896199226, -0.01535105612128973, -0.005099189467728138, -0.06308017671108246, 0.015787875279784203, -0.04318264499306679, 0.05109886825084686, 0.018292896449565887, 0.014031684957444668, -0.024265721440315247, -0.04304001107811928, -0.013773160055279732, -0.03751291707158089, 0.026316095143556595, -0.0067305732518434525, 0.00020573378424160182, 0.007042586337774992, -0.024426186457276344, 0.034713711589574814, -0.013149132952094078, -0.01596616767346859, -0.053238388150930405, -0.02080683223903179, -0.006204607896506786, 0.037940822541713715, 0.0365501344203949, -0.04164932295680046, -0.009859621524810791, 0.02176961489021778, -0.003733016550540924, -0.012097202241420746, 0.013559207320213318, 0.04414542764425278, -0.028348639607429504, -0.018863433972001076, 0.05470039322972298, 0.01717856153845787, -0.026316095143556595, 0.007813705131411552, -0.06211739778518677, 0.0014753773575648665, 0.026583535596728325, 0.05477171018719673, -0.05612673982977867, 0.003597067901864648, 0.007020299788564444, 0.013095645233988762, 0.03211062774062157, 0.0048094624653458595, -0.002716744551435113, -0.04831749200820923, -0.05220428854227066, -0.0316648967564106, -0.00395588343963027, 0.06322281807661057, -0.015538264065980911, 0.019665753468871117, -0.03480285778641701, -0.022286666557192802, -0.051740724593400955, -0.06675302237272263, 0.01745491661131382, -0.010430159978568554, -0.05548488348722458, -0.011045271530747414, -0.017811503261327744, -0.005130390636622906, -0.01137511432170868, 0.021448686718940735, -0.03819043189287186, 0.009387143887579441, 0.02380215935409069, -0.018506847321987152, -0.02924010530114174, -0.009097416885197163, 0.05042135342955589, -0.015146018005907536, -0.040793515741825104, 0.004450647160410881, 0.005536007694900036, 0.037120670080184937, -0.015154932625591755, 0.0592290461063385, 0.029026154428720474, -0.020396757870912552, 0.02312464453279972, 0.02244712971150875, -0.051205843687057495, -0.015395629219710827, 0.005848021246492863, 0.018292896449565887, 0.027011439204216003, 0.05887245759367943, 0.0362292043864727, 0.006926695816218853, 0.01569872722029686, 0.032663337886333466, 0.02895483747124672, -0.07409870624542236, -0.006752859801054001, 0.03137962520122528, 0.03262767940759659, -0.004711401183158159, -0.019433973357081413, -0.0064586759544909, -0.041043125092983246, -0.02813468687236309, -0.036728426814079285, 0.02396262437105179, -0.008344127796590328, -0.0019846276845782995, 0.06361506134271622, 0.030220719054341316, 0.01555609330534935, 0.07003361731767654, 0.002565195318311453, 0.03405402600765228, -0.00450190668925643, -0.03070211224257946, 0.03439278155565262, -0.018346384167671204, 0.03246721625328064, -0.028295151889324188, 0.003494549309834838, -0.03719198703765869, 0.01580570451915264, -0.02098512463271618, -0.019790560007095337, -0.003104532603174448, 0.007323398720473051, -0.014486333355307579, 0.01554717868566513, -0.012168520130217075, 0.018595993518829346, -0.04657021909952164, -0.01773127168416977, -0.004608882591128349, -0.011517749167978764, 0.06183212623000145, 0.02706492692232132, -0.00459551066160202, -0.002389130648225546, 0.012694485485553741, -0.04047258570790291, 0.04097180813550949, 0.011178991757333279, 0.030220719054341316, 0.02640524134039879, 0.009164277464151382, -0.03844004124403, -0.046605877578258514, 0.03139745444059372, -0.02328510954976082, 0.05223994702100754, 0.0637933537364006, 0.0009282396640628576, -0.01548477541655302, -0.053915902972221375, -0.01568981260061264, 0.027902906760573387, 0.013496804982423782, 0.02030760981142521, -0.0017885050037875772, -0.03154008835554123, -0.005669727921485901, -0.029382741078734398, -0.016572365537285805, -0.04264776408672333, 0.0007995341438800097, -0.03883228823542595, 0.04692680388689041, 0.056590303778648376, 0.017499489709734917, -0.034178830683231354, -0.019130874425172806, -0.002172949956730008, 0.02636958286166191, 0.0760955959558487, 0.027225391939282417, 0.010020085610449314, -0.019826218485832214, -0.03351914510130882, -0.028312981128692627, -0.019398314878344536, 0.022108372300863266, 0.0034477473236620426, 0.024515332654118538, -0.04218420013785362, 0.039688095450401306, 0.0005607882631011307, 0.006173406727612019, -0.019951023161411285, 0.010519306175410748, 0.04211288318037987, -0.04749734327197075, -0.016162291169166565, -0.016064228489995003, -0.06461350619792938, -0.006784061435610056, 0.006436389405280352, 0.0478895902633667, 0.049422912299633026, 0.03737028315663338, -0.023356426507234573, -0.010447989217936993, -0.030363354831933975, 0.003104532603174448, -0.019041728228330612, 0.051348477602005005, -0.057446110993623734, 0.039010580629110336, 0.004513049963861704, 0.0037508460227400064, 0.009164277464151382, -0.08429708331823349, -0.028651738539338112, 0.06675302237272263, 0.007100531831383705, 0.028081199154257774, 0.025068042799830437, -0.04913764074444771, 0.002944068517535925, 0.019540948793292046, -0.07566768676042557, 0.06350808590650558, 0.005299769341945648, 0.08543816208839417, -0.009922023862600327, -0.01372858602553606, -0.06596853584051132, 0.017954139038920403, -0.03826174885034561, 0.0973481610417366, -0.02053939178586006, -0.007604210637509823, 0.01839987188577652, 0.021306052803993225, -0.012177434749901295, -0.014263466000556946, -0.007354599889367819, 0.00805885810405016, 0.027546320110559464, -0.023570377379655838, -0.010813490487635136, -0.02991762012243271, 0.01624252274632454, 0.02947188727557659, 0.019968852400779724, 0.008304012008011341, 0.04357488825917244, -0.005946082528680563, 0.005509263835847378, -0.02339208498597145, 0.05537790805101395, 0.012819290161132812, 0.019380485638976097, -0.01439718622714281, 0.014691370539367199, 0.02487191930413246, 0.045785728842020035, 0.034161001443862915, 0.028865689411759377, -0.005946082528680563, 0.03398270905017853, 0.00878540426492691, -0.03291294723749161, 0.004163149278610945, 0.003030986525118351, -0.014156490564346313, -0.00007354599802056327, -0.013701842166483402, -0.009021642617881298, 0.013006498105823994, -0.02649438939988613, 0.02287503518164158, -0.018845604732632637, -0.004446189850568771, -0.00005616936323349364, -0.039010580629110336, 0.009841792285442352, -0.006971269380301237, -0.009939853101968765, -0.06407862156629562, 0.013719671405851841, 0.028616080060601234, -0.03628269210457802, -0.01117007713764906, -0.0006268125143833458, -0.002451533218845725, -0.038903605192899704, -0.015056871809065342, -0.028116857632994652, -0.04992213100194931, -0.011027442291378975, 0.040222976356744766, -0.026012996211647987, -0.003581467317417264, -0.01609988696873188, -0.024729285389184952, 0.0538802444934845, 0.006075345445424318, 0.022803716361522675, 0.01292626652866602, 0.023463401943445206, -0.004760432057082653, 0.038333065807819366, -0.01550260465592146, 0.004484077449887991, 0.017339026555418968, 0.050100427120923996, -0.006387358531355858, -0.015466946177184582, 0.011615810915827751, 0.006828634534031153, 0.013773160055279732, 0.03369744122028351, 0.00677068904042244, 0.008825520053505898, -0.058230601251125336, -0.03751291707158089, 0.016260351985692978, -0.017419258132576942, -0.032003652304410934, 0.009017185308039188, -0.0026409700512886047, 0.025906020775437355, 0.029864132404327393, -0.0011934509966522455, 0.008415444754064083, 0.014539821073412895, -0.02423006296157837, 0.019540948793292046, 0.05441512539982796, -0.06258095800876617, -0.05437946692109108, -0.0011689356761053205, -0.022518448531627655, 0.0205572210252285, -0.013247194699943066, 0.004308012779802084, 0.03804779797792435, -0.0354447141289711, 0.01757080852985382, -0.001736131263896823, -0.00919993594288826, -0.008776489645242691, -0.014423930086195469, 0.03574781119823456, -0.008379786275327206, -0.02720756269991398, 0.03029203601181507, -0.03761989250779152, -0.018310725688934326, -0.002207494340837002, 0.002589710522443056, 0.03385790437459946, 0.033875733613967896, 0.056233715265989304, -0.03744160011410713, -0.0007009156397543848, 0.023427743464708328, -0.032823801040649414, 0.02139519900083542, -0.018043285235762596, -0.054308149963617325, 0.031201332807540894, 0.005816820077598095, -0.012961925007402897, 0.0004465690872166306, -0.039010580629110336, 0.035908278077840805, 0.024390527978539467, -0.029792815446853638, 0.011704957112669945, 0.06518404185771942, 0.03514161705970764, -0.05505698174238205, -0.007604210637509823, -0.015885936096310616, -0.04382450133562088, -0.011606895364820957, -0.028865689411759377, 0.0731002688407898, -0.006405187770724297, 0.007367971818894148, 0.013434402644634247, 0.033465657383203506, -0.010403416119515896, -0.039830729365348816, 0.017909565940499306, 0.030755599960684776, 0.03662145137786865, -0.007394715677946806, 0.03844004124403, -0.013015412725508213, 0.00832629855722189, -0.0096100103110075, -0.01244487427175045, 0.039545461535453796, 0.025192847475409508, -0.010777832008898258, -0.02027195133268833, 0.0007850478286854923, 0.03608657047152519, 0.03804779797792435, 0.0011611352674663067, -0.014156490564346313, -0.03150442987680435, 0.012141775339841843, -0.020646367222070694, 0.023784330114722252, -0.03883228823542595, 0.0020258580334484577, 0.013496804982423782, 0.008210407570004463, -0.009467375464737415, -0.0188277754932642, 0.011874335817992687, -0.02248278819024563, 0.0271719042211771, 0.017267709597945213, 0.006079802755266428, -0.008295097388327122, -0.007113903760910034, 0.0031357340048998594, 0.012462703511118889, -0.03478502854704857, -0.059870898723602295, -0.05894377455115318, -0.014441759325563908, 0.004934268072247505, -0.01360378134995699, -0.0070960745215415955, -0.00046857717097736895, -0.04760431870818138, -0.009173192083835602, 0.029400570318102837, -0.004082917235791683, 0.07509715110063553, -0.006596853025257587, 0.025460287928581238, 0.02312464453279972, -0.057945333421230316, 0.01934482716023922, -0.046891145408153534, 0.04304001107811928, 0.013514634221792221, -0.017820417881011963, 0.04197024926543236, 0.0595499724149704, 0.04057956114411354, 0.021591322496533394, -0.03394705057144165, -0.04938725382089615, -0.013247194699943066, 0.011187906377017498, -0.02608431503176689, -0.006449761334806681, 0.016714999452233315, 0.011517749167978764, 0.004234466701745987, 0.04428806155920029, 0.056233715265989304, -0.03139745444059372, -0.014022770337760448, 0.034285806119441986, 0.006204607896506786, 0.013095645233988762, 0.04314698651432991, -0.034161001443862915, 0.05470039322972298, 0.011098760180175304, -0.042255520820617676, -0.011009613052010536, 0.010376672260463238, -0.03546254336833954, 0.006035229191184044, -0.047426026314496994, 0.019184362143278122, 0.006097631994634867, -0.021876592189073563, -0.001798533950932324, 0.008018742315471172, 0.01164255477488041, -0.040258634835481644, 0.014940980821847916, 0.017811503261327744, -0.039295848459005356, -0.018489018082618713, -0.014771602116525173, 0.029436228796839714, -0.005446861032396555, 0.005749959964305162, -0.010581709444522858, 0.04778261110186577, -0.03662145137786865, -0.005464690737426281, -0.0009126389632001519, -0.005954997148364782, -0.054058536887168884, -0.017927395179867744, 0.01675957255065441, 0.0017873906763270497, -0.04218420013785362, 0.013282853178679943, 0.00197571306489408, -0.03858267515897751, 0.017276624217629433, -0.017125073820352554, 0.02041458711028099, -0.0061154612340033054, -0.03858267515897751, -0.030345525592565536, -0.04154234752058983, 0.04468030855059624, -0.022144030779600143, 0.013666183687746525, -0.03854701668024063, 0.010234037414193153, -0.027296708896756172, 0.01746383123099804, -0.018453359603881836, -0.0009365971782244742, 0.004831749480217695, 0.012204178608953953, -0.0048986091278493404, -0.02694012224674225, -0.001958997920155525, 0.023998282849788666, 0.020182805135846138, 0.02920444682240486, 0.04963686317205429, -0.011277053505182266, 0.01690220832824707, 0.018916921690106392, -0.0035524945706129074, 0.004082917235791683, 0.010029000230133533, 0.013149132952094078, 0.01689329370856285, -0.06226003170013428, 0.026048654690384865, -0.030505988746881485, 0.00415646331384778, 0.026316095143556595, -0.0011711643310263753, -0.05641201138496399, 0.0016168976435437799, -0.007604210637509823, -0.0056741852313280106, -0.018471188843250275, 0.01907738670706749, -0.015270823612809181, 0.04393147677183151, 0.01973707228899002, 0.006886580027639866, 0.03801213949918747, 0.00879877619445324, 0.014735943637788296, 0.024550991132855415, -0.06643209606409073, -0.011187906377017498, -0.034963320940732956, -0.011936738155782223, 0.004009371157735586, -0.01718747615814209, -0.02758197858929634, 0.03744160011410713, -0.04232683777809143, 0.04139970988035202, 0.004105203785002232, 0.027902906760573387, -0.008304012008011341, 0.005090274382382631, -0.05926470458507538, 0.03000676818192005, 0.023445572704076767, -0.01934482716023922, -0.007760217413306236, 0.014192149043083191, -0.0019300252897664905, -0.0010212864726781845, 0.03542688488960266, 0.0252819936722517, -0.00792068149894476, 0.023713013157248497, -0.01608205772936344, -0.02096729539334774, -0.019558778032660484, -0.019772730767726898, 0.01624252274632454, 0.05263219028711319, 0.017508404329419136, 0.00480500515550375, -0.01719639077782631, -0.007047043647617102, 0.014085172675549984, 0.02704709768295288, -0.015315396711230278, -0.0014776060124859214, -0.03301992639899254, 0.013978197239339352, 0.038083456456661224, -0.038333065807819366, -0.055270932614803314, -0.0017996482783928514, -0.0007672184729017317, -0.02460447885096073, -0.02301766909658909, 0.023320768028497696, -0.037120670080184937, -0.013987111859023571, 0.027118414640426636, 0.05316707119345665, -0.022768057882785797, -0.021181248128414154, 0.06315150111913681, 0.03177187219262123, -0.01773127168416977, 0.012953010387718678, -0.0006546708173118532, 0.014718114398419857, -0.039046239107847214, -0.04692680388689041, -0.013559207320213318, -0.03298426792025566, -0.024140916764736176, -0.01312238909304142, 0.0051482198759913445, -0.03230675309896469, 0.029703669250011444, 0.03100520931184292, 0.02585253305733204, -0.007318941410630941 ]
Shared-account Cross-domain Sequential Recommendation (SCSR) is an emerging yet challenging task that simultaneously considers the shared-account and cross-domain characteristics in the sequential recommendation. Existing works on SCSR are mainly based on Recurrent Neural Network (RNN) and Graph Neural Network (GNN) but they ignore the fact that although multiple users share a single account, it is mainly occupied by one user at a time. This observation motivates us to learn a more accurate user-specific account representation by attentively focusing on its recent behaviors. Furthermore, though existing works endow lower weights to irrelevant interactions, they may still dilute the domain information and impede the cross-domain recommendation. To address the above issues, we propose a reinforcement learning-based solution, namely RL-ISN, which consists of a basic cross-domain recommender and a reinforcement learning-based domain filter. Specifically, to model the account representation in the shared-account scenario, the basic recommender first clusters users' mixed behaviors as latent users, and then leverages an attention model over them to conduct user identification. To reduce the impact of irrelevant domain information, we formulate the domain filter as a hierarchical reinforcement learning task, where a high-level task is utilized to decide whether to revise the whole transferred sequence or not, and if it does, a low-level task is further performed to determine whether to remove each interaction within it or not. To evaluate the performance of our solution, we conduct extensive experiments on two real-world datasets, and the experimental results demonstrate the superiority of our RL-ISN method compared with the state-of-the-art recommendation methods.
