
hopefield network

hopefield network (allengil amari-hopefield network, oru neural netvarkkinte icing model allengil icing-lense-littil model) aavarthichulla krithrima neural netvarkkinte oru roopavum 1982 ll joonn hopefield janapriyamaakkiya oru tharam spin glass sistavumaanu. 
1974ll wilhem lensumaayi chernnu icing modalil nadatthiya pravartthanatthe adisthaanamaakki. hopefield netvarkkukal bainari threashold nodukalulla allengil thudarchayaaya veriyabilukalulla ulladakka-vilaasamulla ("associative") memory sistangalaayi pravartthikkunnu. hopefield netvarkkukal manushyante oormma manassilakkunnathinulla oru maathrkayum nalkunnu.
uthbhavam.
oru laining memory modalaayi aavarthichulla neural netvarkkinte icing model aadyam nirddeshichathu 1972 ll shunnichi amari pinneedu vilyam eiii. 1974ll, hopefield 1982leeii thante prabandhatthil addehathe amgeekarichu. thudarchayaaya chalanathmakathayulla shringalakal hopefield thante 1984 leeii prabandhatthil vikasippicheduthu. network dynamicsilum oorjja pravartthanatthilum vanna maattatthiloode 2016ll crotove hopefield memory sambharana seshiyil oru pradhana munnettam vikasippichu. 2017ll demirsijilum sahakaarikalum eee ashayam kooduthal vipuleekarichu. valia memory kappasitti modalukalude thudarchayaaya chalanathmakatha 2016num 2020num idayil niravadhi pepparukalilaayi vikasippicheduthu. valia memory storeju kappasitti hopefield nettvarkkukale ippol dense associative memmarikal allengil aadhunika hopefield netvarkkukal ennu vilikkunnu.
ghadana.
hopefield nettukalile unitukal bainari threashold yoonittukalaan, athaayath.iii. unitukal avayude avasthakalkku rund vyathyastha moolyangal maathrame edukkunnulloo, yoonittinte inputt athinte threashold formula _ 1 kaviyunnundo illayo ennathine adisthaanamaakkiyaanu moolyam nirnnayikkunnath. discreet hopefield nettukal bainari (firing allengil nottu-firing) neuron formula _ 2 thammilulla bandhathe vivarikkunnu. oru nischitha samayat, neural nettinte avasthaye oru vekttar formula _ 3 vivarikkunnu, ithu eathu neuronukal formula _ 4 bittukalude bainari padatthil fayar cheiyunnu ennu rekhappeduthunnu.
neuronukal thammilulla parasparapravartthana soothravaakyam _ 5 nuu saadhaaranayaayi 1 allengil −1 moolyangal edukkunna unitukal undu, eee kanvenshan eee lekhanathiludaneelam upayogikkum. ennirunnaalum, mattu saahityangal 0,1 ennivayude moolyangal edukkunna unitukal upayogichekkaam. eee edapedalukal hebinte association niyamathiloode "padicha" aanu, athaayath, oru prathyeka avastha formula _ 6 num vyathyastha nodukal formula _ 7 num. 
soothravaakyam _ 8
ennaal formula _ 9.
network parisheelichukazhinjaal, formula _ 5 inii vikasikkilla. neuron formula _ 13 enna puthiya avastha neural netvarkkil avatharippikkukayaanenkil, nettu neuronukalil pravartthikkunnu.
ivide soothravaakyam _ 18 ennathu i 'th neuroninte threashold moolyamaanu (palappozhum 0 aayi kanakkakkunnu). eee reethiyil, hopefield netvarkkukalkku interaakshan maatriksil sambharichirikkunna avasthakal "oormmikkaanulla" kazhivundu, kaaranam oru puthiya stettu formula _ 19 interaakshan matrixinu vidheyamaanengil, oro neuron yadhaartha stettu formula _ 20-maayi poruthappedunnathuvare maarum (chuvadeyulla apdettukal vibhaagam kaanuka).
oru hopefield nettile kanakshanukalkku saadhaaranayaayi inipparayunna niyanthranangalund
bharangal samamithiyaanenna niyanthranam sajeevamaakkal niyamangal paalikkumbol oorjja pravartthanam ekathaanamaayi kurayunnuvennu urappu nalkunnu. asamamaya bharamullah oru network chila aanukaalikamo araajakathvamo aaya swabhaavam prakadippichekkaam; ennirunnaalum, eee swabhaavam ghatta idathinte thaarathamyena cheria bhaagangalil parimithappedutthiyittunne ulladakka-vilaasamulla associative memory sisttamaayi pravarthikkaanulla netvarkkinte kazhivine thadassappeduthunnilnum hopefield kandethi.
hopefield thudarchayaaya moolyangalkkaayi neural nettukale maathrkayaakki, athil oro neuroninteyum vaidyutha outtputtu binarialla, marichu 0 num 1 num idayil chila moolyamaanu. itharathilulla netvarkkinu oormmappeduthiyittalla avasthakal sambharikkaanum punarnirmmikkaanum kazhiyumennu addeham kandethi.
oru hopefield nettvarkkile oro jody unitukalaaya "i", "j" ennivaykku connectivity veytt formula _ 5 vivarikkunna oru kanakshan undennu shradhikkuka. eee ardhathil, hopefield nettvarkkine aupachaarikamaayi oru poornnamaaya dishaabodhamillaatha graph formula _ 24 aayi vivarikkaam, ivide formula _ 25 ennathu mccullock-pitt neuronukalude oru koottamaanu, formula _ 26 ennathu yoonittukalude jodikale oru yadhaartha moolyavumaayi bandhippikkunna oru pravarthanamaanu, connectivity bharam.
update cheiyunnu.