[ 0.006581076420843601, -0.003503199899569154, -0.03459295630455017, -0.016884874552488327, -0.00032956834184005857, -0.04620930925011635, 0.022464383393526077, -0.0002758312621153891, -0.042440854012966156, 0.007225921377539635, 0.002299260813742876, -0.04602637514472008, -0.016482418403029442, -0.06421008706092834, 0.024293730035424232, 0.027147512882947922, 0.008776293136179447, 0.001416600774973631, -0.011387686245143414, -0.02932443656027317, 0.01772637479007244, 0.028556110337376595, -0.0036015273071825504, 0.028354881331324577, 0.0028697883244603872, 0.05740491673350334, 0.013802425004541874, -0.002956682350486517, -0.08561345189809799, 0.012210892513394356, 0.016025081276893616, 0.024458372965455055, 0.03852605074644089, 0.013656076975166798, -0.0663687139749527, -0.011351099237799644, 0.04240426793694496, 0.08202792704105377, -0.04419702664017677, 0.041270073503255844, 0.002490198938176036, 0.04873380810022354, -0.07123477756977081, -0.0031830640509724617, 0.006416435353457928, -0.022921720519661903, -0.06731997430324554, 0.01779954880475998, -0.038855332881212234, 0.018933743238449097, 0.02120213396847248, -0.015256755985319614, 0.005625242833048105, -0.0048706368543207645, -0.02566574141383171, 0.023232709616422653, 0.020324047654867172, -0.02070821076631546, 0.024970589205622673, 0.03768455237150192, -0.006192340049892664, 0.020049644634127617, -0.014744538813829422, -0.006453022360801697, 0.030293989926576614, -0.06984447687864304, 0.03428196534514427, -0.04935578629374504, 0.028245121240615845, -0.04408726841211319, -0.09907744079828262, 0.07266166806221008, 0.021659471094608307, -0.027129219844937325, -0.01897033117711544, 0.037611380219459534, 0.05001435428857803, 0.03638571500778198, 0.013948772102594376, 0.004875210113823414, -0.00029083763365633786, 0.056270718574523926, -0.018769102171063423, 0.041562769562006, 0.03499541059136391, -0.023671753704547882, -0.006667970679700375, -0.057148806750774384, 0.0861988365650177, -0.03578203171491623, -0.01692146249115467, -0.033202651888132095, -0.02239120937883854, -0.05433161184191704, -0.04683128744363785, -0.02405591495335102, 0.03384292498230934, -0.0015949620865285397, -0.05820982903242111, 0.012896898202598095, -0.014076827093958855, 0.0006151180132292211, -0.03373316302895546, -0.015640918165445328, 0.026580415666103363, -0.0014120273990556598, -0.04924602806568146, 0.001632692408747971, -0.06929567456245422, 0.10902909189462662, 0.015485423617064953, 0.0008346396498382092, 0.0020248587243258953, 0.038965094834566116, -0.034446608275175095, -0.004356132820248604, -0.05619754642248154, -0.01800992339849472, 0.03281848877668381, -0.07046645134687424, 0.009361684322357178, 0.05070950463414192, 0.0010461579076945782, -0.03622107580304146, -0.01084802858531475, 0.06256367266178131, -0.00006542060145875439, 0.04258720204234123, 0.009357110597193241, 0.05531945824623108, -0.030733032152056694, -0.023104654625058174, -0.04251402989029884, -0.0396602489054203, 0.0014737677993252873, 0.04577026516199112, 0.015887880697846413, 0.02125701494514942, -0.006937799043953419, -0.022720491513609886, -0.03236115351319313, -0.03483077138662338, -0.010381544940173626, 0.022336330264806747, 0.026086490601301193, 0.02584867551922798, -0.00709786731749773, 0.04408726841211319, -0.03794066235423088, 0.005337120499461889, 0.009361684322357178, 0.06728339195251465, -0.007761005312204361, 0.04335552826523781, 0.0015572317643091083, 0.029964707791805267, -0.006603943184018135, -0.04738009348511696, 0.007129880599677563, 0.003898796159774065, 0.03230627253651619, -0.001680712797679007, 0.00440415320917964, 0.04394092038273811, 0.02475106716156006, 0.021128959953784943, 0.023342469707131386, 0.009832740761339664, -0.06431984901428223, 0.055831678211688995, -0.03342217206954956, 0.03664182499051094, -0.007321962155401707, 0.01696719601750374, 0.038416292518377304, 0.007148174103349447, 0.07741797715425491, -0.057441502809524536, -0.04112372547388077, 0.042440854012966156, -0.026525534689426422, 0.04935578629374504, -0.04192863777279854, 0.02908661961555481, 0.04686787351965904, 0.0015252182492986321, 0.05736832693219185, -0.010893763042986393, -0.010226051323115826, -0.03548933565616608, 0.012915191240608692, 0.016326922923326492, 0.056270718574523926, -0.005730430129915476, 0.01655559241771698, 0.013683517463505268, -0.03757479041814804, 0.008131448179483414, 0.024915708228945732, -0.030476924031972885, -0.05425843968987465, -0.0009964226046577096, 0.0015457983827218413, -0.003116750391200185, 0.03349534794688225, -0.0027005737647414207, 0.01785442791879177, 0.013601195998489857, -0.04873380810022354, -0.05140465497970581, -0.004692275542765856, -0.0043995799496769905, -0.048148419708013535, -0.042074985802173615, -0.007765579037368298, -0.011479153297841549, 0.024879122152924538, 0.001253102789632976, 0.027604850009083748, 0.008451583795249462, -0.010518746450543404, -0.007139027584344149, 0.06461254507303238, -0.019738655537366867, 0.015503717586398125, -0.03547104075551033, -0.018055656924843788, 0.06366128474473953, -0.005410294514149427, -0.011698675341904163, 0.01510126143693924, -0.0008083427674137056, -0.03406244516372681, 0.007010973058640957, -0.01097608357667923, 0.014186587184667587, 0.015119554474949837, -0.041818875819444656, -0.019519135355949402, -0.03933096304535866, 0.004847770091146231, 0.02299489453434944, -0.0008392130257561803, 0.03031228296458721, 0.04408726841211319, -0.006686264183372259, 0.0035054865293204784, 0.05001435428857803, 0.04946554824709892, 0.008145168423652649, -0.015119554474949837, -0.01966548152267933, -0.03991635516285896, 0.023397350683808327, -0.03501370549201965, 0.04119689762592316, 0.03962365910410881, -0.012750550173223019, 0.0038530626334249973, -0.046977635473012924, 0.026269426569342613, 0.017891015857458115, 0.018357498571276665, 0.008378409780561924, 0.02208022028207779, 0.011524887755513191, 0.04968506842851639, -0.030659860000014305, 0.0960773155093193, 0.048587460070848465, 0.004328692797571421, -0.02125701494514942, -0.05960013344883919, -0.05436819791793823, -0.042074985802173615, -0.006073432508856058, 0.035690564662218094, -0.04950213432312012, 0.02548280730843544, 0.02400103583931923, 0.00022881131735630333, -0.0018133404664695263, -0.024586426094174385, 0.015494571067392826, -0.03547104075551033, -0.03495882451534271, -0.05758785083889961, -0.024915708228945732, -0.01720501109957695, 0.033019717782735825, -0.03678817301988602, -0.032525792717933655, -0.025830382481217384, 0.016409244388341904, 0.07844240963459015, 0.04825817793607712, -0.006558209657669067, 0.04942896217107773, 0.03236115351319313, -0.038160182535648346, -0.03881874680519104, 0.0056298160925507545, 0.042184747755527496, -0.005286813247948885, -0.02809877321124077, 0.02244609035551548, -0.01125048566609621, 0.026013316586613655, -0.014021946117281914, -0.033696576952934265, -0.00734940217807889, -0.028793925419449806, -0.049319200217723846, 0.008634518831968307, -0.027019457891583443, 0.00943028461188078, 0.05092902481555939, -0.02431202493607998, 0.031336717307567596, -0.028428055346012115, 0.06399056315422058, 0.026562120765447617, -0.07514958083629608, 0.0023598577827215195, -0.029123207554221153, -0.005895071197301149, 0.008675679564476013, 0.007765579037368298, -0.032269686460494995, -0.016720233485102654, 0.021092373877763748, -0.0036609810777008533, -0.024202262982726097, -0.03459295630455017, 0.0003404300950933248, 0.035251520574092865, -0.008264075964689255, 0.05319741740822792, -0.08268649131059647, -0.07097867131233215, 0.0035992406774312258, -0.013930479064583778, 0.04042857140302658, 0.037977248430252075, -0.014927472919225693, 0.032964836806058884, -0.03591008484363556, 0.026580415666103363, 0.007559777237474918, 0.022537557408213615, 0.0009278220240958035, -0.014122560620307922, 0.03397097811102867, 0.010253490880131721, 0.07778384536504745, -0.059124503284692764, -0.022592438384890556, -0.013628636486828327, 0.015979347750544548, 0.004705995786935091, -0.022354623302817345, -0.09007705748081207, -0.10661435127258301, 0.029159793630242348, -0.03918461874127388, -0.0029040887020528316, -0.03892850875854492, 0.011186458170413971, 0.04416044056415558, -0.011570621281862259, -0.07156406342983246, 0.016637912020087242, 0.005666403099894524, -0.018412379547953606, -0.029800066724419594, 0.018714221194386482, 0.0015275048790499568, 0.006722851190716028, -0.014131707139313221, 0.046977635473012924, 0.03706257417798042, 0.012686522677540779, -0.056270718574523926, -0.005090158432722092, -0.0041571916081011295, 0.002378151286393404, 0.020378928631544113, 0.013500582426786423, -0.01298836525529623, -0.010308371856808662, -0.037830900400877, 0.001173068885691464, -0.04953872039914131, -0.03962365910410881, 0.006315821316093206, -0.02187899313867092, -0.00952175259590149, 0.017653200775384903, 0.003969683311879635, -0.025995023548603058, -0.016226310282945633, -0.01097608357667923, -0.011332806199789047, 0.018878862261772156, -0.03633083403110504, -0.002613679738715291, 0.02127530798316002, -0.03214162960648537, 0.012686522677540779, 0.025007177144289017, 0.0006877201958559453, -0.03521493449807167, -0.031665999442338943, 0.023653458803892136, 0.020763089880347252, 0.034757595509290695, -0.051002200692892075, -0.003747875103726983, 0.02039722166955471, -0.03303800895810127, -0.021092373877763748, -0.014406109228730202, 0.06966154277324677, 0.02851952239871025, -0.060002587735652924, 0.06629554182291031, 0.05012411251664162, -0.01388474553823471, -0.003937670029699802, -0.05034363642334938, 0.014113414101302624, 0.0514412447810173, 0.040757857263088226, -0.047709375619888306, -0.02952566370368004, 0.007436296436935663, -0.002981835976243019, -0.009270217269659042, -0.014067679643630981, -0.009183323010802269, -0.0006231213919818401, -0.043867744505405426, -0.08085714280605316, -0.0001683571026660502, 0.06684434413909912, -0.03342217206954956, 0.047782547771930695, -0.03119036927819252, -0.04061150923371315, -0.03256237879395485, -0.05963671952486038, 0.018183711916208267, -0.0350320003926754, -0.02654382772743702, -0.0027554542757570744, -0.015183581970632076, 0.008556771092116833, -0.018128830939531326, 0.022226568311452866, 0.009229056537151337, -0.007139027584344149, 0.02776949107646942, 0.02127530798316002, -0.05506335198879242, -0.0011227618670091033, 0.06007576361298561, -0.053416937589645386, -0.03380633518099785, -0.006274661049246788, -0.006645103916525841, 0.025501100346446037, 0.004310399293899536, 0.04800207167863846, -0.019519135355949402, -0.021860698238015175, 0.037977248430252075, 0.05839276313781738, -0.09176005423069, 0.004257805645465851, -0.028940273448824883, 0.016390951350331306, 0.025647448375821114, 0.03826994448900223, 0.020689917728304863, 0.051002200692892075, 0.010619360953569412, 0.016098255291581154, 0.03298313170671463, -0.060295283794403076, -0.021787526085972786, 0.03356852009892464, 0.009649806655943394, -0.020324047654867172, -0.01795504242181778, -0.04222133383154869, -0.048367939889431, -0.01537566352635622, -0.050636328756809235, 0.06867369264364243, -0.04148959368467331, 0.020817970857024193, 0.015329930000007153, 0.040831029415130615, 0.011524887755513191, 0.014890885911881924, 0.00709786731749773, 0.03311118483543396, 0.005648109596222639, -0.019025210291147232, 0.04170911759138107, 0.008762572892010212, 0.054660893976688385, -0.011186458170413971, 0.00027197247254662216, -0.013281060382723808, 0.019372787326574326, -0.021165547892451286, -0.023799806833267212, 0.026214545592665672, 0.03826994448900223, -0.01323532685637474, 0.023799806833267212, -0.012887750752270222, 0.009631512686610222, -0.023561991751194, -0.0027485941536724567, 0.010125436820089817, -0.0034734730143100023, 0.04522146284580231, 0.040391985327005386, 0.009155882522463799, 0.03483077138662338, 0.00578073738142848, -0.04979483038187027, 0.04891674593091011, -0.008195475675165653, 0.04262378811836243, 0.03025740198791027, 0.00841957051306963, -0.01575068011879921, -0.041379835456609726, 0.06841758638620377, -0.021677764132618904, 