hopefield shringalayile oru yoonit (krithrima neuronine anukarikkunna graphile nooad) update cheiyunnathu inipparayunna niyamam upayogichaan
soothravaakyam _ 27
evide
hopefield nettvarkkile apdettukal rund vyathyastha reethikalil nadatthaam
neuronukal avasthayil "parasparam aakarshikkukayo pinthirippikkukayo cheiyunnu".
rund unitukalkkidayilulla bharam neuronukalude moolyangalil sakthamaaya swaadheenam cheluthunnu. i, j ennee rund neuronukal thammilulla kanakshan veytt formula _ 28 pariganikkuka. formula _ 32 aanenkil, update cheiyunna niyamam soochippikkunnathu
athinaal, neuronukal thammilulla bharam positteev aanenkil "i", "j" ennivayude moolyangal othucherum. athupole, bharam negatteevu aanenkil avaa verpiriyunnu.
vyathirikthavum thudarchayaayathumaaya hopefield nettvarkkukalude pravartthana thathwangal.
1990-ll thante prabandhatthil discreet hopefield nettvarkkile oru neuroninte samyojanam theliyikkumbol bruck athinte swabhaavathekkurichu velicham veeshunnu. thudarnnulla oru prabandham discreet-time, condinues-time hopefield netvarkkukalile eathenkilum neuroninte swabhaavam kooduthal anweshichu. neuron "jeey" athinte avastha maattunnuvenn bruck kaanikkunnu, "athu inipparayunna pakshapathaparamaaya suedo-katt kurachaal maathram. hopefield network hopefield nettinte synaptic veytt matrixinaayi inipparayunna pakshapathaparamaaya suedo-katt kuraykkunnu.
soothravaakyam _ 39
formula _ 40 umm formula _ 41 umm yathaakramam −1 umm + 1 umm aaya neuronukalude koottatthe prathinidheekarikkunnu, time formula _ 42 ll. kooduthal vishadaamshangalkku, sameepakaala paper kaanuka.
discreet-time hopefield network ellaayppozhum thaazhepparayunna kapada-katt krithyamaayi kuraykkunnu
thudarchayaaya samaya hopefield shringhala ellaayppozhum thaazhepparayunna waited katt oru upper boundu kuraykkunnu
ivide formula _ 45 oru seero-centered sigmoid functionaanu.
maruvashathu, sankeernamaaya hopefield shringhala saadhaaranayaayi nettinte sankeernamaaya bhaara maatriksinte shado-katt ennu vilikkappedunnava kuraykkunnu.
oorjjam.
hopefield nettukalkk netvarkkinte oro avasthayumaayi bandhapetta oru scaler moolyamundu, athine netvarkkinte "oorjjam" ennu vilikkunnu, iii, evide
network unitukal update cheyyumbol ithu kurayukayo athepadi thudarukayo cheiyunnathinaal eee alavine "oorjjam" ennu vilikkunnu. koodaathe, aavarthichulla updatinginu keezhil network oduvil oorjja pravartthanatthile oru praadeshika minimum avasthayilekku (ithu oru liapunov functionaayi kanakkaakkappedunnu) othucherum. athinaal, oru samsthaanam oorjja pravartthanatthil oru praadeshika minimum aanenkil athu netvarkkinu sthirathayulla oru avasthayaanu. eee oorjja pravartthanam icing modalukalude peril bhauthikashaasthrathile oru pothu klaas modalukalil pedunnathaanennu shradhikkuka; iva markov nettvarkkukalude oru prathyeka kesaanu, kaaranam anubandha probability alavu, gibbs alavu, markov property undu.
optimaiseshanil hopefield network.
1985-ll hopefield tank classical travelling-salesman prashnam pariharikkunnathin hopefield network aaplikkeshan avatharippichu. athinusesham, hopefield network optimaiseshanaayi vyaapakamaayi upayogikkunnu. opttimaiseshan prasnangalil hopefield network upayogikkuka enna ashayam neraanu hopefield energy function iii roopathil oru niyantritha/aniyanthrithamaaya chelavu function ezhuthaan kazhiyumenkil, santulita pooyintukal parimithamaaya/aniyanthrithamaaya opttimaiseshan prashnathinulla parihaarangale prathinidheekarikkunna oru hopefield network nilavilundu.  hopefield oorjja pravartthanam kuraykkunnathu vasthunishtamaaya pravartthanam kuraykkunnu, koodaathe netvarkkinte synaptic bhaarangalil niyanthranangal ulcherthirikkunnathil parimithikale thripthippeduthunnu. synaptic bhaarangalilekku opttimaiseshan parimithikal saadhyamaaya ettavum mikacha reethiyil ulppeduthunnathu oru velluvili niranja joliyaanengilum, vividha vishayangalile parimithikalulla niravadhi budhimuttulla opttimaiseshan prasnangal hopefield energy functionaayi parivartthanam cheythittunda associative memory sisttangal, analog-tuu-digital parivartthanam, job-shope sheduling prashnam, quadratic assainmentum mattu anubandha enpi-poornnamaaya prashnangalum, wireless netvarkkukalile chaanal alokkeshan prashnam, mobail addu-hoock network ruting prashnam, imej restoration, sisttam identification, kompinettoriyal opttimaiseshan muthalaayava. kooduthal vishadaamshangal iii. yill kaanam.jii. paper.
aarambikkunnathum pravarthippikkunnathum.
yoonittukalude moolyangal aavasyamulla staartt paattenilekk krameekarichaanu hopefield nettvarkkukalude arambham nadathunnathu. network oru aakarshakamaaya paattenilekk othucherunnathuvare aavarthichulla apdettukal nadathunnu. eee nonleeniyar dynamical sisttathinte akarshanangal sthirathayullathaanennum mattu chila sistangalilennapole aanukaalikamo araajakathvamo allennum hopefield theliyichathinaal, othucheral pothuve urappaan. athinaal, hopefield nettvarkkukalude pashchaathalatthil, oru aakarshakamaaya paatten oru anthima sthirathayulla avasthayaanu, updatinginu keezhil athinullile oru moolyavum maattaan kazhiyaatha oru paatten.
pariseelanam.
oru hopefield nettu parisheelippikkunnathil nettu "oormmikkenda" avasthakalude oorjjam kuraykkunnathu ulppedunnu. ithu nettine oru ulladakka adrus cheyyaavunna memory sisttamaayi pravartthikkaan anuvadikkunnu, athaayath, samsthaanathinte oru bhagam maathram nalkiyaal network oru "oormmikkappedunna" avasthayilekku othucherum. valachodicha inputtil ninnu aaa inputtinodu ettavum saamyamulla pariseelanam labhicha avasthayilekku veendedukkaan nettu upayogikkaam. samaanathayude adisthaanathil oormmakal veendedukkunnathinaal ithine associative memory ennu vilikkunnu. udaaharanathinu, anchu yoonittukalulla oru hopefield nettine parisheelippikkukayaanenkil, aaa avastha (1,, −1,1, −1,1) oru oorjja minimum aakukayum, netvarkkinu (1,, −1, −1, −1) enna avastha nalkukayum cheythaal athu (1,, −1,1, −1,1) aayi othucherum. athinaal, network oormmikkenda avasthakalude oorjjam praadeshika minimayaayirikkumbol network shariyaayi parisheelippikkappedunnu. perseptron parisheelanathinu vipareethamaayi, neuronukalude paridhi orikkalum update cheyyappedunnilla ennathu shradhikkuka.
patana niyamangal.
hopefield netvarkkinte oormmayil vivarangal sambharikkaan vividha patana niyamangalund. oru patana niyamathinu inipparayunna rund gunangalum undaayirikkendathu abhikaamyamaanu
eee gunangal abhikaamyamaanu, kaaranam avaye thripthippeduthunna oru patana niyamam jaivashaasthraparamaayi kooduthal vishwasaneeyamaanu. udaaharanathinu, manushya masthishkam ellaayppozhum puthiya ashayangal padikkunnathinaal, manushya patanam vardhichuvarunnathaanenna oraalkk nyaayeekarikkam. vardhanavu illaatha oru patana samvidaanam saadhaaranayaayi oru thavana maathrame parisheelippikkukayulloo, oru valia baachu pariseelana daatta.
hopefield netvarkkukalkkulla hebbian patana niyamam.
1949-ll donald hebb "associative laining" vishadeekarikkunnathinaayi hebbian sidhaantham avatharippichu, athil neuron koshangalude oresamayam sajeevamaakunnath aaa koshangal thammilulla synaptic shakthiyil vyakthamaaya vardhanavinu kaaranamaakunnu. orumichu thee koluthunna, orumichu vayar cheiyunna neuronukal" ennaanu ithine palappozhum samgrahikkunnathu. samanvayippikkaathe theepidikkunna neuronukal bandhippikkunnathil paraajayappedunnu.
hebbian bharanam praadeshikavum vardhichuvarunnathumaan. hopefield netvarkkukalkkaayi, formula _ 47 padikkumbol ithu inipparayunna reethiyilaan nadappilaakkunnathu.
bainari paattenukal
soothravaakyam _ 48
ivide formula _ 49 paatten formula _ 50 ll ninnulla bitt i yeei prathinidheekarikkunnu.
neuronukal i, j ennivayumaayi bandhapetta bittukal paatten formula _ 50 ll thulyamaanengil, uthppanna formula _ 52 positteev aayirikkum. ithu, bharam formula oru nalla prabhavam cheluthukayum i, j ennivayude moolyangal thulyamaakukayum cheyyum. neuronukalaaya i, j ennivaykku anuyojyamaaya bittukal vyathyasthamaanenkil nere vipareethamaanu sambhavikkunnath.
storkki patana niyamam.
1997ll amos storkki avatharippicha eee niyamam praadeshikavum vardhichuvarunnathumaan. eee niyamam upayogichu pariseelanam labhicha oru hopefield netvarkkinu hebbian niyamam upayogichu pariseelanam labhicha anubandha nettvarkkinekkaal kooduthal sheshiyundennum storkki kaanichu. oru aakarshakamaaya neural netvarkkinte veytt matricks anusarikkukayaanenkil storkki laining niyamam paalikkumenn parayappedunnu
formula _ 54
ivide neuron i-leeii "local feeld"-nte oru roopamaanu formula _ 55.
synapsukal avayude vashangalile neuronukal maathram kanakkiledukkunnathinal eee patana niyamam praadesikamaanu. praadeshika feeldinte swaadheenam kaaranam, pothuvalkkaricha hebbian niyamathekkaal paattenukalil ninnum thookkangalil ninnumulla kooduthal vivarangal niyamam upayogikkunnu.
vyaja paattenukal.
parisheelanathinaayi network upayogikkunna paattenukal ("veendedukkal avasthakal" ennu vilikkunnu) sisttathinte aakarshakangalayi maarunnu. aavarthichulla apdettukal oduvil veendedukkal avasthakalilonnil othucherunnathilekku nayikkum. ennirunnaalum, chilappol network vyaja paattenukalilekku (pariseelana paattenukalil ninnu vyathyasthamayi) othucherum. eee vyaja paattenukalile oorjjavum oru praadeshika minimum aanu. oro sambharicha paatten x-num, nishedham-x oru vyaja paatten aanu.
oru vyajaavastha ennathu otappetta ennam veendedukkal avasthakalude oru rekheeya samyojanavum aakam. udaaharanathinu, 3 paattenukal formula _ 56 upayogikkumbol, oraalkk inipparayunna vyaja avastha labikkum
soothravaakyam _ 57
poojyathilekku koodaan saadyathayullathinaal thulya ennam avasthakalulla vyaja paattenukal nilanilkkilla.