0.02257414534687996, 0.02597673051059246, 0.011973077431321144, 0.0055337753146886826, -0.03541616350412369, 0.0035649402998387814, 0.034318555146455765, 0.025812089443206787, 0.04979483038187027, 0.016107402741909027, -0.0359649658203125, 0.0063889953307807446, -0.04357505217194557, 0.0031784907914698124, -0.007244214881211519, -0.042440854012966156, -0.04320918023586273, 0.016930608078837395, 0.03737356513738632, 0.031848933547735214, -0.02529987134039402, 0.009759567677974701, 0.0019368213834241033, -0.005620669107884169, 0.04723374545574188, 0.02008623257279396, -0.003308831714093685, -0.013381674885749817, 0.007139027584344149, -0.0038896494079381227, -0.03353193402290344, 0.011323658749461174, 0.05151441693305969, 0.009869327768683434, -0.029342729598283768, 0.049611896276474, 0.019921591505408287, -0.023086361587047577, -0.028263414278626442, 0.005067291669547558, 0.0334770530462265, -0.047892309725284576, 0.0012576761655509472, 0.0006139746401458979, -0.03684305399656296, 0.009713833220303059, -0.01634521782398224, 0.036623530089855194, 0.04346529021859169, 0.004545927979052067, 0.007857046090066433, -0.034135617315769196, -0.017159277573227882, 0.0017184430034831166, -0.013619489967823029, 0.03870898857712746, -0.052246157079935074, 0.001165065448731184, 0.031464770436286926, -0.011982223950326443, -0.009091855958104134, -0.026982871815562248, -0.00766039127483964, 0.04748985171318054, 0.025647448375821114, 0.06567356735467911, 0.030897675082087517, -0.015082967467606068, 0.01528419554233551, 0.028610989451408386, -0.038855332881212234, 0.026635294780135155, 0.013848158530890942, 0.085540272295475, -0.0026594134978950024, 0.01211942546069622, -0.04222133383154869, -0.010399838909506798, -0.03567226976156235, 0.09410162270069122, -0.0038370557595044374, -0.0010404412169009447, 0.030458630993962288, 0.02765972912311554, -0.04818500578403473, -0.0018224871018901467, 0.019445961341261864, -0.0009832740761339664, -0.0021814964711666107, -0.03422708436846733, -0.04675811529159546, -0.01026263739913702, 0.018668487668037415, 0.04097737744450569, -0.0022055066656321287, -0.006983533035963774, 0.029964707791805267, -0.021604590117931366, 0.018147123977541924, -0.011415126733481884, 0.044672660529613495, 0.0013068398693576455, -0.003244804684072733, -0.03638571500778198, 0.010189464315772057, 0.0356539785861969, 0.008565918542444706, 0.01803736388683319, 0.01997647061944008, 0.016601325944066048, 0.028720751404762268, -0.011570621281862259, -0.004200638737529516, 0.021714352071285248, -0.0005719568580389023, 0.026927990838885307, -0.01972036249935627, 0.0009535472490824759, -0.00443616695702076, -0.002558799460530281, -0.04251402989029884, 0.028043892234563828, 0.010500452481210232, -0.0035169199109077454, -0.00835554301738739, 0.0018945176852867007, 0.042879898101091385, -0.039477311074733734, -0.03331241384148598, -0.07123477756977081, 0.033202651888132095, 0.020488688722252846, -0.037117455154657364, -0.013491435907781124, 0.02319612167775631, 0.013317647390067577, -0.04379457235336304, -0.045880027115345, -0.004683129023760557, 0.0037730284966528416, -0.0023644312750548124, 0.02864757739007473, -0.015238462015986443, 0.0075963642448186874, 0.011186458170413971, -0.022226568311452866, 0.043428704142570496, -0.018202004954218864, -0.0024810521863400936, 0.021074078977108, 0.0294524896889925, 0.002698287134990096, 0.00471056904643774, -0.034190498292446136, 0.009169602766633034, 0.021750938147306442, 0.02561086043715477, -0.015421397052705288, -0.015339076519012451, 0.020799677819013596, 0.01600678823888302, 0.01320788636803627, 0.0036495476961135864, 0.00821376871317625, 0.017040370032191277, -0.04518487676978111, -0.016070814803242683, 0.010427279397845268, 0.01267737615853548, -0.05301448330283165, 0.0008832316962070763, 0.02387298084795475, 0.027934132143855095, 0.02778778411448002, -0.028117066249251366, 0.0011484870919957757, 0.010582773946225643, 0.013399967923760414, 0.02797071821987629, 0.037117455154657364, -0.07335682213306427, -0.029854945838451385, -0.0025793795939534903, 0.016747673973441124, 0.010747415013611317, -0.010509599931538105, 0.007267081644386053, 0.03442831337451935, -0.005895071197301149, -0.010902909561991692, -0.004934663884341717, -0.010930349119007587, -0.01966548152267933, -0.018512994050979614, 0.017397092655301094, -0.009366258047521114, -0.027678024023771286, -0.003112176898866892, -0.05407550185918808, 0.0007100153598003089, 0.03629424795508385, 0.03095255419611931, 0.007157321088016033, 0.014836005866527557, 0.050380222499370575, -0.04536781087517738, -0.011186458170413971, 0.02089114487171173, -0.014625631272792816, 0.02919638156890869, -0.032891660928726196, -0.06856393069028854, 0.03715404123067856, 0.013454848900437355, 0.0012279492802917957, 0.015549451112747192, 0.0058722044341266155, 0.022116808220744133, 0.05425843968987465, -0.001652129227295518, -0.027641436085104942, 0.03398926928639412, 0.0006802884745411575, -0.04116031154990196, -0.004491047468036413, -0.014214027673006058, -0.06523451954126358, 0.011652941815555096, -0.03373316302895546, 0.05418526381254196, -0.022738786414265633, -0.012869457714259624, 0.01779954880475998, 0.02028745971620083, -0.0006414148374460638, -0.006942372769117355, 0.023287590593099594, 0.023598579689860344, 0.047965481877326965, 0.011305365711450577, 0.029873240739107132, -0.005693843122571707, 0.03995294123888016, -0.028446348384022713, -0.001177642261609435, 0.027385327965021133, -0.02101919986307621, -0.012201745994389057, 0.021531416103243828, -0.010061409324407578, -0.009329671040177345, 0.013125565834343433, -0.021238721907138824, -0.00748660322278738, 0.0040245638228952885, -0.031409893184900284, -0.03300142288208008, 0.03523322567343712, -0.0029589692130684853, -0.0072487881407141685, 0.02158629707992077, 0.014031092636287212, 0.01500979345291853, 0.005620669107884169, 0.0027966145426034927, -0.004184631630778313, 0.027293860912322998, -0.01084802858531475, -0.006393568590283394, -0.02281196042895317, 0.011771849356591702, 0.003818762255832553, -0.030550098046660423, -0.0384528785943985, -0.010244344361126423, -0.03874557465314865, -0.036623530089855194, 0.005309680476784706, -0.019921591505408287, -0.016665352508425713, -0.011927343904972076, -0.024403491988778114, -0.011259632185101509, 0.0004070297582075, 0.020122818648815155, 0.06303930282592773, -0.003878216026350856, 0.025446219369769096, 0.044855594635009766, -0.028629284352064133, 0.0022569571156054735, -0.0402822270989418, 0.01532078254967928, -0.006603943184018135, 0.010729121044278145, 0.03580032289028168, 0.05001435428857803, 0.04683128744363785, 0.0025176391936838627, -0.015339076519012451, -0.061722174286842346, -0.0241839699447155, -0.0010570196900516748, -0.01940937340259552, 0.037172336131334305, 0.011918197385966778, -0.01007970329374075, 0.012238333001732826, 0.025885263457894325, 0.04456289857625961, -0.027915839105844498, -0.024787655100226402, 0.03622107580304146, 0.043501876294612885, 0.032269686460494995, 0.03977000713348389, -0.0144152557477355, 0.05319741740822792, 0.005227359477430582, -0.01922643929719925, 0.00948516558855772, 0.011780995875597, -0.013290207833051682, 0.010564479976892471, -0.05923426151275635, 0.014021946117281914, -0.027257272973656654, -0.000562524248380214, -0.01156147476285696, -0.04909968003630638, -0.0006013978854753077, -0.05177052691578865, 0.004429306834936142, 0.014707951806485653, -0.046099551022052765, -0.007893633097410202, -0.01302495226264, 0.028921978548169136, -0.023104654625058174, 0.019299613311886787, -0.03702598810195923, 0.06344176083803177, -0.037611380219459534, -0.02989153377711773, -0.021366775035858154, -0.0008266362710855901, -0.04844111576676369, -0.008991241455078125, 0.03801383450627327, -0.04086761549115181, -0.013217033818364143, -0.008972948417067528, 0.013253620825707912, -0.05034363642334938, 0.01320788636803627, -0.020122818648815155, 0.028226828202605247, -0.00734940217807889, -0.030861087143421173, -0.033092889934778214, -0.04042857140302658, 0.057148806750774384, 0.019061798229813576, -0.001248529413715005, -0.04562392085790634, 0.016665352508425713, -0.047709375619888306, 0.01180843636393547, -0.005410294514149427, 0.01577811874449253, -0.0025953862350434065, 0.02226315625011921, -0.0019059510668739676, -0.027056045830249786, 0.011094991117715836, 0.02101919986307621, -0.008780866861343384, 0.04309941828250885, 0.03323923796415329, -0.011762702837586403, 0.022519264370203018, -0.03329411894083023, 0.01128707267343998, 0.027257272973656654, 0.032855074852705, -0.014342081733047962, -0.004520774353295565, -0.03292825073003769, 0.04372139647603035, 0.002062588930130005, 0.023360764607787132, 0.012595055624842644, 0.027732903137803078, -0.031153783202171326, 0.009064415469765663, -0.018723368644714355, -0.0017493133200332522, -0.01616228185594082, 0.03998953104019165, -0.0042532323859632015, 0.028574403375387192, 0.007367695681750774, 0.035068586468696594, 0.006809744983911514, -0.004806609824299812, 0.004406440071761608, 0.01922643929719925, -0.06329541653394699, -0.026690175756812096, -0.04236768186092377, 0.0009501171880401671, 0.003631254192441702, -0.014845152385532856, -0.034885652363300323, 0.005981965456157923, -0.05473406985402107, 0.030220815911889076, -0.016308629885315895, 0.02703775092959404, -0.01922643929719925, 0.0038850761484354734, -0.07368610799312592, 0.0023735780268907547, -0.011872462928295135, 0.012311507016420364, -0.027495088055729866, 0.026580415666103363, 0.001708152936771512, 0.0025084924418479204, 0.03583691269159317, 0.015741532668471336, 0.003587807295843959, 0.027915839105844498, 0.0022809673100709915, -0.025391338393092155, -0.030861087143421173, 0.021933872252702713, -0.001536651630885899, 0.04375798627734184, 0.036623530089855194, 0.010930349119007587, -0.011790142394602299, -0.031464770436286926, 0.03647718206048012, 0.026306012645363808, -0.04233109578490257, 0.002817194676026702, -0.008684826083481312, 0.013793277554214, 0.016729380935430527, -0.05151441693305969, -0.0489899180829525, 0.011634647846221924, 0.019610602408647537, -0.021220427006483078, -0.03505029156804085, 0.021915579214692116, -0.001253102789632976, -0.01476283185184002, 0.03126354515552521, 0.039038270711898804, -0.0071618943475186825, -0.007015546318143606, 0.05480724200606346, 0.021970460191369057, -0.037830900400877, 0.03666011616587639, 0.013079832307994366, 0.006283807568252087, -0.014991500414907932, -0.05158759281039238, 0.006073432508856058, -0.024275436997413635, -0.03591008484363556, -0.01741538569331169, 0.028812218457460403, -0.023799806833267212, 0.030001293867826462, 0.003292825073003769, 0.031098902225494385, -0.018412379547953606 ]
Many neural network-based out-of-distribution (OoD) detection methods have been proposed. However, they require many training data for each target task. We propose a simple yet effective meta-learning method to detect OoD with small in-distribution data in a target task. With the proposed method, the OoD detection is performed by density estimation in a latent space. A neural network shared among all tasks is used to flexibly map instances in the original space to the latent space. The neural network is meta-learned such that the expected OoD detection performance is improved by using various tasks that are different from the target tasks. This meta-learning procedure enables us to obtain appropriate representations in the latent space for OoD detection. For density estimation, we use a Gaussian mixture model (GMM) with full covariance for each class. We can adapt the GMM parameters to in-distribution data in each task in a closed form by maximizing the likelihood. Since the closed form solution is differentiable, we can meta-learn the neural network efficiently with a stochastic gradient descent method by incorporating the solution into the meta-learning objective function. In experiments using six datasets, we demonstrate that the proposed method achieves better performance than existing meta-learning and OoD detection methods.
[ -0.02857986092567444, -0.02181329019367695, -0.02119005285203457, -0.01575898937880993, 0.028010044246912003, 0.030040016397833824, 0.0011641173623502254, 0.04950281232595444, -0.06310718506574631, -0.015589824877679348, -0.02457333914935589, 0.01451251469552517, 0.028989417478442192, -0.033868469297885895, -0.009286228567361832, -0.00011282256309641525, -0.014646065421402454, -0.023273443803191185, 0.006040945649147034, -0.0445169173181057, 0.06424681842327118, -0.03105500154197216, -0.007296322844922543, -0.003728291718289256, 0.032443929463624954, 0.02366519346833229, 0.0721530169248581, 0.008119885809719563, -0.029594846069812775, 0.04861247539520264, -0.00638372590765357, 0.024074748158454895, -0.04665372893214226, -0.012660611420869827, -0.06168264150619507, 0.007830525748431683, 0.05972389504313469, 0.057266563177108765, -0.012785258702933788, 0.02484044060111046, 0.02715531922876835, -0.015251495875418186, 0.002766726305708289, -0.006272433791309595, -0.013595466502010822, -0.07165443152189255, -0.03034273162484169, -0.06784377992153168, 0.019195694476366043, 0.0024462046567350626, -0.03864068537950516, -0.0351683646440506, 0.030022209510207176, -0.015616534277796745, -0.06624117493629456, 0.06798623502254486, 0.0409199520945549, 0.016622617840766907, 0.06819991767406464, -0.02081611007452011, -0.03443828597664833, 0.02856205403804779, 0.004182364325970411, -0.02457333914935589, 0.007363098207861185, 0.010666253045201302, 0.04344851151108742, -0.04879054054617882, 0.024252817034721375, 0.01939156837761402, -0.0453716404736042, -0.02411036193370819, -0.028401793912053108, 0.008823253214359283, -0.0012609417317435145, 0.032337088137865067, 0.011298393830657005, -0.0012720709200948477, -0.028010044246912003, -0.0471523180603981, 0.02172425575554371, 0.02322002500295639, 0.038854364305734634, 0.04312799125909805, 0.028775734826922417, -0.023647386580705643, -0.010238890536129475, -0.05505852401256561, 0.023344671353697777, -0.011868210509419441, -0.028277145698666573, 0.026104720309376717, 0.01896420679986477, 0.1005013957619667, 0.014610452577471733, 0.05235189571976662, -0.03970909118652344, 0.010755287483334541, -0.07062163949012756, 0.06545767188072205, 0.004856795538216829, -0.00992727279663086, 0.044908665120601654, 0.018305355682969093, -0.002608691342175007, -0.014067346230149269, -0.01472619641572237, -0.009223905391991138, 0.011022388935089111, 0.11161281168460846, 0.01843000389635563, 0.035364240407943726, -0.05384766310453415, 0.05399011820554733, -0.009651267901062965, 0.03361917659640312, -0.04084872454404831, -0.039103660732507706, 0.01046147570014, -0.04633320868015289, 0.01607060804963112, 0.05110542103648186, 0.01633770950138569, -0.00558242155238986, -0.03657509759068489, 0.011592205613851547, 0.0013655564980581403, 0.032800063490867615, -0.004741051699966192, 0.03034273162484169, 0.06827114522457123, 0.0090146753937006, 0.031891919672489166, -0.033601369708776474, 0.007630199659615755, 0.016435645520687103, -0.008084272034466267, 0.09743862599134445, -0.03278225660324097, -0.016524679958820343, 0.02028190717101097, -0.049609653651714325, -0.020602429285645485, 0.02377203479409218, 0.019551830366253853, 0.01771773397922516, -0.020851723849773407, 0.04857686161994934, -0.04074188321828842, 0.01526039931923151, -0.01752185821533203, 0.04156099259853363, -0.005773844197392464, 0.02170644886791706, 0.04772213473916054, 0.03406434506177902, -0.011494267731904984, 0.03630799800157547, -0.05448870733380318, -0.045692164450883865, 0.07820732146501541, -0.04134731367230415, 0.02386106736958027, 0.04031452164053917, 0.041703447699546814, 0.03445609286427498, 0.02029971405863762, 0.002096746815368533, -0.05452432110905647, 0.05345591530203819, 0.001866371720097959, 0.036717552691698074, 0.01805606111884117, 0.02982633374631405, -0.0373585969209671, 0.08176867663860321, 0.052992939949035645, 0.0025263349525630474, -0.013096877373754978, -0.0017639828147366643, -0.05399011820554733, 0.0351327508687973, 0.09216782450675964, 0.012651707977056503, 0.00833801832050085, 0.00529306149110198, 0.030645444989204407, -0.0235939659178257, 0.0685204416513443, 0.039566636085510254, -0.011093615554273129, 0.009268422611057758, 0.03363698348402977, 0.0064905667677521706, -0.004683179780840874, -0.02546367608010769, -0.06367699801921844, 0.03278225660324097, 0.003013795241713524, 0.00010544944962020963, -0.010167663916945457, -0.06307157129049301, 0.020406555384397507, -0.027351193130016327, 0.00034528435207903385, 0.0025864329654723406, 0.01046147570014, 0.009767011739313602, -0.014850843697786331, -0.06132650375366211, 0.025926653295755386, -0.07428982853889465, -0.053099777549505234, 0.010140953585505486, -0.02430623769760132, -0.009749204851686954, 0.0021957969292998314, 0.02847301959991455, -0.04394710063934326, 0.012170924805104733, 0.010203277692198753, -0.015162462368607521, 0.035025909543037415, -0.005618034861981869, -0.06364138424396515, -0.02045997604727745, 0.03461635485291481, 0.028455212712287903, -0.01210860162973404, 0.003975360654294491, -0.024519918486475945, -0.034847844392061234, -0.009722494520246983, -0.04579900577664375, -0.01736159808933735, 0.004959184676408768, 0.01631990261375904, -0.004028780851513147, 0.02110101841390133, -0.0409555621445179, 0.007594585884362459, -0.0035880636423826218, -0.007260709069669247, -0.0498589463531971, 0.035186171531677246, 0.01967647671699524, -0.008075368590652943, 0.005613583140075207, 0.0373942106962204, 0.031268682330846786, -0.0158035047352314, -0.04886176809668541, -0.008738670498132706, 0.04316360130906105, -0.06620556116104126, 0.045692164450883865, 0.0073141297325491905, -0.01814509555697441, -0.004999249707907438, -0.052458737045526505, 0.06520838290452957, 0.0400652252137661, -0.0471879318356514, 0.019284728914499283, -0.02546367608010769, 0.022846082225441933, 0.09045837819576263, 0.000622123945504427, 0.03287129104137421, 0.00942868273705244, 0.013203717768192291, -0.05463116243481636, -0.07165443152189255, -0.0262471754103899, 0.056554291397333145, -0.01921350136399269, 0.08319321274757385, -0.012215442024171352, 0.04245133325457573, 0.033672597259283066, 0.02508973516523838, 0.042486947029829025, -0.019017627462744713, 0.001042808755300939, 0.0315713994204998, -0.02900722250342369, -0.028526440262794495, 0.00696244603022933, -0.032515157014131546, 0.011476460844278336, -0.01642674207687378, -0.0077103301882743835, -0.051212262362241745, 0.022276265546679497, 0.017771152779459953, 0.03860507160425186, -0.03682439401745796, -0.02482263371348381, 0.024537725374102592, -0.051390331238508224, -0.044018328189849854, -0.02003261260688305, -0.00778600899502635, 0.023380285128951073, -0.00691792881116271, -0.042949922382831573, 0.014708389528095722, 0.00749664893373847, -0.057088494300842285, -0.04038574919104576, 0.024359656497836113, -0.01134291011840105, -0.022543366998434067, -0.028508633375167847, -0.026656730100512505, 0.002740016207098961, 0.00273779034614563, 0.0011162617010995746, 0.011832596734166145, -0.030129048973321915, -0.004901312757283449, 0.04280746728181839, -0.09708249568939209, 0.0002683535567484796, 0.00332541367970407, -0.026478663086891174, 0.003919714596122503, 0.009945079684257507, -0.06912586838006973, 0.01767321676015854, -0.038925591856241226, -0.010132050141692162, -0.04262939840555191, -0.01339959166944027, -0.013230428099632263, 0.029434585943818092, -0.03044957108795643, 0.04847002029418945, -0.0355779193341732, -0.04084872454404831, 0.033156201243400574, -0.009722494520246983, -0.0186971053481102, -0.02054900862276554, -0.04084872454404831, -0.01036353874951601, -0.030502991750836372, -0.0038150998298078775, -0.04547848179936409, 0.007803815416991711, 0.0007445454248227179, -0.03450951352715492, -0.022489946335554123, 0.060186874121427536, 0.014200896956026554, 0.009023578837513924, -0.03967347741127014, 0.054061345756053925, 0.012758548371493816, -0.003327639540657401, 0.01548298355191946, -0.06834237277507782, -0.05356275662779808, -0.0249116662889719, -0.06773693859577179, 0.058334968984127045, 0.005128348711878061, 0.04067065566778183, 0.005462225992232561, 0.048541247844696045, 0.007545617409050465, 0.01152988150715828, 0.0016026090597733855, 0.02528560906648636, -0.044801823794841766, -0.0017495148349553347, 0.00751890754327178, 0.012464736588299274, -0.024413077160716057, 0.011360717006027699, -0.002490721642971039, 0.0014835263136774302, -0.0445169173181057, 0.00850273109972477, 0.02126128040254116, 0.07065725326538086, 0.0182519368827343, -0.009339649230241776, -0.05794322118163109, 0.05078490078449249, 0.011423041112720966, -0.04102678969502449, -0.00009265083645004779, 0.028081271797418594, 0.06802184879779816, 0.0351327508687973, 0.024947280064225197, -0.031090615317225456, 0.019640864804387093, 0.003844035789370537, -0.011253876611590385, 0.02847301959991455, 0.029060643166303635, 0.003011569380760193, -0.015678858384490013, -0.02688821777701378, 0.023344671353697777, 0.0037750345654785633, -0.008489375934004784, -0.008533893153071404, 0.0142454132437706, -0.0253746435046196, 0.017014365643262863, 0.07147636264562607, 0.017379404976963997, 0.04608391225337982, -0.008774284273386002, 0.03388627618551254, -0.008987965993583202, 0.001029453705996275, -0.001316587789915502, -0.04074188321828842, 0.01687191240489483, -0.015153558924794197, -0.01765540987253189, 0.006503921467810869, -0.007153868675231934, -0.006214561872184277, 0.007750395219773054, -0.0783497765660286, 0.003060538088902831, 0.008805446326732635, 0.04156099259853363, -0.0347231961786747, -0.001945389318279922, 0.02054900862276554, 0.009455393068492413, 0.012304475530982018, -0.02241871878504753, -0.0007317468407563865, 0.008533893153071404, -0.027529262006282806, 0.008084272034466267, 0.0010261149145662785, -0.014913166873157024, -0.08383426070213318, 0.0008786526741459966, -0.02313099056482315, -0.0018953077960759401, -0.05676797404885292, -0.05901162698864937, 0.008200015872716904, -0.013800244778394699, -0.04476621374487877, 0.05028631165623665, -0.011200455948710442, 0.014841940253973007, -0.009980692528188229, 0.03365479037165642, -0.006143334787338972, 0.023291250690817833, 0.047472842037677765, 0.007692523300647736, -0.0217954833060503, -0.012527060694992542, 0.018483424559235573, -0.057800766080617905, -0.05755146965384483, 0.03353014215826988, -0.006085462402552366, 0.03370821103453636, -0.0453716404736042, 0.01672055386006832, -0.008066465146839619, 0.06004441902041435, 0.05979512259364128, -0.05196014419198036, -0.026478663086891174, 0.021688641980290413, -0.02117224596440792, 0.023896681144833565, 0.017842380329966545, -0.00332541367970407, -0.002319331280887127, 0.001459041959606111, 0.003830680623650551, 0.03433144837617874, 0.006686441134661436, 0.007216192316263914, -0.03105500154197216, -0.004177912604063749, -0.02847301959991455, 0.02341589890420437, -0.05676797404885292, 0.001963196089491248, -0.051639623939991, -0.05455993488430977, -0.00696244603022933, 0.06577819585800171, 0.06962446123361588, 0.011449751444160938, -0.0418102890253067, 0.0011374072637408972, 0.0418102890253067, 0.027796363458037376, 0.008974610827863216, 0.03499029576778412, 0.02003261260688305, 0.05345591530203819, -0.00005422021422418766, 0.026585502550005913, -0.00908145122230053, 0.01569666527211666, -0.02954142726957798, 0.03985154628753662, 0.027190933004021645, 0.0008858866640366614, -0.05359836667776108, 0.07083532214164734, 0.01958744414150715, 0.003182959510013461, 0.022276265546679497, 0.0036548390053212643, -0.012491446919739246, -0.027475841343402863, 0.0168986227363348, 0.06396190822124481, -0.03878313675522804, 0.04832756519317627, -0.026104720309376717, -0.05434625223278999, 0.02678137831389904, -0.01771773397922516, -0.025837618857622147, -0.02208039164543152, -0.0018619201146066189, 0.01851903833448887, 0.011138132773339748, -0.030413957312703133, -0.05135471746325493, 0.003694904036819935, -0.025499289855360985, 0.022009164094924927, -0.03584502264857292, 0.005529001355171204, -0.0016983203822746873, 0.017949221655726433, -0.05929653346538544, 0.015456274151802063, 0.030324924737215042, 0.024608951061964035, 0.02617594785988331, 0.0071761272847652435, 0.03443828597664833, 0.013470819219946861, -0.02963045984506607, -0.038320161402225494, -0.015910346060991287, -0.01233118586242199, -0.009028030559420586, 0.042415719479322433, 0.04027890786528587, 0.00013828068040311337, -0.03263980522751808, 0.0019420505268499255, -0.0347231961786747, 0.007492197211831808, 0.050321921706199646, -0.017975931987166405, 0.03867629915475845, 0.0013266041642054915, 0.014085153117775917, 0.009094806388020515, -0.008907834999263287, 0.006797733251005411, -0.025837618857622147, 0.02865108847618103, -0.03707369044423103, -0.006806636694818735, -0.014797423034906387, 0.01940937526524067, -0.02181329019367695, 0.03450951352715492, 0.046226367354393005, 0.0126873217523098, -0.016043897718191147, -0.012527060694992542, -0.039103660732507706, -0.006290240213274956, 0.019071048125624657, 0.023469319567084312, 0.024341849610209465, -0.024893859401345253, -0.018750526010990143, -0.02045997604727745, 0.0006850040517747402, 0.014031732454895973, 0.012509253807365894, 0.03775034472346306, -0.004264720715582371, 0.014690582640469074, 0.011396330781280994, -0.02012164704501629, 0.03356575593352318, -0.016684940084815025, -0.006463856436312199, 0.020353134721517563, 0.020709270611405373, -0.016346612945199013, -0.019801124930381775, 0.012705128639936447, 0.004349302966147661, 0.033957503736019135, -0.025036314502358437, 0.031820692121982574, 0.02197355031967163, 0.06745203584432602, 0.0153583362698555, -0.013461915776133537, -0.017771152779459953, 0.03187411278486252, -0.006984704174101353, 0.02029971405863762, -0.012348992750048637, 0.005978622008115053, 0.05555711314082146, 0.034046538174152374, 0.007127158343791962, -0.02767171524465084, -0.00862737838178873, -0.01574118249118328, 0.02252556011080742, -0.010924451984465122, -0.00912596844136715, -0.027564875781536102, -0.00013848935486748815, 0.012633901089429855, -0.03559572622179985, -0.001597044407390058, 0.02297072857618332, -0.010114243254065514, 