sheshi.
hopefield network modalinte network sheshi nirnnayikkunnath oru nischitha netvarkkinullile neuron alavukalum kanakshanukalum anusarichaanu. athinaal, sambharikkaan kazhiyunna oormmakalude ennam neuronukaleyum kanakshanukaleyum aasrayichirikkunnu. koodaathe, vektarukalum nodukalum thammilulla thirichuvilikkal krithyatha 0.138 aanennu kaanichu (oro 1000 nodukalkkum sambharanathil ninnu ekadesham 138 vektarukal thirichuvilikkaan kazhiyum) (hearts thudangiyava.1991). athinaal, oraal dhaaraalam vektarukal sambharikkaan sramichaal niravadhi thettukal sambhavikkumennu vyakthamaan. hopefield model sariyaaya paatten oormmikkaathappol, oru nuzhanjukayattam nadannirikkaam, kaaranam ardhavumaayi bandhapetta enangal vyakthiye aashayakkuzhappathilaakkum thettaaya paatten oormmikkukayum cheiyunnu. athinaal, hopefield network model veendedukkumbol oru sambharicha inathe mattonninumayi aashayakkuzhappathilaakkunnathu kaanikkunnu. mikacha thirichuvilikkalum uyarnna seshiyum,> 0.14, storkki laining reethi vazhi netvarkkil looad cheyyaan kazhiyum; ettam, ettam pareekshanangalum. hopefield shringalayil ninnu prachodanam ulkkonda ulterior modalukal pinneedu sambharana paridhi uyarthunnathinum veendedukkal pishak nirakk kuraykkunnathinum roopakalppana cheythu, chilath otta shoat padanatthinu praapthamaanu.
sambharana sheshi formula _ 58 aayi nalkaam, ivide formula _ 47 nettile neuronukalude ennamaanu.
manushya oormma.
memory vektarukal samyojippikkunnathiloode hopefield model associative memoric kaaranamaakunnu. memory vektarukal cheruthaayi upayogikkaam, ithu nettvarkkile ettavum samanamaaya vektarinte veendedukkalinu kaaranamakum. ennirunnaalum, eee prakriya kaaranam nuzhanjukayatangal sambhavikkaamenn njangal kandethum. hopefield netvarkkinulla associative memmariyil, rund tharam pravarthanangalundu oottoo-association, hettero-association. aadyathethu oru vekttar thannodu thanne bandhappettirikkumbol, randaamathethu sambharanathil rund vyathyastha vekttarukal bandhappettirikkumbol. koodaathe, rund tharatthilulla pravartthanangalum orotta memory matrixinullil sambharikkaan kazhiyum, ennaal aaa praathinidhya matricks onno allengil mattoo pravarthanangalallenkil, marichu randinteyum samyojanam (oottoo-associative, hettero-associative) aanenkil maathram. hopefieldinte network model hebinte (1949) patana niyamatthinte athe patana niyamam upayogikkunnu ennathu sradhikkendathaanu, ithu adisthaanaparamaayi pravartthanam nadakkumbol bharam shakthippeduthunnathinte falamaayaanu patanam sambhavikkunnathenn kaanikkan shramichu.
oru probabilistik-laining algoritam ulppeduthunnathiloode oormmappeduthal krithyathayude aavarthanathinu neural network modalinu kaaranamaakumenn kaanikkan resuitoic kahanaykkum (2001) kazhinju. veendedukkal prakriyayil, oru padanavum nadakkunnilla. thalphalamaayi, netvarkkinte bharam sthiramaayi thudarunnu, ithu modalinu oru patana ghattathil ninnu thirichuvilikkunna ghattathilekku marran kazhiyumennu kaanikkunnu. sandarbhochithamaaya vyathiyaanam cherkkunnathiloode oru cude-rikkal task samayat oru hopefield modalil sambhavikkunna druthagathiyilulla marakkal kaanikkan avarkk kazhinju. eathu orotta nodinteyum sajeevamakkalil maattam varuthaan muzhuvan netvarkkum sambhavana cheiyunnu.
neuronukalude swabhaavam vivarikkunna mccullock aandu pitts (1943) dynamic ruul, onniladhikam neuronukalude sajeevamaakkal oru puthiya neuroninte firing nirakk sajeevamaakkunnathilekk engane mapp cheiyunnuvennum neuronukalude bharam engane shakthippeduthunnuvennum kaanikkunna vidhathilaan angane cheiyunnathu. hopefield netvarkkil veendedukkal engane saadhyamaanennu kaanikkunnathin hopefield mccullock-pitsinte chalanathmaka niyamam upayogikkum. ennirunnaalum, hopefield athu aavarthichulla reethiyil cheiyumennathu sradhikkendathaanu. hopefield oru leanier function upayogikkunathinupakaram oru nonleeniyar aaktiveshan function upayogikkum. athinaal ithu hopefield dynamic niyamam srishtikkum, ithu upayogichu, nonleeniyar aaktiveshan function upayogichu, dynamic niyamam ellaayppozhum store cheytha paattenukalilonninte dishayil stettu vektarinte moolyangal parishkkarikkumenn kaanikkan hopefieldinu kazhinju.
dense associative memory allengil aadhunika hopefield network.
sthira pooyint aakarshakamaaya avasthakalilekku othucherunna chalanathmaka sanjaarapathangalulla aavarthichulla neural netvarkkukalaanu hopefield netvarkkukal, avaye oru oorjja pravartthanam vivarikkunnu. oro model neuron formulayude avasthayum nirvachikkunnath samayathe aashrayichirikkunna variable formulayanu, athu vyathirikthamo thudarchayullatho aayi thiranjedukkaam. oro neuroninteyum bhaaviyile pravartthanam ellah neuronukaludeyum nilavilullatho munbullatho aaya pravartthanatthe engane aasrayichirikkunnu ennathinte ganithathe oru samboornna maathruka vivarikkunnu.