0.008743122220039368, -0.012242152355611324, 0.02777855657041073, 0.0025753036607056856, 0.021831097081303596, 0.02688821777701378, -0.018153999000787735, 0.021581800654530525, 0.06196754798293114, -0.03653948754072189, 0.001309910323470831, 0.00016471259004902095, 0.021243473514914513, -0.009010223671793938, -0.01841219700872898, 0.034830037504434586, -0.03303155303001404, -0.007603489328175783, -0.010657349601387978, 0.020442169159650803, -0.02252556011080742, -0.012224345467984676, -0.04380464553833008, 0.007220644038170576, -0.0064905667677521706, 0.0090146753937006, 0.03060983307659626, -0.018625877797603607, 0.052814871072769165, 0.02455553226172924, -0.017058882862329483, 0.01184150017797947, 0.027742942795157433, 0.025873232632875443, -0.040172066539525986, 0.004954732954502106, 0.00770142674446106, 0.025249995291233063, -0.014833036810159683, -0.0035168365575373173, 0.007781557273119688, 0.03409995883703232, 0.00279121077619493, -0.0596526674926281, 0.003979812376201153, 0.012206538580358028, 0.0462975949048996, -0.0632140189409256, 0.02366519346833229, -0.033672597259283066, -0.026140334084630013, 0.019783318042755127, 0.05997319146990776, 0.024413077160716057, -0.020976372063159943, -0.024787019938230515, -0.019623057916760445, 0.005987525451928377, -0.013577659614384174, -0.031446751207113266, 0.010301214642822742, -0.05028631165623665, 0.0280456580221653, 0.0021479411516338587, 0.032960325479507446, -0.01598157361149788, 0.01651577651500702, -0.035720374435186386, -0.007665812969207764, 0.035916250199079514, 0.008587313815951347, -0.025392450392246246, 0.02829495258629322, 0.007403163239359856, 0.026478663086891174, 0.017459534108638763, 0.01656029373407364, -0.02838398702442646, 0.06428243219852448, -0.036361418664455414, 0.025695165619254112, -0.00036754278698936105, -0.04903983697295189, -0.04665372893214226, -0.0067621199414134026, 0.006098817568272352, -0.02475140616297722, 0.03221243992447853, -0.005515646189451218, 0.07443228363990784, -0.04369780793786049, -0.028063464909791946, -0.0014712840784341097, -0.0013922665966674685, -0.0035479983780533075, -0.004798923619091511, 0.036895621567964554, -0.0037794862873852253, -0.006499469745904207, 0.07578559964895248, -0.00152915611397475, 0.030663251876831055, -0.03931733965873718, 0.006677537690848112, -0.011618915013968945, 0.024092555046081543, 0.056269384920597076, 0.011788079515099525, 0.01281196903437376, 0.061290889978408813, -0.018999820575118065, -0.02208039164543152, -0.0480426587164402, -0.06300034373998642, -0.01077309437096119, -0.004393819719552994, 0.01660481095314026, 0.0005369852879084647, 0.011583302170038223, 0.019177887588739395, -0.008422601036727428, 0.0498233325779438, 0.018198516219854355, 0.04579900577664375, 0.025481482967734337, -0.06713151186704636, -0.01771773397922516, 0.022311879321932793, -0.032443929463624954, 0.05523659288883209, -0.0032163471914827824, 0.029327744618058205, -0.033138394355773926, 0.010523798875510693, 0.02428843080997467, 0.06638363003730774, -0.030360538512468338, -0.013550949282944202, 0.030146855860948563, -0.014013925567269325, -0.022668015211820602, -0.009891659021377563, 0.013675596565008163, -0.020780496299266815, -0.019017627462744713, -0.030040016397833824, 0.008208919316530228, -0.039388567209243774, 0.004754406865686178, -0.02651427686214447, -0.03123306855559349, 0.041774675250053406, -0.02553490363061428, 0.02322002500295639, 0.027173126116394997, -0.016132930293679237, 0.02963045984506607, 0.002755597233772278, -0.0195696372538805, 0.03256857767701149, -0.023807646706700325, -0.0030894740484654903, 0.01783347688615322, -0.05106980726122856, -0.03935295343399048, -0.024252817034721375, 0.0009526620269753039, 0.040706269443035126, -0.006690892856568098, 0.02929213084280491, 0.002045552246272564, -0.011253876611590385, -0.03570256754755974, -0.0006399306585080922, 0.004896861035376787, -0.02010384015738964, -0.019444989040493965, -0.011325104162096977, -0.00896125566214323, 0.001644900068640709, -0.02019287459552288, -0.033957503736019135, -0.013844761066138744, -0.03185630589723587, -0.005123896989971399, 0.030912548303604126, -0.00469653494656086, 0.04558532312512398, -0.014298833906650543, 0.0005380982183851302, 0.019338149577379227, -0.022383106872439384, 0.02802785113453865, -0.035453274846076965, 0.0551653653383255, 0.013631080277264118, 0.03196314722299576, 0.009891659021377563, 0.02216942422091961, 0.03214121609926224, -0.00939306989312172, -0.04038574919104576, -0.028259338811039925, 0.008778735995292664, -0.008885576389729977, -0.008676347322762012, -0.008867769502103329, -0.015518597327172756, 0.03789279982447624, -0.00905919261276722, 0.005444419104605913, 0.009989595972001553, 0.024413077160716057, 0.010710770264267921, 0.03326303884387016, 0.05562834069132805, 0.023718614131212234, -0.012918809428811073, 0.0006360354600474238, 0.017637602984905243, 0.0017728862585499883, 0.014859747141599655, 0.014619356021285057, 0.046226367354393005, 0.03817771002650261, 0.0002698838070500642, -0.05017947033047676, -0.005569066386669874, -0.044445689767599106, 0.0012153118150308728, 0.01237570308148861, -0.021314699202775955, 0.06752326339483261, -0.018305355682969093, 0.01027450431138277, -0.010310118086636066, 0.005502291023731232, -0.001802935148589313, -0.013800244778394699, -0.012518157251179218, 0.03399311751127243, 0.025071928277611732, -0.05837058275938034, 0.033512335270643234, 0.008520537987351418, 0.013720113784074783, -0.0014134121593087912, -0.045442868024110794, -0.04968088120222092, -0.015296013094484806, -0.013782437890768051, -0.029488006606698036, -0.017397211864590645, 0.04387587308883667, 0.027458034455776215, 0.010256697423756123, 0.031197454780340195, 0.016373321413993835, 0.02918529137969017, -0.0006677537458017468, -0.027921009808778763, 0.001943163457326591, 0.02475140616297722, 0.03166043013334274, -0.006806636694818735, 0.04056381434202194, 0.013355075381696224, -0.002512980019673705, 0.03247954323887825, -0.016132930293679237, -0.01361327338963747, 0.0409199520945549, -0.026585502550005913, 0.06460294872522354, 0.0006104382337071002, 0.00502596003934741, -0.012135311961174011, 0.042843081057071686, 0.012242152355611324, 0.011868210509419441, 0.008222274482250214, 0.01669384352862835, 0.016310999169945717, -0.0217954833060503, -0.008311308920383453, 0.0038128739688545465, -0.01041695848107338, 0.00885886698961258, 0.03988715633749962, -0.03166043013334274, 0.018643684685230255, 0.005622486583888531, 0.01591924950480461, 0.04127608612179756, 0.025036314502358437, -0.006432694382965565, 0.0231487974524498, -0.039566636085510254, -0.021510574966669083, -0.020976372063159943, 0.04911106452345848, -0.020887337625026703, 0.053171005100011826, 0.04305676370859146, -0.05124787613749504, 0.044623758643865585, -0.03871191293001175, -0.01992577314376831, 0.018091674894094467, -0.04173906147480011, -0.0516040101647377, 0.03016466274857521, -0.01629319228231907, -0.007118254899978638, 0.048185110092163086, -0.013550949282944202, 0.015865828841924667, -0.024341849610209465, 0.04259378835558891, 0.026300594210624695, 0.05153278261423111, -0.04380464553833008, -0.011129229329526424, -0.012286669574677944, 0.05345591530203819, -0.025036314502358437, -0.016417838633060455, -0.007202837150543928, -0.00552009791135788, 0.004022103268653154, -0.028686702251434326, 0.005800554528832436, 0.06057862192392349, 0.003937521483749151, 0.00007449628174072132, 0.0036815491039305925, -0.02350493147969246, -0.04644005000591278, -0.012589383870363235, 0.03171385079622269, -0.009820432402193546, 0.02589103952050209, 0.013355075381696224, -0.02642524242401123, -0.017797863110899925, 0.01905324123799801, -0.03214121609926224, -0.022632401436567307, 0.02927432395517826, 0.02688821777701378, -0.03370821103453636, 0.013194814324378967, 0.004442788194864988, -0.040528200566768646, 0.028686702251434326, -0.03970909118652344, -0.031998760998249054, 0.005805006250739098, 0.04847002029418945, -0.014841940253973007, -0.02259678766131401, -0.048932995647192, 0.06257297843694687, 0.015723375603556633, -0.004295882303267717, 0.05167523771524429, -0.00961565412580967, 0.022472139447927475, 0.01077309437096119, -0.007256257347762585, -0.02633620798587799, -0.007291871123015881, 0.0032207989133894444, -0.00556016294285655, 0.015945959836244583, -0.06510154157876968, 0.022098198533058167, 0.0157856997102499, -0.006085462402552366, 0.059937577694654465, -0.031161842867732048, -0.013470819219946861, 0.015126848593354225 ]
The rise of AI methods to make predictions and decisions has led to a pressing need for more explainable artificial intelligence (XAI) methods. One common approach for XAI is to produce a post-hoc explanation, explaining why a black box ML model made a certain prediction. Formal approaches to post-hoc explanations provide succinct reasons for why a prediction was made, as well as why not another prediction was made. But these approaches assume that features are independent and uniformly distributed. While this means that "why" explanations are correct, they may be longer than required. It also means the "why not" explanations may be suspect as the counterexamples they rely on may not be meaningful. In this paper, we show how one can apply background knowledge to give more succinct "why" formal explanations, that are presumably easier to interpret by humans, and give more accurate "why not" explanations. In addition, we show how to use existing rule induction techniques to efficiently extract background information from a dataset, and also how to report which background information was used to make an explanation, allowing a human to examine it if they doubt the correctness of the explanation.
[ 0.012176821008324623, -0.02182985283434391, -0.034835655242204666, -0.04841253533959389, 0.060018282383680344, 0.010675443336367607, 0.00043521542102098465, -0.00007922820805106312, -0.04424920678138733, -0.013429504819214344, 0.001458777696825564, -0.04144908860325813, 0.05331273749470711, -0.005310088861733675, -0.019361330196261406, 0.04535451531410217, 0.045870326459407806, 0.015290108509361744, -0.013549246825277805, -0.04347549006342888, -0.00012593039718922228, 0.0231009591370821, -0.013291341252624989, 0.03997534513473511, 0.01680990867316723, 0.022087758406996727, -0.002714915433898568, -0.001124306581914425, -0.08503510802984238, 0.08459298312664032, 0.02967754751443863, -0.01506904698908329, 0.0022313427180051804, -0.047859881073236465, -0.07950856536626816, 0.008285212330520153, -0.002226737095043063, 0.0020367621909826994, -0.01727045327425003, 0.0803191214799881, -0.004082735162228346, 0.020614013075828552, 0.03590412065386772, -0.036640994250774384, -0.01941659487783909, -0.02024557814002037, -0.09564607590436935, -0.04645982384681702, -0.028535395860671997, -0.06403423845767975, -0.011771541088819504, -0.044912390410900116, 0.04461764171719551, -0.003942268900573254, -0.01238867174834013, 0.07365042716264725, 0.00235684122890234, -0.022843053564429283, 0.05681288614869118, -0.02350623905658722, -0.03336191177368164, 0.03450406342744827, -0.021866697818040848, -0.004216293338686228, 0.029014362022280693, -0.047086164355278015, 0.004566308110952377, 0.0044189332984387875, -0.0316302590072155, 0.007884537801146507, -0.018007326871156693, 0.006424608640372753, 0.03063548170030117, 0.01538221724331379, 0.004844937939196825, -0.0032445425167679787, 0.049407314509153366, 0.042591240257024765, -0.019398173317313194, -0.002625108929350972, 0.03293820843100548, 0.03199869766831398, -0.006005512550473213, 0.001752375392243266, 0.056886572390794754, -0.01545590441673994, 0.0076266322284936905, -0.050181031227111816, 0.00854311790317297, -0.03072759136557579, -0.013134756125509739, 0.00440281443297863, 0.011338628828525543, -0.07085031270980835, -0.00415411964058876, 0.02790905348956585, 0.02287989668548107, -0.013696621172130108, -0.03538830950856209, -0.020908761769533157, 0.03479881212115288, 0.009404337964951992, -0.0010235622758045793, 0.0440281443297863, 0.03385930135846138, -0.05909718945622444, 0.005904192570596933, -0.003654428059235215, -0.028572238981723785, 0.1380162537097931, -0.02146141789853573, 0.025164201855659485, -0.04852306842803955, -0.00034253066405653954, -0.022308820858597755, -0.016478314995765686, -0.046275604516267776, -0.05909718945622444, 0.053533799946308136, -0.033509284257888794, 0.014359806664288044, 0.048670440912246704, 0.04686510190367699, -0.008888526819646358, -0.027835365384817123, 0.07110821455717087, 0.025901075452566147, -0.039238471537828445, 0.017187556251883507, -0.01652437075972557, -0.013447926379740238, 0.06956078112125397, 0.011522846296429634, -0.013015014119446278, 0.028295911848545074, -0.0030511135701090097, 0.05029156059026718, 0.05132318288087845, 0.006438425276428461, -0.01572302170097828, -0.03699100762605667, -0.062007836997509, -0.06609748303890228, -0.0011173983803018928, 0.05585495010018349, -0.001958469394594431, 0.01801653765141964, 0.0372120700776577, -0.055891793221235275, 0.02595634013414383, -0.02492471970617771, 0.05714447796344757, -0.01755599118769169, -0.00973593071103096, 0.035517264157533646, 0.01086887251585722, -0.014175588265061378, -0.006816072389483452, 0.008142443373799324, 0.039680592715740204, 0.07405570894479752, -0.03684363514184952, -0.013291341252624989, 0.05379170551896095, 0.05077052861452103, -0.007575972471386194, -0.027430085465312004, -0.052207428961992264, -0.053349584341049194, 0.056076012551784515, -0.0064107924699783325, 0.00803191214799881, -0.04634929075837135, 0.04970206320285797, -0.018956050276756287, 0.047086164355278015, 0.031022340059280396, 0.026287933811545372, -0.050033655017614365, -0.02754061669111252, -0.05419698730111122, -0.03395140916109085, 0.04517029598355293, -0.017602046951651573, 0.025072094053030014, -0.023266755044460297, 0.03979112580418587, 0.005406803451478481, 0.035830434411764145, -0.006728568580001593, -0.02831433340907097, -0.01733493059873581, 0.02381940931081772, 0.004964679945260286, 0.02669321373105049, -0.014903250150382519, -0.023948362097144127, -0.053128521889448166, -0.03188816457986832, -0.009031295776367188, -0.0030188753735274076, -0.05913403257727623, -0.004085037857294083, 0.0018007326871156693, 0.04955468699336052, 0.03221976011991501, 0.006604221649467945, -0.012057079002261162, -0.029567016288638115, -0.06985553354024887, 0.009422759525477886, 0.018707355484366417, -0.04329127073287964, -0.08112968504428864, -0.033104006201028824, -0.0019803454633802176, 0.01037148293107748, -0.024814188480377197, -0.03625413775444031, -0.032606616616249084, -0.0007172995246946812, 0.011716275475919247, 0.030101248994469643, 0.004808094352483749, 0.07055556029081345, 0.02976965717971325, 0.02359834872186184, -0.026895852759480476, 0.035333044826984406, 0.013715042732656002, -0.011375471949577332, 0.033840879797935486, 0.03481723368167877, -0.012112344615161419, 0.02332202158868313, 0.01652437075972557, 0.0049600740894675255, -0.018523138016462326, 0.02151668258011341, -0.03883318975567818, -0.007198324892669916, -0.0249615628272295, -0.017371773719787598, -0.03780156746506691, 0.0737977996468544, -0.0027724835090339184, 0.02409573644399643, 0.03308558464050293, 0.041375402361154556, 0.013042646460235119, -0.0017316507874056697, 0.005411408841609955, 0.05788135156035423, -0.0031961852218955755, 0.0031455252319574356, 0.033969830721616745, 0.0514705590903759, -0.03426457941532135, 0.010518857277929783, -0.008087177760899067, 0.07405570894479752, 0.019048159942030907, 0.02759588323533535, 0.05091790482401848, -0.036825213581323624, -0.026177402585744858, 0.051175806671381, -0.0030695353634655476, 0.02840644307434559, 0.037193648517131805, 0.047675661742687225, -0.04406498745083809, 0.006097621750086546, 0.0062219686806201935, -0.015078257769346237, -0.06690803915262222, 0.02223513275384903, -0.002006826689466834, -0.014709820970892906, 0.0016383903566747904, -0.021406151354312897, 0.01696649380028248, 0.0033320460934191942, 0.012968959286808968, 0.011992602609097958, -0.04071221500635147, -0.039238471537828445, 0.005383776035159826, -0.05692341551184654, -0.04211227595806122, -0.0008773390436545014, 0.029935453087091446, -0.027061650529503822, 0.022382507100701332, 0.02387467585504055, 0.045907169580459595, -0.043549176305532455, -0.009104982949793339, 0.07320830225944519, -0.04034378007054329, -0.018099434673786163, -0.03890687972307205, -0.006871338002383709, 0.04038062319159508, -0.0006395824602805078, 0.04111749678850174, 0.006516717839986086, 0.12327880412340164, -0.0209271851927042, 0.011126778088510036, 0.021774588152766228, 0.045538730919361115, -0.018412606790661812, -0.006825283169746399, -0.002121963072568178, 0.049591533839702606, -0.019766610115766525, -0.08953002840280533, -0.0015716112684458494, -0.053754862397909164, -0.000860068597830832, -0.02614055946469307, -0.11222571134567261, 0.01602698117494583, 0.0024892480578273535, 0.008847077377140522, -0.010233319364488125, 0.038648974150419235, -0.012397883459925652, -0.0008416468044742942, -0.0750504806637764, -0.023837830871343613, -0.02019031159579754, 0.001545129925943911, -0.0009354829089716077, -0.030801277607679367, -0.008197708986699581, 0.009699086658656597, -0.03857528418302536, -0.027153758332133293, 0.007000290788710117, -0.004223201423883438, -0.07040818780660629, -0.0579918809235096, -0.016883594915270805, -0.03489092364907265, -0.04255439713597298, 0.01086887251585722, 0.01662568934261799, -0.02958543784916401, 0.0010920683853328228, 0.002436285372823477, -0.028645925223827362, 0.005351537838578224, -0.008731941692531109, -0.040785904973745346, -0.041412245482206345, 0.03236713260412216, 0.02759588323533535, 0.038870032876729965, 0.07604525983333588, -0.02477734349668026, -0.046901945024728775, 0.000054222029575612396, -0.08289817720651627, -0.01704939268529415, -0.03634624555706978, 0.006327894050627947, -0.020227154716849327, 0.009468814358115196, -0.010988613590598106, 0.09137221425771713, 0.0034034308046102524, 0.03553568571805954, 0.033564552664756775, -0.001341338618658483, -0.0018755713244900107, -0.03697258606553078, -0.020135046914219856, 0.04907572269439697, -0.01919553428888321, 0.003939966205507517, -0.003857068018987775, 0.037506818771362305, -0.04870728403329849, 0.007502285297960043, -0.016266465187072754, 0.00906813982874155, -0.0006890911026857793, 0.02087191864848137, 0.01789679564535618, -0.019913984462618828, 0.008188498206436634, -0.06550798565149307, 0.06628169864416122, 0.017067814245820045, 0.011310995556414127, -0.01291369367390871, 0.06311314553022385, 0.017104657366871834, 0.014387439005076885, 0.014111111871898174, 0.023174645379185677, 0.01259131170809269, -0.03284610062837601, 0.007884537801146507, 0.004771250765770674, 0.03172237053513527, 0.043733395636081696, 0.0038777925074100494, 0.037469975650310516, 0.033509284257888794, -0.02849855087697506, -0.05692341551184654, -0.001249229535460472, 0.01320844329893589, -0.0651027038693428, 0.029217002913355827, 0.01854155957698822, -0.0005549572524614632, -0.03420931473374367, 0.004492620471864939, 0.008750363253057003, -0.0169020164757967, -0.0049600740894675255, -0.0028784088790416718, -0.03581201285123825, -0.012968959286808968, -0.012462359853088856, -0.021866697818040848, 0.047491446137428284, 0.025256311520934105, 0.009726719930768013, -0.009901726618409157, -0.05077052861452103, -0.029474908486008644, -0.03934900090098381, 0.010555701330304146, 0.02260356955230236, -0.0031109843403100967, -0.019177112728357315, 0.008870105259120464, -0.00726280128583312, -0.013070279732346535, -0.03979112580418587, -0.023672034963965416, -0.010288584977388382, 0.03544357791543007, -0.010878083296120167, -0.0018962958129122853, -0.0725451186299324, -0.006470663473010063, -0.07560313493013382, -0.031298667192459106, 0.027614304795861244, -0.043954454362392426, 0.010905715636909008, -0.019913984462618828, 0.03174079209566116, -0.061786774545907974, -0.023929940536618233, 0.04192805662751198, 0.018550770357251167, 0.018145490437746048, 0.009206303395330906, 0.0025974763557314873, -0.043401800096035004, -0.04564926400780678, -0.001694807200692594, -0.007143059745430946, 0.04579663649201393, 0.004877176135778427, 0.0018744198605418205, -0.03511198237538338, 0.00403898349031806, 0.007405570708215237, 0.04071221500635147, -0.07641369849443436, 0.027116915211081505, -0.024077314883470535, 0.03853844106197357, -0.0215535257011652, 0.0009084258927032351, 0.021092981100082397, -0.02182985283434391, 0.04660719633102417, -0.009947781451046467, 0.025882653892040253, -0.020263999700546265, -0.041228026151657104, -0.05567073076963425, -0.031114449724555016, 0.019213955849409103, -0.010030679404735565, 0.034430377185344696, -0.02669321373105049, -0.03205396234989166, -0.0008882770198397338, 0.06248680502176285, 0.049628376960754395, 0.0036797579377889633, -0.02545895241200924, -0.0455755777657032, -0.039422690868377686, 0.07085031270980835, 0.00036411872133612633, 0.011191253550350666, 0.016054613515734673, 0.016634900122880936, -0.004218596033751965, -0.005181136075407267, 0.0019469558028504252, 0.013309762813150883, -0.00781545601785183, -0.0004835727158933878, -0.003838646225631237, 0.013263708911836147, -0.024722078815102577, 0.0645132064819336, -0.01014121063053608, 0.019453439861536026, -0.012922904454171658, 0.015391428023576736, 0.04995996877551079, -0.02822222374379635, 0.029695969074964523, 0.021571947261691093, 0.013457137160003185, 0.036917321383953094, -0.00642000325024128, -0.0033021108247339725, 0.03594096377491951, 0.0012411699863150716, -0.025937918573617935, 0.018624456599354744, -0.0048403325490653515, 0.04859675467014313, 0.03717522695660591, 0.0017926731379702687, -0.030303889885544777, -0.08768784999847412, 0.039091095328330994, 0.04410183057188988, 0.02101929299533367, -0.010159632191061974, -0.020890340209007263, 0.02849855087697506, 0.022621991112828255, 0.004174844361841679, 0.03041442111134529, 0.00694502517580986, 0.028203802183270454, 0.00838653277605772, -0.014608501456677914, 0.029419641941785812, 0.00492323050275445, -0.0044649881310760975, 0.015584857203066349, -0.002684979932382703, 0.011292573995888233, 0.04089643433690071, -0.009966203011572361, 0.02019031159579754, -0.012425515800714493, -0.0032952025067061186, -0.007893748581409454, 0.03205396234989166, 0.053902238607406616, -0.0073503050953149796, 0.041817523539066315, -0.03809631988406181, 0.0002271064731758088, -0.032514508813619614, 0.039827968925237656, 0.03697258606553078, 0.02477734349668026, -0.0011997208930552006, -0.04907572269439697, -0.033104006201028824, 0.005245612468570471, 0.027614304795861244, 0.009800407104194164, -0.03205396234989166, -0.016570424661040306, -0.0017270453972741961, -0.026066871359944344, -0.05618654191493988, -0.003815618809312582, -0.008856289088726044, 0.021700900048017502, -0.026877431198954582, 0.04679141566157341, 0.021590370684862137, -0.005706158000975847, 0.016321729868650436, 0.05165477469563484, 0.0446544848382473, -0.02927226759493351, -0.004499529022723436, -0.0527232401072979, 0.04314389452338219, -0.019950827583670616, 0.05320220813155174, 0.02923542447388172, 0.023174645379185677, -0.010988613590598106, 0.01652437075972557, -0.012462359853088856, 0.03249608725309372, 0.00010894778097281232, 0.00006109422974986956, -0.008649042807519436, -0.014636133797466755, -0.02551421709358692, 0.05578126385807991, -0.03081970103085041, 0.06090252846479416, -0.024224689230322838, 0.01223208662122488, 0.013742676004767418, 0.04539135843515396, -0.009192487224936485, 0.035609371960163116, -0.02105613797903061, 0.010601756162941456, 0.028351176530122757, -0.017574414610862732, -0.029345955699682236, 0.007285828702151775, 0.03373034670948982, -0.011568901129066944, 0.01004910096526146, -0.03704627603292465, -0.002615898149088025, 0.03304874151945114, 0.0051258704625070095, 0.008404954336583614, 0.06053408980369568, 0.02359834872186184, -0.007824666798114777, -0.010454380884766579, 0.003124800743535161, -0.030709169805049896, 0.07077661901712418, -0.020724544301629066, -0.0014392044395208359, 0.020135046914219856, 0.006728568580001593, 0.018394185230135918, 0.024943141266703606, 0.0012526835780590773, 0.03155657276511192, -0.01656121388077736, 0.03715680539608002, -0.0033942197915166616, -0.004739012569189072, -0.01513352245092392, -0.012047868221998215, 0.03444879874587059, 0.035369887948036194, 0.021885119378566742, 0.014811141416430473, 0.029124893248081207, 0.036106761544942856, 0.0032030935399234295, -0.006548956036567688, 0.010657020844519138, 0.01754678040742874, 0.006834494415670633, 0.031925007700920105, -0.030119670554995537, -0.0034540907945483923, -0.05758659914135933, 0.05213374271988869, 0.025495795533061028, -0.01602698117494583, -0.013392660766839981, 0.01107151247560978, 0.01761125773191452, -0.0014702912885695696, -0.04704932123422623, 0.01527168694883585, 0.018034959211945534, 0.005135081708431244, -0.02350623905658722, -0.005176530685275793, 0.020908761769533157, -0.010334639810025692, -0.009335256181657314, 0.002115054987370968, -0.01578749716281891, 0.017813896760344505, 0.017813896760344505, -0.007852300070226192, -0.007709530647844076, -0.019342908635735512, 0.005116659682244062, -0.02241935208439827, 0.012858428061008453, -0.016284886747598648, -0.048449378460645676, 0.04797041043639183, 0.017436249181628227, 0.007230563089251518, -0.031925007700920105, 0.0018721171654760838, 0.019213955849409103, -0.011688643135130405, -0.031206559389829636, -0.029345955699682236, 0.009634610265493393, 0.019527126103639603, -0.013125544413924217, 0.003458696184679866, 0.02763272635638714, 0.03466986119747162, 0.02750377357006073, -0.054491735994815826, -0.021903540939092636, 0.011080723255872726, 0.04933362826704979, -0.005729184951633215, -0.003389614401385188, -0.018523138016462326, -0.01097940281033516, 0.051765307784080505, 0.01594408228993416, 0.018154701218008995, 0.0021046926267445087, 0.002618200844153762, 0.021166667342185974, -0.006645670626312494, -0.0508442148566246, 0.020540326833724976, 0.03975428268313408, -0.01692965067923069, 0.024482594802975655, 0.026766899973154068, -0.0003891608794219792, -0.009266174398362637, 0.0030695353634655476, 0.003226120723411441, 0.01593487150967121, -0.03780156746506691, -0.0010080188512802124, 0.030561795458197594, 0.011366261169314384, -0.0032975052017718554, -0.0289959404617548, 0.023524660617113113, 0.05537598207592964, 0.004598546307533979, 0.04458079859614372, -0.005112054292112589, -0.022898318246006966, 0.00289913360029459, 0.02536684274673462, 0.023450972512364388, 0.02474050037562847, -0.05054946616292, -0.0019055067095905542, 0.05917087569832802, -0.012941326946020126, 0.03634624555706978, 0.09233015030622482, 0.0005480490508489311, -0.0036843635607510805, 0.010242530144751072, 0.0046077570877969265, -0.01727045327425003, 0.037598930299282074, -0.018734987825155258, 0.0029613070655614138, -0.05681288614869118, 0.012628155760467052, -0.009114193730056286, 0.012167610228061676, -0.01695728302001953, -0.020006094127893448, 0.020356107503175735, 0.013908471912145615, 0.04012271761894226, -0.0016671745106577873, -0.010721497237682343, -0.04167015105485916, 0.014801930636167526, -0.013143966905772686, -0.05614969879388809, 0.01575065404176712, 0.02450101636350155, -0.010758341290056705, 0.013457137160003185, 0.03185132145881653, -0.034872498363256454, 0.05913403257727623, -0.02800116315484047, -0.006152886897325516, -0.04815462976694107, 0.043954454362392426, -0.01715071126818657, 0.028885409235954285, -0.0030188753735274076, 0.009717508219182491, -0.016054613515734673, -0.004709077067673206, -0.023119380697607994, -0.015649333596229553, -0.04734406992793083, 0.020706122741103172, 0.0334908626973629, 0.029880188405513763, 0.02663794718682766, 0.004596243612468243, 0.04424920678138733, 0.06381317228078842, -0.008870105259120464, -0.015244053676724434, 0.0190665815025568, -0.0053377216681838036, -0.0024224689695984125, -0.023045692592859268, -0.07416623830795288, -0.020595591515302658, 0.0092247249558568, -0.03839106857776642, -0.014894039370119572, 0.0013137058122083545, 0.0052824560552835464, -0.014636133797466755, -0.06410792469978333, 0.03137235343456268, 0.026195824146270752, -0.04391761124134064, -0.022677257657051086, -0.04793356731534004, 0.05976037681102753, -0.03850159794092178, 