associative memmariyude yadhaartha hopefield maathrkayil, variableukal bainarikalaayirunnu, neuronukalude avasthayude oru thavana update cheythaanu chalanathmakatha vivarichathu. 61 enna soothravaakyathile oru oorjja pravartthanatthe quadratic aayi nirvachichu, angane cheiyunnathu sisttathinte motham oorjjam kuraykkunnundengil maathrame oro neuron soothravaakyathinteyum pravartthanam maattunnath dynamicsil ulppedukayulloo. neuron formula 63-nte aouttputtine prathinidheekarikkunna oru thudarchayaaya variable aaya formula 61-nuu, formula 61 oru inputt karantinte monotonic function aayirikkunnathilekkum ithe ashayam vyapippichu. sisttathinte "oorjjam" ellaayppozhum kurayunna phastt-oordar deferential samavaakyangalude oru koottamaayi chalanathmakatha prakadippikkappettu.  thudarchayaaya kesil oorjjathinu 61 enna soothravaakyathil (bainari modalilennapole) chathuraakrithiyilulla oru padavum geyin functione (neuroninte aaktiveshan function) aashrayichirikkunna randaamathe padavum undu. associative memmariyude niravadhi abhikaamyamaaya gunangal ullappol, eee rund classical sisttangalum cheria memory sambharana sheshi anubavikkunnu, ithu inputt savisheshathakalude ennathinanusarichu rekheeyamaayi skeyil cheiyunnu.
inputt savisheshathakalude ennavum sambharichirikkunna oormmakalude ennavum thammilulla leanier scaling bandhathe thakarkkunna classical hopefield nettvarkkukalude saamaanyavalkkaranangalaanu dense associative memmarikal (aadhunika hopefield netvarkkukal ennum ariyappedunnu). savisheshathayulla neuronukalude ennathinte pravartthanamaayi suuppar-leanier (exponential) memory sambharana sheshiyilekk nayikkunna sakthamaaya noonn-linearitykal (oorjja pravartthanatthilo neuronukalude sajeevamaakkal pravartthanangalilo) avatharippikkunnathiloode ithu kaivarikkunnath. netvarkkinu ippozhum mathiyaya ennam maranjirikkunna neuronukal aavasyamaanu.
aadhunika hopefield netvarkkukalkku pinnile pradhana saidhaanthika ashayam classical hopefield nettvarkkumaayi thaarathamyappeduthumbol neuroninte konfigareshanukalude idathile sambharicha memmarikalkku chuttum kooduthal kuthane uyarunna oru oorjja pravartthanavum update niyamavum upayogikkuka ennathaanu.
vyathirikthamaya variableukal.
aadhunika hopefield shringalayude oru lalithamaaya udaaharanam, sajeevamaaya soothravaakyathe prathinidheekarikkunna bainari variable formula _ 61-nte adisthaanathil ezhuthaam, koodaathe model neuroninte nishkriyamaaya soothravaakyam _ 70 avasthaye prathinidheekarikkunnu, eee soothravaakyam bhaara soothravaakyam _ 73 memory vektarukalude maatriksine prathinidheekarikkunnu (soochika soothravaakyam _ 74 vyathyastha memmarikal kanakkakkunnu, soochika soothravaakyam _ 75 formula _ 63-aamm savisheshatha neuronumaayi bandhapetta oro memmariyudeyum ulladakkam kanakkakkunnu), koodaathe function formula _ 77 athivegam valarunna noonn-leanier functionaanu. vyakthigatha neuronukalude (asinkranas kesil) update niyamam inipparayunna formula 78 ll ezhuthaam, ithu formula 79-th neuroninte update cheytha avastha kanakkaakkunnathin network rund oorjjangale thaarathamyam cheiyunnuvennu prasthaavikkunnu oonn avasthayil formula 63-th neuronulla netvarkkinte oorjjavum backie neuroninte avastha kanakkiledukkumbol oof avasthayil formula 63-th neuronulla netvarkkinte oorjjavum. 63-aamm neuron enna soothravaakyathinte naveekaricha avastha rund oorjjangalil ettavum kuranja avastha thiranjedukkunnu.
parimithappedutthunna saahacharyathil noonn-leanier energy function quadratic formula _ 83 aayirikkumbol eee samavaakyangal parichithamaaya energy functionilekkum classical bainari hopefield netvarkkinte update niyamathilekkum kurayunnu.
eee nettvarkkukalude memory sambharana sheshi kramarahithamaya bainari paattenukalkkaayi kanakkakkaam. power energy function formulakku _ 84 pishakukalillathe eee netvarkkil ninnu sambharikkaanum veendedukkaanum kazhiyunna memmarikalude paramavadhi ennam oru exponential energy function formulakku biformula nalkunnu _ 86 savisheshatha neuronformulayude ennathil memory sambharana sheshi exponentialaanu _ 87
thudarchayaaya variableukal.
aadhunika hopefield netvarkkukal allengil saandramaaya associative memmarikal thudarchayaaya veriyabilukalilum thudarchayaaya samayathilum nannayi manassilakkaan kazhiyum. fig.1 ll kaanichirikkunna network architecture neuroninte avasthakalude parinaamathinulla samavaakyangalum pariganikkuka, avide savisheshatha neuronukalude vaidyuthadhaarakal formula _ 88 kondu soochippikkunnu, memory neuronukalude vaidyuthadhaarakal formula _ 89 kondu soochippikkunnu (formula _ 90 maranjirikkunna neuronukale soochippikkunnu). savisheshatha neuronukalkko memory neuronukalkko idayil synaptic kanakshanukalonnumilla. oru matricks formula _ 91 oru feature neuron formula _ 63 muthal memory neuron formula _ 50 vareyulla sinaapsukalude sakthiye soochippikkunnu. synapsukal cemetric aanennu anumaanikkappedunnu, athinaal athe moolyam memory neuron formula _ 50 muthal feature neuron formula _ 63 vare vyathyasthamaaya physical sinaapsinte swabhaavamaanu. memory neuronukaludeyum feature neuronukaludeyum aouttputtukal formula _ 96, formula _ 97 ennivayaal soochippikkunnu, avaa anubandha vaidyuthadhaarakalude noonn-leanier functionukalaanu. pothuve eee aouttputtukal aaa paaliyile ellah neuronukaludeyum vaidyuthadhaaraye ashrayichirikkum, athinaal formula 98 umm formula 99 umm. eee aaktiveshan functionukale neuronstinte rund grouppukalude lagranchian functionukalude derivateevukalaayi nirvachikkunnath soukaryapradamaanu. eee reethiyil neuroninte avasthakalkkaayulla samavaakyangalude nirddishta roopam lagranchian functionukal vyakthamaakkikkazhinjaal poornnamaayum nirvachikkappedunnu. avasaanamaayi, neuronukalude rund grouppukalude samaya sthiraangangale formula 100, formula 101 ennivayaal soochippikkunnu, formula 102 ennathu netvarkkilekkulla inputt karantaanu, athu avatharippicha dattayaal nayikkaan kazhiyum.  
noonn-leanier deferential samavaakyangalude pothuvaaya samvidaanangalkku noonn-leeniyarittikaludeyum prarambha vyavasthakaludeyum thiranjeduppine aashrayich niravadhi sankeernamaaya perumattangal undakam. ennirunnaalum, hopefield nettvarkkukale sambandhichidatholam, ithu anganeyalla-chalanathmaka sanjaarapathangal ellaayppozhum oru nischitha pooyint aakarshakamaaya avasthayilekku othucherunnu. eee samavaakyangal prathyekamaayi enchiniyaring cheythathinaal avaykku oru antharleenamaaya oorjja pravarthanamullathinaal eee savisheshatha kaivarikkunnu, chathura brackettukalaayi tharamthirickunna padangal neuronukalude avasthakalumaayi bandhappett lagranchian pravartthanatthinte oru itihaasa parivartthanatthe prathinidheekarikkunnu. lagranchian functionukalude hessian maatriksukal positteev ardha-nischithamaanenkil, oorjja pravartthanam chalanathmaka pathayil kurayumennu urappaan, eee savisheshatha neuronukalude pravartthanangalude thaalkkaalika parinaamatthe vivarikkunna chalanathmaka samavaakyangalude samvidaanam oduvil oru nischitha pooyint aakarshakaavasthayilethumenna theliyikkaan sahayikkunnu.
chila saahacharyangalil, savisheshatha neuronukalaaya formula _ 103 neey apekshichu maranjirikkunna neuronukalude chalanathmakatha valare vegathil samaya skailil santhulithamaakumennu oraalkk anumanikkaam. eee saahacharyathil sisttathile randaamathe samavaakyathinte sthiramaaya avastha pariharam () savisheshatha neuronukalude aouttputtukaliloode maranjirikkunna yoonittukalude vaidyuthadhaarakal prakadippikkaan upayogikkaam. ithu pothuvaaya sidhaanthathe () savisheshatha neuronukalkku maathram phalapradamaaya sidhaanthamaayi kuraykkaan saadhyamaakkunnu. thathfalamaayundaakunna phalapradamaaya update niyamangalum lagranchian functionukalude vividha pothu thiranjeduppukalkkulla oorjjavum fig.2 ll kaanichirikkunnu. logue-summ-exponential lagranchian functionte kaaryatthil savisheshatha neuronukalude avasthakalkkulla update niyamam (orikkal prayogichaal) pala aadhunika iai sisttangalilum saadhaaranayaayi upayogikkunna shradha samvidaanamaanu (ruffer kaanuka. thudarchayaaya samaya roopeekaranathil ninnu eee phalatthinte vyulppaadanathinaayi).
thudarchayaaya veriyabilukalulla classical hopefield netvarkkumaayulla bandham.
thudarchayaaya hopefield nettvarkkukalude classical formulation oru maranjirikkunna paaliyulla aadhunika hopefield nettvarkkukalude oru prathyeka parimithappedutthunna kesai manassilakkaam. graducheytha prathikaranamulla neuronukalkkaayulla thudarchayaaya hopefield nettvarkkukale saadhaaranayaayi dynamic samavaakyangalum oorjja pravartthanavum vivarikkunnu, avide formula 104, formula 105 enniva aaktiveshan function formula 106-nte vipareethamaanu. eee model modalukalude classinte oru prathyeka paridhiyaan, modalukal eiii ennu vilikkunnu, inipparayunna lagranchian functionukal thiranjedukkunnu, nirvachanam () anusarichu, maranjirikkunna neuronukale samyojippikkukayaanenkil aaktiveshan functionukalilekku nayikkunnu, samavaakyangalude sisttam () formula 107 upayogichu neuronukalude savisheshathayile samavaakyangalilekku kurayunnu, oorjjathinte pothuvaaya expression () phalapradamaaya oorjjathilekku kurayunnu, athesamayam samavaakyathile aadya rund padangal () samavaakyathile () samaanamaan, moonnaamathe padangal upariplavamaayi vyathyasthamayi kaanapedunnu. samavaakyathil () ithu savisheshatha neuronukalude lagranchiyante oru itihaasa parivarthanamaanu, athesamayam () ll moonnaamathe padam vipareeta sajeevamaakkal pravartthanatthinte avibhaajya gadakamaanu. ennirunnaalum, eee rund padaprayogangalum yadhaarthathil thulyamaanu, kaaranam oru functionte derivetteevukalum athinte legender transform parasparam vipareeta pravarthanangalaanu. eee rund padangalum thulyamaanennu vyakthamaayi kaananulla ettavum eluppamaarggam formula _ 108-maayi bandhappett oronnum verthirikkuka ennathaanu. rund padaprayogangalkkum eee vyathyaasangalude phalangal formula _ 109-nuu thulyamaanu. athinaal, rund padaprayogangalum oru additteev sthiraankathinu thulyamaanu. thudarchayaaya avasthakalulla classical hopefield network aadhunika hopefield netvarkkinte () oorjjam () ulla oru prathyeka parimithappedutthunna kesaanennathinte thelivu ithu poortthiyaakkunnu.