0.0003330319013912231, 0.04288598895072937, 0.011992602609097958, 0.0048403325490653515, 0.010693864896893501, -0.04240702465176582, -0.0017420131480321288, 0.016201987862586975, 0.0015324648702517152, -0.009680665098130703, -0.026877431198954582, -0.0003744809946510941, 0.051175806671381, 0.007755585014820099, -0.06034987419843674, -0.015861185267567635, 0.009929359890520573, -0.01863366737961769, -0.016082245856523514, 0.022529883310198784, 0.04421235993504524, -0.012397883459925652, -0.012342617847025394, 0.03293820843100548, 0.013226864859461784, -0.016634900122880936, -0.0193797517567873, -0.0021991045214235783, -0.0579918809235096, 0.010426748543977737, -0.017823107540607452, -0.021903540939092636, -0.06432898342609406, -0.003992929123342037, -0.010592545382678509, -0.036733102053403854, 0.024574704468250275, 0.0060791997238993645, 0.023616770282387733, 0.02306411601603031, 0.01965607888996601, 0.0036521253641694784, -0.016459893435239792, -0.024519437924027443, 0.017169132828712463, 0.03890687972307205, -0.030690748244524002, 0.0286827702075243, -0.00181570032145828, -0.02400362864136696, -0.023616770282387733, -0.02691427432000637, -0.015437482856214046, 0.0013493981678038836, 0.05474964156746864, 0.015888817608356476, -0.007691108621656895, 0.04144908860325813, 0.004340640734881163, -0.018495503813028336, 0.0068298885598778725, 0.024335220456123352, 0.0003120195178780705, 0.021314041689038277, 0.02052190527319908, -0.006728568580001593, 0.028793299570679665, 0.03212764859199524, -0.0038916089106351137, 0.00621736329048872, -0.013705831952393055, 0.03094865381717682, -0.014682188630104065, -0.01014121063053608, 0.00455939956009388, 0.017344141378998756, 0.022308820858597755, 0.016542792320251465, -0.020319264382123947, -0.053718019276857376, -0.041375402361154556, -0.028240645304322243, -0.0082944231107831, 0.03883318975567818, 0.06838178634643555, 0.018937628716230392, 0.008957608602941036, -0.00194350176025182, -0.00011117854592157528, 0.002121963072568178, 0.02405889332294464, -0.008722730912268162, -0.005346932448446751, -0.013991369865834713, 0.01014121063053608, -0.021977227181196213, 0.027798522263765335, 0.004715985152870417, 0.01820075511932373, -0.04704932123422623, -0.0020425189286470413, -0.009155643172562122, -0.009385915473103523, -0.023395707830786705, 0.0455755777657032, -0.0019354422111064196, -0.010500435717403889, 0.008897737599909306, 0.0013401871547102928, 0.028516972437500954, 0.02087191864848137, 0.0098464610055089, -0.007797033991664648, -0.015363795682787895, 0.030746012926101685, 0.010675443336367607, -0.02291673980653286, -0.05640760436654091, 0.041228026151657104, -0.006304867099970579, -0.001860603573732078, 0.013751886785030365, -0.008160864934325218, 0.03522251546382904, 0.002825446194037795, -0.048265162855386734, -0.009662243537604809, -0.02855381742119789, -0.019232377409934998, -0.004587032366544008, -0.07936118543148041, -0.06959762424230576, -0.029788078740239143, -0.010767552070319653, -0.023653613403439522, -0.0032952025067061186, 0.03454090654850006, 0.03244081884622574, -0.03444879874587059, 0.009243146516382694, -0.013171599246561527, 0.0037096934393048286, -0.01259131170809269, 0.05349695682525635, 0.03507513925433159, -0.007133848965167999, 0.001019532443024218, -0.021185090765357018, -0.03575674816966057, 0.0359778106212616, 0.00003957812441512942, 0.004890992306172848, 0.01996924914419651, -0.004062010906636715, 0.027577459812164307, -0.0014576263492926955, -0.03861212730407715, -0.02083507552742958, 0.006369343493133783, -0.013153177686035633, 0.03402509540319443, 0.018209965899586678, 0.010546490550041199, 0.03758050873875618, -0.004234715364873409, 0.009128010831773281, 0.04612823203206062, -0.021811431273818016, 0.021866697818040848, 0.046901945024728775, -0.0004749374638777226, -0.017620468512177467, 0.05246533453464508, 0.013134756125509739, 0.01243472658097744, 0.020706122741103172, 0.04251755401492119, -0.022529883310198784, 0.010334639810025692, -0.01763889007270336, -0.010850450024008751, 0.0249615628272295, -0.020411374047398567, 0.011246519163250923, -0.03653046488761902, -0.012812374159693718, -0.03023020178079605 ]
In the last decade, reinforcement learning successfully solved complex control tasks and decision-making problems, like the Go board game. Yet, there are few success stories when it comes to deploying those algorithms to real-world scenarios. One of the reasons is the lack of guarantees when dealing with and avoiding unsafe states, a fundamental requirement in critical control engineering systems. In this paper, we introduce Guided Safe Shooting (GuSS), a model-based RL approach that can learn to control systems with minimal violations of the safety constraints. The model is learned on the data collected during the operation of the system in an iterated batch fashion, and is then used to plan for the best action to perform at each time step. We propose three different safe planners, one based on a simple random shooting strategy and two based on MAP-Elites, a more advanced divergent-search algorithm. Experiments show that these planners help the learning agent avoid unsafe situations while maximally exploring the state space, a necessary aspect when learning an accurate model of the system. Furthermore, compared to model-free approaches, learning a model allows GuSS reducing the number of interactions with the real-system while still reaching high rewards, a fundamental requirement when handling engineering systems.
[ 0.0651121661067009, 0.007173060905188322, -0.030596433207392693, -0.035125814378261566, 0.035014890134334564, 0.027009902521967888, -0.02567881904542446, 0.029893916100263596, -0.06134076416492462, -0.018320884555578232, 0.00018602816271595657, 0.02357126958668232, 0.057828180491924286, 0.01592678390443325, -0.021426746621727943, 0.07320959120988846, -0.010362114757299423, 0.03416447713971138, -0.027583006769418716, -0.04115266352891922, 0.08119609206914902, 0.0044461884535849094, -0.03728882595896721, 0.05871557071805, 0.0175813939422369, -0.006354999262839556, -0.006733988411724567, 0.03658630698919296, -0.040745943784713745, 0.030097275972366333, 0.010399089194834232, 0.03244515880942345, -0.02488386631011963, 0.05668197199702263, -0.028414934873580933, 0.002468050690367818, 0.0021352798212319613, 0.04662489518523216, -0.06958608329296112, 0.05856767296791077, 0.018746092915534973, -0.03721487522125244, -0.011129336431622505, -0.037251848727464676, -0.015936026349663734, -0.013403271324932575, -0.015667961910367012, -0.020058687776327133, -0.0385274700820446, 0.02188892848789692, 0.005162570159882307, -0.035458583384752274, 0.08060450106859207, -0.003045777790248394, -0.041300561279058456, -0.03985855355858803, 0.03823167458176613, 0.01755366288125515, 0.05612735450267792, 0.0003391258651390672, -0.010297409258782864, -0.03736277297139168, -0.06481637060642242, 0.0024449415504932404, -0.015473845414817333, -0.09554221481084824, 0.04784505441784859, -0.015381408855319023, 0.006988188251852989, -0.02786031737923622, 0.011415889486670494, 0.0024010343477129936, -0.0537240095436573, -0.0026829650159925222, 0.03529220074415207, 0.026843516156077385, 0.03617958724498749, 0.02898803912103176, -0.012109162285923958, 0.03985855355858803, 0.03190902993083, 0.019559532403945923, -0.06193235516548157, 0.0032491376623511314, 0.056201301515102386, 0.011665468104183674, 0.03531068563461304, -0.063374362885952, 0.05054419860243797, -0.006336512044072151, 0.016315016895532608, 0.017988113686442375, -0.019282223656773567, -0.016176361590623856, -0.017276354134082794, 0.019614994525909424, -0.003602706827223301, -0.026658643037080765, 0.001893789740279317, 0.07572385668754578, -0.027786366641521454, -0.0125620998442173, -0.03741823509335518, -0.028636781498789787, 0.0023051316384226084, -0.013948645442724228, -0.07387512922286987, 0.017904920503497124, 0.0073302024975419044, 0.12704452872276306, 0.028599807992577553, 0.021482208743691444, 0.003182121319696307, -0.01169319823384285, -0.07210035622119904, -0.046550948172807693, -0.011471351608633995, -0.050285376608371735, 0.02026204764842987, -0.0125620998442173, -0.015362922102212906, 0.10094049572944641, 0.012737729586660862, -0.032260287553071976, -0.03915603831410408, 0.014457045122981071, 0.03745520859956741, -0.03259305655956268, -0.013948645442724228, 0.034201450645923615, 0.025013277307152748, -0.012636049650609493, -0.003008803352713585, 0.008203726261854172, 0.0012617561733350158, 0.006761719007045031, -0.022332623600959778, -0.062449999153614044, -0.015002420172095299, -0.0004821133625227958, -0.039562758058309555, -0.060268502682447433, -0.008069693110883236, 0.007565915584564209, 0.026547720655798912, 0.006105421110987663, -0.026418309658765793, 0.020668769255280495, -0.027583006769418716, 0.035458583384752274, -0.040671996772289276, 0.05224502459168434, 0.014355365186929703, 0.06474242359399796, 0.04814085364341736, -0.002282022498548031, -0.07646334916353226, 0.012423445470631123, 0.008753722533583641, -0.027157800272107124, 0.03882326930761337, -0.0451459139585495, 0.025586381554603577, 0.08326666802167892, 0.06304159015417099, 0.03577286750078201, 0.016536863520741463, -0.011332697235047817, -0.02567881904542446, 0.03571740537881851, -0.03860142081975937, -0.024902353063225746, -0.02431076020002365, 0.045182887464761734, 0.06211723014712334, -0.0015240443171933293, 0.0485105961561203, 0.05768028274178505, -0.025974614545702934, 0.011637737043201923, -0.06503821909427643, 0.007750788237899542, 0.02207380160689354, 0.03349893540143967, 0.04322323948144913, 0.026769567281007767, 0.023404885083436966, -0.037621594965457916, 0.034700606018304825, -0.005301224999129772, 0.00682642450556159, 0.006752475630491972, 0.025641843676567078, -0.029080476611852646, -0.006489031948149204, -0.024902353063225746, -0.03666025772690773, -0.00424513965845108, -0.0039470321498811245, -0.00020321554620750248, 0.0022981988731771708, 0.009678086265921593, 0.025549408048391342, 0.0008024630951695144, 0.0016349679790437222, 0.03542160987854004, -0.004705010447651148, -0.004000183194875717, -0.029967864975333214, -0.07420790195465088, -0.01275621633976698, -0.012543613091111183, -0.0533912368118763, -0.0453677624464035, -0.024717479944229126, -0.009779766201972961, -0.00031919428147375584, 0.0077600316144526005, -0.0035426232498139143, -0.03641992434859276, 0.010131023824214935, 0.039119064807891846, 0.03237121179699898, -0.029468709602952003, -0.03739974647760391, 0.05235594883561134, 0.02475445531308651, 0.019189786165952682, 0.0008677462465129793, -0.03934091329574585, -0.004601019434630871, 0.024033451452851295, 0.04607027769088745, 0.03754764795303345, 0.01629652827978134, 0.05560971051454544, -0.0014454734046012163, 0.04577448219060898, -0.012765460647642612, 0.00988144613802433, -0.013384783640503883, -0.020169612020254135, -0.025364534929394722, -0.014087299816310406, 0.02680654264986515, 0.04422155022621155, 0.03368380665779114, 0.022295648232102394, 0.04973075911402702, -0.024329248815774918, -0.07006675750017166, -0.03555102273821831, -0.050470247864723206, -0.029265349730849266, -0.017692318186163902, 0.043925754725933075, 0.055646684020757675, -0.07786837965250015, 0.046366073191165924, 0.0013276170939207077, 0.039119064807891846, 0.02774939313530922, 0.0028285523876547813, 0.028156112879514694, -0.03945183381438255, 0.022092288359999657, 0.023552782833576202, 0.027583006769418716, -0.01293184608221054, 0.025235123932361603, -0.013292347081005573, -0.038675371557474136, -0.01900491490960121, -0.02312757447361946, -0.00991842057555914, -0.052023179829120636, 0.01190580241382122, 0.039562758058309555, -0.019337685778737068, 0.023275474086403847, -0.002216161461547017, -0.05224502459168434, 0.012109162285923958, -0.005661726463586092, 0.00997388269752264, -0.054722320288419724, -0.054093752056360245, 0.02486537955701351, -0.08504144102334976, 0.03440481051802635, 0.010140268132090569, 0.022036826238036156, -0.01296882051974535, 0.031188026070594788, 0.10057075321674347, 0.06714576482772827, -0.0234973207116127, -0.024366222321987152, -0.030781304463744164, -0.003900814102962613, -0.02749057114124298, 0.018727604299783707, 0.016666274517774582, -0.005010050255805254, -0.012349496595561504, -0.015279728919267654, -0.028340985998511314, 0.023534296080470085, -0.026917465031147003, -0.02869224362075329, 0.006650795694440603, 0.01645367033779621, -0.05575760826468468, -0.051209740340709686, 0.014725110493600368, 0.020557845011353493, 0.05904834344983101, 0.03222331404685974, -0.035125814378261566, 0.00589281739667058, 0.009026410058140755, -0.01156378723680973, -0.041559383273124695, 0.026233436539769173, 0.02967206947505474, -0.009807497262954712, -0.012728485278785229, 0.030910715460777283, -0.07169363647699356, -0.019356172531843185, 0.008966325782239437, -0.005250385031104088, -0.07350538671016693, -0.009613380767405033, 0.007944904267787933, -0.014124274253845215, -0.06111891567707062, 0.022240186110138893, -0.004423079546540976, -0.031798105686903, -0.0019330752547830343, -0.006160882767289877, -0.053095441311597824, 0.020594818517565727, 0.020724229514598846, -0.00692348275333643, 0.019189786165952682, 0.028008215129375458, -0.053095441311597824, -0.006646173540502787, 0.0011219462612643838, -0.0036003959830850363, 0.005934413988143206, -0.05376098304986954, 0.03518127650022507, -0.04984167963266373, 0.05975085869431496, 0.016250310465693474, -0.05387190729379654, -0.001146788476034999, 0.03140987083315849, -0.07014070451259613, -0.03610564023256302, 0.05993572995066643, -0.04159635677933693, 0.0655558630824089, -0.008739857003092766, -0.040561072528362274, 0.012469664216041565, -0.002071729628369212, -0.00233517331071198, 0.011896558105945587, 0.07882972061634064, -0.013606631197035313, 0.03845352306962013, -0.02974601835012436, 0.006045337300747633, -0.028895603492856026, -0.07882972061634064, 0.02331244759261608, -0.015529307536780834, 0.05775423347949982, -0.039562758058309555, -0.006008362863212824, 0.0017505134455859661, 0.057088691741228104, 0.016971314325928688, -0.046366073191165924, 0.034016579389572144, -0.007441126275807619, 