aadhunika hopefield shringalayude pothuvaaya roopeekaranam.
vividha kosha tharangalude kaaryatthil biological neural netvarkkukalkku valia alavilulla vaividhyamund. eee vibhaagam poornnamaayum bandhippichirikkunna aadhunika hopefield shringalayude oru ganithashaasthra maathrkaye vivarikkunnu, ithu vaividhyathinte angeyattatthe alavu oohikkunnu oro neuron vyathyasthamaan. prathyekamaayi, oro neuron athintethaaya aaktiveshan function kainettik time skeyilum undennu karuthiyaanu oru oorjja pravartthanavum anubandha chalanathmaka samavaakyangalum vivarikkunnath.  network poornnamaayum bandhippichirikkunnave anumaanikkappedunnu, athinaal oro neuron bhaara soothravaakyam _ 110, soochika soothravaakyam _ 111, soothravaakyam _ 112 ennivayude samamiti matricks upayogichu matellaa neuronukalumaayum bandhippichirikkunnu, nettvarkkile vyathyastha neuronukal kanakkakkunnu, fig.3 kaanuka. eee prashnam ganithashaasthraparamaayi roopappeduthunnathinulla ettavum eluppamaargam nettvarkkile ellah neuronukaludeyum pravartthanangale aashrayichirikkunna oru lagranchian function soothravaakyam _ 113 vazhi vaasthuvidya nirvachikkuka ennathaanu. oro neuroninteyum aaktiveshan functione nirvachichirikkunnathu aaa neuroninte pravartthanavumaayi bandhappett labranchiyante bhagika derivative aanu, biological veekshanakonil ninnu oraalkk neuron formula 111-nte axonal auttputtaayi formula 114-nekkurichu chinthikkam. ettavum lalithamaaya saahacharyathil, vyathyastha neuronukalkku lagranchian additteev aakumbol, eee nirvachanam aaa neuroninte pravartthanatthinte noonn-leanier functionaaya aaktiveshan undaakkunnu. noonn-additteev lagranchianmarkku eee aaktiveshan function oru koottam neuronukalude pravartthanangale ashrayichirikkum. udaaharanathinu, ithil contrastive (softmaaks) allengil detectiving normalisation adangiyirikkaam. oru nischitha neuroninte thaalkkaalika parinaamatthe vivarikkunna chalanathmaka samavaakyangal eee samavaakyam nalkunnathu neuro sayansile firing rettu modalukal ennu vilikkunna modalukalude vibhaagathil pedunnu. oro neuron formula _ 111 ellah neuronukalil ninnum aaksanal outtputtu formula _ 117 shekharikkukayum synaptic cofficient formula _ 110 upayogichu avaye thookkukayum athintethaaya samayathe aasrayikkunna pravartthana formula _ 119 nirmmikkukayum cheiyunnu. temporal parinaamathinu oru samaya sthiraanka formula _ 120 undu, ithu pothuve oro neuron vyathyasthamayirikkum. eee shringalaykku oru aagola oorjja pravartthanamundu, avide aadyathe rund padangal neuronukalude vaidyuthadhaara soothravaakyam _ 119 maayi bandhappett lagranchian functionte legender parivartthanatthe prathinidheekarikkunnu. eee oorjja pravartthanatthinte thaalkkaalika derivative avasana asamathva chinnathilekku nayikkunna chalanathmaka pathakalil kanakkakkaam, matricks soothravaakyam _ 122 (allengil athinte samamiti bhagam) positteev ardha-nischithamaanenkil. ithinupurame, oorjja pravartthanam noonn-leanier dynamic samavaakyangalkk thaazhe ninnu parimithappeduthiyittunde oru nischitha pooyint aakarshakamaaya avasthayilekku othucherumennu urappaan. lagranchian functionukalude adisthaanathil eee shringhala roopappeduthunnathinte prayojanam, aaktiveshan functionukalude vyathyastha thiranjeduppukalum neuronukalude vyathyastha vasthuvidyaa krameekaranangalum eluppathil pareekshikkaan ithu saadhyamaakkunnu ennathaanu. aaa vazhakkamulla thiranjeduppukalellaam, matricks formula _ 123-nte gunangalum oorjja pravartthanatthil thaazhnna paridhiyude nilanilppum anusarichaanu othucheralinte vyavasthakal nirnnayikkunnath.
sreniparamaaya associative memory network.