0.0367896668612957, -0.03218633681535721, -0.06507518887519836, -0.025142688304185867, 0.02307211421430111, 0.008559606038033962, 0.03274095430970192, -0.06644324958324432, -0.01602846384048462, -0.043740883469581604, 0.018967939540743828, -0.030023327097296715, -0.03660479560494423, 0.061451688408851624, -0.026972927153110504, 0.03649387136101723, -0.02412588708102703, -0.019282223656773567, -0.012321765534579754, -0.014115030877292156, 0.03218633681535721, -0.028784679248929024, 0.012913358397781849, -0.0034779177512973547, 0.04263164475560188, 0.01362511795014143, -0.01602846384048462, -0.024329248815774918, -0.016860390082001686, -0.060638245195150375, -0.030448533594608307, 0.06481637060642242, 0.037751007825136185, 0.05161646008491516, -0.03978460654616356, 0.012173867784440517, 0.014420070685446262, 0.029154425486922264, -0.05416770279407501, -0.07653729617595673, 0.016758710145950317, -0.005948279052972794, -0.015427627600729465, -0.06840290129184723, -0.018718361854553223, 0.00733944633975625, 0.004242828581482172, 0.023534296080470085, -0.009474726393818855, -0.02556789480149746, 0.019337685778737068, -0.033147674053907394, -0.03116953745484352, -0.008952460251748562, 0.03590228036046028, -0.04063501954078674, -0.02249900810420513, 0.0010872825514525175, 0.010805809870362282, -0.004547868389636278, -0.04632909968495369, 0.013615874573588371, -0.018126768991351128, -0.007709191646426916, 0.04433247447013855, -0.0056894575245678425, 0.023053625598549843, -0.032075412571430206, 0.004302912391722202, -0.021741030737757683, 0.028544345870614052, 0.03736277297139168, 0.06267184764146805, -0.05368703231215477, 0.04063501954078674, 0.030503995716571808, 0.007177682593464851, -0.022609932348132133, 0.00441383570432663, 0.012025969102978706, 0.026159487664699554, -0.005731053650379181, -0.0006054581026546657, -0.03797285258769989, -0.008208348415791988, 0.031391385942697525, -0.03294431418180466, -0.016315016895532608, -0.007163817062973976, -0.05021142587065697, 0.01829315349459648, 0.004672657698392868, -0.002971828682348132, -0.029893916100263596, -0.001118479878641665, -0.013662092387676239, 0.07099112123250961, -0.06211723014712334, -0.004464675672352314, -0.018986426293849945, -0.025364534929394722, -0.021925901994109154, -0.06296764314174652, 0.023183036595582962, 0.01779399812221527, -0.0031474577262997627, 0.006766341160982847, 0.004522448405623436, 0.040376197546720505, -0.00321909599006176, 0.039377886801958084, -0.022905727848410606, 0.012534369714558125, 0.0010162221733480692, 0.016019219532608986, 0.007921795360744, 0.003403968643397093, 0.04396272823214531, 0.018783066421747208, -0.015242754481732845, 0.011887314729392529, 0.03627202287316322, 0.004078754223883152, -0.0352737121284008, -0.002344416920095682, 0.006803315598517656, 0.028969552367925644, -0.011092361994087696, 0.07524318993091583, 0.011683954857289791, -0.03124348632991314, -0.006059202831238508, -0.018967939540743828, 0.02431076020002365, -0.0276754442602396, 0.021778004243969917, 0.010824296623468399, -0.010399089194834232, 0.03148382157087326, 0.03641992434859276, -0.06518611311912537, 0.0567559190094471, -0.028008215129375458, -0.0518752820789814, -0.033018264919519424, -0.023090600967407227, -0.022831778973340988, 0.01576964184641838, 0.027712417766451836, -0.024477146565914154, -0.04976773262023926, -0.0024819159880280495, 0.020465407520532608, 0.020668769255280495, -0.01564023084938526, 0.010084806010127068, 0.01655535027384758, -0.03231574967503548, 0.015520063228905201, 0.009511700831353664, -0.0017643788596615195, 0.03566194325685501, -0.011378915049135685, 0.017664587125182152, -0.0008769899141043425, -0.013431002385914326, -0.013227641582489014, -0.0036951431538909674, -0.011295721866190434, 0.0034432541579008102, 0.042742568999528885, -0.013107474893331528, -0.015667961910367012, -0.026473771780729294, 0.01976289227604866, -0.039119064807891846, 0.006202479358762503, 0.03878629207611084, 0.030226686969399452, -0.024218324571847916, 0.00014248196384869516, 0.013125961646437645, 0.006590711884200573, -0.008642799220979214, 0.00005517294630408287, -0.006022228393703699, -0.03011576272547245, -0.01900491490960121, -0.02225867286324501, 0.02580823004245758, -0.033461958169937134, -0.015057881362736225, 0.011887314729392529, 0.010593205690383911, 0.009594893082976341, -0.012617561966180801, -0.043925754725933075, -0.016703248023986816, 0.020964564755558968, -0.030189713463187218, -0.06614745408296585, 0.0013888562098145485, -0.0023848579730838537, 0.0011161689180880785, -0.07779443264007568, -0.013264616951346397, 0.00011901180550921708, -0.017572149634361267, -0.011776391416788101, -0.04170728102326393, 0.05612735450267792, 0.007223900873214006, -0.01902340166270733, 0.008203726261854172, -0.018930964171886444, 0.006244075484573841, 0.03250062093138695, 0.0019550288561731577, -0.0041665686294436455, -0.037066977471113205, 0.010667155496776104, 0.0016638543456792831, 0.014087299816310406, -0.07265496999025345, 0.014244441874325275, -0.0032006087712943554, -0.00743650458753109, -0.019485583528876305, 0.019688943400979042, -0.0011358116753399372, 0.010352871380746365, 0.006498275324702263, 0.021962877362966537, -0.013514194637537003, -0.003598084906116128, 0.019873816519975662, 0.001386545249260962, -0.01001085713505745, -0.006914238911122084, -0.00807893741875887, 0.0009850248461589217, -0.004358374048024416, -0.048473622649908066, -0.007186926435679197, 0.025290586054325104, 0.02649225853383541, 0.02575276792049408, 0.04388878121972084, 0.008786074817180634, -0.0016950515564531088, -0.03568043187260628, -0.015510819852352142, -0.019115837290883064, 0.03224179893732071, -0.004723497666418552, 0.02281329222023487, 0.033443473279476166, -0.008531874977052212, 0.01645367033779621, 0.032204825431108475, 0.012090674601495266, 0.011092361994087696, 0.04377785697579384, 0.0434081107378006, 0.0037482939660549164, -0.0012767771258950233, 0.022905727848410606, 0.006354999262839556, -0.012155380100011826, 0.011166311800479889, 0.0064705447293818, 0.012377227656543255, -0.003796823089942336, 0.00814826413989067, 0.03897116705775261, 0.033942628651857376, 0.022369597107172012, 0.02225867286324501, -0.01283940952271223, 0.06389200687408447, -0.04551566019654274, -0.02549394592642784, -0.040302250534296036, 0.02749057114124298, 0.003722873982042074, -0.012192354537546635, -0.02288724109530449, 0.04270559549331665, -0.008869268000125885, -0.03416447713971138, 0.030762817710638046, -0.00981674063950777, 0.023330936208367348, 0.00041047518607228994, -0.013181423768401146, -0.005620130337774754, 0.0034686741419136524, 0.023608244955539703, -0.029524171724915504, 0.01178563479334116, -0.06929028779268265, -0.042114000767469406, -0.012340253219008446, -0.0006794072105549276, 0.021611619740724564, 0.006775584537535906, -0.031798105686903, -0.02693595364689827, 0.02861829474568367, 0.052466873079538345, -0.04081989452242851, 0.0029533414635807276, -0.041374512016773224, 0.01981835439801216, 0.046476997435092926, -0.015695692971348763, -0.0014339189510792494, 0.029468709602952003, 0.0012513571418821812, -0.003734428668394685, -0.0026067050639539957, 0.037011515349149704, -0.01371755450963974, 0.017137698829174042, 0.014993175864219666, -0.022295648232102394, 0.016564594581723213, -0.05413072928786278, -0.006086933892220259, 0.054722320288419724, 0.008730613626539707, 0.010204973630607128, 0.0019527178956195712, -0.06030547618865967, -0.021925901994109154, -0.008069693110883236, 0.0030411561019718647, -0.024403197690844536, 0.010306653566658497, -0.011979751288890839, 0.026473771780729294, -0.05671894550323486, -0.023164549842476845, -0.002567419782280922, 0.023977989330887794, -0.008550362661480904, -0.0027546032797545195, -0.024458657950162888, -0.0069465916603803635, -0.015002420172095299, 0.05867859721183777, 0.013477220200002193, 0.060638245195150375, -0.05117276310920715, -0.00549996318295598, -0.030393073335289955, -0.01078732218593359, 0.012552856467664242, -0.005065511912107468, 0.0014720489270985126, 0.06330041587352753, 0.007089868187904358, 0.0486215204000473, 0.0034247669391334057, -0.055461812764406204, 0.015205780044198036, 0.0068865083158016205, 0.016647787764668465, -0.024532608687877655, -0.005837355740368366, 0.04425852373242378, 0.051209740340709686, 0.016934338957071304, 0.003189054084941745, 0.032759442925453186, -0.013523438014090061, 0.013957888819277287, 0.005712566431611776, -0.0016938961343839765, 0.00427749240770936, 0.014983932487666607, 0.02462504431605339, 0.01802508905529976, -0.03340649604797363, -0.005509206559509039, -0.01197050791233778, -0.002872459590435028, 0.005666348617523909, -0.0486215204000473, 0.012220085598528385, -0.0486215204000473, -0.01883852854371071, -0.0233863964676857, 0.021537670865654945, -0.011702442541718483, 0.03592076525092125, -0.015251997858285904, -0.02693595364689827, 0.011249504052102566, -0.00042491836939007044, -0.014919226989150047, 0.004582532215863466, -0.06592560559511185, 0.028267037123441696, 0.051283687353134155, -0.003392414189875126, -0.011489838361740112, -0.020687256008386612, 0.001659232540987432, -0.05279964581131935, -0.027083851397037506, 0.009992369450628757, 0.010620936751365662, 0.02898803912103176, -0.014309147372841835, -0.020243560895323753, -0.02774939313530922, 0.007353311870247126, 0.04507196694612503, 0.00598525395616889, 0.05102486535906792, 0.01920827478170395, -0.018810797482728958, 0.029357785359025, -0.01894945278763771, -0.021408259868621826, -0.0028216196224093437, 0.04000645503401756, 0.018727604299783707, -0.03849049657583237, -0.0075844028033316135, -0.02967206947505474, -0.01702677644789219, -0.014466289430856705, -0.025586381554603577, -0.015039394609630108, -0.04932403936982155, 0.008245322853326797, 0.058900441974401474, 0.0034109014086425304, 0.0217040553689003, 0.10153208673000336, -0.04721648991107941, 0.01866289973258972, -0.04651397094130516, 0.026214949786663055, 0.010325140319764614, -0.0017713116249069571, 0.008300784043967724, 0.027287211269140244, -0.029782991856336594, 0.012257060036063194, -0.024828404188156128, -0.007810871582478285, -0.027546033263206482, -0.007524318993091583, -0.00604995945468545, -0.0022877997253090143, -0.01698055863380432, -0.03349893540143967, -0.013320078141987324, 0.031021639704704285, 0.014734354801476002, 0.01477132923901081, 0.0029533414635807276, 0.023719167336821556, 0.029135938733816147, 0.09058762341737747, -0.035440098494291306, -0.008504144847393036, -0.003272246802225709, -0.00834238063544035, 0.021796490997076035, 0.00018299509247299284, 0.024976301938295364, 0.046846743673086166, -0.0023848579730838537, -0.04440642520785332, -0.0335359089076519, -0.044480372220277786, -0.0069928099401295185, 0.051542509347200394, -0.03242667391896248, 0.02299816533923149, -0.02769393101334572, 0.050285376608371735, -0.004741984885185957, -0.02438470907509327, -0.03281490504741669, -0.017988113686442375, 0.003660479560494423, -0.03547707200050354, 0.021685568615794182, -0.03564345836639404, 0.02438470907509327, 0.016324259340763092, 0.006128530018031597, -0.04244677349925041, 0.006544493604451418, -0.0336468331515789, -0.00911884568631649, 0.015649475157260895, -0.05705171823501587, -0.03930393606424332, 0.01870911754667759, 0.02312757447361946, -0.029450220987200737, -0.016749467700719833, -0.004564044997096062, 0.01792340911924839, -0.02725023590028286, -0.060453373938798904, 0.021741030737757683, 0.003445565002039075, 0.011674711480736732, -0.008314649574458599, -0.0004237628891132772, 0.0043861051090061665, 0.012543613091111183, -0.004143459256738424, -0.011573031544685364, 0.012164624407887459, 0.013606631197035313, -0.031465332955121994, 0.0300603024661541, 0.011952020227909088, -0.01902340166270733, -0.05834582448005676, 0.026159487664699554, -0.0006840290152467787, 0.005125595722347498, -0.03886024281382561, -0.011831853538751602, 0.04070897027850151, -0.011360427364706993, -0.014235198497772217, 0.0234973207116127, 0.023959502577781677, 0.027767879888415337, -0.0022519805934280157, -0.019873816519975662, -0.0036466140300035477, 0.014669649302959442, 0.018884746357798576, 0.015538550913333893, 0.03492245450615883, 0.02499479055404663, -0.008476413786411285, 0.02998635172843933, -0.003843041369691491, -0.015288972295820713, 0.002182653406634927, 0.008915485814213753, 0.005666348617523909, 0.0023964124266058207, 0.0011583430459722877, 0.013754528947174549, 0.010380602441728115, -0.007833980955183506, 0.0070020537823438644, -0.000027586473152041435, -0.025142688304185867, -0.01269151084125042, -0.058382801711559296, -0.056090377271175385, -0.0003986317606177181, -0.005255006719380617, -0.015963757410645485, -0.028710730373859406, 0.08859100192785263, -0.03200146555900574, 0.011120093055069447, -0.03177961707115173, -0.003403968643397093, -0.01203521341085434, 0.05579458177089691, -0.063707135617733, -0.0012929535005241632, -0.03373926877975464, 0.016435183584690094, -0.00637810816988349, -0.0369005911052227, 0.022739343345165253, -0.0037043867632746696, -0.01362511795014143, -0.01639820821583271, -0.019966252148151398, -0.007362555246800184, -0.03967368230223656, -0.01283940952271223, 0.0434081107378006, -0.01860743761062622, 0.0251241996884346, -0.01957801915705204, -0.02848888374865055, -0.02249900810420513, 0.0007608667365275323, 0.004122661426663399, 0.006904995534569025, 0.012571344152092934, -0.0015922161983326077, -0.005010050255805254, 0.021778004243969917, -0.05254082381725311, -0.028082164004445076, 0.0025651087053120136, 0.020539358258247375, -0.017313329502940178, 0.05357610806822777, -0.014281416311860085, 0.015612499788403511, -0.0017978870309889317, -0.02712082490324974, 0.05143158510327339, 0.021722542122006416, 0.015020906925201416, 0.052023179829120636, 0.023109087720513344, 0.021648593246936798, 0.00637810816988349, -0.0420030802488327, -0.04658792167901993, 0.026640156283974648, -0.004298290237784386, -0.02617797441780567, -0.0002339795173611492, -0.05387190729379654, 0.007607511710375547, -0.004820555914193392, -0.016878878697752953, 0.04984167963266373, -0.026270411908626556, 0.021778004243969917, -0.023959502577781677 ]