oru nischitha paaliyile oro neuron ore aaktiveshan function ore dynamic time skeyilum ullathinaal neuronukale paalikalaayi krameekarikkaan kazhiyum. leyarinullil neuronukalkkidayil thirascheenamaaya bandhangalonnumillennum (laattaral kanakshanukal) skip-lair kanakshanukalumillennum nammal anumaanikkukayaanenkil, pothuvaayi poornnamaayum bandhippicha network (), () fig.4 ll kaanichirikkunna vaasthuvidyayilekku kurayunnu. ithinu formula 124 undu, thudarchayaaya variable formula 125 vivarikkunna avasthakalumaayi aavarthichu bandhippicha neuronukalude paalikal, aaktiveshan function formula 126, soochika formula 127 netvarkkinte paalikale kanakkakkunnu, soochika formula 63 aaa paaliyile vyakthigatha neuronukale kanakkakkunnu. sajeevamaakkal pravartthanangal paaliyile ellah neuronukaludeyum pravartthanangale ashrayichirikkum. oro paalikkum vyathyastha ennam neuronukal formula 129 undayirikkaam. eee neuronukal munbatheyum thudarnnulla paalikalileyum neuronukalumaayi aavarthichu bandhippichirikkunnu. neuronukale 127,131 ennee lairukalumaayi bandhippikkunna bhaarangalude maatriksukale formula 132 kondu soochippikkunnu (bhaarangalude mukalile soochikakalude kramam thaazhnna soochikakalude kramatthinu thulyamaanu, ithinu mukalilulla udaaharanathil soochi soothravaakyam _ 63 lair formula _ 127 leeii neuronukale kanakkakkunnu, soochika formula _ 135 lair formula _ 131 leeii neuronukale kanakkakkunnu). feedford bharangalum feedback bharangalum thulyamaanu. neuronukalude avasthakalude chalanathmaka samavaakyangal \xi ^ {(a, a-1)} _ {ij} g _ j ^ {a-1} + \sum\limt _ {j = 1} ^ {n _ {a + 1}} \xi ^ {(a, a + 1)} _ {ij} g _ j ^ {a + 1}-x _ i ^ a </math ennu ezhuthaam.>|}} athirthi vyavasthakalkkoppam eee samavaakyangalum parambaraagatha feedford netvarkkukalil ninnullavayum thammilulla pradhana vyathyasam randaamathe padatthinte saannidyamaanu, ithu uyarnna paalikalil ninnulla prathikaranatthinu kaaranamaakunnu. eee topp-daun signalukal thaazhathe paalikalilulla neuronukale avatharippicha uthejakangalodulla prathikaranathekkurichu theerumaanikkaan sahayikkunnu. pothuvaaya paachakakkuripp pinthudarnnu 127-aamm maranjirikkunna paaliyude formulakku oru lagranchian function formula _ 137 avatharippikkunnath soukaryapradamaanu, athu aaa paaliyile ellah neuronukaludeyum pravartthanangale aasrayichirikkunnu. aaa paaliyile sajeevamaakkal pravartthanangale eee nirvachanangal upayogichu lagranchiyante bhagika derivateevukalaayi nirvachikkaam, oorjja (liapunov) function nalkunnathu \big [\sum\limets _ {i = 1} ^ {n _ a} x _ i ^ a g _ i ^ a-l ^ {a} \big]-\sum\limets _ {a = 1} ^ {n _ \text {Layer}-1} \sum\limets _ {i = 1} ^ {n _ {a + 1}} \sum\limets _ {j = 1} ^ {n _ a} g _ i ^ {a + 1} \xi ^ {(a + 1, a) _ {gij/math>|}} oro paaliyudeyum hessians positteev ardha-nischithavum mothatthilulla oorjjam thaazhe ninnu parimithappeduthunnathumaa reethiyil lagranchian functionukal allengil thathulyamaaya aaktiveshan functionukal thiranjedukkukayaanenkil, eee sisttam oru nischitha pooyint aakarshakamaaya avasthayilekku othucherumennu urappaan. eee oorjja pravartthanatthinte thaalkkaalika derivative nalkunnathu \tau _ a\sum\limt _ {i, j = 1} ^ {n _ a} \frac {dx _ j ^ a} {dt} \frac {\parial ^ 2l ^ {a}} {\parial x _ j ^ {a} \parial x _ i ^ {a}} \frac {dx _ i ^ a} {dt} \leq0 </math>|}} athinaal, sreniparamaaya paalikalulla shringhala theerchayaayum aagola oorjja pravartthanamulla oru aakarshakamaaya shringalayaanu. oro prathyeka prashnathinum padikkaan kazhiyunna synaptic bhaarangalude oru sreniparamaaya koottamaanu eee shringalaye vivarikkunnath.
munkootty pariseelanam labhicha cnn, associative memory baank enniva upayogichu melnottamillaatha patanam.
samagramaya label cheytha daattaasettil ninnu verthirichedutha aazhathilulla convalutional savisheshathakalil, oru puthiya domainil phalapradamaayi upayogikkaan kazhiyunna ganyamaaya praathinidyangal adangiyirikkunnu. pala vishwal jolikalilum pothuvaaya savisheshathakal nalla phalangal kaivarichittundenkilum, munkootty pariseelanam labhicha deep cnn modalukalkk kooduthal falapradamaakaanum athyaadhunika prakadanam nalkaanum phine-tuning aavasyamaanu. oru melnottatthilulla krameekaranatthil backpropagation algoritam upayogichu phine tuning cheiyunnathu samayavum vibhavangalum upayogikkunna oru prakriyayaan. eee prabandhatthil, automated feature extraction anuvadikkumbol munkootty pariseelanam labhicha cnn adisthaanamaakkiyulla melnottatthilulla aazhathilulla patana sameepanangalumayi bandhapetta mikacha tuningumaayi melpparanja prashnam abhisambodhana cheiyunna oru puthiya vaasthuvidya melnottamillaatha object recognitionulla oru sameepanavum njangal avatharippikkunnu. nilavilulla kruthikalil ninnu vyathyasthamayi, njangalude sameepanam pothuvaaya object recognission jolikalkku baadhakamaan. vargeekarana aavasyangalkkaayi paattenukal sambharikkunnathin hopefield network adisthaanamaakkiyulla associative memory baankumaayi pipeline cheytha automated feature extraakshanaayi ithu oru munkootty pariseelanam labhicha (anubandha domainil) cnn model upayogikkunnu. njangalude chattakkoodile associative memory baankinte upayogam kaanaatha daattaasettil malsaraadhishtitha prakadanam nalkumbol backpropagation illaathaakkaan anuvadikkunnu.

